Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{129}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.17891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −5.17891 | −1.56150 | −0.780750 | − | 0.624844i | \(-0.785163\pi\) | ||||
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.17891 | 0.729292 | 0.364646 | − | 0.931146i | \(-0.381190\pi\) | ||||
0.364646 | + | 0.931146i | \(0.381190\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −5.17891 | −1.10415 | ||||||||
\(23\) | −8.17891 | −1.70542 | −0.852710 | − | 0.522384i | \(-0.825043\pi\) | ||||
−0.852710 | + | 0.522384i | \(0.825043\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −3.17891 | −0.590308 | −0.295154 | − | 0.955450i | \(-0.595371\pi\) | ||||
−0.295154 | + | 0.955450i | \(0.595371\pi\) | |||||||
\(30\) | 2.00000 | 0.365148 | ||||||||
\(31\) | 4.17891 | 0.750554 | 0.375277 | − | 0.926913i | \(-0.377548\pi\) | ||||
0.375277 | + | 0.926913i | \(0.377548\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.17891 | 0.901532 | ||||||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 3.17891 | 0.515687 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | −7.17891 | −1.12116 | −0.560579 | − | 0.828101i | \(-0.689421\pi\) | ||||
−0.560579 | + | 0.828101i | \(0.689421\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 12.1789 | 1.85727 | 0.928633 | − | 0.371000i | \(-0.120985\pi\) | ||||
0.928633 | + | 0.371000i | \(0.120985\pi\) | |||||||
\(44\) | −5.17891 | −0.780750 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | −8.17891 | −1.20591 | ||||||||
\(47\) | −7.17891 | −1.04715 | −0.523576 | − | 0.851979i | \(-0.675402\pi\) | ||||
−0.523576 | + | 0.851979i | \(0.675402\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 10.3578 | 1.39665 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.17891 | −0.421057 | ||||||||
\(58\) | −3.17891 | −0.417411 | ||||||||
\(59\) | −12.1789 | −1.58556 | −0.792779 | − | 0.609509i | \(-0.791367\pi\) | ||||
−0.792779 | + | 0.609509i | \(0.791367\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | −3.00000 | −0.384111 | −0.192055 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(62\) | 4.17891 | 0.530722 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.17891 | 0.637480 | ||||||||
\(67\) | −3.82109 | −0.466821 | −0.233410 | − | 0.972378i | \(-0.574989\pi\) | ||||
−0.233410 | + | 0.972378i | \(0.574989\pi\) | |||||||
\(68\) | 5.00000 | 0.606339 | ||||||||
\(69\) | 8.17891 | 0.984625 | ||||||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | −2.17891 | −0.258589 | −0.129294 | − | 0.991606i | \(-0.541271\pi\) | ||||
−0.129294 | + | 0.991606i | \(0.541271\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 3.17891 | 0.364646 | ||||||||
\(77\) | 5.17891 | 0.590191 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.1789 | 1.48274 | 0.741372 | − | 0.671095i | \(-0.234176\pi\) | ||||
0.741372 | + | 0.671095i | \(0.234176\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.17891 | −0.792778 | ||||||||
\(83\) | 6.17891 | 0.678223 | 0.339112 | − | 0.940746i | \(-0.389874\pi\) | ||||
0.339112 | + | 0.940746i | \(0.389874\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −10.0000 | −1.08465 | ||||||||
\(86\) | 12.1789 | 1.31329 | ||||||||
\(87\) | 3.17891 | 0.340815 | ||||||||
\(88\) | −5.17891 | −0.552073 | ||||||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.17891 | −0.852710 | ||||||||
\(93\) | −4.17891 | −0.433333 | ||||||||
\(94\) | −7.17891 | −0.740448 | ||||||||
\(95\) | −6.35782 | −0.652298 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.3578 | −1.05168 | −0.525838 | − | 0.850584i | \(-0.676248\pi\) | ||||
−0.525838 | + | 0.850584i | \(0.676248\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −5.17891 | −0.520500 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 6.35782 | 0.632626 | 0.316313 | − | 0.948655i | \(-0.397555\pi\) | ||||
0.316313 | + | 0.948655i | \(0.397555\pi\) | |||||||
\(102\) | −5.00000 | −0.495074 | ||||||||
\(103\) | −8.17891 | −0.805892 | −0.402946 | − | 0.915224i | \(-0.632014\pi\) | ||||
−0.402946 | + | 0.915224i | \(0.632014\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | −3.00000 | −0.291386 | ||||||||
\(107\) | 19.1789 | 1.85410 | 0.927048 | − | 0.374944i | \(-0.122338\pi\) | ||||
0.927048 | + | 0.374944i | \(0.122338\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 10.3578 | 0.987579 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 18.3578 | 1.72696 | 0.863479 | − | 0.504385i | \(-0.168281\pi\) | ||||
0.863479 | + | 0.504385i | \(0.168281\pi\) | |||||||
\(114\) | −3.17891 | −0.297732 | ||||||||
\(115\) | 16.3578 | 1.52537 | ||||||||
\(116\) | −3.17891 | −0.295154 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.1789 | −1.12116 | ||||||||
\(119\) | −5.00000 | −0.458349 | ||||||||
\(120\) | 2.00000 | 0.182574 | ||||||||
\(121\) | 15.8211 | 1.43828 | ||||||||
\(122\) | −3.00000 | −0.271607 | ||||||||
\(123\) | 7.17891 | 0.647300 | ||||||||
\(124\) | 4.17891 | 0.375277 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.1789 | −1.07229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5367 | −1.27008 | −0.635040 | − | 0.772479i | \(-0.719016\pi\) | ||||
−0.635040 | + | 0.772479i | \(0.719016\pi\) | |||||||
\(132\) | 5.17891 | 0.450766 | ||||||||
\(133\) | −3.17891 | −0.275646 | ||||||||
\(134\) | −3.82109 | −0.330092 | ||||||||
\(135\) | 2.00000 | 0.172133 | ||||||||
\(136\) | 5.00000 | 0.428746 | ||||||||
\(137\) | 6.35782 | 0.543185 | 0.271592 | − | 0.962412i | \(-0.412450\pi\) | ||||
0.271592 | + | 0.962412i | \(0.412450\pi\) | |||||||
\(138\) | 8.17891 | 0.696235 | ||||||||
\(139\) | −6.82109 | −0.578557 | −0.289279 | − | 0.957245i | \(-0.593415\pi\) | ||||
−0.289279 | + | 0.957245i | \(0.593415\pi\) | |||||||
\(140\) | 2.00000 | 0.169031 | ||||||||
\(141\) | 7.17891 | 0.604573 | ||||||||
\(142\) | −2.17891 | −0.182850 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 6.35782 | 0.527988 | ||||||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 16.1789 | 1.32543 | 0.662714 | − | 0.748873i | \(-0.269405\pi\) | ||||
0.662714 | + | 0.748873i | \(0.269405\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 19.5367 | 1.58988 | 0.794938 | − | 0.606691i | \(-0.207503\pi\) | ||||
0.794938 | + | 0.606691i | \(0.207503\pi\) | |||||||
\(152\) | 3.17891 | 0.257844 | ||||||||
\(153\) | 5.00000 | 0.404226 | ||||||||
\(154\) | 5.17891 | 0.417328 | ||||||||
\(155\) | −8.35782 | −0.671316 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 13.1789 | 1.04846 | ||||||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 8.17891 | 0.644588 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −20.1789 | −1.58053 | −0.790267 | − | 0.612763i | \(-0.790058\pi\) | ||||
−0.790267 | + | 0.612763i | \(0.790058\pi\) | |||||||
\(164\) | −7.17891 | −0.560579 | ||||||||
\(165\) | −10.3578 | −0.806355 | ||||||||
\(166\) | 6.17891 | 0.479576 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −10.0000 | −0.766965 | ||||||||
\(171\) | 3.17891 | 0.243097 | ||||||||
\(172\) | 12.1789 | 0.928633 | ||||||||
\(173\) | 4.00000 | 0.304114 | 0.152057 | − | 0.988372i | \(-0.451410\pi\) | ||||
0.152057 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(174\) | 3.17891 | 0.240992 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −5.17891 | −0.390375 | ||||||||
\(177\) | 12.1789 | 0.915423 | ||||||||
\(178\) | 9.00000 | 0.674579 | ||||||||
\(179\) | 8.35782 | 0.624693 | 0.312346 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312346 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 19.1789 | 1.42556 | 0.712779 | − | 0.701389i | \(-0.247436\pi\) | ||||
0.712779 | + | 0.701389i | \(0.247436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.00000 | 0.221766 | ||||||||
\(184\) | −8.17891 | −0.602957 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | −4.17891 | −0.306412 | ||||||||
\(187\) | −25.8945 | −1.89360 | ||||||||
\(188\) | −7.17891 | −0.523576 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −6.35782 | −0.461245 | ||||||||
\(191\) | −6.53673 | −0.472981 | −0.236490 | − | 0.971634i | \(-0.575997\pi\) | ||||
−0.236490 | + | 0.971634i | \(0.575997\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −13.5367 | −0.974395 | −0.487197 | − | 0.873292i | \(-0.661981\pi\) | ||||
−0.487197 | + | 0.873292i | \(0.661981\pi\) | |||||||
\(194\) | −10.3578 | −0.743648 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 17.0000 | 1.21120 | 0.605600 | − | 0.795769i | \(-0.292933\pi\) | ||||
0.605600 | + | 0.795769i | \(0.292933\pi\) | |||||||
\(198\) | −5.17891 | −0.368049 | ||||||||
\(199\) | 24.1789 | 1.71400 | 0.856999 | − | 0.515319i | \(-0.172326\pi\) | ||||
0.856999 | + | 0.515319i | \(0.172326\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 3.82109 | 0.269519 | ||||||||
\(202\) | 6.35782 | 0.447334 | ||||||||
\(203\) | 3.17891 | 0.223116 | ||||||||
\(204\) | −5.00000 | −0.350070 | ||||||||
\(205\) | 14.3578 | 1.00279 | ||||||||
\(206\) | −8.17891 | −0.569852 | ||||||||
\(207\) | −8.17891 | −0.568473 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.4633 | −1.13879 | ||||||||
\(210\) | −2.00000 | −0.138013 | ||||||||
\(211\) | −6.35782 | −0.437690 | −0.218845 | − | 0.975760i | \(-0.570229\pi\) | ||||
−0.218845 | + | 0.975760i | \(0.570229\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | 2.17891 | 0.149296 | ||||||||
\(214\) | 19.1789 | 1.31104 | ||||||||
\(215\) | −24.3578 | −1.66119 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −4.17891 | −0.283683 | ||||||||
\(218\) | 4.00000 | 0.270914 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 10.3578 | 0.698324 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | −2.17891 | −0.145910 | −0.0729552 | − | 0.997335i | \(-0.523243\pi\) | ||||
−0.0729552 | + | 0.997335i | \(0.523243\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 18.3578 | 1.22114 | ||||||||
\(227\) | −14.3578 | −0.952962 | −0.476481 | − | 0.879185i | \(-0.658088\pi\) | ||||
−0.476481 | + | 0.879185i | \(0.658088\pi\) | |||||||
\(228\) | −3.17891 | −0.210528 | ||||||||
\(229\) | 1.00000 | 0.0660819 | 0.0330409 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330409 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(230\) | 16.3578 | 1.07860 | ||||||||
\(231\) | −5.17891 | −0.340747 | ||||||||
\(232\) | −3.17891 | −0.208706 | ||||||||
\(233\) | 22.3578 | 1.46471 | 0.732355 | − | 0.680923i | \(-0.238421\pi\) | ||||
0.732355 | + | 0.680923i | \(0.238421\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.3578 | 0.936601 | ||||||||
\(236\) | −12.1789 | −0.792779 | ||||||||
\(237\) | −13.1789 | −0.856062 | ||||||||
\(238\) | −5.00000 | −0.324102 | ||||||||
\(239\) | 10.1789 | 0.658419 | 0.329209 | − | 0.944257i | \(-0.393218\pi\) | ||||
0.329209 | + | 0.944257i | \(0.393218\pi\) | |||||||
\(240\) | 2.00000 | 0.129099 | ||||||||
\(241\) | 4.35782 | 0.280712 | 0.140356 | − | 0.990101i | \(-0.455175\pi\) | ||||
0.140356 | + | 0.990101i | \(0.455175\pi\) | |||||||
\(242\) | 15.8211 | 1.01702 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.00000 | −0.192055 | ||||||||
\(245\) | −2.00000 | −0.127775 | ||||||||
\(246\) | 7.17891 | 0.457710 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.17891 | 0.265361 | ||||||||
\(249\) | −6.17891 | −0.391572 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | 22.1789 | 1.39992 | 0.699960 | − | 0.714182i | \(-0.253201\pi\) | ||||
0.699960 | + | 0.714182i | \(0.253201\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 42.3578 | 2.66301 | ||||||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 10.0000 | 0.626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.7156 | −1.22983 | −0.614914 | − | 0.788594i | \(-0.710809\pi\) | ||||
−0.614914 | + | 0.788594i | \(0.710809\pi\) | |||||||
\(258\) | −12.1789 | −0.758226 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.17891 | −0.196769 | ||||||||
\(262\) | −14.5367 | −0.898082 | ||||||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | 5.17891 | 0.318740 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −3.17891 | −0.194911 | ||||||||
\(267\) | −9.00000 | −0.550791 | ||||||||
\(268\) | −3.82109 | −0.233410 | ||||||||
\(269\) | −4.35782 | −0.265701 | −0.132850 | − | 0.991136i | \(-0.542413\pi\) | ||||
−0.132850 | + | 0.991136i | \(0.542413\pi\) | |||||||
\(270\) | 2.00000 | 0.121716 | ||||||||
\(271\) | 19.8211 | 1.20405 | 0.602023 | − | 0.798479i | \(-0.294362\pi\) | ||||
0.602023 | + | 0.798479i | \(0.294362\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.35782 | 0.384090 | ||||||||
\(275\) | 5.17891 | 0.312300 | ||||||||
\(276\) | 8.17891 | 0.492312 | ||||||||
\(277\) | 5.64218 | 0.339006 | 0.169503 | − | 0.985530i | \(-0.445784\pi\) | ||||
0.169503 | + | 0.985530i | \(0.445784\pi\) | |||||||
\(278\) | −6.82109 | −0.409102 | ||||||||
\(279\) | 4.17891 | 0.250185 | ||||||||
\(280\) | 2.00000 | 0.119523 | ||||||||
\(281\) | 28.3578 | 1.69169 | 0.845843 | − | 0.533432i | \(-0.179098\pi\) | ||||
0.845843 | + | 0.533432i | \(0.179098\pi\) | |||||||
\(282\) | 7.17891 | 0.427498 | ||||||||
\(283\) | 7.64218 | 0.454281 | 0.227140 | − | 0.973862i | \(-0.427062\pi\) | ||||
0.227140 | + | 0.973862i | \(0.427062\pi\) | |||||||
\(284\) | −2.17891 | −0.129294 | ||||||||
\(285\) | 6.35782 | 0.376605 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.17891 | 0.423758 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 6.35782 | 0.373344 | ||||||||
\(291\) | 10.3578 | 0.607186 | ||||||||
\(292\) | 4.00000 | 0.234082 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 24.3578 | 1.41817 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 5.17891 | 0.300511 | ||||||||
\(298\) | 16.1789 | 0.937219 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −12.1789 | −0.701981 | ||||||||
\(302\) | 19.5367 | 1.12421 | ||||||||
\(303\) | −6.35782 | −0.365247 | ||||||||
\(304\) | 3.17891 | 0.182323 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 5.00000 | 0.285831 | ||||||||
\(307\) | −31.8945 | −1.82032 | −0.910159 | − | 0.414259i | \(-0.864041\pi\) | ||||
−0.910159 | + | 0.414259i | \(0.864041\pi\) | |||||||
\(308\) | 5.17891 | 0.295096 | ||||||||
\(309\) | 8.17891 | 0.465282 | ||||||||
\(310\) | −8.35782 | −0.474692 | ||||||||
\(311\) | 25.5367 | 1.44805 | 0.724027 | − | 0.689771i | \(-0.242289\pi\) | ||||
0.724027 | + | 0.689771i | \(0.242289\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.00000 | 0.226093 | 0.113047 | − | 0.993590i | \(-0.463939\pi\) | ||||
0.113047 | + | 0.993590i | \(0.463939\pi\) | |||||||
\(314\) | 2.00000 | 0.112867 | ||||||||
\(315\) | 2.00000 | 0.112687 | ||||||||
\(316\) | 13.1789 | 0.741372 | ||||||||
\(317\) | −4.17891 | −0.234711 | −0.117355 | − | 0.993090i | \(-0.537442\pi\) | ||||
−0.117355 | + | 0.993090i | \(0.537442\pi\) | |||||||
\(318\) | 3.00000 | 0.168232 | ||||||||
\(319\) | 16.4633 | 0.921766 | ||||||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | −19.1789 | −1.07046 | ||||||||
\(322\) | 8.17891 | 0.455793 | ||||||||
\(323\) | 15.8945 | 0.884396 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.1789 | −1.11761 | ||||||||
\(327\) | −4.00000 | −0.221201 | ||||||||
\(328\) | −7.17891 | −0.396389 | ||||||||
\(329\) | 7.17891 | 0.395786 | ||||||||
\(330\) | −10.3578 | −0.570179 | ||||||||
\(331\) | −1.64218 | −0.0902626 | −0.0451313 | − | 0.998981i | \(-0.514371\pi\) | ||||
−0.0451313 | + | 0.998981i | \(0.514371\pi\) | |||||||
\(332\) | 6.17891 | 0.339112 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 7.64218 | 0.417537 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 33.5367 | 1.82686 | 0.913431 | − | 0.406994i | \(-0.133423\pi\) | ||||
0.913431 | + | 0.406994i | \(0.133423\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.3578 | −0.997060 | ||||||||
\(340\) | −10.0000 | −0.542326 | ||||||||
\(341\) | −21.6422 | −1.17199 | ||||||||
\(342\) | 3.17891 | 0.171896 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 12.1789 | 0.656643 | ||||||||
\(345\) | −16.3578 | −0.880675 | ||||||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | −19.1789 | −1.02958 | −0.514789 | − | 0.857317i | \(-0.672130\pi\) | ||||
−0.514789 | + | 0.857317i | \(0.672130\pi\) | |||||||
\(348\) | 3.17891 | 0.170407 | ||||||||
\(349\) | 8.17891 | 0.437807 | 0.218903 | − | 0.975747i | \(-0.429752\pi\) | ||||
0.218903 | + | 0.975747i | \(0.429752\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.17891 | −0.276037 | ||||||||
\(353\) | 4.17891 | 0.222421 | 0.111210 | − | 0.993797i | \(-0.464527\pi\) | ||||
0.111210 | + | 0.993797i | \(0.464527\pi\) | |||||||
\(354\) | 12.1789 | 0.647302 | ||||||||
\(355\) | 4.35782 | 0.231289 | ||||||||
\(356\) | 9.00000 | 0.476999 | ||||||||
\(357\) | 5.00000 | 0.264628 | ||||||||
\(358\) | 8.35782 | 0.441724 | ||||||||
\(359\) | −10.3578 | −0.546665 | −0.273332 | − | 0.961920i | \(-0.588126\pi\) | ||||
−0.273332 | + | 0.961920i | \(0.588126\pi\) | |||||||
\(360\) | −2.00000 | −0.105409 | ||||||||
\(361\) | −8.89454 | −0.468134 | ||||||||
\(362\) | 19.1789 | 1.00802 | ||||||||
\(363\) | −15.8211 | −0.830392 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.00000 | −0.418739 | ||||||||
\(366\) | 3.00000 | 0.156813 | ||||||||
\(367\) | −8.17891 | −0.426936 | −0.213468 | − | 0.976950i | \(-0.568476\pi\) | ||||
−0.213468 | + | 0.976950i | \(0.568476\pi\) | |||||||
\(368\) | −8.17891 | −0.426355 | ||||||||
\(369\) | −7.17891 | −0.373719 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 3.00000 | 0.155752 | ||||||||
\(372\) | −4.17891 | −0.216666 | ||||||||
\(373\) | −20.0000 | −1.03556 | −0.517780 | − | 0.855514i | \(-0.673242\pi\) | ||||
−0.517780 | + | 0.855514i | \(0.673242\pi\) | |||||||
\(374\) | −25.8945 | −1.33897 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | −7.17891 | −0.370224 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −24.7156 | −1.26956 | −0.634778 | − | 0.772694i | \(-0.718909\pi\) | ||||
−0.634778 | + | 0.772694i | \(0.718909\pi\) | |||||||
\(380\) | −6.35782 | −0.326149 | ||||||||
\(381\) | −12.0000 | −0.614779 | ||||||||
\(382\) | −6.53673 | −0.334448 | ||||||||
\(383\) | 21.1789 | 1.08219 | 0.541096 | − | 0.840961i | \(-0.318010\pi\) | ||||
0.541096 | + | 0.840961i | \(0.318010\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −10.3578 | −0.527883 | ||||||||
\(386\) | −13.5367 | −0.689001 | ||||||||
\(387\) | 12.1789 | 0.619089 | ||||||||
\(388\) | −10.3578 | −0.525838 | ||||||||
\(389\) | −12.1789 | −0.617495 | −0.308748 | − | 0.951144i | \(-0.599910\pi\) | ||||
−0.308748 | + | 0.951144i | \(0.599910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.8945 | −2.06813 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 14.5367 | 0.733281 | ||||||||
\(394\) | 17.0000 | 0.856448 | ||||||||
\(395\) | −26.3578 | −1.32621 | ||||||||
\(396\) | −5.17891 | −0.260250 | ||||||||
\(397\) | 3.00000 | 0.150566 | 0.0752828 | − | 0.997162i | \(-0.476014\pi\) | ||||
0.0752828 | + | 0.997162i | \(0.476014\pi\) | |||||||
\(398\) | 24.1789 | 1.21198 | ||||||||
\(399\) | 3.17891 | 0.159144 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 9.64218 | 0.481508 | 0.240754 | − | 0.970586i | \(-0.422605\pi\) | ||||
0.240754 | + | 0.970586i | \(0.422605\pi\) | |||||||
\(402\) | 3.82109 | 0.190579 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.35782 | 0.316313 | ||||||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 3.17891 | 0.157767 | ||||||||
\(407\) | −10.3578 | −0.513418 | ||||||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | −36.3578 | −1.79778 | −0.898889 | − | 0.438176i | \(-0.855625\pi\) | ||||
−0.898889 | + | 0.438176i | \(0.855625\pi\) | |||||||
\(410\) | 14.3578 | 0.709082 | ||||||||
\(411\) | −6.35782 | −0.313608 | ||||||||
\(412\) | −8.17891 | −0.402946 | ||||||||
\(413\) | 12.1789 | 0.599285 | ||||||||
\(414\) | −8.17891 | −0.401971 | ||||||||
\(415\) | −12.3578 | −0.606621 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.82109 | 0.334030 | ||||||||
\(418\) | −16.4633 | −0.805245 | ||||||||
\(419\) | −26.8945 | −1.31388 | −0.656942 | − | 0.753941i | \(-0.728150\pi\) | ||||
−0.656942 | + | 0.753941i | \(0.728150\pi\) | |||||||
\(420\) | −2.00000 | −0.0975900 | ||||||||
\(421\) | 10.7156 | 0.522248 | 0.261124 | − | 0.965305i | \(-0.415907\pi\) | ||||
0.261124 | + | 0.965305i | \(0.415907\pi\) | |||||||
\(422\) | −6.35782 | −0.309494 | ||||||||
\(423\) | −7.17891 | −0.349050 | ||||||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | −5.00000 | −0.242536 | ||||||||
\(426\) | 2.17891 | 0.105568 | ||||||||
\(427\) | 3.00000 | 0.145180 | ||||||||
\(428\) | 19.1789 | 0.927048 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.3578 | −1.17464 | ||||||||
\(431\) | 10.1789 | 0.490301 | 0.245150 | − | 0.969485i | \(-0.421163\pi\) | ||||
0.245150 | + | 0.969485i | \(0.421163\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 34.3578 | 1.65113 | 0.825566 | − | 0.564306i | \(-0.190856\pi\) | ||||
0.825566 | + | 0.564306i | \(0.190856\pi\) | |||||||
\(434\) | −4.17891 | −0.200594 | ||||||||
\(435\) | −6.35782 | −0.304834 | ||||||||
\(436\) | 4.00000 | 0.191565 | ||||||||
\(437\) | −26.0000 | −1.24375 | ||||||||
\(438\) | −4.00000 | −0.191127 | ||||||||
\(439\) | 40.7156 | 1.94325 | 0.971626 | − | 0.236524i | \(-0.0760083\pi\) | ||||
0.971626 | + | 0.236524i | \(0.0760083\pi\) | |||||||
\(440\) | 10.3578 | 0.493790 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.17891 | 0.151034 | 0.0755172 | − | 0.997144i | \(-0.475939\pi\) | ||||
0.0755172 | + | 0.997144i | \(0.475939\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | −18.0000 | −0.853282 | ||||||||
\(446\) | −2.17891 | −0.103174 | ||||||||
\(447\) | −16.1789 | −0.765236 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 37.1789 | 1.75069 | ||||||||
\(452\) | 18.3578 | 0.863479 | ||||||||
\(453\) | −19.5367 | −0.917915 | ||||||||
\(454\) | −14.3578 | −0.673846 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.17891 | −0.148866 | ||||||||
\(457\) | 24.8945 | 1.16452 | 0.582259 | − | 0.813004i | \(-0.302169\pi\) | ||||
0.582259 | + | 0.813004i | \(0.302169\pi\) | |||||||
\(458\) | 1.00000 | 0.0467269 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | 16.3578 | 0.762687 | ||||||||
\(461\) | 20.7156 | 0.964823 | 0.482412 | − | 0.875945i | \(-0.339761\pi\) | ||||
0.482412 | + | 0.875945i | \(0.339761\pi\) | |||||||
\(462\) | −5.17891 | −0.240945 | ||||||||
\(463\) | 27.8945 | 1.29637 | 0.648185 | − | 0.761483i | \(-0.275528\pi\) | ||||
0.648185 | + | 0.761483i | \(0.275528\pi\) | |||||||
\(464\) | −3.17891 | −0.147577 | ||||||||
\(465\) | 8.35782 | 0.387584 | ||||||||
\(466\) | 22.3578 | 1.03571 | ||||||||
\(467\) | −22.8945 | −1.05943 | −0.529717 | − | 0.848175i | \(-0.677702\pi\) | ||||
−0.529717 | + | 0.848175i | \(0.677702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.82109 | 0.176442 | ||||||||
\(470\) | 14.3578 | 0.662277 | ||||||||
\(471\) | −2.00000 | −0.0921551 | ||||||||
\(472\) | −12.1789 | −0.560580 | ||||||||
\(473\) | −63.0735 | −2.90012 | ||||||||
\(474\) | −13.1789 | −0.605327 | ||||||||
\(475\) | −3.17891 | −0.145858 | ||||||||
\(476\) | −5.00000 | −0.229175 | ||||||||
\(477\) | −3.00000 | −0.137361 | ||||||||
\(478\) | 10.1789 | 0.465572 | ||||||||
\(479\) | −41.1789 | −1.88151 | −0.940756 | − | 0.339084i | \(-0.889883\pi\) | ||||
−0.940756 | + | 0.339084i | \(0.889883\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.35782 | 0.198493 | ||||||||
\(483\) | −8.17891 | −0.372153 | ||||||||
\(484\) | 15.8211 | 0.719141 | ||||||||
\(485\) | 20.7156 | 0.940648 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −26.8211 | −1.21538 | −0.607690 | − | 0.794174i | \(-0.707904\pi\) | ||||
−0.607690 | + | 0.794174i | \(0.707904\pi\) | |||||||
\(488\) | −3.00000 | −0.135804 | ||||||||
\(489\) | 20.1789 | 0.912522 | ||||||||
\(490\) | −2.00000 | −0.0903508 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 7.17891 | 0.323650 | ||||||||
\(493\) | −15.8945 | −0.715854 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3578 | 0.465549 | ||||||||
\(496\) | 4.17891 | 0.187639 | ||||||||
\(497\) | 2.17891 | 0.0977374 | ||||||||
\(498\) | −6.17891 | −0.276884 | ||||||||
\(499\) | 8.17891 | 0.366138 | 0.183069 | − | 0.983100i | \(-0.441397\pi\) | ||||
0.183069 | + | 0.983100i | \(0.441397\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | 22.1789 | 0.989893 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −12.7156 | −0.565838 | ||||||||
\(506\) | 42.3578 | 1.88303 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | −16.7156 | −0.740907 | −0.370454 | − | 0.928851i | \(-0.620798\pi\) | ||||
−0.370454 | + | 0.928851i | \(0.620798\pi\) | |||||||
\(510\) | 10.0000 | 0.442807 | ||||||||
\(511\) | −4.00000 | −0.176950 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.17891 | −0.140352 | ||||||||
\(514\) | −19.7156 | −0.869619 | ||||||||
\(515\) | 16.3578 | 0.720812 | ||||||||
\(516\) | −12.1789 | −0.536147 | ||||||||
\(517\) | 37.1789 | 1.63513 | ||||||||
\(518\) | −2.00000 | −0.0878750 | ||||||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.17891 | 0.314514 | 0.157257 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157257 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(522\) | −3.17891 | −0.139137 | ||||||||
\(523\) | 11.5367 | 0.504466 | 0.252233 | − | 0.967667i | \(-0.418835\pi\) | ||||
0.252233 | + | 0.967667i | \(0.418835\pi\) | |||||||
\(524\) | −14.5367 | −0.635040 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | 20.8945 | 0.910181 | ||||||||
\(528\) | 5.17891 | 0.225383 | ||||||||
\(529\) | 43.8945 | 1.90846 | ||||||||
\(530\) | 6.00000 | 0.260623 | ||||||||
\(531\) | −12.1789 | −0.528520 | ||||||||
\(532\) | −3.17891 | −0.137823 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.00000 | −0.389468 | ||||||||
\(535\) | −38.3578 | −1.65835 | ||||||||
\(536\) | −3.82109 | −0.165046 | ||||||||
\(537\) | −8.35782 | −0.360666 | ||||||||
\(538\) | −4.35782 | −0.187879 | ||||||||
\(539\) | −5.17891 | −0.223071 | ||||||||
\(540\) | 2.00000 | 0.0860663 | ||||||||
\(541\) | −20.3578 | −0.875251 | −0.437625 | − | 0.899157i | \(-0.644180\pi\) | ||||
−0.437625 | + | 0.899157i | \(0.644180\pi\) | |||||||
\(542\) | 19.8211 | 0.851389 | ||||||||
\(543\) | −19.1789 | −0.823046 | ||||||||
\(544\) | 5.00000 | 0.214373 | ||||||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.0000 | 1.53925 | 0.769624 | − | 0.638497i | \(-0.220443\pi\) | ||||
0.769624 | + | 0.638497i | \(0.220443\pi\) | |||||||
\(548\) | 6.35782 | 0.271592 | ||||||||
\(549\) | −3.00000 | −0.128037 | ||||||||
\(550\) | 5.17891 | 0.220829 | ||||||||
\(551\) | −10.1055 | −0.430507 | ||||||||
\(552\) | 8.17891 | 0.348117 | ||||||||
\(553\) | −13.1789 | −0.560424 | ||||||||
\(554\) | 5.64218 | 0.239713 | ||||||||
\(555\) | 4.00000 | 0.169791 | ||||||||
\(556\) | −6.82109 | −0.289279 | ||||||||
\(557\) | 23.7156 | 1.00486 | 0.502432 | − | 0.864617i | \(-0.332439\pi\) | ||||
0.502432 | + | 0.864617i | \(0.332439\pi\) | |||||||
\(558\) | 4.17891 | 0.176907 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 25.8945 | 1.09327 | ||||||||
\(562\) | 28.3578 | 1.19620 | ||||||||
\(563\) | −18.3578 | −0.773690 | −0.386845 | − | 0.922145i | \(-0.626435\pi\) | ||||
−0.386845 | + | 0.922145i | \(0.626435\pi\) | |||||||
\(564\) | 7.17891 | 0.302287 | ||||||||
\(565\) | −36.7156 | −1.54464 | ||||||||
\(566\) | 7.64218 | 0.321225 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −2.17891 | −0.0914250 | ||||||||
\(569\) | −3.64218 | −0.152688 | −0.0763441 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763441 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(570\) | 6.35782 | 0.266300 | ||||||||
\(571\) | −34.1789 | −1.43034 | −0.715171 | − | 0.698949i | \(-0.753651\pi\) | ||||
−0.715171 | + | 0.698949i | \(0.753651\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.53673 | 0.273076 | ||||||||
\(574\) | 7.17891 | 0.299642 | ||||||||
\(575\) | 8.17891 | 0.341084 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −28.3578 | −1.18055 | −0.590276 | − | 0.807202i | \(-0.700981\pi\) | ||||
−0.590276 | + | 0.807202i | \(0.700981\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | 13.5367 | 0.562567 | ||||||||
\(580\) | 6.35782 | 0.263994 | ||||||||
\(581\) | −6.17891 | −0.256344 | ||||||||
\(582\) | 10.3578 | 0.429345 | ||||||||
\(583\) | 15.5367 | 0.643465 | ||||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 0.178908 | 0.00738434 | 0.00369217 | − | 0.999993i | \(-0.498825\pi\) | ||||
0.00369217 | + | 0.999993i | \(0.498825\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 13.2844 | 0.547373 | ||||||||
\(590\) | 24.3578 | 1.00280 | ||||||||
\(591\) | −17.0000 | −0.699287 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −33.0000 | −1.35515 | −0.677574 | − | 0.735455i | \(-0.736969\pi\) | ||||
−0.677574 | + | 0.735455i | \(0.736969\pi\) | |||||||
\(594\) | 5.17891 | 0.212493 | ||||||||
\(595\) | 10.0000 | 0.409960 | ||||||||
\(596\) | 16.1789 | 0.662714 | ||||||||
\(597\) | −24.1789 | −0.989577 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.1789 | 1.64167 | 0.820833 | − | 0.571168i | \(-0.193510\pi\) | ||||
0.820833 | + | 0.571168i | \(0.193510\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | −12.1789 | −0.496375 | ||||||||
\(603\) | −3.82109 | −0.155607 | ||||||||
\(604\) | 19.5367 | 0.794938 | ||||||||
\(605\) | −31.6422 | −1.28644 | ||||||||
\(606\) | −6.35782 | −0.258269 | ||||||||
\(607\) | −0.536725 | −0.0217850 | −0.0108925 | − | 0.999941i | \(-0.503467\pi\) | ||||
−0.0108925 | + | 0.999941i | \(0.503467\pi\) | |||||||
\(608\) | 3.17891 | 0.128922 | ||||||||
\(609\) | −3.17891 | −0.128816 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 5.00000 | 0.202113 | ||||||||
\(613\) | 15.6422 | 0.631782 | 0.315891 | − | 0.948796i | \(-0.397697\pi\) | ||||
0.315891 | + | 0.948796i | \(0.397697\pi\) | |||||||
\(614\) | −31.8945 | −1.28716 | ||||||||
\(615\) | −14.3578 | −0.578963 | ||||||||
\(616\) | 5.17891 | 0.208664 | ||||||||
\(617\) | 32.0000 | 1.28827 | 0.644136 | − | 0.764911i | \(-0.277217\pi\) | ||||
0.644136 | + | 0.764911i | \(0.277217\pi\) | |||||||
\(618\) | 8.17891 | 0.329004 | ||||||||
\(619\) | 25.5367 | 1.02641 | 0.513204 | − | 0.858267i | \(-0.328458\pi\) | ||||
0.513204 | + | 0.858267i | \(0.328458\pi\) | |||||||
\(620\) | −8.35782 | −0.335658 | ||||||||
\(621\) | 8.17891 | 0.328208 | ||||||||
\(622\) | 25.5367 | 1.02393 | ||||||||
\(623\) | −9.00000 | −0.360577 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 4.00000 | 0.159872 | ||||||||
\(627\) | 16.4633 | 0.657480 | ||||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 2.00000 | 0.0796819 | ||||||||
\(631\) | 25.8945 | 1.03085 | 0.515423 | − | 0.856936i | \(-0.327635\pi\) | ||||
0.515423 | + | 0.856936i | \(0.327635\pi\) | |||||||
\(632\) | 13.1789 | 0.524229 | ||||||||
\(633\) | 6.35782 | 0.252701 | ||||||||
\(634\) | −4.17891 | −0.165966 | ||||||||
\(635\) | −24.0000 | −0.952411 | ||||||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.4633 | 0.651787 | ||||||||
\(639\) | −2.17891 | −0.0861963 | ||||||||
\(640\) | −2.00000 | −0.0790569 | ||||||||
\(641\) | 27.0735 | 1.06934 | 0.534668 | − | 0.845062i | \(-0.320436\pi\) | ||||
0.534668 | + | 0.845062i | \(0.320436\pi\) | |||||||
\(642\) | −19.1789 | −0.756931 | ||||||||
\(643\) | −8.82109 | −0.347870 | −0.173935 | − | 0.984757i | \(-0.555648\pi\) | ||||
−0.173935 | + | 0.984757i | \(0.555648\pi\) | |||||||
\(644\) | 8.17891 | 0.322294 | ||||||||
\(645\) | 24.3578 | 0.959088 | ||||||||
\(646\) | 15.8945 | 0.625362 | ||||||||
\(647\) | 47.8945 | 1.88293 | 0.941464 | − | 0.337113i | \(-0.109450\pi\) | ||||
0.941464 | + | 0.337113i | \(0.109450\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 63.0735 | 2.47585 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.17891 | 0.163784 | ||||||||
\(652\) | −20.1789 | −0.790267 | ||||||||
\(653\) | 21.0000 | 0.821794 | 0.410897 | − | 0.911682i | \(-0.365216\pi\) | ||||
0.410897 | + | 0.911682i | \(0.365216\pi\) | |||||||
\(654\) | −4.00000 | −0.156412 | ||||||||
\(655\) | 29.0735 | 1.13599 | ||||||||
\(656\) | −7.17891 | −0.280289 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 7.17891 | 0.279863 | ||||||||
\(659\) | 17.5367 | 0.683134 | 0.341567 | − | 0.939857i | \(-0.389042\pi\) | ||||
0.341567 | + | 0.939857i | \(0.389042\pi\) | |||||||
\(660\) | −10.3578 | −0.403177 | ||||||||
\(661\) | 16.5367 | 0.643204 | 0.321602 | − | 0.946875i | \(-0.395779\pi\) | ||||
0.321602 | + | 0.946875i | \(0.395779\pi\) | |||||||
\(662\) | −1.64218 | −0.0638253 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.17891 | 0.239788 | ||||||||
\(665\) | 6.35782 | 0.246546 | ||||||||
\(666\) | 2.00000 | 0.0774984 | ||||||||
\(667\) | 26.0000 | 1.00672 | ||||||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | 2.17891 | 0.0842415 | ||||||||
\(670\) | 7.64218 | 0.295243 | ||||||||
\(671\) | 15.5367 | 0.599789 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −1.00000 | −0.0385472 | −0.0192736 | − | 0.999814i | \(-0.506135\pi\) | ||||
−0.0192736 | + | 0.999814i | \(0.506135\pi\) | |||||||
\(674\) | 33.5367 | 1.29179 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0000 | 0.461197 | 0.230599 | − | 0.973049i | \(-0.425932\pi\) | ||||
0.230599 | + | 0.973049i | \(0.425932\pi\) | |||||||
\(678\) | −18.3578 | −0.705028 | ||||||||
\(679\) | 10.3578 | 0.397497 | ||||||||
\(680\) | −10.0000 | −0.383482 | ||||||||
\(681\) | 14.3578 | 0.550193 | ||||||||
\(682\) | −21.6422 | −0.828722 | ||||||||
\(683\) | 8.35782 | 0.319803 | 0.159901 | − | 0.987133i | \(-0.448882\pi\) | ||||
0.159901 | + | 0.987133i | \(0.448882\pi\) | |||||||
\(684\) | 3.17891 | 0.121549 | ||||||||
\(685\) | −12.7156 | −0.485839 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −1.00000 | −0.0381524 | ||||||||
\(688\) | 12.1789 | 0.464317 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −16.3578 | −0.622731 | ||||||||
\(691\) | −40.0000 | −1.52167 | −0.760836 | − | 0.648944i | \(-0.775211\pi\) | ||||
−0.760836 | + | 0.648944i | \(0.775211\pi\) | |||||||
\(692\) | 4.00000 | 0.152057 | ||||||||
\(693\) | 5.17891 | 0.196730 | ||||||||
\(694\) | −19.1789 | −0.728021 | ||||||||
\(695\) | 13.6422 | 0.517478 | ||||||||
\(696\) | 3.17891 | 0.120496 | ||||||||
\(697\) | −35.8945 | −1.35960 | ||||||||
\(698\) | 8.17891 | 0.309576 | ||||||||
\(699\) | −22.3578 | −0.845650 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −21.7156 | −0.820188 | −0.410094 | − | 0.912043i | \(-0.634504\pi\) | ||||
−0.410094 | + | 0.912043i | \(0.634504\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.35782 | 0.239790 | ||||||||
\(704\) | −5.17891 | −0.195187 | ||||||||
\(705\) | −14.3578 | −0.540747 | ||||||||
\(706\) | 4.17891 | 0.157275 | ||||||||
\(707\) | −6.35782 | −0.239110 | ||||||||
\(708\) | 12.1789 | 0.457711 | ||||||||
\(709\) | −16.0000 | −0.600893 | −0.300446 | − | 0.953799i | \(-0.597136\pi\) | ||||
−0.300446 | + | 0.953799i | \(0.597136\pi\) | |||||||
\(710\) | 4.35782 | 0.163546 | ||||||||
\(711\) | 13.1789 | 0.494248 | ||||||||
\(712\) | 9.00000 | 0.337289 | ||||||||
\(713\) | −34.1789 | −1.28001 | ||||||||
\(714\) | 5.00000 | 0.187120 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.35782 | 0.312346 | ||||||||
\(717\) | −10.1789 | −0.380138 | ||||||||
\(718\) | −10.3578 | −0.386550 | ||||||||
\(719\) | −37.1789 | −1.38654 | −0.693270 | − | 0.720678i | \(-0.743831\pi\) | ||||
−0.693270 | + | 0.720678i | \(0.743831\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 8.17891 | 0.304598 | ||||||||
\(722\) | −8.89454 | −0.331021 | ||||||||
\(723\) | −4.35782 | −0.162069 | ||||||||
\(724\) | 19.1789 | 0.712779 | ||||||||
\(725\) | 3.17891 | 0.118062 | ||||||||
\(726\) | −15.8211 | −0.587176 | ||||||||
\(727\) | 34.5367 | 1.28090 | 0.640448 | − | 0.768001i | \(-0.278749\pi\) | ||||
0.640448 | + | 0.768001i | \(0.278749\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.00000 | −0.296093 | ||||||||
\(731\) | 60.8945 | 2.25227 | ||||||||
\(732\) | 3.00000 | 0.110883 | ||||||||
\(733\) | 19.7156 | 0.728214 | 0.364107 | − | 0.931357i | \(-0.381374\pi\) | ||||
0.364107 | + | 0.931357i | \(0.381374\pi\) | |||||||
\(734\) | −8.17891 | −0.301889 | ||||||||
\(735\) | 2.00000 | 0.0737711 | ||||||||
\(736\) | −8.17891 | −0.301479 | ||||||||
\(737\) | 19.7891 | 0.728940 | ||||||||
\(738\) | −7.17891 | −0.264259 | ||||||||
\(739\) | −16.1789 | −0.595151 | −0.297575 | − | 0.954698i | \(-0.596178\pi\) | ||||
−0.297575 | + | 0.954698i | \(0.596178\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | 31.8211 | 1.16740 | 0.583701 | − | 0.811968i | \(-0.301604\pi\) | ||||
0.583701 | + | 0.811968i | \(0.301604\pi\) | |||||||
\(744\) | −4.17891 | −0.153206 | ||||||||
\(745\) | −32.3578 | −1.18550 | ||||||||
\(746\) | −20.0000 | −0.732252 | ||||||||
\(747\) | 6.17891 | 0.226074 | ||||||||
\(748\) | −25.8945 | −0.946798 | ||||||||
\(749\) | −19.1789 | −0.700782 | ||||||||
\(750\) | −12.0000 | −0.438178 | ||||||||
\(751\) | −35.8945 | −1.30981 | −0.654905 | − | 0.755711i | \(-0.727291\pi\) | ||||
−0.654905 | + | 0.755711i | \(0.727291\pi\) | |||||||
\(752\) | −7.17891 | −0.261788 | ||||||||
\(753\) | −22.1789 | −0.808244 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.0735 | −1.42203 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −20.3578 | −0.739917 | −0.369959 | − | 0.929048i | \(-0.620628\pi\) | ||||
−0.369959 | + | 0.929048i | \(0.620628\pi\) | |||||||
\(758\) | −24.7156 | −0.897712 | ||||||||
\(759\) | −42.3578 | −1.53749 | ||||||||
\(760\) | −6.35782 | −0.230622 | ||||||||
\(761\) | −43.4313 | −1.57438 | −0.787191 | − | 0.616709i | \(-0.788465\pi\) | ||||
−0.787191 | + | 0.616709i | \(0.788465\pi\) | |||||||
\(762\) | −12.0000 | −0.434714 | ||||||||
\(763\) | −4.00000 | −0.144810 | ||||||||
\(764\) | −6.53673 | −0.236490 | ||||||||
\(765\) | −10.0000 | −0.361551 | ||||||||
\(766\) | 21.1789 | 0.765225 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 18.3578 | 0.662000 | 0.331000 | − | 0.943631i | \(-0.392614\pi\) | ||||
0.331000 | + | 0.943631i | \(0.392614\pi\) | |||||||
\(770\) | −10.3578 | −0.373270 | ||||||||
\(771\) | 19.7156 | 0.710041 | ||||||||
\(772\) | −13.5367 | −0.487197 | ||||||||
\(773\) | 14.7156 | 0.529285 | 0.264642 | − | 0.964347i | \(-0.414746\pi\) | ||||
0.264642 | + | 0.964347i | \(0.414746\pi\) | |||||||
\(774\) | 12.1789 | 0.437762 | ||||||||
\(775\) | −4.17891 | −0.150111 | ||||||||
\(776\) | −10.3578 | −0.371824 | ||||||||
\(777\) | 2.00000 | 0.0717496 | ||||||||
\(778\) | −12.1789 | −0.436635 | ||||||||
\(779\) | −22.8211 | −0.817650 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2844 | 0.403786 | ||||||||
\(782\) | −40.8945 | −1.46239 | ||||||||
\(783\) | 3.17891 | 0.113605 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 14.5367 | 0.518508 | ||||||||
\(787\) | −10.8211 | −0.385730 | −0.192865 | − | 0.981225i | \(-0.561778\pi\) | ||||
−0.192865 | + | 0.981225i | \(0.561778\pi\) | |||||||
\(788\) | 17.0000 | 0.605600 | ||||||||
\(789\) | 12.0000 | 0.427211 | ||||||||
\(790\) | −26.3578 | −0.937769 | ||||||||
\(791\) | −18.3578 | −0.652729 | ||||||||
\(792\) | −5.17891 | −0.184024 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 3.00000 | 0.106466 | ||||||||
\(795\) | −6.00000 | −0.212798 | ||||||||
\(796\) | 24.1789 | 0.856999 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 3.17891 | 0.112532 | ||||||||
\(799\) | −35.8945 | −1.26986 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 9.00000 | 0.317999 | ||||||||
\(802\) | 9.64218 | 0.340477 | ||||||||
\(803\) | −20.7156 | −0.731039 | ||||||||
\(804\) | 3.82109 | 0.134760 | ||||||||
\(805\) | −16.3578 | −0.576537 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.35782 | 0.153402 | ||||||||
\(808\) | 6.35782 | 0.223667 | ||||||||
\(809\) | −20.0000 | −0.703163 | −0.351581 | − | 0.936157i | \(-0.614356\pi\) | ||||
−0.351581 | + | 0.936157i | \(0.614356\pi\) | |||||||
\(810\) | −2.00000 | −0.0702728 | ||||||||
\(811\) | −12.7156 | −0.446506 | −0.223253 | − | 0.974761i | \(-0.571668\pi\) | ||||
−0.223253 | + | 0.974761i | \(0.571668\pi\) | |||||||
\(812\) | 3.17891 | 0.111558 | ||||||||
\(813\) | −19.8211 | −0.695156 | ||||||||
\(814\) | −10.3578 | −0.363041 | ||||||||
\(815\) | 40.3578 | 1.41367 | ||||||||
\(816\) | −5.00000 | −0.175035 | ||||||||
\(817\) | 38.7156 | 1.35449 | ||||||||
\(818\) | −36.3578 | −1.27122 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.3578 | 0.501397 | ||||||||
\(821\) | 0.284367 | 0.00992446 | 0.00496223 | − | 0.999988i | \(-0.498420\pi\) | ||||
0.00496223 | + | 0.999988i | \(0.498420\pi\) | |||||||
\(822\) | −6.35782 | −0.221754 | ||||||||
\(823\) | 32.7156 | 1.14040 | 0.570198 | − | 0.821508i | \(-0.306867\pi\) | ||||
0.570198 | + | 0.821508i | \(0.306867\pi\) | |||||||
\(824\) | −8.17891 | −0.284926 | ||||||||
\(825\) | −5.17891 | −0.180306 | ||||||||
\(826\) | 12.1789 | 0.423758 | ||||||||
\(827\) | −40.7156 | −1.41582 | −0.707911 | − | 0.706302i | \(-0.750362\pi\) | ||||
−0.707911 | + | 0.706302i | \(0.750362\pi\) | |||||||
\(828\) | −8.17891 | −0.284237 | ||||||||
\(829\) | −3.17891 | −0.110408 | −0.0552040 | − | 0.998475i | \(-0.517581\pi\) | ||||
−0.0552040 | + | 0.998475i | \(0.517581\pi\) | |||||||
\(830\) | −12.3578 | −0.428946 | ||||||||
\(831\) | −5.64218 | −0.195725 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.00000 | 0.173240 | ||||||||
\(834\) | 6.82109 | 0.236195 | ||||||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | −16.4633 | −0.569394 | ||||||||
\(837\) | −4.17891 | −0.144444 | ||||||||
\(838\) | −26.8945 | −0.929057 | ||||||||
\(839\) | 11.6422 | 0.401933 | 0.200966 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200966 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(840\) | −2.00000 | −0.0690066 | ||||||||
\(841\) | −18.8945 | −0.651536 | ||||||||
\(842\) | 10.7156 | 0.369285 | ||||||||
\(843\) | −28.3578 | −0.976695 | ||||||||
\(844\) | −6.35782 | −0.218845 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.17891 | −0.246816 | ||||||||
\(847\) | −15.8211 | −0.543619 | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | −7.64218 | −0.262279 | ||||||||
\(850\) | −5.00000 | −0.171499 | ||||||||
\(851\) | −16.3578 | −0.560739 | ||||||||
\(852\) | 2.17891 | 0.0746482 | ||||||||
\(853\) | 27.7156 | 0.948965 | 0.474483 | − | 0.880265i | \(-0.342635\pi\) | ||||
0.474483 | + | 0.880265i | \(0.342635\pi\) | |||||||
\(854\) | 3.00000 | 0.102658 | ||||||||
\(855\) | −6.35782 | −0.217433 | ||||||||
\(856\) | 19.1789 | 0.655522 | ||||||||
\(857\) | −10.7156 | −0.366039 | −0.183020 | − | 0.983109i | \(-0.558587\pi\) | ||||
−0.183020 | + | 0.983109i | \(0.558587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.8945 | 0.678793 | 0.339397 | − | 0.940643i | \(-0.389777\pi\) | ||||
0.339397 | + | 0.940643i | \(0.389777\pi\) | |||||||
\(860\) | −24.3578 | −0.830595 | ||||||||
\(861\) | −7.17891 | −0.244657 | ||||||||
\(862\) | 10.1789 | 0.346695 | ||||||||
\(863\) | 13.6422 | 0.464385 | 0.232193 | − | 0.972670i | \(-0.425410\pi\) | ||||
0.232193 | + | 0.972670i | \(0.425410\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −8.00000 | −0.272008 | ||||||||
\(866\) | 34.3578 | 1.16753 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | −4.17891 | −0.141841 | ||||||||
\(869\) | −68.2524 | −2.31530 | ||||||||
\(870\) | −6.35782 | −0.215550 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.00000 | 0.135457 | ||||||||
\(873\) | −10.3578 | −0.350559 | ||||||||
\(874\) | −26.0000 | −0.879463 | ||||||||
\(875\) | −12.0000 | −0.405674 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | −40.3578 | −1.36279 | −0.681393 | − | 0.731917i | \(-0.738626\pi\) | ||||
−0.681393 | + | 0.731917i | \(0.738626\pi\) | |||||||
\(878\) | 40.7156 | 1.37409 | ||||||||
\(879\) | −12.0000 | −0.404750 | ||||||||
\(880\) | 10.3578 | 0.349162 | ||||||||
\(881\) | 11.4633 | 0.386208 | 0.193104 | − | 0.981178i | \(-0.438145\pi\) | ||||
0.193104 | + | 0.981178i | \(0.438145\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −3.46327 | −0.116548 | −0.0582742 | − | 0.998301i | \(-0.518560\pi\) | ||||
−0.0582742 | + | 0.998301i | \(0.518560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.3578 | −0.818779 | ||||||||
\(886\) | 3.17891 | 0.106798 | ||||||||
\(887\) | −45.5367 | −1.52897 | −0.764487 | − | 0.644639i | \(-0.777008\pi\) | ||||
−0.764487 | + | 0.644639i | \(0.777008\pi\) | |||||||
\(888\) | −2.00000 | −0.0671156 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | −18.0000 | −0.603361 | ||||||||
\(891\) | −5.17891 | −0.173500 | ||||||||
\(892\) | −2.17891 | −0.0729552 | ||||||||
\(893\) | −22.8211 | −0.763679 | ||||||||
\(894\) | −16.1789 | −0.541104 | ||||||||
\(895\) | −16.7156 | −0.558742 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.0000 | −0.467186 | ||||||||
\(899\) | −13.2844 | −0.443058 | ||||||||
\(900\) | −1.00000 | −0.0333333 | ||||||||
\(901\) | −15.0000 | −0.499722 | ||||||||
\(902\) | 37.1789 | 1.23792 | ||||||||
\(903\) | 12.1789 | 0.405289 | ||||||||
\(904\) | 18.3578 | 0.610572 | ||||||||
\(905\) | −38.3578 | −1.27506 | ||||||||
\(906\) | −19.5367 | −0.649064 | ||||||||
\(907\) | 49.6102 | 1.64728 | 0.823639 | − | 0.567114i | \(-0.191940\pi\) | ||||
0.823639 | + | 0.567114i | \(0.191940\pi\) | |||||||
\(908\) | −14.3578 | −0.476481 | ||||||||
\(909\) | 6.35782 | 0.210875 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.7156 | 0.951391 | 0.475696 | − | 0.879610i | \(-0.342196\pi\) | ||||
0.475696 | + | 0.879610i | \(0.342196\pi\) | |||||||
\(912\) | −3.17891 | −0.105264 | ||||||||
\(913\) | −32.0000 | −1.05905 | ||||||||
\(914\) | 24.8945 | 0.823438 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | 1.00000 | 0.0330409 | ||||||||
\(917\) | 14.5367 | 0.480045 | ||||||||
\(918\) | −5.00000 | −0.165025 | ||||||||
\(919\) | −58.2524 | −1.92157 | −0.960784 | − | 0.277298i | \(-0.910561\pi\) | ||||
−0.960784 | + | 0.277298i | \(0.910561\pi\) | |||||||
\(920\) | 16.3578 | 0.539301 | ||||||||
\(921\) | 31.8945 | 1.05096 | ||||||||
\(922\) | 20.7156 | 0.682233 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −5.17891 | −0.170374 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 27.8945 | 0.916672 | ||||||||
\(927\) | −8.17891 | −0.268631 | ||||||||
\(928\) | −3.17891 | −0.104353 | ||||||||
\(929\) | 39.0000 | 1.27955 | 0.639774 | − | 0.768563i | \(-0.279028\pi\) | ||||
0.639774 | + | 0.768563i | \(0.279028\pi\) | |||||||
\(930\) | 8.35782 | 0.274064 | ||||||||
\(931\) | 3.17891 | 0.104185 | ||||||||
\(932\) | 22.3578 | 0.732355 | ||||||||
\(933\) | −25.5367 | −0.836035 | ||||||||
\(934\) | −22.8945 | −0.749132 | ||||||||
\(935\) | 51.7891 | 1.69368 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.0735 | 0.688440 | 0.344220 | − | 0.938889i | \(-0.388143\pi\) | ||||
0.344220 | + | 0.938889i | \(0.388143\pi\) | |||||||
\(938\) | 3.82109 | 0.124763 | ||||||||
\(939\) | −4.00000 | −0.130535 | ||||||||
\(940\) | 14.3578 | 0.468300 | ||||||||
\(941\) | −20.0000 | −0.651981 | −0.325991 | − | 0.945373i | \(-0.605698\pi\) | ||||
−0.325991 | + | 0.945373i | \(0.605698\pi\) | |||||||
\(942\) | −2.00000 | −0.0651635 | ||||||||
\(943\) | 58.7156 | 1.91204 | ||||||||
\(944\) | −12.1789 | −0.396390 | ||||||||
\(945\) | −2.00000 | −0.0650600 | ||||||||
\(946\) | −63.0735 | −2.05069 | ||||||||
\(947\) | −40.2524 | −1.30803 | −0.654013 | − | 0.756483i | \(-0.726916\pi\) | ||||
−0.654013 | + | 0.756483i | \(0.726916\pi\) | |||||||
\(948\) | −13.1789 | −0.428031 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.17891 | −0.103137 | ||||||||
\(951\) | 4.17891 | 0.135510 | ||||||||
\(952\) | −5.00000 | −0.162051 | ||||||||
\(953\) | −2.71563 | −0.0879680 | −0.0439840 | − | 0.999032i | \(-0.514005\pi\) | ||||
−0.0439840 | + | 0.999032i | \(0.514005\pi\) | |||||||
\(954\) | −3.00000 | −0.0971286 | ||||||||
\(955\) | 13.0735 | 0.423047 | ||||||||
\(956\) | 10.1789 | 0.329209 | ||||||||
\(957\) | −16.4633 | −0.532182 | ||||||||
\(958\) | −41.1789 | −1.33043 | ||||||||
\(959\) | −6.35782 | −0.205305 | ||||||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | −13.5367 | −0.436669 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.1789 | 0.618032 | ||||||||
\(964\) | 4.35782 | 0.140356 | ||||||||
\(965\) | 27.0735 | 0.871525 | ||||||||
\(966\) | −8.17891 | −0.263152 | ||||||||
\(967\) | 11.6422 | 0.374387 | 0.187194 | − | 0.982323i | \(-0.440061\pi\) | ||||
0.187194 | + | 0.982323i | \(0.440061\pi\) | |||||||
\(968\) | 15.8211 | 0.508509 | ||||||||
\(969\) | −15.8945 | −0.510606 | ||||||||
\(970\) | 20.7156 | 0.665139 | ||||||||
\(971\) | −28.1789 | −0.904304 | −0.452152 | − | 0.891941i | \(-0.649344\pi\) | ||||
−0.452152 | + | 0.891941i | \(0.649344\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 6.82109 | 0.218674 | ||||||||
\(974\) | −26.8211 | −0.859403 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.00000 | −0.0960277 | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | 20.1789 | 0.645250 | ||||||||
\(979\) | −46.6102 | −1.48967 | ||||||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | 4.00000 | 0.127710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0735 | −0.416978 | −0.208489 | − | 0.978025i | \(-0.566855\pi\) | ||||
−0.208489 | + | 0.978025i | \(0.566855\pi\) | |||||||
\(984\) | 7.17891 | 0.228855 | ||||||||
\(985\) | −34.0000 | −1.08333 | ||||||||
\(986\) | −15.8945 | −0.506185 | ||||||||
\(987\) | −7.17891 | −0.228507 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −99.6102 | −3.16742 | ||||||||
\(990\) | 10.3578 | 0.329193 | ||||||||
\(991\) | −49.5367 | −1.57359 | −0.786793 | − | 0.617217i | \(-0.788260\pi\) | ||||
−0.786793 | + | 0.617217i | \(0.788260\pi\) | |||||||
\(992\) | 4.17891 | 0.132680 | ||||||||
\(993\) | 1.64218 | 0.0521131 | ||||||||
\(994\) | 2.17891 | 0.0691108 | ||||||||
\(995\) | −48.3578 | −1.53305 | ||||||||
\(996\) | −6.17891 | −0.195786 | ||||||||
\(997\) | 12.2844 | 0.389050 | 0.194525 | − | 0.980898i | \(-0.437683\pi\) | ||||
0.194525 | + | 0.980898i | \(0.437683\pi\) | |||||||
\(998\) | 8.17891 | 0.258899 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 7098.2.a.br.1.1 | 2 | ||
13.3 | even | 3 | 546.2.l.k.295.2 | yes | 4 | ||
13.9 | even | 3 | 546.2.l.k.211.2 | ✓ | 4 | ||
13.12 | even | 2 | 7098.2.a.bk.1.2 | 2 | |||
39.29 | odd | 6 | 1638.2.r.ba.1387.1 | 4 | |||
39.35 | odd | 6 | 1638.2.r.ba.757.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.k.211.2 | ✓ | 4 | 13.9 | even | 3 | ||
546.2.l.k.295.2 | yes | 4 | 13.3 | even | 3 | ||
1638.2.r.ba.757.1 | 4 | 39.35 | odd | 6 | |||
1638.2.r.ba.1387.1 | 4 | 39.29 | odd | 6 | |||
7098.2.a.bk.1.2 | 2 | 13.12 | even | 2 | |||
7098.2.a.br.1.1 | 2 | 1.1 | even | 1 | trivial |