Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 13x^{7} + 32x^{6} + 40x^{5} - 79x^{4} - 39x^{3} + 58x^{2} + 9x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.761439\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.461945 | 0.206588 | 0.103294 | − | 0.994651i | \(-0.467062\pi\) | ||||
0.103294 | + | 0.994651i | \(0.467062\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.732054 | 0.276691 | 0.138345 | − | 0.990384i | \(-0.455822\pi\) | ||||
0.138345 | + | 0.990384i | \(0.455822\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.317021 | 0.0955854 | 0.0477927 | − | 0.998857i | \(-0.484781\pi\) | ||||
0.0477927 | + | 0.998857i | \(0.484781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.73156 | 0.480249 | 0.240124 | − | 0.970742i | \(-0.422812\pi\) | ||||
0.240124 | + | 0.970742i | \(0.422812\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.461945 | −0.119274 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.85694 | −0.450375 | −0.225187 | − | 0.974315i | \(-0.572299\pi\) | ||||
−0.225187 | + | 0.974315i | \(0.572299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.400818 | −0.0919540 | −0.0459770 | − | 0.998942i | \(-0.514640\pi\) | ||||
−0.0459770 | + | 0.998942i | \(0.514640\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.732054 | −0.159747 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78661 | −0.957321 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76393 | −0.496417 | −0.248208 | − | 0.968707i | \(-0.579842\pi\) | ||||
−0.248208 | + | 0.968707i | \(0.579842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.317021 | −0.0551863 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.338169 | 0.0571610 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.86987 | 1.12940 | 0.564700 | − | 0.825296i | \(-0.308992\pi\) | ||||
0.564700 | + | 0.825296i | \(0.308992\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.73156 | −0.277272 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.88726 | 0.450915 | 0.225457 | − | 0.974253i | \(-0.427612\pi\) | ||||
0.225457 | + | 0.974253i | \(0.427612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.54434 | 1.15050 | 0.575250 | − | 0.817977i | \(-0.304905\pi\) | ||||
0.575250 | + | 0.817977i | \(0.304905\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.461945 | 0.0688627 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3820 | −1.66024 | −0.830118 | − | 0.557588i | \(-0.811727\pi\) | ||||
−0.830118 | + | 0.557588i | \(0.811727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.46410 | −0.923442 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85694 | 0.260024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8018 | −1.48374 | −0.741872 | − | 0.670541i | \(-0.766062\pi\) | ||||
−0.741872 | + | 0.670541i | \(0.766062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.146446 | 0.0197468 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.400818 | 0.0530896 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.88177 | 0.505364 | 0.252682 | − | 0.967549i | \(-0.418687\pi\) | ||||
0.252682 | + | 0.967549i | \(0.418687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.01686 | −0.514306 | −0.257153 | − | 0.966371i | \(-0.582784\pi\) | ||||
−0.257153 | + | 0.966371i | \(0.582784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.732054 | 0.0922302 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.799886 | 0.0992137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.53778 | −0.798716 | −0.399358 | − | 0.916795i | \(-0.630767\pi\) | ||||
−0.399358 | + | 0.916795i | \(0.630767\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.411185 | −0.0487987 | −0.0243994 | − | 0.999702i | \(-0.507767\pi\) | ||||
−0.0243994 | + | 0.999702i | \(0.507767\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9499 | −1.63271 | −0.816354 | − | 0.577552i | \(-0.804008\pi\) | ||||
−0.816354 | + | 0.577552i | \(0.804008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.78661 | 0.552710 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.232077 | 0.0264476 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1974 | 1.25980 | 0.629902 | − | 0.776675i | \(-0.283095\pi\) | ||||
0.629902 | + | 0.776675i | \(0.283095\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.15780 | 0.675906 | 0.337953 | − | 0.941163i | \(-0.390265\pi\) | ||||
0.337953 | + | 0.941163i | \(0.390265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.857805 | −0.0930420 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.04181 | −0.428431 | −0.214216 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214216 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.26760 | 0.132880 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.76393 | 0.286606 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.185156 | −0.0189966 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3181 | 1.04765 | 0.523823 | − | 0.851827i | \(-0.324505\pi\) | ||||
0.523823 | + | 0.851827i | \(0.324505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.317021 | 0.0318618 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5404 | −1.14832 | −0.574159 | − | 0.818744i | \(-0.694671\pi\) | ||||
−0.574159 | + | 0.818744i | \(0.694671\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.595012 | −0.0586283 | −0.0293142 | − | 0.999570i | \(-0.509332\pi\) | ||||
−0.0293142 | + | 0.999570i | \(0.509332\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.338169 | −0.0330019 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.20690 | 0.406696 | 0.203348 | − | 0.979107i | \(-0.434818\pi\) | ||||
0.203348 | + | 0.979107i | \(0.434818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.09440 | 0.104824 | 0.0524122 | − | 0.998626i | \(-0.483309\pi\) | ||||
0.0524122 | + | 0.998626i | \(0.483309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.86987 | −0.652059 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.54021 | −0.238963 | −0.119481 | − | 0.992836i | \(-0.538123\pi\) | ||||
−0.119481 | + | 0.992836i | \(0.538123\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.461945 | −0.0430766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.73156 | 0.160083 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.35938 | −0.124614 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8995 | −0.990863 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.88726 | −0.260336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.52087 | −0.404359 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.35997 | −0.298149 | −0.149075 | − | 0.988826i | \(-0.547630\pi\) | ||||
−0.149075 | + | 0.988826i | \(0.547630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.54434 | −0.664242 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.65661 | 0.406850 | 0.203425 | − | 0.979091i | \(-0.434793\pi\) | ||||
0.203425 | + | 0.979091i | \(0.434793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.293421 | −0.0254428 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.461945 | −0.0397579 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.5798 | −1.16020 | −0.580102 | − | 0.814544i | \(-0.696987\pi\) | ||||
−0.580102 | + | 0.814544i | \(0.696987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8371 | −1.00401 | −0.502005 | − | 0.864865i | \(-0.667404\pi\) | ||||
−0.502005 | + | 0.864865i | \(0.667404\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3820 | 0.958538 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.548941 | 0.0459048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.461945 | 0.0383624 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.46410 | 0.533150 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.83537 | 0.232283 | 0.116141 | − | 0.993233i | \(-0.462947\pi\) | ||||
0.116141 | + | 0.993233i | \(0.462947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.46767 | −0.607711 | −0.303855 | − | 0.952718i | \(-0.598274\pi\) | ||||
−0.303855 | + | 0.952718i | \(0.598274\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.85694 | −0.150125 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.27678 | −0.102554 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3488 | 1.22497 | 0.612483 | − | 0.790484i | \(-0.290171\pi\) | ||||
0.612483 | + | 0.790484i | \(0.290171\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.8018 | 0.856641 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.732054 | −0.0576940 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.837150 | −0.0655706 | −0.0327853 | − | 0.999462i | \(-0.510438\pi\) | ||||
−0.0327853 | + | 0.999462i | \(0.510438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.146446 | −0.0114008 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.4774 | 1.42982 | 0.714912 | − | 0.699214i | \(-0.246467\pi\) | ||||
0.714912 | + | 0.699214i | \(0.246467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0017 | −0.769361 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.400818 | −0.0306513 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.9553 | −0.908943 | −0.454471 | − | 0.890761i | \(-0.650172\pi\) | ||||
−0.454471 | + | 0.890761i | \(0.650172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.50406 | −0.264882 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.88177 | −0.291772 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.15766 | −0.385502 | −0.192751 | − | 0.981248i | \(-0.561741\pi\) | ||||
−0.192751 | + | 0.981248i | \(0.561741\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.3614 | 1.95942 | 0.979712 | − | 0.200409i | \(-0.0642273\pi\) | ||||
0.979712 | + | 0.200409i | \(0.0642273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.01686 | 0.296935 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.17350 | 0.233321 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.588689 | −0.0430492 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.732054 | −0.0532491 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.6094 | −0.912385 | −0.456192 | − | 0.889881i | \(-0.650787\pi\) | ||||
−0.456192 | + | 0.889881i | \(0.650787\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.78062 | 0.416098 | 0.208049 | − | 0.978118i | \(-0.433289\pi\) | ||||
0.208049 | + | 0.978118i | \(0.433289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.799886 | −0.0572810 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.44739 | 0.673099 | 0.336549 | − | 0.941666i | \(-0.390740\pi\) | ||||
0.336549 | + | 0.941666i | \(0.390740\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8323 | 1.05143 | 0.525717 | − | 0.850659i | \(-0.323797\pi\) | ||||
0.525717 | + | 0.850659i | \(0.323797\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.53778 | 0.461139 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.732054 | 0.0513801 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.33376 | 0.0931536 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.127068 | −0.00878946 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.306888 | −0.0211270 | −0.0105635 | − | 0.999944i | \(-0.503363\pi\) | ||||
−0.0105635 | + | 0.999944i | \(0.503363\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.411185 | 0.0281739 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.48507 | 0.237680 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.02335 | −0.137354 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.9499 | 0.942645 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.21541 | −0.216292 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.86424 | 0.459664 | 0.229832 | − | 0.973230i | \(-0.426182\pi\) | ||||
0.229832 | + | 0.973230i | \(0.426182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.78661 | −0.319107 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9875 | 0.795640 | 0.397820 | − | 0.917463i | \(-0.369767\pi\) | ||||
0.397820 | + | 0.917463i | \(0.369767\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.07143 | −0.533375 | −0.266687 | − | 0.963783i | \(-0.585929\pi\) | ||||
−0.266687 | + | 0.963783i | \(0.585929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.232077 | −0.0152695 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4991 | 1.27743 | 0.638715 | − | 0.769444i | \(-0.279466\pi\) | ||||
0.638715 | + | 0.769444i | \(0.279466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.25786 | −0.342985 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.1974 | −0.727348 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.4626 | −1.71173 | −0.855863 | − | 0.517203i | \(-0.826973\pi\) | ||||
−0.855863 | + | 0.517203i | \(0.826973\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.62601 | 0.297988 | 0.148994 | − | 0.988838i | \(-0.452397\pi\) | ||||
0.148994 | + | 0.988838i | \(0.452397\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.98606 | −0.190772 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.694041 | −0.0441608 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.15780 | −0.390235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.5425 | −1.54911 | −0.774554 | − | 0.632507i | \(-0.782026\pi\) | ||||
−0.774554 | + | 0.632507i | \(0.782026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.317021 | −0.0199309 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.857805 | 0.0537178 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.88448 | 0.304685 | 0.152343 | − | 0.988328i | \(-0.451318\pi\) | ||||
0.152343 | + | 0.988328i | \(0.451318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.02912 | 0.312494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.37549 | −0.146479 | −0.0732394 | − | 0.997314i | \(-0.523334\pi\) | ||||
−0.0732394 | + | 0.997314i | \(0.523334\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.98985 | −0.306524 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.04181 | 0.247355 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0953 | −0.737462 | −0.368731 | − | 0.929536i | \(-0.620208\pi\) | ||||
−0.368731 | + | 0.929536i | \(0.620208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.76866 | 0.532658 | 0.266329 | − | 0.963882i | \(-0.414189\pi\) | ||||
0.266329 | + | 0.963882i | \(0.414189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.26760 | −0.0767185 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.51745 | −0.0915060 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.7407 | −1.90712 | −0.953558 | − | 0.301209i | \(-0.902610\pi\) | ||||
−0.953558 | + | 0.301209i | \(0.902610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.76393 | −0.165472 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.92770 | −0.114997 | −0.0574985 | − | 0.998346i | \(-0.518312\pi\) | ||||
−0.0574985 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.84260 | −0.228419 | −0.114209 | − | 0.993457i | \(-0.536433\pi\) | ||||
−0.114209 | + | 0.993457i | \(0.536433\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.185156 | 0.0109677 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.11363 | 0.124764 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5518 | −0.797163 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.3181 | −0.604858 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.6858 | −1.15005 | −0.575027 | − | 0.818134i | \(-0.695008\pi\) | ||||
−0.575027 | + | 0.818134i | \(0.695008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.79317 | 0.104402 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.317021 | −0.0183954 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.73156 | −0.100139 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.52287 | 0.318333 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.5404 | 0.662981 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.85557 | −0.106250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.2630 | −0.928177 | −0.464089 | − | 0.885789i | \(-0.653618\pi\) | ||||
−0.464089 | + | 0.885789i | \(0.653618\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.595012 | 0.0338491 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.8702 | −0.673098 | −0.336549 | − | 0.941666i | \(-0.609260\pi\) | ||||
−0.336549 | + | 0.941666i | \(0.609260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.8326 | 0.725339 | 0.362669 | − | 0.931918i | \(-0.381865\pi\) | ||||
0.362669 | + | 0.931918i | \(0.381865\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.338169 | 0.0190537 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.37675 | −0.470485 | −0.235243 | − | 0.971937i | \(-0.575588\pi\) | ||||
−0.235243 | + | 0.971937i | \(0.575588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.317021 | 0.0177498 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.20690 | −0.234806 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.744296 | 0.0414137 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.28830 | −0.459752 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.09440 | −0.0605203 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.33224 | −0.459372 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.7411 | 1.74465 | 0.872323 | − | 0.488930i | \(-0.162613\pi\) | ||||
0.872323 | + | 0.488930i | \(0.162613\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.86987 | 0.376467 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.02009 | −0.165005 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.506781 | 0.0276061 | 0.0138031 | − | 0.999905i | \(-0.495606\pi\) | ||||
0.0138031 | + | 0.999905i | \(0.495606\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.54021 | 0.137965 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.876224 | −0.0474502 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.85645 | −0.532198 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.461945 | 0.0248703 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.6598 | −1.86064 | −0.930319 | − | 0.366751i | \(-0.880470\pi\) | ||||
−0.930319 | + | 0.366751i | \(0.880470\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.55271 | −0.404288 | −0.202144 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202144 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.73156 | −0.0924239 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.3957 | −0.606530 | −0.303265 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303265 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.189945 | −0.0100812 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.35938 | 0.0719461 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.8148 | −1.04579 | −0.522894 | − | 0.852398i | \(-0.675147\pi\) | ||||
−0.522894 | + | 0.852398i | \(0.675147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8393 | −0.991544 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8995 | 0.572075 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.44407 | −0.337298 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.49275 | −0.338919 | −0.169459 | − | 0.985537i | \(-0.554202\pi\) | ||||
−0.169459 | + | 0.985537i | \(0.554202\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.88726 | 0.150305 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.90752 | −0.410538 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.33591 | 0.172727 | 0.0863634 | − | 0.996264i | \(-0.472475\pi\) | ||||
0.0863634 | + | 0.996264i | \(0.472475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.52087 | 0.233457 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.73156 | 0.0891800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1538 | 1.08660 | 0.543298 | − | 0.839540i | \(-0.317176\pi\) | ||||
0.543298 | + | 0.839540i | \(0.317176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.35997 | 0.172137 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.256376 | −0.0131002 | −0.00655010 | − | 0.999979i | \(-0.502085\pi\) | ||||
−0.00655010 | + | 0.999979i | \(0.502085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.107207 | 0.00546375 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.54434 | 0.383500 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.2812 | −1.53532 | −0.767659 | − | 0.640859i | \(-0.778578\pi\) | ||||
−0.767659 | + | 0.640859i | \(0.778578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.85694 | 0.0939096 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.65661 | −0.234895 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.17257 | 0.260260 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.3664 | −1.07235 | −0.536174 | − | 0.844107i | \(-0.680131\pi\) | ||||
−0.536174 | + | 0.844107i | \(0.680131\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.293421 | 0.0146894 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.637327 | 0.0318266 | 0.0159133 | − | 0.999873i | \(-0.494934\pi\) | ||||
0.0159133 | + | 0.999873i | \(0.494934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.78592 | −0.238404 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.461945 | 0.0229542 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.17789 | 0.107954 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.4021 | −1.25605 | −0.628025 | − | 0.778193i | \(-0.716137\pi\) | ||||
−0.628025 | + | 0.778193i | \(0.716137\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5798 | 0.669844 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.84167 | 0.139829 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.84456 | 0.139634 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.8371 | 0.579665 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0239 | 0.489698 | 0.244849 | − | 0.969561i | \(-0.421262\pi\) | ||||
0.244849 | + | 0.969561i | \(0.421262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9276 | −0.873736 | −0.436868 | − | 0.899526i | \(-0.643912\pi\) | ||||
−0.436868 | + | 0.899526i | \(0.643912\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.3820 | −0.553412 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.88845 | 0.431153 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.94056 | −0.142304 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.548941 | −0.0265031 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.7837 | −0.663935 | −0.331968 | − | 0.943291i | \(-0.607713\pi\) | ||||
−0.331968 | + | 0.943291i | \(0.607713\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.149916 | −0.00720452 | −0.00360226 | − | 0.999994i | \(-0.501147\pi\) | ||||
−0.00360226 | + | 0.999994i | \(0.501147\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.461945 | −0.0221486 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.400818 | 0.0191737 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7877 | 1.13533 | 0.567663 | − | 0.823261i | \(-0.307848\pi\) | ||||
0.567663 | + | 0.823261i | \(0.307848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.46410 | −0.307814 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.0166 | 0.713462 | 0.356731 | − | 0.934207i | \(-0.383891\pi\) | ||||
0.356731 | + | 0.934207i | \(0.383891\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.86710 | −0.0885088 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.83537 | −0.134108 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.20526 | −0.0568798 | −0.0284399 | − | 0.999596i | \(-0.509054\pi\) | ||||
−0.0284399 | + | 0.999596i | \(0.509054\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.915323 | 0.0431009 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.46767 | 0.350862 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.585560 | 0.0274515 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.3509 | −1.60687 | −0.803433 | − | 0.595395i | \(-0.796996\pi\) | ||||
−0.803433 | + | 0.595395i | \(0.796996\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.85694 | 0.0866746 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.6738 | 1.10260 | 0.551301 | − | 0.834307i | \(-0.314132\pi\) | ||||
0.551301 | + | 0.834307i | \(0.314132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.41151 | −0.344442 | −0.172221 | − | 0.985058i | \(-0.555094\pi\) | ||||
−0.172221 | + | 0.985058i | \(0.555094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.27678 | 0.0592095 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.8498 | 1.24246 | 0.621230 | − | 0.783628i | \(-0.286633\pi\) | ||||
0.621230 | + | 0.783628i | \(0.286633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.78601 | −0.220997 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.3488 | −0.707234 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.39171 | 0.109971 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.91856 | 0.0880295 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.8018 | −0.494582 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.7862 | −0.904054 | −0.452027 | − | 0.892004i | \(-0.649299\pi\) | ||||
−0.452027 | + | 0.892004i | \(0.649299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.8956 | 0.542393 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.732054 | 0.0333096 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.76640 | 0.216431 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0323 | 0.635864 | 0.317932 | − | 0.948114i | \(-0.397012\pi\) | ||||
0.317932 | + | 0.948114i | \(0.397012\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.837150 | 0.0378572 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7827 | 0.712263 | 0.356132 | − | 0.934436i | \(-0.384095\pi\) | ||||
0.356132 | + | 0.934436i | \(0.384095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.85694 | −0.0836325 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.146446 | 0.00658227 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.301010 | −0.0135021 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.7879 | 1.51255 | 0.756277 | − | 0.654251i | \(-0.227016\pi\) | ||||
0.756277 | + | 0.654251i | \(0.227016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.4774 | −0.825510 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.28079 | 0.413810 | 0.206905 | − | 0.978361i | \(-0.433661\pi\) | ||||
0.206905 | + | 0.978361i | \(0.433661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.33105 | −0.237229 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0017 | 0.444191 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.4886 | −1.48436 | −0.742178 | − | 0.670203i | \(-0.766207\pi\) | ||||
−0.742178 | + | 0.670203i | \(0.766207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2121 | −0.451755 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.400818 | 0.0176965 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.274863 | −0.0121119 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.60833 | −0.158694 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9553 | 0.524778 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.16840 | −0.226432 | −0.113216 | − | 0.993570i | \(-0.536115\pi\) | ||||
−0.113216 | + | 0.993570i | \(0.536115\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.5421 | −1.81651 | −0.908255 | − | 0.418418i | \(-0.862585\pi\) | ||||
−0.908255 | + | 0.418418i | \(0.862585\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.50406 | 0.152930 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.13246 | 0.223574 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.88177 | 0.168455 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.99947 | 0.216551 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.94336 | 0.0840186 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.15766 | 0.222570 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.04925 | −0.0882676 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0593 | −1.37834 | −0.689169 | − | 0.724601i | \(-0.742024\pi\) | ||||
−0.689169 | + | 0.724601i | \(0.742024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.3614 | −1.13127 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.505552 | 0.0216555 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.66351 | −0.327668 | −0.163834 | − | 0.986488i | \(-0.552386\pi\) | ||||
−0.163834 | + | 0.986488i | \(0.552386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.01686 | −0.171435 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.400818 | −0.0170754 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.19709 | 0.348576 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.17350 | −0.134708 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8923 | −0.546266 | −0.273133 | − | 0.961976i | \(-0.588060\pi\) | ||||
−0.273133 | + | 0.961976i | \(0.588060\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.0635 | 0.552527 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.588689 | 0.0248545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.73204 | 0.199432 | 0.0997158 | − | 0.995016i | \(-0.468207\pi\) | ||||
0.0997158 | + | 0.995016i | \(0.468207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.17344 | −0.0493668 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.732054 | 0.0307434 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.82884 | 0.244358 | 0.122179 | − | 0.992508i | \(-0.461012\pi\) | ||||
0.122179 | + | 0.992508i | \(0.461012\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.1737 | −1.76492 | −0.882458 | − | 0.470392i | \(-0.844113\pi\) | ||||
−0.882458 | + | 0.470392i | \(0.844113\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.6094 | 0.526766 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.78661 | 0.199615 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.8790 | −1.11899 | −0.559495 | − | 0.828834i | \(-0.689005\pi\) | ||||
−0.559495 | + | 0.828834i | \(0.689005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.78062 | −0.240234 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.50784 | 0.187017 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.42441 | −0.141824 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.799886 | 0.0330712 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.54458 | −0.311398 | −0.155699 | − | 0.987805i | \(-0.549763\pi\) | ||||
−0.155699 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.10783 | 0.0456475 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.44739 | −0.388614 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.59461 | −0.352938 | −0.176469 | − | 0.984306i | \(-0.556468\pi\) | ||||
−0.176469 | + | 0.984306i | \(0.556468\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.627960 | −0.0257438 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.8323 | −0.607046 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.5984 | 1.33193 | 0.665967 | − | 0.745982i | \(-0.268019\pi\) | ||||
0.665967 | + | 0.745982i | \(0.268019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4526 | 1.65010 | 0.825049 | − | 0.565061i | \(-0.191148\pi\) | ||||
0.825049 | + | 0.565061i | \(0.191148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.53778 | −0.266239 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.03497 | −0.204701 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1015 | 0.491185 | 0.245592 | − | 0.969373i | \(-0.421018\pi\) | ||||
0.245592 | + | 0.969373i | \(0.421018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.732054 | −0.0296643 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7086 | −0.797326 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.4357 | −0.825391 | −0.412695 | − | 0.910869i | \(-0.635413\pi\) | ||||
−0.412695 | + | 0.910869i | \(0.635413\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.33376 | −0.0537823 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.24679 | −0.211228 | −0.105614 | − | 0.994407i | \(-0.533681\pi\) | ||||
−0.105614 | + | 0.994407i | \(0.533681\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.6009 | 0.828021 | 0.414011 | − | 0.910272i | \(-0.364128\pi\) | ||||
0.414011 | + | 0.910272i | \(0.364128\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.95883 | −0.118543 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.8446 | 0.873786 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.127068 | 0.00507460 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.7570 | −0.508653 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.3896 | −1.36903 | −0.684515 | − | 0.728999i | \(-0.739986\pi\) | ||||
−0.684515 | + | 0.728999i | \(0.739986\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.306888 | 0.0121977 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.55212 | −0.0615941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.1930 | −0.443482 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.411185 | −0.0162662 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.0313102 | −0.00123668 | −0.000618339 | − | 1.00000i | \(-0.500197\pi\) | ||||
−0.000618339 | 1.00000i | \(0.500197\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9158 | 0.785404 | 0.392702 | − | 0.919666i | \(-0.371540\pi\) | ||||
0.392702 | + | 0.919666i | \(0.371540\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.48507 | −0.137224 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.9631 | 0.431003 | 0.215501 | − | 0.976504i | \(-0.430861\pi\) | ||||
0.215501 | + | 0.976504i | \(0.430861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.23060 | 0.0483054 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.02335 | 0.0793013 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.5105 | −1.58530 | −0.792650 | − | 0.609678i | \(-0.791299\pi\) | ||||
−0.792650 | + | 0.609678i | \(0.791299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.15110 | 0.0840503 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.9499 | −0.544236 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.5209 | −1.18893 | −0.594463 | − | 0.804123i | \(-0.702635\pi\) | ||||
−0.594463 | + | 0.804123i | \(0.702635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5037 | 1.14756 | 0.573780 | − | 0.819009i | \(-0.305476\pi\) | ||||
0.573780 | + | 0.819009i | \(0.305476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.21541 | 0.124876 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.135544 | −0.00525618 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.86424 | −0.265387 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.27343 | −0.0491602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1124 | 0.428352 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.78661 | 0.184237 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.8437 | −0.724224 | −0.362112 | − | 0.932135i | \(-0.617944\pi\) | ||||
−0.362112 | + | 0.932135i | \(0.617944\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.55342 | 0.289874 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.9875 | −0.459363 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.7086 | −1.40461 | −0.702307 | − | 0.711874i | \(-0.747847\pi\) | ||||
−0.702307 | + | 0.711874i | \(0.747847\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.27314 | −0.239684 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.07143 | 0.307944 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.7040 | −0.712567 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0074 | 0.380698 | 0.190349 | − | 0.981717i | \(-0.439038\pi\) | ||||
0.190349 | + | 0.981717i | \(0.439038\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.232077 | 0.00881586 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.46809 | −0.207416 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.36148 | −0.203081 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.4991 | −0.737524 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.3727 | −0.618387 | −0.309194 | − | 0.950999i | \(-0.600059\pi\) | ||||
−0.309194 | + | 0.950999i | \(0.600059\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.75357 | −0.103853 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.25786 | 0.198022 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.44824 | −0.317729 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.6058 | 1.22454 | 0.612269 | − | 0.790649i | \(-0.290257\pi\) | ||||
0.612269 | + | 0.790649i | \(0.290257\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.1974 | 0.419934 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.76393 | 0.103510 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.253581 | 0.00948338 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.4626 | 0.988265 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.9583 | −1.07996 | −0.539981 | − | 0.841677i | \(-0.681569\pi\) | ||||
−0.539981 | + | 0.841677i | \(0.681569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.435581 | −0.0162219 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.62601 | −0.172043 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.78661 | −0.177770 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.81774 | 0.364120 | 0.182060 | − | 0.983287i | \(-0.441724\pi\) | ||||
0.182060 | + | 0.983287i | \(0.441724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.0094 | −0.518156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.1524 | −0.596602 | −0.298301 | − | 0.954472i | \(-0.596420\pi\) | ||||
−0.298301 | + | 0.954472i | \(0.596420\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.98606 | 0.110142 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.07261 | −0.0763456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0100 | −0.736080 | −0.368040 | − | 0.929810i | \(-0.619971\pi\) | ||||
−0.368040 | + | 0.929810i | \(0.619971\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.694041 | 0.0254962 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.3919 | 1.44515 | 0.722574 | − | 0.691293i | \(-0.242959\pi\) | ||||
0.722574 | + | 0.691293i | \(0.242959\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.30978 | 0.0479868 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.15780 | 0.225302 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.07968 | 0.112529 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.4945 | 1.25872 | 0.629361 | − | 0.777113i | \(-0.283317\pi\) | ||||
0.629361 | + | 0.777113i | \(0.283317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.5425 | 0.894378 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.44966 | −0.125546 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.9383 | 0.724668 | 0.362334 | − | 0.932048i | \(-0.381980\pi\) | ||||
0.362334 | + | 0.932048i | \(0.381980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.317021 | 0.0115071 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.1351 | −1.20115 | −0.600573 | − | 0.799570i | \(-0.705061\pi\) | ||||
−0.600573 | + | 0.799570i | \(0.705061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.801159 | 0.0290039 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.857805 | −0.0310140 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.72153 | 0.242700 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.4214 | 0.988842 | 0.494421 | − | 0.869223i | \(-0.335380\pi\) | ||||
0.494421 | + | 0.869223i | \(0.335380\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.88448 | −0.175910 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.99277 | −0.215545 | −0.107773 | − | 0.994176i | \(-0.534372\pi\) | ||||
−0.107773 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.2299 | 0.475231 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.02912 | −0.180419 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.15727 | −0.0414634 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.130354 | −0.00466444 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.09029 | 0.253063 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.17329 | −0.0774694 | −0.0387347 | − | 0.999250i | \(-0.512333\pi\) | ||||
−0.0387347 | + | 0.999250i | \(0.512333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.37549 | 0.0845696 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.85957 | −0.0661187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.95544 | −0.246995 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.98985 | 0.176972 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.7622 | −0.416638 | −0.208319 | − | 0.978061i | \(-0.566799\pi\) | ||||
−0.208319 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1357 | 0.747728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.04181 | −0.142810 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.42240 | −0.156063 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.338169 | −0.0119189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.0953 | 0.425774 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.8832 | 1.33190 | 0.665950 | − | 0.745996i | \(-0.268026\pi\) | ||||
0.665950 | + | 0.745996i | \(0.268026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.4144 | 0.471044 | 0.235522 | − | 0.971869i | \(-0.424320\pi\) | ||||
0.235522 | + | 0.971869i | \(0.424320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.76866 | −0.307530 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.386717 | −0.0135461 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.02391 | −0.105793 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.26760 | 0.0442934 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.6086 | −0.963548 | −0.481774 | − | 0.876296i | \(-0.660007\pi\) | ||||
−0.481774 | + | 0.876296i | \(0.660007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5881 | 0.473650 | 0.236825 | − | 0.971552i | \(-0.423893\pi\) | ||||
0.236825 | + | 0.971552i | \(0.423893\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.51745 | 0.0528310 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.2467 | −1.64293 | −0.821465 | − | 0.570259i | \(-0.806843\pi\) | ||||
−0.821465 | + | 0.570259i | \(0.806843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.2463 | 0.772646 | 0.386323 | − | 0.922364i | \(-0.373745\pi\) | ||||
0.386323 | + | 0.922364i | \(0.373745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.7407 | 1.10107 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0035 | 0.415895 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.53555 | 0.295385 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.76393 | 0.0955355 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.31344 | −0.252488 | −0.126244 | − | 0.991999i | \(-0.540292\pi\) | ||||
−0.126244 | + | 0.991999i | \(0.540292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.92770 | 0.0663935 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.62023 | −0.158941 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.97902 | −0.274163 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.84260 | 0.131878 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.86987 | −0.235496 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.07973 | −0.0712084 | −0.0356042 | − | 0.999366i | \(-0.511336\pi\) | ||||
−0.0356042 | + | 0.999366i | \(0.511336\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.185156 | −0.00633220 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.1501 | 0.517519 | 0.258759 | − | 0.965942i | \(-0.416686\pi\) | ||||
0.258759 | + | 0.965942i | \(0.416686\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.02894 | 0.103346 | 0.0516731 | − | 0.998664i | \(-0.483545\pi\) | ||||
0.0516731 | + | 0.998664i | \(0.483545\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.11363 | −0.0720324 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.84761 | 0.301176 | 0.150588 | − | 0.988597i | \(-0.451883\pi\) | ||||
0.150588 | + | 0.988597i | \(0.451883\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.52268 | −0.187777 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.5518 | 0.460242 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.54980 | 0.120419 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3206 | −0.383583 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.3181 | 0.349215 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.30953 | −0.111882 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.8391 | 0.973826 | 0.486913 | − | 0.873450i | \(-0.338123\pi\) | ||||
0.486913 | + | 0.873450i | \(0.338123\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.6858 | 0.663984 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2832 | 0.346449 | 0.173224 | − | 0.984882i | \(-0.444581\pi\) | ||||
0.173224 | + | 0.984882i | \(0.444581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.4793 | 0.621877 | 0.310939 | − | 0.950430i | \(-0.399357\pi\) | ||||
0.310939 | + | 0.950430i | \(0.399357\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.79317 | −0.0602766 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.63853 | −0.256477 | −0.128238 | − | 0.991743i | \(-0.540932\pi\) | ||||
−0.128238 | + | 0.991743i | \(0.540932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.45968 | −0.0824951 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.317021 | 0.0106206 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.56211 | 0.152665 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.38256 | −0.0796401 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.73156 | 0.0578152 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.76393 | −0.0921823 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0584 | 0.668241 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.52287 | −0.183789 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.1775 | 0.404794 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.2717 | 0.341066 | 0.170533 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170533 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.5404 | −0.382773 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.0741 | −1.16206 | −0.581028 | − | 0.813883i | \(-0.697349\pi\) | ||||
−0.581028 | + | 0.813883i | \(0.697349\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.95215 | 0.0646068 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.85557 | 0.0613432 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.40889 | 0.112572 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.48065 | 0.312738 | 0.156369 | − | 0.987699i | \(-0.450021\pi\) | ||||
0.156369 | + | 0.987699i | \(0.450021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.2630 | 0.535883 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.711992 | −0.0234355 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.8834 | −1.08120 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.595012 | −0.0195428 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.7195 | −0.909446 | −0.454723 | − | 0.890633i | \(-0.650262\pi\) | ||||
−0.454723 | + | 0.890633i | \(0.650262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.59093 | 0.0849142 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.8702 | 0.388613 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.271942 | −0.00889346 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.67875 | −0.152848 | −0.0764241 | − | 0.997075i | \(-0.524350\pi\) | ||||
−0.0764241 | + | 0.997075i | \(0.524350\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.8326 | −0.418774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.2302 | 0.333494 | 0.166747 | − | 0.986000i | \(-0.446674\pi\) | ||||
0.166747 | + | 0.986000i | \(0.446674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.88726 | −0.0940222 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.338169 | −0.0110006 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.94865 | 0.193305 | 0.0966526 | − | 0.995318i | \(-0.469186\pi\) | ||||
0.0966526 | + | 0.995318i | \(0.469186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.1551 | −0.784106 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.37675 | 0.271635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.7092 | −1.25391 | −0.626957 | − | 0.779054i | \(-0.715700\pi\) | ||||
−0.626957 | + | 0.779054i | \(0.715700\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.82485 | −0.188488 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.317021 | −0.0102478 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.94118 | −0.321017 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3607 | −0.753570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.20690 | 0.135565 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.67033 | 0.0859609 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.2411 | 0.522279 | 0.261140 | − | 0.965301i | \(-0.415902\pi\) | ||||
0.261140 | + | 0.965301i | \(0.415902\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.744296 | −0.0239102 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.6266 | −1.14331 | −0.571656 | − | 0.820494i | \(-0.693699\pi\) | ||||
−0.571656 | + | 0.820494i | \(0.693699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.66540 | −0.277800 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.28830 | 0.265438 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.0107 | −1.28005 | −0.640027 | − | 0.768352i | \(-0.721077\pi\) | ||||
−0.640027 | + | 0.768352i | \(0.721077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.28134 | −0.0409518 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.09440 | 0.0349414 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.1699 | 1.28122 | 0.640611 | − | 0.767865i | \(-0.278681\pi\) | ||||
0.640611 | + | 0.767865i | \(0.278681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.36418 | 0.139054 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.33224 | 0.265218 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.54434 | −0.239896 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.3207 | 0.772571 | 0.386286 | − | 0.922379i | \(-0.373758\pi\) | ||||
0.386286 | + | 0.922379i | \(0.373758\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.7411 | −1.00727 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.85171 | 0.217214 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.3032 | −1.24475 | −0.622373 | − | 0.782721i | \(-0.713831\pi\) | ||||
−0.622373 | + | 0.782721i | \(0.713831\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.86987 | −0.217353 |
(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 | 8004.2.a.e.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.e.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |