Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 13 x^{10} + 60 x^{9} + 48 x^{8} - 289 x^{7} - 89 x^{6} + 602 x^{5} + 161 x^{4} + \cdots + 82 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.18762\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.18762 | −0.685671 | −0.342835 | − | 0.939396i | \(-0.611387\pi\) | ||||
−0.342835 | + | 0.939396i | \(0.611387\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.03337 | 0.462138 | 0.231069 | − | 0.972937i | \(-0.425778\pi\) | ||||
0.231069 | + | 0.972937i | \(0.425778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.52681 | 0.955044 | 0.477522 | − | 0.878620i | \(-0.341535\pi\) | ||||
0.477522 | + | 0.878620i | \(0.341535\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.58957 | −0.529856 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.63016 | 1.39605 | 0.698023 | − | 0.716076i | \(-0.254063\pi\) | ||||
0.698023 | + | 0.716076i | \(0.254063\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.51519 | −1.52964 | −0.764820 | − | 0.644245i | \(-0.777172\pi\) | ||||
−0.764820 | + | 0.644245i | \(0.777172\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.22725 | −0.316874 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35203 | 0.998424 | 0.499212 | − | 0.866480i | \(-0.333623\pi\) | ||||
0.499212 | + | 0.866480i | \(0.333623\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00088 | −0.654845 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.68684 | −0.977273 | −0.488636 | − | 0.872488i | \(-0.662506\pi\) | ||||
−0.488636 | + | 0.872488i | \(0.662506\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.93214 | −0.786429 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.45065 | 1.04898 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.15402 | −1.51416 | −0.757081 | − | 0.653321i | \(-0.773375\pi\) | ||||
−0.757081 | + | 0.653321i | \(0.773375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.288042 | −0.0517339 | −0.0258670 | − | 0.999665i | \(-0.508235\pi\) | ||||
−0.0258670 | + | 0.999665i | \(0.508235\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.49885 | −0.957227 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.61113 | 0.441362 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.28324 | −1.36176 | −0.680878 | − | 0.732397i | \(-0.738402\pi\) | ||||
−0.680878 | + | 0.732397i | \(0.738402\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.54993 | 1.04883 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.92083 | 0.924679 | 0.462339 | − | 0.886703i | \(-0.347010\pi\) | ||||
0.462339 | + | 0.886703i | \(0.347010\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.48394 | −0.683794 | −0.341897 | − | 0.939737i | \(-0.611069\pi\) | ||||
−0.341897 | + | 0.939737i | \(0.611069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.64261 | −0.244866 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.50830 | −0.803467 | −0.401734 | − | 0.915757i | \(-0.631592\pi\) | ||||
−0.401734 | + | 0.915757i | \(0.631592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.615243 | −0.0878919 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.18762 | 0.166300 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.79017 | 0.520620 | 0.260310 | − | 0.965525i | \(-0.416175\pi\) | ||||
0.260310 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.78467 | 0.645165 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.16854 | −0.684590 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.623587 | 0.0798421 | 0.0399210 | − | 0.999203i | \(-0.487289\pi\) | ||||
0.0399210 | + | 0.999203i | \(0.487289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.01653 | −0.506035 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.69924 | −0.706904 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7757 | −1.31646 | −0.658229 | − | 0.752818i | \(-0.728694\pi\) | ||||
−0.658229 | + | 0.752818i | \(0.728694\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.56616 | 0.670087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.81909 | 0.215886 | 0.107943 | − | 0.994157i | \(-0.465574\pi\) | ||||
0.107943 | + | 0.994157i | \(0.465574\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.894382 | 0.104680 | 0.0523398 | − | 0.998629i | \(-0.483332\pi\) | ||||
0.0523398 | + | 0.998629i | \(0.483332\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.66988 | 0.539231 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.6995 | 1.33328 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.647603 | 0.0728610 | 0.0364305 | − | 0.999336i | \(-0.488401\pi\) | ||||
0.0364305 | + | 0.999336i | \(0.488401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.70457 | −0.189397 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.53842 | 0.607920 | 0.303960 | − | 0.952685i | \(-0.401691\pi\) | ||||
0.303960 | + | 0.952685i | \(0.401691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.03337 | −0.112085 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.68384 | 1.03822 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.18899 | −0.126033 | −0.0630166 | − | 0.998012i | \(-0.520072\pi\) | ||||
−0.0630166 | + | 0.998012i | \(0.520072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.9358 | −1.46087 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.342084 | 0.0354724 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.49726 | 0.461409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.08803 | −0.922749 | −0.461375 | − | 0.887205i | \(-0.652644\pi\) | ||||
−0.461375 | + | 0.887205i | \(0.652644\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.35995 | −0.739703 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.33733 | −0.232573 | −0.116286 | − | 0.993216i | \(-0.537099\pi\) | ||||
−0.116286 | + | 0.993216i | \(0.537099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.01022 | 0.592204 | 0.296102 | − | 0.955156i | \(-0.404313\pi\) | ||||
0.296102 | + | 0.955156i | \(0.404313\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.10102 | −0.302629 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.5086 | −1.88597 | −0.942984 | − | 0.332838i | \(-0.891994\pi\) | ||||
−0.942984 | + | 0.332838i | \(0.891994\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.1263 | 1.83197 | 0.915983 | − | 0.401217i | \(-0.131413\pi\) | ||||
0.915983 | + | 0.401217i | \(0.131413\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.83731 | 0.933716 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.29162 | −0.497794 | −0.248897 | − | 0.968530i | \(-0.580068\pi\) | ||||
−0.248897 | + | 0.968530i | \(0.580068\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.84324 | −0.451634 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.76677 | 0.810488 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.52681 | −0.231632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4384 | 0.948943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.03168 | −0.634025 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.23022 | −0.825576 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5684 | 1.29274 | 0.646370 | − | 0.763024i | \(-0.276286\pi\) | ||||
0.646370 | + | 0.763024i | \(0.276286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.32520 | 0.468858 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.64696 | −0.143896 | −0.0719479 | − | 0.997408i | \(-0.522922\pi\) | ||||
−0.0719479 | + | 0.997408i | \(0.522922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9967 | 0.953538 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.63254 | 0.484772 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.99828 | 0.170725 | 0.0853625 | − | 0.996350i | \(-0.472795\pi\) | ||||
0.0853625 | + | 0.996350i | \(0.472795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6631 | −1.41335 | −0.706673 | − | 0.707540i | \(-0.749805\pi\) | ||||
−0.706673 | + | 0.707540i | \(0.749805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.54174 | 0.550914 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.5362 | −2.13545 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.42613 | −0.699752 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.730673 | 0.0602649 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.2853 | −1.08837 | −0.544187 | − | 0.838964i | \(-0.683162\pi\) | ||||
−0.544187 | + | 0.838964i | \(0.683162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.45570 | −0.769494 | −0.384747 | − | 0.923022i | \(-0.625711\pi\) | ||||
−0.384747 | + | 0.923022i | \(0.625711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.58957 | 0.128509 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.297655 | −0.0239082 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1686 | 0.971160 | 0.485580 | − | 0.874192i | \(-0.338608\pi\) | ||||
0.485580 | + | 0.874192i | \(0.338608\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.50127 | −0.356974 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.8427 | −0.933338 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.6966 | −1.85606 | −0.928030 | − | 0.372506i | \(-0.878499\pi\) | ||||
−0.928030 | + | 0.372506i | \(0.878499\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.68236 | −0.442371 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1640 | 1.17343 | 0.586713 | − | 0.809795i | \(-0.300422\pi\) | ||||
0.586713 | + | 0.809795i | \(0.300422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.4173 | 1.33980 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.91784 | −0.529021 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1395 | 0.998978 | 0.499489 | − | 0.866320i | \(-0.333521\pi\) | ||||
0.499489 | + | 0.866320i | \(0.333521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.93577 | −0.751074 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.18762 | −0.0892667 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.9694 | 1.04412 | 0.522059 | − | 0.852909i | \(-0.325164\pi\) | ||||
0.522059 | + | 0.852909i | \(0.325164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.23709 | 0.463599 | 0.231799 | − | 0.972764i | \(-0.425539\pi\) | ||||
0.231799 | + | 0.972764i | \(0.425539\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.740581 | −0.0547454 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.55966 | −0.629319 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.63016 | −0.338591 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.7727 | 1.00182 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.28159 | 0.454520 | 0.227260 | − | 0.973834i | \(-0.427023\pi\) | ||||
0.227260 | + | 0.973834i | \(0.427023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.1330 | −1.30524 | −0.652621 | − | 0.757684i | \(-0.726331\pi\) | ||||
−0.652621 | + | 0.757684i | \(0.726331\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.76851 | 0.484703 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.3431 | −0.879411 | −0.439706 | − | 0.898142i | \(-0.644917\pi\) | ||||
−0.439706 | + | 0.898142i | \(0.644917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.76295 | −0.550301 | −0.275151 | − | 0.961401i | \(-0.588728\pi\) | ||||
−0.275151 | + | 0.961401i | \(0.588728\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.7974 | 0.902657 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.6036 | −1.44609 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.11842 | 0.427329 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.45004 | 0.517814 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.1506 | 1.39385 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9000 | 0.888074 | 0.444037 | − | 0.896009i | \(-0.353546\pi\) | ||||
0.444037 | + | 0.896009i | \(0.353546\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.16038 | −0.148027 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.63357 | −0.316007 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.727828 | −0.0494082 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.06218 | −0.0717757 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.51519 | 0.370992 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.9830 | −1.00333 | −0.501667 | − | 0.865061i | \(-0.667280\pi\) | ||||
−0.501667 | + | 0.865061i | \(0.667280\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.25041 | 0.416694 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.65735 | −0.242747 | −0.121374 | − | 0.992607i | \(-0.538730\pi\) | ||||
−0.121374 | + | 0.992607i | \(0.538730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3092 | 0.681249 | 0.340624 | − | 0.940199i | \(-0.389362\pi\) | ||||
0.340624 | + | 0.940199i | \(0.389362\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.8945 | −0.914194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.6674 | −1.61602 | −0.808009 | − | 0.589171i | \(-0.799455\pi\) | ||||
−0.808009 | + | 0.589171i | \(0.799455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.69211 | −0.371313 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.769103 | −0.0499586 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.11018 | −0.330550 | −0.165275 | − | 0.986248i | \(-0.552851\pi\) | ||||
−0.165275 | + | 0.986248i | \(0.552851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.4630 | −1.18930 | −0.594652 | − | 0.803983i | \(-0.702710\pi\) | ||||
−0.594652 | + | 0.803983i | \(0.702710\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.3276 | −0.919113 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.635774 | −0.0406181 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0023 | −1.52723 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.57751 | −0.416833 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.44336 | 0.469821 | 0.234910 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234910 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.7008 | −1.36432 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.22725 | 0.0768533 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.58926 | −0.348649 | −0.174324 | − | 0.984688i | \(-0.555774\pi\) | ||||
−0.174324 | + | 0.984688i | \(0.555774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.9302 | −1.30054 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.9614 | 0.802288 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.41046 | −0.518611 | −0.259305 | − | 0.965795i | \(-0.583494\pi\) | ||||
−0.259305 | + | 0.965795i | \(0.583494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.91666 | 0.240598 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.41207 | 0.0864172 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.36903 | −0.388327 | −0.194163 | − | 0.980969i | \(-0.562199\pi\) | ||||
−0.194163 | + | 0.980969i | \(0.562199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.6443 | 1.31480 | 0.657398 | − | 0.753544i | \(-0.271657\pi\) | ||||
0.657398 | + | 0.753544i | \(0.271657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.5504 | 1.00168 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.2065 | −1.09789 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4894 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.457863 | 0.0274115 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.662298 | −0.0395094 | −0.0197547 | − | 0.999805i | \(-0.506289\pi\) | ||||
−0.0197547 | + | 0.999805i | \(0.506289\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.52952 | 0.0909208 | 0.0454604 | − | 0.998966i | \(-0.485525\pi\) | ||||
0.0454604 | + | 0.998966i | \(0.485525\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.34102 | −0.316375 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.9608 | 0.883108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.7931 | 0.632702 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.2926 | −0.776564 | −0.388282 | − | 0.921541i | \(-0.626931\pi\) | ||||
−0.388282 | + | 0.921541i | \(0.626931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.03337 | 0.0601652 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.2374 | 1.46442 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.8488 | 1.49487 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3301 | −0.653053 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.77585 | 0.159468 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.644396 | 0.0368980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3656 | −0.819887 | −0.409944 | − | 0.912111i | \(-0.634452\pi\) | ||||
−0.409944 | + | 0.912111i | \(0.634452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.13783 | −0.406057 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.6746 | −1.00223 | −0.501117 | − | 0.865380i | \(-0.667077\pi\) | ||||
−0.501117 | + | 0.865380i | \(0.667077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.2229 | −1.31264 | −0.656318 | − | 0.754484i | \(-0.727887\pi\) | ||||
−0.656318 | + | 0.754484i | \(0.727887\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.15057 | −0.233858 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.36278 | 0.469700 | 0.234850 | − | 0.972032i | \(-0.424540\pi\) | ||||
0.234850 | + | 0.972032i | \(0.424540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.7544 | −2.11384 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.1687 | 1.29315 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.35203 | −0.242153 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.6865 | 1.20295 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.7147 | −1.25612 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.9184 | −0.767346 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2097 | −1.22076 | −0.610379 | − | 0.792110i | \(-0.708983\pi\) | ||||
−0.610379 | + | 0.792110i | \(0.708983\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.1668 | 0.721535 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.1353 | −0.608385 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.1815 | 1.31725 | 0.658625 | − | 0.752471i | \(-0.271138\pi\) | ||||
0.658625 | + | 0.752471i | \(0.271138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.28442 | 0.341323 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.33368 | −0.0722229 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.2423 | −1.03898 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.75191 | 0.309672 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.7712 | 1.16874 | 0.584370 | − | 0.811487i | \(-0.301342\pi\) | ||||
0.584370 | + | 0.811487i | \(0.301342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.197978 | −0.0105975 | −0.00529877 | − | 0.999986i | \(-0.501687\pi\) | ||||
−0.00529877 | + | 0.999986i | \(0.501687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.0614 | −1.60456 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.6504 | −1.47168 | −0.735841 | − | 0.677154i | \(-0.763213\pi\) | ||||
−0.735841 | + | 0.677154i | \(0.763213\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.87980 | 0.0997692 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.00088 | 0.158823 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.5218 | −0.766429 | −0.383214 | − | 0.923659i | \(-0.625183\pi\) | ||||
−0.383214 | + | 0.923659i | \(0.625183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0598483 | −0.00314991 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3968 | −0.650662 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.924229 | 0.0483763 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.0002 | 1.25280 | 0.626401 | − | 0.779501i | \(-0.284527\pi\) | ||||
0.626401 | + | 0.779501i | \(0.284527\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.41157 | −0.489947 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.57704 | 0.497215 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6393 | −0.550881 | −0.275441 | − | 0.961318i | \(-0.588824\pi\) | ||||
−0.275441 | + | 0.961318i | \(0.588824\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.9620 | 0.566073 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.9710 | 2.31612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.06460 | 0.157418 | 0.0787089 | − | 0.996898i | \(-0.474920\pi\) | ||||
0.0787089 | + | 0.996898i | \(0.474920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3017 | −0.886394 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.1353 | −1.48874 | −0.744372 | − | 0.667765i | \(-0.767251\pi\) | ||||
−0.744372 | + | 0.667765i | \(0.767251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0899 | 0.616161 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.12753 | 0.362313 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.8129 | 0.903150 | 0.451575 | − | 0.892233i | \(-0.350862\pi\) | ||||
0.451575 | + | 0.892233i | \(0.350862\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.68684 | 0.237023 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.95596 | 0.0986651 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.669214 | 0.0336718 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.9205 | 1.80280 | 0.901400 | − | 0.432988i | \(-0.142541\pi\) | ||||
0.901400 | + | 0.432988i | \(0.142541\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.0599 | −0.653813 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.0902 | −1.60251 | −0.801255 | − | 0.598323i | \(-0.795834\pi\) | ||||
−0.801255 | + | 0.598323i | \(0.795834\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.58861 | 0.0791342 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.76145 | −0.0875274 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −38.3527 | −1.90107 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.6614 | −1.61500 | −0.807500 | − | 0.589867i | \(-0.799180\pi\) | ||||
−0.807500 | + | 0.589867i | \(0.799180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.37320 | −0.117061 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.52681 | 0.124336 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.72324 | 0.280943 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.7894 | 0.969090 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.6891 | −0.815314 | −0.407657 | − | 0.913135i | \(-0.633654\pi\) | ||||
−0.407657 | + | 0.913135i | \(0.633654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.8125 | 0.624441 | 0.312221 | − | 0.950010i | \(-0.398927\pi\) | ||||
0.312221 | + | 0.950010i | \(0.398927\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.75581 | 0.425722 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.93214 | 0.190737 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.57568 | 0.0762527 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.3272 | 1.46421 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5966 | 0.654927 | 0.327463 | − | 0.944864i | \(-0.393806\pi\) | ||||
0.327463 | + | 0.944864i | \(0.393806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.9831 | 1.39284 | 0.696420 | − | 0.717634i | \(-0.254775\pi\) | ||||
0.696420 | + | 0.717634i | \(0.254775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.0070 | 0.479799 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.3972 | −0.975732 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8551 | −0.708997 | −0.354498 | − | 0.935057i | \(-0.615348\pi\) | ||||
−0.354498 | + | 0.935057i | \(0.615348\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.977970 | 0.0465700 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.99505 | −0.237322 | −0.118661 | − | 0.992935i | \(-0.537860\pi\) | ||||
−0.118661 | + | 0.992935i | \(0.537860\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.22867 | −0.0582447 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.7778 | 0.746266 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.6933 | 1.54289 | 0.771445 | − | 0.636296i | \(-0.219534\pi\) | ||||
0.771445 | + | 0.636296i | \(0.219534\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.4144 | 1.29089 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.2297 | 0.527619 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.4009 | −0.675124 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.8505 | 1.39635 | 0.698174 | − | 0.715928i | \(-0.253996\pi\) | ||||
0.698174 | + | 0.715928i | \(0.253996\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.45065 | −0.254414 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.9016 | −1.11321 | −0.556604 | − | 0.830778i | \(-0.687896\pi\) | ||||
−0.556604 | + | 0.830778i | \(0.687896\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.1565 | 1.54091 | 0.770457 | − | 0.637492i | \(-0.220028\pi\) | ||||
0.770457 | + | 0.637492i | \(0.220028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.353499 | 0.0163931 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.0742 | 1.16030 | 0.580149 | − | 0.814511i | \(-0.302994\pi\) | ||||
0.580149 | + | 0.814511i | \(0.302994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.2281 | −1.25728 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.4516 | −0.665896 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.7614 | −0.954608 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.1128 | −0.785189 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.02474 | −0.275854 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.64989 | 0.303841 | 0.151921 | − | 0.988393i | \(-0.451454\pi\) | ||||
0.151921 | + | 0.988393i | \(0.451454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.6837 | 2.08300 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.0646 | 0.639962 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.39131 | −0.426437 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.5561 | 0.931487 | 0.465744 | − | 0.884920i | \(-0.345787\pi\) | ||||
0.465744 | + | 0.884920i | \(0.345787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.1424 | 1.27265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.1923 | −0.956393 | −0.478197 | − | 0.878253i | \(-0.658709\pi\) | ||||
−0.478197 | + | 0.878253i | \(0.658709\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.15402 | 0.367238 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.60556 | −0.341845 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.59649 | 0.206181 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.2403 | −0.861313 | −0.430656 | − | 0.902516i | \(-0.641718\pi\) | ||||
−0.430656 | + | 0.902516i | \(0.641718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0090 | −0.804583 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.3508 | −0.595285 | −0.297642 | − | 0.954677i | \(-0.596200\pi\) | ||||
−0.297642 | + | 0.954677i | \(0.596200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.41533 | −0.107481 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.6851 | −0.918659 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.7144 | 1.67166 | 0.835832 | − | 0.548986i | \(-0.184986\pi\) | ||||
0.835832 | + | 0.548986i | \(0.184986\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.25993 | 0.0999735 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.7214 | 1.04732 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.21078 | 0.273680 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.5043 | −1.12168 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.6047 | −0.684970 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.26252 | 0.230555 | 0.115277 | − | 0.993333i | \(-0.463224\pi\) | ||||
0.115277 | + | 0.993333i | \(0.463224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.41943 | −0.368156 | −0.184078 | − | 0.982912i | \(-0.558930\pi\) | ||||
−0.184078 | + | 0.982912i | \(0.558930\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.7999 | 0.514989 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.288042 | 0.0125473 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.03358 | −0.0449381 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.58957 | −0.0689814 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.6545 | −1.41442 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.1596 | −0.871577 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.5902 | −0.715921 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.84867 | −0.122701 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0821 | 0.863398 | 0.431699 | − | 0.902018i | \(-0.357914\pi\) | ||||
0.431699 | + | 0.902018i | \(0.357914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.40726 | −0.317876 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.7646 | 0.846620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.01168 | 0.0860131 | 0.0430066 | − | 0.999075i | \(-0.486306\pi\) | ||||
0.0430066 | + | 0.999075i | \(0.486306\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.991233 | −0.0423048 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.4865 | −1.51178 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.63637 | 0.0695854 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.1656 | 0.431505 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.1857 | 0.897668 | 0.448834 | − | 0.893615i | \(-0.351840\pi\) | ||||
0.448834 | + | 0.893615i | \(0.351840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.7298 | 1.04596 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.49885 | 0.232162 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.3745 | −0.563667 | −0.281834 | − | 0.959463i | \(-0.590943\pi\) | ||||
−0.281834 | + | 0.959463i | \(0.590943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.46821 | −0.230049 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.30712 | −0.180882 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.8533 | 0.958060 | 0.479030 | − | 0.877799i | \(-0.340988\pi\) | ||||
0.479030 | + | 0.877799i | \(0.340988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3829 | 0.476359 | 0.238179 | − | 0.971221i | \(-0.423449\pi\) | ||||
0.238179 | + | 0.971221i | \(0.423449\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.46011 | −0.311651 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.4293 | 0.768555 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.1452 | −0.838655 | −0.419328 | − | 0.907835i | \(-0.637734\pi\) | ||||
−0.419328 | + | 0.907835i | \(0.637734\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.5351 | 0.894967 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.9945 | 0.580590 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.5491 | 0.726810 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.05933 | 0.374557 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.3827 | 0.469816 | 0.234908 | − | 0.972018i | \(-0.424521\pi\) | ||||
0.234908 | + | 0.972018i | \(0.424521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.25357 | −0.0516524 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.6589 | 0.602986 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.7338 | −1.75487 | −0.877433 | − | 0.479699i | \(-0.840746\pi\) | ||||
−0.877433 | + | 0.479699i | \(0.840746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.61113 | −0.107046 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.21941 | 0.377325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.7320 | 1.25568 | 0.627839 | − | 0.778344i | \(-0.283940\pi\) | ||||
0.627839 | + | 0.778344i | \(0.283940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.1861 | −1.23132 | −0.615658 | − | 0.788014i | \(-0.711110\pi\) | ||||
−0.615658 | + | 0.788014i | \(0.711110\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.1287 | 0.697533 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.7867 | 0.438542 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.0474 | 0.854288 | 0.427144 | − | 0.904184i | \(-0.359520\pi\) | ||||
0.427144 | + | 0.904184i | \(0.359520\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.4692 | 0.991542 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.3793 | 1.22902 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4809 | 0.907995 | 0.453998 | − | 0.891003i | \(-0.349997\pi\) | ||||
0.453998 | + | 0.891003i | \(0.349997\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.26633 | −0.293007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.7816 | −1.92361 | −0.961806 | − | 0.273730i | \(-0.911742\pi\) | ||||
−0.961806 | + | 0.273730i | \(0.911742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.12745 | −0.0453161 | −0.0226580 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226580 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.5463 | −1.02514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00436 | −0.120367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.1225 | 0.404899 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −23.9312 | −0.955719 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.28324 | 0.330274 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.8411 | −0.431576 | −0.215788 | − | 0.976440i | \(-0.569232\pi\) | ||||
−0.215788 | + | 0.976440i | \(0.569232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.3203 | −0.608926 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.0546 | 0.597424 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.39318 | 0.134443 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.89157 | −0.114389 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.4969 | 0.691086 | 0.345543 | − | 0.938403i | \(-0.387695\pi\) | ||||
0.345543 | + | 0.938403i | \(0.387695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.7035 | 1.56575 | 0.782877 | − | 0.622176i | \(-0.213751\pi\) | ||||
0.782877 | + | 0.622176i | \(0.213751\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.50291 | 0.216677 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.0242 | −0.669290 | −0.334645 | − | 0.942344i | \(-0.608616\pi\) | ||||
−0.334645 | + | 0.942344i | \(0.608616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.63016 | 0.181750 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.864380 | 0.0338777 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.7887 | 1.59618 | 0.798092 | − | 0.602536i | \(-0.205843\pi\) | ||||
0.798092 | + | 0.602536i | \(0.205843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.70192 | −0.0664996 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.42168 | −0.0554651 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.20821 | −0.280792 | −0.140396 | − | 0.990095i | \(-0.544838\pi\) | ||||
−0.140396 | + | 0.990095i | \(0.544838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.9067 | 1.35771 | 0.678857 | − | 0.734270i | \(-0.262475\pi\) | ||||
0.678857 | + | 0.734270i | \(0.262475\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.54993 | −0.254378 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3637 | 0.440666 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.2165 | 1.47975 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.7940 | 0.687957 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.88730 | 0.111463 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.96846 | −0.268614 | −0.134307 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134307 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.4327 | −0.824946 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8553 | 1.10900 | 0.554500 | − | 0.832184i | \(-0.312910\pi\) | ||||
0.554500 | + | 0.832184i | \(0.312910\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.9637 | −0.881266 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.34353 | 0.166445 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.0525 | 1.53257 | 0.766283 | − | 0.642503i | \(-0.222104\pi\) | ||||
0.766283 | + | 0.642503i | \(0.222104\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.06497 | 0.0788984 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.2433 | −0.467112 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.9035 | −0.796361 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.5665 | −0.401969 | −0.200985 | − | 0.979594i | \(-0.564414\pi\) | ||||
−0.200985 | + | 0.979594i | \(0.564414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.5972 | −0.706449 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.2192 | −0.653161 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.92083 | −0.224268 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.2954 | 1.10806 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.6541 | −1.34664 | −0.673319 | − | 0.739352i | \(-0.735132\pi\) | ||||
−0.673319 | + | 0.739352i | \(0.735132\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.0489 | −1.35961 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.76005 | 0.254598 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.90598 | −0.222117 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.2597 | −0.497979 | −0.248990 | − | 0.968506i | \(-0.580098\pi\) | ||||
−0.248990 | + | 0.968506i | \(0.580098\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.02941 | −0.0386058 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.35001 | 0.0505582 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.3884 | −0.986870 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.06893 | 0.226648 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.7261 | −1.33236 | −0.666180 | − | 0.745791i | \(-0.732072\pi\) | ||||
−0.666180 | + | 0.745791i | \(0.732072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.1867 | 0.565581 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.9269 | 0.815471 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.0628 | 1.19078 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.6976 | 1.69483 | 0.847415 | − | 0.530932i | \(-0.178158\pi\) | ||||
0.847415 | + | 0.530932i | \(0.178158\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.1294 | 0.819606 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.48394 | 0.165845 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.7661 | −0.951691 | −0.475846 | − | 0.879529i | \(-0.657858\pi\) | ||||
−0.475846 | + | 0.879529i | \(0.657858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.755056 | 0.0278507 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −49.8931 | −1.83784 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.5492 | 0.939843 | 0.469922 | − | 0.882708i | \(-0.344282\pi\) | ||||
0.469922 | + | 0.882708i | \(0.344282\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.5055 | 1.04718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.7258 | 1.64083 | 0.820415 | − | 0.571769i | \(-0.193743\pi\) | ||||
0.820415 | + | 0.571769i | \(0.193743\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.7286 | −0.502978 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.80369 | −0.322110 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.2945 | −1.80118 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4166 | 1.00045 | 0.500224 | − | 0.865896i | \(-0.333251\pi\) | ||||
0.500224 | + | 0.865896i | \(0.333251\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.83985 | −0.322142 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.77124 | −0.355612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.8335 | 0.975280 | 0.487640 | − | 0.873045i | \(-0.337858\pi\) | ||||
0.487640 | + | 0.873045i | \(0.337858\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.7722 | 0.935472 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.6103 | −1.36337 | −0.681686 | − | 0.731645i | \(-0.738753\pi\) | ||||
−0.681686 | + | 0.731645i | \(0.738753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.3284 | 1.74961 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.64261 | 0.0593888 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.51519 | −0.199142 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.0477 | 1.19173 | 0.595866 | − | 0.803084i | \(-0.296809\pi\) | ||||
0.595866 | + | 0.803084i | \(0.296809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.63790 | 0.239058 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.1772 | −1.01347 | −0.506733 | − | 0.862103i | \(-0.669147\pi\) | ||||
−0.506733 | + | 0.862103i | \(0.669147\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.13262 | 0.0406851 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.8570 | 0.891740 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.7676 | 0.923221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.42268 | 0.301387 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −44.4446 | −1.58832 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.5747 | 0.448810 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5459 | 0.518507 | 0.259253 | − | 0.965809i | \(-0.416524\pi\) | ||||
0.259253 | + | 0.965809i | \(0.416524\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.98839 | 0.355596 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.3709 | −0.475415 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.43920 | −0.122130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.65148 | −0.164971 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.5698 | 0.799462 | 0.399731 | − | 0.916633i | \(-0.369104\pi\) | ||||
0.399731 | + | 0.916633i | \(0.369104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.50830 | 0.194869 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.88999 | 0.0667794 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.14113 | 0.146137 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.2379 | −0.431331 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.56396 | 0.266264 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.61148 | 0.126973 | 0.0634865 | − | 0.997983i | \(-0.479778\pi\) | ||||
0.0634865 | + | 0.997983i | \(0.479778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.7605 | 1.18549 | 0.592746 | − | 0.805390i | \(-0.298044\pi\) | ||||
0.592746 | + | 0.805390i | \(0.298044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.7051 | −0.901517 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.4874 | −0.857755 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.5142 | −0.682717 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.1519 | 0.774052 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.93314 | −0.276869 | −0.138434 | − | 0.990372i | \(-0.544207\pi\) | ||||
−0.138434 | + | 0.990372i | \(0.544207\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.6073 | −0.439463 | −0.219731 | − | 0.975560i | \(-0.570518\pi\) | ||||
−0.219731 | + | 0.975560i | \(0.570518\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.6223 | 0.752791 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.0830 | 1.53292 | 0.766458 | − | 0.642294i | \(-0.222017\pi\) | ||||
0.766458 | + | 0.642294i | \(0.222017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.4568 | −0.606300 | −0.303150 | − | 0.952943i | \(-0.598038\pi\) | ||||
−0.303150 | + | 0.952943i | \(0.598038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.0840 | 1.00891 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.615243 | 0.0213169 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.6700 | 0.542284 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.57002 | −0.0542677 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.3730 | −1.80812 | −0.904058 | − | 0.427410i | \(-0.859426\pi\) | ||||
−0.904058 | + | 0.427410i | \(0.859426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.4880 | 1.29269 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.786555 | 0.0270904 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.9986 | 0.619170 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.3758 | 0.906282 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.81649 | −0.0623417 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.8222 | 1.33081 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.1584 | 1.61467 | 0.807336 | − | 0.590092i | \(-0.200909\pi\) | ||||
0.807336 | + | 0.590092i | \(0.200909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.14870 | −0.244480 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.84517 | −0.336305 | −0.168152 | − | 0.985761i | \(-0.553780\pi\) | ||||
−0.168152 | + | 0.985761i | \(0.553780\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2690 | 0.555091 | 0.277546 | − | 0.960712i | \(-0.410479\pi\) | ||||
0.277546 | + | 0.960712i | \(0.410479\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.7677 | −0.605521 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.7237 | 0.637362 | 0.318681 | − | 0.947862i | \(-0.396760\pi\) | ||||
0.318681 | + | 0.947862i | \(0.396760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5780 | 0.461665 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.18762 | −0.0403336 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.99850 | 0.101717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59.4299 | 2.01371 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.4460 | 0.488924 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.3230 | −0.788461 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.9591 | 1.61946 | 0.809732 | − | 0.586799i | \(-0.199612\pi\) | ||||
0.809732 | + | 0.586799i | \(0.199612\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.7865 | 0.532467 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.3116 | −1.22337 | −0.611685 | − | 0.791102i | \(-0.709508\pi\) | ||||
−0.611685 | + | 0.791102i | \(0.709508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.7832 | 0.497493 | 0.248746 | − | 0.968569i | \(-0.419981\pi\) | ||||
0.248746 | + | 0.968569i | \(0.419981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.22725 | −0.0412535 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.5647 | −0.589765 | −0.294882 | − | 0.955534i | \(-0.595281\pi\) | ||||
−0.294882 | + | 0.955534i | \(0.595281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.8117 | 1.23462 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.89244 | −0.264407 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.9723 | −0.802201 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.4355 | 0.482526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.6985 | −1.02499 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.34870 | 0.0783336 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.79017 | −0.126269 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.4558 | 0.447779 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.44522 | 0.214247 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.9853 | −0.896034 | −0.448017 | − | 0.894025i | \(-0.647870\pi\) | ||||
−0.448017 | + | 0.894025i | \(0.647870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.71534 | 0.123230 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0678 | 0.499217 | 0.249609 | − | 0.968347i | \(-0.419698\pi\) | ||||
0.249609 | + | 0.968347i | \(0.419698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.6437 | 0.848684 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.765296 | −0.0252999 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.16156 | −0.137427 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0500 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.0608 | 0.562172 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.0326 | −0.330228 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.5709 | 1.07092 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.55365 | −0.313783 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.6977 | −0.613451 | −0.306725 | − | 0.951798i | \(-0.599233\pi\) | ||||
−0.306725 | + | 0.951798i | \(0.599233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.67755 | −0.0877533 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.9906 | 0.687202 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.78467 | −0.156476 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.18701 | −0.104115 | −0.0520576 | − | 0.998644i | \(-0.516578\pi\) | ||||
−0.0520576 | + | 0.998644i | \(0.516578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.5799 | 0.900036 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.3743 | 0.435989 | 0.217994 | − | 0.975950i | \(-0.430049\pi\) | ||||
0.217994 | + | 0.975950i | \(0.430049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.7500 | −0.903663 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.2323 | 0.462978 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.1771 | 0.850641 | 0.425321 | − | 0.905043i | \(-0.360161\pi\) | ||||
0.425321 | + | 0.905043i | \(0.360161\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.93269 | −0.160122 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.93177 | −0.322060 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.8044 | −1.45136 | −0.725679 | − | 0.688034i | \(-0.758474\pi\) | ||||
−0.725679 | + | 0.688034i | \(0.758474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.49121 | 0.210051 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 44.8377 | 1.44940 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.04928 | 0.163050 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9170 | −0.997324 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.0103 | 0.999291 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.7381 | −0.603202 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.2867 | 0.459430 | 0.229715 | − | 0.973258i | \(-0.426221\pi\) | ||||
0.229715 | + | 0.973258i | \(0.426221\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.16854 | 0.166037 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.2314 | 1.06645 | 0.533224 | − | 0.845974i | \(-0.320980\pi\) | ||||
0.533224 | + | 0.845974i | \(0.320980\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.1045 | −1.34981 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.7553 | −0.824829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.86530 | −0.251633 | −0.125817 | − | 0.992054i | \(-0.540155\pi\) | ||||
−0.125817 | + | 0.992054i | \(0.540155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.50523 | −0.175948 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.4025 | −0.970678 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −60.8191 | −1.93983 | −0.969914 | − | 0.243447i | \(-0.921722\pi\) | ||||
−0.969914 | + | 0.243447i | \(0.921722\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.7550 | −0.406409 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.5297 | 0.526147 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.0155 | 0.668254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1698 | −0.386588 | −0.193294 | − | 0.981141i | \(-0.561917\pi\) | ||||
−0.193294 | + | 0.981141i | \(0.561917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.3766 | 0.837037 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.02201 | −0.254315 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.0742 | −1.58587 | −0.792933 | − | 0.609308i | \(-0.791447\pi\) | ||||
−0.792933 | + | 0.609308i | \(0.791447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −45.1490 | −1.42845 |
(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 | 4012.2.a.g.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.g.1.5 | ✓ | 12 | 1.1 | even | 1 | trivial |