Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.52493\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −2.52493 | −1.45777 | −0.728885 | − | 0.684636i | \(-0.759961\pi\) | ||||
−0.728885 | + | 0.684636i | \(0.759961\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.43935 | 1.53812 | 0.769062 | − | 0.639174i | \(-0.220724\pi\) | ||||
0.769062 | + | 0.639174i | \(0.220724\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.37528 | 1.12509 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.68412 | −2.24223 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.56793 | −1.59296 | −0.796478 | − | 0.604667i | \(-0.793306\pi\) | ||||
−0.796478 | + | 0.604667i | \(0.793306\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.74521 | 0.629795 | 0.314897 | − | 0.949126i | \(-0.398030\pi\) | ||||
0.314897 | + | 0.949126i | \(0.398030\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.52493 | −0.550985 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.80225 | −0.584310 | −0.292155 | − | 0.956371i | \(-0.594372\pi\) | ||||
−0.292155 | + | 0.956371i | \(0.594372\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.82912 | 1.36582 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.947546 | −0.182355 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.240184 | 0.0446010 | 0.0223005 | − | 0.999751i | \(-0.492901\pi\) | ||||
0.0223005 | + | 0.999751i | \(0.492901\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.281315 | 0.0505257 | 0.0252628 | − | 0.999681i | \(-0.491958\pi\) | ||||
0.0252628 | + | 0.999681i | \(0.491958\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.52493 | 0.439534 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.43935 | 0.581356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.95065 | 0.978281 | 0.489140 | − | 0.872205i | \(-0.337311\pi\) | ||||
0.489140 | + | 0.872205i | \(0.337311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.52493 | 0.404313 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4744 | 1.79200 | 0.895998 | − | 0.444059i | \(-0.146462\pi\) | ||||
0.895998 | + | 0.444059i | \(0.146462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.59622 | −0.853416 | −0.426708 | − | 0.904389i | \(-0.640327\pi\) | ||||
−0.426708 | + | 0.904389i | \(0.640327\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.6088 | 1.73053 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.3176 | −1.94257 | −0.971287 | − | 0.237912i | \(-0.923537\pi\) | ||||
−0.971287 | + | 0.237912i | \(0.923537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.5836 | 2.32216 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.03445 | 0.416813 | 0.208407 | − | 0.978042i | \(-0.433172\pi\) | ||||
0.208407 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.43935 | −0.463762 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.93147 | −0.918095 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.5644 | −1.50555 | −0.752776 | − | 0.658276i | \(-0.771286\pi\) | ||||
−0.752776 | + | 0.658276i | \(0.771286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.183548 | −0.0235009 | −0.0117504 | − | 0.999931i | \(-0.503740\pi\) | ||||
−0.0117504 | + | 0.999931i | \(0.503740\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.37528 | 0.425245 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.43935 | −0.426599 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.658984 | 0.0805077 | 0.0402538 | − | 0.999189i | \(-0.487183\pi\) | ||||
0.0402538 | + | 0.999189i | \(0.487183\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.07550 | 0.851790 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.80420 | −0.688832 | −0.344416 | − | 0.938817i | \(-0.611923\pi\) | ||||
−0.344416 | + | 0.938817i | \(0.611923\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.78419 | −1.02811 | −0.514056 | − | 0.857757i | \(-0.671858\pi\) | ||||
−0.514056 | + | 0.857757i | \(0.671858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.2431 | −1.99106 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.408207 | −0.0459268 | −0.0229634 | − | 0.999736i | \(-0.507310\pi\) | ||||
−0.0229634 | + | 0.999736i | \(0.507310\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.73334 | −0.859260 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.01797 | −0.550794 | −0.275397 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275397 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.5894 | −2.45016 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.606448 | −0.0650180 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.72200 | 0.394532 | 0.197266 | − | 0.980350i | \(-0.436794\pi\) | ||||
0.197266 | + | 0.980350i | \(0.436794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.710301 | −0.0736548 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.44174 | 0.968702 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.91747 | 0.194689 | 0.0973447 | − | 0.995251i | \(-0.468965\pi\) | ||||
0.0973447 | + | 0.995251i | \(0.468965\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.37528 | −0.339228 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.841815 | −0.0837637 | −0.0418819 | − | 0.999123i | \(-0.513335\pi\) | ||||
−0.0418819 | + | 0.999123i | \(0.513335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4270 | 1.32301 | 0.661503 | − | 0.749943i | \(-0.269919\pi\) | ||||
0.661503 | + | 0.749943i | \(0.269919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.68412 | −0.847483 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.29003 | −0.608080 | −0.304040 | − | 0.952659i | \(-0.598336\pi\) | ||||
−0.304040 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.94525 | 0.186321 | 0.0931607 | − | 0.995651i | \(-0.470303\pi\) | ||||
0.0931607 | + | 0.995651i | \(0.470303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0250 | −1.42611 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.3415 | −1.63135 | −0.815674 | − | 0.578512i | \(-0.803634\pi\) | ||||
−0.815674 | + | 0.578512i | \(0.803634\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.63793 | −0.898741 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.37528 | −0.312044 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.56793 | −0.602081 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −28.9720 | −2.61232 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.29100 | 0.562684 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.69408 | −0.682740 | −0.341370 | − | 0.939929i | \(-0.610891\pi\) | ||||
−0.341370 | + | 0.939929i | \(0.610891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.1301 | 1.24408 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.11125 | −0.271831 | −0.135915 | − | 0.990720i | \(-0.543398\pi\) | ||||
−0.135915 | + | 0.990720i | \(0.543398\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.74521 | 0.238040 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.25894 | −0.280485 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.81615 | −0.155164 | −0.0775822 | − | 0.996986i | \(-0.524720\pi\) | ||||
−0.0775822 | + | 0.996986i | \(0.524720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.63326 | −0.477807 | −0.238904 | − | 0.971043i | \(-0.576788\pi\) | ||||
−0.238904 | + | 0.971043i | \(0.576788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.6261 | 2.83182 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.826076 | 0.0686019 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.52493 | −0.208253 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2141 | 1.08254 | 0.541271 | − | 0.840848i | \(-0.317943\pi\) | ||||
0.541271 | + | 0.840848i | \(0.317943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9976 | 1.13911 | 0.569554 | − | 0.821954i | \(-0.307116\pi\) | ||||
0.569554 | + | 0.821954i | \(0.307116\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.1686 | −1.79222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.967541 | 0.0777148 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.59693 | −0.287066 | −0.143533 | − | 0.989645i | \(-0.545846\pi\) | ||||
−0.143533 | + | 0.989645i | \(0.545846\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.66176 | −0.607617 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.80225 | −0.220849 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.82244 | 0.221071 | 0.110535 | − | 0.993872i | \(-0.464743\pi\) | ||||
0.110535 | + | 0.993872i | \(0.464743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.68412 | 0.676058 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.5586 | −1.82302 | −0.911511 | − | 0.411277i | \(-0.865083\pi\) | ||||
−0.911511 | + | 0.411277i | \(0.865083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.26584 | 0.708577 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.55235 | 0.194052 | 0.0970259 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970259 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.82912 | 0.516233 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.1992 | 2.19475 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.648782 | −0.0484923 | −0.0242461 | − | 0.999706i | \(-0.507719\pi\) | ||||
−0.0242461 | + | 0.999706i | \(0.507719\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5072 | 1.07831 | 0.539155 | − | 0.842207i | \(-0.318744\pi\) | ||||
0.539155 | + | 0.842207i | \(0.318744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.463445 | 0.0342589 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.4664 | 1.50472 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.56793 | 0.480294 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.947546 | −0.0689238 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5571 | −1.12567 | −0.562837 | − | 0.826568i | \(-0.690290\pi\) | ||||
−0.562837 | + | 0.826568i | \(0.690290\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9774 | 1.29404 | 0.647019 | − | 0.762474i | \(-0.276015\pi\) | ||||
0.647019 | + | 0.762474i | \(0.276015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.68412 | 0.621883 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.43697 | −0.601109 | −0.300555 | − | 0.953765i | \(-0.597172\pi\) | ||||
−0.300555 | + | 0.953765i | \(0.597172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3769 | 1.01915 | 0.509575 | − | 0.860426i | \(-0.329803\pi\) | ||||
0.509575 | + | 0.860426i | \(0.329803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.66389 | −0.117362 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.240184 | 0.0168576 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 39.4644 | 2.75631 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.45838 | −0.657403 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.74521 | −0.189890 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.79465 | −0.398920 | −0.199460 | − | 0.979906i | \(-0.563919\pi\) | ||||
−0.199460 | + | 0.979906i | \(0.563919\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.6552 | 1.00416 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.2474 | −1.31266 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.281315 | 0.0190969 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.1795 | 1.49875 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.56793 | 0.441807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.1268 | −1.54868 | −0.774342 | − | 0.632767i | \(-0.781919\pi\) | ||||
−0.774342 | + | 0.632767i | \(0.781919\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 23.0502 | 1.53668 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8937 | 0.789410 | 0.394705 | − | 0.918808i | \(-0.370847\pi\) | ||||
0.394705 | + | 0.918808i | \(0.370847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.61599 | −0.569361 | −0.284680 | − | 0.958622i | \(-0.591887\pi\) | ||||
−0.284680 | + | 0.958622i | \(0.591887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.52493 | 0.166128 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.5697 | −1.34756 | −0.673781 | − | 0.738931i | \(-0.735331\pi\) | ||||
−0.673781 | + | 0.738931i | \(0.735331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −45.8039 | −2.98792 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.03069 | 0.0669507 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3524 | −1.51054 | −0.755269 | − | 0.655415i | \(-0.772494\pi\) | ||||
−0.755269 | + | 0.655415i | \(0.772494\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0162209 | −0.00104488 | −0.000522440 | − | 1.00000i | \(-0.500166\pi\) | ||||
−0.000522440 | 1.00000i | \(0.500166\pi\) | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3688 | 1.43496 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.43935 | 0.219732 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.74521 | −0.174674 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6700 | 0.802931 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2276 | −0.961160 | −0.480580 | − | 0.876951i | \(-0.659574\pi\) | ||||
−0.480580 | + | 0.876951i | \(0.659574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.80225 | 0.176176 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 57.0367 | 3.57177 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.29617 | −0.330366 | −0.165183 | − | 0.986263i | \(-0.552822\pi\) | ||||
−0.165183 | + | 0.986263i | \(0.552822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.95065 | 0.369755 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.810687 | 0.0501802 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.3030 | 1.93023 | 0.965113 | − | 0.261833i | \(-0.0843271\pi\) | ||||
0.965113 | + | 0.261833i | \(0.0843271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4365 | 0.641110 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.39780 | −0.575136 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.990063 | 0.0603652 | 0.0301826 | − | 0.999544i | \(-0.490391\pi\) | ||||
0.0301826 | + | 0.999544i | \(0.490391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7198 | 1.56237 | 0.781183 | − | 0.624302i | \(-0.214616\pi\) | ||||
0.781183 | + | 0.624302i | \(0.214616\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.52493 | 0.152816 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.82912 | −0.411812 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.5474 | −1.05432 | −0.527159 | − | 0.849766i | \(-0.676743\pi\) | ||||
−0.527159 | + | 0.849766i | \(0.676743\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.949516 | 0.0568460 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.54813 | 0.330974 | 0.165487 | − | 0.986212i | \(-0.447080\pi\) | ||||
0.165487 | + | 0.986212i | \(0.447080\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.14592 | −0.424781 | −0.212390 | − | 0.977185i | \(-0.568125\pi\) | ||||
−0.212390 | + | 0.977185i | \(0.568125\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.8397 | −1.41214 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4744 | 0.677311 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.1377 | 1.53751 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.84147 | −0.283812 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.9967 | −0.992956 | −0.496478 | − | 0.868049i | \(-0.665374\pi\) | ||||
−0.496478 | + | 0.868049i | \(0.665374\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.7739 | −2.31573 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.947546 | 0.0549822 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.80225 | 0.162059 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.59622 | −0.322561 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.12552 | 0.122108 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.631285 | −0.0361473 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7792 | 1.18593 | 0.592966 | − | 0.805228i | \(-0.297957\pi\) | ||||
0.592966 | + | 0.805228i | \(0.297957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.9023 | −1.92864 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.483400 | 0.0274111 | 0.0137055 | − | 0.999906i | \(-0.495637\pi\) | ||||
0.0137055 | + | 0.999906i | \(0.495637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.43420 | −0.250636 | −0.125318 | − | 0.992117i | \(-0.539995\pi\) | ||||
−0.125318 | + | 0.992117i | \(0.539995\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.6088 | 0.654079 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.4308 | 0.979012 | 0.489506 | − | 0.872000i | \(-0.337177\pi\) | ||||
0.489506 | + | 0.872000i | \(0.337177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.240184 | −0.0134477 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.8819 | 0.886441 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0303 | −1.00323 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.82912 | −0.378812 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.91163 | −0.271614 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.3176 | −0.734224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.6243 | −1.68327 | −0.841633 | − | 0.540050i | \(-0.818405\pi\) | ||||
−0.841633 | + | 0.540050i | \(0.818405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.0851 | 1.10066 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.26648 | 0.123831 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.1976 | 1.80839 | 0.904195 | − | 0.427119i | \(-0.140471\pi\) | ||||
0.904195 | + | 0.427119i | \(0.140471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.7860 | 2.37813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.281315 | −0.0152341 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.3351 | 1.31016 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.82249 | 0.151519 | 0.0757596 | − | 0.997126i | \(-0.475862\pi\) | ||||
0.0757596 | + | 0.997126i | \(0.475862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.9939 | −1.81965 | −0.909826 | − | 0.414991i | \(-0.863785\pi\) | ||||
−0.909826 | + | 0.414991i | \(0.863785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.947546 | 0.0505763 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9223 | 0.953909 | 0.476955 | − | 0.878928i | \(-0.341741\pi\) | ||||
0.476955 | + | 0.878928i | \(0.341741\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.9627 | −1.05951 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.5836 | 0.877695 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.1800 | 1.32895 | 0.664475 | − | 0.747311i | \(-0.268655\pi\) | ||||
0.664475 | + | 0.747311i | \(0.268655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4638 | −0.603359 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.52493 | −0.132525 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.2119 | −1.58136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.8746 | −1.66384 | −0.831921 | − | 0.554894i | \(-0.812759\pi\) | ||||
−0.831921 | + | 0.554894i | \(0.812759\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 38.7292 | 2.01616 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.03445 | 0.157541 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.2256 | −0.788352 | −0.394176 | − | 0.919035i | \(-0.628970\pi\) | ||||
−0.394176 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.8843 | −0.820263 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.240184 | −0.0123701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.2654 | −0.527298 | −0.263649 | − | 0.964619i | \(-0.584926\pi\) | ||||
−0.263649 | + | 0.964619i | \(0.584926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.4270 | 0.995277 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.1745 | −0.622087 | −0.311043 | − | 0.950396i | \(-0.600678\pi\) | ||||
−0.311043 | + | 0.950396i | \(0.600678\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.43935 | −0.175285 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.8888 | −0.960172 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.85013 | 0.448720 | 0.224360 | − | 0.974506i | \(-0.427971\pi\) | ||||
0.224360 | + | 0.974506i | \(0.427971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.4050 | 0.930781 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.85568 | 0.396267 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.40397 | −0.0706412 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.2258 | −1.91850 | −0.959248 | − | 0.282565i | \(-0.908815\pi\) | ||||
−0.959248 | + | 0.282565i | \(0.908815\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.93147 | −0.347007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.93458 | −0.0966083 | −0.0483041 | − | 0.998833i | \(-0.515382\pi\) | ||||
−0.0483041 | + | 0.998833i | \(0.515382\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.281315 | −0.0140133 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −26.5977 | −1.32165 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.95065 | −0.294963 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0589 | −0.546827 | −0.273414 | − | 0.961897i | \(-0.588153\pi\) | ||||
−0.273414 | + | 0.961897i | \(0.588153\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.58566 | 0.226194 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.5644 | −0.569045 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.2586 | −0.847190 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.2236 | 0.696533 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.7518 | −1.40462 | −0.702310 | − | 0.711872i | \(-0.747848\pi\) | ||||
−0.702310 | + | 0.711872i | \(0.747848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95139 | −0.143842 | −0.0719209 | − | 0.997410i | \(-0.522913\pi\) | ||||
−0.0719209 | + | 0.997410i | \(0.522913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −44.9506 | −2.18557 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.8532 | −2.17570 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.183548 | −0.00888250 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.52493 | −0.121905 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.3266 | −0.545585 | −0.272793 | − | 0.962073i | \(-0.587947\pi\) | ||||
−0.272793 | + | 0.962073i | \(0.587947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.7738 | −1.57501 | −0.787504 | − | 0.616309i | \(-0.788627\pi\) | ||||
−0.787504 | + | 0.616309i | \(0.788627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.08578 | −0.100006 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.69278 | −0.367995 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.05878 | 0.336897 | 0.168449 | − | 0.985710i | \(-0.446124\pi\) | ||||
0.168449 | + | 0.985710i | \(0.446124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.37528 | 0.160727 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.75409 | −0.273385 | −0.136692 | − | 0.990614i | \(-0.543647\pi\) | ||||
−0.136692 | + | 0.990614i | \(0.543647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.8013 | 0.606838 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.3647 | −1.57810 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.18170 | −0.197347 | −0.0986734 | − | 0.995120i | \(-0.531460\pi\) | ||||
−0.0986734 | + | 0.995120i | \(0.531460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4744 | −0.540307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.3429 | −1.66056 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.43935 | −0.161239 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.5675 | −1.19600 | −0.597999 | − | 0.801497i | \(-0.704037\pi\) | ||||
−0.597999 | + | 0.801497i | \(0.704037\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.22341 | 0.290484 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5020 | −0.535699 | −0.267850 | − | 0.963461i | \(-0.586313\pi\) | ||||
−0.267850 | + | 0.963461i | \(0.586313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.1859 | 1.49580 | 0.747902 | − | 0.663809i | \(-0.231061\pi\) | ||||
0.747902 | + | 0.663809i | \(0.231061\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.44297 | −0.113290 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.2239 | 1.58370 | 0.791848 | − | 0.610719i | \(-0.209119\pi\) | ||||
0.791848 | + | 0.610719i | \(0.209119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.658984 | 0.0304290 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.08201 | 0.418477 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.59622 | 0.257315 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.7474 | 0.860189 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.2421 | 0.468953 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.8111 | 0.676735 | 0.338368 | − | 0.941014i | \(-0.390125\pi\) | ||||
0.338368 | + | 0.941014i | \(0.390125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.95065 | −0.271326 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.07550 | 0.321946 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.59484 | 0.299456 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.9171 | 0.494700 | 0.247350 | − | 0.968926i | \(-0.420440\pi\) | ||||
0.247350 | + | 0.968926i | \(0.420440\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.12648 | −0.322270 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.5095 | −1.46713 | −0.733566 | − | 0.679618i | \(-0.762145\pi\) | ||||
−0.733566 | + | 0.679618i | \(0.762145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.57751 | −0.0710475 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.6088 | −0.521775 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.80420 | −0.260354 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.38207 | −0.196168 | −0.0980842 | − | 0.995178i | \(-0.531271\pi\) | ||||
−0.0980842 | + | 0.995178i | \(0.531271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 59.4839 | 2.65754 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.31536 | −0.237000 | −0.118500 | − | 0.992954i | \(-0.537809\pi\) | ||||
−0.118500 | + | 0.992954i | \(0.537809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.89530 | −0.128839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.52493 | −0.112136 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.7539 | −0.565309 | −0.282654 | − | 0.959222i | \(-0.591215\pi\) | ||||
−0.282654 | + | 0.959222i | \(0.591215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.78419 | −0.388590 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.60121 | −0.114846 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 46.1803 | 2.03495 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3176 | 0.585708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.44451 | −0.282883 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.7866 | −0.910678 | −0.455339 | − | 0.890318i | \(-0.650482\pi\) | ||||
−0.455339 | + | 0.890318i | \(0.650482\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.6386 | 0.771284 | 0.385642 | − | 0.922649i | \(-0.373980\pi\) | ||||
0.385642 | + | 0.922649i | \(0.373980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.2431 | −0.752549 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.84766 | −0.0804852 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.1474 | −0.658582 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.0329 | −1.69389 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.4744 | −0.497010 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.6336 | −0.935303 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.63813 | 0.0706905 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.81067 | −0.206827 | −0.103414 | − | 0.994638i | \(-0.532976\pi\) | ||||
−0.103414 | + | 0.994638i | \(0.532976\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.6296 | −1.57193 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.69040 | 0.286585 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.81951 | −0.291581 | −0.145791 | − | 0.989315i | \(-0.546573\pi\) | ||||
−0.145791 | + | 0.989315i | \(0.546573\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.619524 | −0.0264406 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.659355 | 0.0280895 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.408207 | −0.0173587 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −51.6762 | −2.19353 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.9966 | −1.77945 | −0.889726 | − | 0.456494i | \(-0.849105\pi\) | ||||
−0.889726 | + | 0.456494i | \(0.849105\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.59622 | 0.236695 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.5836 | −0.700158 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.5581 | −0.866420 | −0.433210 | − | 0.901293i | \(-0.642619\pi\) | ||||
−0.433210 | + | 0.901293i | \(0.642619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −59.6434 | −2.50921 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.73334 | −0.324770 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.7553 | 1.49894 | 0.749471 | − | 0.662037i | \(-0.230308\pi\) | ||||
0.749471 | + | 0.662037i | \(0.230308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.24964 | 0.303388 | 0.151694 | − | 0.988428i | \(-0.451527\pi\) | ||||
0.151694 | + | 0.988428i | \(0.451527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.2806 | 1.64097 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.1369 | −0.798065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.7885 | 0.615652 | 0.307826 | − | 0.951443i | \(-0.400399\pi\) | ||||
0.307826 | + | 0.951443i | \(0.400399\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −45.3916 | −1.88641 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.01797 | −0.208181 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.03445 | −0.125674 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.6088 | −0.479963 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.33172 | −0.0549658 | −0.0274829 | − | 0.999622i | \(-0.508749\pi\) | ||||
−0.0274829 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.772269 | 0.0318208 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.3028 | 0.876278 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0893 | 0.455382 | 0.227691 | − | 0.973733i | \(-0.426882\pi\) | ||||
0.227691 | + | 0.973733i | \(0.426882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.5894 | −0.926075 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.3006 | −1.48569 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.2983 | 0.951943 | 0.475971 | − | 0.879461i | \(-0.342097\pi\) | ||||
0.475971 | + | 0.879461i | \(0.342097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9967 | −1.26438 | −0.632190 | − | 0.774813i | \(-0.717844\pi\) | ||||
−0.632190 | + | 0.774813i | \(0.717844\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.22425 | 0.0905786 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.43935 | 0.139829 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.8510 | −0.643374 | −0.321687 | − | 0.946846i | \(-0.604250\pi\) | ||||
−0.321687 | + | 0.946846i | \(0.604250\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.606448 | −0.0245745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.3176 | 0.538773 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.70288 | 0.109168 | 0.0545841 | − | 0.998509i | \(-0.482617\pi\) | ||||
0.0545841 | + | 0.998509i | \(0.482617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −99.6448 | −4.01807 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.3787 | 1.62558 | 0.812792 | − | 0.582554i | \(-0.197947\pi\) | ||||
0.812792 | + | 0.582554i | \(0.197947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.98989 | 0.0799806 | 0.0399903 | − | 0.999200i | \(-0.487267\pi\) | ||||
0.0399903 | + | 0.999200i | \(0.487267\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.65526 | 0.106552 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.72200 | 0.149119 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5087 | −0.500347 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.93147 | 0.276816 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39.0834 | −1.55836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4417 | −0.614726 | −0.307363 | − | 0.951592i | \(-0.599447\pi\) | ||||
−0.307363 | + | 0.951592i | \(0.599447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.6311 | 0.581534 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.4626 | −1.05014 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.5908 | −0.775000 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.74295 | −0.108340 | −0.0541700 | − | 0.998532i | \(-0.517251\pi\) | ||||
−0.0541700 | + | 0.998532i | \(0.517251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.68302 | −0.302989 | −0.151494 | − | 0.988458i | \(-0.548409\pi\) | ||||
−0.151494 | + | 0.988458i | \(0.548409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.5983 | 1.91356 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.4155 | 0.684674 | 0.342337 | − | 0.939577i | \(-0.388782\pi\) | ||||
0.342337 | + | 0.939577i | \(0.388782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.5644 | 0.453941 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.710301 | −0.0278389 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.2655 | −0.793052 | −0.396526 | − | 0.918024i | \(-0.629784\pi\) | ||||
−0.396526 | + | 0.918024i | \(0.629784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7007 | −0.418109 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.6491 | −1.15672 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.4566 | 1.34224 | 0.671119 | − | 0.741349i | \(-0.265814\pi\) | ||||
0.671119 | + | 0.741349i | \(0.265814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.4705 | −1.30185 | −0.650925 | − | 0.759142i | \(-0.725619\pi\) | ||||
−0.650925 | + | 0.759142i | \(0.725619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.5836 | −0.644052 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.44174 | 0.366135 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.673056 | −0.0260608 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 58.3936 | 2.25763 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.183548 | 0.00708578 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.8896 | 1.38344 | 0.691721 | − | 0.722165i | \(-0.256853\pi\) | ||||
0.691721 | + | 0.722165i | \(0.256853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.47091 | −0.249065 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.0190 | −1.15372 | −0.576862 | − | 0.816842i | \(-0.695723\pi\) | ||||
−0.576862 | + | 0.816842i | \(0.695723\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.91747 | 0.0735856 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.0307 | −1.15078 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.4667 | −1.16577 | −0.582887 | − | 0.812553i | \(-0.698077\pi\) | ||||
−0.582887 | + | 0.812553i | \(0.698077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.24638 | −0.238662 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.7548 | 0.829997 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.03445 | −0.115603 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.9026 | 0.909296 | 0.454648 | − | 0.890671i | \(-0.349765\pi\) | ||||
0.454648 | + | 0.890671i | \(0.349765\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.37528 | −0.128216 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.3748 | −0.734927 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −75.3628 | −2.85457 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.9370 | 1.96444 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.97966 | 0.263618 | 0.131809 | − | 0.991275i | \(-0.457921\pi\) | ||||
0.131809 | + | 0.991275i | \(0.457921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3358 | 0.616116 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 115.652 | 4.35570 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.841815 | −0.0316597 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.2603 | 1.32423 | 0.662115 | − | 0.749402i | \(-0.269659\pi\) | ||||
0.662115 | + | 0.749402i | \(0.269659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.37781 | −0.0516719 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.788316 | −0.0295227 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.43935 | 0.128624 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 58.9631 | 2.20202 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.35967 | −0.162588 | −0.0812941 | − | 0.996690i | \(-0.525905\pi\) | ||||
−0.0812941 | + | 0.996690i | \(0.525905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.4270 | 0.500049 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0409567 | 0.00152320 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.64025 | 0.0609172 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.6893 | −0.730234 | −0.365117 | − | 0.930962i | \(-0.618971\pi\) | ||||
−0.365117 | + | 0.930962i | \(0.618971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.2796 | −1.23258 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.7556 | 1.35945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.6532 | −1.02140 | −0.510698 | − | 0.859760i | \(-0.670613\pi\) | ||||
−0.510698 | + | 0.859760i | \(0.670613\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.68412 | −0.320319 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.658984 | −0.0242740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.4502 | 1.96620 | 0.983099 | − | 0.183077i | \(-0.0586056\pi\) | ||||
0.983099 | + | 0.183077i | \(0.0586056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.93147 | 0.254634 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0130 | −0.660832 | −0.330416 | − | 0.943835i | \(-0.607189\pi\) | ||||
−0.330416 | + | 0.943835i | \(0.607189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.4480 | 1.66509 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.9370 | −0.619694 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.29003 | −0.229833 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7010 | 0.609429 | 0.304715 | − | 0.952444i | \(-0.401439\pi\) | ||||
0.304715 | + | 0.952444i | \(0.401439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.4487 | 1.40115 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.1426 | 1.75209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.5971 | −1.69360 | −0.846801 | − | 0.531910i | \(-0.821475\pi\) | ||||
−0.846801 | + | 0.531910i | \(0.821475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.07550 | −0.256824 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.9618 | 0.977364 | 0.488682 | − | 0.872462i | \(-0.337478\pi\) | ||||
0.488682 | + | 0.872462i | \(0.337478\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.94525 | 0.0704228 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −76.2454 | −2.75666 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.5644 | 0.417565 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.3803 | 1.13160 | 0.565801 | − | 0.824542i | \(-0.308567\pi\) | ||||
0.565801 | + | 0.824542i | \(0.308567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.3725 | 0.481598 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.02622 | 0.108846 | 0.0544228 | − | 0.998518i | \(-0.482668\pi\) | ||||
0.0544228 | + | 0.998518i | \(0.482668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.92114 | 0.0690092 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.0250 | −0.539018 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.4996 | 1.12859 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.80420 | 0.207691 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.227585 | −0.00813323 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.3711 | −0.441544 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.3970 | −1.15483 | −0.577414 | − | 0.816452i | \(-0.695938\pi\) | ||||
−0.577414 | + | 0.816452i | \(0.695938\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −79.0379 | −2.81382 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.3415 | −0.616592 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.183548 | 0.00651797 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.3515 | −0.934591 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.99600 | 0.106124 | 0.0530618 | − | 0.998591i | \(-0.483102\pi\) | ||||
0.0530618 | + | 0.998591i | \(0.483102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 87.4691 | 3.09443 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.5628 | 0.443884 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.78419 | 0.309987 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.63793 | −0.339692 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.49984 | −0.0879986 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.05449 | 0.0722320 | 0.0361160 | − | 0.999348i | \(-0.488501\pi\) | ||||
0.0361160 | + | 0.999348i | \(0.488501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.9259 | −0.524118 | −0.262059 | − | 0.965052i | \(-0.584402\pi\) | ||||
−0.262059 | + | 0.965052i | \(0.584402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −64.9407 | −2.27757 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.70737 | 0.340034 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.3628 | −0.537477 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.37528 | −0.117942 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.4503 | 1.02782 | 0.513911 | − | 0.857843i | \(-0.328196\pi\) | ||||
0.513911 | + | 0.857843i | \(0.328196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.3023 | −1.47457 | −0.737283 | − | 0.675584i | \(-0.763892\pi\) | ||||
−0.737283 | + | 0.675584i | \(0.763892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.2431 | 0.600327 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.8903 | 0.552559 | 0.276279 | − | 0.961077i | \(-0.410898\pi\) | ||||
0.276279 | + | 0.961077i | \(0.410898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.4270 | −1.57774 | −0.788872 | − | 0.614558i | \(-0.789335\pi\) | ||||
−0.788872 | + | 0.614558i | \(0.789335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44.3059 | 1.53695 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.56793 | −0.227565 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −81.0263 | −2.80403 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.266559 | −0.00921363 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.1543 | −0.523186 | −0.261593 | − | 0.965178i | \(-0.584248\pi\) | ||||
−0.261593 | + | 0.965178i | \(0.584248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9423 | −0.998011 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.0086 | −0.482483 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.43935 | 0.118317 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.0429 | 0.619232 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.6752 | −0.571620 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.4014 | 1.55452 | 0.777258 | − | 0.629182i | \(-0.216610\pi\) | ||||
0.777258 | + | 0.629182i | \(0.216610\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.8685 | 1.08988 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.01882 | −0.239758 | −0.119879 | − | 0.992788i | \(-0.538251\pi\) | ||||
−0.119879 | + | 0.992788i | \(0.538251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.1710 | 1.02942 | 0.514711 | − | 0.857363i | \(-0.327899\pi\) | ||||
0.514711 | + | 0.857363i | \(0.327899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.9720 | −0.987363 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.9524 | 1.42808 | 0.714038 | − | 0.700107i | \(-0.246865\pi\) | ||||
0.714038 | + | 0.700107i | \(0.246865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.77843 | 0.298476 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −65.9958 | −2.24133 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.408207 | 0.0138475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.658984 | −0.0223288 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.47198 | 0.219043 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.29100 | 0.212675 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.08406 | 0.104141 | 0.0520707 | − | 0.998643i | \(-0.483418\pi\) | ||||
0.0520707 | + | 0.998643i | \(0.483418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.9154 | 1.44750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.7931 | −0.666848 | −0.333424 | − | 0.942777i | \(-0.608204\pi\) | ||||
−0.333424 | + | 0.942777i | \(0.608204\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.24420 | −0.243787 | −0.121893 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121893 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 100.426 | 3.37580 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.8221 | −1.94148 | −0.970738 | − | 0.240139i | \(-0.922807\pi\) | ||||
−0.970738 | + | 0.240139i | \(0.922807\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.69408 | −0.258051 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.73334 | 0.259077 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.5597 | −1.22342 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.23139 | −0.0745871 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.07550 | −0.236244 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0675673 | 0.00225350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.9300 | −0.663965 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.1301 | 0.470220 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.8952 | 1.65857 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5234 | 0.349423 | 0.174711 | − | 0.984620i | \(-0.444101\pi\) | ||||
0.174711 | + | 0.984620i | \(0.444101\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.84136 | −0.0942419 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.294005 | −0.00974081 | −0.00487041 | − | 0.999988i | \(-0.501550\pi\) | ||||
−0.00487041 | + | 0.999988i | \(0.501550\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.01797 | 0.166071 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.59395 | 0.0526944 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.11125 | −0.102742 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.9983 | 1.25345 | 0.626725 | − | 0.779241i | \(-0.284395\pi\) | ||||
0.626725 | + | 0.779241i | \(0.284395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −52.4660 | −1.72881 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.80420 | 0.191048 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.6377 | 1.33616 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45.3200 | 1.48850 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.6251 | −1.00478 | −0.502388 | − | 0.864642i | \(-0.667545\pi\) | ||||
−0.502388 | + | 0.864642i | \(0.667545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.74521 | 0.0899706 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.22055 | −0.0399591 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.5894 | 0.738752 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.0781 | 0.361906 | 0.180953 | − | 0.983492i | \(-0.442082\pi\) | ||||
0.180953 | + | 0.983492i | \(0.442082\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.1960 | 0.365369 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.9511 | 0.682986 | 0.341493 | − | 0.939884i | \(-0.389067\pi\) | ||||
0.341493 | + | 0.939884i | \(0.389067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.1541 | −1.04708 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.25894 | −0.106013 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.2717 | 1.69860 | 0.849300 | − | 0.527910i | \(-0.177024\pi\) | ||||
0.849300 | + | 0.527910i | \(0.177024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.78419 | 0.285147 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.0116 | −1.42717 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.4013 | 0.952402 | 0.476201 | − | 0.879336i | \(-0.342013\pi\) | ||||
0.476201 | + | 0.879336i | \(0.342013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −53.5063 | −1.73142 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.606448 | 0.0196037 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.81615 | −0.0586466 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9209 | −0.997447 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.2306 | −0.684146 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 61.8304 | 1.99039 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.32741 | −0.235634 | −0.117817 | − | 0.993035i | \(-0.537590\pi\) | ||||
−0.117817 | + | 0.993035i | \(0.537590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45.5254 | 1.46249 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.1549 | −1.54536 | −0.772682 | − | 0.634793i | \(-0.781085\pi\) | ||||
−0.772682 | + | 0.634793i | \(0.781085\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.63326 | −0.180594 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.2431 | 0.552220 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.6859 | 1.23767 | 0.618835 | − | 0.785521i | \(-0.287605\pi\) | ||||
0.618835 | + | 0.785521i | \(0.287605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.72200 | −0.118956 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.56576 | 0.209629 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.0645 | −1.50113 | −0.750563 | − | 0.660799i | \(-0.770218\pi\) | ||||
−0.750563 | + | 0.660799i | \(0.770218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.0177 | −0.924580 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 33.6261 | 1.07033 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.6820 | 0.498660 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.6427 | −0.846335 | −0.423167 | − | 0.906052i | \(-0.639082\pi\) | ||||
−0.423167 | + | 0.906052i | \(0.639082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 77.3244 | 2.45381 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.4471 | 1.56758 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.4075 | −0.487959 | −0.243980 | − | 0.969780i | \(-0.578453\pi\) | ||||
−0.243980 | + | 0.969780i | \(0.578453\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.63852 | −0.178395 |
(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 | 8008.2.a.y.1.3 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.3 | ✓ | 14 | 1.1 | even | 1 | trivial |