Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7120,2,Mod(1,7120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7120.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7120 = 2^{4} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7120.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: | \(56.8534862392\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 8x^{5} + 6x^{4} + 19x^{3} - 10x^{2} - 12x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 445) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.96388\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7120.1 |
$q$-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 | ||||||||
\(3\) | 0.931146 | 0.537597 | 0.268799 | − | 0.963196i | \(-0.413373\pi\) | ||||
0.268799 | + | 0.963196i | \(0.413373\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.580377 | 0.219362 | 0.109681 | − | 0.993967i | \(-0.465017\pi\) | ||||
0.109681 | + | 0.993967i | \(0.465017\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.13297 | −0.710989 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.74359 | 1.43025 | 0.715123 | − | 0.698998i | \(-0.246371\pi\) | ||||
0.715123 | + | 0.698998i | \(0.246371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.25246 | 1.73412 | 0.867060 | − | 0.498204i | \(-0.166007\pi\) | ||||
0.867060 | + | 0.498204i | \(0.166007\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.931146 | 0.240421 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.87935 | −1.42595 | −0.712976 | − | 0.701189i | \(-0.752653\pi\) | ||||
−0.712976 | + | 0.701189i | \(0.752653\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.41445 | 1.24216 | 0.621080 | − | 0.783747i | \(-0.286694\pi\) | ||||
0.621080 | + | 0.783747i | \(0.286694\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.540416 | 0.117928 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.56239 | 1.78538 | 0.892691 | − | 0.450669i | \(-0.148815\pi\) | ||||
0.892691 | + | 0.450669i | \(0.148815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.77954 | −0.919823 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.96542 | −0.736361 | −0.368180 | − | 0.929754i | \(-0.620019\pi\) | ||||
−0.368180 | + | 0.929754i | \(0.620019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.68893 | −1.02176 | −0.510881 | − | 0.859652i | \(-0.670681\pi\) | ||||
−0.510881 | + | 0.859652i | \(0.670681\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.41697 | 0.768897 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.580377 | 0.0981017 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.495300 | 0.0814269 | 0.0407134 | − | 0.999171i | \(-0.487037\pi\) | ||||
0.0407134 | + | 0.999171i | \(0.487037\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.82195 | 0.932258 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8503 | 1.85071 | 0.925356 | − | 0.379098i | \(-0.123766\pi\) | ||||
0.925356 | + | 0.379098i | \(0.123766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.78767 | 0.730113 | 0.365056 | − | 0.930985i | \(-0.381050\pi\) | ||||
0.365056 | + | 0.930985i | \(0.381050\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.13297 | −0.317964 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.78707 | 0.552401 | 0.276201 | − | 0.961100i | \(-0.410925\pi\) | ||||
0.276201 | + | 0.961100i | \(0.410925\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66316 | −0.951880 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.47453 | −0.766588 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.91925 | −1.08779 | −0.543897 | − | 0.839152i | \(-0.683052\pi\) | ||||
−0.543897 | + | 0.839152i | \(0.683052\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.74359 | 0.639626 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.04164 | 0.667782 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.6416 | −1.38542 | −0.692711 | − | 0.721216i | \(-0.743584\pi\) | ||||
−0.692711 | + | 0.721216i | \(0.743584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.77193 | 1.25117 | 0.625584 | − | 0.780157i | \(-0.284861\pi\) | ||||
0.625584 | + | 0.780157i | \(0.284861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.23793 | −0.155964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.25246 | 0.775522 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.35061 | −0.165004 | −0.0825019 | − | 0.996591i | \(-0.526291\pi\) | ||||
−0.0825019 | + | 0.996591i | \(0.526291\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.97283 | 0.959816 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7514 | 1.27595 | 0.637976 | − | 0.770056i | \(-0.279772\pi\) | ||||
0.637976 | + | 0.770056i | \(0.279772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.31208 | 0.153567 | 0.0767834 | − | 0.997048i | \(-0.475535\pi\) | ||||
0.0767834 | + | 0.997048i | \(0.475535\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.931146 | 0.107519 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.75307 | 0.313742 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.492431 | −0.0554028 | −0.0277014 | − | 0.999616i | \(-0.508819\pi\) | ||||
−0.0277014 | + | 0.999616i | \(0.508819\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.94845 | 0.216495 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.62413 | −0.178272 | −0.0891359 | − | 0.996019i | \(-0.528411\pi\) | ||||
−0.0891359 | + | 0.996019i | \(0.528411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.87935 | −0.637705 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.69239 | −0.395866 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | 0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.62878 | 0.380400 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.29722 | −0.549296 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.41445 | 0.555511 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.61533 | −0.976289 | −0.488144 | − | 0.872763i | \(-0.662326\pi\) | ||||
−0.488144 | + | 0.872763i | \(0.662326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.1179 | −1.01689 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.72415 | 0.470070 | 0.235035 | − | 0.971987i | \(-0.424479\pi\) | ||||
0.235035 | + | 0.971987i | \(0.424479\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.17345 | −0.509755 | −0.254877 | − | 0.966973i | \(-0.582035\pi\) | ||||
−0.254877 | + | 0.966973i | \(0.582035\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.540416 | 0.0527392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.68158 | −0.549259 | −0.274630 | − | 0.961550i | \(-0.588555\pi\) | ||||
−0.274630 | + | 0.961550i | \(0.588555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.48821 | −0.621458 | −0.310729 | − | 0.950499i | \(-0.600573\pi\) | ||||
−0.310729 | + | 0.950499i | \(0.600573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.461197 | 0.0437749 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.49005 | 0.892749 | 0.446375 | − | 0.894846i | \(-0.352715\pi\) | ||||
0.446375 | + | 0.894846i | \(0.352715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.56239 | 0.798447 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.3363 | −1.23294 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.41224 | −0.312800 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5017 | 1.04561 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.0344 | 0.994938 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.22863 | 0.730173 | 0.365087 | − | 0.930974i | \(-0.381039\pi\) | ||||
0.365087 | + | 0.930974i | \(0.381039\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.45802 | 0.392507 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.92961 | 0.430702 | 0.215351 | − | 0.976537i | \(-0.430910\pi\) | ||||
0.215351 | + | 0.976537i | \(0.430910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.14242 | 0.272483 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.77954 | −0.411357 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.9905 | −1.02442 | −0.512211 | − | 0.858860i | \(-0.671173\pi\) | ||||
−0.512211 | + | 0.858860i | \(0.671173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0960 | −1.53488 | −0.767440 | − | 0.641120i | \(-0.778470\pi\) | ||||
−0.767440 | + | 0.641120i | \(0.778470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.52632 | 0.296969 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.6591 | 2.48022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.96542 | −0.329311 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.20438 | −0.511728 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.9604 | −1.63522 | −0.817609 | − | 0.575773i | \(-0.804701\pi\) | ||||
−0.817609 | + | 0.575773i | \(0.804701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.01450 | 0.733589 | 0.366795 | − | 0.930302i | \(-0.380455\pi\) | ||||
0.366795 | + | 0.930302i | \(0.380455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.5405 | 1.01384 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.68893 | −0.456946 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.23610 | −0.737121 | −0.368561 | − | 0.929604i | \(-0.620149\pi\) | ||||
−0.368561 | + | 0.929604i | \(0.620149\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.37398 | −0.584795 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.96942 | 0.391645 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2838 | 1.51043 | 0.755213 | − | 0.655479i | \(-0.227533\pi\) | ||||
0.755213 | + | 0.655479i | \(0.227533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.41697 | 0.343861 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.8161 | 1.92033 | 0.960163 | − | 0.279439i | \(-0.0901485\pi\) | ||||
0.960163 | + | 0.279439i | \(0.0901485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.0932 | 2.00717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.5488 | −0.883163 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.0185 | −1.29389 | −0.646945 | − | 0.762537i | \(-0.723954\pi\) | ||||
−0.646945 | + | 0.762537i | \(0.723954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.580377 | 0.0438724 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.90890 | −0.744799 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.10678 | 0.456442 | 0.228221 | − | 0.973609i | \(-0.426709\pi\) | ||||
0.228221 | + | 0.973609i | \(0.426709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.02757 | −0.0763785 | −0.0381892 | − | 0.999271i | \(-0.512159\pi\) | ||||
−0.0381892 | + | 0.999271i | \(0.512159\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.09909 | 0.672624 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.495300 | 0.0364152 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.8892 | −2.03946 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.77394 | −0.201774 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3023 | 0.817808 | 0.408904 | − | 0.912577i | \(-0.365911\pi\) | ||||
0.408904 | + | 0.912577i | \(0.365911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0759 | −1.37311 | −0.686555 | − | 0.727077i | \(-0.740878\pi\) | ||||
−0.686555 | + | 0.727077i | \(0.740878\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.82195 | 0.416918 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.1996 | 1.43916 | 0.719580 | − | 0.694409i | \(-0.244334\pi\) | ||||
0.719580 | + | 0.694409i | \(0.244334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2701 | 0.798915 | 0.399457 | − | 0.916752i | \(-0.369199\pi\) | ||||
0.399457 | + | 0.916752i | \(0.369199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.25762 | −0.0887055 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.30144 | −0.161530 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8503 | 0.827664 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.2633 | −1.26939 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.6839 | 1.77660 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.09599 | −0.419665 | −0.209833 | − | 0.977737i | \(-0.567292\pi\) | ||||
−0.209833 | + | 0.977737i | \(0.567292\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.0111 | 0.685948 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.78767 | 0.326516 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.30172 | −0.224136 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.22173 | 0.0825571 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.7604 | −2.47277 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.65809 | −0.512824 | −0.256412 | − | 0.966568i | \(-0.582540\pi\) | ||||
−0.256412 | + | 0.966568i | \(0.582540\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13297 | −0.142198 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29.5274 | 1.95980 | 0.979900 | − | 0.199490i | \(-0.0639285\pi\) | ||||
0.979900 | + | 0.199490i | \(0.0639285\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.14724 | 0.472303 | 0.236151 | − | 0.971716i | \(-0.424114\pi\) | ||||
0.236151 | + | 0.971716i | \(0.424114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.56351 | 0.168667 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.9605 | −0.718045 | −0.359023 | − | 0.933329i | \(-0.616890\pi\) | ||||
−0.359023 | + | 0.933329i | \(0.616890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.78707 | 0.247041 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.458525 | −0.0297844 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.7441 | −1.27714 | −0.638571 | − | 0.769563i | \(-0.720474\pi\) | ||||
−0.638571 | + | 0.769563i | \(0.720474\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2285 | −1.23862 | −0.619309 | − | 0.785148i | \(-0.712587\pi\) | ||||
−0.619309 | + | 0.785148i | \(0.712587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1529 | 1.03621 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.66316 | −0.425694 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.8536 | 2.15405 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.51231 | −0.0958385 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.44743 | 0.154481 | 0.0772403 | − | 0.997013i | \(-0.475389\pi\) | ||||
0.0772403 | + | 0.997013i | \(0.475389\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.6165 | 2.55354 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.47453 | −0.342828 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.5627 | 1.28267 | 0.641333 | − | 0.767263i | \(-0.278382\pi\) | ||||
0.641333 | + | 0.767263i | \(0.278382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.287461 | 0.0178620 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.45812 | 0.523545 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4549 | −0.644679 | −0.322340 | − | 0.946624i | \(-0.604469\pi\) | ||||
−0.322340 | + | 0.946624i | \(0.604469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.91925 | −0.486476 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.931146 | 0.0569852 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.2193 | 1.59862 | 0.799308 | − | 0.600921i | \(-0.205199\pi\) | ||||
0.799308 | + | 0.600921i | \(0.205199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.6659 | −1.25536 | −0.627681 | − | 0.778470i | \(-0.715996\pi\) | ||||
−0.627681 | + | 0.778470i | \(0.715996\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.37893 | 0.204502 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.74359 | 0.286049 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.433915 | 0.0260714 | 0.0130357 | − | 0.999915i | \(-0.495850\pi\) | ||||
0.0130357 | + | 0.999915i | \(0.495850\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.1343 | 0.726461 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7226 | 0.997585 | 0.498793 | − | 0.866721i | \(-0.333777\pi\) | ||||
0.498793 | + | 0.866721i | \(0.333777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.4735 | 0.622587 | 0.311293 | − | 0.950314i | \(-0.399238\pi\) | ||||
0.311293 | + | 0.950314i | \(0.399238\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.04164 | 0.298641 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.87767 | 0.405976 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.5668 | 1.03334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.95327 | −0.524850 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.94600 | 0.464210 | 0.232105 | − | 0.972691i | \(-0.425439\pi\) | ||||
0.232105 | + | 0.972691i | \(0.425439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6416 | −0.619579 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.6722 | −1.31557 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 53.5360 | 3.09607 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.77865 | 0.160159 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.39887 | 0.252708 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.77193 | 0.559539 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.11312 | 0.120602 | 0.0603011 | − | 0.998180i | \(-0.480794\pi\) | ||||
0.0603011 | + | 0.998180i | \(0.480794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.81723 | −0.274043 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.66507 | 0.491351 | 0.245675 | − | 0.969352i | \(-0.420990\pi\) | ||||
0.245675 | + | 0.969352i | \(0.420990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0660 | 0.908105 | 0.454052 | − | 0.890975i | \(-0.349978\pi\) | ||||
0.454052 | + | 0.890975i | \(0.349978\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.23793 | −0.0697492 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.70619 | −0.0958291 | −0.0479146 | − | 0.998851i | \(-0.515258\pi\) | ||||
−0.0479146 | + | 0.998851i | \(0.515258\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.8104 | −1.05318 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.29038 | −0.295280 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.8335 | −1.77126 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.25246 | 0.346824 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.04147 | −0.334094 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.19793 | 0.121176 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.90149 | 0.434305 | 0.217153 | − | 0.976138i | \(-0.430323\pi\) | ||||
0.217153 | + | 0.976138i | \(0.430323\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.05646 | −0.0578936 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.35061 | −0.0737919 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.99703 | 0.435626 | 0.217813 | − | 0.975991i | \(-0.430108\pi\) | ||||
0.217813 | + | 0.975991i | \(0.430108\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.83662 | 0.479939 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.9859 | −1.46137 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.92979 | −0.428168 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.97283 | 0.429243 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.24790 | −0.335405 | −0.167702 | − | 0.985838i | \(-0.553635\pi\) | ||||
−0.167702 | + | 0.985838i | \(0.553635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.07360 | 0.378641 | 0.189320 | − | 0.981915i | \(-0.439372\pi\) | ||||
0.189320 | + | 0.981915i | \(0.439372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.8839 | −1.59508 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.2887 | 0.920184 | 0.460092 | − | 0.887871i | \(-0.347816\pi\) | ||||
0.460092 | + | 0.887871i | \(0.347816\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.7514 | 0.570623 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.17729 | −0.168160 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.3384 | −0.651193 | −0.325597 | − | 0.945509i | \(-0.605565\pi\) | ||||
−0.325597 | + | 0.945509i | \(0.605565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3163 | 0.542962 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7097 | 0.562115 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.31208 | 0.0686771 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.6605 | −1.60047 | −0.800233 | − | 0.599689i | \(-0.795291\pi\) | ||||
−0.800233 | + | 0.599689i | \(0.795291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.2764 | −1.31584 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.59616 | −0.238621 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.45234 | −0.282312 | −0.141156 | − | 0.989987i | \(-0.545082\pi\) | ||||
−0.141156 | + | 0.989987i | \(0.545082\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.931146 | 0.0480842 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.7936 | −1.27694 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.5232 | 1.82471 | 0.912353 | − | 0.409405i | \(-0.134264\pi\) | ||||
0.912353 | + | 0.409405i | \(0.134264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.66206 | 0.392539 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.8946 | 0.658882 | 0.329441 | − | 0.944176i | \(-0.393140\pi\) | ||||
0.329441 | + | 0.944176i | \(0.393140\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.75307 | 0.140310 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2119 | −0.519102 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.2948 | −1.43460 | −0.717300 | − | 0.696764i | \(-0.754622\pi\) | ||||
−0.717300 | + | 0.696764i | \(0.754622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50.3413 | −2.54587 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.59018 | 0.231544 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.492431 | −0.0247769 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.7862 | −1.64549 | −0.822745 | − | 0.568411i | \(-0.807558\pi\) | ||||
−0.822745 | + | 0.568411i | \(0.807558\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.92606 | 0.146486 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.8756 | 0.992538 | 0.496269 | − | 0.868169i | \(-0.334703\pi\) | ||||
0.496269 | + | 0.868169i | \(0.334703\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35.5698 | −1.77186 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.94845 | 0.0968194 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.34950 | 0.116461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6891 | 1.22080 | 0.610398 | − | 0.792095i | \(-0.291009\pi\) | ||||
0.610398 | + | 0.792095i | \(0.291009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.1649 | −0.550726 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.17616 | −0.303909 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.62413 | −0.0797256 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.8500 | −0.825148 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.6692 | 1.15632 | 0.578159 | − | 0.815924i | \(-0.303771\pi\) | ||||
0.578159 | + | 0.815924i | \(0.303771\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9257 | 0.776169 | 0.388085 | − | 0.921624i | \(-0.373137\pi\) | ||||
0.388085 | + | 0.921624i | \(0.373137\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.07770 | −0.392751 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.87935 | −0.285190 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.67141 | 0.274459 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.6169 | 1.33336 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.78225 | −0.374858 | −0.187429 | − | 0.982278i | \(-0.560015\pi\) | ||||
−0.187429 | + | 0.982278i | \(0.560015\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.59930 | −0.172971 | −0.0864856 | − | 0.996253i | \(-0.527564\pi\) | ||||
−0.0864856 | + | 0.996253i | \(0.527564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.69239 | −0.177036 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 46.3606 | 2.21773 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.2840 | −1.44538 | −0.722689 | − | 0.691173i | \(-0.757094\pi\) | ||||
−0.722689 | + | 0.691173i | \(0.757094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.2123 | 0.676777 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.1094 | −0.717870 | −0.358935 | − | 0.933362i | \(-0.616860\pi\) | ||||
−0.358935 | + | 0.933362i | \(0.616860\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.5860 | −0.879089 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3101 | 0.864106 | 0.432053 | − | 0.901848i | \(-0.357789\pi\) | ||||
0.432053 | + | 0.901848i | \(0.357789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 56.2132 | 2.64698 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.39381 | 0.394376 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.62878 | 0.170120 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.0509 | −0.984720 | −0.492360 | − | 0.870392i | \(-0.663866\pi\) | ||||
−0.492360 | + | 0.870392i | \(0.663866\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.1006 | 1.31162 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.8056 | −1.80735 | −0.903677 | − | 0.428214i | \(-0.859143\pi\) | ||||
−0.903677 | + | 0.428214i | \(0.859143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1126 | 0.562921 | 0.281460 | − | 0.959573i | \(-0.409181\pi\) | ||||
0.281460 | + | 0.959573i | \(0.409181\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.29722 | −0.245653 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.25635 | −0.104411 | −0.0522056 | − | 0.998636i | \(-0.516625\pi\) | ||||
−0.0522056 | + | 0.998636i | \(0.516625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.783866 | −0.0361955 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.60016 | −0.396274 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.7107 | 1.04424 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.41445 | 0.248432 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.8915 | 0.773409 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.237254 | −0.0108404 | −0.00542022 | − | 0.999985i | \(-0.501725\pi\) | ||||
−0.00542022 | + | 0.999985i | \(0.501725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.09684 | 0.141204 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.62725 | 0.210547 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.61533 | −0.436610 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.69314 | −0.0767237 | −0.0383619 | − | 0.999264i | \(-0.512214\pi\) | ||||
−0.0383619 | + | 0.999264i | \(0.512214\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.9561 | 0.812001 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2064 | 0.821641 | 0.410821 | − | 0.911716i | \(-0.365242\pi\) | ||||
0.410821 | + | 0.911716i | \(0.365242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.3141 | 1.05002 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.1179 | −0.454767 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.23985 | 0.279896 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0254 | −0.896462 | −0.448231 | − | 0.893918i | \(-0.647946\pi\) | ||||
−0.448231 | + | 0.893918i | \(0.647946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.1074 | 1.03236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.4990 | −1.49365 | −0.746824 | − | 0.665021i | \(-0.768422\pi\) | ||||
−0.746824 | + | 0.665021i | \(0.768422\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.72415 | 0.210222 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.2966 | 1.07905 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.2860 | −0.677541 | −0.338770 | − | 0.940869i | \(-0.610011\pi\) | ||||
−0.338770 | + | 0.940869i | \(0.610011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.761499 | 0.0336867 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.8786 | −1.14257 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.17345 | −0.227969 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.9643 | 0.790070 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.8467 | −0.695592 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7850 | −1.04204 | −0.521021 | − | 0.853544i | \(-0.674449\pi\) | ||||
−0.521021 | + | 0.853544i | \(0.674449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.9989 | −1.18058 | −0.590290 | − | 0.807192i | \(-0.700986\pi\) | ||||
−0.590290 | + | 0.807192i | \(0.700986\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.540416 | 0.0235857 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.4472 | 1.45698 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.3145 | 2.18759 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.6982 | 0.985020 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 74.0938 | 3.20936 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.68158 | −0.245636 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.68630 | 0.245382 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.6073 | −1.36142 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0584 | −0.905370 | −0.452685 | − | 0.891671i | \(-0.649534\pi\) | ||||
−0.452685 | + | 0.891671i | \(0.649534\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.956815 | −0.0410609 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.48821 | −0.277924 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6410 | −0.540491 | −0.270245 | − | 0.962792i | \(-0.587105\pi\) | ||||
−0.270245 | + | 0.962792i | \(0.587105\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.8432 | −0.889567 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.4706 | −0.914678 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.285796 | −0.0121533 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.461197 | 0.0195767 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.81870 | 0.331289 | 0.165644 | − | 0.986186i | \(-0.447030\pi\) | ||||
0.165644 | + | 0.986186i | \(0.447030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.9347 | 1.26610 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.9689 | −1.09641 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.7792 | 0.875737 | 0.437869 | − | 0.899039i | \(-0.355734\pi\) | ||||
0.437869 | + | 0.899039i | \(0.355734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.49005 | 0.399250 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.13084 | 0.0474908 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.4719 | −0.816307 | −0.408153 | − | 0.912913i | \(-0.633827\pi\) | ||||
−0.408153 | + | 0.912913i | \(0.633827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.07799 | 0.379902 | 0.189951 | − | 0.981794i | \(-0.439167\pi\) | ||||
0.189951 | + | 0.981794i | \(0.439167\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5241 | 0.439651 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.56239 | 0.357076 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.99714 | 0.416186 | 0.208093 | − | 0.978109i | \(-0.433274\pi\) | ||||
0.208093 | + | 0.978109i | \(0.433274\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.7624 | −0.738181 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.942611 | −0.0391061 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.5657 | −1.55581 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.3363 | −0.551388 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.0697 | 1.19984 | 0.599918 | − | 0.800062i | \(-0.295200\pi\) | ||||
0.599918 | + | 0.800062i | \(0.295200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.8024 | −1.26919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.8088 | 0.773689 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.26916 | −0.298509 | −0.149254 | − | 0.988799i | \(-0.547687\pi\) | ||||
−0.149254 | + | 0.988799i | \(0.547687\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.41224 | −0.139888 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.4941 | 0.429494 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.9436 | −0.651438 | −0.325719 | − | 0.945467i | \(-0.605606\pi\) | ||||
−0.325719 | + | 0.945467i | \(0.605606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.56369 | −0.308530 | −0.154265 | − | 0.988030i | \(-0.549301\pi\) | ||||
−0.154265 | + | 0.988030i | \(0.549301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.88081 | 0.117316 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.5017 | 0.467609 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.88969 | 0.0767000 | 0.0383500 | − | 0.999264i | \(-0.487790\pi\) | ||||
0.0383500 | + | 0.999264i | \(0.487790\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.14298 | −0.0868379 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.6785 | 0.957930 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4920 | −0.504548 | −0.252274 | − | 0.967656i | \(-0.581178\pi\) | ||||
−0.252274 | + | 0.967656i | \(0.581178\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.0344 | 0.444950 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.0989 | −0.406567 | −0.203284 | − | 0.979120i | \(-0.565161\pi\) | ||||
−0.203284 | + | 0.979120i | \(0.565161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.5158 | 1.22653 | 0.613266 | − | 0.789876i | \(-0.289855\pi\) | ||||
0.613266 | + | 0.789876i | \(0.289855\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.9243 | −1.64224 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.580377 | 0.0232523 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.9155 | 0.955093 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.91204 | −0.116111 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5337 | 0.618386 | 0.309193 | − | 0.950999i | \(-0.399941\pi\) | ||||
0.309193 | + | 0.950999i | \(0.399941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.67625 | −0.225611 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.22863 | 0.326543 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.6611 | −1.65067 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.9323 | −0.907188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5661 | −0.693818 | −0.346909 | − | 0.937899i | \(-0.612769\pi\) | ||||
−0.346909 | + | 0.937899i | \(0.612769\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.7523 | 1.60712 | 0.803558 | − | 0.595227i | \(-0.202938\pi\) | ||||
0.803558 | + | 0.595227i | \(0.202938\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.45802 | 0.175534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.1397 | 0.791775 | 0.395887 | − | 0.918299i | \(-0.370437\pi\) | ||||
0.395887 | + | 0.918299i | \(0.370437\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −50.4795 | −1.98149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.07439 | −0.120495 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.5360 | −1.23410 | −0.617050 | − | 0.786924i | \(-0.711672\pi\) | ||||
−0.617050 | + | 0.786924i | \(0.711672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.92961 | 0.192616 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.79861 | −0.109184 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.91412 | −0.308290 | −0.154145 | − | 0.988048i | \(-0.549262\pi\) | ||||
−0.154145 | + | 0.988048i | \(0.549262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.7578 | −1.54640 | −0.773200 | − | 0.634163i | \(-0.781345\pi\) | ||||
−0.773200 | + | 0.634163i | \(0.781345\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −34.2293 | −1.32935 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.14242 | 0.121858 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.9535 | −1.31469 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.13080 | −0.275693 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.3540 | 1.78948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.6297 | 0.833763 | 0.416882 | − | 0.908961i | \(-0.363123\pi\) | ||||
0.416882 | + | 0.908961i | \(0.363123\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.77954 | −0.183965 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.7735 | −0.644658 | −0.322329 | − | 0.946628i | \(-0.604466\pi\) | ||||
−0.322329 | + | 0.946628i | \(0.604466\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.58052 | −0.214161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.4943 | 1.05358 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.7665 | −0.947663 | −0.473832 | − | 0.880615i | \(-0.657129\pi\) | ||||
−0.473832 | + | 0.880615i | \(0.657129\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.9905 | −0.458135 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.65512 | 0.253909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.5148 | −1.88636 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.4194 | −1.80392 | −0.901959 | − | 0.431822i | \(-0.857871\pi\) | ||||
−0.901959 | + | 0.431822i | \(0.857871\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.87222 | −0.223067 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.0960 | −0.686420 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −69.6723 | −2.63903 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.2058 | −0.386019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9075 | 1.31844 | 0.659218 | − | 0.751952i | \(-0.270887\pi\) | ||||
0.659218 | + | 0.751952i | \(0.270887\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.68178 | 0.101145 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.52632 | 0.132809 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.74179 | 0.103116 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.6918 | 1.82866 | 0.914330 | − | 0.404970i | \(-0.132718\pi\) | ||||
0.914330 | + | 0.404970i | \(0.132718\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.05034 | 0.0393908 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48.7108 | −1.82423 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.6591 | 1.10919 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.3847 | −0.686588 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.5414 | −1.32547 | −0.662736 | − | 0.748853i | \(-0.730605\pi\) | ||||
−0.662736 | + | 0.748853i | \(0.730605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00255 | −0.111821 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.9045 | −0.665877 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.96542 | −0.147272 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.22393 | −0.0824812 | −0.0412406 | − | 0.999149i | \(-0.513131\pi\) | ||||
−0.0412406 | + | 0.999149i | \(0.513131\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.19536 | 0.340569 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.1484 | −1.04111 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.92710 | −0.366666 | −0.183333 | − | 0.983051i | \(-0.558689\pi\) | ||||
−0.183333 | + | 0.983051i | \(0.558689\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.20438 | −0.228852 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.40676 | −0.235996 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.1642 | 0.373896 | 0.186948 | − | 0.982370i | \(-0.440140\pi\) | ||||
0.186948 | + | 0.982370i | \(0.440140\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.5227 | 1.15801 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.3395 | 1.58997 | 0.794985 | − | 0.606629i | \(-0.207478\pi\) | ||||
0.794985 | + | 0.606629i | \(0.207478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.9604 | −0.731292 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.46423 | 0.126749 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.29746 | −0.120487 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.92124 | 0.143088 | 0.0715440 | − | 0.997437i | \(-0.477207\pi\) | ||||
0.0715440 | + | 0.997437i | \(0.477207\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.27892 | 0.0830484 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.01450 | 0.328071 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.19956 | 0.261672 | 0.130836 | − | 0.991404i | \(-0.458234\pi\) | ||||
0.130836 | + | 0.991404i | \(0.458234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.8199 | 1.37277 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.8629 | 1.48128 | 0.740639 | − | 0.671903i | \(-0.234523\pi\) | ||||
0.740639 | + | 0.671903i | \(0.234523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.76561 | −0.136324 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.5405 | 0.453401 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −66.5363 | −2.40249 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.3277 | 1.85092 | 0.925462 | − | 0.378840i | \(-0.123677\pi\) | ||||
0.925462 | + | 0.378840i | \(0.123677\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.1469 | 0.689558 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.66946 | −0.0960137 | −0.0480069 | − | 0.998847i | \(-0.515287\pi\) | ||||
−0.0480069 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.68893 | −0.204352 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.267668 | 0.00960254 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 64.1631 | 2.29888 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.0001 | 1.82493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.9529 | 0.677322 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.23610 | −0.329651 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.3284 | 0.582043 | 0.291022 | − | 0.956716i | \(-0.406005\pi\) | ||||
0.291022 | + | 0.956716i | \(0.406005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.73507 | −0.346578 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.50781 | 0.195835 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.0986 | 2.16967 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.37398 | −0.261528 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.8557 | 1.23465 | 0.617325 | − | 0.786708i | \(-0.288216\pi\) | ||||
0.617325 | + | 0.786708i | \(0.288216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.2655 | −0.787698 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.13297 | −0.0753647 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.22395 | 0.219638 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.96942 | 0.175149 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.4140 | 0.859412 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.4204 | −1.45626 | −0.728132 | − | 0.685437i | \(-0.759611\pi\) | ||||
−0.728132 | + | 0.685437i | \(0.759611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.34996 | −0.258092 | −0.129046 | − | 0.991639i | \(-0.541192\pi\) | ||||
−0.129046 | + | 0.991639i | \(0.541192\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.2429 | −0.674880 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.2838 | 0.675483 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.9226 | 0.906917 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.74008 | −0.270460 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.8242 | −1.35498 | −0.677488 | − | 0.735534i | \(-0.736931\pi\) | ||||
−0.677488 | + | 0.735534i | \(0.736931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.4901 | 0.749099 | 0.374550 | − | 0.927207i | \(-0.377797\pi\) | ||||
0.374550 | + | 0.927207i | \(0.377797\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.41697 | 0.153779 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.6349 | −0.682771 | −0.341386 | − | 0.939923i | \(-0.610896\pi\) | ||||
−0.341386 | + | 0.939923i | \(0.610896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.8272 | −0.723358 | −0.361679 | − | 0.932303i | \(-0.617796\pi\) | ||||
−0.361679 | + | 0.932303i | \(0.617796\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.404038 | 0.0140159 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.1751 | 1.35734 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.8161 | 0.858796 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.1905 | 0.939840 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.3217 | −0.770630 | −0.385315 | − | 0.922785i | \(-0.625907\pi\) | ||||
−0.385315 | + | 0.922785i | \(0.625907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2754 | −0.457773 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.5712 | 0.536299 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.0932 | 0.897634 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.67530 | 0.229366 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.75238 | 0.334701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.24096 | 0.145378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.79245 | −0.164090 | −0.0820452 | − | 0.996629i | \(-0.526145\pi\) | ||||
−0.0820452 | + | 0.996629i | \(0.526145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.5488 | −0.394962 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.1822 | 1.68003 | 0.840016 | − | 0.542561i | \(-0.182545\pi\) | ||||
0.840016 | + | 0.542561i | \(0.182545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.6426 | −1.55731 | −0.778653 | − | 0.627454i | \(-0.784097\pi\) | ||||
−0.778653 | + | 0.627454i | \(0.784097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.40412 | 0.218252 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.9728 | −0.577761 | −0.288880 | − | 0.957365i | \(-0.593283\pi\) | ||||
−0.288880 | + | 0.957365i | \(0.593283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.0185 | −0.578645 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.3572 | 0.555520 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.33589 | −0.0792397 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.44465 | −0.286136 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.5092 | 0.694131 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.580377 | 0.0196203 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.47951 | −0.218797 | −0.109399 | − | 0.993998i | \(-0.534893\pi\) | ||||
−0.109399 | + | 0.993998i | \(0.534893\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.39888 | 0.249558 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0221 | −0.438724 | −0.219362 | − | 0.975644i | \(-0.570398\pi\) | ||||
−0.219362 | + | 0.975644i | \(0.570398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.1962 | −0.814268 | −0.407134 | − | 0.913369i | \(-0.633472\pi\) | ||||
−0.407134 | + | 0.913369i | \(0.633472\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.90890 | −0.333084 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.6517 | 0.626264 | 0.313132 | − | 0.949710i | \(-0.398622\pi\) | ||||
0.313132 | + | 0.949710i | \(0.398622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.77571 | 0.160172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.24267 | 0.309641 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.5049 | 0.686171 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.10678 | 0.204127 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.8498 | 1.66444 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.5590 | 0.752385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.5601 | 1.55114 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.58733 | 0.0861010 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.02757 | −0.0341575 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.1208 | 0.634896 | 0.317448 | − | 0.948276i | \(-0.397174\pi\) | ||||
0.317448 | + | 0.948276i | \(0.397174\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0765 | −0.334215 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.04981 | −0.200439 | −0.100220 | − | 0.994965i | \(-0.531955\pi\) | ||||
−0.100220 | + | 0.994965i | \(0.531955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.70423 | −0.254973 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.09909 | 0.300807 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.86103 | 0.0944796 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.9158 | −0.656962 | −0.328481 | − | 0.944511i | \(-0.606537\pi\) | ||||
−0.328481 | + | 0.944511i | \(0.606537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.96762 | 0.0648354 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.2224 | 2.21265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.495300 | 0.0162854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.0348 | 0.362430 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.333759 | 0.0109503 | 0.00547514 | − | 0.999985i | \(-0.498257\pi\) | ||||
0.00547514 | + | 0.999985i | \(0.498257\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.0774 | −1.18239 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.06844 | 0.264149 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.8892 | −0.912075 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.6611 | −0.478957 | −0.239479 | − | 0.970902i | \(-0.576977\pi\) | ||||
−0.239479 | + | 0.970902i | \(0.576977\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.9598 | 0.488194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.63624 | −0.151137 | −0.0755686 | − | 0.997141i | \(-0.524077\pi\) | ||||
−0.0755686 | + | 0.997141i | \(0.524077\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 101.467 | 3.30423 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.77394 | −0.0902362 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.9543 | −0.355965 | −0.177983 | − | 0.984034i | \(-0.556957\pi\) | ||||
−0.177983 | + | 0.984034i | \(0.556957\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.20369 | 0.266303 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.58871 | −0.0515175 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.4968 | −0.858315 | −0.429158 | − | 0.903230i | \(-0.641190\pi\) | ||||
−0.429158 | + | 0.903230i | \(0.641190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.3023 | 0.365735 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.5152 | −0.566185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.95904 | −0.224719 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.36388 | 0.0439962 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.1186 | 0.390517 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.0759 | −0.614074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.1812 | 1.90314 | 0.951569 | − | 0.307435i | \(-0.0994706\pi\) | ||||
0.951569 | + | 0.307435i | \(0.0994706\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.6416 | −0.952225 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.45699 | 0.175123 | 0.0875616 | − | 0.996159i | \(-0.472093\pi\) | ||||
0.0875616 | + | 0.996159i | \(0.472093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.5025 | −0.336695 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.82195 | 0.186452 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.0837 | 0.546555 | 0.273278 | − | 0.961935i | \(-0.411892\pi\) | ||||
0.273278 | + | 0.961935i | \(0.411892\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.74359 | 0.151606 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8391 | 0.441850 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.1851 | −1.34549 | −0.672747 | − | 0.739872i | \(-0.734886\pi\) | ||||
−0.672747 | + | 0.739872i | \(0.734886\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.1996 | 0.643612 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.04659 | 0.0651438 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.9939 | 1.30353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.7224 | 0.372375 | 0.186188 | − | 0.982514i | \(-0.440387\pi\) | ||||
0.186188 | + | 0.982514i | \(0.440387\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.35744 | 0.233481 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.2701 | 0.357286 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.629575 | 0.0199388 | 0.00996942 | − | 0.999950i | \(-0.496827\pi\) | ||||
0.00996942 | + | 0.999950i | \(0.496827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.36731 | −0.0748983 |
(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 | 7120.2.a.bj.1.4 | 7 | ||
4.3 | odd | 2 | 445.2.a.f.1.6 | ✓ | 7 | ||
12.11 | even | 2 | 4005.2.a.o.1.2 | 7 | |||
20.19 | odd | 2 | 2225.2.a.k.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.f.1.6 | ✓ | 7 | 4.3 | odd | 2 | ||
2225.2.a.k.1.2 | 7 | 20.19 | odd | 2 | |||
4005.2.a.o.1.2 | 7 | 12.11 | even | 2 | |||
7120.2.a.bj.1.4 | 7 | 1.1 | even | 1 | trivial |