Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,2,Mod(1,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.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: | \(11.5783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.470683 | −0.271749 | −0.135875 | − | 0.990726i | \(-0.543384\pi\) | ||||
−0.135875 | + | 0.990726i | \(0.543384\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.470683 | −0.192156 | ||||||||
\(7\) | 3.30777 | 1.25022 | 0.625110 | − | 0.780536i | \(-0.285054\pi\) | ||||
0.625110 | + | 0.780536i | \(0.285054\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.77846 | −0.926152 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.71982 | 1.42308 | 0.711540 | − | 0.702645i | \(-0.247998\pi\) | ||||
0.711540 | + | 0.702645i | \(0.247998\pi\) | |||||||
\(12\) | −0.470683 | −0.135875 | ||||||||
\(13\) | −2.24914 | −0.623799 | −0.311900 | − | 0.950115i | \(-0.600965\pi\) | ||||
−0.311900 | + | 0.950115i | \(0.600965\pi\) | |||||||
\(14\) | 3.30777 | 0.884040 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.719824 | −0.174583 | −0.0872915 | − | 0.996183i | \(-0.527821\pi\) | ||||
−0.0872915 | + | 0.996183i | \(0.527821\pi\) | |||||||
\(18\) | −2.77846 | −0.654889 | ||||||||
\(19\) | −0.470683 | −0.107982 | −0.0539911 | − | 0.998541i | \(-0.517194\pi\) | ||||
−0.0539911 | + | 0.998541i | \(0.517194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.55691 | −0.339747 | ||||||||
\(22\) | 4.71982 | 1.00627 | ||||||||
\(23\) | 5.80605 | 1.21065 | 0.605323 | − | 0.795980i | \(-0.293044\pi\) | ||||
0.605323 | + | 0.795980i | \(0.293044\pi\) | |||||||
\(24\) | −0.470683 | −0.0960779 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.24914 | −0.441093 | ||||||||
\(27\) | 2.71982 | 0.523430 | ||||||||
\(28\) | 3.30777 | 0.625110 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2181 | 1.83523 | 0.917613 | − | 0.397475i | \(-0.130114\pi\) | ||||
0.917613 | + | 0.397475i | \(0.130114\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.22154 | −0.386721 | ||||||||
\(34\) | −0.719824 | −0.123449 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.77846 | −0.463076 | ||||||||
\(37\) | −1.02760 | −0.168936 | −0.0844680 | − | 0.996426i | \(-0.526919\pi\) | ||||
−0.0844680 | + | 0.996426i | \(0.526919\pi\) | |||||||
\(38\) | −0.470683 | −0.0763549 | ||||||||
\(39\) | 1.05863 | 0.169517 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0275977 | −0.00431003 | −0.00215501 | − | 0.999998i | \(-0.500686\pi\) | ||||
−0.00215501 | + | 0.999998i | \(0.500686\pi\) | |||||||
\(42\) | −1.55691 | −0.240237 | ||||||||
\(43\) | −6.61555 | −1.00886 | −0.504431 | − | 0.863452i | \(-0.668298\pi\) | ||||
−0.504431 | + | 0.863452i | \(0.668298\pi\) | |||||||
\(44\) | 4.71982 | 0.711540 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.80605 | 0.856056 | ||||||||
\(47\) | −4.33537 | −0.632379 | −0.316189 | − | 0.948696i | \(-0.602404\pi\) | ||||
−0.316189 | + | 0.948696i | \(0.602404\pi\) | |||||||
\(48\) | −0.470683 | −0.0679373 | ||||||||
\(49\) | 3.94137 | 0.563052 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.338809 | 0.0474428 | ||||||||
\(52\) | −2.24914 | −0.311900 | ||||||||
\(53\) | −10.7474 | −1.47627 | −0.738136 | − | 0.674652i | \(-0.764294\pi\) | ||||
−0.738136 | + | 0.674652i | \(0.764294\pi\) | |||||||
\(54\) | 2.71982 | 0.370121 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.30777 | 0.442020 | ||||||||
\(57\) | 0.221543 | 0.0293441 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 11.0276 | 1.43567 | 0.717835 | − | 0.696213i | \(-0.245133\pi\) | ||||
0.717835 | + | 0.696213i | \(0.245133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.35342 | 0.173287 | 0.0866437 | − | 0.996239i | \(-0.472386\pi\) | ||||
0.0866437 | + | 0.996239i | \(0.472386\pi\) | |||||||
\(62\) | 10.2181 | 1.29770 | ||||||||
\(63\) | −9.19051 | −1.15790 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.22154 | −0.273453 | ||||||||
\(67\) | 8.80605 | 1.07583 | 0.537915 | − | 0.842999i | \(-0.319212\pi\) | ||||
0.537915 | + | 0.842999i | \(0.319212\pi\) | |||||||
\(68\) | −0.719824 | −0.0872915 | ||||||||
\(69\) | −2.73281 | −0.328992 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.80605 | −0.689052 | −0.344526 | − | 0.938777i | \(-0.611960\pi\) | ||||
−0.344526 | + | 0.938777i | \(0.611960\pi\) | |||||||
\(72\) | −2.77846 | −0.327444 | ||||||||
\(73\) | −3.64658 | −0.426800 | −0.213400 | − | 0.976965i | \(-0.568454\pi\) | ||||
−0.213400 | + | 0.976965i | \(0.568454\pi\) | |||||||
\(74\) | −1.02760 | −0.119456 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.470683 | −0.0539911 | ||||||||
\(77\) | 15.6121 | 1.77917 | ||||||||
\(78\) | 1.05863 | 0.119867 | ||||||||
\(79\) | 16.6707 | 1.87561 | 0.937803 | − | 0.347169i | \(-0.112857\pi\) | ||||
0.937803 | + | 0.347169i | \(0.112857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.05520 | 0.783911 | ||||||||
\(82\) | −0.0275977 | −0.00304765 | ||||||||
\(83\) | 5.21811 | 0.572761 | 0.286381 | − | 0.958116i | \(-0.407548\pi\) | ||||
0.286381 | + | 0.958116i | \(0.407548\pi\) | |||||||
\(84\) | −1.55691 | −0.169873 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.61555 | −0.713373 | ||||||||
\(87\) | −0.470683 | −0.0504626 | ||||||||
\(88\) | 4.71982 | 0.503135 | ||||||||
\(89\) | 9.08623 | 0.963139 | 0.481569 | − | 0.876408i | \(-0.340067\pi\) | ||||
0.481569 | + | 0.876408i | \(0.340067\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.43965 | −0.779887 | ||||||||
\(92\) | 5.80605 | 0.605323 | ||||||||
\(93\) | −4.80949 | −0.498721 | ||||||||
\(94\) | −4.33537 | −0.447159 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.470683 | −0.0480389 | ||||||||
\(97\) | 11.1905 | 1.13622 | 0.568112 | − | 0.822951i | \(-0.307674\pi\) | ||||
0.568112 | + | 0.822951i | \(0.307674\pi\) | |||||||
\(98\) | 3.94137 | 0.398138 | ||||||||
\(99\) | −13.1138 | −1.31799 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.02760 | −0.301257 | −0.150629 | − | 0.988590i | \(-0.548130\pi\) | ||||
−0.150629 | + | 0.988590i | \(0.548130\pi\) | |||||||
\(102\) | 0.338809 | 0.0335471 | ||||||||
\(103\) | 6.01461 | 0.592637 | 0.296318 | − | 0.955089i | \(-0.404241\pi\) | ||||
0.296318 | + | 0.955089i | \(0.404241\pi\) | |||||||
\(104\) | −2.24914 | −0.220546 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7474 | −1.04388 | ||||||||
\(107\) | −11.7474 | −1.13567 | −0.567833 | − | 0.823144i | \(-0.692218\pi\) | ||||
−0.567833 | + | 0.823144i | \(0.692218\pi\) | |||||||
\(108\) | 2.71982 | 0.261715 | ||||||||
\(109\) | −9.92332 | −0.950482 | −0.475241 | − | 0.879856i | \(-0.657639\pi\) | ||||
−0.475241 | + | 0.879856i | \(0.657639\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.483673 | 0.0459082 | ||||||||
\(112\) | 3.30777 | 0.312555 | ||||||||
\(113\) | −14.0276 | −1.31961 | −0.659803 | − | 0.751439i | \(-0.729360\pi\) | ||||
−0.659803 | + | 0.751439i | \(0.729360\pi\) | |||||||
\(114\) | 0.221543 | 0.0207494 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 6.24914 | 0.577733 | ||||||||
\(118\) | 11.0276 | 1.01517 | ||||||||
\(119\) | −2.38101 | −0.218267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.2767 | 1.02516 | ||||||||
\(122\) | 1.35342 | 0.122533 | ||||||||
\(123\) | 0.0129898 | 0.00117125 | ||||||||
\(124\) | 10.2181 | 0.917613 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.19051 | −0.818755 | ||||||||
\(127\) | −16.2181 | −1.43912 | −0.719562 | − | 0.694428i | \(-0.755657\pi\) | ||||
−0.719562 | + | 0.694428i | \(0.755657\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.11383 | 0.274157 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.3630 | 1.86649 | 0.933246 | − | 0.359239i | \(-0.116964\pi\) | ||||
0.933246 | + | 0.359239i | \(0.116964\pi\) | |||||||
\(132\) | −2.22154 | −0.193360 | ||||||||
\(133\) | −1.55691 | −0.135002 | ||||||||
\(134\) | 8.80605 | 0.760727 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.719824 | −0.0617244 | ||||||||
\(137\) | −9.54392 | −0.815392 | −0.407696 | − | 0.913118i | \(-0.633668\pi\) | ||||
−0.407696 | + | 0.913118i | \(0.633668\pi\) | |||||||
\(138\) | −2.73281 | −0.232633 | ||||||||
\(139\) | −3.74742 | −0.317852 | −0.158926 | − | 0.987290i | \(-0.550803\pi\) | ||||
−0.158926 | + | 0.987290i | \(0.550803\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.04059 | 0.171848 | ||||||||
\(142\) | −5.80605 | −0.487233 | ||||||||
\(143\) | −10.6155 | −0.887717 | ||||||||
\(144\) | −2.77846 | −0.231538 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.64658 | −0.301793 | ||||||||
\(147\) | −1.85514 | −0.153009 | ||||||||
\(148\) | −1.02760 | −0.0844680 | ||||||||
\(149\) | 2.00000 | 0.163846 | 0.0819232 | − | 0.996639i | \(-0.473894\pi\) | ||||
0.0819232 | + | 0.996639i | \(0.473894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2491 | −1.15958 | −0.579789 | − | 0.814766i | \(-0.696865\pi\) | ||||
−0.579789 | + | 0.814766i | \(0.696865\pi\) | |||||||
\(152\) | −0.470683 | −0.0381775 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 15.6121 | 1.25806 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.05863 | 0.0847585 | ||||||||
\(157\) | −12.2035 | −0.973945 | −0.486973 | − | 0.873417i | \(-0.661899\pi\) | ||||
−0.486973 | + | 0.873417i | \(0.661899\pi\) | |||||||
\(158\) | 16.6707 | 1.32625 | ||||||||
\(159\) | 5.05863 | 0.401176 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.2051 | 1.51358 | ||||||||
\(162\) | 7.05520 | 0.554308 | ||||||||
\(163\) | −17.5845 | −1.37733 | −0.688663 | − | 0.725082i | \(-0.741802\pi\) | ||||
−0.688663 | + | 0.725082i | \(0.741802\pi\) | |||||||
\(164\) | −0.0275977 | −0.00215501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.21811 | 0.405003 | ||||||||
\(167\) | −11.7914 | −0.912450 | −0.456225 | − | 0.889865i | \(-0.650799\pi\) | ||||
−0.456225 | + | 0.889865i | \(0.650799\pi\) | |||||||
\(168\) | −1.55691 | −0.120119 | ||||||||
\(169\) | −7.94137 | −0.610874 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.30777 | 0.100008 | ||||||||
\(172\) | −6.61555 | −0.504431 | ||||||||
\(173\) | 20.7880 | 1.58048 | 0.790242 | − | 0.612795i | \(-0.209955\pi\) | ||||
0.790242 | + | 0.612795i | \(0.209955\pi\) | |||||||
\(174\) | −0.470683 | −0.0356824 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.71982 | 0.355770 | ||||||||
\(177\) | −5.19051 | −0.390142 | ||||||||
\(178\) | 9.08623 | 0.681042 | ||||||||
\(179\) | −7.74742 | −0.579069 | −0.289535 | − | 0.957168i | \(-0.593501\pi\) | ||||
−0.289535 | + | 0.957168i | \(0.593501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.7440 | −1.46756 | −0.733779 | − | 0.679388i | \(-0.762245\pi\) | ||||
−0.733779 | + | 0.679388i | \(0.762245\pi\) | |||||||
\(182\) | −7.43965 | −0.551463 | ||||||||
\(183\) | −0.637031 | −0.0470907 | ||||||||
\(184\) | 5.80605 | 0.428028 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.80949 | −0.352649 | ||||||||
\(187\) | −3.39744 | −0.248446 | ||||||||
\(188\) | −4.33537 | −0.316189 | ||||||||
\(189\) | 8.99656 | 0.654404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.397442 | 0.0287579 | 0.0143790 | − | 0.999897i | \(-0.495423\pi\) | ||||
0.0143790 | + | 0.999897i | \(0.495423\pi\) | |||||||
\(192\) | −0.470683 | −0.0339686 | ||||||||
\(193\) | −4.35342 | −0.313366 | −0.156683 | − | 0.987649i | \(-0.550080\pi\) | ||||
−0.156683 | + | 0.987649i | \(0.550080\pi\) | |||||||
\(194\) | 11.1905 | 0.803432 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.94137 | 0.281526 | ||||||||
\(197\) | 6.70683 | 0.477842 | 0.238921 | − | 0.971039i | \(-0.423206\pi\) | ||||
0.238921 | + | 0.971039i | \(0.423206\pi\) | |||||||
\(198\) | −13.1138 | −0.931959 | ||||||||
\(199\) | −9.36297 | −0.663723 | −0.331862 | − | 0.943328i | \(-0.607677\pi\) | ||||
−0.331862 | + | 0.943328i | \(0.607677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.14486 | −0.292356 | ||||||||
\(202\) | −3.02760 | −0.213021 | ||||||||
\(203\) | 3.30777 | 0.232160 | ||||||||
\(204\) | 0.338809 | 0.0237214 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.01461 | 0.419058 | ||||||||
\(207\) | −16.1319 | −1.12124 | ||||||||
\(208\) | −2.24914 | −0.155950 | ||||||||
\(209\) | −2.22154 | −0.153667 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.5665 | −1.69123 | −0.845613 | − | 0.533797i | \(-0.820765\pi\) | ||||
−0.845613 | + | 0.533797i | \(0.820765\pi\) | |||||||
\(212\) | −10.7474 | −0.738136 | ||||||||
\(213\) | 2.73281 | 0.187249 | ||||||||
\(214\) | −11.7474 | −0.803037 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.71982 | 0.185061 | ||||||||
\(217\) | 33.7992 | 2.29444 | ||||||||
\(218\) | −9.92332 | −0.672092 | ||||||||
\(219\) | 1.71639 | 0.115983 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.61899 | 0.108905 | ||||||||
\(222\) | 0.483673 | 0.0324620 | ||||||||
\(223\) | 2.11727 | 0.141783 | 0.0708913 | − | 0.997484i | \(-0.477416\pi\) | ||||
0.0708913 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(224\) | 3.30777 | 0.221010 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0276 | −0.933102 | ||||||||
\(227\) | −15.9138 | −1.05623 | −0.528117 | − | 0.849172i | \(-0.677102\pi\) | ||||
−0.528117 | + | 0.849172i | \(0.677102\pi\) | |||||||
\(228\) | 0.221543 | 0.0146720 | ||||||||
\(229\) | −22.2897 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.34836 | −0.483487 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −23.3871 | −1.53214 | −0.766071 | − | 0.642756i | \(-0.777791\pi\) | ||||
−0.766071 | + | 0.642756i | \(0.777791\pi\) | |||||||
\(234\) | 6.24914 | 0.408519 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.0276 | 0.717835 | ||||||||
\(237\) | −7.84664 | −0.509694 | ||||||||
\(238\) | −2.38101 | −0.154338 | ||||||||
\(239\) | 20.2277 | 1.30842 | 0.654209 | − | 0.756314i | \(-0.273002\pi\) | ||||
0.654209 | + | 0.756314i | \(0.273002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.26375 | 0.0814052 | 0.0407026 | − | 0.999171i | \(-0.487040\pi\) | ||||
0.0407026 | + | 0.999171i | \(0.487040\pi\) | |||||||
\(242\) | 11.2767 | 0.724896 | ||||||||
\(243\) | −11.4802 | −0.736457 | ||||||||
\(244\) | 1.35342 | 0.0866437 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0129898 | 0.000828197 0 | ||||||||
\(247\) | 1.05863 | 0.0673592 | ||||||||
\(248\) | 10.2181 | 0.648850 | ||||||||
\(249\) | −2.45608 | −0.155647 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.63971 | 0.608453 | 0.304226 | − | 0.952600i | \(-0.401602\pi\) | ||||
0.304226 | + | 0.952600i | \(0.401602\pi\) | |||||||
\(252\) | −9.19051 | −0.578948 | ||||||||
\(253\) | 27.4036 | 1.72285 | ||||||||
\(254\) | −16.2181 | −1.01761 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.43965 | −0.588829 | −0.294415 | − | 0.955678i | \(-0.595125\pi\) | ||||
−0.294415 | + | 0.955678i | \(0.595125\pi\) | |||||||
\(258\) | 3.11383 | 0.193858 | ||||||||
\(259\) | −3.39906 | −0.211207 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.77846 | −0.171982 | ||||||||
\(262\) | 21.3630 | 1.31981 | ||||||||
\(263\) | 11.6646 | 0.719272 | 0.359636 | − | 0.933093i | \(-0.382901\pi\) | ||||
0.359636 | + | 0.933093i | \(0.382901\pi\) | |||||||
\(264\) | −2.22154 | −0.136727 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.55691 | −0.0954605 | ||||||||
\(267\) | −4.27674 | −0.261732 | ||||||||
\(268\) | 8.80605 | 0.537915 | ||||||||
\(269\) | −20.1414 | −1.22804 | −0.614022 | − | 0.789289i | \(-0.710449\pi\) | ||||
−0.614022 | + | 0.789289i | \(0.710449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.0422 | −1.64270 | −0.821349 | − | 0.570427i | \(-0.806778\pi\) | ||||
−0.821349 | + | 0.570427i | \(0.806778\pi\) | |||||||
\(272\) | −0.719824 | −0.0436457 | ||||||||
\(273\) | 3.50172 | 0.211934 | ||||||||
\(274\) | −9.54392 | −0.576570 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.73281 | −0.164496 | ||||||||
\(277\) | −12.4216 | −0.746342 | −0.373171 | − | 0.927763i | \(-0.621729\pi\) | ||||
−0.373171 | + | 0.927763i | \(0.621729\pi\) | |||||||
\(278\) | −3.74742 | −0.224755 | ||||||||
\(279\) | −28.3906 | −1.69970 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8957 | 1.48515 | 0.742577 | − | 0.669761i | \(-0.233603\pi\) | ||||
0.742577 | + | 0.669761i | \(0.233603\pi\) | |||||||
\(282\) | 2.04059 | 0.121515 | ||||||||
\(283\) | −4.83709 | −0.287535 | −0.143768 | − | 0.989611i | \(-0.545922\pi\) | ||||
−0.143768 | + | 0.989611i | \(0.545922\pi\) | |||||||
\(284\) | −5.80605 | −0.344526 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.6155 | −0.627710 | ||||||||
\(287\) | −0.0912868 | −0.00538849 | ||||||||
\(288\) | −2.77846 | −0.163722 | ||||||||
\(289\) | −16.4819 | −0.969521 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.26719 | −0.308768 | ||||||||
\(292\) | −3.64658 | −0.213400 | ||||||||
\(293\) | 33.5190 | 1.95820 | 0.979101 | − | 0.203377i | \(-0.0651917\pi\) | ||||
0.979101 | + | 0.203377i | \(0.0651917\pi\) | |||||||
\(294\) | −1.85514 | −0.108194 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.02760 | −0.0597279 | ||||||||
\(297\) | 12.8371 | 0.744884 | ||||||||
\(298\) | 2.00000 | 0.115857 | ||||||||
\(299\) | −13.0586 | −0.755200 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.8827 | −1.26130 | ||||||||
\(302\) | −14.2491 | −0.819946 | ||||||||
\(303\) | 1.42504 | 0.0818664 | ||||||||
\(304\) | −0.470683 | −0.0269955 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | −12.3680 | −0.705880 | −0.352940 | − | 0.935646i | \(-0.614818\pi\) | ||||
−0.352940 | + | 0.935646i | \(0.614818\pi\) | |||||||
\(308\) | 15.6121 | 0.889583 | ||||||||
\(309\) | −2.83098 | −0.161049 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3224 | 0.868853 | 0.434426 | − | 0.900707i | \(-0.356951\pi\) | ||||
0.434426 | + | 0.900707i | \(0.356951\pi\) | |||||||
\(312\) | 1.05863 | 0.0599333 | ||||||||
\(313\) | 22.1268 | 1.25068 | 0.625341 | − | 0.780352i | \(-0.284960\pi\) | ||||
0.625341 | + | 0.780352i | \(0.284960\pi\) | |||||||
\(314\) | −12.2035 | −0.688683 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.6707 | 0.937803 | ||||||||
\(317\) | 10.1775 | 0.571626 | 0.285813 | − | 0.958285i | \(-0.407736\pi\) | ||||
0.285813 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(318\) | 5.05863 | 0.283674 | ||||||||
\(319\) | 4.71982 | 0.264259 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.52932 | 0.308616 | ||||||||
\(322\) | 19.2051 | 1.07026 | ||||||||
\(323\) | 0.338809 | 0.0188518 | ||||||||
\(324\) | 7.05520 | 0.391955 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.5845 | −0.973916 | ||||||||
\(327\) | 4.67074 | 0.258293 | ||||||||
\(328\) | −0.0275977 | −0.00152383 | ||||||||
\(329\) | −14.3404 | −0.790613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.69834 | 0.478104 | 0.239052 | − | 0.971007i | \(-0.423163\pi\) | ||||
0.239052 | + | 0.971007i | \(0.423163\pi\) | |||||||
\(332\) | 5.21811 | 0.286381 | ||||||||
\(333\) | 2.85514 | 0.156460 | ||||||||
\(334\) | −11.7914 | −0.645199 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.55691 | −0.0849366 | ||||||||
\(337\) | 16.7198 | 0.910787 | 0.455393 | − | 0.890290i | \(-0.349499\pi\) | ||||
0.455393 | + | 0.890290i | \(0.349499\pi\) | |||||||
\(338\) | −7.94137 | −0.431953 | ||||||||
\(339\) | 6.60256 | 0.358602 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.2277 | 2.61167 | ||||||||
\(342\) | 1.30777 | 0.0707163 | ||||||||
\(343\) | −10.1173 | −0.546281 | ||||||||
\(344\) | −6.61555 | −0.356686 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.7880 | 1.11757 | ||||||||
\(347\) | 6.74398 | 0.362036 | 0.181018 | − | 0.983480i | \(-0.442061\pi\) | ||||
0.181018 | + | 0.983480i | \(0.442061\pi\) | |||||||
\(348\) | −0.470683 | −0.0252313 | ||||||||
\(349\) | 7.42504 | 0.397453 | 0.198727 | − | 0.980055i | \(-0.436319\pi\) | ||||
0.198727 | + | 0.980055i | \(0.436319\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.11727 | −0.326516 | ||||||||
\(352\) | 4.71982 | 0.251567 | ||||||||
\(353\) | 3.36802 | 0.179262 | 0.0896309 | − | 0.995975i | \(-0.471431\pi\) | ||||
0.0896309 | + | 0.995975i | \(0.471431\pi\) | |||||||
\(354\) | −5.19051 | −0.275872 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.08623 | 0.481569 | ||||||||
\(357\) | 1.12070 | 0.0593140 | ||||||||
\(358\) | −7.74742 | −0.409464 | ||||||||
\(359\) | 1.81111 | 0.0955868 | 0.0477934 | − | 0.998857i | \(-0.484781\pi\) | ||||
0.0477934 | + | 0.998857i | \(0.484781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7785 | −0.988340 | ||||||||
\(362\) | −19.7440 | −1.03772 | ||||||||
\(363\) | −5.30777 | −0.278586 | ||||||||
\(364\) | −7.43965 | −0.389944 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.637031 | −0.0332981 | ||||||||
\(367\) | −30.8268 | −1.60914 | −0.804572 | − | 0.593855i | \(-0.797605\pi\) | ||||
−0.804572 | + | 0.593855i | \(0.797605\pi\) | |||||||
\(368\) | 5.80605 | 0.302662 | ||||||||
\(369\) | 0.0766789 | 0.00399174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.5500 | −1.84567 | ||||||||
\(372\) | −4.80949 | −0.249361 | ||||||||
\(373\) | 2.06207 | 0.106770 | 0.0533850 | − | 0.998574i | \(-0.482999\pi\) | ||||
0.0533850 | + | 0.998574i | \(0.482999\pi\) | |||||||
\(374\) | −3.39744 | −0.175678 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.33537 | −0.223580 | ||||||||
\(377\) | −2.24914 | −0.115837 | ||||||||
\(378\) | 8.99656 | 0.462733 | ||||||||
\(379\) | −7.29478 | −0.374708 | −0.187354 | − | 0.982292i | \(-0.559991\pi\) | ||||
−0.187354 | + | 0.982292i | \(0.559991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.63359 | 0.391081 | ||||||||
\(382\) | 0.397442 | 0.0203349 | ||||||||
\(383\) | −15.7846 | −0.806554 | −0.403277 | − | 0.915078i | \(-0.632129\pi\) | ||||
−0.403277 | + | 0.915078i | \(0.632129\pi\) | |||||||
\(384\) | −0.470683 | −0.0240195 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.35342 | −0.221583 | ||||||||
\(387\) | 18.3810 | 0.934359 | ||||||||
\(388\) | 11.1905 | 0.568112 | ||||||||
\(389\) | −13.3534 | −0.677045 | −0.338523 | − | 0.940958i | \(-0.609927\pi\) | ||||
−0.338523 | + | 0.940958i | \(0.609927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.17934 | −0.211358 | ||||||||
\(392\) | 3.94137 | 0.199069 | ||||||||
\(393\) | −10.0552 | −0.507218 | ||||||||
\(394\) | 6.70683 | 0.337885 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −13.1138 | −0.658995 | ||||||||
\(397\) | 20.2130 | 1.01446 | 0.507232 | − | 0.861810i | \(-0.330669\pi\) | ||||
0.507232 | + | 0.861810i | \(0.330669\pi\) | |||||||
\(398\) | −9.36297 | −0.469323 | ||||||||
\(399\) | 0.732814 | 0.0366866 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.2897 | 0.763533 | 0.381766 | − | 0.924259i | \(-0.375316\pi\) | ||||
0.381766 | + | 0.924259i | \(0.375316\pi\) | |||||||
\(402\) | −4.14486 | −0.206727 | ||||||||
\(403\) | −22.9820 | −1.14481 | ||||||||
\(404\) | −3.02760 | −0.150629 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.30777 | 0.164162 | ||||||||
\(407\) | −4.85008 | −0.240410 | ||||||||
\(408\) | 0.338809 | 0.0167736 | ||||||||
\(409\) | 14.8302 | 0.733307 | 0.366653 | − | 0.930358i | \(-0.380503\pi\) | ||||
0.366653 | + | 0.930358i | \(0.380503\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.49217 | 0.221582 | ||||||||
\(412\) | 6.01461 | 0.296318 | ||||||||
\(413\) | 36.4768 | 1.79491 | ||||||||
\(414\) | −16.1319 | −0.792838 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.24914 | −0.110273 | ||||||||
\(417\) | 1.76385 | 0.0863761 | ||||||||
\(418\) | −2.22154 | −0.108659 | ||||||||
\(419\) | −13.8647 | −0.677334 | −0.338667 | − | 0.940906i | \(-0.609976\pi\) | ||||
−0.338667 | + | 0.940906i | \(0.609976\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.70178 | 0.131677 | 0.0658383 | − | 0.997830i | \(-0.479028\pi\) | ||||
0.0658383 | + | 0.997830i | \(0.479028\pi\) | |||||||
\(422\) | −24.5665 | −1.19588 | ||||||||
\(423\) | 12.0456 | 0.585679 | ||||||||
\(424\) | −10.7474 | −0.521941 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.73281 | 0.132405 | ||||||||
\(427\) | 4.47680 | 0.216647 | ||||||||
\(428\) | −11.7474 | −0.567833 | ||||||||
\(429\) | 4.99656 | 0.241236 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3009 | −1.31504 | −0.657519 | − | 0.753438i | \(-0.728394\pi\) | ||||
−0.657519 | + | 0.753438i | \(0.728394\pi\) | |||||||
\(432\) | 2.71982 | 0.130858 | ||||||||
\(433\) | −0.262130 | −0.0125972 | −0.00629859 | − | 0.999980i | \(-0.502005\pi\) | ||||
−0.00629859 | + | 0.999980i | \(0.502005\pi\) | |||||||
\(434\) | 33.7992 | 1.62241 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.92332 | −0.475241 | ||||||||
\(437\) | −2.73281 | −0.130728 | ||||||||
\(438\) | 1.71639 | 0.0820121 | ||||||||
\(439\) | 20.4983 | 0.978330 | 0.489165 | − | 0.872191i | \(-0.337302\pi\) | ||||
0.489165 | + | 0.872191i | \(0.337302\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.9509 | −0.521472 | ||||||||
\(442\) | 1.61899 | 0.0770073 | ||||||||
\(443\) | −0.456076 | −0.0216688 | −0.0108344 | − | 0.999941i | \(-0.503449\pi\) | ||||
−0.0108344 | + | 0.999941i | \(0.503449\pi\) | |||||||
\(444\) | 0.483673 | 0.0229541 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.11727 | 0.100255 | ||||||||
\(447\) | −0.941367 | −0.0445251 | ||||||||
\(448\) | 3.30777 | 0.156278 | ||||||||
\(449\) | −8.62854 | −0.407206 | −0.203603 | − | 0.979054i | \(-0.565265\pi\) | ||||
−0.203603 | + | 0.979054i | \(0.565265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.130256 | −0.00613352 | ||||||||
\(452\) | −14.0276 | −0.659803 | ||||||||
\(453\) | 6.70683 | 0.315115 | ||||||||
\(454\) | −15.9138 | −0.746870 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.221543 | 0.0103747 | ||||||||
\(457\) | −11.6872 | −0.546703 | −0.273351 | − | 0.961914i | \(-0.588132\pi\) | ||||
−0.273351 | + | 0.961914i | \(0.588132\pi\) | |||||||
\(458\) | −22.2897 | −1.04153 | ||||||||
\(459\) | −1.95779 | −0.0913820 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.82066 | −0.0847967 | −0.0423984 | − | 0.999101i | \(-0.513500\pi\) | ||||
−0.0423984 | + | 0.999101i | \(0.513500\pi\) | |||||||
\(462\) | −7.34836 | −0.341877 | ||||||||
\(463\) | 26.8241 | 1.24662 | 0.623311 | − | 0.781974i | \(-0.285787\pi\) | ||||
0.623311 | + | 0.781974i | \(0.285787\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.3871 | −1.08339 | ||||||||
\(467\) | −0.366407 | −0.0169553 | −0.00847764 | − | 0.999964i | \(-0.502699\pi\) | ||||
−0.00847764 | + | 0.999964i | \(0.502699\pi\) | |||||||
\(468\) | 6.24914 | 0.288867 | ||||||||
\(469\) | 29.1284 | 1.34503 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.74398 | 0.264669 | ||||||||
\(472\) | 11.0276 | 0.507586 | ||||||||
\(473\) | −31.2242 | −1.43569 | ||||||||
\(474\) | −7.84664 | −0.360408 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.38101 | −0.109134 | ||||||||
\(477\) | 29.8613 | 1.36725 | ||||||||
\(478\) | 20.2277 | 0.925191 | ||||||||
\(479\) | 13.7363 | 0.627625 | 0.313813 | − | 0.949485i | \(-0.398394\pi\) | ||||
0.313813 | + | 0.949485i | \(0.398394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.31121 | 0.105382 | ||||||||
\(482\) | 1.26375 | 0.0575622 | ||||||||
\(483\) | −9.03953 | −0.411313 | ||||||||
\(484\) | 11.2767 | 0.512579 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11.4802 | −0.520754 | ||||||||
\(487\) | 22.9414 | 1.03957 | 0.519786 | − | 0.854296i | \(-0.326012\pi\) | ||||
0.519786 | + | 0.854296i | \(0.326012\pi\) | |||||||
\(488\) | 1.35342 | 0.0612663 | ||||||||
\(489\) | 8.27674 | 0.374287 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8241 | 0.578744 | 0.289372 | − | 0.957217i | \(-0.406554\pi\) | ||||
0.289372 | + | 0.957217i | \(0.406554\pi\) | |||||||
\(492\) | 0.0129898 | 0.000585624 0 | ||||||||
\(493\) | −0.719824 | −0.0324192 | ||||||||
\(494\) | 1.05863 | 0.0476302 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.2181 | 0.458806 | ||||||||
\(497\) | −19.2051 | −0.861467 | ||||||||
\(498\) | −2.45608 | −0.110059 | ||||||||
\(499\) | −0.349979 | −0.0156672 | −0.00783361 | − | 0.999969i | \(-0.502494\pi\) | ||||
−0.00783361 | + | 0.999969i | \(0.502494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.55004 | 0.247957 | ||||||||
\(502\) | 9.63971 | 0.430241 | ||||||||
\(503\) | 34.1629 | 1.52325 | 0.761624 | − | 0.648019i | \(-0.224402\pi\) | ||||
0.761624 | + | 0.648019i | \(0.224402\pi\) | |||||||
\(504\) | −9.19051 | −0.409378 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 27.4036 | 1.21824 | ||||||||
\(507\) | 3.73787 | 0.166005 | ||||||||
\(508\) | −16.2181 | −0.719562 | ||||||||
\(509\) | −33.7586 | −1.49632 | −0.748162 | − | 0.663517i | \(-0.769063\pi\) | ||||
−0.748162 | + | 0.663517i | \(0.769063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0621 | −0.533595 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.28018 | −0.0565212 | ||||||||
\(514\) | −9.43965 | −0.416365 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.11383 | 0.137079 | ||||||||
\(517\) | −20.4622 | −0.899926 | ||||||||
\(518\) | −3.39906 | −0.149346 | ||||||||
\(519\) | −9.78457 | −0.429495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.3810 | 1.37483 | 0.687414 | − | 0.726266i | \(-0.258746\pi\) | ||||
0.687414 | + | 0.726266i | \(0.258746\pi\) | |||||||
\(522\) | −2.77846 | −0.121610 | ||||||||
\(523\) | 38.0303 | 1.66295 | 0.831474 | − | 0.555564i | \(-0.187498\pi\) | ||||
0.831474 | + | 0.555564i | \(0.187498\pi\) | |||||||
\(524\) | 21.3630 | 0.933246 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.6646 | 0.508602 | ||||||||
\(527\) | −7.35524 | −0.320399 | ||||||||
\(528\) | −2.22154 | −0.0966802 | ||||||||
\(529\) | 10.7103 | 0.465664 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.6397 | −1.32965 | ||||||||
\(532\) | −1.55691 | −0.0675008 | ||||||||
\(533\) | 0.0620710 | 0.00268859 | ||||||||
\(534\) | −4.27674 | −0.185073 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.80605 | 0.380364 | ||||||||
\(537\) | 3.64658 | 0.157362 | ||||||||
\(538\) | −20.1414 | −0.868359 | ||||||||
\(539\) | 18.6026 | 0.801269 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.7862 | −1.83952 | −0.919761 | − | 0.392479i | \(-0.871618\pi\) | ||||
−0.919761 | + | 0.392479i | \(0.871618\pi\) | |||||||
\(542\) | −27.0422 | −1.16156 | ||||||||
\(543\) | 9.29317 | 0.398808 | ||||||||
\(544\) | −0.719824 | −0.0308622 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.50172 | 0.149860 | ||||||||
\(547\) | −28.0974 | −1.20136 | −0.600679 | − | 0.799490i | \(-0.705103\pi\) | ||||
−0.600679 | + | 0.799490i | \(0.705103\pi\) | |||||||
\(548\) | −9.54392 | −0.407696 | ||||||||
\(549\) | −3.76041 | −0.160490 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.470683 | −0.0200518 | ||||||||
\(552\) | −2.73281 | −0.116316 | ||||||||
\(553\) | 55.1430 | 2.34492 | ||||||||
\(554\) | −12.4216 | −0.527743 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.74742 | −0.158926 | ||||||||
\(557\) | 12.6155 | 0.534538 | 0.267269 | − | 0.963622i | \(-0.413879\pi\) | ||||
0.267269 | + | 0.963622i | \(0.413879\pi\) | |||||||
\(558\) | −28.3906 | −1.20187 | ||||||||
\(559\) | 14.8793 | 0.629327 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.59912 | 0.0675149 | ||||||||
\(562\) | 24.8957 | 1.05016 | ||||||||
\(563\) | 33.7586 | 1.42276 | 0.711378 | − | 0.702810i | \(-0.248072\pi\) | ||||
0.711378 | + | 0.702810i | \(0.248072\pi\) | |||||||
\(564\) | 2.04059 | 0.0859242 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.83709 | −0.203318 | ||||||||
\(567\) | 23.3370 | 0.980061 | ||||||||
\(568\) | −5.80605 | −0.243617 | ||||||||
\(569\) | 5.66119 | 0.237329 | 0.118665 | − | 0.992934i | \(-0.462139\pi\) | ||||
0.118665 | + | 0.992934i | \(0.462139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6105 | 1.28101 | 0.640505 | − | 0.767954i | \(-0.278725\pi\) | ||||
0.640505 | + | 0.767954i | \(0.278725\pi\) | |||||||
\(572\) | −10.6155 | −0.443858 | ||||||||
\(573\) | −0.187070 | −0.00781494 | ||||||||
\(574\) | −0.0912868 | −0.00381024 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.77846 | −0.115769 | ||||||||
\(577\) | −2.94298 | −0.122518 | −0.0612590 | − | 0.998122i | \(-0.519512\pi\) | ||||
−0.0612590 | + | 0.998122i | \(0.519512\pi\) | |||||||
\(578\) | −16.4819 | −0.685555 | ||||||||
\(579\) | 2.04908 | 0.0851569 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.2603 | 0.716078 | ||||||||
\(582\) | −5.26719 | −0.218332 | ||||||||
\(583\) | −50.7259 | −2.10085 | ||||||||
\(584\) | −3.64658 | −0.150897 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.5190 | 1.38466 | ||||||||
\(587\) | −14.5715 | −0.601431 | −0.300716 | − | 0.953714i | \(-0.597225\pi\) | ||||
−0.300716 | + | 0.953714i | \(0.597225\pi\) | |||||||
\(588\) | −1.85514 | −0.0765045 | ||||||||
\(589\) | −4.80949 | −0.198172 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.15680 | −0.129853 | ||||||||
\(592\) | −1.02760 | −0.0422340 | ||||||||
\(593\) | −19.0552 | −0.782503 | −0.391252 | − | 0.920284i | \(-0.627958\pi\) | ||||
−0.391252 | + | 0.920284i | \(0.627958\pi\) | |||||||
\(594\) | 12.8371 | 0.526712 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.00000 | 0.0819232 | ||||||||
\(597\) | 4.40699 | 0.180366 | ||||||||
\(598\) | −13.0586 | −0.534007 | ||||||||
\(599\) | 5.86631 | 0.239691 | 0.119845 | − | 0.992793i | \(-0.461760\pi\) | ||||
0.119845 | + | 0.992793i | \(0.461760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.3285 | −1.27792 | −0.638958 | − | 0.769242i | \(-0.720634\pi\) | ||||
−0.638958 | + | 0.769242i | \(0.720634\pi\) | |||||||
\(602\) | −21.8827 | −0.891874 | ||||||||
\(603\) | −24.4672 | −0.996383 | ||||||||
\(604\) | −14.2491 | −0.579789 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.42504 | 0.0578883 | ||||||||
\(607\) | 11.0061 | 0.446724 | 0.223362 | − | 0.974736i | \(-0.428297\pi\) | ||||
0.223362 | + | 0.974736i | \(0.428297\pi\) | |||||||
\(608\) | −0.470683 | −0.0190887 | ||||||||
\(609\) | −1.55691 | −0.0630893 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.75086 | 0.394478 | ||||||||
\(612\) | 2.00000 | 0.0808452 | ||||||||
\(613\) | −14.7068 | −0.594003 | −0.297002 | − | 0.954877i | \(-0.595987\pi\) | ||||
−0.297002 | + | 0.954877i | \(0.595987\pi\) | |||||||
\(614\) | −12.3680 | −0.499133 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.6121 | 0.629030 | ||||||||
\(617\) | 20.1579 | 0.811525 | 0.405762 | − | 0.913979i | \(-0.367006\pi\) | ||||
0.405762 | + | 0.913979i | \(0.367006\pi\) | |||||||
\(618\) | −2.83098 | −0.113879 | ||||||||
\(619\) | 39.9379 | 1.60524 | 0.802620 | − | 0.596490i | \(-0.203438\pi\) | ||||
0.802620 | + | 0.596490i | \(0.203438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.7914 | 0.633689 | ||||||||
\(622\) | 15.3224 | 0.614372 | ||||||||
\(623\) | 30.0552 | 1.20414 | ||||||||
\(624\) | 1.05863 | 0.0423792 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.1268 | 0.884366 | ||||||||
\(627\) | 1.04564 | 0.0417590 | ||||||||
\(628\) | −12.2035 | −0.486973 | ||||||||
\(629\) | 0.739689 | 0.0294933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.3189 | 1.60507 | 0.802536 | − | 0.596604i | \(-0.203484\pi\) | ||||
0.802536 | + | 0.596604i | \(0.203484\pi\) | |||||||
\(632\) | 16.6707 | 0.663127 | ||||||||
\(633\) | 11.5630 | 0.459589 | ||||||||
\(634\) | 10.1775 | 0.404201 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.05863 | 0.200588 | ||||||||
\(637\) | −8.86469 | −0.351232 | ||||||||
\(638\) | 4.71982 | 0.186860 | ||||||||
\(639\) | 16.1319 | 0.638167 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.7992 | −1.41398 | −0.706991 | − | 0.707222i | \(-0.749948\pi\) | ||||
−0.706991 | + | 0.707222i | \(0.749948\pi\) | |||||||
\(642\) | 5.52932 | 0.218225 | ||||||||
\(643\) | −21.1741 | −0.835024 | −0.417512 | − | 0.908671i | \(-0.637098\pi\) | ||||
−0.417512 | + | 0.908671i | \(0.637098\pi\) | |||||||
\(644\) | 19.2051 | 0.756788 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.338809 | 0.0133303 | ||||||||
\(647\) | 33.6742 | 1.32387 | 0.661934 | − | 0.749562i | \(-0.269736\pi\) | ||||
0.661934 | + | 0.749562i | \(0.269736\pi\) | |||||||
\(648\) | 7.05520 | 0.277154 | ||||||||
\(649\) | 52.0483 | 2.04308 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.9087 | −0.623512 | ||||||||
\(652\) | −17.5845 | −0.688663 | ||||||||
\(653\) | −28.3500 | −1.10942 | −0.554710 | − | 0.832044i | \(-0.687171\pi\) | ||||
−0.554710 | + | 0.832044i | \(0.687171\pi\) | |||||||
\(654\) | 4.67074 | 0.182640 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.0275977 | −0.00107751 | ||||||||
\(657\) | 10.1319 | 0.395282 | ||||||||
\(658\) | −14.3404 | −0.559048 | ||||||||
\(659\) | −13.1268 | −0.511348 | −0.255674 | − | 0.966763i | \(-0.582297\pi\) | ||||
−0.255674 | + | 0.966763i | \(0.582297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.3078 | −0.906567 | −0.453284 | − | 0.891366i | \(-0.649748\pi\) | ||||
−0.453284 | + | 0.891366i | \(0.649748\pi\) | |||||||
\(662\) | 8.69834 | 0.338071 | ||||||||
\(663\) | −0.762030 | −0.0295948 | ||||||||
\(664\) | 5.21811 | 0.202502 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.85514 | 0.110634 | ||||||||
\(667\) | 5.80605 | 0.224811 | ||||||||
\(668\) | −11.7914 | −0.456225 | ||||||||
\(669\) | −0.996562 | −0.0385293 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.38789 | 0.246602 | ||||||||
\(672\) | −1.55691 | −0.0600593 | ||||||||
\(673\) | 27.4784 | 1.05922 | 0.529608 | − | 0.848243i | \(-0.322339\pi\) | ||||
0.529608 | + | 0.848243i | \(0.322339\pi\) | |||||||
\(674\) | 16.7198 | 0.644024 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.94137 | −0.305437 | ||||||||
\(677\) | −35.6363 | −1.36961 | −0.684807 | − | 0.728725i | \(-0.740113\pi\) | ||||
−0.684807 | + | 0.728725i | \(0.740113\pi\) | |||||||
\(678\) | 6.60256 | 0.253570 | ||||||||
\(679\) | 37.0157 | 1.42053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.49035 | 0.287031 | ||||||||
\(682\) | 48.2277 | 1.84673 | ||||||||
\(683\) | 10.3319 | 0.395340 | 0.197670 | − | 0.980269i | \(-0.436662\pi\) | ||||
0.197670 | + | 0.980269i | \(0.436662\pi\) | |||||||
\(684\) | 1.30777 | 0.0500040 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.1173 | −0.386279 | ||||||||
\(687\) | 10.4914 | 0.400272 | ||||||||
\(688\) | −6.61555 | −0.252215 | ||||||||
\(689\) | 24.1725 | 0.920897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.02148 | 0.114943 | 0.0574713 | − | 0.998347i | \(-0.481696\pi\) | ||||
0.0574713 | + | 0.998347i | \(0.481696\pi\) | |||||||
\(692\) | 20.7880 | 0.790242 | ||||||||
\(693\) | −43.3776 | −1.64778 | ||||||||
\(694\) | 6.74398 | 0.255998 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.470683 | −0.0178412 | ||||||||
\(697\) | 0.0198655 | 0.000752458 0 | ||||||||
\(698\) | 7.42504 | 0.281042 | ||||||||
\(699\) | 11.0079 | 0.416358 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.5500 | 1.41825 | 0.709123 | − | 0.705085i | \(-0.249091\pi\) | ||||
0.709123 | + | 0.705085i | \(0.249091\pi\) | |||||||
\(702\) | −6.11727 | −0.230881 | ||||||||
\(703\) | 0.483673 | 0.0182421 | ||||||||
\(704\) | 4.71982 | 0.177885 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.36802 | 0.126757 | ||||||||
\(707\) | −10.0146 | −0.376638 | ||||||||
\(708\) | −5.19051 | −0.195071 | ||||||||
\(709\) | −23.7586 | −0.892273 | −0.446136 | − | 0.894965i | \(-0.647200\pi\) | ||||
−0.446136 | + | 0.894965i | \(0.647200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −46.3189 | −1.73710 | ||||||||
\(712\) | 9.08623 | 0.340521 | ||||||||
\(713\) | 59.3269 | 2.22181 | ||||||||
\(714\) | 1.12070 | 0.0419413 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.74742 | −0.289535 | ||||||||
\(717\) | −9.52082 | −0.355562 | ||||||||
\(718\) | 1.81111 | 0.0675901 | ||||||||
\(719\) | 48.4768 | 1.80788 | 0.903940 | − | 0.427660i | \(-0.140662\pi\) | ||||
0.903940 | + | 0.427660i | \(0.140662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8950 | 0.740927 | ||||||||
\(722\) | −18.7785 | −0.698862 | ||||||||
\(723\) | −0.594825 | −0.0221218 | ||||||||
\(724\) | −19.7440 | −0.733779 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.30777 | −0.196990 | ||||||||
\(727\) | −31.5208 | −1.16904 | −0.584521 | − | 0.811378i | \(-0.698718\pi\) | ||||
−0.584521 | + | 0.811378i | \(0.698718\pi\) | |||||||
\(728\) | −7.43965 | −0.275732 | ||||||||
\(729\) | −15.7620 | −0.583779 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.76203 | 0.176130 | ||||||||
\(732\) | −0.637031 | −0.0235453 | ||||||||
\(733\) | −21.5017 | −0.794184 | −0.397092 | − | 0.917779i | \(-0.629981\pi\) | ||||
−0.397092 | + | 0.917779i | \(0.629981\pi\) | |||||||
\(734\) | −30.8268 | −1.13784 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.80605 | 0.214014 | ||||||||
\(737\) | 41.5630 | 1.53099 | ||||||||
\(738\) | 0.0766789 | 0.00282259 | ||||||||
\(739\) | 12.5604 | 0.462040 | 0.231020 | − | 0.972949i | \(-0.425794\pi\) | ||||
0.231020 | + | 0.972949i | \(0.425794\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.498281 | −0.0183048 | ||||||||
\(742\) | −35.5500 | −1.30508 | ||||||||
\(743\) | −26.5275 | −0.973199 | −0.486600 | − | 0.873625i | \(-0.661763\pi\) | ||||
−0.486600 | + | 0.873625i | \(0.661763\pi\) | |||||||
\(744\) | −4.80949 | −0.176325 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.06207 | 0.0754978 | ||||||||
\(747\) | −14.4983 | −0.530464 | ||||||||
\(748\) | −3.39744 | −0.124223 | ||||||||
\(749\) | −38.8578 | −1.41983 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.4232 | −1.36559 | −0.682796 | − | 0.730609i | \(-0.739236\pi\) | ||||
−0.682796 | + | 0.730609i | \(0.739236\pi\) | |||||||
\(752\) | −4.33537 | −0.158095 | ||||||||
\(753\) | −4.53725 | −0.165347 | ||||||||
\(754\) | −2.24914 | −0.0819089 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.99656 | 0.327202 | ||||||||
\(757\) | 30.0844 | 1.09344 | 0.546718 | − | 0.837317i | \(-0.315877\pi\) | ||||
0.546718 | + | 0.837317i | \(0.315877\pi\) | |||||||
\(758\) | −7.29478 | −0.264958 | ||||||||
\(759\) | −12.8984 | −0.468182 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.1690 | 1.52863 | 0.764313 | − | 0.644845i | \(-0.223078\pi\) | ||||
0.764313 | + | 0.644845i | \(0.223078\pi\) | |||||||
\(762\) | 7.63359 | 0.276536 | ||||||||
\(763\) | −32.8241 | −1.18831 | ||||||||
\(764\) | 0.397442 | 0.0143790 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.7846 | −0.570320 | ||||||||
\(767\) | −24.8026 | −0.895571 | ||||||||
\(768\) | −0.470683 | −0.0169843 | ||||||||
\(769\) | −29.9587 | −1.08034 | −0.540168 | − | 0.841557i | \(-0.681639\pi\) | ||||
−0.540168 | + | 0.841557i | \(0.681639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.44309 | 0.160014 | ||||||||
\(772\) | −4.35342 | −0.156683 | ||||||||
\(773\) | −50.1966 | −1.80545 | −0.902723 | − | 0.430221i | \(-0.858436\pi\) | ||||
−0.902723 | + | 0.430221i | \(0.858436\pi\) | |||||||
\(774\) | 18.3810 | 0.660692 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.1905 | 0.401716 | ||||||||
\(777\) | 1.59988 | 0.0573954 | ||||||||
\(778\) | −13.3534 | −0.478743 | ||||||||
\(779\) | 0.0129898 | 0.000465406 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.4036 | −0.980576 | ||||||||
\(782\) | −4.17934 | −0.149453 | ||||||||
\(783\) | 2.71982 | 0.0971986 | ||||||||
\(784\) | 3.94137 | 0.140763 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.0552 | −0.358657 | ||||||||
\(787\) | −44.5845 | −1.58927 | −0.794633 | − | 0.607090i | \(-0.792337\pi\) | ||||
−0.794633 | + | 0.607090i | \(0.792337\pi\) | |||||||
\(788\) | 6.70683 | 0.238921 | ||||||||
\(789\) | −5.49035 | −0.195462 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.4001 | −1.64980 | ||||||||
\(792\) | −13.1138 | −0.465980 | ||||||||
\(793\) | −3.04403 | −0.108097 | ||||||||
\(794\) | 20.2130 | 0.717334 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.36297 | −0.331862 | ||||||||
\(797\) | −23.3155 | −0.825878 | −0.412939 | − | 0.910759i | \(-0.635498\pi\) | ||||
−0.412939 | + | 0.910759i | \(0.635498\pi\) | |||||||
\(798\) | 0.732814 | 0.0259413 | ||||||||
\(799\) | 3.12070 | 0.110403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.2457 | −0.892013 | ||||||||
\(802\) | 15.2897 | 0.539899 | ||||||||
\(803\) | −17.2112 | −0.607371 | ||||||||
\(804\) | −4.14486 | −0.146178 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −22.9820 | −0.809505 | ||||||||
\(807\) | 9.48024 | 0.333720 | ||||||||
\(808\) | −3.02760 | −0.106511 | ||||||||
\(809\) | 50.6570 | 1.78100 | 0.890502 | − | 0.454978i | \(-0.150353\pi\) | ||||
0.890502 | + | 0.454978i | \(0.150353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.6949 | 1.42899 | 0.714496 | − | 0.699640i | \(-0.246656\pi\) | ||||
0.714496 | + | 0.699640i | \(0.246656\pi\) | |||||||
\(812\) | 3.30777 | 0.116080 | ||||||||
\(813\) | 12.7283 | 0.446402 | ||||||||
\(814\) | −4.85008 | −0.169995 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.338809 | 0.0118607 | ||||||||
\(817\) | 3.11383 | 0.108939 | ||||||||
\(818\) | 14.8302 | 0.518526 | ||||||||
\(819\) | 20.6707 | 0.722294 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.8421 | −0.413294 | −0.206647 | − | 0.978416i | \(-0.566255\pi\) | ||||
−0.206647 | + | 0.978416i | \(0.566255\pi\) | |||||||
\(822\) | 4.49217 | 0.156682 | ||||||||
\(823\) | 14.5243 | 0.506284 | 0.253142 | − | 0.967429i | \(-0.418536\pi\) | ||||
0.253142 | + | 0.967429i | \(0.418536\pi\) | |||||||
\(824\) | 6.01461 | 0.209529 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.4768 | 1.26919 | ||||||||
\(827\) | −30.9183 | −1.07513 | −0.537567 | − | 0.843221i | \(-0.680656\pi\) | ||||
−0.537567 | + | 0.843221i | \(0.680656\pi\) | |||||||
\(828\) | −16.1319 | −0.560621 | ||||||||
\(829\) | 1.26719 | 0.0440112 | 0.0220056 | − | 0.999758i | \(-0.492995\pi\) | ||||
0.0220056 | + | 0.999758i | \(0.492995\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.84664 | 0.202818 | ||||||||
\(832\) | −2.24914 | −0.0779749 | ||||||||
\(833\) | −2.83709 | −0.0982994 | ||||||||
\(834\) | 1.76385 | 0.0610771 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.22154 | −0.0768337 | ||||||||
\(837\) | 27.7914 | 0.960613 | ||||||||
\(838\) | −13.8647 | −0.478948 | ||||||||
\(839\) | 33.1855 | 1.14569 | 0.572845 | − | 0.819664i | \(-0.305840\pi\) | ||||
0.572845 | + | 0.819664i | \(0.305840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 2.70178 | 0.0931094 | ||||||||
\(843\) | −11.7180 | −0.403590 | ||||||||
\(844\) | −24.5665 | −0.845613 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0456 | 0.414138 | ||||||||
\(847\) | 37.3009 | 1.28167 | ||||||||
\(848\) | −10.7474 | −0.369068 | ||||||||
\(849\) | 2.27674 | 0.0781375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.96629 | −0.204522 | ||||||||
\(852\) | 2.73281 | 0.0936247 | ||||||||
\(853\) | −42.7743 | −1.46456 | −0.732281 | − | 0.681002i | \(-0.761544\pi\) | ||||
−0.732281 | + | 0.681002i | \(0.761544\pi\) | |||||||
\(854\) | 4.47680 | 0.153193 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.7474 | −0.401519 | ||||||||
\(857\) | 44.7061 | 1.52713 | 0.763565 | − | 0.645731i | \(-0.223447\pi\) | ||||
0.763565 | + | 0.645731i | \(0.223447\pi\) | |||||||
\(858\) | 4.99656 | 0.170580 | ||||||||
\(859\) | −7.01643 | −0.239397 | −0.119699 | − | 0.992810i | \(-0.538193\pi\) | ||||
−0.119699 | + | 0.992810i | \(0.538193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0429672 | 0.00146432 | ||||||||
\(862\) | −27.3009 | −0.929872 | ||||||||
\(863\) | 40.4768 | 1.37785 | 0.688923 | − | 0.724834i | \(-0.258084\pi\) | ||||
0.688923 | + | 0.724834i | \(0.258084\pi\) | |||||||
\(864\) | 2.71982 | 0.0925303 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.262130 | −0.00890755 | ||||||||
\(867\) | 7.75774 | 0.263466 | ||||||||
\(868\) | 33.7992 | 1.14722 | ||||||||
\(869\) | 78.6830 | 2.66914 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.8061 | −0.671103 | ||||||||
\(872\) | −9.92332 | −0.336046 | ||||||||
\(873\) | −31.0923 | −1.05232 | ||||||||
\(874\) | −2.73281 | −0.0924388 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.71639 | 0.0579913 | ||||||||
\(877\) | 6.14325 | 0.207443 | 0.103721 | − | 0.994606i | \(-0.466925\pi\) | ||||
0.103721 | + | 0.994606i | \(0.466925\pi\) | |||||||
\(878\) | 20.4983 | 0.691783 | ||||||||
\(879\) | −15.7768 | −0.532140 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.6639 | −1.90905 | −0.954527 | − | 0.298124i | \(-0.903639\pi\) | ||||
−0.954527 | + | 0.298124i | \(0.903639\pi\) | |||||||
\(882\) | −10.9509 | −0.368737 | ||||||||
\(883\) | −49.5389 | −1.66712 | −0.833558 | − | 0.552432i | \(-0.813700\pi\) | ||||
−0.833558 | + | 0.552432i | \(0.813700\pi\) | |||||||
\(884\) | 1.61899 | 0.0544524 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.456076 | −0.0153222 | ||||||||
\(887\) | −1.03265 | −0.0346731 | −0.0173366 | − | 0.999850i | \(-0.505519\pi\) | ||||
−0.0173366 | + | 0.999850i | \(0.505519\pi\) | |||||||
\(888\) | 0.483673 | 0.0162310 | ||||||||
\(889\) | −53.6458 | −1.79922 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.2993 | 1.11557 | ||||||||
\(892\) | 2.11727 | 0.0708913 | ||||||||
\(893\) | 2.04059 | 0.0682857 | ||||||||
\(894\) | −0.941367 | −0.0314840 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.30777 | 0.110505 | ||||||||
\(897\) | 6.14648 | 0.205225 | ||||||||
\(898\) | −8.62854 | −0.287938 | ||||||||
\(899\) | 10.2181 | 0.340793 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.73625 | 0.257732 | ||||||||
\(902\) | −0.130256 | −0.00433705 | ||||||||
\(903\) | 10.2998 | 0.342757 | ||||||||
\(904\) | −14.0276 | −0.466551 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.70683 | 0.222820 | ||||||||
\(907\) | −8.04059 | −0.266983 | −0.133492 | − | 0.991050i | \(-0.542619\pi\) | ||||
−0.133492 | + | 0.991050i | \(0.542619\pi\) | |||||||
\(908\) | −15.9138 | −0.528117 | ||||||||
\(909\) | 8.41205 | 0.279010 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0456 | 0.465353 | 0.232676 | − | 0.972554i | \(-0.425252\pi\) | ||||
0.232676 | + | 0.972554i | \(0.425252\pi\) | |||||||
\(912\) | 0.221543 | 0.00733602 | ||||||||
\(913\) | 24.6285 | 0.815086 | ||||||||
\(914\) | −11.6872 | −0.386577 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.2897 | −0.736473 | ||||||||
\(917\) | 70.6639 | 2.33353 | ||||||||
\(918\) | −1.95779 | −0.0646168 | ||||||||
\(919\) | 15.5163 | 0.511836 | 0.255918 | − | 0.966698i | \(-0.417622\pi\) | ||||
0.255918 | + | 0.966698i | \(0.417622\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.82142 | 0.191822 | ||||||||
\(922\) | −1.82066 | −0.0599603 | ||||||||
\(923\) | 13.0586 | 0.429830 | ||||||||
\(924\) | −7.34836 | −0.241743 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.8241 | 0.881495 | ||||||||
\(927\) | −16.7113 | −0.548872 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 6.93181 | 0.227425 | 0.113713 | − | 0.993514i | \(-0.463726\pi\) | ||||
0.113713 | + | 0.993514i | \(0.463726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.85514 | −0.0607996 | ||||||||
\(932\) | −23.3871 | −0.766071 | ||||||||
\(933\) | −7.21199 | −0.236110 | ||||||||
\(934\) | −0.366407 | −0.0119892 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.24914 | 0.204260 | ||||||||
\(937\) | 45.3189 | 1.48051 | 0.740253 | − | 0.672329i | \(-0.234706\pi\) | ||||
0.740253 | + | 0.672329i | \(0.234706\pi\) | |||||||
\(938\) | 29.1284 | 0.951077 | ||||||||
\(939\) | −10.4147 | −0.339872 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.75086 | 0.252671 | 0.126335 | − | 0.991988i | \(-0.459678\pi\) | ||||
0.126335 | + | 0.991988i | \(0.459678\pi\) | |||||||
\(942\) | 5.74398 | 0.187149 | ||||||||
\(943\) | −0.160234 | −0.00521792 | ||||||||
\(944\) | 11.0276 | 0.358918 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.2242 | −1.01519 | ||||||||
\(947\) | 11.1544 | 0.362470 | 0.181235 | − | 0.983440i | \(-0.441991\pi\) | ||||
0.181235 | + | 0.983440i | \(0.441991\pi\) | |||||||
\(948\) | −7.84664 | −0.254847 | ||||||||
\(949\) | 8.20168 | 0.266238 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.79039 | −0.155339 | ||||||||
\(952\) | −2.38101 | −0.0771691 | ||||||||
\(953\) | 55.1492 | 1.78646 | 0.893228 | − | 0.449604i | \(-0.148435\pi\) | ||||
0.893228 | + | 0.449604i | \(0.148435\pi\) | |||||||
\(954\) | 29.8613 | 0.966794 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.2277 | 0.654209 | ||||||||
\(957\) | −2.22154 | −0.0718123 | ||||||||
\(958\) | 13.7363 | 0.443798 | ||||||||
\(959\) | −31.5691 | −1.01942 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.4097 | 2.36805 | ||||||||
\(962\) | 2.31121 | 0.0745165 | ||||||||
\(963\) | 32.6397 | 1.05180 | ||||||||
\(964\) | 1.26375 | 0.0407026 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.03953 | −0.290842 | ||||||||
\(967\) | 28.8984 | 0.929310 | 0.464655 | − | 0.885492i | \(-0.346178\pi\) | ||||
0.464655 | + | 0.885492i | \(0.346178\pi\) | |||||||
\(968\) | 11.2767 | 0.362448 | ||||||||
\(969\) | −0.159472 | −0.00512297 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1932 | −0.391298 | −0.195649 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195649 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(972\) | −11.4802 | −0.368229 | ||||||||
\(973\) | −12.3956 | −0.397385 | ||||||||
\(974\) | 22.9414 | 0.735089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.35342 | 0.0433218 | ||||||||
\(977\) | −20.5861 | −0.658609 | −0.329304 | − | 0.944224i | \(-0.606814\pi\) | ||||
−0.329304 | + | 0.944224i | \(0.606814\pi\) | |||||||
\(978\) | 8.27674 | 0.264661 | ||||||||
\(979\) | 42.8854 | 1.37062 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.5715 | 0.880291 | ||||||||
\(982\) | 12.8241 | 0.409233 | ||||||||
\(983\) | 19.7681 | 0.630506 | 0.315253 | − | 0.949008i | \(-0.397911\pi\) | ||||
0.315253 | + | 0.949008i | \(0.397911\pi\) | |||||||
\(984\) | 0.0129898 | 0.000414098 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.719824 | −0.0229239 | ||||||||
\(987\) | 6.74980 | 0.214849 | ||||||||
\(988\) | 1.05863 | 0.0336796 | ||||||||
\(989\) | −38.4102 | −1.22137 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.5139 | 1.50933 | 0.754665 | − | 0.656110i | \(-0.227799\pi\) | ||||
0.754665 | + | 0.656110i | \(0.227799\pi\) | |||||||
\(992\) | 10.2181 | 0.324425 | ||||||||
\(993\) | −4.09416 | −0.129924 | ||||||||
\(994\) | −19.2051 | −0.609149 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.45608 | −0.0778237 | ||||||||
\(997\) | 31.7276 | 1.00482 | 0.502411 | − | 0.864629i | \(-0.332446\pi\) | ||||
0.502411 | + | 0.864629i | \(0.332446\pi\) | |||||||
\(998\) | −0.349979 | −0.0110784 | ||||||||
\(999\) | −2.79488 | −0.0884262 |
(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 | 1450.2.a.s.1.2 | yes | 3 | |
5.2 | odd | 4 | 1450.2.b.k.349.5 | 6 | |||
5.3 | odd | 4 | 1450.2.b.k.349.2 | 6 | |||
5.4 | even | 2 | 1450.2.a.q.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1450.2.a.q.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
1450.2.a.s.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
1450.2.b.k.349.2 | 6 | 5.3 | odd | 4 | |||
1450.2.b.k.349.5 | 6 | 5.2 | odd | 4 |