Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 4 x^{14} - 27 x^{13} + 106 x^{12} + 266 x^{11} - 1004 x^{10} - 1105 x^{9} + 4076 x^{8} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.61011\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.61011 | −1.61449 | −0.807245 | − | 0.590217i | \(-0.799042\pi\) | ||||
−0.807245 | + | 0.590217i | \(0.799042\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.982804 | 0.371465 | 0.185732 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185732 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.24397 | −0.978093 | −0.489047 | − | 0.872258i | \(-0.662655\pi\) | ||||
−0.489047 | + | 0.872258i | \(0.662655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88731 | 0.800797 | 0.400398 | − | 0.916341i | \(-0.368872\pi\) | ||||
0.400398 | + | 0.916341i | \(0.368872\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.61011 | −0.932126 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.659840 | −0.160035 | −0.0800173 | − | 0.996793i | \(-0.525498\pi\) | ||||
−0.0800173 | + | 0.996793i | \(0.525498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.91239 | 0.668147 | 0.334074 | − | 0.942547i | \(-0.391577\pi\) | ||||
0.334074 | + | 0.942547i | \(0.391577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.982804 | 0.214465 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.79366 | −0.374003 | −0.187002 | − | 0.982360i | \(-0.559877\pi\) | ||||
−0.187002 | + | 0.982360i | \(0.559877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.03288 | 1.60658 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.94801 | 0.918822 | 0.459411 | − | 0.888224i | \(-0.348061\pi\) | ||||
0.459411 | + | 0.888224i | \(0.348061\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.83768 | 0.330057 | 0.165029 | − | 0.986289i | \(-0.447228\pi\) | ||||
0.165029 | + | 0.986289i | \(0.447228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.24397 | −0.564702 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.54803 | −0.599726 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.7471 | −1.93122 | −0.965609 | − | 0.260000i | \(-0.916277\pi\) | ||||
−0.965609 | + | 0.260000i | \(0.916277\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.88731 | 0.462340 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.21052 | −0.501398 | −0.250699 | − | 0.968065i | \(-0.580661\pi\) | ||||
−0.250699 | + | 0.968065i | \(0.580661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.99865 | −1.21978 | −0.609891 | − | 0.792485i | \(-0.708787\pi\) | ||||
−0.609891 | + | 0.792485i | \(0.708787\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.61011 | −0.538163 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.45741 | 0.941910 | 0.470955 | − | 0.882157i | \(-0.343910\pi\) | ||||
0.470955 | + | 0.882157i | \(0.343910\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.03410 | −0.862014 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.659840 | −0.0923960 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.47583 | 0.202721 | 0.101360 | − | 0.994850i | \(-0.467681\pi\) | ||||
0.101360 | + | 0.994850i | \(0.467681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7111 | 1.57912 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.91239 | 0.385755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.809188 | −0.105347 | −0.0526737 | − | 0.998612i | \(-0.516774\pi\) | ||||
−0.0526737 | + | 0.998612i | \(0.516774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89425 | 1.26683 | 0.633414 | − | 0.773813i | \(-0.281653\pi\) | ||||
0.633414 | + | 0.773813i | \(0.281653\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.982804 | 0.123822 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4235 | −1.29288 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.49893 | 0.916140 | 0.458070 | − | 0.888916i | \(-0.348541\pi\) | ||||
0.458070 | + | 0.888916i | \(0.348541\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.79366 | −0.215931 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1492 | −1.32316 | −0.661582 | − | 0.749873i | \(-0.730115\pi\) | ||||
−0.661582 | + | 0.749873i | \(0.730115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6862 | 1.25072 | 0.625362 | − | 0.780335i | \(-0.284951\pi\) | ||||
0.625362 | + | 0.780335i | \(0.284951\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.03288 | 0.927557 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.18818 | −0.363327 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.03225 | 0.566172 | 0.283086 | − | 0.959094i | \(-0.408642\pi\) | ||||
0.283086 | + | 0.959094i | \(0.408642\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.32413 | 0.364871 | 0.182435 | − | 0.983218i | \(-0.441602\pi\) | ||||
0.182435 | + | 0.983218i | \(0.441602\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.38209 | 0.258374 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.94801 | 0.530482 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.58863 | −0.804394 | −0.402197 | − | 0.915553i | \(-0.631753\pi\) | ||||
−0.402197 | + | 0.915553i | \(0.631753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.83766 | 0.297468 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.83768 | 0.190559 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.5140 | −1.07872 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.87712 | −0.292127 | −0.146064 | − | 0.989275i | \(-0.546660\pi\) | ||||
−0.146064 | + | 0.989275i | \(0.546660\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.24397 | −0.326031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.3446 | −1.62635 | −0.813174 | − | 0.582021i | \(-0.802262\pi\) | ||||
−0.813174 | + | 0.582021i | \(0.802262\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.54509 | 0.250775 | 0.125388 | − | 0.992108i | \(-0.459983\pi\) | ||||
0.125388 | + | 0.992108i | \(0.459983\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.54803 | −0.346252 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.87320 | −0.471110 | −0.235555 | − | 0.971861i | \(-0.575691\pi\) | ||||
−0.235555 | + | 0.971861i | \(0.575691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.63845 | 0.731631 | 0.365816 | − | 0.930687i | \(-0.380790\pi\) | ||||
0.365816 | + | 0.930687i | \(0.380790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.7471 | −1.11499 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.11980 | −0.481630 | −0.240815 | − | 0.970571i | \(-0.577415\pi\) | ||||
−0.240815 | + | 0.970571i | \(0.577415\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.47529 | 0.603824 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.88731 | 0.266932 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.648493 | −0.0594472 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.476671 | −0.0433337 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.21052 | −0.289483 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9490 | −0.979309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.6475 | −1.56596 | −0.782979 | − | 0.622048i | \(-0.786301\pi\) | ||||
−0.782979 | + | 0.622048i | \(0.786301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.99865 | −0.704242 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.70788 | 0.149218 | 0.0746090 | − | 0.997213i | \(-0.476229\pi\) | ||||
0.0746090 | + | 0.997213i | \(0.476229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.86231 | 0.248193 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.61011 | −0.310709 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.5861 | −1.58792 | −0.793959 | − | 0.607971i | \(-0.791984\pi\) | ||||
−0.793959 | + | 0.607971i | \(0.791984\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.89774 | 0.330602 | 0.165301 | − | 0.986243i | \(-0.447140\pi\) | ||||
0.165301 | + | 0.986243i | \(0.447140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.45741 | 0.543812 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.36636 | −0.783254 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.8628 | −1.48343 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.03410 | −0.497684 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.10505 | 0.336299 | 0.168149 | − | 0.985762i | \(-0.446221\pi\) | ||||
0.168149 | + | 0.985762i | \(0.446221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4204 | −1.17351 | −0.586757 | − | 0.809763i | \(-0.699596\pi\) | ||||
−0.586757 | + | 0.809763i | \(0.699596\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.659840 | −0.0533449 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.63422 | −0.532874 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.50079 | 0.359202 | 0.179601 | − | 0.983740i | \(-0.442519\pi\) | ||||
0.179601 | + | 0.983740i | \(0.442519\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.47583 | 0.117041 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.76281 | −0.138929 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2204 | 1.03550 | 0.517749 | − | 0.855532i | \(-0.326770\pi\) | ||||
0.517749 | + | 0.855532i | \(0.326770\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.7111 | 0.911706 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.6872 | −1.91035 | −0.955176 | − | 0.296038i | \(-0.904334\pi\) | ||||
−0.955176 | + | 0.296038i | \(0.904334\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.66342 | −0.358724 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.91239 | 0.222716 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.0619 | −1.14513 | −0.572566 | − | 0.819859i | \(-0.694052\pi\) | ||||
−0.572566 | + | 0.819859i | \(0.694052\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.89474 | 0.596786 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.809188 | −0.0608223 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9460 | −1.64032 | −0.820161 | − | 0.572134i | \(-0.806116\pi\) | ||||
−0.820161 | + | 0.572134i | \(0.806116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.3387 | −1.51176 | −0.755882 | − | 0.654708i | \(-0.772792\pi\) | ||||
−0.755882 | + | 0.654708i | \(0.772792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.89425 | 0.731404 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 42.4084 | 3.11793 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14050 | 0.156529 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.982804 | 0.0714885 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.04043 | 0.364713 | 0.182356 | − | 0.983233i | \(-0.441628\pi\) | ||||
0.182356 | + | 0.983233i | \(0.441628\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.77910 | 0.128062 | 0.0640311 | − | 0.997948i | \(-0.479604\pi\) | ||||
0.0640311 | + | 0.997948i | \(0.479604\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.4235 | −0.746443 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.17972 | 0.226546 | 0.113273 | − | 0.993564i | \(-0.463867\pi\) | ||||
0.113273 | + | 0.993564i | \(0.463867\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0516 | −0.854312 | −0.427156 | − | 0.904178i | \(-0.640485\pi\) | ||||
−0.427156 | + | 0.904178i | \(0.640485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.49893 | 0.528934 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.86292 | 0.341310 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.5903 | 0.809502 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.79366 | −0.124668 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.44769 | −0.653510 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.06555 | −0.417570 | −0.208785 | − | 0.977962i | \(-0.566951\pi\) | ||||
−0.208785 | + | 0.977962i | \(0.566951\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.1492 | −0.763929 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.8760 | 1.96933 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.80608 | 0.122605 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.6862 | 0.722105 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.90516 | −0.128155 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.4945 | −1.84117 | −0.920583 | − | 0.390547i | \(-0.872286\pi\) | ||||
−0.920583 | + | 0.390547i | \(0.872286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.03288 | 0.535525 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.283813 | −0.0188373 | −0.00941867 | − | 0.999956i | \(-0.502998\pi\) | ||||
−0.00941867 | + | 0.999956i | \(0.502998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0508 | 1.12675 | 0.563375 | − | 0.826201i | \(-0.309503\pi\) | ||||
0.563375 | + | 0.826201i | \(0.309503\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.18818 | −0.209767 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.24231 | 0.146899 | 0.0734494 | − | 0.997299i | \(-0.476599\pi\) | ||||
0.0734494 | + | 0.997299i | \(0.476599\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.3119 | −1.52070 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.03225 | 0.326880 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.40186 | −0.220048 | −0.110024 | − | 0.993929i | \(-0.535093\pi\) | ||||
−0.110024 | + | 0.993929i | \(0.535093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0872 | −1.10069 | −0.550343 | − | 0.834939i | \(-0.685503\pi\) | ||||
−0.550343 | + | 0.834939i | \(0.685503\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.7837 | 1.39171 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.40898 | 0.535050 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.32413 | 0.210658 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.1261 | 1.90154 | 0.950771 | − | 0.309894i | \(-0.100293\pi\) | ||||
0.950771 | + | 0.309894i | \(0.100293\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.81857 | 0.365810 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.38209 | 0.149172 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.5832 | −0.784919 | −0.392459 | − | 0.919769i | \(-0.628376\pi\) | ||||
−0.392459 | + | 0.919769i | \(0.628376\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.5451 | −0.717380 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.94801 | 0.306274 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.6752 | −1.89151 | −0.945755 | − | 0.324879i | \(-0.894676\pi\) | ||||
−0.945755 | + | 0.324879i | \(0.894676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.32790 | −0.327290 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.58863 | −0.464417 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.8127 | −1.20800 | −0.604002 | − | 0.796983i | \(-0.706428\pi\) | ||||
−0.604002 | + | 0.796983i | \(0.706428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.89053 | −0.297078 | −0.148539 | − | 0.988907i | \(-0.547457\pi\) | ||||
−0.148539 | + | 0.988907i | \(0.547457\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.83766 | 0.171743 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.0584 | −1.57138 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.15322 | 0.249543 | 0.124771 | − | 0.992186i | \(-0.460180\pi\) | ||||
0.124771 | + | 0.992186i | \(0.460180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.83768 | 0.110019 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.7832 | 1.89603 | 0.948014 | − | 0.318229i | \(-0.103088\pi\) | ||||
0.948014 | + | 0.318229i | \(0.103088\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6889 | 0.694832 | 0.347416 | − | 0.937711i | \(-0.387059\pi\) | ||||
0.347416 | + | 0.937711i | \(0.387059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.5140 | −0.622797 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.15531 | −0.186252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5646 | −0.974389 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.87712 | −0.168660 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.6797 | 1.73391 | 0.866954 | − | 0.498389i | \(-0.166075\pi\) | ||||
0.866954 | + | 0.498389i | \(0.166075\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.92126 | 0.170082 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.24397 | −0.188234 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.17885 | −0.299501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.86110 | −0.453106 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.3446 | −0.938972 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −35.7193 | −2.04528 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.25970 | 0.471406 | 0.235703 | − | 0.971825i | \(-0.424261\pi\) | ||||
0.235703 | + | 0.971825i | \(0.424261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.54509 | 0.144785 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.6765 | −1.28587 | −0.642934 | − | 0.765921i | \(-0.722283\pi\) | ||||
−0.642934 | + | 0.765921i | \(0.722283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.6755 | 1.05560 | 0.527800 | − | 0.849369i | \(-0.323017\pi\) | ||||
0.527800 | + | 0.849369i | \(0.323017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.54803 | −0.199909 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.1281 | −0.568849 | −0.284425 | − | 0.958698i | \(-0.591803\pi\) | ||||
−0.284425 | + | 0.958698i | \(0.591803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0512 | −0.898693 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.87320 | −0.271995 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.92171 | −0.106927 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.1934 | 1.28654 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.63845 | 0.422407 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.34636 | 0.349886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.0075 | −1.42950 | −0.714752 | − | 0.699378i | \(-0.753460\pi\) | ||||
−0.714752 | + | 0.699378i | \(0.753460\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.7471 | −0.643739 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27.0719 | −1.47910 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.94577 | −0.323887 | −0.161943 | − | 0.986800i | \(-0.551776\pi\) | ||||
−0.161943 | + | 0.986800i | \(0.551776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.11980 | −0.278069 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.96138 | −0.322827 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.8100 | −0.691673 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.47529 | 0.348618 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.2019 | −0.923446 | −0.461723 | − | 0.887024i | \(-0.652769\pi\) | ||||
−0.461723 | + | 0.887024i | \(0.652769\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.9725 | −1.33675 | −0.668373 | − | 0.743826i | \(-0.733009\pi\) | ||||
−0.668373 | + | 0.743826i | \(0.733009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.88731 | 0.154113 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.7066 | 1.04888 | 0.524439 | − | 0.851448i | \(-0.324275\pi\) | ||||
0.524439 | + | 0.851448i | \(0.324275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 40.2497 | 2.13623 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.648493 | −0.0343219 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.4459 | −1.50132 | −0.750659 | − | 0.660690i | \(-0.770264\pi\) | ||||
−0.750659 | + | 0.660690i | \(0.770264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5180 | −0.553579 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.476671 | −0.0250187 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38.5783 | −2.01928 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.27326 | −0.327461 | −0.163731 | − | 0.986505i | \(-0.552353\pi\) | ||||
−0.163731 | + | 0.986505i | \(0.552353\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.21052 | −0.167133 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.45045 | 0.0753036 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.2395 | −0.633739 | −0.316869 | − | 0.948469i | \(-0.602632\pi\) | ||||
−0.316869 | + | 0.948469i | \(0.602632\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.9490 | −0.565404 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.2865 | 0.735790 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.1898 | 1.80758 | 0.903791 | − | 0.427975i | \(-0.140773\pi\) | ||||
0.903791 | + | 0.427975i | \(0.140773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.6475 | −0.904107 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.5142 | −0.894933 | −0.447466 | − | 0.894301i | \(-0.647674\pi\) | ||||
−0.447466 | + | 0.894301i | \(0.647674\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.5097 | 0.586588 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.99865 | −0.406594 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.0155 | −1.01482 | −0.507412 | − | 0.861703i | \(-0.669398\pi\) | ||||
−0.507412 | + | 0.861703i | \(0.669398\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18353 | 0.0598535 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.70788 | 0.0861511 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.1670 | −0.914079 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1966 | 0.511754 | 0.255877 | − | 0.966709i | \(-0.417636\pi\) | ||||
0.255877 | + | 0.966709i | \(0.417636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.86231 | 0.143294 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.4700 | 1.77129 | 0.885644 | − | 0.464365i | \(-0.153718\pi\) | ||||
0.885644 | + | 0.464365i | \(0.153718\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.30596 | 0.264309 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.61011 | −0.179388 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.1073 | 1.88891 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.916877 | 0.0453367 | 0.0226683 | − | 0.999743i | \(-0.492784\pi\) | ||||
0.0226683 | + | 0.999743i | \(0.492784\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.5861 | −0.916785 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.795273 | −0.0391328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0005 | −0.589080 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.89774 | 0.190873 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.3084 | 0.601306 | 0.300653 | − | 0.953734i | \(-0.402795\pi\) | ||||
0.300653 | + | 0.953734i | \(0.402795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.6876 | −0.959513 | −0.479756 | − | 0.877402i | \(-0.659275\pi\) | ||||
−0.479756 | + | 0.877402i | \(0.659275\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.45741 | 0.313970 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.30041 | −0.257108 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.72410 | 0.470582 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.36636 | −0.452212 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.5878 | −0.654502 | −0.327251 | − | 0.944937i | \(-0.606122\pi\) | ||||
−0.327251 | + | 0.944937i | \(0.606122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.3972 | 1.50886 | 0.754428 | − | 0.656383i | \(-0.227915\pi\) | ||||
0.754428 | + | 0.656383i | \(0.227915\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.8628 | −0.856458 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.22382 | −0.249889 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.8580 | 1.90232 | 0.951159 | − | 0.308702i | \(-0.0998946\pi\) | ||||
0.951159 | + | 0.308702i | \(0.0998946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.03410 | −0.287338 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2583 | 0.487388 | 0.243694 | − | 0.969852i | \(-0.421641\pi\) | ||||
0.243694 | + | 0.969852i | \(0.421641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.3958 | 1.29868 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.10505 | 0.194162 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.6778 | 0.787076 | 0.393538 | − | 0.919308i | \(-0.371251\pi\) | ||||
0.393538 | + | 0.919308i | \(0.371251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4148 | 0.490414 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.4204 | −0.677529 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.2443 | −0.480259 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.16028 | −0.241388 | −0.120694 | − | 0.992690i | \(-0.538512\pi\) | ||||
−0.120694 | + | 0.992690i | \(0.538512\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.659840 | −0.0307987 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.8986 | 1.25279 | 0.626397 | − | 0.779504i | \(-0.284529\pi\) | ||||
0.626397 | + | 0.779504i | \(0.284529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9121 | 0.925394 | 0.462697 | − | 0.886516i | \(-0.346882\pi\) | ||||
0.462697 | + | 0.886516i | \(0.346882\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.63422 | −0.307655 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.8936 | −0.874291 | −0.437145 | − | 0.899391i | \(-0.644010\pi\) | ||||
−0.437145 | + | 0.899391i | \(0.644010\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.36998 | 0.340314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.50079 | 0.207385 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.9474 | 1.19306 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.3948 | 1.07343 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.47583 | 0.0675735 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.4848 | 0.753208 | 0.376604 | − | 0.926374i | \(-0.377092\pi\) | ||||
0.376604 | + | 0.926374i | \(0.377092\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.9177 | −1.54651 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.76281 | −0.0802108 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3867 | 0.471636 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.18003 | 0.370672 | 0.185336 | − | 0.982675i | \(-0.440663\pi\) | ||||
0.185336 | + | 0.982675i | \(0.440663\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.2204 | 0.597845 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.85552 | −0.309385 | −0.154693 | − | 0.987963i | \(-0.549439\pi\) | ||||
−0.154693 | + | 0.987963i | \(0.549439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.26489 | −0.147043 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.7111 | 0.526374 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.9575 | −0.491509 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7738 | 0.661366 | 0.330683 | − | 0.943742i | \(-0.392721\pi\) | ||||
0.330683 | + | 0.943742i | \(0.392721\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.6872 | −1.10294 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 59.0057 | 2.62572 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.66342 | −0.207110 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5415 | −0.777513 | −0.388756 | − | 0.921341i | \(-0.627095\pi\) | ||||
−0.388756 | + | 0.921341i | \(0.627095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.5024 | 0.464600 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.91239 | 0.128585 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.18806 | −0.404874 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.9476 | −0.921275 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0619 | −0.661142 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1933 | 0.665629 | 0.332815 | − | 0.942992i | \(-0.392002\pi\) | ||||
0.332815 | + | 0.942992i | \(0.392002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1425 | 0.487227 | 0.243613 | − | 0.969872i | \(-0.421667\pi\) | ||||
0.243613 | + | 0.969872i | \(0.421667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.89474 | 0.344555 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.21257 | −0.0528205 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7828 | −0.860122 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.809188 | −0.0351158 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.26977 | −0.401518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.5928 | 0.760602 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.9460 | −0.947040 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.5744 | 0.843130 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.2768 | −1.60265 | −0.801327 | − | 0.598227i | \(-0.795872\pi\) | ||||
−0.801327 | + | 0.598227i | \(0.795872\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.3387 | −0.872817 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.5756 | −1.18121 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.50714 | −0.192711 | −0.0963556 | − | 0.995347i | \(-0.530719\pi\) | ||||
−0.0963556 | + | 0.995347i | \(0.530719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.89425 | 0.422276 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4105 | 0.613909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.94571 | 0.210313 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.4084 | 1.80014 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.53654 | 0.361705 | 0.180852 | − | 0.983510i | \(-0.442114\pi\) | ||||
0.180852 | + | 0.983510i | \(0.442114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.0946 | −0.976798 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.14050 | 0.0903719 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.17805 | −0.386809 | −0.193404 | − | 0.981119i | \(-0.561953\pi\) | ||||
−0.193404 | + | 0.981119i | \(0.561953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.4830 | 0.777586 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.982804 | 0.0412739 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.61067 | 0.193289 | 0.0966447 | − | 0.995319i | \(-0.469189\pi\) | ||||
0.0966447 | + | 0.995319i | \(0.469189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.0793 | −1.76097 | −0.880483 | − | 0.474078i | \(-0.842781\pi\) | ||||
−0.880483 | + | 0.474078i | \(0.842781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.04043 | 0.210567 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.4082 | −0.600864 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7259 | −0.779568 | −0.389784 | − | 0.920906i | \(-0.627450\pi\) | ||||
−0.389784 | + | 0.920906i | \(0.627450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.77910 | 0.0739368 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.26697 | 0.135537 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.78754 | −0.198280 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.4235 | −0.430959 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3897 | 0.717751 | 0.358875 | − | 0.933386i | \(-0.383160\pi\) | ||||
0.358875 | + | 0.933386i | \(0.383160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.35204 | 0.220527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.17972 | 0.130796 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.8250 | −0.526659 | −0.263329 | − | 0.964706i | \(-0.584821\pi\) | ||||
−0.263329 | + | 0.964706i | \(0.584821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.34113 | 0.0959769 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.0516 | −0.493238 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.8287 | 1.62736 | 0.813679 | − | 0.581314i | \(-0.197461\pi\) | ||||
0.813679 | + | 0.581314i | \(0.197461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5019 | −0.591544 | −0.295772 | − | 0.955259i | \(-0.595577\pi\) | ||||
−0.295772 | + | 0.955259i | \(0.595577\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.49893 | 0.305380 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.72083 | 0.0699619 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.7344 | 1.65336 | 0.826679 | − | 0.562674i | \(-0.190227\pi\) | ||||
0.826679 | + | 0.562674i | \(0.190227\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.86292 | 0.197055 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.6446 | 0.754278 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.7028 | 0.432283 | 0.216142 | − | 0.976362i | \(-0.430653\pi\) | ||||
0.216142 | + | 0.976362i | \(0.430653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.5903 | 0.467366 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.7939 | 0.676097 | 0.338048 | − | 0.941129i | \(-0.390233\pi\) | ||||
0.338048 | + | 0.941129i | \(0.390233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.2650 | 0.653747 | 0.326874 | − | 0.945068i | \(-0.394005\pi\) | ||||
0.326874 | + | 0.945068i | \(0.394005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.79366 | −0.0719770 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.45814 | −0.298804 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.637277 | −0.0254911 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.44769 | −0.377304 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.75122 | 0.309062 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.68508 | −0.186510 | −0.0932550 | − | 0.995642i | \(-0.529727\pi\) | ||||
−0.0932550 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.06555 | −0.241084 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 63.7092 | 2.52822 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.4223 | −0.690298 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.1492 | −0.441055 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.2973 | 1.11768 | 0.558838 | − | 0.829277i | \(-0.311247\pi\) | ||||
0.558838 | + | 0.829277i | \(0.311247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0424 | −0.396034 | −0.198017 | − | 0.980199i | \(-0.563450\pi\) | ||||
−0.198017 | + | 0.980199i | \(0.563450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.8760 | 1.13699 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.03715 | −0.0407745 | −0.0203872 | − | 0.999792i | \(-0.506490\pi\) | ||||
−0.0203872 | + | 0.999792i | \(0.506490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.62498 | 0.103040 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.80608 | 0.0707858 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.4029 | 0.524497 | 0.262249 | − | 0.965000i | \(-0.415536\pi\) | ||||
0.262249 | + | 0.965000i | \(0.415536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.16562 | −0.240911 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.6862 | 0.416908 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.5472 | 0.956222 | 0.478111 | − | 0.878300i | \(-0.341322\pi\) | ||||
0.478111 | + | 0.878300i | \(0.341322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5544 | −0.799474 | −0.399737 | − | 0.916630i | \(-0.630899\pi\) | ||||
−0.399737 | + | 0.916630i | \(0.630899\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.90516 | −0.0739904 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.3332 | −0.400705 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.87503 | −0.343642 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.4945 | −1.06300 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.0966 | −1.23908 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.8226 | −1.03394 | −0.516968 | − | 0.856004i | \(-0.672940\pi\) | ||||
−0.516968 | + | 0.856004i | \(0.672940\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.03288 | 0.309186 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.8612 | −0.571164 | −0.285582 | − | 0.958354i | \(-0.592187\pi\) | ||||
−0.285582 | + | 0.958354i | \(0.592187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.82764 | −0.108515 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.283813 | −0.0108757 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.4164 | 0.972531 | 0.486266 | − | 0.873811i | \(-0.338359\pi\) | ||||
0.486266 | + | 0.873811i | \(0.338359\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 67.0979 | 2.56368 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.0508 | 0.650529 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.26118 | 0.162338 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5592 | 0.667985 | 0.333993 | − | 0.942576i | \(-0.391604\pi\) | ||||
0.333993 | + | 0.942576i | \(0.391604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.18818 | −0.121109 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.0713 | −0.533753 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.11843 | 0.0802411 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.24231 | 0.0848121 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.15151 | −0.307878 | −0.153939 | − | 0.988080i | \(-0.549196\pi\) | ||||
−0.153939 | + | 0.988080i | \(0.549196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.2122 | −1.29034 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.3119 | −0.877978 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.0635 | −0.604131 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.77253 | 0.254348 | 0.127174 | − | 0.991880i | \(-0.459409\pi\) | ||||
0.127174 | + | 0.991880i | \(0.459409\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.03225 | 0.188724 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.29617 | −0.123442 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.8136 | 1.26456 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.40186 | −0.127045 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.3219 | 0.683293 | 0.341646 | − | 0.939829i | \(-0.389015\pi\) | ||||
0.341646 | + | 0.939829i | \(0.389015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.50133 | 0.0931543 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.0872 | −0.635481 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.7467 | 1.47616 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7886 | −0.511393 | −0.255696 | − | 0.966757i | \(-0.582305\pi\) | ||||
−0.255696 | + | 0.966757i | \(0.582305\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.27782 | 0.195207 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.1474 | −0.781098 | −0.390549 | − | 0.920582i | \(-0.627715\pi\) | ||||
−0.390549 | + | 0.920582i | \(0.627715\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.7837 | 0.803505 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.3263 | −0.896070 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.3081 | 0.599903 | 0.299951 | − | 0.953954i | \(-0.403030\pi\) | ||||
0.299951 | + | 0.953954i | \(0.403030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.40898 | 0.308911 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.49786 | −0.311756 | −0.155878 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155878 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.8197 | −0.542950 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.32413 | 0.121624 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.78940 | −0.175001 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.21411 | −0.153775 | −0.0768876 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768876 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.1261 | 1.09786 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 52.0591 | 1.89463 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.1650 | −1.16906 | −0.584529 | − | 0.811373i | \(-0.698721\pi\) | ||||
−0.584529 | + | 0.811373i | \(0.698721\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.81857 | 0.211201 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.2414 | −0.697500 | −0.348750 | − | 0.937216i | \(-0.613394\pi\) | ||||
−0.348750 | + | 0.937216i | \(0.613394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.50710 | 0.271775 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.38209 | 0.0861247 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.33638 | −0.0843618 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.1211 | 0.689525 | 0.344762 | − | 0.938690i | \(-0.387959\pi\) | ||||
0.344762 | + | 0.938690i | \(0.387959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.5832 | −0.453173 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.6237 | −0.669849 | −0.334924 | − | 0.942245i | \(-0.608711\pi\) | ||||
−0.334924 | + | 0.942245i | \(0.608711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.7619 | 0.530262 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.5451 | −0.414179 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.35027 | −0.335008 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.1676 | 1.29418 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.94801 | 0.176827 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.2483 | −0.579928 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.1489 | 1.68068 | 0.840339 | − | 0.542062i | \(-0.182356\pi\) | ||||
0.840339 | + | 0.542062i | \(0.182356\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.6752 | −1.09206 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.03175 | −0.178909 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.5678 | 1.01447 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.32790 | −0.188961 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.7918 | 0.382267 | 0.191133 | − | 0.981564i | \(-0.438784\pi\) | ||||
0.191133 | + | 0.981564i | \(0.438784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.26085 | −0.150738 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.58863 | −0.268131 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.6656 | −1.22332 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.36394 | 0.224300 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.8127 | −0.697441 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5806 | 0.688416 | 0.344208 | − | 0.938893i | \(-0.388147\pi\) | ||||
0.344208 | + | 0.938893i | \(0.388147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.14317 | 0.250831 | 0.125415 | − | 0.992104i | \(-0.459974\pi\) | ||||
0.125415 | + | 0.992104i | \(0.459974\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.89053 | −0.171518 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47.7269 | −1.67180 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.2952 | −0.814994 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.83766 | 0.0991560 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0758 | 0.700649 | 0.350325 | − | 0.936628i | \(-0.386071\pi\) | ||||
0.350325 | + | 0.936628i | \(0.386071\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.7764 | −1.31680 | −0.658401 | − | 0.752667i | \(-0.728767\pi\) | ||||
−0.658401 | + | 0.752667i | \(0.728767\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −26.0584 | −0.907237 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.1818 | 0.562696 | 0.281348 | − | 0.959606i | \(-0.409218\pi\) | ||||
0.281348 | + | 0.959606i | \(0.409218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.75821 | −0.130528 | −0.0652641 | − | 0.997868i | \(-0.520789\pi\) | ||||
−0.0652641 | + | 0.997868i | \(0.520789\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.15322 | 0.144074 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.98154 | 0.137952 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 89.1234 | 3.08424 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.83768 | 0.0635195 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.2261 | 0.698284 | 0.349142 | − | 0.937070i | \(-0.386473\pi\) | ||||
0.349142 | + | 0.937070i | \(0.386473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.51722 | −0.155766 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.7832 | 1.09467 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.8354 | 0.579156 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.468474 | −0.0160970 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.6889 | 0.401161 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.0703 | 0.722282 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.1132 | −0.380508 | −0.190254 | − | 0.981735i | \(-0.560931\pi\) | ||||
−0.190254 | + | 0.981735i | \(0.560931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.5140 | −0.359572 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.1874 | −1.09950 | −0.549750 | − | 0.835329i | \(-0.685277\pi\) | ||||
−0.549750 | + | 0.835329i | \(0.685277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.71379 | −0.331430 | −0.165715 | − | 0.986174i | \(-0.552993\pi\) | ||||
−0.165715 | + | 0.986174i | \(0.552993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.15531 | −0.107533 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.5958 | −0.428765 | −0.214383 | − | 0.976750i | \(-0.568774\pi\) | ||||
−0.214383 | + | 0.976750i | \(0.568774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.3749 | 1.84880 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.5646 | −0.562564 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.3245 | −0.553769 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.6518 | 0.733642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.87712 | −0.0973757 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.7607 | −0.363779 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.7071 | 1.47588 | 0.737942 | − | 0.674865i | \(-0.235798\pi\) | ||||
0.737942 | + | 0.674865i | \(0.235798\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.6797 | 1.00107 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.6184 | −0.492507 | −0.246253 | − | 0.969205i | \(-0.579200\pi\) | ||||
−0.246253 | + | 0.969205i | \(0.579200\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.2901 | −0.480899 | −0.240450 | − | 0.970662i | \(-0.577295\pi\) | ||||
−0.240450 | + | 0.970662i | \(0.577295\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.92126 | 0.0981970 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.5310 | −0.991554 | −0.495777 | − | 0.868450i | \(-0.665117\pi\) | ||||
−0.495777 | + | 0.868450i | \(0.665117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.3440 | −0.581699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.24397 | −0.108677 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.8065 | 0.629334 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 79.2274 | 2.64828 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.17885 | −0.172917 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.09285 | 0.303264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.973810 | −0.0324423 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.86110 | −0.261601 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 73.4249 | 2.44073 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.87205 | 0.261387 | 0.130694 | − | 0.991423i | \(-0.458280\pi\) | ||||
0.130694 | + | 0.991423i | \(0.458280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.3446 | −0.542116 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.6372 | −0.849398 | −0.424699 | − | 0.905335i | \(-0.639620\pi\) | ||||
−0.424699 | + | 0.905335i | \(0.639620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.7834 | −0.356877 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −35.7193 | −1.18084 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.67851 | 0.0554293 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.6491 | 1.57180 | 0.785900 | − | 0.618354i | \(-0.212200\pi\) | ||||
0.785900 | + | 0.618354i | \(0.212200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.25970 | 0.272166 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.1912 | −1.05959 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −94.3633 | −3.10265 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.54509 | 0.0835918 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.1854 | −1.31844 | −0.659221 | − | 0.751949i | \(-0.729114\pi\) | ||||
−0.659221 | + | 0.751949i | \(0.729114\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5736 | −0.575952 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.6765 | −0.742397 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.72743 | −0.252714 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.331054 | 0.0108151 | 0.00540753 | − | 0.999985i | \(-0.498279\pi\) | ||||
0.00540753 | + | 0.999985i | \(0.498279\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.6755 | 0.609451 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.4168 | 1.44795 | 0.723973 | − | 0.689828i | \(-0.242314\pi\) | ||||
0.723973 | + | 0.689828i | \(0.242314\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.75857 | 0.187525 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.54803 | −0.115417 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.5325 | 1.70708 | 0.853538 | − | 0.521030i | \(-0.174452\pi\) | ||||
0.853538 | + | 0.521030i | \(0.174452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.8544 | 1.00158 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.1281 | −0.328425 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3105 | 1.04664 | 0.523320 | − | 0.852136i | \(-0.324693\pi\) | ||||
0.523320 | + | 0.852136i | \(0.324693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.1965 | −0.588825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.0512 | −0.518861 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.2665 | −0.589856 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6229 | −0.891062 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.87320 | −0.157037 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.42274 | −0.206755 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4425 | 0.914648 | 0.457324 | − | 0.889300i | \(-0.348808\pi\) | ||||
0.457324 | + | 0.889300i | \(0.348808\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.92171 | −0.0617342 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.2913 | −0.940004 | −0.470002 | − | 0.882665i | \(-0.655747\pi\) | ||||
−0.470002 | + | 0.882665i | \(0.655747\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.83071 | 0.122807 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.1934 | 0.742785 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.6562 | −0.724835 | −0.362417 | − | 0.932016i | \(-0.618048\pi\) | ||||
−0.362417 | + | 0.932016i | \(0.618048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.6173 | 0.786772 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.63845 | 0.243877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.2148 | −0.517173 | −0.258587 | − | 0.965988i | \(-0.583257\pi\) | ||||
−0.258587 | + | 0.965988i | \(0.583257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4791 | −0.365755 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.34636 | 0.202007 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3468 | 0.456203 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.9491 | 1.58669 | 0.793343 | − | 0.608774i | \(-0.208339\pi\) | ||||
0.793343 | + | 0.608774i | \(0.208339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.0075 | −0.825324 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.5074 | 1.37928 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.5213 | −1.85339 | −0.926694 | − | 0.375818i | \(-0.877362\pi\) | ||||
−0.926694 | + | 0.375818i | \(0.877362\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.7471 | −0.371663 |
(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 | 6036.2.a.g.1.3 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.g.1.3 | ✓ | 15 | 1.1 | even | 1 | trivial |