Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 79 x^{11} + 274 x^{10} - 747 x^{9} - 1422 x^{8} + 3287 x^{7} + \cdots - 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.64615\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 1.64615 | 0.950403 | 0.475202 | − | 0.879877i | \(-0.342375\pi\) | ||||
0.475202 | + | 0.879877i | \(0.342375\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.00715 | −1.79205 | −0.896025 | − | 0.444003i | \(-0.853558\pi\) | ||||
−0.896025 | + | 0.444003i | \(0.853558\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.94760 | −1.11409 | −0.557044 | − | 0.830483i | \(-0.688064\pi\) | ||||
−0.557044 | + | 0.830483i | \(0.688064\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.290201 | −0.0967337 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00704 | 1.20817 | 0.604084 | − | 0.796920i | \(-0.293539\pi\) | ||||
0.604084 | + | 0.796920i | \(0.293539\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51643 | 0.697933 | 0.348966 | − | 0.937135i | \(-0.386533\pi\) | ||||
0.348966 | + | 0.937135i | \(0.386533\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.59635 | −1.70317 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.26481 | −0.306762 | −0.153381 | − | 0.988167i | \(-0.549016\pi\) | ||||
−0.153381 | + | 0.988167i | \(0.549016\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.62365 | 1.74898 | 0.874492 | − | 0.485039i | \(-0.161195\pi\) | ||||
0.874492 | + | 0.485039i | \(0.161195\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.85218 | −1.05883 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.11058 | 0.440087 | 0.220043 | − | 0.975490i | \(-0.429380\pi\) | ||||
0.220043 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.0572 | 2.21144 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.41615 | −1.04234 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.18258 | 0.219600 | 0.109800 | − | 0.993954i | \(-0.464979\pi\) | ||||
0.109800 | + | 0.993954i | \(0.464979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.32238 | −0.955928 | −0.477964 | − | 0.878379i | \(-0.658625\pi\) | ||||
−0.477964 | + | 0.878379i | \(0.658625\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.59618 | 1.14825 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.8115 | 1.99650 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.498716 | −0.0819884 | −0.0409942 | − | 0.999159i | \(-0.513053\pi\) | ||||
−0.0409942 | + | 0.999159i | \(0.513053\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.14242 | 0.663318 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.30758 | 0.360384 | 0.180192 | − | 0.983631i | \(-0.442328\pi\) | ||||
0.180192 | + | 0.983631i | \(0.442328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.3629 | −1.88532 | −0.942661 | − | 0.333753i | \(-0.891685\pi\) | ||||
−0.942661 | + | 0.333753i | \(0.891685\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.16288 | 0.173352 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.43666 | −1.37648 | −0.688239 | − | 0.725484i | \(-0.741616\pi\) | ||||
−0.688239 | + | 0.725484i | \(0.741616\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.68834 | 0.241191 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.08206 | −0.291547 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.82052 | 1.07423 | 0.537116 | − | 0.843509i | \(-0.319514\pi\) | ||||
0.537116 | + | 0.843509i | \(0.319514\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.0568 | −2.16510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.5496 | 1.66224 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.36116 | −0.177208 | −0.0886040 | − | 0.996067i | \(-0.528241\pi\) | ||||
−0.0886040 | + | 0.996067i | \(0.528241\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6863 | −1.36824 | −0.684122 | − | 0.729368i | \(-0.739814\pi\) | ||||
−0.684122 | + | 0.729368i | \(0.739814\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.855396 | 0.107770 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.0837 | −1.25073 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.80774 | −0.587359 | −0.293680 | − | 0.955904i | \(-0.594880\pi\) | ||||
−0.293680 | + | 0.955904i | \(0.594880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.47433 | 0.418260 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.78259 | −1.16098 | −0.580490 | − | 0.814268i | \(-0.697139\pi\) | ||||
−0.580490 | + | 0.814268i | \(0.697139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.77485 | 0.675895 | 0.337948 | − | 0.941165i | \(-0.390267\pi\) | ||||
0.337948 | + | 0.941165i | \(0.390267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18.2018 | 2.10176 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.8112 | −1.34601 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.33597 | −0.375326 | −0.187663 | − | 0.982233i | \(-0.560091\pi\) | ||||
−0.187663 | + | 0.982233i | \(0.560091\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.04518 | −0.893909 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.29630 | 0.142288 | 0.0711440 | − | 0.997466i | \(-0.477335\pi\) | ||||
0.0711440 | + | 0.997466i | \(0.477335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.06828 | 0.549732 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.94670 | 0.208709 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.9752 | −1.48137 | −0.740686 | − | 0.671852i | \(-0.765499\pi\) | ||||
−0.740686 | + | 0.671852i | \(0.765499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.41744 | −0.777559 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.76142 | −0.908517 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −30.5491 | −3.13427 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.37411 | −0.139519 | −0.0697597 | − | 0.997564i | \(-0.522223\pi\) | ||||
−0.0697597 | + | 0.997564i | \(0.522223\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.16285 | −0.116871 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0215 | 1.39520 | 0.697598 | − | 0.716489i | \(-0.254252\pi\) | ||||
0.697598 | + | 0.716489i | \(0.254252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.16148 | −0.607109 | −0.303554 | − | 0.952814i | \(-0.598173\pi\) | ||||
−0.303554 | + | 0.952814i | \(0.598173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.4434 | 1.89748 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.0443 | 1.84108 | 0.920540 | − | 0.390648i | \(-0.127749\pi\) | ||||
0.920540 | + | 0.390648i | \(0.127749\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.03123 | 0.481904 | 0.240952 | − | 0.970537i | \(-0.422540\pi\) | ||||
0.240952 | + | 0.970537i | \(0.422540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.820960 | −0.0779221 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2857 | −1.34389 | −0.671945 | − | 0.740601i | \(-0.734541\pi\) | ||||
−0.671945 | + | 0.740601i | \(0.734541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.45741 | −0.788658 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.730271 | −0.0675136 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.72815 | 0.341759 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.05638 | 0.459671 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.79862 | 0.342510 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −24.2722 | −2.17097 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.43426 | −0.304741 | −0.152371 | − | 0.988323i | \(-0.548691\pi\) | ||||
−0.152371 | + | 0.988323i | \(0.548691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.3511 | −1.79182 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.73505 | −0.588444 | −0.294222 | − | 0.955737i | \(-0.595061\pi\) | ||||
−0.294222 | + | 0.955737i | \(0.595061\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.4715 | −1.94852 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.7033 | 1.86792 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.110622 | −0.00945104 | −0.00472552 | − | 0.999989i | \(-0.501504\pi\) | ||||
−0.00472552 | + | 0.999989i | \(0.501504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.52678 | 0.468775 | 0.234388 | − | 0.972143i | \(-0.424692\pi\) | ||||
0.234388 | + | 0.972143i | \(0.424692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.5341 | −1.30821 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.0835 | 0.843221 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.73878 | −0.393534 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.77926 | 0.229229 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.17645 | 0.587918 | 0.293959 | − | 0.955818i | \(-0.405027\pi\) | ||||
0.293959 | + | 0.955818i | \(0.405027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4763 | −1.09668 | −0.548341 | − | 0.836255i | \(-0.684740\pi\) | ||||
−0.548341 | + | 0.836255i | \(0.684740\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.367049 | 0.0296742 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.3276 | 1.71307 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.9660 | −1.11461 | −0.557304 | − | 0.830309i | \(-0.688164\pi\) | ||||
−0.557304 | + | 0.830309i | \(0.688164\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.8737 | 1.02095 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.22115 | −0.490295 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.7137 | −1.38744 | −0.693722 | − | 0.720243i | \(-0.744030\pi\) | ||||
−0.693722 | + | 0.720243i | \(0.744030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −26.4319 | −2.05772 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.6357 | 1.13254 | 0.566271 | − | 0.824219i | \(-0.308386\pi\) | ||||
0.566271 | + | 0.824219i | \(0.308386\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.66756 | −0.512890 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.21239 | −0.169186 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9679 | 1.44210 | 0.721050 | − | 0.692883i | \(-0.243660\pi\) | ||||
0.721050 | + | 0.692883i | \(0.243660\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −32.5923 | −2.46374 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.24067 | −0.168419 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.1969 | −1.43485 | −0.717423 | − | 0.696638i | \(-0.754678\pi\) | ||||
−0.717423 | + | 0.696638i | \(0.754678\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.2798 | −1.21007 | −0.605033 | − | 0.796200i | \(-0.706840\pi\) | ||||
−0.605033 | + | 0.796200i | \(0.706840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.5913 | −1.30038 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.99843 | 0.146927 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.06815 | −0.370620 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.9646 | 1.16126 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.4396 | −1.76839 | −0.884194 | − | 0.467119i | \(-0.845292\pi\) | ||||
−0.884194 | + | 0.467119i | \(0.845292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.20612 | 0.662671 | 0.331335 | − | 0.943513i | \(-0.392501\pi\) | ||||
0.331335 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.5993 | −1.18870 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.2336 | −0.729117 | −0.364558 | − | 0.931181i | \(-0.618780\pi\) | ||||
−0.364558 | + | 0.931181i | \(0.618780\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5062 | 0.957433 | 0.478716 | − | 0.877970i | \(-0.341102\pi\) | ||||
0.478716 | + | 0.877970i | \(0.341102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.91425 | −0.558228 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.48578 | −0.244654 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.24683 | −0.645826 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.612493 | −0.0425712 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.5483 | 2.11307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.2735 | −1.67105 | −0.835527 | − | 0.549449i | \(-0.814838\pi\) | ||||
−0.835527 | + | 0.549449i | \(0.814838\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.1036 | −1.10340 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 49.5399 | 3.37859 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.6882 | 1.06499 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.50625 | 0.642373 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.18281 | −0.214099 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.35768 | 0.157882 | 0.0789411 | − | 0.996879i | \(-0.474846\pi\) | ||||
0.0789411 | + | 0.996879i | \(0.474846\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.20882 | −0.213921 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.2348 | −1.27666 | −0.638330 | − | 0.769763i | \(-0.720374\pi\) | ||||
−0.638330 | + | 0.769763i | \(0.720374\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.0398429 | 0.00263289 | 0.00131645 | − | 0.999999i | \(-0.499581\pi\) | ||||
0.00131645 | + | 0.999999i | \(0.499581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.4429 | −1.27925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.4704 | 0.751448 | 0.375724 | − | 0.926732i | \(-0.377394\pi\) | ||||
0.375724 | + | 0.926732i | \(0.377394\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.8141 | 2.46672 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.49150 | −0.356711 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.388834 | 0.0251516 | 0.0125758 | − | 0.999921i | \(-0.495997\pi\) | ||||
0.0125758 | + | 0.999921i | \(0.495997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3151 | −1.37302 | −0.686512 | − | 0.727119i | \(-0.740859\pi\) | ||||
−0.686512 | + | 0.727119i | \(0.740859\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.00491 | 0.192765 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.76543 | −0.432227 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.1844 | 1.22067 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.13391 | 0.135231 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.45719 | 0.531699 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.34314 | 0.522467 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.6866 | 1.47753 | 0.738766 | − | 0.673962i | \(-0.235409\pi\) | ||||
0.738766 | + | 0.673962i | \(0.235409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.47001 | 0.0913423 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.343187 | −0.0212427 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.78068 | −0.109802 | −0.0549009 | − | 0.998492i | \(-0.517484\pi\) | ||||
−0.0549009 | + | 0.998492i | \(0.517484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.3380 | −1.92508 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.0053 | −1.40790 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.2554 | −1.35694 | −0.678468 | − | 0.734630i | \(-0.737356\pi\) | ||||
−0.678468 | + | 0.734630i | \(0.737356\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.13028 | −0.250897 | −0.125448 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125448 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.2102 | −0.738994 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 44.3068 | 2.67180 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1537 | −0.850415 | −0.425208 | − | 0.905096i | \(-0.639799\pi\) | ||||
−0.425208 | + | 0.905096i | \(0.639799\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.54456 | 0.0924704 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.35858 | 0.558286 | 0.279143 | − | 0.960250i | \(-0.409950\pi\) | ||||
0.279143 | + | 0.960250i | \(0.409950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.2588 | 0.609825 | 0.304912 | − | 0.952380i | \(-0.401373\pi\) | ||||
0.304912 | + | 0.952380i | \(0.401373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −50.2883 | −2.97882 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.80183 | −0.401499 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4003 | −0.905897 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.26198 | −0.132600 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.0778 | 0.880857 | 0.440429 | − | 0.897788i | \(-0.354826\pi\) | ||||
0.440429 | + | 0.897788i | \(0.354826\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.45437 | 0.317566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.7028 | −1.25932 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.31114 | 0.307151 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.4408 | 2.10041 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.0815 | 1.32600 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 42.8217 | 2.45196 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0145 | 1.48473 | 0.742364 | − | 0.669997i | \(-0.233705\pi\) | ||||
0.742364 | + | 0.669997i | \(0.233705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1427 | −0.576998 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3555 | −0.927435 | −0.463717 | − | 0.885983i | \(-0.653485\pi\) | ||||
−0.463717 | + | 0.885983i | \(0.653485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8511 | 1.46119 | 0.730595 | − | 0.682811i | \(-0.239243\pi\) | ||||
0.730595 | + | 0.682811i | \(0.239243\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.42770 | −0.193129 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.43506 | −0.0806012 | −0.0403006 | − | 0.999188i | \(-0.512832\pi\) | ||||
−0.0403006 | + | 0.999188i | \(0.512832\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.73866 | 0.265314 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.3497 | 1.74977 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.64247 | −0.536521 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.8248 | 1.54344 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.28214 | 0.458003 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.8155 | 1.53352 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.73059 | −0.424911 | −0.212456 | − | 0.977171i | \(-0.568146\pi\) | ||||
−0.212456 | + | 0.977171i | \(0.568146\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.144728 | 0.00793104 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.2653 | 1.05258 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.1721 | 1.64358 | 0.821789 | − | 0.569793i | \(-0.192976\pi\) | ||||
0.821789 | + | 0.569793i | \(0.192976\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.5164 | −1.27724 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.3270 | −1.15492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.6566 | 0.845379 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.9221 | −0.749543 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3337 | −1.25262 | −0.626310 | − | 0.779574i | \(-0.715436\pi\) | ||||
−0.626310 | + | 0.779574i | \(0.715436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.89645 | −0.208572 | −0.104286 | − | 0.994547i | \(-0.533256\pi\) | ||||
−0.104286 | + | 0.994547i | \(0.533256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.6294 | −0.727483 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.8799 | −1.80325 | −0.901624 | − | 0.432521i | \(-0.857624\pi\) | ||||
−0.901624 | + | 0.432521i | \(0.857624\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.2003 | 2.08053 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.13709 | 0.324809 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.2536 | 1.22728 | 0.613639 | − | 0.789586i | \(-0.289705\pi\) | ||||
0.613639 | + | 0.789586i | \(0.289705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.1200 | 2.05895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.32355 | 0.436873 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.1407 | −1.21124 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.0174 | 1.35810 | 0.679048 | − | 0.734094i | \(-0.262393\pi\) | ||||
0.679048 | + | 0.734094i | \(0.262393\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.669663 | −0.0348613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.0518 | −1.19679 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.6393 | −1.58644 | −0.793222 | − | 0.608933i | \(-0.791598\pi\) | ||||
−0.793222 | + | 0.608933i | \(0.791598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −39.9556 | −2.06330 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.97589 | 0.153266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.4667 | −1.20540 | −0.602702 | − | 0.797967i | \(-0.705909\pi\) | ||||
−0.602702 | + | 0.797967i | \(0.705909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.65330 | −0.289627 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.4316 | 1.35059 | 0.675295 | − | 0.737548i | \(-0.264016\pi\) | ||||
0.675295 | + | 0.737548i | \(0.264016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 47.3290 | 2.41211 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.58772 | 0.182374 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.36128 | 0.373232 | 0.186616 | − | 0.982433i | \(-0.440248\pi\) | ||||
0.186616 | + | 0.982433i | \(0.440248\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.66949 | −0.135002 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.0869 | −0.559259 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.3677 | 0.672604 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.8664 | 1.80008 | 0.900042 | − | 0.435803i | \(-0.143536\pi\) | ||||
0.900042 | + | 0.435803i | \(0.143536\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.9913 | −1.85188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.2193 | 1.50908 | 0.754540 | − | 0.656254i | \(-0.227860\pi\) | ||||
0.754540 | + | 0.656254i | \(0.227860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.3934 | −0.667174 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.2382 | 1.60193 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.99838 | −0.0990558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.72859 | 0.233814 | 0.116907 | − | 0.993143i | \(-0.462702\pi\) | ||||
0.116907 | + | 0.993143i | \(0.462702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.182099 | −0.00898230 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.01216 | 0.197425 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.19448 | −0.254987 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.09789 | 0.445526 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.38803 | −0.0678096 | −0.0339048 | − | 0.999425i | \(-0.510794\pi\) | ||||
−0.0339048 | + | 0.999425i | \(0.510794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.4264 | −1.38542 | −0.692710 | − | 0.721216i | \(-0.743583\pi\) | ||||
−0.692710 | + | 0.721216i | \(0.743583\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.73853 | 0.133152 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.9853 | −0.678386 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.4990 | 1.52434 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.5988 | 0.801400 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.2800 | 0.784182 | 0.392091 | − | 0.919926i | \(-0.371752\pi\) | ||||
0.392091 | + | 0.919926i | \(0.371752\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6223 | 0.846873 | 0.423436 | − | 0.905926i | \(-0.360824\pi\) | ||||
0.423436 | + | 0.905926i | \(0.360824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.80073 | −0.374016 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.0903 | 0.769705 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7183 | −0.845648 | −0.422824 | − | 0.906212i | \(-0.638961\pi\) | ||||
−0.422824 | + | 0.906212i | \(0.638961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.489958 | −0.0233313 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.8836 | 1.32479 | 0.662395 | − | 0.749155i | \(-0.269540\pi\) | ||||
0.662395 | + | 0.749155i | \(0.269540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 56.0008 | 2.65469 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.8135 | 0.558759 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.75914 | 0.366176 | 0.183088 | − | 0.983096i | \(-0.441391\pi\) | ||||
0.183088 | + | 0.983096i | \(0.441391\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.24659 | 0.435405 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.1839 | −1.04229 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.7228 | 1.39342 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1166 | 0.473232 | 0.236616 | − | 0.971603i | \(-0.423962\pi\) | ||||
0.236616 | + | 0.971603i | \(0.423962\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.85041 | 0.319750 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.9150 | 1.06726 | 0.533630 | − | 0.845718i | \(-0.320828\pi\) | ||||
0.533630 | + | 0.845718i | \(0.320828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.0040 | −1.81267 | −0.906335 | − | 0.422561i | \(-0.861131\pi\) | ||||
−0.906335 | + | 0.422561i | \(0.861131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 35.1083 | 1.62811 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.9689 | −1.52562 | −0.762809 | − | 0.646624i | \(-0.776180\pi\) | ||||
−0.762809 | + | 0.646624i | \(0.776180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.1713 | 0.654370 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.9901 | −1.05933 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −49.5386 | −2.27779 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 84.2964 | 3.86778 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.26952 | −0.103914 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.10151 | 0.278785 | 0.139392 | − | 0.990237i | \(-0.455485\pi\) | ||||
0.139392 | + | 0.990237i | \(0.455485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.25499 | −0.0572224 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.2409 | −0.465978 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.50624 | 0.250026 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2887 | 0.466224 | 0.233112 | − | 0.972450i | \(-0.425109\pi\) | ||||
0.233112 | + | 0.972450i | \(0.425109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.1593 | −1.31863 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.7687 | −1.79473 | −0.897367 | − | 0.441284i | \(-0.854523\pi\) | ||||
−0.897367 | + | 0.441284i | \(0.854523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.49574 | −0.0673649 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.65970 | 0.209438 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.8351 | 1.29343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.7840 | −1.87051 | −0.935255 | − | 0.353975i | \(-0.884830\pi\) | ||||
−0.935255 | + | 0.353975i | \(0.884830\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0924 | 1.07637 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.1299 | −1.38801 | −0.694007 | − | 0.719968i | \(-0.744156\pi\) | ||||
−0.694007 | + | 0.719968i | \(0.744156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −56.1864 | −2.50026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.9758 | −0.487452 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.9533 | −0.529819 | −0.264909 | − | 0.964273i | \(-0.585342\pi\) | ||||
−0.264909 | + | 0.964273i | \(0.585342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.0219 | −0.753007 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −41.2908 | −1.82304 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.6900 | 1.08797 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.8131 | −1.66302 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.2239 | 1.37058 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.0829 | 1.62463 | 0.812317 | − | 0.583217i | \(-0.198206\pi\) | ||||
0.812317 | + | 0.583217i | \(0.198206\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.2972 | −1.41226 | −0.706128 | − | 0.708084i | \(-0.749560\pi\) | ||||
−0.706128 | + | 0.708084i | \(0.749560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −53.6517 | −2.34155 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.73180 | 0.293242 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5454 | −0.806324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.395010 | 0.0171420 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.80688 | 0.251524 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −76.3132 | −3.29931 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.6010 | −1.36368 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.76525 | 0.291400 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3496 | 0.487957 | 0.243979 | − | 0.969781i | \(-0.421547\pi\) | ||||
0.243979 | + | 0.969781i | \(0.421547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.7989 | −1.15005 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.1609 | −0.863597 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2669 | −0.481737 | −0.240868 | − | 0.970558i | \(-0.577432\pi\) | ||||
−0.240868 | + | 0.970558i | \(0.577432\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.10118 | 0.132355 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.01559 | 0.384077 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.83311 | 0.418147 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.28971 | 0.139640 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.62858 | 0.153748 | 0.0768740 | − | 0.997041i | \(-0.475506\pi\) | ||||
0.0768740 | + | 0.997041i | \(0.475506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.1104 | −1.31583 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.34292 | −0.352238 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.09947 | 0.214917 | 0.107458 | − | 0.994210i | \(-0.465729\pi\) | ||||
0.107458 | + | 0.994210i | \(0.465729\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 57.2450 | 2.40832 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.7140 | 0.995893 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.4211 | −0.520718 | −0.260359 | − | 0.965512i | \(-0.583841\pi\) | ||||
−0.260359 | + | 0.965512i | \(0.583841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.4521 | −1.65102 | −0.825509 | − | 0.564390i | \(-0.809112\pi\) | ||||
−0.825509 | + | 0.564390i | \(0.809112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.2312 | −1.68068 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.3372 | 0.973228 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6957 | 0.445269 | 0.222634 | − | 0.974902i | \(-0.428534\pi\) | ||||
0.222634 | + | 0.974902i | \(0.428534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.1546 | 0.629804 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.82099 | −0.158521 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.3371 | 1.29785 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.92630 | 0.120988 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.90373 | 0.119850 | 0.0599248 | − | 0.998203i | \(-0.480914\pi\) | ||||
0.0599248 | + | 0.998203i | \(0.480914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.5760 | −1.67190 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.8461 | −0.692955 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.79111 | −0.319943 | −0.159971 | − | 0.987122i | \(-0.551140\pi\) | ||||
−0.159971 | + | 0.987122i | \(0.551140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.9393 | −0.612450 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.2333 | 0.909947 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.6048 | −0.555878 | −0.277939 | − | 0.960599i | \(-0.589651\pi\) | ||||
−0.277939 | + | 0.960599i | \(0.589651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.8000 | −0.481333 | −0.240666 | − | 0.970608i | \(-0.577366\pi\) | ||||
−0.240666 | + | 0.970608i | \(0.577366\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.39521 | 0.0568174 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.2617 | −0.823754 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.8716 | 1.37480 | 0.687402 | − | 0.726277i | \(-0.258751\pi\) | ||||
0.687402 | + | 0.726277i | \(0.258751\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.73810 | −0.232520 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.7467 | −0.960690 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50660 | 0.141630 | 0.0708150 | − | 0.997489i | \(-0.477440\pi\) | ||||
0.0708150 | + | 0.997489i | \(0.477440\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.2216 | −0.613796 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.8534 | −1.16159 | −0.580796 | − | 0.814049i | \(-0.697259\pi\) | ||||
−0.580796 | + | 0.814049i | \(0.697259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1357 | 0.447581 | 0.223791 | − | 0.974637i | \(-0.428157\pi\) | ||||
0.223791 | + | 0.974637i | \(0.428157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4312 | −0.458720 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41.1934 | 1.65038 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 41.9761 | 1.67904 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 50.2869 | 2.00827 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.630781 | 0.0251509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.89236 | −0.393809 | −0.196904 | − | 0.980423i | \(-0.563089\pi\) | ||||
−0.196904 | + | 0.980423i | \(0.563089\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.9577 | −1.58818 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.7616 | 0.546112 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.24860 | 0.168335 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.83892 | 0.112306 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.1693 | −0.875636 | −0.437818 | − | 0.899064i | \(-0.644249\pi\) | ||||
−0.437818 | + | 0.899064i | \(0.644249\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.7707 | −1.41066 | −0.705330 | − | 0.708879i | \(-0.749201\pi\) | ||||
−0.705330 | + | 0.708879i | \(0.749201\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 81.5499 | 3.21102 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.8800 | −1.25333 | −0.626666 | − | 0.779288i | \(-0.715581\pi\) | ||||
−0.626666 | + | 0.779288i | \(0.715581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.45423 | −0.214097 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.8252 | 1.01217 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.0375 | 1.17546 | 0.587729 | − | 0.809058i | \(-0.300022\pi\) | ||||
0.587729 | + | 0.809058i | \(0.300022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.9883 | 1.05452 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.67587 | −0.0653818 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.8170 | 0.499279 | 0.249640 | − | 0.968339i | \(-0.419688\pi\) | ||||
0.249640 | + | 0.968339i | \(0.419688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.1905 | −1.67992 | −0.839958 | − | 0.542651i | \(-0.817421\pi\) | ||||
−0.839958 | + | 0.542651i | \(0.817421\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.23937 | −0.203480 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 90.0464 | 3.49185 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.49594 | 0.0966431 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.88109 | 0.150052 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.8205 | −1.65307 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.0699 | −1.93005 | −0.965027 | − | 0.262152i | \(-0.915568\pi\) | ||||
−0.965027 | + | 0.262152i | \(0.915568\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −59.8876 | −2.30508 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.04693 | 0.155536 | 0.0777681 | − | 0.996971i | \(-0.475221\pi\) | ||||
0.0777681 | + | 0.996971i | \(0.475221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.05031 | 0.155437 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.6633 | −1.21334 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.8028 | 1.52301 | 0.761505 | − | 0.648159i | \(-0.224461\pi\) | ||||
0.761505 | + | 0.648159i | \(0.224461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.443277 | 0.0169367 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0655872 | 0.00250231 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.6798 | 0.749741 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.2702 | 1.76020 | 0.880101 | − | 0.474786i | \(-0.157474\pi\) | ||||
0.880101 | + | 0.474786i | \(0.157474\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.42761 | 0.130204 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.1466 | −0.840069 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.91866 | −0.110552 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.8819 | 0.714179 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.5193 | 1.71924 | 0.859619 | − | 0.510935i | \(-0.170701\pi\) | ||||
0.859619 | + | 0.510935i | \(0.170701\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.80204 | −0.143396 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 62.2475 | 2.34438 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.3299 | −1.55437 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3814 | 0.540105 | 0.270052 | − | 0.962846i | \(-0.412959\pi\) | ||||
0.270052 | + | 0.962846i | \(0.412959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.968103 | 0.0363067 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.2333 | −0.420691 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.4059 | −1.51109 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.640078 | 0.0239041 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.7714 | −0.625468 | −0.312734 | − | 0.949841i | \(-0.601245\pi\) | ||||
−0.312734 | + | 0.949841i | \(0.601245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.1616 | 0.676372 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.0877 | −1.30493 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.0761 | 0.485633 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.93316 | −0.220049 | −0.110024 | − | 0.993929i | \(-0.535093\pi\) | ||||
−0.110024 | + | 0.993929i | \(0.535093\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0821 | 1.07711 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.6367 | 0.578344 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.99744 | 0.369264 | 0.184632 | − | 0.982808i | \(-0.440891\pi\) | ||||
0.184632 | + | 0.982808i | \(0.440891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.1369 | −0.410790 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.2648 | −0.709629 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3337 | −0.380132 | −0.190066 | − | 0.981771i | \(-0.560870\pi\) | ||||
−0.190066 | + | 0.981771i | \(0.560870\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.5803 | 1.16013 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.8387 | 1.75503 | 0.877515 | − | 0.479549i | \(-0.159200\pi\) | ||||
0.877515 | + | 0.479549i | \(0.159200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.7571 | −1.05358 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.376189 | −0.0137640 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −56.1349 | −2.05113 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.4574 | −0.491067 | −0.245534 | − | 0.969388i | \(-0.578963\pi\) | ||||
−0.245534 | + | 0.969388i | \(0.578963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.64615 | 0.0599889 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.0013 | 1.96531 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.3385 | 1.57516 | 0.787581 | − | 0.616211i | \(-0.211333\pi\) | ||||
0.787581 | + | 0.616211i | \(0.211333\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.9218 | 0.505328 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8808 | 0.394429 | 0.197214 | − | 0.980360i | \(-0.436811\pi\) | ||||
0.197214 | + | 0.980360i | \(0.436811\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.8300 | −0.536884 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.47082 | −0.0531776 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.42527 | −0.123679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.78016 | 0.244499 | 0.122249 | − | 0.992499i | \(-0.460989\pi\) | ||||
0.122249 | + | 0.992499i | \(0.460989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.9917 | 1.40425 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.5175 | −0.414255 | −0.207128 | − | 0.978314i | \(-0.566412\pi\) | ||||
−0.207128 | + | 0.978314i | \(0.566412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −58.8508 | −2.11398 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.41986 | 0.0868120 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.5922 | 0.630306 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.1992 | −1.40266 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.40505 | −0.228898 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.9638 | 1.99743 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.78796 | −0.313257 | −0.156628 | − | 0.987658i | \(-0.550063\pi\) | ||||
−0.156628 | + | 0.987658i | \(0.550063\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.93127 | −0.104356 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.1086 | 1.49721 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.8914 | −0.954942 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −51.5869 | −1.82960 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.1814 | −0.679441 | −0.339720 | − | 0.940526i | \(-0.610332\pi\) | ||||
−0.339720 | + | 0.940526i | \(0.610332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.9356 | 0.422251 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.05563 | 0.143298 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.1401 | 0.816595 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.9291 | 0.878634 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.6357 | −1.28964 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 55.3029 | 1.94435 | 0.972173 | − | 0.234263i | \(-0.0752676\pi\) | ||||
0.972173 | + | 0.234263i | \(0.0752676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.59127 | 0.336795 | 0.168398 | − | 0.985719i | \(-0.446141\pi\) | ||||
0.168398 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.79905 | −0.238453 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 70.9814 | 2.48637 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −94.2502 | −3.29740 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.15255 | 0.0752161 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.4468 | −1.65590 | −0.827952 | − | 0.560798i | \(-0.810494\pi\) | ||||
−0.827952 | + | 0.560798i | \(0.810494\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.2924 | 0.358771 | 0.179386 | − | 0.983779i | \(-0.442589\pi\) | ||||
0.179386 | + | 0.983779i | \(0.442589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 72.9354 | 2.53929 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.8336 | −0.446267 | −0.223133 | − | 0.974788i | \(-0.571629\pi\) | ||||
−0.223133 | + | 0.974788i | \(0.571629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5004 | 0.399424 | 0.199712 | − | 0.979855i | \(-0.435999\pi\) | ||||
0.199712 | + | 0.979855i | \(0.435999\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.2991 | −0.808238 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.13543 | −0.0739883 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −58.6472 | −2.02957 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.8268 | 0.996401 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0027 | −0.448904 | −0.224452 | − | 0.974485i | \(-0.572059\pi\) | ||||
−0.224452 | + | 0.974485i | \(0.572059\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6015 | −0.951776 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.4056 | 0.530597 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.7179 | 0.919124 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.9042 | −0.512114 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.8876 | 0.579579 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.05258 | −0.0360820 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.2359 | −1.44613 | −0.723064 | − | 0.690781i | \(-0.757267\pi\) | ||||
−0.723064 | + | 0.690781i | \(0.757267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.86537 | 0.303189 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.08818 | −0.139650 | −0.0698248 | − | 0.997559i | \(-0.522244\pi\) | ||||
−0.0698248 | + | 0.997559i | \(0.522244\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.01949 | −0.137143 | −0.0685716 | − | 0.997646i | \(-0.521844\pi\) | ||||
−0.0685716 | + | 0.997646i | \(0.521844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.1968 | −0.381586 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.7841 | 0.537296 | 0.268648 | − | 0.963238i | \(-0.413423\pi\) | ||||
0.268648 | + | 0.963238i | \(0.413423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −76.0070 | −2.58432 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.3511 | −0.860968 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.3674 | −0.453458 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0984 | −0.409937 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.398767 | 0.0134962 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 71.5447 | 2.41865 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.4264 | 1.56771 | 0.783853 | − | 0.620946i | \(-0.213251\pi\) | ||||
0.783853 | + | 0.620946i | \(0.213251\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8203 | 0.837170 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.42346 | −0.0479575 | −0.0239788 | − | 0.999712i | \(-0.507633\pi\) | ||||
−0.0239788 | + | 0.999712i | \(0.507633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9966 | −0.538329 | −0.269164 | − | 0.963094i | \(-0.586748\pi\) | ||||
−0.269164 | + | 0.963094i | \(0.586748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.97869 | 0.301815 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.5685 | 1.36216 | 0.681078 | − | 0.732210i | \(-0.261511\pi\) | ||||
0.681078 | + | 0.732210i | \(0.261511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1228 | 0.339509 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.2374 | −1.07999 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −71.9418 | −2.40744 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 76.9249 | 2.57132 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.74291 | 0.291917 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.29416 | −0.209922 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.89148 | −0.329533 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 59.9869 | 1.99624 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 65.2354 | 2.16850 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.716666 | 0.0237965 | 0.0118983 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118983 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.06907 | −0.134962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.6532 | −0.849928 | −0.424964 | − | 0.905210i | \(-0.639713\pi\) | ||||
−0.424964 | + | 0.905210i | \(0.639713\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.19435 | 0.171908 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 70.4907 | 2.33035 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.8522 | 0.655578 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.9330 | −0.657531 | −0.328765 | − | 0.944412i | \(-0.606632\pi\) | ||||
−0.328765 | + | 0.944412i | \(0.606632\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.8237 | 1.41109 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.6172 | −0.810286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.51442 | −0.181313 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.78807 | 0.0587278 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −60.6545 | −1.99001 | −0.995005 | − | 0.0998220i | \(-0.968173\pi\) | ||||
−0.995005 | + | 0.0998220i | \(0.968173\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.8713 | 0.421840 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.9235 | −0.881437 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.3088 | 0.664169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5007 | 0.604390 | 0.302195 | − | 0.953246i | \(-0.402281\pi\) | ||||
0.302195 | + | 0.953246i | \(0.402281\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.5547 | 1.38872 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.339309 | −0.0110611 | −0.00553057 | − | 0.999985i | \(-0.501760\pi\) | ||||
−0.00553057 | + | 0.999985i | \(0.501760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.87035 | 0.158600 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −63.9727 | −2.08103 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.1857 | 0.363487 | 0.181743 | − | 0.983346i | \(-0.441826\pi\) | ||||
0.181743 | + | 0.983346i | \(0.441826\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.5320 | 0.471730 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.36233 | −0.0766037 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.5040 | −1.15009 | −0.575044 | − | 0.818123i | \(-0.695015\pi\) | ||||
−0.575044 | + | 0.818123i | \(0.695015\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 97.9331 | 3.16904 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.80053 | 0.252155 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.326068 | 0.0105293 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.67225 | −0.0862017 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.52667 | −0.178094 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.8903 | −1.18754 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.6415 | 1.46773 | 0.733865 | − | 0.679295i | \(-0.237714\pi\) | ||||
0.733865 | + | 0.679295i | \(0.237714\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.8729 | −0.509912 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5138 | −0.465770 | −0.232885 | − | 0.972504i | \(-0.574817\pi\) | ||||
−0.232885 | + | 0.972504i | \(0.574817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.2907 | −0.522257 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 45.8036 | 1.46689 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.9724 | 0.766946 | 0.383473 | − | 0.923552i | \(-0.374728\pi\) | ||||
0.383473 | + | 0.923552i | \(0.374728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −55.9993 | −1.78975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.46007 | −0.0466163 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.4862 | 0.493933 | 0.246966 | − | 0.969024i | \(-0.420566\pi\) | ||||
0.246966 | + | 0.969024i | \(0.420566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.0077 | 1.30661 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 45.7884 | 1.45746 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.0929 | −0.829705 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.1189 | 0.734396 | 0.367198 | − | 0.930143i | \(-0.380317\pi\) | ||||
0.367198 | + | 0.930143i | \(0.380317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.7257 | −0.403837 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.1215 | −1.71577 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9176 | −0.567456 | −0.283728 | − | 0.958905i | \(-0.591571\pi\) | ||||
−0.283728 | + | 0.958905i | \(0.591571\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.70112 | 0.0854597 |
(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 | 4016.2.a.j.1.11 | 14 | ||
4.3 | odd | 2 | 1004.2.a.b.1.4 | ✓ | 14 | ||
12.11 | even | 2 | 9036.2.a.m.1.13 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.b.1.4 | ✓ | 14 | 4.3 | odd | 2 | ||
4016.2.a.j.1.11 | 14 | 1.1 | even | 1 | trivial | ||
9036.2.a.m.1.13 | 14 | 12.11 | even | 2 |