Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7448,2,Mod(1,7448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7448, 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("7448.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7448.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: | \(59.4725794254\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.98211824.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 6x^{4} + 15x^{3} + 8x^{2} - 9x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.511631\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7448.1 |
$q$-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 | ||||||||
\(3\) | 0.488369 | 0.281960 | 0.140980 | − | 0.990012i | \(-0.454975\pi\) | ||||
0.140980 | + | 0.990012i | \(0.454975\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.51566 | −1.57225 | −0.786125 | − | 0.618068i | \(-0.787916\pi\) | ||||
−0.786125 | + | 0.618068i | \(0.787916\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.76150 | −0.920499 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.25811 | −0.680845 | −0.340423 | − | 0.940273i | \(-0.610570\pi\) | ||||
−0.340423 | + | 0.940273i | \(0.610570\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.21264 | −0.613676 | −0.306838 | − | 0.951762i | \(-0.599271\pi\) | ||||
−0.306838 | + | 0.951762i | \(0.599271\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.71694 | −0.443312 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.716938 | −0.173883 | −0.0869415 | − | 0.996213i | \(-0.527709\pi\) | ||||
−0.0869415 | + | 0.996213i | \(0.527709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.53470 | −1.57109 | −0.785547 | − | 0.618802i | \(-0.787618\pi\) | ||||
−0.785547 | + | 0.618802i | \(0.787618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.35984 | 1.47197 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.81374 | −0.541504 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.66391 | −1.42315 | −0.711576 | − | 0.702609i | \(-0.752018\pi\) | ||||
−0.711576 | + | 0.702609i | \(0.752018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.473849 | 0.0851058 | 0.0425529 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425529 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.10279 | −0.191971 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.268043 | −0.0440660 | −0.0220330 | − | 0.999757i | \(-0.507014\pi\) | ||||
−0.0220330 | + | 0.999757i | \(0.507014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.08059 | −0.173032 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.9093 | −1.85991 | −0.929956 | − | 0.367670i | \(-0.880156\pi\) | ||||
−0.929956 | + | 0.367670i | \(0.880156\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.26213 | −0.954966 | −0.477483 | − | 0.878641i | \(-0.658451\pi\) | ||||
−0.477483 | + | 0.878641i | \(0.658451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.70847 | 1.44725 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.10998 | 1.03710 | 0.518548 | − | 0.855048i | \(-0.326473\pi\) | ||||
0.518548 | + | 0.855048i | \(0.326473\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.350131 | −0.0490281 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.16643 | −0.297583 | −0.148791 | − | 0.988869i | \(-0.547538\pi\) | ||||
−0.148791 | + | 0.988869i | \(0.547538\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.93873 | 1.07046 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.488369 | −0.0646861 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0795286 | −0.0103537 | −0.00517687 | − | 0.999987i | \(-0.501648\pi\) | ||||
−0.00517687 | + | 0.999987i | \(0.501648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.1946 | 1.94547 | 0.972734 | − | 0.231925i | \(-0.0745022\pi\) | ||||
0.972734 | + | 0.231925i | \(0.0745022\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.77889 | 0.964852 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.97595 | 0.974418 | 0.487209 | − | 0.873285i | \(-0.338015\pi\) | ||||
0.487209 | + | 0.873285i | \(0.338015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.67972 | −0.442986 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.764655 | 0.0907479 | 0.0453739 | − | 0.998970i | \(-0.485552\pi\) | ||||
0.0453739 | + | 0.998970i | \(0.485552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2795 | −1.20313 | −0.601564 | − | 0.798825i | \(-0.705455\pi\) | ||||
−0.601564 | + | 0.798825i | \(0.705455\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.59432 | 0.415036 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.9272 | −1.67945 | −0.839723 | − | 0.543015i | \(-0.817283\pi\) | ||||
−0.839723 | + | 0.543015i | \(0.817283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.91034 | 0.767816 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.68887 | −0.404906 | −0.202453 | − | 0.979292i | \(-0.564891\pi\) | ||||
−0.202453 | + | 0.979292i | \(0.564891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.52051 | 0.273388 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.74282 | −0.401272 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.22816 | 0.236184 | 0.118092 | − | 0.993003i | \(-0.462322\pi\) | ||||
0.118092 | + | 0.993003i | \(0.462322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.231413 | 0.0239964 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.51566 | 0.360699 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.09236 | 0.720120 | 0.360060 | − | 0.932929i | \(-0.382756\pi\) | ||||
0.360060 | + | 0.932929i | \(0.382756\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.23575 | 0.626717 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.61873 | 0.559085 | 0.279542 | − | 0.960133i | \(-0.409817\pi\) | ||||
0.279542 | + | 0.960133i | \(0.409817\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.529025 | −0.0521263 | −0.0260632 | − | 0.999660i | \(-0.508297\pi\) | ||||
−0.0260632 | + | 0.999660i | \(0.508297\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.1976 | −1.56588 | −0.782938 | − | 0.622099i | \(-0.786280\pi\) | ||||
−0.782938 | + | 0.622099i | \(0.786280\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.24340 | 0.885357 | 0.442678 | − | 0.896680i | \(-0.354028\pi\) | ||||
0.442678 | + | 0.896680i | \(0.354028\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.130904 | −0.0124249 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.3591 | −0.974498 | −0.487249 | − | 0.873263i | \(-0.662000\pi\) | ||||
−0.487249 | + | 0.873263i | \(0.662000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.4894 | 2.47015 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.11020 | 0.564888 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.90095 | −0.536450 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.81611 | −0.524421 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.29639 | −0.742052 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9388 | −1.14813 | −0.574066 | − | 0.818809i | \(-0.694635\pi\) | ||||
−0.574066 | + | 0.818809i | \(0.694635\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.05823 | −0.269262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.5212 | −1.53084 | −0.765419 | − | 0.643533i | \(-0.777468\pi\) | ||||
−0.765419 | + | 0.643533i | \(0.777468\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.89213 | 0.851379 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.30076 | 0.623746 | 0.311873 | − | 0.950124i | \(-0.399044\pi\) | ||||
0.311873 | + | 0.950124i | \(0.399044\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.40692 | 0.713066 | 0.356533 | − | 0.934283i | \(-0.383959\pi\) | ||||
0.356533 | + | 0.934283i | \(0.383959\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.47229 | 0.292420 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.99638 | 0.417819 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.9437 | 2.23755 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.99634 | 0.491239 | 0.245620 | − | 0.969366i | \(-0.421009\pi\) | ||||
0.245620 | + | 0.969366i | \(0.421009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0572 | −1.79499 | −0.897494 | − | 0.441027i | \(-0.854614\pi\) | ||||
−0.897494 | + | 0.441027i | \(0.854614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.97982 | 0.160059 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.66589 | −0.133808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.7625 | 1.65703 | 0.828513 | − | 0.559969i | \(-0.189187\pi\) | ||||
0.828513 | + | 0.559969i | \(0.189187\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.05802 | −0.0839064 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0347 | 0.785982 | 0.392991 | − | 0.919542i | \(-0.371440\pi\) | ||||
0.392991 | + | 0.919542i | \(0.371440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.87703 | 0.301826 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.4994 | 0.889854 | 0.444927 | − | 0.895567i | \(-0.353230\pi\) | ||||
0.444927 | + | 0.895567i | \(0.353230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.10422 | −0.623401 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.76150 | 0.211177 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.407066 | 0.0309487 | 0.0154743 | − | 0.999880i | \(-0.495074\pi\) | ||||
0.0154743 | + | 0.999880i | \(0.495074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0388393 | −0.00291934 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0666375 | 0.00498072 | 0.00249036 | − | 0.999997i | \(-0.499207\pi\) | ||||
0.00249036 | + | 0.999997i | \(0.499207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.64418 | −0.568188 | −0.284094 | − | 0.958796i | \(-0.591693\pi\) | ||||
−0.284094 | + | 0.958796i | \(0.591693\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.42057 | 0.548544 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.942348 | 0.0692828 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.61892 | 0.118387 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8535 | −0.857687 | −0.428844 | − | 0.903379i | \(-0.641079\pi\) | ||||
−0.428844 | + | 0.903379i | \(0.641079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.34976 | 0.529047 | 0.264523 | − | 0.964379i | \(-0.414785\pi\) | ||||
0.264523 | + | 0.964379i | \(0.414785\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.79897 | 0.272050 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.2535 | 1.44300 | 0.721500 | − | 0.692414i | \(-0.243453\pi\) | ||||
0.721500 | + | 0.692414i | \(0.243453\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8733 | 1.19611 | 0.598057 | − | 0.801453i | \(-0.295940\pi\) | ||||
0.598057 | + | 0.801453i | \(0.295940\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.89521 | 0.274747 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 41.8688 | 2.92425 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.8070 | 1.44619 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.25811 | 0.156197 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9286 | 0.821197 | 0.410598 | − | 0.911816i | \(-0.365320\pi\) | ||||
0.410598 | + | 0.911816i | \(0.365320\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.373434 | 0.0255873 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.0155 | 1.50145 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.02020 | −0.339234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.58633 | 0.106708 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.2754 | −1.55863 | −0.779317 | − | 0.626630i | \(-0.784434\pi\) | ||||
−0.779317 | + | 0.626630i | \(0.784434\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.3242 | −1.35494 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.56606 | −0.103943 | −0.0519714 | − | 0.998649i | \(-0.516550\pi\) | ||||
−0.0519714 | + | 0.998649i | \(0.516550\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8669 | 0.916350 | 0.458175 | − | 0.888862i | \(-0.348503\pi\) | ||||
0.458175 | + | 0.888862i | \(0.348503\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.3117 | −0.937590 | −0.468795 | − | 0.883307i | \(-0.655312\pi\) | ||||
−0.468795 | + | 0.883307i | \(0.655312\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.9962 | −1.63057 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.29000 | −0.473537 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.4532 | 1.77580 | 0.887899 | − | 0.460037i | \(-0.152164\pi\) | ||||
0.887899 | + | 0.460037i | \(0.152164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.58000 | −0.552686 | −0.276343 | − | 0.961059i | \(-0.589123\pi\) | ||||
−0.276343 | + | 0.961059i | \(0.589123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.8160 | 0.757997 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.21264 | 0.140787 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.80153 | −0.114167 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.23766 | −0.204359 | −0.102180 | − | 0.994766i | \(-0.532582\pi\) | ||||
−0.102180 | + | 0.994766i | \(0.532582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.0142 | 1.06967 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.23094 | 0.0770844 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.41758 | 0.0884263 | 0.0442132 | − | 0.999022i | \(-0.485922\pi\) | ||||
0.0442132 | + | 0.999022i | \(0.485922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.1639 | 1.31001 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.57536 | −0.158803 | −0.0794017 | − | 0.996843i | \(-0.525301\pi\) | ||||
−0.0794017 | + | 0.996843i | \(0.525301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.61644 | 0.467874 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.08816 | 0.0665946 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.9509 | −0.667685 | −0.333843 | − | 0.942629i | \(-0.608345\pi\) | ||||
−0.333843 | + | 0.942629i | \(0.608345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1518 | 1.40637 | 0.703186 | − | 0.711006i | \(-0.251760\pi\) | ||||
0.703186 | + | 0.711006i | \(0.251760\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.6193 | −1.00218 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0972 | −0.847017 | −0.423508 | − | 0.905892i | \(-0.639202\pi\) | ||||
−0.423508 | + | 0.905892i | \(0.639202\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.30853 | −0.0783398 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.341082 | 0.0203473 | 0.0101736 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101736 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.97496 | 0.592950 | 0.296475 | − | 0.955041i | \(-0.404189\pi\) | ||||
0.296475 | + | 0.955041i | \(0.404189\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.71694 | 0.101703 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4860 | −0.969765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.46369 | 0.203045 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.6737 | −1.26619 | −0.633097 | − | 0.774073i | \(-0.718216\pi\) | ||||
−0.633097 | + | 0.774073i | \(0.718216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.279595 | 0.0162787 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.35372 | 0.368680 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.6716 | 0.964143 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.74402 | 0.157640 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −53.4189 | −3.05876 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.6231 | 1.17702 | 0.588510 | − | 0.808490i | \(-0.299715\pi\) | ||||
0.588510 | + | 0.808490i | \(0.299715\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.258359 | −0.0146975 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.92634 | 0.449461 | 0.224731 | − | 0.974421i | \(-0.427850\pi\) | ||||
0.224731 | + | 0.974421i | \(0.427850\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7662 | −0.608542 | −0.304271 | − | 0.952586i | \(-0.598413\pi\) | ||||
−0.304271 | + | 0.952586i | \(0.598413\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.02183 | −0.450551 | −0.225275 | − | 0.974295i | \(-0.572328\pi\) | ||||
−0.225275 | + | 0.974295i | \(0.572328\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.3059 | 0.968947 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.91039 | −0.441515 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.716938 | 0.0398915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.2847 | −0.903312 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.51419 | 0.249635 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5703 | 0.690928 | 0.345464 | − | 0.938432i | \(-0.387722\pi\) | ||||
0.345464 | + | 0.938432i | \(0.387722\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.740200 | 0.0405627 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.0407 | −1.53203 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.7552 | 1.40297 | 0.701487 | − | 0.712683i | \(-0.252520\pi\) | ||||
0.701487 | + | 0.712683i | \(0.252520\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.05904 | −0.274770 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.07000 | −0.0579439 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.9366 | 0.696484 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.18123 | 0.331826 | 0.165913 | − | 0.986140i | \(-0.446943\pi\) | ||||
0.165913 | + | 0.986140i | \(0.446943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.99215 | 0.481339 | 0.240669 | − | 0.970607i | \(-0.422633\pi\) | ||||
0.240669 | + | 0.970607i | \(0.422633\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.22579 | 0.332308 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.0593 | −0.907977 | −0.453989 | − | 0.891007i | \(-0.649999\pi\) | ||||
−0.453989 | + | 0.891007i | \(0.649999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.68827 | −0.142678 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6501 | 0.878757 | 0.439379 | − | 0.898302i | \(-0.355199\pi\) | ||||
0.439379 | + | 0.898302i | \(0.355199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.88184 | −0.151257 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.1393 | 1.89162 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.1117 | 1.72842 | 0.864209 | − | 0.503134i | \(-0.167820\pi\) | ||||
0.864209 | + | 0.503134i | \(0.167820\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.8873 | 1.71205 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.2511 | 1.72167 | 0.860837 | − | 0.508880i | \(-0.169940\pi\) | ||||
0.860837 | + | 0.508880i | \(0.169940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.05170 | −0.209229 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.9575 | 0.873355 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.1510 | −1.44602 | −0.723011 | − | 0.690837i | \(-0.757242\pi\) | ||||
−0.723011 | + | 0.690837i | \(0.757242\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.31891 | −0.323727 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.7648 | 1.16323 | 0.581614 | − | 0.813465i | \(-0.302421\pi\) | ||||
0.581614 | + | 0.813465i | \(0.302421\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.2929 | 0.879045 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.90959 | −0.198224 | −0.0991121 | − | 0.995076i | \(-0.531600\pi\) | ||||
−0.0991121 | + | 0.995076i | \(0.531600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.40192 | 0.273187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.55683 | −0.431635 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 52.4790 | 2.64051 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.80489 | −0.341527 | −0.170764 | − | 0.985312i | \(-0.554623\pi\) | ||||
−0.170764 | + | 0.985312i | \(0.554623\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.05449 | −0.452160 | −0.226080 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226080 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.04846 | −0.0522274 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.2944 | −1.20720 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.605270 | 0.0300021 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.697334 | 0.0344810 | 0.0172405 | − | 0.999851i | \(-0.494512\pi\) | ||||
0.0172405 | + | 0.999851i | \(0.494512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.56547 | 0.175872 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9688 | 0.636613 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.10568 | 0.201056 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.91019 | −0.484145 | −0.242072 | − | 0.970258i | \(-0.577827\pi\) | ||||
−0.242072 | + | 0.970258i | \(0.577827\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.5825 | −1.14934 | −0.574670 | − | 0.818385i | \(-0.694870\pi\) | ||||
−0.574670 | + | 0.818385i | \(0.694870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.6342 | −0.954646 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.27655 | −0.255950 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.44008 | 0.117808 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.43559 | 0.0691498 | 0.0345749 | − | 0.999402i | \(-0.488992\pi\) | ||||
0.0345749 | + | 0.999402i | \(0.488992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.4216 | −1.79837 | −0.899185 | − | 0.437569i | \(-0.855839\pi\) | ||||
−0.899185 | + | 0.437569i | \(0.855839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.1585 | 0.630900 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.53470 | 0.360434 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.2865 | −1.39777 | −0.698885 | − | 0.715234i | \(-0.746320\pi\) | ||||
−0.698885 | + | 0.715234i | \(0.746320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.27913 | 0.108285 | 0.0541424 | − | 0.998533i | \(-0.482757\pi\) | ||||
0.0541424 | + | 0.998533i | \(0.482757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.83344 | −0.371341 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.92843 | 0.138510 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.22719 | 0.246686 | 0.123343 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123343 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.8924 | 1.26631 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.7720 | −0.506115 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.2735 | −1.50969 | −0.754845 | − | 0.655903i | \(-0.772288\pi\) | ||||
−0.754845 | + | 0.655903i | \(0.772288\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.01728 | 0.0941584 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.1333 | −1.21715 | −0.608576 | − | 0.793496i | \(-0.708259\pi\) | ||||
−0.608576 | + | 0.793496i | \(0.708259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.42014 | 0.298369 | 0.149185 | − | 0.988809i | \(-0.452335\pi\) | ||||
0.149185 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.813570 | −0.0377284 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.8516 | −1.01117 | −0.505586 | − | 0.862776i | \(-0.668724\pi\) | ||||
−0.505586 | + | 0.862776i | \(0.668724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.1398 | 0.467215 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.1406 | 0.650184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.35984 | −0.337693 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.98260 | 0.273924 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.9775 | 1.32402 | 0.662008 | − | 0.749497i | \(-0.269704\pi\) | ||||
0.662008 | + | 0.749497i | \(0.269704\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.593083 | 0.0270423 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.9343 | −1.13221 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8101 | −1.07894 | −0.539469 | − | 0.842006i | \(-0.681375\pi\) | ||||
−0.539469 | + | 0.842006i | \(0.681375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.90066 | 0.221616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.5199 | 1.06144 | 0.530718 | − | 0.847548i | \(-0.321922\pi\) | ||||
0.530718 | + | 0.847548i | \(0.321922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.49455 | 0.247462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.9228 | −0.985355 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4365 | 0.556734 | 0.278367 | − | 0.960475i | \(-0.410207\pi\) | ||||
0.278367 | + | 0.960475i | \(0.410207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.61597 | 0.250903 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.3309 | 0.951099 | 0.475549 | − | 0.879689i | \(-0.342249\pi\) | ||||
0.475549 | + | 0.879689i | \(0.342249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.7535 | −0.879021 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.95785 | −0.175774 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.7523 | 1.89496 | 0.947481 | − | 0.319814i | \(-0.103620\pi\) | ||||
0.947481 | + | 0.319814i | \(0.103620\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.81374 | 0.124230 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.85987 | 0.0819556 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0551 | −0.706102 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.198799 | 0.00872629 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.9707 | 1.09398 | 0.546992 | − | 0.837138i | \(-0.315773\pi\) | ||||
0.546992 | + | 0.837138i | \(0.315773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9078 | 0.695599 | 0.347800 | − | 0.937569i | \(-0.386929\pi\) | ||||
0.347800 | + | 0.937569i | \(0.386929\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.339721 | −0.0147985 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.7717 | 1.46834 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.219618 | 0.00953060 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.3509 | 1.14138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 56.9450 | 2.46195 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0325437 | 0.00140437 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.68783 | −0.373519 | −0.186759 | − | 0.982406i | \(-0.559798\pi\) | ||||
−0.186759 | + | 0.982406i | \(0.559798\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.73318 | −0.160206 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.4966 | −1.39200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.9468 | −1.15216 | −0.576081 | − | 0.817393i | \(-0.695419\pi\) | ||||
−0.576081 | + | 0.817393i | \(0.695419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41.9598 | −1.79080 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.66391 | 0.326494 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.460213 | 0.0195350 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.0535 | −1.78187 | −0.890933 | − | 0.454135i | \(-0.849948\pi\) | ||||
−0.890933 | + | 0.454135i | \(0.849948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8559 | 0.586040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.790632 | 0.0333805 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.9858 | 1.09517 | 0.547586 | − | 0.836749i | \(-0.315547\pi\) | ||||
0.547586 | + | 0.836749i | \(0.315547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.4189 | 1.53215 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.8816 | −0.456182 | −0.228091 | − | 0.973640i | \(-0.573248\pi\) | ||||
−0.228091 | + | 0.973640i | \(0.573248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.6649 | 0.488163 | 0.244081 | − | 0.969755i | \(-0.421514\pi\) | ||||
0.244081 | + | 0.969755i | \(0.421514\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.78887 | −0.241834 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −55.4542 | −2.31260 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.1757 | −1.46439 | −0.732193 | − | 0.681097i | \(-0.761503\pi\) | ||||
−0.732193 | + | 0.681097i | \(0.761503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.58939 | 0.149170 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.89204 | 0.202608 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.4814 | −0.888145 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.9581 | 0.741212 | 0.370606 | − | 0.928790i | \(-0.379150\pi\) | ||||
0.370606 | + | 0.928790i | \(0.379150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.473849 | −0.0195246 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.89117 | 0.406868 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.85554 | 0.322588 | 0.161294 | − | 0.986906i | \(-0.448433\pi\) | ||||
0.161294 | + | 0.986906i | \(0.448433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.24039 | 0.337257 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.7639 | −0.603236 | −0.301618 | − | 0.953429i | \(-0.597527\pi\) | ||||
−0.301618 | + | 0.953429i | \(0.597527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.67351 | 0.272218 | 0.136109 | − | 0.990694i | \(-0.456540\pi\) | ||||
0.136109 | + | 0.990694i | \(0.456540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0256 | −0.896950 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.7457 | 0.843433 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.8693 | −1.53707 | −0.768534 | − | 0.639809i | \(-0.779014\pi\) | ||||
−0.768534 | + | 0.639809i | \(0.779014\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.7318 | −0.636442 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6730 | 0.713805 | 0.356902 | − | 0.934142i | \(-0.383833\pi\) | ||||
0.356902 | + | 0.934142i | \(0.383833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.4475 | 0.824521 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.9720 | −0.643009 | −0.321505 | − | 0.946908i | \(-0.604189\pi\) | ||||
−0.321505 | + | 0.946908i | \(0.604189\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.8682 | −1.40147 | −0.700735 | − | 0.713422i | \(-0.747144\pi\) | ||||
−0.700735 | + | 0.713422i | \(0.747144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.2007 | 0.850753 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.63195 | −0.305278 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.10279 | 0.0440412 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.192170 | 0.00766233 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4788 | −0.576393 | −0.288197 | − | 0.957571i | \(-0.593056\pi\) | ||||
−0.288197 | + | 0.957571i | \(0.593056\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.82555 | 0.231545 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 45.4883 | 1.80515 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.11159 | −0.0835333 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.5138 | 1.12623 | 0.563113 | − | 0.826380i | \(-0.309604\pi\) | ||||
0.563113 | + | 0.826380i | \(0.309604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7793 | 0.937763 | 0.468882 | − | 0.883261i | \(-0.344657\pi\) | ||||
0.468882 | + | 0.883261i | \(0.344657\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.7517 | 0.423348 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.5860 | −1.39903 | −0.699514 | − | 0.714619i | \(-0.746600\pi\) | ||||
−0.699514 | + | 0.714619i | \(0.746600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.179584 | 0.00704929 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.24174 | −0.361657 | −0.180829 | − | 0.983515i | \(-0.557878\pi\) | ||||
−0.180829 | + | 0.983515i | \(0.557878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 61.5986 | 2.40686 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.3869 | 1.10748 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.4715 | −0.914320 | −0.457160 | − | 0.889384i | \(-0.651133\pi\) | ||||
−0.457160 | + | 0.889384i | \(0.651133\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1636 | 0.395317 | 0.197658 | − | 0.980271i | \(-0.436666\pi\) | ||||
0.197658 | + | 0.980271i | \(0.436666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.774714 | 0.0300874 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 57.7453 | 2.23591 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.3670 | −0.439472 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.3110 | −1.32456 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0320 | −0.425251 | −0.212626 | − | 0.977134i | \(-0.568201\pi\) | ||||
−0.212626 | + | 0.977134i | \(0.568201\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.7087 | −0.797076 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.5867 | 1.32928 | 0.664638 | − | 0.747165i | \(-0.268586\pi\) | ||||
0.664638 | + | 0.747165i | \(0.268586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.764814 | −0.0293077 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.0946 | −0.998480 | −0.499240 | − | 0.866464i | \(-0.666387\pi\) | ||||
−0.499240 | + | 0.866464i | \(0.666387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.6670 | −0.980685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.77216 | 0.258374 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.79354 | 0.182619 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.51398 | −0.323887 | −0.161944 | − | 0.986800i | \(-0.551776\pi\) | ||||
−0.161944 | + | 0.986800i | \(0.551776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.5559 | −1.12112 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.53820 | 0.323407 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.98939 | −0.264363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.20119 | −0.271985 | −0.135993 | − | 0.990710i | \(-0.543422\pi\) | ||||
−0.135993 | + | 0.990710i | \(0.543422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.268043 | 0.0101094 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.2074 | −0.459757 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.9748 | −0.787726 | −0.393863 | − | 0.919169i | \(-0.628861\pi\) | ||||
−0.393863 | + | 0.919169i | \(0.628861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.2215 | 1.54593 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.57031 | −0.133709 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.5656 | −0.656915 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.4073 | 0.500704 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.7635 | −1.10999 | −0.554996 | − | 0.831853i | \(-0.687280\pi\) | ||||
−0.554996 | + | 0.831853i | \(0.687280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.19021 | −0.155835 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −56.4052 | −2.09484 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.9856 | −0.815401 | −0.407700 | − | 0.913116i | \(-0.633669\pi\) | ||||
−0.407700 | + | 0.913116i | \(0.633669\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.9605 | −0.554091 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.48956 | 0.166052 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.0702 | −1.51696 | −0.758482 | − | 0.651694i | \(-0.774058\pi\) | ||||
−0.758482 | + | 0.651694i | \(0.774058\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.0106 | −0.663428 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.2697 | 0.782417 | 0.391209 | − | 0.920302i | \(-0.372057\pi\) | ||||
0.391209 | + | 0.920302i | \(0.372057\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.08059 | 0.0396963 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.24375 | −0.229061 | −0.114531 | − | 0.993420i | \(-0.536536\pi\) | ||||
−0.114531 | + | 0.993420i | \(0.536536\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.0811 | −0.772351 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.1868 | 0.372715 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.3670 | 0.670222 | 0.335111 | − | 0.942179i | \(-0.391226\pi\) | ||||
0.335111 | + | 0.942179i | \(0.391226\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.58117 | −0.0576211 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 77.5455 | 2.82217 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.63834 | −0.132238 | −0.0661188 | − | 0.997812i | \(-0.521062\pi\) | ||||
−0.0661188 | + | 0.997812i | \(0.521062\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.30919 | 0.301605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.98449 | 0.216938 | 0.108469 | − | 0.994100i | \(-0.465405\pi\) | ||||
0.108469 | + | 0.994100i | \(0.465405\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.96037 | −0.251653 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.175968 | 0.00635385 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.7519 | 1.64986 | 0.824928 | − | 0.565238i | \(-0.191216\pi\) | ||||
0.824928 | + | 0.565238i | \(0.191216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.692303 | 0.0249327 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.5347 | −1.20616 | −0.603080 | − | 0.797681i | \(-0.706060\pi\) | ||||
−0.603080 | + | 0.797681i | \(0.706060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.48745 | 0.125273 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.9093 | 0.426693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.72667 | −0.0617853 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.5642 | 0.770643 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −72.9938 | −2.60526 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.51073 | 0.125144 | 0.0625719 | − | 0.998040i | \(-0.480070\pi\) | ||||
0.0625719 | + | 0.998040i | \(0.480070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.25772 | −0.0447762 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.6202 | −1.19389 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.71963 | 0.131922 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.1264 | 0.535806 | 0.267903 | − | 0.963446i | \(-0.413669\pi\) | ||||
0.267903 | + | 0.963446i | \(0.413669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.09741 | −0.180334 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.15305 | −0.217407 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.2123 | 0.819144 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.34806 | −0.188261 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.38201 | −0.0837470 | −0.0418735 | − | 0.999123i | \(-0.513333\pi\) | ||||
−0.0418735 | + | 0.999123i | \(0.513333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.9215 | 0.910228 | 0.455114 | − | 0.890433i | \(-0.349599\pi\) | ||||
0.455114 | + | 0.890433i | \(0.349599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.3066 | 0.396541 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.2787 | −1.23576 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.26213 | 0.219084 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.8970 | −1.88102 | −0.940509 | − | 0.339769i | \(-0.889651\pi\) | ||||
−0.940509 | + | 0.339769i | \(0.889651\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.9577 | 0.451677 | 0.225838 | − | 0.974165i | \(-0.427488\pi\) | ||||
0.225838 | + | 0.974165i | \(0.427488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.11636 | −0.282575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8634 | 1.03845 | 0.519226 | − | 0.854637i | \(-0.326220\pi\) | ||||
0.519226 | + | 0.854637i | \(0.326220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.7956 | 1.38216 | 0.691079 | − | 0.722780i | \(-0.257136\pi\) | ||||
0.691079 | + | 0.722780i | \(0.257136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.88462 | −0.238825 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.4281 | −1.39907 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.33329 | −0.0460851 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.5209 | 1.43346 | 0.716731 | − | 0.697350i | \(-0.245638\pi\) | ||||
0.716731 | + | 0.697350i | \(0.245638\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.7356 | 1.02536 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.166574 | 0.00573711 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.4916 | 0.980142 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.87147 | 0.167188 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.01962 | 0.0692318 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0014 | −0.513637 | −0.256818 | − | 0.966460i | \(-0.582674\pi\) | ||||
−0.256818 | + | 0.966460i | \(0.582674\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.70847 | −0.332023 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.3427 | −0.729053 | −0.364527 | − | 0.931193i | \(-0.618769\pi\) | ||||
−0.364527 | + | 0.931193i | \(0.618769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.7738 | −0.811151 | −0.405576 | − | 0.914062i | \(-0.632929\pi\) | ||||
−0.405576 | + | 0.914062i | \(0.632929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5643 | −0.870217 | −0.435109 | − | 0.900378i | \(-0.643290\pi\) | ||||
−0.435109 | + | 0.900378i | \(0.643290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.43111 | −0.0486590 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.05125 | −0.273435 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.7073 | 1.14344 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.6479 | −0.597977 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.5855 | −0.662869 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.1296 | −0.342053 | −0.171026 | − | 0.985266i | \(-0.554708\pi\) | ||||
−0.171026 | + | 0.985266i | \(0.554708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5848 | −0.357016 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.6185 | −1.13264 | −0.566319 | − | 0.824186i | \(-0.691633\pi\) | ||||
−0.566319 | + | 0.824186i | \(0.691633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.8755 | 1.10635 | 0.553174 | − | 0.833066i | \(-0.313416\pi\) | ||||
0.553174 | + | 0.833066i | \(0.313416\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.136546 | 0.00458993 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.6026 | −1.49761 | −0.748804 | − | 0.662792i | \(-0.769371\pi\) | ||||
−0.748804 | + | 0.662792i | \(0.769371\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.6043 | −0.522764 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.10998 | −0.237926 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.234275 | −0.00783094 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.14189 | 0.271850 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.63154 | −0.121119 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.55320 | 0.0517446 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.8743 | 0.893333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.6897 | −1.71633 | −0.858164 | − | 0.513376i | \(-0.828395\pi\) | ||||
−0.858164 | + | 0.513376i | \(0.828395\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5161 | −0.514637 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.0623 | 0.929745 | 0.464872 | − | 0.885378i | \(-0.346100\pi\) | ||||
0.464872 | + | 0.885378i | \(0.346100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.32986 | 0.275678 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26.0882 | −0.862448 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.7561 | 0.717669 | 0.358834 | − | 0.933401i | \(-0.383174\pi\) | ||||
0.358834 | + | 0.933401i | \(0.383174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0717 | 0.331873 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.69191 | −0.0556898 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.97275 | −0.0648638 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.46090 | 0.0479822 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.4361 | −1.72037 | −0.860186 | − | 0.509980i | \(-0.829653\pi\) | ||||
−0.860186 | + | 0.509980i | \(0.829653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.87098 | 0.126730 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.69158 | −0.186135 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.48443 | 0.211837 | 0.105919 | − | 0.994375i | \(-0.466222\pi\) | ||||
0.105919 | + | 0.994375i | \(0.466222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.25788 | −0.171585 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.12436 | −0.167049 | −0.0835247 | − | 0.996506i | \(-0.526618\pi\) | ||||
−0.0835247 | + | 0.996506i | \(0.526618\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 89.7327 | 2.92210 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.3046 | −0.562325 | −0.281163 | − | 0.959660i | \(-0.590720\pi\) | ||||
−0.281163 | + | 0.959660i | \(0.590720\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.7449 | 0.738331 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.91761 | −0.127037 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.4552 | −1.69919 | −0.849595 | − | 0.527436i | \(-0.823153\pi\) | ||||
−0.849595 | + | 0.527436i | \(0.823153\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.6727 | 1.34850 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.45169 | 0.273204 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7755 | −0.992757 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 44.7295 | 1.44139 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.8392 | −0.831794 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.0111 | 1.25451 | 0.627256 | − | 0.778813i | \(-0.284178\pi\) | ||||
0.627256 | + | 0.778813i | \(0.284178\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.350131 | 0.0112478 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.7693 | −0.826975 | −0.413488 | − | 0.910510i | \(-0.635689\pi\) | ||||
−0.413488 | + | 0.910510i | \(0.635689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.95294 | −0.254698 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.35129 | −0.107217 | −0.0536087 | − | 0.998562i | \(-0.517072\pi\) | ||||
−0.0536087 | + | 0.998562i | \(0.517072\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.03142 | −0.160805 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5256 | −0.814970 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.3969 | 0.810037 | 0.405018 | − | 0.914309i | \(-0.367265\pi\) | ||||
0.405018 | + | 0.914309i | \(0.367265\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −71.2043 | −2.26876 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.1833 | 1.50034 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.6136 | −1.13130 | −0.565651 | − | 0.824645i | \(-0.691375\pi\) | ||||
−0.565651 | + | 0.824645i | \(0.691375\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.13896 | 0.194814 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −59.3206 | −1.88059 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0273 | 0.919303 | 0.459651 | − | 0.888099i | \(-0.347974\pi\) | ||||
0.459651 | + | 0.888099i | \(0.347974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.754203 | 0.0238619 |
(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 | 7448.2.a.bn.1.3 | yes | 6 | |
7.6 | odd | 2 | 7448.2.a.bm.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7448.2.a.bm.1.4 | ✓ | 6 | 7.6 | odd | 2 | ||
7448.2.a.bn.1.3 | yes | 6 | 1.1 | even | 1 | trivial |