Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, 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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 4x^{7} - 8x^{6} + 36x^{5} + 17x^{4} - 76x^{3} - 20x^{2} + 44x + 17 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(3.08774\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-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 | ||||||||
\(3\) | 3.08774 | 1.78271 | 0.891355 | − | 0.453307i | \(-0.149756\pi\) | ||||
0.891355 | + | 0.453307i | \(0.149756\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.25463 | 1.45551 | 0.727757 | − | 0.685835i | \(-0.240563\pi\) | ||||
0.727757 | + | 0.685835i | \(0.240563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.53416 | 2.17805 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12130 | −1.54413 | −0.772064 | − | 0.635544i | \(-0.780776\pi\) | ||||
−0.772064 | + | 0.635544i | \(0.780776\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.13386 | 1.42388 | 0.711939 | − | 0.702242i | \(-0.247817\pi\) | ||||
0.711939 | + | 0.702242i | \(0.247817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.0495 | 2.59476 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.25326 | −1.20518 | −0.602590 | − | 0.798051i | \(-0.705865\pi\) | ||||
−0.602590 | + | 0.798051i | \(0.705865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.97171 | 1.45370 | 0.726851 | − | 0.686795i | \(-0.240983\pi\) | ||||
0.726851 | + | 0.686795i | \(0.240983\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.59260 | 1.11852 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.9126 | 2.10013 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.39300 | −0.630064 | −0.315032 | − | 0.949081i | \(-0.602015\pi\) | ||||
−0.315032 | + | 0.949081i | \(0.602015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.35553 | 0.423065 | 0.211533 | − | 0.977371i | \(-0.432155\pi\) | ||||
0.211533 | + | 0.977371i | \(0.432155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.8132 | −2.75273 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.60498 | 0.428257 | 0.214128 | − | 0.976806i | \(-0.431309\pi\) | ||||
0.214128 | + | 0.976806i | \(0.431309\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.8520 | 2.53836 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.70525 | −0.891010 | −0.445505 | − | 0.895280i | \(-0.646976\pi\) | ||||
−0.445505 | + | 0.895280i | \(0.646976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.18641 | 0.180926 | 0.0904631 | − | 0.995900i | \(-0.471165\pi\) | ||||
0.0904631 | + | 0.995900i | \(0.471165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21.2662 | 3.17019 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.70250 | 0.685930 | 0.342965 | − | 0.939348i | \(-0.388569\pi\) | ||||
0.342965 | + | 0.939348i | \(0.388569\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.08774 | −0.432371 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0116 | 1.37521 | 0.687603 | − | 0.726087i | \(-0.258663\pi\) | ||||
0.687603 | + | 0.726087i | \(0.258663\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.6679 | −2.24750 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.2207 | −2.14849 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.0991 | −1.70536 | −0.852678 | − | 0.522436i | \(-0.825023\pi\) | ||||
−0.852678 | + | 0.522436i | \(0.825023\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.78135 | 0.228079 | 0.114039 | − | 0.993476i | \(-0.463621\pi\) | ||||
0.114039 | + | 0.993476i | \(0.463621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.7088 | 2.07247 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1779 | −1.36559 | −0.682796 | − | 0.730609i | \(-0.739236\pi\) | ||||
−0.682796 | + | 0.730609i | \(0.739236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.5269 | 2.59153 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.21864 | 1.09405 | 0.547026 | − | 0.837116i | \(-0.315760\pi\) | ||||
0.547026 | + | 0.837116i | \(0.315760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6608 | 1.71591 | 0.857957 | − | 0.513722i | \(-0.171734\pi\) | ||||
0.857957 | + | 0.513722i | \(0.171734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.2685 | 1.99400 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.05802 | 0.231545 | 0.115773 | − | 0.993276i | \(-0.463066\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463066\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.0927 | 1.56586 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7006 | −1.72336 | −0.861681 | − | 0.507450i | \(-0.830588\pi\) | ||||
−0.861681 | + | 0.507450i | \(0.830588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.25463 | −0.353014 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4767 | −1.12322 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.91321 | −0.732799 | −0.366399 | − | 0.930458i | \(-0.619410\pi\) | ||||
−0.366399 | + | 0.930458i | \(0.619410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.27326 | 0.754202 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.0974 | −1.75416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5244 | 1.06859 | 0.534295 | − | 0.845298i | \(-0.320577\pi\) | ||||
0.534295 | + | 0.845298i | \(0.320577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −33.4634 | −3.36319 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.06349 | −0.404333 | −0.202166 | − | 0.979351i | \(-0.564798\pi\) | ||||
−0.202166 | + | 0.979351i | \(0.564798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0639 | −1.38576 | −0.692880 | − | 0.721053i | \(-0.743658\pi\) | ||||
−0.692880 | + | 0.721053i | \(0.743658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.0690 | 1.45678 | 0.728388 | − | 0.685165i | \(-0.240270\pi\) | ||||
0.728388 | + | 0.685165i | \(0.240270\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.50389 | 0.239829 | 0.119914 | − | 0.992784i | \(-0.461738\pi\) | ||||
0.119914 | + | 0.992784i | \(0.461738\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.04352 | 0.763457 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.3088 | −1.53421 | −0.767103 | − | 0.641524i | \(-0.778302\pi\) | ||||
−0.767103 | + | 0.641524i | \(0.778302\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.6903 | 2.11588 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33.5455 | 3.10128 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2277 | 1.38433 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.6163 | −1.58841 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.92869 | 0.172507 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.50639 | −0.311142 | −0.155571 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155571 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.66334 | 0.322539 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.11641 | 0.796505 | 0.398252 | − | 0.917276i | \(-0.369617\pi\) | ||||
0.398252 | + | 0.917276i | \(0.369617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 35.5164 | 3.05676 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0279 | −0.856738 | −0.428369 | − | 0.903604i | \(-0.640912\pi\) | ||||
−0.428369 | + | 0.903604i | \(0.640912\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1157 | 0.858002 | 0.429001 | − | 0.903304i | \(-0.358866\pi\) | ||||
0.429001 | + | 0.903304i | \(0.358866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.5201 | 1.22281 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.2920 | −2.19865 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.0429 | −0.917067 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5436 | −1.10954 | −0.554769 | − | 0.832005i | \(-0.687193\pi\) | ||||
−0.554769 | + | 0.832005i | \(0.687193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8102 | −1.36799 | −0.683997 | − | 0.729485i | \(-0.739760\pi\) | ||||
−0.683997 | + | 0.729485i | \(0.739760\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.53416 | −0.528255 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.66636 | 0.615777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.7407 | 1.41586 | 0.707932 | − | 0.706280i | \(-0.249628\pi\) | ||||
0.707932 | + | 0.706280i | \(0.249628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.9134 | 2.45159 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.3081 | −1.27735 | −0.638673 | − | 0.769478i | \(-0.720516\pi\) | ||||
−0.638673 | + | 0.769478i | \(0.720516\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −51.4662 | −4.00664 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.3427 | −1.72893 | −0.864463 | − | 0.502696i | \(-0.832342\pi\) | ||||
−0.864463 | + | 0.502696i | \(0.832342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.3565 | 1.02743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.3256 | −2.62495 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.13505 | 0.390410 | 0.195205 | − | 0.980762i | \(-0.437463\pi\) | ||||
0.195205 | + | 0.980762i | \(0.437463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −40.4466 | −3.04015 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.67240 | 0.423975 | 0.211987 | − | 0.977272i | \(-0.432006\pi\) | ||||
0.211987 | + | 0.977272i | \(0.432006\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7700 | −0.874858 | −0.437429 | − | 0.899253i | \(-0.644111\pi\) | ||||
−0.437429 | + | 0.899253i | \(0.644111\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.50036 | 0.406598 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.47825 | 0.623333 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.12130 | 0.374506 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.741528 | −0.0536551 | −0.0268275 | − | 0.999640i | \(-0.508540\pi\) | ||||
−0.0268275 | + | 0.999640i | \(0.508540\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7110 | −0.842979 | −0.421490 | − | 0.906833i | \(-0.638493\pi\) | ||||
−0.421490 | + | 0.906833i | \(0.638493\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 51.5925 | 3.69462 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.93898 | −0.280641 | −0.140320 | − | 0.990106i | \(-0.544813\pi\) | ||||
−0.140320 | + | 0.990106i | \(0.544813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.68257 | −0.615491 | −0.307746 | − | 0.951469i | \(-0.599575\pi\) | ||||
−0.307746 | + | 0.951469i | \(0.599575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −34.5143 | −2.43445 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.5684 | −1.29688 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 45.5543 | 3.16624 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.9035 | 1.86095 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.05236 | −0.623190 | −0.311595 | − | 0.950215i | \(-0.600863\pi\) | ||||
−0.311595 | + | 0.950215i | \(0.600863\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 28.4648 | 1.95038 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.86133 | 0.263340 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 45.2687 | 3.05897 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.13386 | −0.345341 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.2667 | −0.821442 | −0.410721 | − | 0.911761i | \(-0.634723\pi\) | ||||
−0.410721 | + | 0.911761i | \(0.634723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36.5429 | 2.43619 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.1364 | 1.13739 | 0.568693 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568693 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.5237 | 1.42232 | 0.711162 | − | 0.703028i | \(-0.248169\pi\) | ||||
0.711162 | + | 0.703028i | \(0.248169\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.2290 | −1.25974 | −0.629868 | − | 0.776702i | \(-0.716891\pi\) | ||||
−0.629868 | + | 0.776702i | \(0.716891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.3049 | 0.998381 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.35463 | 0.412778 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.19767 | 0.530263 | 0.265132 | − | 0.964212i | \(-0.414585\pi\) | ||||
0.265132 | + | 0.964212i | \(0.414585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.4006 | −1.63620 | −0.818099 | − | 0.575078i | \(-0.804972\pi\) | ||||
−0.818099 | + | 0.575078i | \(0.804972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7771 | 0.691349 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.9695 | −1.71603 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −48.4794 | −3.07226 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.15836 | 0.262473 | 0.131237 | − | 0.991351i | \(-0.458105\pi\) | ||||
0.131237 | + | 0.991351i | \(0.458105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.7042 | −2.24470 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.0495 | −0.629321 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6639 | 1.10185 | 0.550923 | − | 0.834556i | \(-0.314276\pi\) | ||||
0.550923 | + | 0.834556i | \(0.314276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.1704 | −1.37231 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.6955 | −1.52279 | −0.761395 | − | 0.648288i | \(-0.775485\pi\) | ||||
−0.761395 | + | 0.648288i | \(0.775485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.5842 | 2.00163 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.3462 | −1.30637 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7507 | 0.899365 | 0.449683 | − | 0.893188i | \(-0.351537\pi\) | ||||
0.449683 | + | 0.893188i | \(0.351537\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00715 | 0.486400 | 0.243200 | − | 0.969976i | \(-0.421803\pi\) | ||||
0.243200 | + | 0.969976i | \(0.421803\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.6414 | −1.72714 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.21306 | −0.373307 | −0.186653 | − | 0.982426i | \(-0.559764\pi\) | ||||
−0.186653 | + | 0.982426i | \(0.559764\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.3914 | 0.921458 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0264 | −0.657777 | −0.328889 | − | 0.944369i | \(-0.606674\pi\) | ||||
−0.328889 | + | 0.944369i | \(0.606674\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.8967 | −1.00440 | −0.502201 | − | 0.864751i | \(-0.667476\pi\) | ||||
−0.502201 | + | 0.864751i | \(0.667476\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −52.7924 | −3.12715 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.4966 | 1.90498 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.3788 | −1.30738 | −0.653692 | − | 0.756761i | \(-0.726781\pi\) | ||||
−0.653692 | + | 0.756761i | \(0.726781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −42.6327 | −2.48217 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −55.8865 | −3.24286 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 35.7918 | 2.06989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.5470 | −0.720808 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.79764 | 0.331972 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.01060 | 0.114751 | 0.0573755 | − | 0.998353i | \(-0.481727\pi\) | ||||
0.0573755 | + | 0.998353i | \(0.481727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −43.4258 | −2.47041 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.0533120 | −0.00302305 | −0.00151152 | − | 0.999999i | \(-0.500481\pi\) | ||||
−0.00151152 | + | 0.999999i | \(0.500481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0370 | 0.962988 | 0.481494 | − | 0.876449i | \(-0.340094\pi\) | ||||
0.481494 | + | 0.876449i | \(0.340094\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.5722 | 1.66094 | 0.830471 | − | 0.557062i | \(-0.188071\pi\) | ||||
0.830471 | + | 0.557062i | \(0.188071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.3765 | 0.972900 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 46.5292 | 2.59701 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.25326 | 0.292299 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.7116 | 1.59263 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.73136 | 0.427545 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.0575 | 1.37729 | 0.688643 | − | 0.725101i | \(-0.258207\pi\) | ||||
0.688643 | + | 0.725101i | \(0.258207\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.0214 | 0.932766 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −36.3798 | −1.98764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.187963 | 0.0102390 | 0.00511949 | − | 0.999987i | \(-0.498370\pi\) | ||||
0.00511949 | + | 0.999987i | \(0.498370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −50.3575 | −2.73504 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0634 | −0.653267 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 70.0619 | 3.77201 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.39627 | 0.397053 | 0.198526 | − | 0.980096i | \(-0.436384\pi\) | ||||
0.198526 | + | 0.980096i | \(0.436384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.1736 | −1.61516 | −0.807579 | − | 0.589760i | \(-0.799222\pi\) | ||||
−0.807579 | + | 0.589760i | \(0.799222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 56.0236 | 2.99032 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.5872 | −0.723174 | −0.361587 | − | 0.932338i | \(-0.617765\pi\) | ||||
−0.361587 | + | 0.932338i | \(0.617765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.0032 | 1.59241 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.6480 | 1.40643 | 0.703214 | − | 0.710978i | \(-0.251748\pi\) | ||||
0.703214 | + | 0.710978i | \(0.251748\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.59676 | 0.452461 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 47.0192 | 2.46787 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.7153 | 2.49753 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.0287 | −1.30649 | −0.653244 | − | 0.757147i | \(-0.726592\pi\) | ||||
−0.653244 | + | 0.757147i | \(0.726592\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −37.2790 | −1.94067 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6096 | 0.911790 | 0.455895 | − | 0.890034i | \(-0.349319\pi\) | ||||
0.455895 | + | 0.890034i | \(0.349319\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.95529 | 0.307530 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.4192 | −0.897134 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6143 | −0.596589 | −0.298295 | − | 0.954474i | \(-0.596418\pi\) | ||||
−0.298295 | + | 0.954474i | \(0.596418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.8268 | −0.554675 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.89518 | −0.147937 | −0.0739684 | − | 0.997261i | \(-0.523566\pi\) | ||||
−0.0739684 | + | 0.997261i | \(0.523566\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.75220 | 0.394067 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.7804 | 1.35782 | 0.678910 | − | 0.734221i | \(-0.262452\pi\) | ||||
0.678910 | + | 0.734221i | \(0.262452\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.97171 | −0.352575 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.1491 | 1.41994 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.69809 | 0.337017 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.1376 | 1.36200 | 0.680998 | − | 0.732285i | \(-0.261546\pi\) | ||||
0.680998 | + | 0.732285i | \(0.261546\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9281 | 0.695534 | 0.347767 | − | 0.937581i | \(-0.386940\pi\) | ||||
0.347767 | + | 0.937581i | \(0.386940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0930 | 0.602393 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 45.8666 | 2.27913 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.3409 | −0.661284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3532 | 0.511933 | 0.255967 | − | 0.966686i | \(-0.417606\pi\) | ||||
0.255967 | + | 0.966686i | \(0.417606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.9635 | −1.52732 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −51.0995 | −2.50838 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.2347 | 1.52957 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.50968 | −0.171459 | −0.0857294 | − | 0.996318i | \(-0.527322\pi\) | ||||
−0.0857294 | + | 0.996318i | \(0.527322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5824 | 0.515755 | 0.257877 | − | 0.966178i | \(-0.416977\pi\) | ||||
0.257877 | + | 0.966178i | \(0.416977\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.7269 | 1.49399 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.59260 | −0.271281 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −81.1830 | −3.91955 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.665241 | −0.0320435 | −0.0160218 | − | 0.999872i | \(-0.505100\pi\) | ||||
−0.0160218 | + | 0.999872i | \(0.505100\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.1221 | 0.486435 | 0.243217 | − | 0.969972i | \(-0.421797\pi\) | ||||
0.243217 | + | 0.969972i | \(0.421797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.0978 | −1.63486 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −36.6242 | −1.75197 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.6542 | 0.747134 | 0.373567 | − | 0.927603i | \(-0.378135\pi\) | ||||
0.373567 | + | 0.927603i | \(0.378135\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.1217 | −1.62117 | −0.810585 | − | 0.585621i | \(-0.800851\pi\) | ||||
−0.810585 | + | 0.585621i | \(0.800851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.4999 | −1.06660 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −41.8192 | −1.97798 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.06845 | 0.427967 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.2183 | 1.37583 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −51.9056 | −2.43874 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.7883 | −1.11277 | −0.556384 | − | 0.830925i | \(-0.687812\pi\) | ||||
−0.556384 | + | 0.830925i | \(0.687812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.9126 | −0.509355 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.4966 | −1.00119 | −0.500597 | − | 0.865680i | \(-0.666886\pi\) | ||||
−0.500597 | + | 0.865680i | \(0.666886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.55322 | −0.118658 | −0.0593292 | − | 0.998238i | \(-0.518896\pi\) | ||||
−0.0593292 | + | 0.998238i | \(0.518896\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.6718 | 1.09775 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.1634 | −0.933053 | −0.466526 | − | 0.884507i | \(-0.654495\pi\) | ||||
−0.466526 | + | 0.884507i | \(0.654495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 54.7788 | 2.52407 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.07597 | −0.279373 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.3794 | −1.34802 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 65.4177 | 2.99527 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.4499 | 0.797305 | 0.398652 | − | 0.917102i | \(-0.369478\pi\) | ||||
0.398652 | + | 0.917102i | \(0.369478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3736 | 0.609785 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.2529 | 1.55535 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.1143 | 1.77244 | 0.886219 | − | 0.463266i | \(-0.153323\pi\) | ||||
0.886219 | + | 0.463266i | \(0.153323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −50.3551 | −2.27714 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.3590 | 0.963917 | 0.481958 | − | 0.876194i | \(-0.339926\pi\) | ||||
0.481958 | + | 0.876194i | \(0.339926\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.39300 | 0.152813 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −108.911 | −4.89517 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.4317 | 1.40708 | 0.703538 | − | 0.710657i | \(-0.251602\pi\) | ||||
0.703538 | + | 0.710657i | \(0.251602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −68.9884 | −3.08217 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.1087 | 0.896603 | 0.448302 | − | 0.893882i | \(-0.352029\pi\) | ||||
0.448302 | + | 0.893882i | \(0.352029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2252 | −0.588512 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 41.2416 | 1.83160 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.0898 | 0.757490 | 0.378745 | − | 0.925501i | \(-0.376356\pi\) | ||||
0.378745 | + | 0.925501i | \(0.376356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −57.3266 | −2.53103 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.7728 | −2.01699 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.0829 | −1.05916 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.8557 | 0.695988 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.41261 | −0.324752 | −0.162376 | − | 0.986729i | \(-0.551916\pi\) | ||||
−0.162376 | + | 0.986729i | \(0.551916\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.240819 | −0.0105303 | −0.00526515 | − | 0.999986i | \(-0.501676\pi\) | ||||
−0.00526515 | + | 0.999986i | \(0.501676\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.35553 | −0.102608 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.6048 | 1.11325 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −85.5915 | −3.71436 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.2899 | −1.26869 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.0440 | 2.12036 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.5149 | 0.755824 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.9932 | 1.16053 | 0.580265 | − | 0.814428i | \(-0.302949\pi\) | ||||
0.580265 | + | 0.814428i | \(0.302949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.3428 | −1.55962 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.14922 | 0.349074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0657 | 0.857947 | 0.428973 | − | 0.903317i | \(-0.358875\pi\) | ||||
0.428973 | + | 0.903317i | \(0.358875\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.6396 | 0.496768 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.8243 | 0.759341 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.1787 | 1.11122 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.84986 | 0.120753 | 0.0603763 | − | 0.998176i | \(-0.480770\pi\) | ||||
0.0603763 | + | 0.998176i | \(0.480770\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.09088 | 0.257617 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8132 | 0.667636 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.4232 | 1.24004 | 0.620021 | − | 0.784586i | \(-0.287124\pi\) | ||||
0.620021 | + | 0.784586i | \(0.287124\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −53.0792 | −2.23306 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.4141 | −1.48463 | −0.742317 | − | 0.670048i | \(-0.766273\pi\) | ||||
−0.742317 | + | 0.670048i | \(0.766273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.5965 | −1.07118 | −0.535590 | − | 0.844478i | \(-0.679911\pi\) | ||||
−0.535590 | + | 0.844478i | \(0.679911\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.28965 | −0.0956514 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.9900 | 1.62599 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.7244 | 1.65375 | 0.826874 | − | 0.562388i | \(-0.190117\pi\) | ||||
0.826874 | + | 0.562388i | \(0.190117\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.1607 | −1.50279 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.2726 | −2.12349 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 109.178 | 4.51395 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.00154296 | −6.36846e−5 0 | −3.18423e−5 | − | 1.00000i | \(-0.500010\pi\) | ||||
−3.18423e−5 | 1.00000i | \(0.500010\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.3742 | −0.509870 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1626 | −0.500301 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.3965 | −0.919714 | −0.459857 | − | 0.887993i | \(-0.652099\pi\) | ||||
−0.459857 | + | 0.887993i | \(0.652099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.8096 | −1.09724 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.8107 | 0.441713 | 0.220857 | − | 0.975306i | \(-0.429115\pi\) | ||||
0.220857 | + | 0.975306i | \(0.429115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.5231 | 0.796364 | 0.398182 | − | 0.917306i | \(-0.369641\pi\) | ||||
0.398182 | + | 0.917306i | \(0.369641\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −73.0379 | −2.97433 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 49.5604 | 2.01492 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1715 | 0.575203 | 0.287601 | − | 0.957750i | \(-0.407142\pi\) | ||||
0.287601 | + | 0.957750i | \(0.407142\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.1420 | 0.976681 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.61930 | −0.307741 | −0.153870 | − | 0.988091i | \(-0.549174\pi\) | ||||
−0.153870 | + | 0.988091i | \(0.549174\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −57.3346 | −2.31195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.52135 | −0.182023 | −0.0910113 | − | 0.995850i | \(-0.529010\pi\) | ||||
−0.0910113 | + | 0.995850i | \(0.529010\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.8625 | −1.11989 | −0.559943 | − | 0.828531i | \(-0.689177\pi\) | ||||
−0.559943 | + | 0.828531i | \(0.689177\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 76.0793 | 3.05296 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.6858 | −0.867433 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 83.0711 | 3.31754 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.60498 | −0.103868 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1123 | 1.31818 | 0.659090 | − | 0.752064i | \(-0.270942\pi\) | ||||
0.659090 | + | 0.752064i | \(0.270942\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.9513 | −1.11097 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.4120 | −0.452871 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 60.2361 | 2.38290 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.2853 | −0.801221 | −0.400610 | − | 0.916249i | \(-0.631202\pi\) | ||||
−0.400610 | + | 0.916249i | \(0.631202\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.6066 | 0.457718 | 0.228859 | − | 0.973460i | \(-0.426500\pi\) | ||||
0.228859 | + | 0.973460i | \(0.426500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.9228 | 0.469459 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.4179 | 0.684770 | 0.342385 | − | 0.939560i | \(-0.388765\pi\) | ||||
0.342385 | + | 0.939560i | \(0.388765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 67.0843 | 2.63329 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1391 | −1.21857 | −0.609284 | − | 0.792952i | \(-0.708543\pi\) | ||||
−0.609284 | + | 0.792952i | \(0.708543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.6705 | 1.15932 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 95.7958 | 3.73735 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.6601 | −1.27226 | −0.636128 | − | 0.771583i | \(-0.719465\pi\) | ||||
−0.636128 | + | 0.771583i | \(0.719465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.1904 | −0.746420 | −0.373210 | − | 0.927747i | \(-0.621743\pi\) | ||||
−0.373210 | + | 0.927747i | \(0.621743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.8520 | −0.615643 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.6550 | −0.915925 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.8766 | −1.46439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.12283 | −0.352183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.61344 | 0.216382 | 0.108191 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108191 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 61.0296 | 2.34903 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.4047 | 1.43758 | 0.718789 | − | 0.695228i | \(-0.244697\pi\) | ||||
0.718789 | + | 0.695228i | \(0.244697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.9129 | 2.02763 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.0019 | −0.841880 | −0.420940 | − | 0.907089i | \(-0.638300\pi\) | ||||
−0.420940 | + | 0.907089i | \(0.638300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.6370 | −1.24699 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 66.4596 | 2.53559 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 51.3984 | 1.95812 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.7800 | −0.980717 | −0.490359 | − | 0.871521i | \(-0.663134\pi\) | ||||
−0.490359 | + | 0.871521i | \(0.663134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.9228 | 1.24883 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.70525 | 0.216102 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −59.3744 | −2.24574 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.82347 | 0.333258 | 0.166629 | − | 0.986020i | \(-0.446712\pi\) | ||||
0.166629 | + | 0.986020i | \(0.446712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.6847 | −0.516127 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 47.2576 | 1.77982 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4925 | −0.431609 | −0.215805 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215805 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4474 | 0.504318 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.4221 | 0.615011 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −85.5708 | −3.20017 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.3123 | 0.945305 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.74362 | 0.363376 | 0.181688 | − | 0.983356i | \(-0.441844\pi\) | ||||
0.181688 | + | 0.983356i | \(0.441844\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −78.4306 | −2.91686 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.9757 | −0.704739 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.2530 | 0.825316 | 0.412658 | − | 0.910886i | \(-0.364600\pi\) | ||||
0.412658 | + | 0.910886i | \(0.364600\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.00142 | −0.333386 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.18641 | −0.0438810 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2214 | 0.599150 | 0.299575 | − | 0.954073i | \(-0.403155\pi\) | ||||
0.299575 | + | 0.954073i | \(0.403155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 57.2451 | 2.10865 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.6708 | 1.01789 | 0.508943 | − | 0.860800i | \(-0.330036\pi\) | ||||
0.508943 | + | 0.860800i | \(0.330036\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −83.2750 | −3.05918 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.5594 | −0.607507 | −0.303754 | − | 0.952751i | \(-0.598240\pi\) | ||||
−0.303754 | + | 0.952751i | \(0.598240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.0795 | −1.61495 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −102.590 | −3.75358 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.2453 | −1.14016 | −0.570078 | − | 0.821591i | \(-0.693087\pi\) | ||||
−0.570078 | + | 0.821591i | \(0.693087\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.8399 | 0.467913 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54.7109 | −1.99113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.7582 | −0.427359 | −0.213680 | − | 0.976904i | \(-0.568545\pi\) | ||||
−0.213680 | + | 0.976904i | \(0.568545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −110.245 | −4.00165 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.17953 | −0.151508 | −0.0757540 | − | 0.997127i | \(-0.524136\pi\) | ||||
−0.0757540 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.2662 | −0.768883 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −67.2489 | −2.42822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.863383 | 0.0311344 | 0.0155672 | − | 0.999879i | \(-0.495045\pi\) | ||||
0.0155672 | + | 0.999879i | \(0.495045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.5417 | 1.96427 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.0952 | 1.37019 | 0.685094 | − | 0.728454i | \(-0.259761\pi\) | ||||
0.685094 | + | 0.728454i | \(0.259761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.1735 | 0.473207 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.9711 | 1.07383 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.2114 | −1.68936 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37.0263 | −1.32321 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 57.7395 | 2.06081 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.9204 | 1.74383 | 0.871913 | − | 0.489661i | \(-0.162880\pi\) | ||||
0.871913 | + | 0.489661i | \(0.162880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −76.2534 | −2.71469 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.14522 | 0.324756 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 100.612 | 3.56833 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.4404 | 1.46789 | 0.733946 | − | 0.679208i | \(-0.237676\pi\) | ||||
0.733946 | + | 0.679208i | \(0.237676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.70250 | −0.166363 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −45.1720 | −1.59607 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −75.0821 | −2.64959 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 45.5463 | 1.60331 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.3338 | 0.433633 | 0.216816 | − | 0.976212i | \(-0.430433\pi\) | ||||
0.216816 | + | 0.976212i | \(0.430433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.92765 | −0.243263 | −0.121631 | − | 0.992575i | \(-0.538813\pi\) | ||||
−0.121631 | + | 0.992575i | \(0.538813\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.7240 | 0.867109 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −53.0767 | −1.85920 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.23253 | −0.218049 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.22857 | −0.217379 | −0.108689 | − | 0.994076i | \(-0.534665\pi\) | ||||
−0.108689 | + | 0.994076i | \(0.534665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2597 | 0.880497 | 0.440249 | − | 0.897876i | \(-0.354890\pi\) | ||||
0.440249 | + | 0.897876i | \(0.354890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −88.4371 | −3.07899 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.2451 | −0.738764 | −0.369382 | − | 0.929278i | \(-0.620431\pi\) | ||||
−0.369382 | + | 0.929278i | \(0.620431\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.9143 | 0.552725 | 0.276362 | − | 0.961053i | \(-0.410871\pi\) | ||||
0.276362 | + | 0.961053i | \(0.410871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.1843 | −0.665497 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −72.7170 | −2.51648 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.7049 | 0.888490 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.58809 | −0.158398 | −0.0791992 | − | 0.996859i | \(-0.525236\pi\) | ||||
−0.0791992 | + | 0.996859i | \(0.525236\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.4876 | −0.603020 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −34.0466 | −1.17263 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.4706 | 1.49543 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −52.1725 | −1.79056 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.1612 | 0.622558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.8442 | −1.39848 | −0.699240 | − | 0.714887i | \(-0.746478\pi\) | ||||
−0.699240 | + | 0.714887i | \(0.746478\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −111.717 | −3.82065 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.0503896 | −0.00172128 | −0.000860638 | − | 1.00000i | \(-0.500274\pi\) | ||||
−0.000860638 | 1.00000i | \(0.500274\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7256 | 0.502431 | 0.251215 | − | 0.967931i | \(-0.419170\pi\) | ||||
0.251215 | + | 0.967931i | \(0.419170\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.1275 | −0.855349 | −0.427675 | − | 0.903933i | \(-0.640667\pi\) | ||||
−0.427675 | + | 0.903933i | \(0.640667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.7127 | 0.568247 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.08774 | 0.104865 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5397 | −0.357536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.3856 | −1.94444 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 68.7680 | 2.32744 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.1059 | 0.645161 | 0.322581 | − | 0.946542i | \(-0.395450\pi\) | ||||
0.322581 | + | 0.946542i | \(0.395450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −69.1000 | −2.33069 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.2649 | 0.750124 | 0.375062 | − | 0.927000i | \(-0.377621\pi\) | ||||
0.375062 | + | 0.927000i | \(0.377621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.2839 | 0.682607 | 0.341303 | − | 0.939953i | \(-0.389132\pi\) | ||||
0.341303 | + | 0.939953i | \(0.389132\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −131.639 | −4.42499 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.3402 | −1.32092 | −0.660458 | − | 0.750863i | \(-0.729638\pi\) | ||||
−0.660458 | + | 0.750863i | \(0.729638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −72.1731 | −2.41789 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.7035 | −0.826670 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.4615 | 0.617101 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 110.516 | 3.69002 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.99230 | −0.266558 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0116 | −0.333536 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −38.3070 | −1.27337 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.2290 | −0.572080 | −0.286040 | − | 0.958218i | \(-0.592339\pi\) | ||||
−0.286040 | + | 0.958218i | \(0.592339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.5515 | −0.880658 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.5456 | −0.912628 | −0.456314 | − | 0.889819i | \(-0.650831\pi\) | ||||
−0.456314 | + | 0.889819i | \(0.650831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 80.4073 | 2.66109 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.9016 | 0.591809 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.05113 | 0.133634 | 0.0668172 | − | 0.997765i | \(-0.478716\pi\) | ||||
0.0668172 | + | 0.997765i | \(0.478716\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.20821 | 0.204568 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47.3272 | 1.55780 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.5686 | 0.479014 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −91.8959 | −3.01826 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.3767 | −1.35753 | −0.678763 | − | 0.734358i | \(-0.737484\pi\) | ||||
−0.678763 | + | 0.734358i | \(0.737484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.164614 | −0.00538922 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.6679 | 0.545099 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.85113 | 0.321823 | 0.160911 | − | 0.986969i | \(-0.448557\pi\) | ||||
0.160911 | + | 0.986969i | \(0.448557\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.6059 | 1.71673 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.0786 | −1.01313 | −0.506567 | − | 0.862200i | \(-0.669086\pi\) | ||||
−0.506567 | + | 0.862200i | \(0.669086\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.7753 | −1.29526 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.8811 | −1.26347 | −0.631733 | − | 0.775186i | \(-0.717656\pi\) | ||||
−0.631733 | + | 0.775186i | \(0.717656\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 75.2664 | 2.44325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 91.3115 | 2.96098 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.4465 | 1.82848 | 0.914242 | − | 0.405170i | \(-0.132788\pi\) | ||||
0.914242 | + | 0.405170i | \(0.132788\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.41340 | −0.0780957 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 53.6543 | 1.73440 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.4515 | −0.821016 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 98.4632 | 3.17293 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.1151 | −1.22697 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.1217 | −0.454122 | −0.227061 | − | 0.973881i | \(-0.572912\pi\) | ||||
−0.227061 | + | 0.973881i | \(0.572912\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.2207 | 0.521085 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.5180 | 0.401723 | 0.200861 | − | 0.979620i | \(-0.435626\pi\) | ||||
0.200861 | + | 0.979620i | \(0.435626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 88.6541 | 2.83920 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.0496 | −0.833402 | −0.416701 | − | 0.909044i | \(-0.636814\pi\) | ||||
−0.416701 | + | 0.909044i | \(0.636814\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.4046 | 1.13154 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.3608 | 0.522360 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.4621 | −0.429374 | −0.214687 | − | 0.976683i | \(-0.568873\pi\) | ||||
−0.214687 | + | 0.976683i | \(0.568873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8199 | −0.408476 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.27132 | 0.263013 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.8991 | −0.663882 | −0.331941 | − | 0.943300i | \(-0.607703\pi\) | ||||
−0.331941 | + | 0.943300i | \(0.607703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 77.3712 | 2.45530 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.2585 | −0.895856 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.9728 | 1.13927 | 0.569636 | − | 0.821897i | \(-0.307084\pi\) | ||||
0.569636 | + | 0.821897i | \(0.307084\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.4271 | 0.899393 |
(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 | 3332.2.a.u.1.7 | yes | 8 | |
7.6 | odd | 2 | 3332.2.a.t.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3332.2.a.t.1.2 | ✓ | 8 | 7.6 | odd | 2 | ||
3332.2.a.u.1.7 | yes | 8 | 1.1 | even | 1 | trivial |