Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6534,2,Mod(1,6534)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6534, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6534.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6534.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: | \(52.1742526807\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 594) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6534.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.85410 | −1.07875 | −0.539375 | − | 0.842066i | \(-0.681339\pi\) | ||||
−0.539375 | + | 0.842066i | \(0.681339\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.23607 | 0.390879 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.23607 | 1.72957 | 0.864787 | − | 0.502139i | \(-0.167453\pi\) | ||||
0.864787 | + | 0.502139i | \(0.167453\pi\) | |||||||
\(14\) | −2.85410 | −0.762791 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.23607 | −1.51247 | −0.756234 | − | 0.654301i | \(-0.772963\pi\) | ||||
−0.756234 | + | 0.654301i | \(0.772963\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 1.23607 | 0.276393 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.61803 | −1.58847 | −0.794235 | − | 0.607611i | \(-0.792128\pi\) | ||||
−0.794235 | + | 0.607611i | \(0.792128\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 6.23607 | 1.22299 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.85410 | −0.539375 | ||||||||
\(29\) | 7.09017 | 1.31661 | 0.658306 | − | 0.752751i | \(-0.271273\pi\) | ||||
0.658306 | + | 0.752751i | \(0.271273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.23607 | −1.06948 | ||||||||
\(35\) | −3.52786 | −0.596318 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.00000 | 1.47959 | 0.739795 | − | 0.672832i | \(-0.234922\pi\) | ||||
0.739795 | + | 0.672832i | \(0.234922\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.23607 | 0.195440 | ||||||||
\(41\) | 3.38197 | 0.528174 | 0.264087 | − | 0.964499i | \(-0.414929\pi\) | ||||
0.264087 | + | 0.964499i | \(0.414929\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.708204 | 0.108000 | 0.0540000 | − | 0.998541i | \(-0.482803\pi\) | ||||
0.0540000 | + | 0.998541i | \(0.482803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.61803 | −1.12322 | ||||||||
\(47\) | −1.76393 | −0.257296 | −0.128648 | − | 0.991690i | \(-0.541064\pi\) | ||||
−0.128648 | + | 0.991690i | \(0.541064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.14590 | 0.163700 | ||||||||
\(50\) | −3.47214 | −0.491034 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.23607 | 0.864787 | ||||||||
\(53\) | −10.0902 | −1.38599 | −0.692996 | − | 0.720942i | \(-0.743710\pi\) | ||||
−0.692996 | + | 0.720942i | \(0.743710\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.85410 | −0.381395 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.09017 | 0.930985 | ||||||||
\(59\) | −9.32624 | −1.21417 | −0.607086 | − | 0.794636i | \(-0.707662\pi\) | ||||
−0.607086 | + | 0.794636i | \(0.707662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.47214 | −0.444561 | −0.222281 | − | 0.974983i | \(-0.571350\pi\) | ||||
−0.222281 | + | 0.974983i | \(0.571350\pi\) | |||||||
\(62\) | −7.00000 | −0.889001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.70820 | 0.956085 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.09017 | −0.744033 | −0.372016 | − | 0.928226i | \(-0.621333\pi\) | ||||
−0.372016 | + | 0.928226i | \(0.621333\pi\) | |||||||
\(68\) | −6.23607 | −0.756234 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.52786 | −0.421660 | ||||||||
\(71\) | −4.52786 | −0.537359 | −0.268679 | − | 0.963230i | \(-0.586587\pi\) | ||||
−0.268679 | + | 0.963230i | \(0.586587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.23607 | 0.495794 | 0.247897 | − | 0.968786i | \(-0.420261\pi\) | ||||
0.247897 | + | 0.968786i | \(0.420261\pi\) | |||||||
\(74\) | 9.00000 | 1.04623 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0000 | −1.68763 | −0.843816 | − | 0.536633i | \(-0.819696\pi\) | ||||
−0.843816 | + | 0.536633i | \(0.819696\pi\) | |||||||
\(80\) | 1.23607 | 0.138197 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.38197 | 0.373476 | ||||||||
\(83\) | −3.76393 | −0.413145 | −0.206573 | − | 0.978431i | \(-0.566231\pi\) | ||||
−0.206573 | + | 0.978431i | \(0.566231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.70820 | −0.836072 | ||||||||
\(86\) | 0.708204 | 0.0763676 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.23607 | −0.449022 | −0.224511 | − | 0.974472i | \(-0.572079\pi\) | ||||
−0.224511 | + | 0.974472i | \(0.572079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.7984 | −1.86578 | ||||||||
\(92\) | −7.61803 | −0.794235 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.76393 | −0.181936 | ||||||||
\(95\) | −6.18034 | −0.634089 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 1.14590 | 0.115753 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.47214 | −0.347214 | ||||||||
\(101\) | 17.0344 | 1.69499 | 0.847495 | − | 0.530803i | \(-0.178110\pi\) | ||||
0.847495 | + | 0.530803i | \(0.178110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.56231 | −0.548070 | −0.274035 | − | 0.961720i | \(-0.588358\pi\) | ||||
−0.274035 | + | 0.961720i | \(0.588358\pi\) | |||||||
\(104\) | 6.23607 | 0.611497 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0902 | −0.980044 | ||||||||
\(107\) | 18.2705 | 1.76628 | 0.883138 | − | 0.469112i | \(-0.155426\pi\) | ||||
0.883138 | + | 0.469112i | \(0.155426\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.32624 | −0.414378 | −0.207189 | − | 0.978301i | \(-0.566432\pi\) | ||||
−0.207189 | + | 0.978301i | \(0.566432\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.85410 | −0.269687 | ||||||||
\(113\) | 2.56231 | 0.241041 | 0.120521 | − | 0.992711i | \(-0.461544\pi\) | ||||
0.120521 | + | 0.992711i | \(0.461544\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.41641 | −0.878085 | ||||||||
\(116\) | 7.09017 | 0.658306 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.32624 | −0.858550 | ||||||||
\(119\) | 17.7984 | 1.63157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.47214 | −0.314352 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.00000 | −0.628619 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.47214 | 0.308102 | 0.154051 | − | 0.988063i | \(-0.450768\pi\) | ||||
0.154051 | + | 0.988063i | \(0.450768\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.70820 | 0.676054 | ||||||||
\(131\) | −6.94427 | −0.606724 | −0.303362 | − | 0.952875i | \(-0.598109\pi\) | ||||
−0.303362 | + | 0.952875i | \(0.598109\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.2705 | 1.23741 | ||||||||
\(134\) | −6.09017 | −0.526111 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.23607 | −0.534738 | ||||||||
\(137\) | −14.1803 | −1.21151 | −0.605754 | − | 0.795652i | \(-0.707128\pi\) | ||||
−0.605754 | + | 0.795652i | \(0.707128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.56231 | 0.726245 | 0.363123 | − | 0.931741i | \(-0.381711\pi\) | ||||
0.363123 | + | 0.931741i | \(0.381711\pi\) | |||||||
\(140\) | −3.52786 | −0.298159 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.52786 | −0.379970 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.76393 | 0.727805 | ||||||||
\(146\) | 4.23607 | 0.350579 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.00000 | 0.739795 | ||||||||
\(149\) | −7.65248 | −0.626915 | −0.313458 | − | 0.949602i | \(-0.601487\pi\) | ||||
−0.313458 | + | 0.949602i | \(0.601487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.85410 | 0.313642 | 0.156821 | − | 0.987627i | \(-0.449875\pi\) | ||||
0.156821 | + | 0.987627i | \(0.449875\pi\) | |||||||
\(152\) | −5.00000 | −0.405554 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.65248 | −0.694984 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.41641 | −0.591894 | −0.295947 | − | 0.955204i | \(-0.595635\pi\) | ||||
−0.295947 | + | 0.955204i | \(0.595635\pi\) | |||||||
\(158\) | −15.0000 | −1.19334 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.23607 | 0.0977198 | ||||||||
\(161\) | 21.7426 | 1.71356 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.76393 | −0.138162 | −0.0690809 | − | 0.997611i | \(-0.522007\pi\) | ||||
−0.0690809 | + | 0.997611i | \(0.522007\pi\) | |||||||
\(164\) | 3.38197 | 0.264087 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.76393 | −0.292138 | ||||||||
\(167\) | −5.38197 | −0.416469 | −0.208235 | − | 0.978079i | \(-0.566772\pi\) | ||||
−0.208235 | + | 0.978079i | \(0.566772\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.8885 | 1.99143 | ||||||||
\(170\) | −7.70820 | −0.591192 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.708204 | 0.0540000 | ||||||||
\(173\) | 3.94427 | 0.299877 | 0.149939 | − | 0.988695i | \(-0.452092\pi\) | ||||
0.149939 | + | 0.988695i | \(0.452092\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.90983 | 0.749113 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.23607 | −0.317507 | ||||||||
\(179\) | 1.79837 | 0.134417 | 0.0672084 | − | 0.997739i | \(-0.478591\pi\) | ||||
0.0672084 | + | 0.997739i | \(0.478591\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3820 | −0.846015 | −0.423007 | − | 0.906126i | \(-0.639026\pi\) | ||||
−0.423007 | + | 0.906126i | \(0.639026\pi\) | |||||||
\(182\) | −17.7984 | −1.31930 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.61803 | −0.561609 | ||||||||
\(185\) | 11.1246 | 0.817898 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.76393 | −0.128648 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.18034 | −0.448369 | ||||||||
\(191\) | −3.67376 | −0.265824 | −0.132912 | − | 0.991128i | \(-0.542433\pi\) | ||||
−0.132912 | + | 0.991128i | \(0.542433\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.4164 | −1.25366 | −0.626830 | − | 0.779156i | \(-0.715648\pi\) | ||||
−0.626830 | + | 0.779156i | \(0.715648\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.14590 | 0.0818499 | ||||||||
\(197\) | −12.3262 | −0.878208 | −0.439104 | − | 0.898436i | \(-0.644704\pi\) | ||||
−0.439104 | + | 0.898436i | \(0.644704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.94427 | 0.137826 | 0.0689129 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689129 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(200\) | −3.47214 | −0.245517 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.0344 | 1.19854 | ||||||||
\(203\) | −20.2361 | −1.42029 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.18034 | 0.291968 | ||||||||
\(206\) | −5.56231 | −0.387544 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.23607 | 0.432394 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3262 | 0.779730 | 0.389865 | − | 0.920872i | \(-0.372522\pi\) | ||||
0.389865 | + | 0.920872i | \(0.372522\pi\) | |||||||
\(212\) | −10.0902 | −0.692996 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.2705 | 1.24895 | ||||||||
\(215\) | 0.875388 | 0.0597010 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.9787 | 1.35624 | ||||||||
\(218\) | −4.32624 | −0.293010 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.8885 | −2.61593 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.41641 | 0.563604 | 0.281802 | − | 0.959473i | \(-0.409068\pi\) | ||||
0.281802 | + | 0.959473i | \(0.409068\pi\) | |||||||
\(224\) | −2.85410 | −0.190698 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.56231 | 0.170442 | ||||||||
\(227\) | −16.7984 | −1.11495 | −0.557474 | − | 0.830195i | \(-0.688229\pi\) | ||||
−0.557474 | + | 0.830195i | \(0.688229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2705 | 1.47168 | 0.735838 | − | 0.677157i | \(-0.236788\pi\) | ||||
0.735838 | + | 0.677157i | \(0.236788\pi\) | |||||||
\(230\) | −9.41641 | −0.620900 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.09017 | 0.465492 | ||||||||
\(233\) | −19.6525 | −1.28748 | −0.643738 | − | 0.765246i | \(-0.722617\pi\) | ||||
−0.643738 | + | 0.765246i | \(0.722617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.18034 | −0.142230 | ||||||||
\(236\) | −9.32624 | −0.607086 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.7984 | 1.15370 | ||||||||
\(239\) | −2.56231 | −0.165742 | −0.0828709 | − | 0.996560i | \(-0.526409\pi\) | ||||
−0.0828709 | + | 0.996560i | \(0.526409\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0344 | 1.29053 | 0.645266 | − | 0.763958i | \(-0.276747\pi\) | ||||
0.645266 | + | 0.763958i | \(0.276747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.47214 | −0.222281 | ||||||||
\(245\) | 1.41641 | 0.0904910 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.1803 | −1.98396 | ||||||||
\(248\) | −7.00000 | −0.444500 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.4721 | −0.662316 | ||||||||
\(251\) | 26.2361 | 1.65601 | 0.828003 | − | 0.560724i | \(-0.189477\pi\) | ||||
0.828003 | + | 0.560724i | \(0.189477\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.47214 | 0.217861 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.47214 | −0.466099 | −0.233050 | − | 0.972465i | \(-0.574870\pi\) | ||||
−0.233050 | + | 0.972465i | \(0.574870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.6869 | −1.59611 | ||||||||
\(260\) | 7.70820 | 0.478043 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.94427 | −0.429019 | ||||||||
\(263\) | 17.9443 | 1.10649 | 0.553246 | − | 0.833018i | \(-0.313389\pi\) | ||||
0.553246 | + | 0.833018i | \(0.313389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.4721 | −0.766157 | ||||||||
\(266\) | 14.2705 | 0.874981 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.09017 | −0.372016 | ||||||||
\(269\) | −9.94427 | −0.606313 | −0.303156 | − | 0.952941i | \(-0.598040\pi\) | ||||
−0.303156 | + | 0.952941i | \(0.598040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.2705 | −0.684635 | −0.342317 | − | 0.939584i | \(-0.611212\pi\) | ||||
−0.342317 | + | 0.939584i | \(0.611212\pi\) | |||||||
\(272\) | −6.23607 | −0.378117 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.1803 | −0.856666 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.145898 | 0.00876616 | 0.00438308 | − | 0.999990i | \(-0.498605\pi\) | ||||
0.00438308 | + | 0.999990i | \(0.498605\pi\) | |||||||
\(278\) | 8.56231 | 0.513533 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.52786 | −0.210830 | ||||||||
\(281\) | −20.1803 | −1.20386 | −0.601929 | − | 0.798550i | \(-0.705601\pi\) | ||||
−0.601929 | + | 0.798550i | \(0.705601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.70820 | −0.398761 | −0.199381 | − | 0.979922i | \(-0.563893\pi\) | ||||
−0.199381 | + | 0.979922i | \(0.563893\pi\) | |||||||
\(284\) | −4.52786 | −0.268679 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.65248 | −0.569768 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.8885 | 1.28756 | ||||||||
\(290\) | 8.76393 | 0.514636 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.23607 | 0.247897 | ||||||||
\(293\) | −21.7639 | −1.27146 | −0.635731 | − | 0.771910i | \(-0.719301\pi\) | ||||
−0.635731 | + | 0.771910i | \(0.719301\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.5279 | −0.671178 | ||||||||
\(296\) | 9.00000 | 0.523114 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.65248 | −0.443296 | ||||||||
\(299\) | −47.5066 | −2.74738 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.02129 | −0.116505 | ||||||||
\(302\) | 3.85410 | 0.221779 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.00000 | −0.286770 | ||||||||
\(305\) | −4.29180 | −0.245748 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.09017 | 0.290511 | 0.145256 | − | 0.989394i | \(-0.453600\pi\) | ||||
0.145256 | + | 0.989394i | \(0.453600\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.65248 | −0.491428 | ||||||||
\(311\) | −13.4721 | −0.763935 | −0.381967 | − | 0.924176i | \(-0.624753\pi\) | ||||
−0.381967 | + | 0.924176i | \(0.624753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.0689 | 1.86916 | 0.934582 | − | 0.355748i | \(-0.115774\pi\) | ||||
0.934582 | + | 0.355748i | \(0.115774\pi\) | |||||||
\(314\) | −7.41641 | −0.418532 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.0000 | −0.843816 | ||||||||
\(317\) | −16.1459 | −0.906844 | −0.453422 | − | 0.891296i | \(-0.649797\pi\) | ||||
−0.453422 | + | 0.891296i | \(0.649797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.23607 | 0.0690983 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.7426 | 1.21167 | ||||||||
\(323\) | 31.1803 | 1.73492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.6525 | −1.20106 | ||||||||
\(326\) | −1.76393 | −0.0976952 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.38197 | 0.186738 | ||||||||
\(329\) | 5.03444 | 0.277558 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.29180 | −0.455758 | −0.227879 | − | 0.973689i | \(-0.573179\pi\) | ||||
−0.227879 | + | 0.973689i | \(0.573179\pi\) | |||||||
\(332\) | −3.76393 | −0.206573 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.38197 | −0.294488 | ||||||||
\(335\) | −7.52786 | −0.411291 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.38197 | −0.129754 | −0.0648770 | − | 0.997893i | \(-0.520665\pi\) | ||||
−0.0648770 | + | 0.997893i | \(0.520665\pi\) | |||||||
\(338\) | 25.8885 | 1.40815 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.70820 | −0.418036 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | 0.708204 | 0.0381838 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.94427 | 0.212045 | ||||||||
\(347\) | −31.3262 | −1.68168 | −0.840840 | − | 0.541283i | \(-0.817939\pi\) | ||||
−0.840840 | + | 0.541283i | \(0.817939\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3262 | −0.927452 | −0.463726 | − | 0.885979i | \(-0.653488\pi\) | ||||
−0.463726 | + | 0.885979i | \(0.653488\pi\) | |||||||
\(350\) | 9.90983 | 0.529703 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.32624 | 0.496386 | 0.248193 | − | 0.968711i | \(-0.420163\pi\) | ||||
0.248193 | + | 0.968711i | \(0.420163\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.59675 | −0.297045 | ||||||||
\(356\) | −4.23607 | −0.224511 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.79837 | 0.0950470 | ||||||||
\(359\) | 32.1246 | 1.69547 | 0.847736 | − | 0.530418i | \(-0.177965\pi\) | ||||
0.847736 | + | 0.530418i | \(0.177965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | −11.3820 | −0.598223 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.7984 | −0.932888 | ||||||||
\(365\) | 5.23607 | 0.274068 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.8541 | −0.670979 | −0.335489 | − | 0.942044i | \(-0.608902\pi\) | ||||
−0.335489 | + | 0.942044i | \(0.608902\pi\) | |||||||
\(368\) | −7.61803 | −0.397117 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.1246 | 0.578341 | ||||||||
\(371\) | 28.7984 | 1.49514 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.7082 | 1.22756 | 0.613782 | − | 0.789475i | \(-0.289647\pi\) | ||||
0.613782 | + | 0.789475i | \(0.289647\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.76393 | −0.0909678 | ||||||||
\(377\) | 44.2148 | 2.27718 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7082 | 0.755510 | 0.377755 | − | 0.925906i | \(-0.376696\pi\) | ||||
0.377755 | + | 0.925906i | \(0.376696\pi\) | |||||||
\(380\) | −6.18034 | −0.317045 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.67376 | −0.187966 | ||||||||
\(383\) | −18.6525 | −0.953097 | −0.476548 | − | 0.879148i | \(-0.658112\pi\) | ||||
−0.476548 | + | 0.879148i | \(0.658112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.4164 | −0.886472 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.00000 | 0.304604 | ||||||||
\(389\) | −29.9230 | −1.51716 | −0.758578 | − | 0.651582i | \(-0.774105\pi\) | ||||
−0.758578 | + | 0.651582i | \(0.774105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 47.5066 | 2.40251 | ||||||||
\(392\) | 1.14590 | 0.0578766 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.3262 | −0.620987 | ||||||||
\(395\) | −18.5410 | −0.932900 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2705 | 1.21810 | 0.609051 | − | 0.793131i | \(-0.291550\pi\) | ||||
0.609051 | + | 0.793131i | \(0.291550\pi\) | |||||||
\(398\) | 1.94427 | 0.0974575 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47214 | −0.173607 | ||||||||
\(401\) | −19.6738 | −0.982461 | −0.491230 | − | 0.871030i | \(-0.663453\pi\) | ||||
−0.491230 | + | 0.871030i | \(0.663453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.6525 | −2.17448 | ||||||||
\(404\) | 17.0344 | 0.847495 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.2361 | −1.00430 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 4.18034 | 0.206452 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.56231 | −0.274035 | ||||||||
\(413\) | 26.6180 | 1.30979 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.65248 | −0.228381 | ||||||||
\(416\) | 6.23607 | 0.305748 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.14590 | −0.202540 | −0.101270 | − | 0.994859i | \(-0.532291\pi\) | ||||
−0.101270 | + | 0.994859i | \(0.532291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.4164 | −1.67735 | −0.838677 | − | 0.544630i | \(-0.816670\pi\) | ||||
−0.838677 | + | 0.544630i | \(0.816670\pi\) | |||||||
\(422\) | 11.3262 | 0.551353 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.0902 | −0.490022 | ||||||||
\(425\) | 21.6525 | 1.05030 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.90983 | 0.479570 | ||||||||
\(428\) | 18.2705 | 0.883138 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.875388 | 0.0422150 | ||||||||
\(431\) | −2.76393 | −0.133134 | −0.0665670 | − | 0.997782i | \(-0.521205\pi\) | ||||
−0.0665670 | + | 0.997782i | \(0.521205\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.527864 | 0.0253675 | 0.0126838 | − | 0.999920i | \(-0.495963\pi\) | ||||
0.0126838 | + | 0.999920i | \(0.495963\pi\) | |||||||
\(434\) | 19.9787 | 0.959009 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.32624 | −0.207189 | ||||||||
\(437\) | 38.0902 | 1.82210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.27051 | 0.251548 | 0.125774 | − | 0.992059i | \(-0.459859\pi\) | ||||
0.125774 | + | 0.992059i | \(0.459859\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −38.8885 | −1.84974 | ||||||||
\(443\) | −3.00000 | −0.142534 | −0.0712672 | − | 0.997457i | \(-0.522704\pi\) | ||||
−0.0712672 | + | 0.997457i | \(0.522704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.23607 | −0.248213 | ||||||||
\(446\) | 8.41641 | 0.398528 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.85410 | −0.134844 | ||||||||
\(449\) | −25.4164 | −1.19947 | −0.599737 | − | 0.800197i | \(-0.704728\pi\) | ||||
−0.599737 | + | 0.800197i | \(0.704728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.56231 | 0.120521 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.7984 | −0.788387 | ||||||||
\(455\) | −22.0000 | −1.03138 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | 22.2705 | 1.04063 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.41641 | −0.439042 | ||||||||
\(461\) | −5.03444 | −0.234477 | −0.117239 | − | 0.993104i | \(-0.537404\pi\) | ||||
−0.117239 | + | 0.993104i | \(0.537404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.1246 | 1.63238 | 0.816190 | − | 0.577784i | \(-0.196082\pi\) | ||||
0.816190 | + | 0.577784i | \(0.196082\pi\) | |||||||
\(464\) | 7.09017 | 0.329153 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.6525 | −0.910383 | ||||||||
\(467\) | −23.7426 | −1.09868 | −0.549339 | − | 0.835599i | \(-0.685121\pi\) | ||||
−0.549339 | + | 0.835599i | \(0.685121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.3820 | 0.802625 | ||||||||
\(470\) | −2.18034 | −0.100572 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.32624 | −0.429275 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.3607 | 0.796563 | ||||||||
\(476\) | 17.7984 | 0.815787 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.56231 | −0.117197 | ||||||||
\(479\) | −3.65248 | −0.166886 | −0.0834429 | − | 0.996513i | \(-0.526592\pi\) | ||||
−0.0834429 | + | 0.996513i | \(0.526592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.1246 | 2.55906 | ||||||||
\(482\) | 20.0344 | 0.912544 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.41641 | 0.336762 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3262 | 0.739812 | 0.369906 | − | 0.929069i | \(-0.379390\pi\) | ||||
0.369906 | + | 0.929069i | \(0.379390\pi\) | |||||||
\(488\) | −3.47214 | −0.157176 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.41641 | 0.0639868 | ||||||||
\(491\) | 30.7082 | 1.38584 | 0.692921 | − | 0.721014i | \(-0.256323\pi\) | ||||
0.692921 | + | 0.721014i | \(0.256323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.2148 | −1.99133 | ||||||||
\(494\) | −31.1803 | −1.40287 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.00000 | −0.314309 | ||||||||
\(497\) | 12.9230 | 0.579675 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.2918 | 0.818853 | 0.409427 | − | 0.912343i | \(-0.365729\pi\) | ||||
0.409427 | + | 0.912343i | \(0.365729\pi\) | |||||||
\(500\) | −10.4721 | −0.468328 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.2361 | 1.17097 | ||||||||
\(503\) | 1.23607 | 0.0551135 | 0.0275568 | − | 0.999620i | \(-0.491227\pi\) | ||||
0.0275568 | + | 0.999620i | \(0.491227\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.0557 | 0.936968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.47214 | 0.154051 | ||||||||
\(509\) | −24.5410 | −1.08776 | −0.543881 | − | 0.839162i | \(-0.683046\pi\) | ||||
−0.543881 | + | 0.839162i | \(0.683046\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0902 | −0.534838 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.47214 | −0.329582 | ||||||||
\(515\) | −6.87539 | −0.302966 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −25.6869 | −1.12862 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.70820 | 0.338027 | ||||||||
\(521\) | 0.236068 | 0.0103423 | 0.00517116 | − | 0.999987i | \(-0.498354\pi\) | ||||
0.00517116 | + | 0.999987i | \(0.498354\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.8885 | 1.21948 | 0.609740 | − | 0.792601i | \(-0.291274\pi\) | ||||
0.609740 | + | 0.792601i | \(0.291274\pi\) | |||||||
\(524\) | −6.94427 | −0.303362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.9443 | 0.782407 | ||||||||
\(527\) | 43.6525 | 1.90153 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.0344 | 1.52324 | ||||||||
\(530\) | −12.4721 | −0.541755 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.2705 | 0.618705 | ||||||||
\(533\) | 21.0902 | 0.913517 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.5836 | 0.976374 | ||||||||
\(536\) | −6.09017 | −0.263055 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.94427 | −0.428728 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.56231 | 0.153155 | 0.0765777 | − | 0.997064i | \(-0.475601\pi\) | ||||
0.0765777 | + | 0.997064i | \(0.475601\pi\) | |||||||
\(542\) | −11.2705 | −0.484110 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.23607 | −0.267369 | ||||||||
\(545\) | −5.34752 | −0.229063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4721 | 1.13187 | 0.565933 | − | 0.824451i | \(-0.308516\pi\) | ||||
0.565933 | + | 0.824451i | \(0.308516\pi\) | |||||||
\(548\) | −14.1803 | −0.605754 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.4508 | −1.51026 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.8115 | 1.82053 | ||||||||
\(554\) | 0.145898 | 0.00619861 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.56231 | 0.363123 | ||||||||
\(557\) | −15.8197 | −0.670301 | −0.335150 | − | 0.942165i | \(-0.608787\pi\) | ||||
−0.335150 | + | 0.942165i | \(0.608787\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.41641 | 0.186794 | ||||||||
\(560\) | −3.52786 | −0.149079 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.1803 | −0.851256 | ||||||||
\(563\) | 41.4508 | 1.74695 | 0.873473 | − | 0.486873i | \(-0.161863\pi\) | ||||
0.873473 | + | 0.486873i | \(0.161863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.16718 | 0.133244 | ||||||||
\(566\) | −6.70820 | −0.281967 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.52786 | −0.189985 | ||||||||
\(569\) | 14.3262 | 0.600587 | 0.300294 | − | 0.953847i | \(-0.402915\pi\) | ||||
0.300294 | + | 0.953847i | \(0.402915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.4508 | −1.31618 | −0.658089 | − | 0.752941i | \(-0.728635\pi\) | ||||
−0.658089 | + | 0.752941i | \(0.728635\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.65248 | −0.402887 | ||||||||
\(575\) | 26.4508 | 1.10308 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.1591 | −1.33880 | −0.669399 | − | 0.742903i | \(-0.733449\pi\) | ||||
−0.669399 | + | 0.742903i | \(0.733449\pi\) | |||||||
\(578\) | 21.8885 | 0.910443 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.76393 | 0.363902 | ||||||||
\(581\) | 10.7426 | 0.445680 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.23607 | 0.175290 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.7639 | −0.899060 | ||||||||
\(587\) | −3.00000 | −0.123823 | −0.0619116 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619116 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.0000 | 1.44215 | ||||||||
\(590\) | −11.5279 | −0.474595 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.00000 | 0.369898 | ||||||||
\(593\) | 22.1459 | 0.909423 | 0.454712 | − | 0.890639i | \(-0.349742\pi\) | ||||
0.454712 | + | 0.890639i | \(0.349742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.0000 | 0.901912 | ||||||||
\(596\) | −7.65248 | −0.313458 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −47.5066 | −1.94269 | ||||||||
\(599\) | 30.5410 | 1.24787 | 0.623936 | − | 0.781475i | \(-0.285533\pi\) | ||||
0.623936 | + | 0.781475i | \(0.285533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.12461 | −0.372201 | −0.186100 | − | 0.982531i | \(-0.559585\pi\) | ||||
−0.186100 | + | 0.982531i | \(0.559585\pi\) | |||||||
\(602\) | −2.02129 | −0.0823815 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.85410 | 0.156821 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1246 | 0.938599 | 0.469300 | − | 0.883039i | \(-0.344506\pi\) | ||||
0.469300 | + | 0.883039i | \(0.344506\pi\) | |||||||
\(608\) | −5.00000 | −0.202777 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.29180 | −0.173770 | ||||||||
\(611\) | −11.0000 | −0.445012 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.4164 | 1.79396 | 0.896981 | − | 0.442069i | \(-0.145755\pi\) | ||||
0.896981 | + | 0.442069i | \(0.145755\pi\) | |||||||
\(614\) | 5.09017 | 0.205423 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.4721 | 0.904694 | 0.452347 | − | 0.891842i | \(-0.350587\pi\) | ||||
0.452347 | + | 0.891842i | \(0.350587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.7426 | −1.11507 | −0.557536 | − | 0.830153i | \(-0.688253\pi\) | ||||
−0.557536 | + | 0.830153i | \(0.688253\pi\) | |||||||
\(620\) | −8.65248 | −0.347492 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.4721 | −0.540183 | ||||||||
\(623\) | 12.0902 | 0.484382 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 33.0689 | 1.32170 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.41641 | −0.295947 | ||||||||
\(629\) | −56.1246 | −2.23783 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.854102 | 0.0340013 | 0.0170006 | − | 0.999855i | \(-0.494588\pi\) | ||||
0.0170006 | + | 0.999855i | \(0.494588\pi\) | |||||||
\(632\) | −15.0000 | −0.596668 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.1459 | −0.641236 | ||||||||
\(635\) | 4.29180 | 0.170315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.14590 | 0.283131 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.23607 | 0.0488599 | ||||||||
\(641\) | −3.03444 | −0.119853 | −0.0599266 | − | 0.998203i | \(-0.519087\pi\) | ||||
−0.0599266 | + | 0.998203i | \(0.519087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.875388 | 0.0345219 | 0.0172610 | − | 0.999851i | \(-0.494505\pi\) | ||||
0.0172610 | + | 0.999851i | \(0.494505\pi\) | |||||||
\(644\) | 21.7426 | 0.856780 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 31.1803 | 1.22677 | ||||||||
\(647\) | −25.5066 | −1.00277 | −0.501384 | − | 0.865225i | \(-0.667175\pi\) | ||||
−0.501384 | + | 0.865225i | \(0.667175\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −21.6525 | −0.849280 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.76393 | −0.0690809 | ||||||||
\(653\) | 9.50658 | 0.372021 | 0.186011 | − | 0.982548i | \(-0.440444\pi\) | ||||
0.186011 | + | 0.982548i | \(0.440444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.58359 | −0.335389 | ||||||||
\(656\) | 3.38197 | 0.132044 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.03444 | 0.196263 | ||||||||
\(659\) | −26.7771 | −1.04309 | −0.521544 | − | 0.853225i | \(-0.674644\pi\) | ||||
−0.521544 | + | 0.853225i | \(0.674644\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.61803 | −0.296307 | −0.148154 | − | 0.988964i | \(-0.547333\pi\) | ||||
−0.148154 | + | 0.988964i | \(0.547333\pi\) | |||||||
\(662\) | −8.29180 | −0.322270 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.76393 | −0.146069 | ||||||||
\(665\) | 17.6393 | 0.684023 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −54.0132 | −2.09140 | ||||||||
\(668\) | −5.38197 | −0.208235 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.52786 | −0.290827 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | −2.38197 | −0.0917499 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.8885 | 0.995713 | ||||||||
\(677\) | −16.3262 | −0.627468 | −0.313734 | − | 0.949511i | \(-0.601580\pi\) | ||||
−0.313734 | + | 0.949511i | \(0.601580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.1246 | −0.657182 | ||||||||
\(680\) | −7.70820 | −0.295596 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.8885 | 1.29671 | 0.648355 | − | 0.761339i | \(-0.275457\pi\) | ||||
0.648355 | + | 0.761339i | \(0.275457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.5279 | −0.669705 | ||||||||
\(686\) | 16.7082 | 0.637922 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.708204 | 0.0270000 | ||||||||
\(689\) | −62.9230 | −2.39717 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.2361 | 1.26436 | 0.632180 | − | 0.774822i | \(-0.282160\pi\) | ||||
0.632180 | + | 0.774822i | \(0.282160\pi\) | |||||||
\(692\) | 3.94427 | 0.149939 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.3262 | −1.18913 | ||||||||
\(695\) | 10.5836 | 0.401459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.0902 | −0.798847 | ||||||||
\(698\) | −17.3262 | −0.655808 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.90983 | 0.374556 | ||||||||
\(701\) | −7.14590 | −0.269897 | −0.134948 | − | 0.990853i | \(-0.543087\pi\) | ||||
−0.134948 | + | 0.990853i | \(0.543087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.0000 | −1.69721 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.32624 | 0.350998 | ||||||||
\(707\) | −48.6180 | −1.82847 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.7214 | −1.71710 | −0.858551 | − | 0.512728i | \(-0.828635\pi\) | ||||
−0.858551 | + | 0.512728i | \(0.828635\pi\) | |||||||
\(710\) | −5.59675 | −0.210042 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.23607 | −0.158753 | ||||||||
\(713\) | 53.3262 | 1.99708 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.79837 | 0.0672084 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.1246 | 1.19888 | ||||||||
\(719\) | 48.7082 | 1.81651 | 0.908255 | − | 0.418418i | \(-0.137415\pi\) | ||||
0.908255 | + | 0.418418i | \(0.137415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8754 | 0.591230 | ||||||||
\(722\) | 6.00000 | 0.223297 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.3820 | −0.423007 | ||||||||
\(725\) | −24.6180 | −0.914291 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.14590 | −0.190851 | −0.0954254 | − | 0.995437i | \(-0.530421\pi\) | ||||
−0.0954254 | + | 0.995437i | \(0.530421\pi\) | |||||||
\(728\) | −17.7984 | −0.659652 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.23607 | 0.193796 | ||||||||
\(731\) | −4.41641 | −0.163347 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7082 | 1.31891 | 0.659456 | − | 0.751743i | \(-0.270787\pi\) | ||||
0.659456 | + | 0.751743i | \(0.270787\pi\) | |||||||
\(734\) | −12.8541 | −0.474454 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.61803 | −0.280804 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.3951 | 1.48596 | 0.742979 | − | 0.669314i | \(-0.233412\pi\) | ||||
0.742979 | + | 0.669314i | \(0.233412\pi\) | |||||||
\(740\) | 11.1246 | 0.408949 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.7984 | 1.05722 | ||||||||
\(743\) | −46.2361 | −1.69624 | −0.848118 | − | 0.529807i | \(-0.822264\pi\) | ||||
−0.848118 | + | 0.529807i | \(0.822264\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.45898 | −0.346550 | ||||||||
\(746\) | 23.7082 | 0.868019 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.1459 | −1.90537 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.6738 | 0.608434 | 0.304217 | − | 0.952603i | \(-0.401605\pi\) | ||||
0.304217 | + | 0.952603i | \(0.401605\pi\) | |||||||
\(752\) | −1.76393 | −0.0643240 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 44.2148 | 1.61021 | ||||||||
\(755\) | 4.76393 | 0.173377 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0344 | −1.30969 | −0.654847 | − | 0.755761i | \(-0.727267\pi\) | ||||
−0.654847 | + | 0.755761i | \(0.727267\pi\) | |||||||
\(758\) | 14.7082 | 0.534226 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.18034 | −0.224184 | ||||||||
\(761\) | 44.9443 | 1.62923 | 0.814614 | − | 0.580003i | \(-0.196949\pi\) | ||||
0.814614 | + | 0.580003i | \(0.196949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3475 | 0.447010 | ||||||||
\(764\) | −3.67376 | −0.132912 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.6525 | −0.673941 | ||||||||
\(767\) | −58.1591 | −2.10000 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.8541 | 0.824140 | 0.412070 | − | 0.911152i | \(-0.364806\pi\) | ||||
0.412070 | + | 0.911152i | \(0.364806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.4164 | −0.626830 | ||||||||
\(773\) | 4.81966 | 0.173351 | 0.0866756 | − | 0.996237i | \(-0.472376\pi\) | ||||
0.0866756 | + | 0.996237i | \(0.472376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.3050 | 0.873060 | ||||||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.9230 | −1.07279 | ||||||||
\(779\) | −16.9098 | −0.605858 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 47.5066 | 1.69883 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.14590 | 0.0409249 | ||||||||
\(785\) | −9.16718 | −0.327191 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.47214 | −0.337645 | −0.168823 | − | 0.985646i | \(-0.553996\pi\) | ||||
−0.168823 | + | 0.985646i | \(0.553996\pi\) | |||||||
\(788\) | −12.3262 | −0.439104 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.5410 | −0.659660 | ||||||||
\(791\) | −7.31308 | −0.260023 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.6525 | −0.768902 | ||||||||
\(794\) | 24.2705 | 0.861328 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.94427 | 0.0689129 | ||||||||
\(797\) | 10.7984 | 0.382498 | 0.191249 | − | 0.981542i | \(-0.438746\pi\) | ||||
0.191249 | + | 0.981542i | \(0.438746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0000 | 0.389152 | ||||||||
\(800\) | −3.47214 | −0.122759 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.6738 | −0.694705 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.8754 | 0.947233 | ||||||||
\(806\) | −43.6525 | −1.53759 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.0344 | 0.599270 | ||||||||
\(809\) | −1.03444 | −0.0363690 | −0.0181845 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181845 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.18034 | −0.146792 | −0.0733958 | − | 0.997303i | \(-0.523384\pi\) | ||||
−0.0733958 | + | 0.997303i | \(0.523384\pi\) | |||||||
\(812\) | −20.2361 | −0.710147 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.18034 | −0.0763740 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.54102 | −0.123885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.18034 | 0.145984 | ||||||||
\(821\) | −5.83282 | −0.203567 | −0.101783 | − | 0.994807i | \(-0.532455\pi\) | ||||
−0.101783 | + | 0.994807i | \(0.532455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2016 | −0.808758 | −0.404379 | − | 0.914592i | \(-0.632512\pi\) | ||||
−0.404379 | + | 0.914592i | \(0.632512\pi\) | |||||||
\(824\) | −5.56231 | −0.193772 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.6180 | 0.926160 | ||||||||
\(827\) | −35.0689 | −1.21946 | −0.609732 | − | 0.792607i | \(-0.708723\pi\) | ||||
−0.609732 | + | 0.792607i | \(0.708723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.2016 | −0.423780 | −0.211890 | − | 0.977294i | \(-0.567962\pi\) | ||||
−0.211890 | + | 0.977294i | \(0.567962\pi\) | |||||||
\(830\) | −4.65248 | −0.161490 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.23607 | 0.216197 | ||||||||
\(833\) | −7.14590 | −0.247591 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.65248 | −0.230218 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.14590 | −0.143218 | ||||||||
\(839\) | −28.3050 | −0.977195 | −0.488598 | − | 0.872509i | \(-0.662491\pi\) | ||||
−0.488598 | + | 0.872509i | \(0.662491\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2705 | 0.733466 | ||||||||
\(842\) | −34.4164 | −1.18607 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.3262 | 0.389865 | ||||||||
\(845\) | 32.0000 | 1.10083 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.0902 | −0.346498 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.6525 | 0.742674 | ||||||||
\(851\) | −68.5623 | −2.35029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.180340 | −0.00617472 | −0.00308736 | − | 0.999995i | \(-0.500983\pi\) | ||||
−0.00308736 | + | 0.999995i | \(0.500983\pi\) | |||||||
\(854\) | 9.90983 | 0.339107 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.2705 | 0.624473 | ||||||||
\(857\) | −9.11146 | −0.311241 | −0.155621 | − | 0.987817i | \(-0.549738\pi\) | ||||
−0.155621 | + | 0.987817i | \(0.549738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.50658 | −0.222002 | −0.111001 | − | 0.993820i | \(-0.535406\pi\) | ||||
−0.111001 | + | 0.993820i | \(0.535406\pi\) | |||||||
\(860\) | 0.875388 | 0.0298505 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.76393 | −0.0941399 | ||||||||
\(863\) | 10.7639 | 0.366409 | 0.183204 | − | 0.983075i | \(-0.441353\pi\) | ||||
0.183204 | + | 0.983075i | \(0.441353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.87539 | 0.165768 | ||||||||
\(866\) | 0.527864 | 0.0179376 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.9787 | 0.678122 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.9787 | −1.28686 | ||||||||
\(872\) | −4.32624 | −0.146505 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.0902 | 1.28842 | ||||||||
\(875\) | 29.8885 | 1.01042 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.59675 | −0.256524 | −0.128262 | − | 0.991740i | \(-0.540940\pi\) | ||||
−0.128262 | + | 0.991740i | \(0.540940\pi\) | |||||||
\(878\) | 5.27051 | 0.177871 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.3262 | 1.69553 | 0.847767 | − | 0.530369i | \(-0.177947\pi\) | ||||
0.847767 | + | 0.530369i | \(0.177947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.2492 | 0.849704 | 0.424852 | − | 0.905263i | \(-0.360326\pi\) | ||||
0.424852 | + | 0.905263i | \(0.360326\pi\) | |||||||
\(884\) | −38.8885 | −1.30796 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.00000 | −0.100787 | ||||||||
\(887\) | −44.4296 | −1.49180 | −0.745899 | − | 0.666059i | \(-0.767980\pi\) | ||||
−0.745899 | + | 0.666059i | \(0.767980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.90983 | −0.332365 | ||||||||
\(890\) | −5.23607 | −0.175513 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.41641 | 0.281802 | ||||||||
\(893\) | 8.81966 | 0.295139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.22291 | 0.0743038 | ||||||||
\(896\) | −2.85410 | −0.0953489 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.4164 | −0.848157 | ||||||||
\(899\) | −49.6312 | −1.65529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.9230 | 2.09627 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.56231 | 0.0852210 | ||||||||
\(905\) | −14.0689 | −0.467666 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.87539 | −0.195089 | −0.0975445 | − | 0.995231i | \(-0.531099\pi\) | ||||
−0.0975445 | + | 0.995231i | \(0.531099\pi\) | |||||||
\(908\) | −16.7984 | −0.557474 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.0000 | −0.729293 | ||||||||
\(911\) | −30.2361 | −1.00177 | −0.500883 | − | 0.865515i | \(-0.666991\pi\) | ||||
−0.500883 | + | 0.865515i | \(0.666991\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6.00000 | −0.198462 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.2705 | 0.735838 | ||||||||
\(917\) | 19.8197 | 0.654503 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.5410 | 1.10642 | 0.553208 | − | 0.833043i | \(-0.313403\pi\) | ||||
0.553208 | + | 0.833043i | \(0.313403\pi\) | |||||||
\(920\) | −9.41641 | −0.310450 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.03444 | −0.165801 | ||||||||
\(923\) | −28.2361 | −0.929401 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.2492 | −1.02747 | ||||||||
\(926\) | 35.1246 | 1.15427 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.09017 | 0.232746 | ||||||||
\(929\) | 20.4508 | 0.670971 | 0.335485 | − | 0.942045i | \(-0.391100\pi\) | ||||
0.335485 | + | 0.942045i | \(0.391100\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.72949 | −0.187776 | ||||||||
\(932\) | −19.6525 | −0.643738 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.7426 | −0.776883 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.70820 | 0.317153 | 0.158577 | − | 0.987347i | \(-0.449310\pi\) | ||||
0.158577 | + | 0.987347i | \(0.449310\pi\) | |||||||
\(938\) | 17.3820 | 0.567541 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.18034 | −0.0711148 | ||||||||
\(941\) | 27.2361 | 0.887870 | 0.443935 | − | 0.896059i | \(-0.353582\pi\) | ||||
0.443935 | + | 0.896059i | \(0.353582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.7639 | −0.838989 | ||||||||
\(944\) | −9.32624 | −0.303543 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.5967 | 0.994261 | 0.497130 | − | 0.867676i | \(-0.334387\pi\) | ||||
0.497130 | + | 0.867676i | \(0.334387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.4164 | 0.857513 | ||||||||
\(950\) | 17.3607 | 0.563255 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.7984 | 0.576849 | ||||||||
\(953\) | 37.8673 | 1.22664 | 0.613320 | − | 0.789834i | \(-0.289833\pi\) | ||||
0.613320 | + | 0.789834i | \(0.289833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.54102 | −0.146944 | ||||||||
\(956\) | −2.56231 | −0.0828709 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.65248 | −0.118006 | ||||||||
\(959\) | 40.4721 | 1.30691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 56.1246 | 1.80953 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.0344 | 0.645266 | ||||||||
\(965\) | −21.5279 | −0.693006 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.29180 | 0.202331 | 0.101165 | − | 0.994870i | \(-0.467743\pi\) | ||||
0.101165 | + | 0.994870i | \(0.467743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.41641 | 0.238127 | ||||||||
\(971\) | 27.8885 | 0.894986 | 0.447493 | − | 0.894287i | \(-0.352317\pi\) | ||||
0.447493 | + | 0.894287i | \(0.352317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.4377 | −0.783437 | ||||||||
\(974\) | 16.3262 | 0.523126 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.47214 | −0.111140 | ||||||||
\(977\) | 33.6525 | 1.07664 | 0.538319 | − | 0.842741i | \(-0.319060\pi\) | ||||
0.538319 | + | 0.842741i | \(0.319060\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.41641 | 0.0452455 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 30.7082 | 0.979938 | ||||||||
\(983\) | 16.1459 | 0.514974 | 0.257487 | − | 0.966282i | \(-0.417106\pi\) | ||||
0.257487 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2361 | −0.485461 | ||||||||
\(986\) | −44.2148 | −1.40809 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.1803 | −0.991979 | ||||||||
\(989\) | −5.39512 | −0.171555 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.7082 | 1.26137 | 0.630686 | − | 0.776038i | \(-0.282773\pi\) | ||||
0.630686 | + | 0.776038i | \(0.282773\pi\) | |||||||
\(992\) | −7.00000 | −0.222250 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.9230 | 0.409892 | ||||||||
\(995\) | 2.40325 | 0.0761882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.9443 | 1.45507 | 0.727535 | − | 0.686071i | \(-0.240666\pi\) | ||||
0.727535 | + | 0.686071i | \(0.240666\pi\) | |||||||
\(998\) | 18.2918 | 0.579017 | ||||||||
\(999\) | 0 | 0 |
(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 | 6534.2.a.cb.1.2 | 2 | ||
3.2 | odd | 2 | 6534.2.a.bv.1.1 | 2 | |||
11.7 | odd | 10 | 594.2.f.j.379.1 | yes | 4 | ||
11.8 | odd | 10 | 594.2.f.j.163.1 | yes | 4 | ||
11.10 | odd | 2 | 6534.2.a.bf.1.2 | 2 | |||
33.8 | even | 10 | 594.2.f.a.163.1 | ✓ | 4 | ||
33.29 | even | 10 | 594.2.f.a.379.1 | yes | 4 | ||
33.32 | even | 2 | 6534.2.a.cm.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
594.2.f.a.163.1 | ✓ | 4 | 33.8 | even | 10 | ||
594.2.f.a.379.1 | yes | 4 | 33.29 | even | 10 | ||
594.2.f.j.163.1 | yes | 4 | 11.8 | odd | 10 | ||
594.2.f.j.379.1 | yes | 4 | 11.7 | odd | 10 | ||
6534.2.a.bf.1.2 | 2 | 11.10 | odd | 2 | |||
6534.2.a.bv.1.1 | 2 | 3.2 | odd | 2 | |||
6534.2.a.cb.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6534.2.a.cm.1.1 | 2 | 33.32 | even | 2 |