Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 36 x^{10} + 105 x^{9} + 465 x^{8} - 1287 x^{7} - 2668 x^{6} + 6443 x^{5} + 7140 x^{4} - 10858 x^{3} - 10086 x^{2} + 2072 x + 1496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.97453\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.97453 | −1.77746 | −0.888731 | − | 0.458428i | \(-0.848413\pi\) | ||||
−0.888731 | + | 0.458428i | \(0.848413\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.10909 | 0.797163 | 0.398581 | − | 0.917133i | \(-0.369503\pi\) | ||||
0.398581 | + | 0.917133i | \(0.369503\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.97453 | 1.25686 | ||||||||
\(11\) | −2.46089 | −0.741986 | −0.370993 | − | 0.928636i | \(-0.620983\pi\) | ||||
−0.370993 | + | 0.928636i | \(0.620983\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.30271 | −0.916007 | −0.458003 | − | 0.888950i | \(-0.651435\pi\) | ||||
−0.458003 | + | 0.888950i | \(0.651435\pi\) | |||||||
\(14\) | −2.10909 | −0.563679 | ||||||||
\(15\) | 3.97453 | 1.02622 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.57490 | −0.381970 | −0.190985 | − | 0.981593i | \(-0.561168\pi\) | ||||
−0.190985 | + | 0.981593i | \(0.561168\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −3.97453 | −0.888731 | ||||||||
\(21\) | −2.10909 | −0.460242 | ||||||||
\(22\) | 2.46089 | 0.524664 | ||||||||
\(23\) | 5.45116 | 1.13665 | 0.568323 | − | 0.822805i | \(-0.307592\pi\) | ||||
0.568323 | + | 0.822805i | \(0.307592\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 10.7969 | 2.15937 | ||||||||
\(26\) | 3.30271 | 0.647715 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.10909 | 0.398581 | ||||||||
\(29\) | −10.0009 | −1.85712 | −0.928558 | − | 0.371187i | \(-0.878951\pi\) | ||||
−0.928558 | + | 0.371187i | \(0.878951\pi\) | |||||||
\(30\) | −3.97453 | −0.725646 | ||||||||
\(31\) | 5.53168 | 0.993519 | 0.496759 | − | 0.867888i | \(-0.334523\pi\) | ||||
0.496759 | + | 0.867888i | \(0.334523\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.46089 | 0.428386 | ||||||||
\(34\) | 1.57490 | 0.270093 | ||||||||
\(35\) | −8.38265 | −1.41693 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.63437 | 1.58388 | 0.791941 | − | 0.610598i | \(-0.209071\pi\) | ||||
0.791941 | + | 0.610598i | \(0.209071\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 3.30271 | 0.528857 | ||||||||
\(40\) | 3.97453 | 0.628428 | ||||||||
\(41\) | −1.80309 | −0.281595 | −0.140797 | − | 0.990038i | \(-0.544967\pi\) | ||||
−0.140797 | + | 0.990038i | \(0.544967\pi\) | |||||||
\(42\) | 2.10909 | 0.325440 | ||||||||
\(43\) | 2.92497 | 0.446054 | 0.223027 | − | 0.974812i | \(-0.428406\pi\) | ||||
0.223027 | + | 0.974812i | \(0.428406\pi\) | |||||||
\(44\) | −2.46089 | −0.370993 | ||||||||
\(45\) | −3.97453 | −0.592488 | ||||||||
\(46\) | −5.45116 | −0.803730 | ||||||||
\(47\) | 3.51719 | 0.513035 | 0.256517 | − | 0.966540i | \(-0.417425\pi\) | ||||
0.256517 | + | 0.966540i | \(0.417425\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −2.55172 | −0.364532 | ||||||||
\(50\) | −10.7969 | −1.52691 | ||||||||
\(51\) | 1.57490 | 0.220530 | ||||||||
\(52\) | −3.30271 | −0.458003 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 9.78088 | 1.31885 | ||||||||
\(56\) | −2.10909 | −0.281840 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 10.0009 | 1.31318 | ||||||||
\(59\) | 2.26193 | 0.294478 | 0.147239 | − | 0.989101i | \(-0.452961\pi\) | ||||
0.147239 | + | 0.989101i | \(0.452961\pi\) | |||||||
\(60\) | 3.97453 | 0.513109 | ||||||||
\(61\) | −0.865226 | −0.110781 | −0.0553904 | − | 0.998465i | \(-0.517640\pi\) | ||||
−0.0553904 | + | 0.998465i | \(0.517640\pi\) | |||||||
\(62\) | −5.53168 | −0.702524 | ||||||||
\(63\) | 2.10909 | 0.265721 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.1267 | 1.62817 | ||||||||
\(66\) | −2.46089 | −0.302915 | ||||||||
\(67\) | 5.26523 | 0.643251 | 0.321625 | − | 0.946867i | \(-0.395771\pi\) | ||||
0.321625 | + | 0.946867i | \(0.395771\pi\) | |||||||
\(68\) | −1.57490 | −0.190985 | ||||||||
\(69\) | −5.45116 | −0.656243 | ||||||||
\(70\) | 8.38265 | 1.00192 | ||||||||
\(71\) | −0.404292 | −0.0479807 | −0.0239903 | − | 0.999712i | \(-0.507637\pi\) | ||||
−0.0239903 | + | 0.999712i | \(0.507637\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −11.0627 | −1.29479 | −0.647396 | − | 0.762154i | \(-0.724142\pi\) | ||||
−0.647396 | + | 0.762154i | \(0.724142\pi\) | |||||||
\(74\) | −9.63437 | −1.11997 | ||||||||
\(75\) | −10.7969 | −1.24672 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −5.19025 | −0.591484 | ||||||||
\(78\) | −3.30271 | −0.373958 | ||||||||
\(79\) | 8.91239 | 1.00272 | 0.501361 | − | 0.865238i | \(-0.332833\pi\) | ||||
0.501361 | + | 0.865238i | \(0.332833\pi\) | |||||||
\(80\) | −3.97453 | −0.444366 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.80309 | 0.199118 | ||||||||
\(83\) | 2.47817 | 0.272014 | 0.136007 | − | 0.990708i | \(-0.456573\pi\) | ||||
0.136007 | + | 0.990708i | \(0.456573\pi\) | |||||||
\(84\) | −2.10909 | −0.230121 | ||||||||
\(85\) | 6.25949 | 0.678937 | ||||||||
\(86\) | −2.92497 | −0.315408 | ||||||||
\(87\) | 10.0009 | 1.07221 | ||||||||
\(88\) | 2.46089 | 0.262332 | ||||||||
\(89\) | 13.5839 | 1.43989 | 0.719943 | − | 0.694033i | \(-0.244168\pi\) | ||||
0.719943 | + | 0.694033i | \(0.244168\pi\) | |||||||
\(90\) | 3.97453 | 0.418952 | ||||||||
\(91\) | −6.96573 | −0.730206 | ||||||||
\(92\) | 5.45116 | 0.568323 | ||||||||
\(93\) | −5.53168 | −0.573608 | ||||||||
\(94\) | −3.51719 | −0.362770 | ||||||||
\(95\) | 3.97453 | 0.407778 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.25414 | −0.736546 | −0.368273 | − | 0.929718i | \(-0.620051\pi\) | ||||
−0.368273 | + | 0.929718i | \(0.620051\pi\) | |||||||
\(98\) | 2.55172 | 0.257763 | ||||||||
\(99\) | −2.46089 | −0.247329 | ||||||||
\(100\) | 10.7969 | 1.07969 | ||||||||
\(101\) | −3.18748 | −0.317166 | −0.158583 | − | 0.987346i | \(-0.550693\pi\) | ||||
−0.158583 | + | 0.987346i | \(0.550693\pi\) | |||||||
\(102\) | −1.57490 | −0.155939 | ||||||||
\(103\) | −6.88698 | −0.678594 | −0.339297 | − | 0.940679i | \(-0.610189\pi\) | ||||
−0.339297 | + | 0.940679i | \(0.610189\pi\) | |||||||
\(104\) | 3.30271 | 0.323857 | ||||||||
\(105\) | 8.38265 | 0.818063 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 15.3991 | 1.48869 | 0.744345 | − | 0.667795i | \(-0.232762\pi\) | ||||
0.744345 | + | 0.667795i | \(0.232762\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −16.0466 | −1.53698 | −0.768491 | − | 0.639860i | \(-0.778992\pi\) | ||||
−0.768491 | + | 0.639860i | \(0.778992\pi\) | |||||||
\(110\) | −9.78088 | −0.932570 | ||||||||
\(111\) | −9.63437 | −0.914454 | ||||||||
\(112\) | 2.10909 | 0.199291 | ||||||||
\(113\) | 17.1265 | 1.61113 | 0.805565 | − | 0.592508i | \(-0.201862\pi\) | ||||
0.805565 | + | 0.592508i | \(0.201862\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −21.6658 | −2.02035 | ||||||||
\(116\) | −10.0009 | −0.928558 | ||||||||
\(117\) | −3.30271 | −0.305336 | ||||||||
\(118\) | −2.26193 | −0.208228 | ||||||||
\(119\) | −3.32162 | −0.304492 | ||||||||
\(120\) | −3.97453 | −0.362823 | ||||||||
\(121\) | −4.94402 | −0.449456 | ||||||||
\(122\) | 0.865226 | 0.0783339 | ||||||||
\(123\) | 1.80309 | 0.162579 | ||||||||
\(124\) | 5.53168 | 0.496759 | ||||||||
\(125\) | −23.0398 | −2.06075 | ||||||||
\(126\) | −2.10909 | −0.187893 | ||||||||
\(127\) | 8.31054 | 0.737441 | 0.368720 | − | 0.929540i | \(-0.379796\pi\) | ||||
0.368720 | + | 0.929540i | \(0.379796\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.92497 | −0.257529 | ||||||||
\(130\) | −13.1267 | −1.15129 | ||||||||
\(131\) | −5.70281 | −0.498256 | −0.249128 | − | 0.968471i | \(-0.580144\pi\) | ||||
−0.249128 | + | 0.968471i | \(0.580144\pi\) | |||||||
\(132\) | 2.46089 | 0.214193 | ||||||||
\(133\) | −2.10909 | −0.182882 | ||||||||
\(134\) | −5.26523 | −0.454847 | ||||||||
\(135\) | 3.97453 | 0.342073 | ||||||||
\(136\) | 1.57490 | 0.135047 | ||||||||
\(137\) | −9.04968 | −0.773166 | −0.386583 | − | 0.922255i | \(-0.626345\pi\) | ||||
−0.386583 | + | 0.922255i | \(0.626345\pi\) | |||||||
\(138\) | 5.45116 | 0.464034 | ||||||||
\(139\) | 10.4617 | 0.887346 | 0.443673 | − | 0.896189i | \(-0.353675\pi\) | ||||
0.443673 | + | 0.896189i | \(0.353675\pi\) | |||||||
\(140\) | −8.38265 | −0.708464 | ||||||||
\(141\) | −3.51719 | −0.296201 | ||||||||
\(142\) | 0.404292 | 0.0339275 | ||||||||
\(143\) | 8.12761 | 0.679664 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 39.7488 | 3.30096 | ||||||||
\(146\) | 11.0627 | 0.915556 | ||||||||
\(147\) | 2.55172 | 0.210462 | ||||||||
\(148\) | 9.63437 | 0.791941 | ||||||||
\(149\) | 9.83811 | 0.805970 | 0.402985 | − | 0.915207i | \(-0.367973\pi\) | ||||
0.402985 | + | 0.915207i | \(0.367973\pi\) | |||||||
\(150\) | 10.7969 | 0.881561 | ||||||||
\(151\) | 9.31710 | 0.758215 | 0.379107 | − | 0.925353i | \(-0.376231\pi\) | ||||
0.379107 | + | 0.925353i | \(0.376231\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −1.57490 | −0.127323 | ||||||||
\(154\) | 5.19025 | 0.418242 | ||||||||
\(155\) | −21.9858 | −1.76594 | ||||||||
\(156\) | 3.30271 | 0.264428 | ||||||||
\(157\) | 3.48510 | 0.278142 | 0.139071 | − | 0.990282i | \(-0.455588\pi\) | ||||
0.139071 | + | 0.990282i | \(0.455588\pi\) | |||||||
\(158\) | −8.91239 | −0.709032 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | 3.97453 | 0.314214 | ||||||||
\(161\) | 11.4970 | 0.906092 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 14.0163 | 1.09784 | 0.548920 | − | 0.835875i | \(-0.315039\pi\) | ||||
0.548920 | + | 0.835875i | \(0.315039\pi\) | |||||||
\(164\) | −1.80309 | −0.140797 | ||||||||
\(165\) | −9.78088 | −0.761440 | ||||||||
\(166\) | −2.47817 | −0.192343 | ||||||||
\(167\) | −14.3928 | −1.11375 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(168\) | 2.10909 | 0.162720 | ||||||||
\(169\) | −2.09211 | −0.160932 | ||||||||
\(170\) | −6.25949 | −0.480081 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 2.92497 | 0.223027 | ||||||||
\(173\) | 14.2954 | 1.08686 | 0.543429 | − | 0.839455i | \(-0.317126\pi\) | ||||
0.543429 | + | 0.839455i | \(0.317126\pi\) | |||||||
\(174\) | −10.0009 | −0.758165 | ||||||||
\(175\) | 22.7716 | 1.72137 | ||||||||
\(176\) | −2.46089 | −0.185497 | ||||||||
\(177\) | −2.26193 | −0.170017 | ||||||||
\(178\) | −13.5839 | −1.01815 | ||||||||
\(179\) | −18.5238 | −1.38453 | −0.692265 | − | 0.721643i | \(-0.743387\pi\) | ||||
−0.692265 | + | 0.721643i | \(0.743387\pi\) | |||||||
\(180\) | −3.97453 | −0.296244 | ||||||||
\(181\) | −12.3606 | −0.918754 | −0.459377 | − | 0.888241i | \(-0.651927\pi\) | ||||
−0.459377 | + | 0.888241i | \(0.651927\pi\) | |||||||
\(182\) | 6.96573 | 0.516334 | ||||||||
\(183\) | 0.865226 | 0.0639594 | ||||||||
\(184\) | −5.45116 | −0.401865 | ||||||||
\(185\) | −38.2921 | −2.81529 | ||||||||
\(186\) | 5.53168 | 0.405602 | ||||||||
\(187\) | 3.87566 | 0.283416 | ||||||||
\(188\) | 3.51719 | 0.256517 | ||||||||
\(189\) | −2.10909 | −0.153414 | ||||||||
\(190\) | −3.97453 | −0.288343 | ||||||||
\(191\) | 9.88051 | 0.714929 | 0.357464 | − | 0.933927i | \(-0.383641\pi\) | ||||
0.357464 | + | 0.933927i | \(0.383641\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 15.7028 | 1.13031 | 0.565155 | − | 0.824985i | \(-0.308816\pi\) | ||||
0.565155 | + | 0.824985i | \(0.308816\pi\) | |||||||
\(194\) | 7.25414 | 0.520817 | ||||||||
\(195\) | −13.1267 | −0.940023 | ||||||||
\(196\) | −2.55172 | −0.182266 | ||||||||
\(197\) | −9.57072 | −0.681885 | −0.340943 | − | 0.940084i | \(-0.610746\pi\) | ||||
−0.340943 | + | 0.940084i | \(0.610746\pi\) | |||||||
\(198\) | 2.46089 | 0.174888 | ||||||||
\(199\) | 22.1102 | 1.56735 | 0.783674 | − | 0.621173i | \(-0.213343\pi\) | ||||
0.783674 | + | 0.621173i | \(0.213343\pi\) | |||||||
\(200\) | −10.7969 | −0.763454 | ||||||||
\(201\) | −5.26523 | −0.371381 | ||||||||
\(202\) | 3.18748 | 0.224270 | ||||||||
\(203\) | −21.0928 | −1.48042 | ||||||||
\(204\) | 1.57490 | 0.110265 | ||||||||
\(205\) | 7.16642 | 0.500524 | ||||||||
\(206\) | 6.88698 | 0.479838 | ||||||||
\(207\) | 5.45116 | 0.378882 | ||||||||
\(208\) | −3.30271 | −0.229002 | ||||||||
\(209\) | 2.46089 | 0.170223 | ||||||||
\(210\) | −8.38265 | −0.578458 | ||||||||
\(211\) | −0.942588 | −0.0648904 | −0.0324452 | − | 0.999474i | \(-0.510329\pi\) | ||||
−0.0324452 | + | 0.999474i | \(0.510329\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | 0.404292 | 0.0277017 | ||||||||
\(214\) | −15.3991 | −1.05266 | ||||||||
\(215\) | −11.6254 | −0.792844 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 11.6668 | 0.791996 | ||||||||
\(218\) | 16.0466 | 1.08681 | ||||||||
\(219\) | 11.0627 | 0.747548 | ||||||||
\(220\) | 9.78088 | 0.659427 | ||||||||
\(221\) | 5.20144 | 0.349887 | ||||||||
\(222\) | 9.63437 | 0.646617 | ||||||||
\(223\) | −23.1801 | −1.55225 | −0.776127 | − | 0.630577i | \(-0.782818\pi\) | ||||
−0.776127 | + | 0.630577i | \(0.782818\pi\) | |||||||
\(224\) | −2.10909 | −0.140920 | ||||||||
\(225\) | 10.7969 | 0.719792 | ||||||||
\(226\) | −17.1265 | −1.13924 | ||||||||
\(227\) | 10.0649 | 0.668029 | 0.334014 | − | 0.942568i | \(-0.391597\pi\) | ||||
0.334014 | + | 0.942568i | \(0.391597\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 2.12287 | 0.140283 | 0.0701417 | − | 0.997537i | \(-0.477655\pi\) | ||||
0.0701417 | + | 0.997537i | \(0.477655\pi\) | |||||||
\(230\) | 21.6658 | 1.42860 | ||||||||
\(231\) | 5.19025 | 0.341493 | ||||||||
\(232\) | 10.0009 | 0.656590 | ||||||||
\(233\) | −27.1529 | −1.77884 | −0.889422 | − | 0.457088i | \(-0.848893\pi\) | ||||
−0.889422 | + | 0.457088i | \(0.848893\pi\) | |||||||
\(234\) | 3.30271 | 0.215905 | ||||||||
\(235\) | −13.9792 | −0.911901 | ||||||||
\(236\) | 2.26193 | 0.147239 | ||||||||
\(237\) | −8.91239 | −0.578922 | ||||||||
\(238\) | 3.32162 | 0.215308 | ||||||||
\(239\) | 5.70151 | 0.368800 | 0.184400 | − | 0.982851i | \(-0.440966\pi\) | ||||
0.184400 | + | 0.982851i | \(0.440966\pi\) | |||||||
\(240\) | 3.97453 | 0.256555 | ||||||||
\(241\) | 16.6620 | 1.07330 | 0.536648 | − | 0.843807i | \(-0.319690\pi\) | ||||
0.536648 | + | 0.843807i | \(0.319690\pi\) | |||||||
\(242\) | 4.94402 | 0.317814 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.865226 | −0.0553904 | ||||||||
\(245\) | 10.1419 | 0.647941 | ||||||||
\(246\) | −1.80309 | −0.114961 | ||||||||
\(247\) | 3.30271 | 0.210146 | ||||||||
\(248\) | −5.53168 | −0.351262 | ||||||||
\(249\) | −2.47817 | −0.157048 | ||||||||
\(250\) | 23.0398 | 1.45717 | ||||||||
\(251\) | 14.9166 | 0.941525 | 0.470762 | − | 0.882260i | \(-0.343979\pi\) | ||||
0.470762 | + | 0.882260i | \(0.343979\pi\) | |||||||
\(252\) | 2.10909 | 0.132860 | ||||||||
\(253\) | −13.4147 | −0.843376 | ||||||||
\(254\) | −8.31054 | −0.521449 | ||||||||
\(255\) | −6.25949 | −0.391985 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.1002 | −0.817169 | −0.408585 | − | 0.912720i | \(-0.633977\pi\) | ||||
−0.408585 | + | 0.912720i | \(0.633977\pi\) | |||||||
\(258\) | 2.92497 | 0.182101 | ||||||||
\(259\) | 20.3198 | 1.26261 | ||||||||
\(260\) | 13.1267 | 0.814084 | ||||||||
\(261\) | −10.0009 | −0.619039 | ||||||||
\(262\) | 5.70281 | 0.352321 | ||||||||
\(263\) | 14.5218 | 0.895452 | 0.447726 | − | 0.894171i | \(-0.352234\pi\) | ||||
0.447726 | + | 0.894171i | \(0.352234\pi\) | |||||||
\(264\) | −2.46089 | −0.151457 | ||||||||
\(265\) | 3.97453 | 0.244153 | ||||||||
\(266\) | 2.10909 | 0.129317 | ||||||||
\(267\) | −13.5839 | −0.831318 | ||||||||
\(268\) | 5.26523 | 0.321625 | ||||||||
\(269\) | 12.6564 | 0.771676 | 0.385838 | − | 0.922567i | \(-0.373912\pi\) | ||||
0.385838 | + | 0.922567i | \(0.373912\pi\) | |||||||
\(270\) | −3.97453 | −0.241882 | ||||||||
\(271\) | −16.5217 | −1.00362 | −0.501810 | − | 0.864978i | \(-0.667332\pi\) | ||||
−0.501810 | + | 0.864978i | \(0.667332\pi\) | |||||||
\(272\) | −1.57490 | −0.0954925 | ||||||||
\(273\) | 6.96573 | 0.421585 | ||||||||
\(274\) | 9.04968 | 0.546711 | ||||||||
\(275\) | −26.5699 | −1.60223 | ||||||||
\(276\) | −5.45116 | −0.328121 | ||||||||
\(277\) | −21.2934 | −1.27939 | −0.639697 | − | 0.768627i | \(-0.720940\pi\) | ||||
−0.639697 | + | 0.768627i | \(0.720940\pi\) | |||||||
\(278\) | −10.4617 | −0.627448 | ||||||||
\(279\) | 5.53168 | 0.331173 | ||||||||
\(280\) | 8.38265 | 0.500959 | ||||||||
\(281\) | 10.6289 | 0.634065 | 0.317033 | − | 0.948415i | \(-0.397314\pi\) | ||||
0.317033 | + | 0.948415i | \(0.397314\pi\) | |||||||
\(282\) | 3.51719 | 0.209446 | ||||||||
\(283\) | −18.8882 | −1.12278 | −0.561392 | − | 0.827550i | \(-0.689734\pi\) | ||||
−0.561392 | + | 0.827550i | \(0.689734\pi\) | |||||||
\(284\) | −0.404292 | −0.0239903 | ||||||||
\(285\) | −3.97453 | −0.235431 | ||||||||
\(286\) | −8.12761 | −0.480595 | ||||||||
\(287\) | −3.80288 | −0.224477 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −14.5197 | −0.854099 | ||||||||
\(290\) | −39.7488 | −2.33413 | ||||||||
\(291\) | 7.25414 | 0.425245 | ||||||||
\(292\) | −11.0627 | −0.647396 | ||||||||
\(293\) | −30.9567 | −1.80851 | −0.904254 | − | 0.426995i | \(-0.859572\pi\) | ||||
−0.904254 | + | 0.426995i | \(0.859572\pi\) | |||||||
\(294\) | −2.55172 | −0.148819 | ||||||||
\(295\) | −8.99011 | −0.523424 | ||||||||
\(296\) | −9.63437 | −0.559987 | ||||||||
\(297\) | 2.46089 | 0.142795 | ||||||||
\(298\) | −9.83811 | −0.569907 | ||||||||
\(299\) | −18.0036 | −1.04118 | ||||||||
\(300\) | −10.7969 | −0.623358 | ||||||||
\(301\) | 6.16904 | 0.355577 | ||||||||
\(302\) | −9.31710 | −0.536139 | ||||||||
\(303\) | 3.18748 | 0.183116 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 3.43887 | 0.196909 | ||||||||
\(306\) | 1.57490 | 0.0900312 | ||||||||
\(307\) | 8.83648 | 0.504325 | 0.252162 | − | 0.967685i | \(-0.418858\pi\) | ||||
0.252162 | + | 0.967685i | \(0.418858\pi\) | |||||||
\(308\) | −5.19025 | −0.295742 | ||||||||
\(309\) | 6.88698 | 0.391786 | ||||||||
\(310\) | 21.9858 | 1.24871 | ||||||||
\(311\) | −10.0178 | −0.568057 | −0.284028 | − | 0.958816i | \(-0.591671\pi\) | ||||
−0.284028 | + | 0.958816i | \(0.591671\pi\) | |||||||
\(312\) | −3.30271 | −0.186979 | ||||||||
\(313\) | −33.7498 | −1.90765 | −0.953825 | − | 0.300363i | \(-0.902892\pi\) | ||||
−0.953825 | + | 0.300363i | \(0.902892\pi\) | |||||||
\(314\) | −3.48510 | −0.196676 | ||||||||
\(315\) | −8.38265 | −0.472309 | ||||||||
\(316\) | 8.91239 | 0.501361 | ||||||||
\(317\) | −22.3335 | −1.25438 | −0.627188 | − | 0.778868i | \(-0.715794\pi\) | ||||
−0.627188 | + | 0.778868i | \(0.715794\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | 24.6111 | 1.37795 | ||||||||
\(320\) | −3.97453 | −0.222183 | ||||||||
\(321\) | −15.3991 | −0.859496 | ||||||||
\(322\) | −11.4970 | −0.640704 | ||||||||
\(323\) | 1.57490 | 0.0876299 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −35.6589 | −1.97800 | ||||||||
\(326\) | −14.0163 | −0.776289 | ||||||||
\(327\) | 16.0466 | 0.887377 | ||||||||
\(328\) | 1.80309 | 0.0995588 | ||||||||
\(329\) | 7.41809 | 0.408972 | ||||||||
\(330\) | 9.78088 | 0.538420 | ||||||||
\(331\) | 9.18190 | 0.504683 | 0.252341 | − | 0.967638i | \(-0.418799\pi\) | ||||
0.252341 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(332\) | 2.47817 | 0.136007 | ||||||||
\(333\) | 9.63437 | 0.527960 | ||||||||
\(334\) | 14.3928 | 0.787541 | ||||||||
\(335\) | −20.9268 | −1.14335 | ||||||||
\(336\) | −2.10909 | −0.115061 | ||||||||
\(337\) | 6.07232 | 0.330781 | 0.165390 | − | 0.986228i | \(-0.447112\pi\) | ||||
0.165390 | + | 0.986228i | \(0.447112\pi\) | |||||||
\(338\) | 2.09211 | 0.113796 | ||||||||
\(339\) | −17.1265 | −0.930186 | ||||||||
\(340\) | 6.25949 | 0.339469 | ||||||||
\(341\) | −13.6129 | −0.737177 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −20.1455 | −1.08775 | ||||||||
\(344\) | −2.92497 | −0.157704 | ||||||||
\(345\) | 21.6658 | 1.16645 | ||||||||
\(346\) | −14.2954 | −0.768524 | ||||||||
\(347\) | −30.0166 | −1.61138 | −0.805688 | − | 0.592340i | \(-0.798204\pi\) | ||||
−0.805688 | + | 0.592340i | \(0.798204\pi\) | |||||||
\(348\) | 10.0009 | 0.536103 | ||||||||
\(349\) | −25.7498 | −1.37835 | −0.689177 | − | 0.724593i | \(-0.742028\pi\) | ||||
−0.689177 | + | 0.724593i | \(0.742028\pi\) | |||||||
\(350\) | −22.7716 | −1.21719 | ||||||||
\(351\) | 3.30271 | 0.176286 | ||||||||
\(352\) | 2.46089 | 0.131166 | ||||||||
\(353\) | −25.4504 | −1.35459 | −0.677293 | − | 0.735713i | \(-0.736847\pi\) | ||||
−0.677293 | + | 0.735713i | \(0.736847\pi\) | |||||||
\(354\) | 2.26193 | 0.120220 | ||||||||
\(355\) | 1.60687 | 0.0852839 | ||||||||
\(356\) | 13.5839 | 0.719943 | ||||||||
\(357\) | 3.32162 | 0.175799 | ||||||||
\(358\) | 18.5238 | 0.979011 | ||||||||
\(359\) | −7.94351 | −0.419242 | −0.209621 | − | 0.977783i | \(-0.567223\pi\) | ||||
−0.209621 | + | 0.977783i | \(0.567223\pi\) | |||||||
\(360\) | 3.97453 | 0.209476 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 12.3606 | 0.649657 | ||||||||
\(363\) | 4.94402 | 0.259494 | ||||||||
\(364\) | −6.96573 | −0.365103 | ||||||||
\(365\) | 43.9690 | 2.30144 | ||||||||
\(366\) | −0.865226 | −0.0452261 | ||||||||
\(367\) | 13.8681 | 0.723910 | 0.361955 | − | 0.932196i | \(-0.382109\pi\) | ||||
0.361955 | + | 0.932196i | \(0.382109\pi\) | |||||||
\(368\) | 5.45116 | 0.284162 | ||||||||
\(369\) | −1.80309 | −0.0938649 | ||||||||
\(370\) | 38.2921 | 1.99071 | ||||||||
\(371\) | −2.10909 | −0.109499 | ||||||||
\(372\) | −5.53168 | −0.286804 | ||||||||
\(373\) | −19.3130 | −0.999989 | −0.499994 | − | 0.866029i | \(-0.666665\pi\) | ||||
−0.499994 | + | 0.866029i | \(0.666665\pi\) | |||||||
\(374\) | −3.87566 | −0.200406 | ||||||||
\(375\) | 23.0398 | 1.18977 | ||||||||
\(376\) | −3.51719 | −0.181385 | ||||||||
\(377\) | 33.0300 | 1.70113 | ||||||||
\(378\) | 2.10909 | 0.108480 | ||||||||
\(379\) | 23.0378 | 1.18337 | 0.591687 | − | 0.806168i | \(-0.298462\pi\) | ||||
0.591687 | + | 0.806168i | \(0.298462\pi\) | |||||||
\(380\) | 3.97453 | 0.203889 | ||||||||
\(381\) | −8.31054 | −0.425762 | ||||||||
\(382\) | −9.88051 | −0.505531 | ||||||||
\(383\) | −11.6881 | −0.597234 | −0.298617 | − | 0.954373i | \(-0.596525\pi\) | ||||
−0.298617 | + | 0.954373i | \(0.596525\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 20.6288 | 1.05134 | ||||||||
\(386\) | −15.7028 | −0.799250 | ||||||||
\(387\) | 2.92497 | 0.148685 | ||||||||
\(388\) | −7.25414 | −0.368273 | ||||||||
\(389\) | 0.549640 | 0.0278678 | 0.0139339 | − | 0.999903i | \(-0.495565\pi\) | ||||
0.0139339 | + | 0.999903i | \(0.495565\pi\) | |||||||
\(390\) | 13.1267 | 0.664697 | ||||||||
\(391\) | −8.58505 | −0.434165 | ||||||||
\(392\) | 2.55172 | 0.128881 | ||||||||
\(393\) | 5.70281 | 0.287669 | ||||||||
\(394\) | 9.57072 | 0.482166 | ||||||||
\(395\) | −35.4225 | −1.78230 | ||||||||
\(396\) | −2.46089 | −0.123664 | ||||||||
\(397\) | −35.9803 | −1.80580 | −0.902899 | − | 0.429852i | \(-0.858566\pi\) | ||||
−0.902899 | + | 0.429852i | \(0.858566\pi\) | |||||||
\(398\) | −22.1102 | −1.10828 | ||||||||
\(399\) | 2.10909 | 0.105587 | ||||||||
\(400\) | 10.7969 | 0.539844 | ||||||||
\(401\) | −18.5237 | −0.925031 | −0.462515 | − | 0.886611i | \(-0.653053\pi\) | ||||
−0.462515 | + | 0.886611i | \(0.653053\pi\) | |||||||
\(402\) | 5.26523 | 0.262606 | ||||||||
\(403\) | −18.2695 | −0.910070 | ||||||||
\(404\) | −3.18748 | −0.158583 | ||||||||
\(405\) | −3.97453 | −0.197496 | ||||||||
\(406\) | 21.0928 | 1.04682 | ||||||||
\(407\) | −23.7091 | −1.17522 | ||||||||
\(408\) | −1.57490 | −0.0779693 | ||||||||
\(409\) | 15.3045 | 0.756759 | 0.378380 | − | 0.925651i | \(-0.376481\pi\) | ||||
0.378380 | + | 0.925651i | \(0.376481\pi\) | |||||||
\(410\) | −7.16642 | −0.353924 | ||||||||
\(411\) | 9.04968 | 0.446388 | ||||||||
\(412\) | −6.88698 | −0.339297 | ||||||||
\(413\) | 4.77063 | 0.234747 | ||||||||
\(414\) | −5.45116 | −0.267910 | ||||||||
\(415\) | −9.84955 | −0.483495 | ||||||||
\(416\) | 3.30271 | 0.161929 | ||||||||
\(417\) | −10.4617 | −0.512310 | ||||||||
\(418\) | −2.46089 | −0.120366 | ||||||||
\(419\) | 2.86981 | 0.140200 | 0.0700998 | − | 0.997540i | \(-0.477668\pi\) | ||||
0.0700998 | + | 0.997540i | \(0.477668\pi\) | |||||||
\(420\) | 8.38265 | 0.409032 | ||||||||
\(421\) | −6.89059 | −0.335827 | −0.167913 | − | 0.985802i | \(-0.553703\pi\) | ||||
−0.167913 | + | 0.985802i | \(0.553703\pi\) | |||||||
\(422\) | 0.942588 | 0.0458844 | ||||||||
\(423\) | 3.51719 | 0.171012 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | −17.0040 | −0.824816 | ||||||||
\(426\) | −0.404292 | −0.0195880 | ||||||||
\(427\) | −1.82484 | −0.0883104 | ||||||||
\(428\) | 15.3991 | 0.744345 | ||||||||
\(429\) | −8.12761 | −0.392404 | ||||||||
\(430\) | 11.6254 | 0.560625 | ||||||||
\(431\) | −11.3253 | −0.545519 | −0.272759 | − | 0.962082i | \(-0.587936\pi\) | ||||
−0.272759 | + | 0.962082i | \(0.587936\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 6.17753 | 0.296873 | 0.148437 | − | 0.988922i | \(-0.452576\pi\) | ||||
0.148437 | + | 0.988922i | \(0.452576\pi\) | |||||||
\(434\) | −11.6668 | −0.560026 | ||||||||
\(435\) | −39.7488 | −1.90581 | ||||||||
\(436\) | −16.0466 | −0.768491 | ||||||||
\(437\) | −5.45116 | −0.260765 | ||||||||
\(438\) | −11.0627 | −0.528597 | ||||||||
\(439\) | −29.3486 | −1.40073 | −0.700366 | − | 0.713784i | \(-0.746980\pi\) | ||||
−0.700366 | + | 0.713784i | \(0.746980\pi\) | |||||||
\(440\) | −9.78088 | −0.466285 | ||||||||
\(441\) | −2.55172 | −0.121511 | ||||||||
\(442\) | −5.20144 | −0.247407 | ||||||||
\(443\) | 23.2012 | 1.10232 | 0.551162 | − | 0.834398i | \(-0.314185\pi\) | ||||
0.551162 | + | 0.834398i | \(0.314185\pi\) | |||||||
\(444\) | −9.63437 | −0.457227 | ||||||||
\(445\) | −53.9894 | −2.55934 | ||||||||
\(446\) | 23.1801 | 1.09761 | ||||||||
\(447\) | −9.83811 | −0.465327 | ||||||||
\(448\) | 2.10909 | 0.0996453 | ||||||||
\(449\) | 12.4029 | 0.585330 | 0.292665 | − | 0.956215i | \(-0.405458\pi\) | ||||
0.292665 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(450\) | −10.7969 | −0.508969 | ||||||||
\(451\) | 4.43720 | 0.208939 | ||||||||
\(452\) | 17.1265 | 0.805565 | ||||||||
\(453\) | −9.31710 | −0.437755 | ||||||||
\(454\) | −10.0649 | −0.472368 | ||||||||
\(455\) | 27.6855 | 1.29791 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −31.5034 | −1.47367 | −0.736833 | − | 0.676075i | \(-0.763680\pi\) | ||||
−0.736833 | + | 0.676075i | \(0.763680\pi\) | |||||||
\(458\) | −2.12287 | −0.0991954 | ||||||||
\(459\) | 1.57490 | 0.0735101 | ||||||||
\(460\) | −21.6658 | −1.01017 | ||||||||
\(461\) | −29.1293 | −1.35669 | −0.678344 | − | 0.734745i | \(-0.737302\pi\) | ||||
−0.678344 | + | 0.734745i | \(0.737302\pi\) | |||||||
\(462\) | −5.19025 | −0.241472 | ||||||||
\(463\) | 23.3457 | 1.08497 | 0.542484 | − | 0.840066i | \(-0.317484\pi\) | ||||
0.542484 | + | 0.840066i | \(0.317484\pi\) | |||||||
\(464\) | −10.0009 | −0.464279 | ||||||||
\(465\) | 21.9858 | 1.01957 | ||||||||
\(466\) | 27.1529 | 1.25783 | ||||||||
\(467\) | 29.9377 | 1.38535 | 0.692677 | − | 0.721248i | \(-0.256431\pi\) | ||||
0.692677 | + | 0.721248i | \(0.256431\pi\) | |||||||
\(468\) | −3.30271 | −0.152668 | ||||||||
\(469\) | 11.1049 | 0.512775 | ||||||||
\(470\) | 13.9792 | 0.644811 | ||||||||
\(471\) | −3.48510 | −0.160585 | ||||||||
\(472\) | −2.26193 | −0.104114 | ||||||||
\(473\) | −7.19803 | −0.330966 | ||||||||
\(474\) | 8.91239 | 0.409360 | ||||||||
\(475\) | −10.7969 | −0.495394 | ||||||||
\(476\) | −3.32162 | −0.152246 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | −5.70151 | −0.260781 | ||||||||
\(479\) | 10.2080 | 0.466413 | 0.233207 | − | 0.972427i | \(-0.425078\pi\) | ||||
0.233207 | + | 0.972427i | \(0.425078\pi\) | |||||||
\(480\) | −3.97453 | −0.181412 | ||||||||
\(481\) | −31.8195 | −1.45085 | ||||||||
\(482\) | −16.6620 | −0.758934 | ||||||||
\(483\) | −11.4970 | −0.523132 | ||||||||
\(484\) | −4.94402 | −0.224728 | ||||||||
\(485\) | 28.8318 | 1.30918 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 30.8479 | 1.39785 | 0.698926 | − | 0.715194i | \(-0.253662\pi\) | ||||
0.698926 | + | 0.715194i | \(0.253662\pi\) | |||||||
\(488\) | 0.865226 | 0.0391670 | ||||||||
\(489\) | −14.0163 | −0.633838 | ||||||||
\(490\) | −10.1419 | −0.458164 | ||||||||
\(491\) | −33.0651 | −1.49221 | −0.746104 | − | 0.665830i | \(-0.768078\pi\) | ||||
−0.746104 | + | 0.665830i | \(0.768078\pi\) | |||||||
\(492\) | 1.80309 | 0.0812894 | ||||||||
\(493\) | 15.7504 | 0.709362 | ||||||||
\(494\) | −3.30271 | −0.148596 | ||||||||
\(495\) | 9.78088 | 0.439618 | ||||||||
\(496\) | 5.53168 | 0.248380 | ||||||||
\(497\) | −0.852691 | −0.0382484 | ||||||||
\(498\) | 2.47817 | 0.111049 | ||||||||
\(499\) | 15.9857 | 0.715620 | 0.357810 | − | 0.933794i | \(-0.383523\pi\) | ||||
0.357810 | + | 0.933794i | \(0.383523\pi\) | |||||||
\(500\) | −23.0398 | −1.03037 | ||||||||
\(501\) | 14.3928 | 0.643025 | ||||||||
\(502\) | −14.9166 | −0.665759 | ||||||||
\(503\) | 0.287024 | 0.0127978 | 0.00639889 | − | 0.999980i | \(-0.497963\pi\) | ||||
0.00639889 | + | 0.999980i | \(0.497963\pi\) | |||||||
\(504\) | −2.10909 | −0.0939465 | ||||||||
\(505\) | 12.6687 | 0.563750 | ||||||||
\(506\) | 13.4147 | 0.596357 | ||||||||
\(507\) | 2.09211 | 0.0929139 | ||||||||
\(508\) | 8.31054 | 0.368720 | ||||||||
\(509\) | 9.07055 | 0.402045 | 0.201023 | − | 0.979587i | \(-0.435574\pi\) | ||||
0.201023 | + | 0.979587i | \(0.435574\pi\) | |||||||
\(510\) | 6.25949 | 0.277175 | ||||||||
\(511\) | −23.3323 | −1.03216 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 13.1002 | 0.577826 | ||||||||
\(515\) | 27.3725 | 1.20618 | ||||||||
\(516\) | −2.92497 | −0.128765 | ||||||||
\(517\) | −8.65542 | −0.380665 | ||||||||
\(518\) | −20.3198 | −0.892801 | ||||||||
\(519\) | −14.2954 | −0.627497 | ||||||||
\(520\) | −13.1267 | −0.575644 | ||||||||
\(521\) | −14.6070 | −0.639944 | −0.319972 | − | 0.947427i | \(-0.603674\pi\) | ||||
−0.319972 | + | 0.947427i | \(0.603674\pi\) | |||||||
\(522\) | 10.0009 | 0.437727 | ||||||||
\(523\) | −31.8464 | −1.39255 | −0.696274 | − | 0.717776i | \(-0.745160\pi\) | ||||
−0.696274 | + | 0.717776i | \(0.745160\pi\) | |||||||
\(524\) | −5.70281 | −0.249128 | ||||||||
\(525\) | −22.7716 | −0.993835 | ||||||||
\(526\) | −14.5218 | −0.633180 | ||||||||
\(527\) | −8.71185 | −0.379494 | ||||||||
\(528\) | 2.46089 | 0.107097 | ||||||||
\(529\) | 6.71519 | 0.291965 | ||||||||
\(530\) | −3.97453 | −0.172642 | ||||||||
\(531\) | 2.26193 | 0.0981595 | ||||||||
\(532\) | −2.10909 | −0.0914408 | ||||||||
\(533\) | 5.95507 | 0.257943 | ||||||||
\(534\) | 13.5839 | 0.587831 | ||||||||
\(535\) | −61.2043 | −2.64609 | ||||||||
\(536\) | −5.26523 | −0.227423 | ||||||||
\(537\) | 18.5238 | 0.799359 | ||||||||
\(538\) | −12.6564 | −0.545657 | ||||||||
\(539\) | 6.27951 | 0.270477 | ||||||||
\(540\) | 3.97453 | 0.171036 | ||||||||
\(541\) | 30.6230 | 1.31658 | 0.658292 | − | 0.752763i | \(-0.271279\pi\) | ||||
0.658292 | + | 0.752763i | \(0.271279\pi\) | |||||||
\(542\) | 16.5217 | 0.709667 | ||||||||
\(543\) | 12.3606 | 0.530443 | ||||||||
\(544\) | 1.57490 | 0.0675234 | ||||||||
\(545\) | 63.7775 | 2.73193 | ||||||||
\(546\) | −6.96573 | −0.298106 | ||||||||
\(547\) | −22.5604 | −0.964613 | −0.482307 | − | 0.876002i | \(-0.660201\pi\) | ||||
−0.482307 | + | 0.876002i | \(0.660201\pi\) | |||||||
\(548\) | −9.04968 | −0.386583 | ||||||||
\(549\) | −0.865226 | −0.0369270 | ||||||||
\(550\) | 26.5699 | 1.13295 | ||||||||
\(551\) | 10.0009 | 0.426052 | ||||||||
\(552\) | 5.45116 | 0.232017 | ||||||||
\(553\) | 18.7971 | 0.799333 | ||||||||
\(554\) | 21.2934 | 0.904669 | ||||||||
\(555\) | 38.2921 | 1.62541 | ||||||||
\(556\) | 10.4617 | 0.443673 | ||||||||
\(557\) | 13.6803 | 0.579653 | 0.289826 | − | 0.957079i | \(-0.406402\pi\) | ||||
0.289826 | + | 0.957079i | \(0.406402\pi\) | |||||||
\(558\) | −5.53168 | −0.234175 | ||||||||
\(559\) | −9.66033 | −0.408588 | ||||||||
\(560\) | −8.38265 | −0.354232 | ||||||||
\(561\) | −3.87566 | −0.163631 | ||||||||
\(562\) | −10.6289 | −0.448352 | ||||||||
\(563\) | −18.9214 | −0.797443 | −0.398722 | − | 0.917072i | \(-0.630546\pi\) | ||||
−0.398722 | + | 0.917072i | \(0.630546\pi\) | |||||||
\(564\) | −3.51719 | −0.148100 | ||||||||
\(565\) | −68.0699 | −2.86372 | ||||||||
\(566\) | 18.8882 | 0.793928 | ||||||||
\(567\) | 2.10909 | 0.0885736 | ||||||||
\(568\) | 0.404292 | 0.0169637 | ||||||||
\(569\) | −15.4115 | −0.646085 | −0.323042 | − | 0.946384i | \(-0.604706\pi\) | ||||
−0.323042 | + | 0.946384i | \(0.604706\pi\) | |||||||
\(570\) | 3.97453 | 0.166475 | ||||||||
\(571\) | −29.8519 | −1.24926 | −0.624631 | − | 0.780920i | \(-0.714751\pi\) | ||||
−0.624631 | + | 0.780920i | \(0.714751\pi\) | |||||||
\(572\) | 8.12761 | 0.339832 | ||||||||
\(573\) | −9.88051 | −0.412764 | ||||||||
\(574\) | 3.80288 | 0.158729 | ||||||||
\(575\) | 58.8555 | 2.45444 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.7365 | 0.571857 | 0.285928 | − | 0.958251i | \(-0.407698\pi\) | ||||
0.285928 | + | 0.958251i | \(0.407698\pi\) | |||||||
\(578\) | 14.5197 | 0.603939 | ||||||||
\(579\) | −15.7028 | −0.652585 | ||||||||
\(580\) | 39.7488 | 1.65048 | ||||||||
\(581\) | 5.22669 | 0.216840 | ||||||||
\(582\) | −7.25414 | −0.300694 | ||||||||
\(583\) | 2.46089 | 0.101920 | ||||||||
\(584\) | 11.0627 | 0.457778 | ||||||||
\(585\) | 13.1267 | 0.542723 | ||||||||
\(586\) | 30.9567 | 1.27881 | ||||||||
\(587\) | 29.3934 | 1.21320 | 0.606598 | − | 0.795008i | \(-0.292534\pi\) | ||||
0.606598 | + | 0.795008i | \(0.292534\pi\) | |||||||
\(588\) | 2.55172 | 0.105231 | ||||||||
\(589\) | −5.53168 | −0.227929 | ||||||||
\(590\) | 8.99011 | 0.370117 | ||||||||
\(591\) | 9.57072 | 0.393687 | ||||||||
\(592\) | 9.63437 | 0.395970 | ||||||||
\(593\) | 16.7364 | 0.687283 | 0.343642 | − | 0.939101i | \(-0.388339\pi\) | ||||
0.343642 | + | 0.939101i | \(0.388339\pi\) | |||||||
\(594\) | −2.46089 | −0.100972 | ||||||||
\(595\) | 13.2019 | 0.541223 | ||||||||
\(596\) | 9.83811 | 0.402985 | ||||||||
\(597\) | −22.1102 | −0.904908 | ||||||||
\(598\) | 18.0036 | 0.736222 | ||||||||
\(599\) | −14.0789 | −0.575249 | −0.287624 | − | 0.957743i | \(-0.592865\pi\) | ||||
−0.287624 | + | 0.957743i | \(0.592865\pi\) | |||||||
\(600\) | 10.7969 | 0.440780 | ||||||||
\(601\) | −5.54555 | −0.226208 | −0.113104 | − | 0.993583i | \(-0.536079\pi\) | ||||
−0.113104 | + | 0.993583i | \(0.536079\pi\) | |||||||
\(602\) | −6.16904 | −0.251431 | ||||||||
\(603\) | 5.26523 | 0.214417 | ||||||||
\(604\) | 9.31710 | 0.379107 | ||||||||
\(605\) | 19.6501 | 0.798892 | ||||||||
\(606\) | −3.18748 | −0.129482 | ||||||||
\(607\) | −13.1971 | −0.535653 | −0.267826 | − | 0.963467i | \(-0.586305\pi\) | ||||
−0.267826 | + | 0.963467i | \(0.586305\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 21.0928 | 0.854723 | ||||||||
\(610\) | −3.43887 | −0.139236 | ||||||||
\(611\) | −11.6163 | −0.469943 | ||||||||
\(612\) | −1.57490 | −0.0636616 | ||||||||
\(613\) | 5.52185 | 0.223025 | 0.111513 | − | 0.993763i | \(-0.464430\pi\) | ||||
0.111513 | + | 0.993763i | \(0.464430\pi\) | |||||||
\(614\) | −8.83648 | −0.356611 | ||||||||
\(615\) | −7.16642 | −0.288978 | ||||||||
\(616\) | 5.19025 | 0.209121 | ||||||||
\(617\) | −47.9540 | −1.93056 | −0.965279 | − | 0.261223i | \(-0.915874\pi\) | ||||
−0.965279 | + | 0.261223i | \(0.915874\pi\) | |||||||
\(618\) | −6.88698 | −0.277035 | ||||||||
\(619\) | 27.8577 | 1.11970 | 0.559848 | − | 0.828595i | \(-0.310860\pi\) | ||||
0.559848 | + | 0.828595i | \(0.310860\pi\) | |||||||
\(620\) | −21.9858 | −0.882971 | ||||||||
\(621\) | −5.45116 | −0.218748 | ||||||||
\(622\) | 10.0178 | 0.401677 | ||||||||
\(623\) | 28.6496 | 1.14782 | ||||||||
\(624\) | 3.30271 | 0.132214 | ||||||||
\(625\) | 37.5881 | 1.50352 | ||||||||
\(626\) | 33.7498 | 1.34891 | ||||||||
\(627\) | −2.46089 | −0.0982785 | ||||||||
\(628\) | 3.48510 | 0.139071 | ||||||||
\(629\) | −15.1732 | −0.604995 | ||||||||
\(630\) | 8.38265 | 0.333973 | ||||||||
\(631\) | 42.5805 | 1.69510 | 0.847552 | − | 0.530712i | \(-0.178075\pi\) | ||||
0.847552 | + | 0.530712i | \(0.178075\pi\) | |||||||
\(632\) | −8.91239 | −0.354516 | ||||||||
\(633\) | 0.942588 | 0.0374645 | ||||||||
\(634\) | 22.3335 | 0.886978 | ||||||||
\(635\) | −33.0305 | −1.31077 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | 8.42759 | 0.333913 | ||||||||
\(638\) | −24.6111 | −0.974361 | ||||||||
\(639\) | −0.404292 | −0.0159936 | ||||||||
\(640\) | 3.97453 | 0.157107 | ||||||||
\(641\) | 5.47068 | 0.216079 | 0.108039 | − | 0.994147i | \(-0.465543\pi\) | ||||
0.108039 | + | 0.994147i | \(0.465543\pi\) | |||||||
\(642\) | 15.3991 | 0.607756 | ||||||||
\(643\) | −18.4437 | −0.727348 | −0.363674 | − | 0.931526i | \(-0.618478\pi\) | ||||
−0.363674 | + | 0.931526i | \(0.618478\pi\) | |||||||
\(644\) | 11.4970 | 0.453046 | ||||||||
\(645\) | 11.6254 | 0.457749 | ||||||||
\(646\) | −1.57490 | −0.0619637 | ||||||||
\(647\) | 6.20660 | 0.244006 | 0.122003 | − | 0.992530i | \(-0.461068\pi\) | ||||
0.122003 | + | 0.992530i | \(0.461068\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.56636 | −0.218499 | ||||||||
\(650\) | 35.6589 | 1.39866 | ||||||||
\(651\) | −11.6668 | −0.457259 | ||||||||
\(652\) | 14.0163 | 0.548920 | ||||||||
\(653\) | 8.02181 | 0.313918 | 0.156959 | − | 0.987605i | \(-0.449831\pi\) | ||||
0.156959 | + | 0.987605i | \(0.449831\pi\) | |||||||
\(654\) | −16.0466 | −0.627470 | ||||||||
\(655\) | 22.6660 | 0.885632 | ||||||||
\(656\) | −1.80309 | −0.0703987 | ||||||||
\(657\) | −11.0627 | −0.431597 | ||||||||
\(658\) | −7.41809 | −0.289187 | ||||||||
\(659\) | −25.8944 | −1.00870 | −0.504352 | − | 0.863498i | \(-0.668269\pi\) | ||||
−0.504352 | + | 0.863498i | \(0.668269\pi\) | |||||||
\(660\) | −9.78088 | −0.380720 | ||||||||
\(661\) | 5.62074 | 0.218622 | 0.109311 | − | 0.994008i | \(-0.465136\pi\) | ||||
0.109311 | + | 0.994008i | \(0.465136\pi\) | |||||||
\(662\) | −9.18190 | −0.356865 | ||||||||
\(663\) | −5.20144 | −0.202007 | ||||||||
\(664\) | −2.47817 | −0.0961716 | ||||||||
\(665\) | 8.38265 | 0.325065 | ||||||||
\(666\) | −9.63437 | −0.373324 | ||||||||
\(667\) | −54.5164 | −2.11088 | ||||||||
\(668\) | −14.3928 | −0.556876 | ||||||||
\(669\) | 23.1801 | 0.896194 | ||||||||
\(670\) | 20.9268 | 0.808473 | ||||||||
\(671\) | 2.12923 | 0.0821979 | ||||||||
\(672\) | 2.10909 | 0.0813601 | ||||||||
\(673\) | 5.07757 | 0.195726 | 0.0978629 | − | 0.995200i | \(-0.468799\pi\) | ||||
0.0978629 | + | 0.995200i | \(0.468799\pi\) | |||||||
\(674\) | −6.07232 | −0.233897 | ||||||||
\(675\) | −10.7969 | −0.415572 | ||||||||
\(676\) | −2.09211 | −0.0804658 | ||||||||
\(677\) | 32.7041 | 1.25692 | 0.628460 | − | 0.777842i | \(-0.283686\pi\) | ||||
0.628460 | + | 0.777842i | \(0.283686\pi\) | |||||||
\(678\) | 17.1265 | 0.657741 | ||||||||
\(679\) | −15.2997 | −0.587147 | ||||||||
\(680\) | −6.25949 | −0.240041 | ||||||||
\(681\) | −10.0649 | −0.385686 | ||||||||
\(682\) | 13.6129 | 0.521263 | ||||||||
\(683\) | −30.4393 | −1.16473 | −0.582364 | − | 0.812928i | \(-0.697872\pi\) | ||||
−0.582364 | + | 0.812928i | \(0.697872\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 35.9682 | 1.37427 | ||||||||
\(686\) | 20.1455 | 0.769158 | ||||||||
\(687\) | −2.12287 | −0.0809927 | ||||||||
\(688\) | 2.92497 | 0.111513 | ||||||||
\(689\) | 3.30271 | 0.125823 | ||||||||
\(690\) | −21.6658 | −0.824803 | ||||||||
\(691\) | −22.4429 | −0.853769 | −0.426884 | − | 0.904306i | \(-0.640389\pi\) | ||||
−0.426884 | + | 0.904306i | \(0.640389\pi\) | |||||||
\(692\) | 14.2954 | 0.543429 | ||||||||
\(693\) | −5.19025 | −0.197161 | ||||||||
\(694\) | 30.0166 | 1.13942 | ||||||||
\(695\) | −41.5801 | −1.57722 | ||||||||
\(696\) | −10.0009 | −0.379082 | ||||||||
\(697\) | 2.83968 | 0.107561 | ||||||||
\(698\) | 25.7498 | 0.974643 | ||||||||
\(699\) | 27.1529 | 1.02702 | ||||||||
\(700\) | 22.7716 | 0.860686 | ||||||||
\(701\) | 30.1518 | 1.13882 | 0.569408 | − | 0.822055i | \(-0.307172\pi\) | ||||
0.569408 | + | 0.822055i | \(0.307172\pi\) | |||||||
\(702\) | −3.30271 | −0.124653 | ||||||||
\(703\) | −9.63437 | −0.363367 | ||||||||
\(704\) | −2.46089 | −0.0927483 | ||||||||
\(705\) | 13.9792 | 0.526486 | ||||||||
\(706\) | 25.4504 | 0.957838 | ||||||||
\(707\) | −6.72269 | −0.252833 | ||||||||
\(708\) | −2.26193 | −0.0850086 | ||||||||
\(709\) | −41.1902 | −1.54693 | −0.773465 | − | 0.633839i | \(-0.781478\pi\) | ||||
−0.773465 | + | 0.633839i | \(0.781478\pi\) | |||||||
\(710\) | −1.60687 | −0.0603048 | ||||||||
\(711\) | 8.91239 | 0.334241 | ||||||||
\(712\) | −13.5839 | −0.509076 | ||||||||
\(713\) | 30.1541 | 1.12928 | ||||||||
\(714\) | −3.32162 | −0.124308 | ||||||||
\(715\) | −32.3034 | −1.20808 | ||||||||
\(716\) | −18.5238 | −0.692265 | ||||||||
\(717\) | −5.70151 | −0.212927 | ||||||||
\(718\) | 7.94351 | 0.296449 | ||||||||
\(719\) | 2.64266 | 0.0985547 | 0.0492773 | − | 0.998785i | \(-0.484308\pi\) | ||||
0.0492773 | + | 0.998785i | \(0.484308\pi\) | |||||||
\(720\) | −3.97453 | −0.148122 | ||||||||
\(721\) | −14.5253 | −0.540950 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −16.6620 | −0.619667 | ||||||||
\(724\) | −12.3606 | −0.459377 | ||||||||
\(725\) | −107.978 | −4.01021 | ||||||||
\(726\) | −4.94402 | −0.183490 | ||||||||
\(727\) | 32.7498 | 1.21462 | 0.607311 | − | 0.794465i | \(-0.292248\pi\) | ||||
0.607311 | + | 0.794465i | \(0.292248\pi\) | |||||||
\(728\) | 6.96573 | 0.258167 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −43.9690 | −1.62737 | ||||||||
\(731\) | −4.60654 | −0.170379 | ||||||||
\(732\) | 0.865226 | 0.0319797 | ||||||||
\(733\) | −50.7532 | −1.87461 | −0.937305 | − | 0.348510i | \(-0.886688\pi\) | ||||
−0.937305 | + | 0.348510i | \(0.886688\pi\) | |||||||
\(734\) | −13.8681 | −0.511882 | ||||||||
\(735\) | −10.1419 | −0.374089 | ||||||||
\(736\) | −5.45116 | −0.200933 | ||||||||
\(737\) | −12.9572 | −0.477283 | ||||||||
\(738\) | 1.80309 | 0.0663725 | ||||||||
\(739\) | −40.6894 | −1.49678 | −0.748392 | − | 0.663257i | \(-0.769174\pi\) | ||||
−0.748392 | + | 0.663257i | \(0.769174\pi\) | |||||||
\(740\) | −38.2921 | −1.40765 | ||||||||
\(741\) | −3.30271 | −0.121328 | ||||||||
\(742\) | 2.10909 | 0.0774273 | ||||||||
\(743\) | −10.8906 | −0.399536 | −0.199768 | − | 0.979843i | \(-0.564019\pi\) | ||||
−0.199768 | + | 0.979843i | \(0.564019\pi\) | |||||||
\(744\) | 5.53168 | 0.202801 | ||||||||
\(745\) | −39.1019 | −1.43258 | ||||||||
\(746\) | 19.3130 | 0.707099 | ||||||||
\(747\) | 2.47817 | 0.0906714 | ||||||||
\(748\) | 3.87566 | 0.141708 | ||||||||
\(749\) | 32.4782 | 1.18673 | ||||||||
\(750\) | −23.0398 | −0.841296 | ||||||||
\(751\) | −10.8828 | −0.397120 | −0.198560 | − | 0.980089i | \(-0.563626\pi\) | ||||
−0.198560 | + | 0.980089i | \(0.563626\pi\) | |||||||
\(752\) | 3.51719 | 0.128259 | ||||||||
\(753\) | −14.9166 | −0.543590 | ||||||||
\(754\) | −33.0300 | −1.20288 | ||||||||
\(755\) | −37.0311 | −1.34770 | ||||||||
\(756\) | −2.10909 | −0.0767070 | ||||||||
\(757\) | 41.3886 | 1.50429 | 0.752147 | − | 0.658996i | \(-0.229019\pi\) | ||||
0.752147 | + | 0.658996i | \(0.229019\pi\) | |||||||
\(758\) | −23.0378 | −0.836772 | ||||||||
\(759\) | 13.4147 | 0.486923 | ||||||||
\(760\) | −3.97453 | −0.144171 | ||||||||
\(761\) | −18.7619 | −0.680117 | −0.340059 | − | 0.940404i | \(-0.610447\pi\) | ||||
−0.340059 | + | 0.940404i | \(0.610447\pi\) | |||||||
\(762\) | 8.31054 | 0.301059 | ||||||||
\(763\) | −33.8437 | −1.22522 | ||||||||
\(764\) | 9.88051 | 0.357464 | ||||||||
\(765\) | 6.25949 | 0.226312 | ||||||||
\(766\) | 11.6881 | 0.422308 | ||||||||
\(767\) | −7.47050 | −0.269744 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 20.6982 | 0.746395 | 0.373197 | − | 0.927752i | \(-0.378261\pi\) | ||||
0.373197 | + | 0.927752i | \(0.378261\pi\) | |||||||
\(770\) | −20.6288 | −0.743410 | ||||||||
\(771\) | 13.1002 | 0.471793 | ||||||||
\(772\) | 15.7028 | 0.565155 | ||||||||
\(773\) | 42.3504 | 1.52324 | 0.761619 | − | 0.648026i | \(-0.224405\pi\) | ||||
0.761619 | + | 0.648026i | \(0.224405\pi\) | |||||||
\(774\) | −2.92497 | −0.105136 | ||||||||
\(775\) | 59.7248 | 2.14538 | ||||||||
\(776\) | 7.25414 | 0.260408 | ||||||||
\(777\) | −20.3198 | −0.728969 | ||||||||
\(778\) | −0.549640 | −0.0197055 | ||||||||
\(779\) | 1.80309 | 0.0646023 | ||||||||
\(780\) | −13.1267 | −0.470012 | ||||||||
\(781\) | 0.994919 | 0.0356010 | ||||||||
\(782\) | 8.58505 | 0.307001 | ||||||||
\(783\) | 10.0009 | 0.357402 | ||||||||
\(784\) | −2.55172 | −0.0911329 | ||||||||
\(785\) | −13.8516 | −0.494386 | ||||||||
\(786\) | −5.70281 | −0.203412 | ||||||||
\(787\) | 2.72995 | 0.0973121 | 0.0486560 | − | 0.998816i | \(-0.484506\pi\) | ||||
0.0486560 | + | 0.998816i | \(0.484506\pi\) | |||||||
\(788\) | −9.57072 | −0.340943 | ||||||||
\(789\) | −14.5218 | −0.516989 | ||||||||
\(790\) | 35.4225 | 1.26028 | ||||||||
\(791\) | 36.1215 | 1.28433 | ||||||||
\(792\) | 2.46089 | 0.0874439 | ||||||||
\(793\) | 2.85759 | 0.101476 | ||||||||
\(794\) | 35.9803 | 1.27689 | ||||||||
\(795\) | −3.97453 | −0.140962 | ||||||||
\(796\) | 22.1102 | 0.783674 | ||||||||
\(797\) | −22.1632 | −0.785061 | −0.392530 | − | 0.919739i | \(-0.628400\pi\) | ||||
−0.392530 | + | 0.919739i | \(0.628400\pi\) | |||||||
\(798\) | −2.10909 | −0.0746611 | ||||||||
\(799\) | −5.53923 | −0.195964 | ||||||||
\(800\) | −10.7969 | −0.381727 | ||||||||
\(801\) | 13.5839 | 0.479962 | ||||||||
\(802\) | 18.5237 | 0.654096 | ||||||||
\(803\) | 27.2241 | 0.960718 | ||||||||
\(804\) | −5.26523 | −0.185690 | ||||||||
\(805\) | −45.6952 | −1.61054 | ||||||||
\(806\) | 18.2695 | 0.643517 | ||||||||
\(807\) | −12.6564 | −0.445527 | ||||||||
\(808\) | 3.18748 | 0.112135 | ||||||||
\(809\) | −20.1693 | −0.709113 | −0.354557 | − | 0.935035i | \(-0.615368\pi\) | ||||
−0.354557 | + | 0.935035i | \(0.615368\pi\) | |||||||
\(810\) | 3.97453 | 0.139651 | ||||||||
\(811\) | 25.1648 | 0.883656 | 0.441828 | − | 0.897100i | \(-0.354330\pi\) | ||||
0.441828 | + | 0.897100i | \(0.354330\pi\) | |||||||
\(812\) | −21.0928 | −0.740212 | ||||||||
\(813\) | 16.5217 | 0.579441 | ||||||||
\(814\) | 23.7091 | 0.831005 | ||||||||
\(815\) | −55.7081 | −1.95137 | ||||||||
\(816\) | 1.57490 | 0.0551326 | ||||||||
\(817\) | −2.92497 | −0.102332 | ||||||||
\(818\) | −15.3045 | −0.535109 | ||||||||
\(819\) | −6.96573 | −0.243402 | ||||||||
\(820\) | 7.16642 | 0.250262 | ||||||||
\(821\) | 35.0158 | 1.22206 | 0.611029 | − | 0.791608i | \(-0.290756\pi\) | ||||
0.611029 | + | 0.791608i | \(0.290756\pi\) | |||||||
\(822\) | −9.04968 | −0.315644 | ||||||||
\(823\) | −37.6598 | −1.31274 | −0.656369 | − | 0.754440i | \(-0.727908\pi\) | ||||
−0.656369 | + | 0.754440i | \(0.727908\pi\) | |||||||
\(824\) | 6.88698 | 0.239919 | ||||||||
\(825\) | 26.5699 | 0.925046 | ||||||||
\(826\) | −4.77063 | −0.165991 | ||||||||
\(827\) | −3.14803 | −0.109468 | −0.0547339 | − | 0.998501i | \(-0.517431\pi\) | ||||
−0.0547339 | + | 0.998501i | \(0.517431\pi\) | |||||||
\(828\) | 5.45116 | 0.189441 | ||||||||
\(829\) | 15.3048 | 0.531556 | 0.265778 | − | 0.964034i | \(-0.414371\pi\) | ||||
0.265778 | + | 0.964034i | \(0.414371\pi\) | |||||||
\(830\) | 9.84955 | 0.341883 | ||||||||
\(831\) | 21.2934 | 0.738659 | ||||||||
\(832\) | −3.30271 | −0.114501 | ||||||||
\(833\) | 4.01871 | 0.139240 | ||||||||
\(834\) | 10.4617 | 0.362258 | ||||||||
\(835\) | 57.2047 | 1.97965 | ||||||||
\(836\) | 2.46089 | 0.0851117 | ||||||||
\(837\) | −5.53168 | −0.191203 | ||||||||
\(838\) | −2.86981 | −0.0991361 | ||||||||
\(839\) | −25.8995 | −0.894151 | −0.447075 | − | 0.894496i | \(-0.647534\pi\) | ||||
−0.447075 | + | 0.894496i | \(0.647534\pi\) | |||||||
\(840\) | −8.38265 | −0.289229 | ||||||||
\(841\) | 71.0176 | 2.44888 | ||||||||
\(842\) | 6.89059 | 0.237465 | ||||||||
\(843\) | −10.6289 | −0.366078 | ||||||||
\(844\) | −0.942588 | −0.0324452 | ||||||||
\(845\) | 8.31515 | 0.286050 | ||||||||
\(846\) | −3.51719 | −0.120923 | ||||||||
\(847\) | −10.4274 | −0.358290 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 18.8882 | 0.648240 | ||||||||
\(850\) | 17.0040 | 0.583233 | ||||||||
\(851\) | 52.5186 | 1.80031 | ||||||||
\(852\) | 0.404292 | 0.0138508 | ||||||||
\(853\) | −48.3913 | −1.65689 | −0.828443 | − | 0.560074i | \(-0.810773\pi\) | ||||
−0.828443 | + | 0.560074i | \(0.810773\pi\) | |||||||
\(854\) | 1.82484 | 0.0624449 | ||||||||
\(855\) | 3.97453 | 0.135926 | ||||||||
\(856\) | −15.3991 | −0.526332 | ||||||||
\(857\) | 19.2617 | 0.657968 | 0.328984 | − | 0.944336i | \(-0.393294\pi\) | ||||
0.328984 | + | 0.944336i | \(0.393294\pi\) | |||||||
\(858\) | 8.12761 | 0.277472 | ||||||||
\(859\) | −16.4311 | −0.560621 | −0.280311 | − | 0.959909i | \(-0.590437\pi\) | ||||
−0.280311 | + | 0.959909i | \(0.590437\pi\) | |||||||
\(860\) | −11.6254 | −0.396422 | ||||||||
\(861\) | 3.80288 | 0.129602 | ||||||||
\(862\) | 11.3253 | 0.385740 | ||||||||
\(863\) | 7.24931 | 0.246769 | 0.123385 | − | 0.992359i | \(-0.460625\pi\) | ||||
0.123385 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −56.8174 | −1.93185 | ||||||||
\(866\) | −6.17753 | −0.209921 | ||||||||
\(867\) | 14.5197 | 0.493114 | ||||||||
\(868\) | 11.6668 | 0.395998 | ||||||||
\(869\) | −21.9324 | −0.744006 | ||||||||
\(870\) | 39.7488 | 1.34761 | ||||||||
\(871\) | −17.3895 | −0.589222 | ||||||||
\(872\) | 16.0466 | 0.543405 | ||||||||
\(873\) | −7.25414 | −0.245515 | ||||||||
\(874\) | 5.45116 | 0.184388 | ||||||||
\(875\) | −48.5932 | −1.64275 | ||||||||
\(876\) | 11.0627 | 0.373774 | ||||||||
\(877\) | 14.4556 | 0.488130 | 0.244065 | − | 0.969759i | \(-0.421519\pi\) | ||||
0.244065 | + | 0.969759i | \(0.421519\pi\) | |||||||
\(878\) | 29.3486 | 0.990467 | ||||||||
\(879\) | 30.9567 | 1.04414 | ||||||||
\(880\) | 9.78088 | 0.329713 | ||||||||
\(881\) | 34.4101 | 1.15930 | 0.579652 | − | 0.814864i | \(-0.303188\pi\) | ||||
0.579652 | + | 0.814864i | \(0.303188\pi\) | |||||||
\(882\) | 2.55172 | 0.0859209 | ||||||||
\(883\) | −39.8251 | −1.34022 | −0.670111 | − | 0.742261i | \(-0.733754\pi\) | ||||
−0.670111 | + | 0.742261i | \(0.733754\pi\) | |||||||
\(884\) | 5.20144 | 0.174943 | ||||||||
\(885\) | 8.99011 | 0.302199 | ||||||||
\(886\) | −23.2012 | −0.779461 | ||||||||
\(887\) | −19.4413 | −0.652774 | −0.326387 | − | 0.945236i | \(-0.605831\pi\) | ||||
−0.326387 | + | 0.945236i | \(0.605831\pi\) | |||||||
\(888\) | 9.63437 | 0.323308 | ||||||||
\(889\) | 17.5277 | 0.587860 | ||||||||
\(890\) | 53.9894 | 1.80973 | ||||||||
\(891\) | −2.46089 | −0.0824429 | ||||||||
\(892\) | −23.1801 | −0.776127 | ||||||||
\(893\) | −3.51719 | −0.117698 | ||||||||
\(894\) | 9.83811 | 0.329036 | ||||||||
\(895\) | 73.6232 | 2.46095 | ||||||||
\(896\) | −2.10909 | −0.0704599 | ||||||||
\(897\) | 18.0036 | 0.601123 | ||||||||
\(898\) | −12.4029 | −0.413891 | ||||||||
\(899\) | −55.3216 | −1.84508 | ||||||||
\(900\) | 10.7969 | 0.359896 | ||||||||
\(901\) | 1.57490 | 0.0524676 | ||||||||
\(902\) | −4.43720 | −0.147743 | ||||||||
\(903\) | −6.16904 | −0.205293 | ||||||||
\(904\) | −17.1265 | −0.569620 | ||||||||
\(905\) | 49.1274 | 1.63305 | ||||||||
\(906\) | 9.31710 | 0.309540 | ||||||||
\(907\) | −26.5232 | −0.880690 | −0.440345 | − | 0.897829i | \(-0.645144\pi\) | ||||
−0.440345 | + | 0.897829i | \(0.645144\pi\) | |||||||
\(908\) | 10.0649 | 0.334014 | ||||||||
\(909\) | −3.18748 | −0.105722 | ||||||||
\(910\) | −27.6855 | −0.917764 | ||||||||
\(911\) | 15.2301 | 0.504596 | 0.252298 | − | 0.967650i | \(-0.418814\pi\) | ||||
0.252298 | + | 0.967650i | \(0.418814\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −6.09850 | −0.201831 | ||||||||
\(914\) | 31.5034 | 1.04204 | ||||||||
\(915\) | −3.43887 | −0.113685 | ||||||||
\(916\) | 2.12287 | 0.0701417 | ||||||||
\(917\) | −12.0278 | −0.397191 | ||||||||
\(918\) | −1.57490 | −0.0519795 | ||||||||
\(919\) | 54.5711 | 1.80014 | 0.900068 | − | 0.435749i | \(-0.143517\pi\) | ||||
0.900068 | + | 0.435749i | \(0.143517\pi\) | |||||||
\(920\) | 21.6658 | 0.714300 | ||||||||
\(921\) | −8.83648 | −0.291172 | ||||||||
\(922\) | 29.1293 | 0.959323 | ||||||||
\(923\) | 1.33526 | 0.0439506 | ||||||||
\(924\) | 5.19025 | 0.170747 | ||||||||
\(925\) | 104.021 | 3.42019 | ||||||||
\(926\) | −23.3457 | −0.767188 | ||||||||
\(927\) | −6.88698 | −0.226198 | ||||||||
\(928\) | 10.0009 | 0.328295 | ||||||||
\(929\) | −23.1136 | −0.758333 | −0.379166 | − | 0.925328i | \(-0.623789\pi\) | ||||
−0.379166 | + | 0.925328i | \(0.623789\pi\) | |||||||
\(930\) | −21.9858 | −0.720943 | ||||||||
\(931\) | 2.55172 | 0.0836293 | ||||||||
\(932\) | −27.1529 | −0.889422 | ||||||||
\(933\) | 10.0178 | 0.327968 | ||||||||
\(934\) | −29.9377 | −0.979593 | ||||||||
\(935\) | −15.4039 | −0.503762 | ||||||||
\(936\) | 3.30271 | 0.107952 | ||||||||
\(937\) | 5.88785 | 0.192348 | 0.0961738 | − | 0.995365i | \(-0.469340\pi\) | ||||
0.0961738 | + | 0.995365i | \(0.469340\pi\) | |||||||
\(938\) | −11.1049 | −0.362587 | ||||||||
\(939\) | 33.7498 | 1.10138 | ||||||||
\(940\) | −13.9792 | −0.455950 | ||||||||
\(941\) | 53.9887 | 1.75998 | 0.879990 | − | 0.474992i | \(-0.157549\pi\) | ||||
0.879990 | + | 0.474992i | \(0.157549\pi\) | |||||||
\(942\) | 3.48510 | 0.113551 | ||||||||
\(943\) | −9.82892 | −0.320074 | ||||||||
\(944\) | 2.26193 | 0.0736196 | ||||||||
\(945\) | 8.38265 | 0.272688 | ||||||||
\(946\) | 7.19803 | 0.234028 | ||||||||
\(947\) | −1.72250 | −0.0559737 | −0.0279869 | − | 0.999608i | \(-0.508910\pi\) | ||||
−0.0279869 | + | 0.999608i | \(0.508910\pi\) | |||||||
\(948\) | −8.91239 | −0.289461 | ||||||||
\(949\) | 36.5369 | 1.18604 | ||||||||
\(950\) | 10.7969 | 0.350297 | ||||||||
\(951\) | 22.3335 | 0.724214 | ||||||||
\(952\) | 3.32162 | 0.107654 | ||||||||
\(953\) | 7.23123 | 0.234243 | 0.117121 | − | 0.993118i | \(-0.462633\pi\) | ||||
0.117121 | + | 0.993118i | \(0.462633\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | −39.2704 | −1.27076 | ||||||||
\(956\) | 5.70151 | 0.184400 | ||||||||
\(957\) | −24.6111 | −0.795563 | ||||||||
\(958\) | −10.2080 | −0.329804 | ||||||||
\(959\) | −19.0866 | −0.616339 | ||||||||
\(960\) | 3.97453 | 0.128277 | ||||||||
\(961\) | −0.400529 | −0.0129203 | ||||||||
\(962\) | 31.8195 | 1.02590 | ||||||||
\(963\) | 15.3991 | 0.496230 | ||||||||
\(964\) | 16.6620 | 0.536648 | ||||||||
\(965\) | −62.4111 | −2.00908 | ||||||||
\(966\) | 11.4970 | 0.369910 | ||||||||
\(967\) | 6.51292 | 0.209441 | 0.104721 | − | 0.994502i | \(-0.466605\pi\) | ||||
0.104721 | + | 0.994502i | \(0.466605\pi\) | |||||||
\(968\) | 4.94402 | 0.158907 | ||||||||
\(969\) | −1.57490 | −0.0505931 | ||||||||
\(970\) | −28.8318 | −0.925733 | ||||||||
\(971\) | −43.8563 | −1.40741 | −0.703707 | − | 0.710490i | \(-0.748473\pi\) | ||||
−0.703707 | + | 0.710490i | \(0.748473\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 22.0646 | 0.707359 | ||||||||
\(974\) | −30.8479 | −0.988431 | ||||||||
\(975\) | 35.6589 | 1.14200 | ||||||||
\(976\) | −0.865226 | −0.0276952 | ||||||||
\(977\) | −17.1241 | −0.547847 | −0.273924 | − | 0.961751i | \(-0.588322\pi\) | ||||
−0.273924 | + | 0.961751i | \(0.588322\pi\) | |||||||
\(978\) | 14.0163 | 0.448191 | ||||||||
\(979\) | −33.4284 | −1.06838 | ||||||||
\(980\) | 10.1419 | 0.323971 | ||||||||
\(981\) | −16.0466 | −0.512327 | ||||||||
\(982\) | 33.0651 | 1.05515 | ||||||||
\(983\) | −9.31816 | −0.297203 | −0.148602 | − | 0.988897i | \(-0.547477\pi\) | ||||
−0.148602 | + | 0.988897i | \(0.547477\pi\) | |||||||
\(984\) | −1.80309 | −0.0574803 | ||||||||
\(985\) | 38.0391 | 1.21203 | ||||||||
\(986\) | −15.7504 | −0.501595 | ||||||||
\(987\) | −7.41809 | −0.236120 | ||||||||
\(988\) | 3.30271 | 0.105073 | ||||||||
\(989\) | 15.9445 | 0.507005 | ||||||||
\(990\) | −9.78088 | −0.310857 | ||||||||
\(991\) | −9.09884 | −0.289034 | −0.144517 | − | 0.989502i | \(-0.546163\pi\) | ||||
−0.144517 | + | 0.989502i | \(0.546163\pi\) | |||||||
\(992\) | −5.53168 | −0.175631 | ||||||||
\(993\) | −9.18190 | −0.291379 | ||||||||
\(994\) | 0.852691 | 0.0270457 | ||||||||
\(995\) | −87.8774 | −2.78590 | ||||||||
\(996\) | −2.47817 | −0.0785238 | ||||||||
\(997\) | 2.24827 | 0.0712034 | 0.0356017 | − | 0.999366i | \(-0.488665\pi\) | ||||
0.0356017 | + | 0.999366i | \(0.488665\pi\) | |||||||
\(998\) | −15.9857 | −0.506020 | ||||||||
\(999\) | −9.63437 | −0.304818 |
(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 | 6042.2.a.be.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.be.1.1 | ✓ | 12 | 1.1 | even | 1 | trivial |