Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6006,2,Mod(1,6006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6006.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: | \(47.9581514540\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 8x^{5} + 23x^{4} + 5x^{3} - 31x^{2} + 18x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.52204\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6006.1 |
$q$-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 | ||||||||
\(5\) | 1.43215 | 0.640476 | 0.320238 | − | 0.947337i | \(-0.396237\pi\) | ||||
0.320238 | + | 0.947337i | \(0.396237\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.43215 | 0.452885 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.43215 | 0.369779 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.60945 | 0.390348 | 0.195174 | − | 0.980769i | \(-0.437473\pi\) | ||||
0.195174 | + | 0.980769i | \(0.437473\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.77694 | 0.866489 | 0.433244 | − | 0.901276i | \(-0.357369\pi\) | ||||
0.433244 | + | 0.901276i | \(0.357369\pi\) | |||||||
\(20\) | 1.43215 | 0.320238 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.24760 | −0.468657 | −0.234328 | − | 0.972157i | \(-0.575289\pi\) | ||||
−0.234328 | + | 0.972157i | \(0.575289\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.94896 | −0.589791 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −9.52558 | −1.76886 | −0.884428 | − | 0.466678i | \(-0.845451\pi\) | ||||
−0.884428 | + | 0.466678i | \(0.845451\pi\) | |||||||
\(30\) | 1.43215 | 0.261473 | ||||||||
\(31\) | 2.81545 | 0.505670 | 0.252835 | − | 0.967509i | \(-0.418637\pi\) | ||||
0.252835 | + | 0.967509i | \(0.418637\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 1.60945 | 0.276018 | ||||||||
\(35\) | 1.43215 | 0.242077 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.04159 | −0.171237 | −0.0856184 | − | 0.996328i | \(-0.527287\pi\) | ||||
−0.0856184 | + | 0.996328i | \(0.527287\pi\) | |||||||
\(38\) | 3.77694 | 0.612700 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 1.43215 | 0.226442 | ||||||||
\(41\) | 10.5588 | 1.64901 | 0.824505 | − | 0.565855i | \(-0.191454\pi\) | ||||
0.824505 | + | 0.565855i | \(0.191454\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 9.10068 | 1.38784 | 0.693920 | − | 0.720052i | \(-0.255882\pi\) | ||||
0.693920 | + | 0.720052i | \(0.255882\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.43215 | 0.213492 | ||||||||
\(46\) | −2.24760 | −0.331391 | ||||||||
\(47\) | 4.41962 | 0.644668 | 0.322334 | − | 0.946626i | \(-0.395533\pi\) | ||||
0.322334 | + | 0.946626i | \(0.395533\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.94896 | −0.417045 | ||||||||
\(51\) | 1.60945 | 0.225368 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 1.70136 | 0.233699 | 0.116850 | − | 0.993150i | \(-0.462720\pi\) | ||||
0.116850 | + | 0.993150i | \(0.462720\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.43215 | 0.193111 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 3.77694 | 0.500268 | ||||||||
\(58\) | −9.52558 | −1.25077 | ||||||||
\(59\) | 5.28919 | 0.688594 | 0.344297 | − | 0.938861i | \(-0.388117\pi\) | ||||
0.344297 | + | 0.938861i | \(0.388117\pi\) | |||||||
\(60\) | 1.43215 | 0.184889 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 2.81545 | 0.357563 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.43215 | 0.177636 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −7.96497 | −0.973076 | −0.486538 | − | 0.873659i | \(-0.661740\pi\) | ||||
−0.486538 | + | 0.873659i | \(0.661740\pi\) | |||||||
\(68\) | 1.60945 | 0.195174 | ||||||||
\(69\) | −2.24760 | −0.270579 | ||||||||
\(70\) | 1.43215 | 0.171174 | ||||||||
\(71\) | −2.42490 | −0.287783 | −0.143891 | − | 0.989593i | \(-0.545962\pi\) | ||||
−0.143891 | + | 0.989593i | \(0.545962\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 9.91613 | 1.16060 | 0.580298 | − | 0.814405i | \(-0.302936\pi\) | ||||
0.580298 | + | 0.814405i | \(0.302936\pi\) | |||||||
\(74\) | −1.04159 | −0.121083 | ||||||||
\(75\) | −2.94896 | −0.340516 | ||||||||
\(76\) | 3.77694 | 0.433244 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 4.75281 | 0.534733 | 0.267366 | − | 0.963595i | \(-0.413847\pi\) | ||||
0.267366 | + | 0.963595i | \(0.413847\pi\) | |||||||
\(80\) | 1.43215 | 0.160119 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.5588 | 1.16603 | ||||||||
\(83\) | −16.2469 | −1.78333 | −0.891665 | − | 0.452695i | \(-0.850463\pi\) | ||||
−0.891665 | + | 0.452695i | \(0.850463\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 2.30496 | 0.250008 | ||||||||
\(86\) | 9.10068 | 0.981351 | ||||||||
\(87\) | −9.52558 | −1.02125 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 9.52558 | 1.00971 | 0.504855 | − | 0.863204i | \(-0.331546\pi\) | ||||
0.504855 | + | 0.863204i | \(0.331546\pi\) | |||||||
\(90\) | 1.43215 | 0.150962 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | −2.24760 | −0.234328 | ||||||||
\(93\) | 2.81545 | 0.291949 | ||||||||
\(94\) | 4.41962 | 0.455849 | ||||||||
\(95\) | 5.40913 | 0.554965 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 13.5717 | 1.37800 | 0.689000 | − | 0.724762i | \(-0.258050\pi\) | ||||
0.689000 | + | 0.724762i | \(0.258050\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −2.94896 | −0.294896 | ||||||||
\(101\) | −15.9399 | −1.58608 | −0.793040 | − | 0.609169i | \(-0.791503\pi\) | ||||
−0.793040 | + | 0.609169i | \(0.791503\pi\) | |||||||
\(102\) | 1.60945 | 0.159359 | ||||||||
\(103\) | −13.2224 | −1.30284 | −0.651421 | − | 0.758716i | \(-0.725827\pi\) | ||||
−0.651421 | + | 0.758716i | \(0.725827\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 1.43215 | 0.139763 | ||||||||
\(106\) | 1.70136 | 0.165250 | ||||||||
\(107\) | −17.4776 | −1.68962 | −0.844812 | − | 0.535063i | \(-0.820288\pi\) | ||||
−0.844812 | + | 0.535063i | \(0.820288\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −0.864294 | −0.0827843 | −0.0413922 | − | 0.999143i | \(-0.513179\pi\) | ||||
−0.0413922 | + | 0.999143i | \(0.513179\pi\) | |||||||
\(110\) | 1.43215 | 0.136550 | ||||||||
\(111\) | −1.04159 | −0.0988636 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 8.87982 | 0.835343 | 0.417671 | − | 0.908598i | \(-0.362846\pi\) | ||||
0.417671 | + | 0.908598i | \(0.362846\pi\) | |||||||
\(114\) | 3.77694 | 0.353743 | ||||||||
\(115\) | −3.21889 | −0.300163 | ||||||||
\(116\) | −9.52558 | −0.884428 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 5.28919 | 0.486910 | ||||||||
\(119\) | 1.60945 | 0.147538 | ||||||||
\(120\) | 1.43215 | 0.130737 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 10.5588 | 0.952056 | ||||||||
\(124\) | 2.81545 | 0.252835 | ||||||||
\(125\) | −11.3841 | −1.01822 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −14.8851 | −1.32084 | −0.660418 | − | 0.750898i | \(-0.729621\pi\) | ||||
−0.660418 | + | 0.750898i | \(0.729621\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.10068 | 0.801270 | ||||||||
\(130\) | 1.43215 | 0.125608 | ||||||||
\(131\) | −3.56826 | −0.311760 | −0.155880 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155880 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 3.77694 | 0.327502 | ||||||||
\(134\) | −7.96497 | −0.688069 | ||||||||
\(135\) | 1.43215 | 0.123260 | ||||||||
\(136\) | 1.60945 | 0.138009 | ||||||||
\(137\) | 11.9505 | 1.02100 | 0.510499 | − | 0.859878i | \(-0.329461\pi\) | ||||
0.510499 | + | 0.859878i | \(0.329461\pi\) | |||||||
\(138\) | −2.24760 | −0.191328 | ||||||||
\(139\) | −7.09539 | −0.601824 | −0.300912 | − | 0.953652i | \(-0.597291\pi\) | ||||
−0.300912 | + | 0.953652i | \(0.597291\pi\) | |||||||
\(140\) | 1.43215 | 0.121038 | ||||||||
\(141\) | 4.41962 | 0.372199 | ||||||||
\(142\) | −2.42490 | −0.203493 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −13.6420 | −1.13291 | ||||||||
\(146\) | 9.91613 | 0.820665 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −1.04159 | −0.0856184 | ||||||||
\(149\) | −8.06216 | −0.660478 | −0.330239 | − | 0.943897i | \(-0.607129\pi\) | ||||
−0.330239 | + | 0.943897i | \(0.607129\pi\) | |||||||
\(150\) | −2.94896 | −0.240781 | ||||||||
\(151\) | −12.9784 | −1.05617 | −0.528085 | − | 0.849192i | \(-0.677090\pi\) | ||||
−0.528085 | + | 0.849192i | \(0.677090\pi\) | |||||||
\(152\) | 3.77694 | 0.306350 | ||||||||
\(153\) | 1.60945 | 0.130116 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 4.03214 | 0.323869 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −7.47415 | −0.596502 | −0.298251 | − | 0.954487i | \(-0.596403\pi\) | ||||
−0.298251 | + | 0.954487i | \(0.596403\pi\) | |||||||
\(158\) | 4.75281 | 0.378113 | ||||||||
\(159\) | 1.70136 | 0.134926 | ||||||||
\(160\) | 1.43215 | 0.113221 | ||||||||
\(161\) | −2.24760 | −0.177136 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −0.632872 | −0.0495703 | −0.0247852 | − | 0.999693i | \(-0.507890\pi\) | ||||
−0.0247852 | + | 0.999693i | \(0.507890\pi\) | |||||||
\(164\) | 10.5588 | 0.824505 | ||||||||
\(165\) | 1.43215 | 0.111492 | ||||||||
\(166\) | −16.2469 | −1.26101 | ||||||||
\(167\) | 10.7176 | 0.829351 | 0.414676 | − | 0.909969i | \(-0.363895\pi\) | ||||
0.414676 | + | 0.909969i | \(0.363895\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.30496 | 0.176783 | ||||||||
\(171\) | 3.77694 | 0.288830 | ||||||||
\(172\) | 9.10068 | 0.693920 | ||||||||
\(173\) | −0.818147 | −0.0622026 | −0.0311013 | − | 0.999516i | \(-0.509901\pi\) | ||||
−0.0311013 | + | 0.999516i | \(0.509901\pi\) | |||||||
\(174\) | −9.52558 | −0.722132 | ||||||||
\(175\) | −2.94896 | −0.222920 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 5.28919 | 0.397560 | ||||||||
\(178\) | 9.52558 | 0.713972 | ||||||||
\(179\) | 13.7701 | 1.02923 | 0.514613 | − | 0.857423i | \(-0.327936\pi\) | ||||
0.514613 | + | 0.857423i | \(0.327936\pi\) | |||||||
\(180\) | 1.43215 | 0.106746 | ||||||||
\(181\) | −3.91133 | −0.290727 | −0.145364 | − | 0.989378i | \(-0.546435\pi\) | ||||
−0.145364 | + | 0.989378i | \(0.546435\pi\) | |||||||
\(182\) | 1.00000 | 0.0741249 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | −2.24760 | −0.165695 | ||||||||
\(185\) | −1.49171 | −0.109673 | ||||||||
\(186\) | 2.81545 | 0.206439 | ||||||||
\(187\) | 1.60945 | 0.117694 | ||||||||
\(188\) | 4.41962 | 0.322334 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 5.40913 | 0.392419 | ||||||||
\(191\) | 19.1085 | 1.38264 | 0.691322 | − | 0.722547i | \(-0.257029\pi\) | ||||
0.691322 | + | 0.722547i | \(0.257029\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 4.78602 | 0.344505 | 0.172253 | − | 0.985053i | \(-0.444895\pi\) | ||||
0.172253 | + | 0.985053i | \(0.444895\pi\) | |||||||
\(194\) | 13.5717 | 0.974393 | ||||||||
\(195\) | 1.43215 | 0.102558 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −5.55247 | −0.395597 | −0.197798 | − | 0.980243i | \(-0.563379\pi\) | ||||
−0.197798 | + | 0.980243i | \(0.563379\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 3.63851 | 0.257927 | 0.128964 | − | 0.991649i | \(-0.458835\pi\) | ||||
0.128964 | + | 0.991649i | \(0.458835\pi\) | |||||||
\(200\) | −2.94896 | −0.208523 | ||||||||
\(201\) | −7.96497 | −0.561806 | ||||||||
\(202\) | −15.9399 | −1.12153 | ||||||||
\(203\) | −9.52558 | −0.668564 | ||||||||
\(204\) | 1.60945 | 0.112684 | ||||||||
\(205\) | 15.1218 | 1.05615 | ||||||||
\(206\) | −13.2224 | −0.921249 | ||||||||
\(207\) | −2.24760 | −0.156219 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 3.77694 | 0.261256 | ||||||||
\(210\) | 1.43215 | 0.0988275 | ||||||||
\(211\) | 24.9174 | 1.71539 | 0.857693 | − | 0.514163i | \(-0.171897\pi\) | ||||
0.857693 | + | 0.514163i | \(0.171897\pi\) | |||||||
\(212\) | 1.70136 | 0.116850 | ||||||||
\(213\) | −2.42490 | −0.166151 | ||||||||
\(214\) | −17.4776 | −1.19474 | ||||||||
\(215\) | 13.0335 | 0.888878 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.81545 | 0.191125 | ||||||||
\(218\) | −0.864294 | −0.0585373 | ||||||||
\(219\) | 9.91613 | 0.670070 | ||||||||
\(220\) | 1.43215 | 0.0965553 | ||||||||
\(221\) | 1.60945 | 0.108263 | ||||||||
\(222\) | −1.04159 | −0.0699072 | ||||||||
\(223\) | 8.40840 | 0.563068 | 0.281534 | − | 0.959551i | \(-0.409157\pi\) | ||||
0.281534 | + | 0.959551i | \(0.409157\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −2.94896 | −0.196597 | ||||||||
\(226\) | 8.87982 | 0.590677 | ||||||||
\(227\) | 8.08174 | 0.536404 | 0.268202 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268202 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(228\) | 3.77694 | 0.250134 | ||||||||
\(229\) | 18.7554 | 1.23939 | 0.619695 | − | 0.784843i | \(-0.287256\pi\) | ||||
0.619695 | + | 0.784843i | \(0.287256\pi\) | |||||||
\(230\) | −3.21889 | −0.212248 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −9.52558 | −0.625385 | ||||||||
\(233\) | 3.61969 | 0.237134 | 0.118567 | − | 0.992946i | \(-0.462170\pi\) | ||||
0.118567 | + | 0.992946i | \(0.462170\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 6.32954 | 0.412894 | ||||||||
\(236\) | 5.28919 | 0.344297 | ||||||||
\(237\) | 4.75281 | 0.308728 | ||||||||
\(238\) | 1.60945 | 0.104325 | ||||||||
\(239\) | 20.6821 | 1.33781 | 0.668906 | − | 0.743347i | \(-0.266763\pi\) | ||||
0.668906 | + | 0.743347i | \(0.266763\pi\) | |||||||
\(240\) | 1.43215 | 0.0924447 | ||||||||
\(241\) | −1.15807 | −0.0745979 | −0.0372989 | − | 0.999304i | \(-0.511875\pi\) | ||||
−0.0372989 | + | 0.999304i | \(0.511875\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 1.43215 | 0.0914965 | ||||||||
\(246\) | 10.5588 | 0.673205 | ||||||||
\(247\) | 3.77694 | 0.240321 | ||||||||
\(248\) | 2.81545 | 0.178781 | ||||||||
\(249\) | −16.2469 | −1.02961 | ||||||||
\(250\) | −11.3841 | −0.719992 | ||||||||
\(251\) | −19.8413 | −1.25237 | −0.626186 | − | 0.779673i | \(-0.715385\pi\) | ||||
−0.626186 | + | 0.779673i | \(0.715385\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −2.24760 | −0.141305 | ||||||||
\(254\) | −14.8851 | −0.933972 | ||||||||
\(255\) | 2.30496 | 0.144342 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.9925 | −1.62137 | −0.810683 | − | 0.585485i | \(-0.800904\pi\) | ||||
−0.810683 | + | 0.585485i | \(0.800904\pi\) | |||||||
\(258\) | 9.10068 | 0.566583 | ||||||||
\(259\) | −1.04159 | −0.0647215 | ||||||||
\(260\) | 1.43215 | 0.0888180 | ||||||||
\(261\) | −9.52558 | −0.589618 | ||||||||
\(262\) | −3.56826 | −0.220448 | ||||||||
\(263\) | −3.67381 | −0.226537 | −0.113268 | − | 0.993564i | \(-0.536132\pi\) | ||||
−0.113268 | + | 0.993564i | \(0.536132\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 2.43659 | 0.149679 | ||||||||
\(266\) | 3.77694 | 0.231579 | ||||||||
\(267\) | 9.52558 | 0.582956 | ||||||||
\(268\) | −7.96497 | −0.486538 | ||||||||
\(269\) | −20.6889 | −1.26142 | −0.630712 | − | 0.776017i | \(-0.717237\pi\) | ||||
−0.630712 | + | 0.776017i | \(0.717237\pi\) | |||||||
\(270\) | 1.43215 | 0.0871577 | ||||||||
\(271\) | −17.9966 | −1.09322 | −0.546608 | − | 0.837388i | \(-0.684081\pi\) | ||||
−0.546608 | + | 0.837388i | \(0.684081\pi\) | |||||||
\(272\) | 1.60945 | 0.0975870 | ||||||||
\(273\) | 1.00000 | 0.0605228 | ||||||||
\(274\) | 11.9505 | 0.721955 | ||||||||
\(275\) | −2.94896 | −0.177829 | ||||||||
\(276\) | −2.24760 | −0.135290 | ||||||||
\(277\) | −9.46887 | −0.568929 | −0.284465 | − | 0.958687i | \(-0.591816\pi\) | ||||
−0.284465 | + | 0.958687i | \(0.591816\pi\) | |||||||
\(278\) | −7.09539 | −0.425553 | ||||||||
\(279\) | 2.81545 | 0.168557 | ||||||||
\(280\) | 1.43215 | 0.0855871 | ||||||||
\(281\) | 12.6854 | 0.756750 | 0.378375 | − | 0.925652i | \(-0.376483\pi\) | ||||
0.378375 | + | 0.925652i | \(0.376483\pi\) | |||||||
\(282\) | 4.41962 | 0.263184 | ||||||||
\(283\) | 23.8795 | 1.41949 | 0.709746 | − | 0.704458i | \(-0.248810\pi\) | ||||
0.709746 | + | 0.704458i | \(0.248810\pi\) | |||||||
\(284\) | −2.42490 | −0.143891 | ||||||||
\(285\) | 5.40913 | 0.320409 | ||||||||
\(286\) | 1.00000 | 0.0591312 | ||||||||
\(287\) | 10.5588 | 0.623267 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −14.4097 | −0.847628 | ||||||||
\(290\) | −13.6420 | −0.801087 | ||||||||
\(291\) | 13.5717 | 0.795588 | ||||||||
\(292\) | 9.91613 | 0.580298 | ||||||||
\(293\) | −9.90847 | −0.578859 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 7.57490 | 0.441028 | ||||||||
\(296\) | −1.04159 | −0.0605414 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −8.06216 | −0.467028 | ||||||||
\(299\) | −2.24760 | −0.129982 | ||||||||
\(300\) | −2.94896 | −0.170258 | ||||||||
\(301\) | 9.10068 | 0.524554 | ||||||||
\(302\) | −12.9784 | −0.746825 | ||||||||
\(303\) | −15.9399 | −0.915724 | ||||||||
\(304\) | 3.77694 | 0.216622 | ||||||||
\(305\) | 2.86429 | 0.164009 | ||||||||
\(306\) | 1.60945 | 0.0920059 | ||||||||
\(307\) | −13.1924 | −0.752932 | −0.376466 | − | 0.926430i | \(-0.622861\pi\) | ||||
−0.376466 | + | 0.926430i | \(0.622861\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | −13.2224 | −0.752196 | ||||||||
\(310\) | 4.03214 | 0.229010 | ||||||||
\(311\) | −30.1280 | −1.70840 | −0.854202 | − | 0.519941i | \(-0.825954\pi\) | ||||
−0.854202 | + | 0.519941i | \(0.825954\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −4.86925 | −0.275227 | −0.137613 | − | 0.990486i | \(-0.543943\pi\) | ||||
−0.137613 | + | 0.990486i | \(0.543943\pi\) | |||||||
\(314\) | −7.47415 | −0.421791 | ||||||||
\(315\) | 1.43215 | 0.0806923 | ||||||||
\(316\) | 4.75281 | 0.267366 | ||||||||
\(317\) | −21.3373 | −1.19842 | −0.599212 | − | 0.800590i | \(-0.704520\pi\) | ||||
−0.599212 | + | 0.800590i | \(0.704520\pi\) | |||||||
\(318\) | 1.70136 | 0.0954073 | ||||||||
\(319\) | −9.52558 | −0.533330 | ||||||||
\(320\) | 1.43215 | 0.0800594 | ||||||||
\(321\) | −17.4776 | −0.975505 | ||||||||
\(322\) | −2.24760 | −0.125254 | ||||||||
\(323\) | 6.07878 | 0.338232 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.94896 | −0.163579 | ||||||||
\(326\) | −0.632872 | −0.0350515 | ||||||||
\(327\) | −0.864294 | −0.0477955 | ||||||||
\(328\) | 10.5588 | 0.583013 | ||||||||
\(329\) | 4.41962 | 0.243661 | ||||||||
\(330\) | 1.43215 | 0.0788371 | ||||||||
\(331\) | 4.73573 | 0.260299 | 0.130150 | − | 0.991494i | \(-0.458454\pi\) | ||||
0.130150 | + | 0.991494i | \(0.458454\pi\) | |||||||
\(332\) | −16.2469 | −0.891665 | ||||||||
\(333\) | −1.04159 | −0.0570790 | ||||||||
\(334\) | 10.7176 | 0.586440 | ||||||||
\(335\) | −11.4070 | −0.623231 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −13.4973 | −0.735243 | −0.367622 | − | 0.929975i | \(-0.619828\pi\) | ||||
−0.367622 | + | 0.929975i | \(0.619828\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 8.87982 | 0.482285 | ||||||||
\(340\) | 2.30496 | 0.125004 | ||||||||
\(341\) | 2.81545 | 0.152465 | ||||||||
\(342\) | 3.77694 | 0.204233 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.10068 | 0.490676 | ||||||||
\(345\) | −3.21889 | −0.173299 | ||||||||
\(346\) | −0.818147 | −0.0439839 | ||||||||
\(347\) | 6.20964 | 0.333351 | 0.166676 | − | 0.986012i | \(-0.446697\pi\) | ||||
0.166676 | + | 0.986012i | \(0.446697\pi\) | |||||||
\(348\) | −9.52558 | −0.510624 | ||||||||
\(349\) | −2.22037 | −0.118854 | −0.0594268 | − | 0.998233i | \(-0.518927\pi\) | ||||
−0.0594268 | + | 0.998233i | \(0.518927\pi\) | |||||||
\(350\) | −2.94896 | −0.157628 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 15.8290 | 0.842494 | 0.421247 | − | 0.906946i | \(-0.361593\pi\) | ||||
0.421247 | + | 0.906946i | \(0.361593\pi\) | |||||||
\(354\) | 5.28919 | 0.281117 | ||||||||
\(355\) | −3.47281 | −0.184318 | ||||||||
\(356\) | 9.52558 | 0.504855 | ||||||||
\(357\) | 1.60945 | 0.0851809 | ||||||||
\(358\) | 13.7701 | 0.727772 | ||||||||
\(359\) | 33.6190 | 1.77434 | 0.887171 | − | 0.461441i | \(-0.152667\pi\) | ||||
0.887171 | + | 0.461441i | \(0.152667\pi\) | |||||||
\(360\) | 1.43215 | 0.0754808 | ||||||||
\(361\) | −4.73474 | −0.249197 | ||||||||
\(362\) | −3.91133 | −0.205575 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 1.00000 | 0.0524142 | ||||||||
\(365\) | 14.2014 | 0.743333 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | −12.3281 | −0.643521 | −0.321761 | − | 0.946821i | \(-0.604275\pi\) | ||||
−0.321761 | + | 0.946821i | \(0.604275\pi\) | |||||||
\(368\) | −2.24760 | −0.117164 | ||||||||
\(369\) | 10.5588 | 0.549670 | ||||||||
\(370\) | −1.49171 | −0.0775505 | ||||||||
\(371\) | 1.70136 | 0.0883300 | ||||||||
\(372\) | 2.81545 | 0.145974 | ||||||||
\(373\) | 1.07576 | 0.0557005 | 0.0278502 | − | 0.999612i | \(-0.491134\pi\) | ||||
0.0278502 | + | 0.999612i | \(0.491134\pi\) | |||||||
\(374\) | 1.60945 | 0.0832225 | ||||||||
\(375\) | −11.3841 | −0.587871 | ||||||||
\(376\) | 4.41962 | 0.227924 | ||||||||
\(377\) | −9.52558 | −0.490592 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −15.2762 | −0.784683 | −0.392342 | − | 0.919820i | \(-0.628335\pi\) | ||||
−0.392342 | + | 0.919820i | \(0.628335\pi\) | |||||||
\(380\) | 5.40913 | 0.277482 | ||||||||
\(381\) | −14.8851 | −0.762585 | ||||||||
\(382\) | 19.1085 | 0.977677 | ||||||||
\(383\) | −12.7804 | −0.653047 | −0.326523 | − | 0.945189i | \(-0.605877\pi\) | ||||
−0.326523 | + | 0.945189i | \(0.605877\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.43215 | 0.0729890 | ||||||||
\(386\) | 4.78602 | 0.243602 | ||||||||
\(387\) | 9.10068 | 0.462613 | ||||||||
\(388\) | 13.5717 | 0.689000 | ||||||||
\(389\) | −1.91676 | −0.0971838 | −0.0485919 | − | 0.998819i | \(-0.515473\pi\) | ||||
−0.0485919 | + | 0.998819i | \(0.515473\pi\) | |||||||
\(390\) | 1.43215 | 0.0725196 | ||||||||
\(391\) | −3.61739 | −0.182939 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −3.56826 | −0.179995 | ||||||||
\(394\) | −5.55247 | −0.279729 | ||||||||
\(395\) | 6.80672 | 0.342483 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 10.6057 | 0.532285 | 0.266143 | − | 0.963934i | \(-0.414251\pi\) | ||||
0.266143 | + | 0.963934i | \(0.414251\pi\) | |||||||
\(398\) | 3.63851 | 0.182382 | ||||||||
\(399\) | 3.77694 | 0.189083 | ||||||||
\(400\) | −2.94896 | −0.147448 | ||||||||
\(401\) | −37.4896 | −1.87214 | −0.936072 | − | 0.351809i | \(-0.885567\pi\) | ||||
−0.936072 | + | 0.351809i | \(0.885567\pi\) | |||||||
\(402\) | −7.96497 | −0.397257 | ||||||||
\(403\) | 2.81545 | 0.140248 | ||||||||
\(404\) | −15.9399 | −0.793040 | ||||||||
\(405\) | 1.43215 | 0.0711639 | ||||||||
\(406\) | −9.52558 | −0.472746 | ||||||||
\(407\) | −1.04159 | −0.0516299 | ||||||||
\(408\) | 1.60945 | 0.0796795 | ||||||||
\(409\) | 0.0908413 | 0.00449181 | 0.00224591 | − | 0.999997i | \(-0.499285\pi\) | ||||
0.00224591 | + | 0.999997i | \(0.499285\pi\) | |||||||
\(410\) | 15.1218 | 0.746811 | ||||||||
\(411\) | 11.9505 | 0.589473 | ||||||||
\(412\) | −13.2224 | −0.651421 | ||||||||
\(413\) | 5.28919 | 0.260264 | ||||||||
\(414\) | −2.24760 | −0.110464 | ||||||||
\(415\) | −23.2680 | −1.14218 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −7.09539 | −0.347463 | ||||||||
\(418\) | 3.77694 | 0.184736 | ||||||||
\(419\) | −22.7777 | −1.11276 | −0.556382 | − | 0.830926i | \(-0.687811\pi\) | ||||
−0.556382 | + | 0.830926i | \(0.687811\pi\) | |||||||
\(420\) | 1.43215 | 0.0698816 | ||||||||
\(421\) | −3.81855 | −0.186105 | −0.0930525 | − | 0.995661i | \(-0.529662\pi\) | ||||
−0.0930525 | + | 0.995661i | \(0.529662\pi\) | |||||||
\(422\) | 24.9174 | 1.21296 | ||||||||
\(423\) | 4.41962 | 0.214889 | ||||||||
\(424\) | 1.70136 | 0.0826251 | ||||||||
\(425\) | −4.74619 | −0.230224 | ||||||||
\(426\) | −2.42490 | −0.117487 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | −17.4776 | −0.844812 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 13.0335 | 0.628531 | ||||||||
\(431\) | −27.2163 | −1.31096 | −0.655482 | − | 0.755211i | \(-0.727535\pi\) | ||||
−0.655482 | + | 0.755211i | \(0.727535\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −1.34458 | −0.0646165 | −0.0323083 | − | 0.999478i | \(-0.510286\pi\) | ||||
−0.0323083 | + | 0.999478i | \(0.510286\pi\) | |||||||
\(434\) | 2.81545 | 0.135146 | ||||||||
\(435\) | −13.6420 | −0.654085 | ||||||||
\(436\) | −0.864294 | −0.0413922 | ||||||||
\(437\) | −8.48904 | −0.406086 | ||||||||
\(438\) | 9.91613 | 0.473811 | ||||||||
\(439\) | 38.0406 | 1.81558 | 0.907790 | − | 0.419425i | \(-0.137768\pi\) | ||||
0.907790 | + | 0.419425i | \(0.137768\pi\) | |||||||
\(440\) | 1.43215 | 0.0682749 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 1.60945 | 0.0765536 | ||||||||
\(443\) | 4.46780 | 0.212272 | 0.106136 | − | 0.994352i | \(-0.466152\pi\) | ||||
0.106136 | + | 0.994352i | \(0.466152\pi\) | |||||||
\(444\) | −1.04159 | −0.0494318 | ||||||||
\(445\) | 13.6420 | 0.646694 | ||||||||
\(446\) | 8.40840 | 0.398149 | ||||||||
\(447\) | −8.06216 | −0.381327 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −20.8862 | −0.985681 | −0.492840 | − | 0.870120i | \(-0.664041\pi\) | ||||
−0.492840 | + | 0.870120i | \(0.664041\pi\) | |||||||
\(450\) | −2.94896 | −0.139015 | ||||||||
\(451\) | 10.5588 | 0.497195 | ||||||||
\(452\) | 8.87982 | 0.417671 | ||||||||
\(453\) | −12.9784 | −0.609780 | ||||||||
\(454\) | 8.08174 | 0.379295 | ||||||||
\(455\) | 1.43215 | 0.0671401 | ||||||||
\(456\) | 3.77694 | 0.176871 | ||||||||
\(457\) | 35.8799 | 1.67839 | 0.839195 | − | 0.543831i | \(-0.183027\pi\) | ||||
0.839195 | + | 0.543831i | \(0.183027\pi\) | |||||||
\(458\) | 18.7554 | 0.876381 | ||||||||
\(459\) | 1.60945 | 0.0751225 | ||||||||
\(460\) | −3.21889 | −0.150082 | ||||||||
\(461\) | 8.71899 | 0.406084 | 0.203042 | − | 0.979170i | \(-0.434917\pi\) | ||||
0.203042 | + | 0.979170i | \(0.434917\pi\) | |||||||
\(462\) | 1.00000 | 0.0465242 | ||||||||
\(463\) | 17.1968 | 0.799203 | 0.399602 | − | 0.916689i | \(-0.369149\pi\) | ||||
0.399602 | + | 0.916689i | \(0.369149\pi\) | |||||||
\(464\) | −9.52558 | −0.442214 | ||||||||
\(465\) | 4.03214 | 0.186986 | ||||||||
\(466\) | 3.61969 | 0.167679 | ||||||||
\(467\) | 15.0891 | 0.698241 | 0.349120 | − | 0.937078i | \(-0.386480\pi\) | ||||
0.349120 | + | 0.937078i | \(0.386480\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −7.96497 | −0.367788 | ||||||||
\(470\) | 6.32954 | 0.291960 | ||||||||
\(471\) | −7.47415 | −0.344391 | ||||||||
\(472\) | 5.28919 | 0.243455 | ||||||||
\(473\) | 9.10068 | 0.418450 | ||||||||
\(474\) | 4.75281 | 0.218304 | ||||||||
\(475\) | −11.1380 | −0.511047 | ||||||||
\(476\) | 1.60945 | 0.0737689 | ||||||||
\(477\) | 1.70136 | 0.0778997 | ||||||||
\(478\) | 20.6821 | 0.945975 | ||||||||
\(479\) | 25.8513 | 1.18118 | 0.590588 | − | 0.806973i | \(-0.298896\pi\) | ||||
0.590588 | + | 0.806973i | \(0.298896\pi\) | |||||||
\(480\) | 1.43215 | 0.0653683 | ||||||||
\(481\) | −1.04159 | −0.0474926 | ||||||||
\(482\) | −1.15807 | −0.0527487 | ||||||||
\(483\) | −2.24760 | −0.102269 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 19.4367 | 0.882575 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 16.5018 | 0.747769 | 0.373885 | − | 0.927475i | \(-0.378026\pi\) | ||||
0.373885 | + | 0.927475i | \(0.378026\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | −0.632872 | −0.0286195 | ||||||||
\(490\) | 1.43215 | 0.0646978 | ||||||||
\(491\) | 16.5846 | 0.748452 | 0.374226 | − | 0.927338i | \(-0.377908\pi\) | ||||
0.374226 | + | 0.927338i | \(0.377908\pi\) | |||||||
\(492\) | 10.5588 | 0.476028 | ||||||||
\(493\) | −15.3309 | −0.690469 | ||||||||
\(494\) | 3.77694 | 0.169932 | ||||||||
\(495\) | 1.43215 | 0.0643702 | ||||||||
\(496\) | 2.81545 | 0.126418 | ||||||||
\(497\) | −2.42490 | −0.108772 | ||||||||
\(498\) | −16.2469 | −0.728042 | ||||||||
\(499\) | −22.9238 | −1.02621 | −0.513106 | − | 0.858325i | \(-0.671505\pi\) | ||||
−0.513106 | + | 0.858325i | \(0.671505\pi\) | |||||||
\(500\) | −11.3841 | −0.509111 | ||||||||
\(501\) | 10.7176 | 0.478826 | ||||||||
\(502\) | −19.8413 | −0.885561 | ||||||||
\(503\) | −20.9904 | −0.935916 | −0.467958 | − | 0.883751i | \(-0.655010\pi\) | ||||
−0.467958 | + | 0.883751i | \(0.655010\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −22.8283 | −1.01585 | ||||||||
\(506\) | −2.24760 | −0.0999180 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −14.8851 | −0.660418 | ||||||||
\(509\) | 30.1848 | 1.33792 | 0.668959 | − | 0.743299i | \(-0.266740\pi\) | ||||
0.668959 | + | 0.743299i | \(0.266740\pi\) | |||||||
\(510\) | 2.30496 | 0.102065 | ||||||||
\(511\) | 9.91613 | 0.438664 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.77694 | 0.166756 | ||||||||
\(514\) | −25.9925 | −1.14648 | ||||||||
\(515\) | −18.9364 | −0.834439 | ||||||||
\(516\) | 9.10068 | 0.400635 | ||||||||
\(517\) | 4.41962 | 0.194375 | ||||||||
\(518\) | −1.04159 | −0.0457650 | ||||||||
\(519\) | −0.818147 | −0.0359127 | ||||||||
\(520\) | 1.43215 | 0.0628038 | ||||||||
\(521\) | 16.2819 | 0.713324 | 0.356662 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356662 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(522\) | −9.52558 | −0.416923 | ||||||||
\(523\) | 14.3709 | 0.628395 | 0.314197 | − | 0.949358i | \(-0.398265\pi\) | ||||
0.314197 | + | 0.949358i | \(0.398265\pi\) | |||||||
\(524\) | −3.56826 | −0.155880 | ||||||||
\(525\) | −2.94896 | −0.128703 | ||||||||
\(526\) | −3.67381 | −0.160186 | ||||||||
\(527\) | 4.53132 | 0.197387 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −17.9483 | −0.780361 | ||||||||
\(530\) | 2.43659 | 0.105839 | ||||||||
\(531\) | 5.28919 | 0.229531 | ||||||||
\(532\) | 3.77694 | 0.163751 | ||||||||
\(533\) | 10.5588 | 0.457353 | ||||||||
\(534\) | 9.52558 | 0.412212 | ||||||||
\(535\) | −25.0305 | −1.08216 | ||||||||
\(536\) | −7.96497 | −0.344034 | ||||||||
\(537\) | 13.7701 | 0.594224 | ||||||||
\(538\) | −20.6889 | −0.891962 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 1.43215 | 0.0616298 | ||||||||
\(541\) | −14.1595 | −0.608763 | −0.304381 | − | 0.952550i | \(-0.598450\pi\) | ||||
−0.304381 | + | 0.952550i | \(0.598450\pi\) | |||||||
\(542\) | −17.9966 | −0.773021 | ||||||||
\(543\) | −3.91133 | −0.167851 | ||||||||
\(544\) | 1.60945 | 0.0690044 | ||||||||
\(545\) | −1.23780 | −0.0530213 | ||||||||
\(546\) | 1.00000 | 0.0427960 | ||||||||
\(547\) | −0.843972 | −0.0360857 | −0.0180428 | − | 0.999837i | \(-0.505744\pi\) | ||||
−0.0180428 | + | 0.999837i | \(0.505744\pi\) | |||||||
\(548\) | 11.9505 | 0.510499 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | −2.94896 | −0.125744 | ||||||||
\(551\) | −35.9775 | −1.53269 | ||||||||
\(552\) | −2.24760 | −0.0956642 | ||||||||
\(553\) | 4.75281 | 0.202110 | ||||||||
\(554\) | −9.46887 | −0.402294 | ||||||||
\(555\) | −1.49171 | −0.0633197 | ||||||||
\(556\) | −7.09539 | −0.300912 | ||||||||
\(557\) | 4.03997 | 0.171179 | 0.0855895 | − | 0.996330i | \(-0.472723\pi\) | ||||
0.0855895 | + | 0.996330i | \(0.472723\pi\) | |||||||
\(558\) | 2.81545 | 0.119188 | ||||||||
\(559\) | 9.10068 | 0.384918 | ||||||||
\(560\) | 1.43215 | 0.0605192 | ||||||||
\(561\) | 1.60945 | 0.0679509 | ||||||||
\(562\) | 12.6854 | 0.535103 | ||||||||
\(563\) | −19.5806 | −0.825223 | −0.412611 | − | 0.910907i | \(-0.635383\pi\) | ||||
−0.412611 | + | 0.910907i | \(0.635383\pi\) | |||||||
\(564\) | 4.41962 | 0.186099 | ||||||||
\(565\) | 12.7172 | 0.535017 | ||||||||
\(566\) | 23.8795 | 1.00373 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −2.42490 | −0.101747 | ||||||||
\(569\) | −29.9841 | −1.25700 | −0.628499 | − | 0.777810i | \(-0.716330\pi\) | ||||
−0.628499 | + | 0.777810i | \(0.716330\pi\) | |||||||
\(570\) | 5.40913 | 0.226563 | ||||||||
\(571\) | 41.2980 | 1.72827 | 0.864135 | − | 0.503261i | \(-0.167867\pi\) | ||||
0.864135 | + | 0.503261i | \(0.167867\pi\) | |||||||
\(572\) | 1.00000 | 0.0418121 | ||||||||
\(573\) | 19.1085 | 0.798270 | ||||||||
\(574\) | 10.5588 | 0.440716 | ||||||||
\(575\) | 6.62807 | 0.276410 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −14.5800 | −0.606973 | −0.303487 | − | 0.952836i | \(-0.598151\pi\) | ||||
−0.303487 | + | 0.952836i | \(0.598151\pi\) | |||||||
\(578\) | −14.4097 | −0.599364 | ||||||||
\(579\) | 4.78602 | 0.198900 | ||||||||
\(580\) | −13.6420 | −0.566454 | ||||||||
\(581\) | −16.2469 | −0.674036 | ||||||||
\(582\) | 13.5717 | 0.562566 | ||||||||
\(583\) | 1.70136 | 0.0704630 | ||||||||
\(584\) | 9.91613 | 0.410332 | ||||||||
\(585\) | 1.43215 | 0.0592120 | ||||||||
\(586\) | −9.90847 | −0.409315 | ||||||||
\(587\) | 9.81642 | 0.405167 | 0.202584 | − | 0.979265i | \(-0.435066\pi\) | ||||
0.202584 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 10.6338 | 0.438158 | ||||||||
\(590\) | 7.57490 | 0.311854 | ||||||||
\(591\) | −5.55247 | −0.228398 | ||||||||
\(592\) | −1.04159 | −0.0428092 | ||||||||
\(593\) | −36.7231 | −1.50804 | −0.754018 | − | 0.656853i | \(-0.771887\pi\) | ||||
−0.754018 | + | 0.656853i | \(0.771887\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 2.30496 | 0.0944943 | ||||||||
\(596\) | −8.06216 | −0.330239 | ||||||||
\(597\) | 3.63851 | 0.148914 | ||||||||
\(598\) | −2.24760 | −0.0919112 | ||||||||
\(599\) | −7.77146 | −0.317533 | −0.158767 | − | 0.987316i | \(-0.550752\pi\) | ||||
−0.158767 | + | 0.987316i | \(0.550752\pi\) | |||||||
\(600\) | −2.94896 | −0.120391 | ||||||||
\(601\) | 14.0502 | 0.573120 | 0.286560 | − | 0.958062i | \(-0.407488\pi\) | ||||
0.286560 | + | 0.958062i | \(0.407488\pi\) | |||||||
\(602\) | 9.10068 | 0.370916 | ||||||||
\(603\) | −7.96497 | −0.324359 | ||||||||
\(604\) | −12.9784 | −0.528085 | ||||||||
\(605\) | 1.43215 | 0.0582250 | ||||||||
\(606\) | −15.9399 | −0.647515 | ||||||||
\(607\) | −12.9738 | −0.526590 | −0.263295 | − | 0.964715i | \(-0.584809\pi\) | ||||
−0.263295 | + | 0.964715i | \(0.584809\pi\) | |||||||
\(608\) | 3.77694 | 0.153175 | ||||||||
\(609\) | −9.52558 | −0.385996 | ||||||||
\(610\) | 2.86429 | 0.115972 | ||||||||
\(611\) | 4.41962 | 0.178799 | ||||||||
\(612\) | 1.60945 | 0.0650580 | ||||||||
\(613\) | 7.71672 | 0.311675 | 0.155838 | − | 0.987783i | \(-0.450192\pi\) | ||||
0.155838 | + | 0.987783i | \(0.450192\pi\) | |||||||
\(614\) | −13.1924 | −0.532403 | ||||||||
\(615\) | 15.1218 | 0.609768 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −16.3666 | −0.658896 | −0.329448 | − | 0.944174i | \(-0.606863\pi\) | ||||
−0.329448 | + | 0.944174i | \(0.606863\pi\) | |||||||
\(618\) | −13.2224 | −0.531883 | ||||||||
\(619\) | −37.3389 | −1.50078 | −0.750389 | − | 0.660996i | \(-0.770134\pi\) | ||||
−0.750389 | + | 0.660996i | \(0.770134\pi\) | |||||||
\(620\) | 4.03214 | 0.161935 | ||||||||
\(621\) | −2.24760 | −0.0901931 | ||||||||
\(622\) | −30.1280 | −1.20802 | ||||||||
\(623\) | 9.52558 | 0.381634 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −1.55888 | −0.0623553 | ||||||||
\(626\) | −4.86925 | −0.194615 | ||||||||
\(627\) | 3.77694 | 0.150836 | ||||||||
\(628\) | −7.47415 | −0.298251 | ||||||||
\(629\) | −1.67639 | −0.0668420 | ||||||||
\(630\) | 1.43215 | 0.0570581 | ||||||||
\(631\) | 14.4793 | 0.576410 | 0.288205 | − | 0.957569i | \(-0.406941\pi\) | ||||
0.288205 | + | 0.957569i | \(0.406941\pi\) | |||||||
\(632\) | 4.75281 | 0.189057 | ||||||||
\(633\) | 24.9174 | 0.990378 | ||||||||
\(634\) | −21.3373 | −0.847414 | ||||||||
\(635\) | −21.3176 | −0.845963 | ||||||||
\(636\) | 1.70136 | 0.0674631 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | −9.52558 | −0.377121 | ||||||||
\(639\) | −2.42490 | −0.0959275 | ||||||||
\(640\) | 1.43215 | 0.0566106 | ||||||||
\(641\) | −24.9986 | −0.987384 | −0.493692 | − | 0.869637i | \(-0.664353\pi\) | ||||
−0.493692 | + | 0.869637i | \(0.664353\pi\) | |||||||
\(642\) | −17.4776 | −0.689786 | ||||||||
\(643\) | −19.5060 | −0.769240 | −0.384620 | − | 0.923075i | \(-0.625667\pi\) | ||||
−0.384620 | + | 0.923075i | \(0.625667\pi\) | |||||||
\(644\) | −2.24760 | −0.0885678 | ||||||||
\(645\) | 13.0335 | 0.513194 | ||||||||
\(646\) | 6.07878 | 0.239166 | ||||||||
\(647\) | 7.85953 | 0.308990 | 0.154495 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154495 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 5.28919 | 0.207619 | ||||||||
\(650\) | −2.94896 | −0.115668 | ||||||||
\(651\) | 2.81545 | 0.110346 | ||||||||
\(652\) | −0.632872 | −0.0247852 | ||||||||
\(653\) | −15.6553 | −0.612638 | −0.306319 | − | 0.951929i | \(-0.599097\pi\) | ||||
−0.306319 | + | 0.951929i | \(0.599097\pi\) | |||||||
\(654\) | −0.864294 | −0.0337966 | ||||||||
\(655\) | −5.11027 | −0.199675 | ||||||||
\(656\) | 10.5588 | 0.412252 | ||||||||
\(657\) | 9.91613 | 0.386865 | ||||||||
\(658\) | 4.41962 | 0.172295 | ||||||||
\(659\) | 23.8376 | 0.928583 | 0.464291 | − | 0.885682i | \(-0.346309\pi\) | ||||
0.464291 | + | 0.885682i | \(0.346309\pi\) | |||||||
\(660\) | 1.43215 | 0.0557462 | ||||||||
\(661\) | −46.6414 | −1.81414 | −0.907070 | − | 0.420979i | \(-0.861686\pi\) | ||||
−0.907070 | + | 0.420979i | \(0.861686\pi\) | |||||||
\(662\) | 4.73573 | 0.184059 | ||||||||
\(663\) | 1.60945 | 0.0625057 | ||||||||
\(664\) | −16.2469 | −0.630503 | ||||||||
\(665\) | 5.40913 | 0.209757 | ||||||||
\(666\) | −1.04159 | −0.0403609 | ||||||||
\(667\) | 21.4097 | 0.828986 | ||||||||
\(668\) | 10.7176 | 0.414676 | ||||||||
\(669\) | 8.40840 | 0.325088 | ||||||||
\(670\) | −11.4070 | −0.440691 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 23.0056 | 0.886801 | 0.443401 | − | 0.896324i | \(-0.353772\pi\) | ||||
0.443401 | + | 0.896324i | \(0.353772\pi\) | |||||||
\(674\) | −13.4973 | −0.519896 | ||||||||
\(675\) | −2.94896 | −0.113505 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −7.22444 | −0.277658 | −0.138829 | − | 0.990316i | \(-0.544334\pi\) | ||||
−0.138829 | + | 0.990316i | \(0.544334\pi\) | |||||||
\(678\) | 8.87982 | 0.341027 | ||||||||
\(679\) | 13.5717 | 0.520835 | ||||||||
\(680\) | 2.30496 | 0.0883913 | ||||||||
\(681\) | 8.08174 | 0.309693 | ||||||||
\(682\) | 2.81545 | 0.107809 | ||||||||
\(683\) | −36.3632 | −1.39140 | −0.695699 | − | 0.718334i | \(-0.744905\pi\) | ||||
−0.695699 | + | 0.718334i | \(0.744905\pi\) | |||||||
\(684\) | 3.77694 | 0.144415 | ||||||||
\(685\) | 17.1148 | 0.653924 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 18.7554 | 0.715562 | ||||||||
\(688\) | 9.10068 | 0.346960 | ||||||||
\(689\) | 1.70136 | 0.0648165 | ||||||||
\(690\) | −3.21889 | −0.122541 | ||||||||
\(691\) | 42.8089 | 1.62853 | 0.814263 | − | 0.580496i | \(-0.197141\pi\) | ||||
0.814263 | + | 0.580496i | \(0.197141\pi\) | |||||||
\(692\) | −0.818147 | −0.0311013 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 6.20964 | 0.235715 | ||||||||
\(695\) | −10.1616 | −0.385453 | ||||||||
\(696\) | −9.52558 | −0.361066 | ||||||||
\(697\) | 16.9938 | 0.643688 | ||||||||
\(698\) | −2.22037 | −0.0840422 | ||||||||
\(699\) | 3.61969 | 0.136909 | ||||||||
\(700\) | −2.94896 | −0.111460 | ||||||||
\(701\) | −20.9827 | −0.792508 | −0.396254 | − | 0.918141i | \(-0.629690\pi\) | ||||
−0.396254 | + | 0.918141i | \(0.629690\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −3.93403 | −0.148375 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 6.32954 | 0.238384 | ||||||||
\(706\) | 15.8290 | 0.595733 | ||||||||
\(707\) | −15.9399 | −0.599482 | ||||||||
\(708\) | 5.28919 | 0.198780 | ||||||||
\(709\) | −36.7027 | −1.37840 | −0.689199 | − | 0.724572i | \(-0.742037\pi\) | ||||
−0.689199 | + | 0.724572i | \(0.742037\pi\) | |||||||
\(710\) | −3.47281 | −0.130332 | ||||||||
\(711\) | 4.75281 | 0.178244 | ||||||||
\(712\) | 9.52558 | 0.356986 | ||||||||
\(713\) | −6.32801 | −0.236986 | ||||||||
\(714\) | 1.60945 | 0.0602320 | ||||||||
\(715\) | 1.43215 | 0.0535593 | ||||||||
\(716\) | 13.7701 | 0.514613 | ||||||||
\(717\) | 20.6821 | 0.772386 | ||||||||
\(718\) | 33.6190 | 1.25465 | ||||||||
\(719\) | −3.54901 | −0.132356 | −0.0661778 | − | 0.997808i | \(-0.521080\pi\) | ||||
−0.0661778 | + | 0.997808i | \(0.521080\pi\) | |||||||
\(720\) | 1.43215 | 0.0533730 | ||||||||
\(721\) | −13.2224 | −0.492428 | ||||||||
\(722\) | −4.73474 | −0.176209 | ||||||||
\(723\) | −1.15807 | −0.0430691 | ||||||||
\(724\) | −3.91133 | −0.145364 | ||||||||
\(725\) | 28.0905 | 1.04325 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −16.0547 | −0.595435 | −0.297717 | − | 0.954654i | \(-0.596225\pi\) | ||||
−0.297717 | + | 0.954654i | \(0.596225\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.2014 | 0.525616 | ||||||||
\(731\) | 14.6471 | 0.541741 | ||||||||
\(732\) | 2.00000 | 0.0739221 | ||||||||
\(733\) | −16.1063 | −0.594899 | −0.297449 | − | 0.954738i | \(-0.596136\pi\) | ||||
−0.297449 | + | 0.954738i | \(0.596136\pi\) | |||||||
\(734\) | −12.3281 | −0.455038 | ||||||||
\(735\) | 1.43215 | 0.0528255 | ||||||||
\(736\) | −2.24760 | −0.0828476 | ||||||||
\(737\) | −7.96497 | −0.293393 | ||||||||
\(738\) | 10.5588 | 0.388675 | ||||||||
\(739\) | 26.6666 | 0.980946 | 0.490473 | − | 0.871456i | \(-0.336824\pi\) | ||||
0.490473 | + | 0.871456i | \(0.336824\pi\) | |||||||
\(740\) | −1.49171 | −0.0548365 | ||||||||
\(741\) | 3.77694 | 0.138749 | ||||||||
\(742\) | 1.70136 | 0.0624587 | ||||||||
\(743\) | −43.1568 | −1.58327 | −0.791635 | − | 0.610994i | \(-0.790770\pi\) | ||||
−0.791635 | + | 0.610994i | \(0.790770\pi\) | |||||||
\(744\) | 2.81545 | 0.103220 | ||||||||
\(745\) | −11.5462 | −0.423020 | ||||||||
\(746\) | 1.07576 | 0.0393862 | ||||||||
\(747\) | −16.2469 | −0.594444 | ||||||||
\(748\) | 1.60945 | 0.0588472 | ||||||||
\(749\) | −17.4776 | −0.638618 | ||||||||
\(750\) | −11.3841 | −0.415688 | ||||||||
\(751\) | −22.0979 | −0.806362 | −0.403181 | − | 0.915120i | \(-0.632096\pi\) | ||||
−0.403181 | + | 0.915120i | \(0.632096\pi\) | |||||||
\(752\) | 4.41962 | 0.161167 | ||||||||
\(753\) | −19.8413 | −0.723058 | ||||||||
\(754\) | −9.52558 | −0.346901 | ||||||||
\(755\) | −18.5870 | −0.676451 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −4.68005 | −0.170099 | −0.0850496 | − | 0.996377i | \(-0.527105\pi\) | ||||
−0.0850496 | + | 0.996377i | \(0.527105\pi\) | |||||||
\(758\) | −15.2762 | −0.554855 | ||||||||
\(759\) | −2.24760 | −0.0815827 | ||||||||
\(760\) | 5.40913 | 0.196210 | ||||||||
\(761\) | 9.11831 | 0.330538 | 0.165269 | − | 0.986248i | \(-0.447151\pi\) | ||||
0.165269 | + | 0.986248i | \(0.447151\pi\) | |||||||
\(762\) | −14.8851 | −0.539229 | ||||||||
\(763\) | −0.864294 | −0.0312895 | ||||||||
\(764\) | 19.1085 | 0.691322 | ||||||||
\(765\) | 2.30496 | 0.0833361 | ||||||||
\(766\) | −12.7804 | −0.461774 | ||||||||
\(767\) | 5.28919 | 0.190982 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 11.1340 | 0.401502 | 0.200751 | − | 0.979642i | \(-0.435662\pi\) | ||||
0.200751 | + | 0.979642i | \(0.435662\pi\) | |||||||
\(770\) | 1.43215 | 0.0516110 | ||||||||
\(771\) | −25.9925 | −0.936096 | ||||||||
\(772\) | 4.78602 | 0.172253 | ||||||||
\(773\) | 3.01604 | 0.108479 | 0.0542397 | − | 0.998528i | \(-0.482726\pi\) | ||||
0.0542397 | + | 0.998528i | \(0.482726\pi\) | |||||||
\(774\) | 9.10068 | 0.327117 | ||||||||
\(775\) | −8.30265 | −0.298240 | ||||||||
\(776\) | 13.5717 | 0.487196 | ||||||||
\(777\) | −1.04159 | −0.0373669 | ||||||||
\(778\) | −1.91676 | −0.0687193 | ||||||||
\(779\) | 39.8800 | 1.42885 | ||||||||
\(780\) | 1.43215 | 0.0512791 | ||||||||
\(781\) | −2.42490 | −0.0867697 | ||||||||
\(782\) | −3.61739 | −0.129358 | ||||||||
\(783\) | −9.52558 | −0.340416 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −10.7041 | −0.382045 | ||||||||
\(786\) | −3.56826 | −0.127276 | ||||||||
\(787\) | 15.1412 | 0.539725 | 0.269862 | − | 0.962899i | \(-0.413022\pi\) | ||||
0.269862 | + | 0.962899i | \(0.413022\pi\) | |||||||
\(788\) | −5.55247 | −0.197798 | ||||||||
\(789\) | −3.67381 | −0.130791 | ||||||||
\(790\) | 6.80672 | 0.242172 | ||||||||
\(791\) | 8.87982 | 0.315730 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 10.6057 | 0.376383 | ||||||||
\(795\) | 2.43659 | 0.0864170 | ||||||||
\(796\) | 3.63851 | 0.128964 | ||||||||
\(797\) | −13.2676 | −0.469963 | −0.234982 | − | 0.972000i | \(-0.575503\pi\) | ||||
−0.234982 | + | 0.972000i | \(0.575503\pi\) | |||||||
\(798\) | 3.77694 | 0.133702 | ||||||||
\(799\) | 7.11314 | 0.251645 | ||||||||
\(800\) | −2.94896 | −0.104261 | ||||||||
\(801\) | 9.52558 | 0.336570 | ||||||||
\(802\) | −37.4896 | −1.32381 | ||||||||
\(803\) | 9.91613 | 0.349933 | ||||||||
\(804\) | −7.96497 | −0.280903 | ||||||||
\(805\) | −3.21889 | −0.113451 | ||||||||
\(806\) | 2.81545 | 0.0991701 | ||||||||
\(807\) | −20.6889 | −0.728284 | ||||||||
\(808\) | −15.9399 | −0.560764 | ||||||||
\(809\) | 18.2846 | 0.642854 | 0.321427 | − | 0.946934i | \(-0.395838\pi\) | ||||
0.321427 | + | 0.946934i | \(0.395838\pi\) | |||||||
\(810\) | 1.43215 | 0.0503205 | ||||||||
\(811\) | −8.66619 | −0.304311 | −0.152156 | − | 0.988357i | \(-0.548621\pi\) | ||||
−0.152156 | + | 0.988357i | \(0.548621\pi\) | |||||||
\(812\) | −9.52558 | −0.334282 | ||||||||
\(813\) | −17.9966 | −0.631169 | ||||||||
\(814\) | −1.04159 | −0.0365078 | ||||||||
\(815\) | −0.906365 | −0.0317486 | ||||||||
\(816\) | 1.60945 | 0.0563419 | ||||||||
\(817\) | 34.3727 | 1.20255 | ||||||||
\(818\) | 0.0908413 | 0.00317619 | ||||||||
\(819\) | 1.00000 | 0.0349428 | ||||||||
\(820\) | 15.1218 | 0.528075 | ||||||||
\(821\) | −26.9338 | −0.939996 | −0.469998 | − | 0.882667i | \(-0.655745\pi\) | ||||
−0.469998 | + | 0.882667i | \(0.655745\pi\) | |||||||
\(822\) | 11.9505 | 0.416821 | ||||||||
\(823\) | −5.55469 | −0.193624 | −0.0968122 | − | 0.995303i | \(-0.530865\pi\) | ||||
−0.0968122 | + | 0.995303i | \(0.530865\pi\) | |||||||
\(824\) | −13.2224 | −0.460624 | ||||||||
\(825\) | −2.94896 | −0.102669 | ||||||||
\(826\) | 5.28919 | 0.184035 | ||||||||
\(827\) | 25.8335 | 0.898318 | 0.449159 | − | 0.893452i | \(-0.351724\pi\) | ||||
0.449159 | + | 0.893452i | \(0.351724\pi\) | |||||||
\(828\) | −2.24760 | −0.0781095 | ||||||||
\(829\) | −56.3722 | −1.95789 | −0.978943 | − | 0.204133i | \(-0.934562\pi\) | ||||
−0.978943 | + | 0.204133i | \(0.934562\pi\) | |||||||
\(830\) | −23.2680 | −0.807643 | ||||||||
\(831\) | −9.46887 | −0.328471 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 1.60945 | 0.0557640 | ||||||||
\(834\) | −7.09539 | −0.245693 | ||||||||
\(835\) | 15.3491 | 0.531179 | ||||||||
\(836\) | 3.77694 | 0.130628 | ||||||||
\(837\) | 2.81545 | 0.0973163 | ||||||||
\(838\) | −22.7777 | −0.786844 | ||||||||
\(839\) | −1.20513 | −0.0416058 | −0.0208029 | − | 0.999784i | \(-0.506622\pi\) | ||||
−0.0208029 | + | 0.999784i | \(0.506622\pi\) | |||||||
\(840\) | 1.43215 | 0.0494138 | ||||||||
\(841\) | 61.7366 | 2.12885 | ||||||||
\(842\) | −3.81855 | −0.131596 | ||||||||
\(843\) | 12.6854 | 0.436910 | ||||||||
\(844\) | 24.9174 | 0.857693 | ||||||||
\(845\) | 1.43215 | 0.0492673 | ||||||||
\(846\) | 4.41962 | 0.151950 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 1.70136 | 0.0584248 | ||||||||
\(849\) | 23.8795 | 0.819544 | ||||||||
\(850\) | −4.74619 | −0.162793 | ||||||||
\(851\) | 2.34108 | 0.0802513 | ||||||||
\(852\) | −2.42490 | −0.0830757 | ||||||||
\(853\) | 29.9832 | 1.02661 | 0.513303 | − | 0.858208i | \(-0.328422\pi\) | ||||
0.513303 | + | 0.858208i | \(0.328422\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | 5.40913 | 0.184988 | ||||||||
\(856\) | −17.4776 | −0.597372 | ||||||||
\(857\) | −17.9974 | −0.614779 | −0.307389 | − | 0.951584i | \(-0.599455\pi\) | ||||
−0.307389 | + | 0.951584i | \(0.599455\pi\) | |||||||
\(858\) | 1.00000 | 0.0341394 | ||||||||
\(859\) | 24.0433 | 0.820345 | 0.410173 | − | 0.912008i | \(-0.365468\pi\) | ||||
0.410173 | + | 0.912008i | \(0.365468\pi\) | |||||||
\(860\) | 13.0335 | 0.444439 | ||||||||
\(861\) | 10.5588 | 0.359843 | ||||||||
\(862\) | −27.2163 | −0.926992 | ||||||||
\(863\) | −55.4481 | −1.88748 | −0.943738 | − | 0.330695i | \(-0.892717\pi\) | ||||
−0.943738 | + | 0.330695i | \(0.892717\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −1.17171 | −0.0398392 | ||||||||
\(866\) | −1.34458 | −0.0456908 | ||||||||
\(867\) | −14.4097 | −0.489378 | ||||||||
\(868\) | 2.81545 | 0.0955627 | ||||||||
\(869\) | 4.75281 | 0.161228 | ||||||||
\(870\) | −13.6420 | −0.462508 | ||||||||
\(871\) | −7.96497 | −0.269883 | ||||||||
\(872\) | −0.864294 | −0.0292687 | ||||||||
\(873\) | 13.5717 | 0.459333 | ||||||||
\(874\) | −8.48904 | −0.287146 | ||||||||
\(875\) | −11.3841 | −0.384852 | ||||||||
\(876\) | 9.91613 | 0.335035 | ||||||||
\(877\) | −0.966996 | −0.0326532 | −0.0163266 | − | 0.999867i | \(-0.505197\pi\) | ||||
−0.0163266 | + | 0.999867i | \(0.505197\pi\) | |||||||
\(878\) | 38.0406 | 1.28381 | ||||||||
\(879\) | −9.90847 | −0.334205 | ||||||||
\(880\) | 1.43215 | 0.0482777 | ||||||||
\(881\) | −43.4442 | −1.46367 | −0.731836 | − | 0.681480i | \(-0.761336\pi\) | ||||
−0.731836 | + | 0.681480i | \(0.761336\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −7.63732 | −0.257016 | −0.128508 | − | 0.991708i | \(-0.541019\pi\) | ||||
−0.128508 | + | 0.991708i | \(0.541019\pi\) | |||||||
\(884\) | 1.60945 | 0.0541315 | ||||||||
\(885\) | 7.57490 | 0.254627 | ||||||||
\(886\) | 4.46780 | 0.150099 | ||||||||
\(887\) | 31.5086 | 1.05796 | 0.528978 | − | 0.848636i | \(-0.322575\pi\) | ||||
0.528978 | + | 0.848636i | \(0.322575\pi\) | |||||||
\(888\) | −1.04159 | −0.0349536 | ||||||||
\(889\) | −14.8851 | −0.499229 | ||||||||
\(890\) | 13.6420 | 0.457282 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 8.40840 | 0.281534 | ||||||||
\(893\) | 16.6926 | 0.558597 | ||||||||
\(894\) | −8.06216 | −0.269639 | ||||||||
\(895\) | 19.7208 | 0.659194 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −2.24760 | −0.0750452 | ||||||||
\(898\) | −20.8862 | −0.696981 | ||||||||
\(899\) | −26.8188 | −0.894457 | ||||||||
\(900\) | −2.94896 | −0.0982985 | ||||||||
\(901\) | 2.73824 | 0.0912240 | ||||||||
\(902\) | 10.5588 | 0.351570 | ||||||||
\(903\) | 9.10068 | 0.302852 | ||||||||
\(904\) | 8.87982 | 0.295338 | ||||||||
\(905\) | −5.60160 | −0.186204 | ||||||||
\(906\) | −12.9784 | −0.431179 | ||||||||
\(907\) | −46.3499 | −1.53902 | −0.769511 | − | 0.638634i | \(-0.779500\pi\) | ||||
−0.769511 | + | 0.638634i | \(0.779500\pi\) | |||||||
\(908\) | 8.08174 | 0.268202 | ||||||||
\(909\) | −15.9399 | −0.528694 | ||||||||
\(910\) | 1.43215 | 0.0474752 | ||||||||
\(911\) | 22.1098 | 0.732531 | 0.366266 | − | 0.930510i | \(-0.380636\pi\) | ||||
0.366266 | + | 0.930510i | \(0.380636\pi\) | |||||||
\(912\) | 3.77694 | 0.125067 | ||||||||
\(913\) | −16.2469 | −0.537694 | ||||||||
\(914\) | 35.8799 | 1.18680 | ||||||||
\(915\) | 2.86429 | 0.0946906 | ||||||||
\(916\) | 18.7554 | 0.619695 | ||||||||
\(917\) | −3.56826 | −0.117834 | ||||||||
\(918\) | 1.60945 | 0.0531196 | ||||||||
\(919\) | 22.5961 | 0.745377 | 0.372689 | − | 0.927956i | \(-0.378436\pi\) | ||||
0.372689 | + | 0.927956i | \(0.378436\pi\) | |||||||
\(920\) | −3.21889 | −0.106124 | ||||||||
\(921\) | −13.1924 | −0.434706 | ||||||||
\(922\) | 8.71899 | 0.287145 | ||||||||
\(923\) | −2.42490 | −0.0798165 | ||||||||
\(924\) | 1.00000 | 0.0328976 | ||||||||
\(925\) | 3.07161 | 0.100994 | ||||||||
\(926\) | 17.1968 | 0.565122 | ||||||||
\(927\) | −13.2224 | −0.434281 | ||||||||
\(928\) | −9.52558 | −0.312692 | ||||||||
\(929\) | −12.2870 | −0.403124 | −0.201562 | − | 0.979476i | \(-0.564602\pi\) | ||||
−0.201562 | + | 0.979476i | \(0.564602\pi\) | |||||||
\(930\) | 4.03214 | 0.132219 | ||||||||
\(931\) | 3.77694 | 0.123784 | ||||||||
\(932\) | 3.61969 | 0.118567 | ||||||||
\(933\) | −30.1280 | −0.986348 | ||||||||
\(934\) | 15.0891 | 0.493731 | ||||||||
\(935\) | 2.30496 | 0.0753804 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −28.3961 | −0.927661 | −0.463831 | − | 0.885924i | \(-0.653525\pi\) | ||||
−0.463831 | + | 0.885924i | \(0.653525\pi\) | |||||||
\(938\) | −7.96497 | −0.260065 | ||||||||
\(939\) | −4.86925 | −0.158902 | ||||||||
\(940\) | 6.32954 | 0.206447 | ||||||||
\(941\) | −1.93152 | −0.0629658 | −0.0314829 | − | 0.999504i | \(-0.510023\pi\) | ||||
−0.0314829 | + | 0.999504i | \(0.510023\pi\) | |||||||
\(942\) | −7.47415 | −0.243521 | ||||||||
\(943\) | −23.7320 | −0.772820 | ||||||||
\(944\) | 5.28919 | 0.172149 | ||||||||
\(945\) | 1.43215 | 0.0465877 | ||||||||
\(946\) | 9.10068 | 0.295889 | ||||||||
\(947\) | −52.7965 | −1.71565 | −0.857827 | − | 0.513938i | \(-0.828186\pi\) | ||||
−0.857827 | + | 0.513938i | \(0.828186\pi\) | |||||||
\(948\) | 4.75281 | 0.154364 | ||||||||
\(949\) | 9.91613 | 0.321891 | ||||||||
\(950\) | −11.1380 | −0.361365 | ||||||||
\(951\) | −21.3373 | −0.691911 | ||||||||
\(952\) | 1.60945 | 0.0521625 | ||||||||
\(953\) | −9.55109 | −0.309390 | −0.154695 | − | 0.987962i | \(-0.549439\pi\) | ||||
−0.154695 | + | 0.987962i | \(0.549439\pi\) | |||||||
\(954\) | 1.70136 | 0.0550834 | ||||||||
\(955\) | 27.3662 | 0.885549 | ||||||||
\(956\) | 20.6821 | 0.668906 | ||||||||
\(957\) | −9.52558 | −0.307918 | ||||||||
\(958\) | 25.8513 | 0.835218 | ||||||||
\(959\) | 11.9505 | 0.385901 | ||||||||
\(960\) | 1.43215 | 0.0462223 | ||||||||
\(961\) | −23.0732 | −0.744298 | ||||||||
\(962\) | −1.04159 | −0.0335823 | ||||||||
\(963\) | −17.4776 | −0.563208 | ||||||||
\(964\) | −1.15807 | −0.0372989 | ||||||||
\(965\) | 6.85428 | 0.220647 | ||||||||
\(966\) | −2.24760 | −0.0723153 | ||||||||
\(967\) | −5.46013 | −0.175586 | −0.0877929 | − | 0.996139i | \(-0.527981\pi\) | ||||
−0.0877929 | + | 0.996139i | \(0.527981\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 6.07878 | 0.195279 | ||||||||
\(970\) | 19.4367 | 0.624075 | ||||||||
\(971\) | 1.75240 | 0.0562371 | 0.0281186 | − | 0.999605i | \(-0.491048\pi\) | ||||
0.0281186 | + | 0.999605i | \(0.491048\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −7.09539 | −0.227468 | ||||||||
\(974\) | 16.5018 | 0.528753 | ||||||||
\(975\) | −2.94896 | −0.0944422 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 15.8161 | 0.506003 | 0.253002 | − | 0.967466i | \(-0.418582\pi\) | ||||
0.253002 | + | 0.967466i | \(0.418582\pi\) | |||||||
\(978\) | −0.632872 | −0.0202370 | ||||||||
\(979\) | 9.52558 | 0.304439 | ||||||||
\(980\) | 1.43215 | 0.0457483 | ||||||||
\(981\) | −0.864294 | −0.0275948 | ||||||||
\(982\) | 16.5846 | 0.529236 | ||||||||
\(983\) | 14.8833 | 0.474703 | 0.237351 | − | 0.971424i | \(-0.423721\pi\) | ||||
0.237351 | + | 0.971424i | \(0.423721\pi\) | |||||||
\(984\) | 10.5588 | 0.336603 | ||||||||
\(985\) | −7.95195 | −0.253370 | ||||||||
\(986\) | −15.3309 | −0.488235 | ||||||||
\(987\) | 4.41962 | 0.140678 | ||||||||
\(988\) | 3.77694 | 0.120160 | ||||||||
\(989\) | −20.4547 | −0.650421 | ||||||||
\(990\) | 1.43215 | 0.0455166 | ||||||||
\(991\) | 27.6215 | 0.877426 | 0.438713 | − | 0.898627i | \(-0.355435\pi\) | ||||
0.438713 | + | 0.898627i | \(0.355435\pi\) | |||||||
\(992\) | 2.81545 | 0.0893907 | ||||||||
\(993\) | 4.73573 | 0.150284 | ||||||||
\(994\) | −2.42490 | −0.0769131 | ||||||||
\(995\) | 5.21088 | 0.165196 | ||||||||
\(996\) | −16.2469 | −0.514803 | ||||||||
\(997\) | 27.6645 | 0.876142 | 0.438071 | − | 0.898940i | \(-0.355662\pi\) | ||||
0.438071 | + | 0.898940i | \(0.355662\pi\) | |||||||
\(998\) | −22.9238 | −0.725641 | ||||||||
\(999\) | −1.04159 | −0.0329545 |
(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 | 6006.2.a.cg.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6006.2.a.cg.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial |