Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, 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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 476) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.61803 | 0.934172 | 0.467086 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.618034 | −0.276393 | −0.138197 | − | 0.990405i | \(-0.544131\pi\) | ||||
−0.138197 | + | 0.990405i | \(0.544131\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.763932 | −0.230334 | −0.115167 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115167 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23607 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.47214 | 1.94364 | 0.971821 | − | 0.235722i | \(-0.0757453\pi\) | ||||
0.971821 | + | 0.235722i | \(0.0757453\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.70820 | −1.60727 | −0.803636 | − | 0.595121i | \(-0.797104\pi\) | ||||
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61803 | −0.923607 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.47214 | −1.05311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.70820 | −1.05999 | −0.529993 | − | 0.848002i | \(-0.677806\pi\) | ||||
−0.529993 | + | 0.848002i | \(0.677806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.32624 | −1.13623 | −0.568113 | − | 0.822951i | \(-0.692326\pi\) | ||||
−0.568113 | + | 0.822951i | \(0.692326\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.23607 | −0.215172 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.472136 | 0.0776187 | 0.0388093 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388093 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0901699 | 0.0140822 | 0.00704109 | − | 0.999975i | \(-0.497759\pi\) | ||||
0.00704109 | + | 0.999975i | \(0.497759\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0902 | −1.84373 | −0.921867 | − | 0.387507i | \(-0.873336\pi\) | ||||
−0.921867 | + | 0.387507i | \(0.873336\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.236068 | 0.0351909 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.47214 | 1.23579 | 0.617894 | − | 0.786261i | \(-0.287986\pi\) | ||||
0.617894 | + | 0.786261i | \(0.287986\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61803 | −0.226570 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7984 | 1.48327 | 0.741635 | − | 0.670803i | \(-0.234050\pi\) | ||||
0.741635 | + | 0.670803i | \(0.234050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.472136 | 0.0636628 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.7082 | 1.81570 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.32624 | 0.938029 | 0.469014 | − | 0.883191i | \(-0.344609\pi\) | ||||
0.469014 | + | 0.883191i | \(0.344609\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.763932 | 0.0947541 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.0902 | −1.59922 | −0.799609 | − | 0.600520i | \(-0.794960\pi\) | ||||
−0.799609 | + | 0.600520i | \(0.794960\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.4721 | −1.50147 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9443 | 1.29885 | 0.649423 | − | 0.760427i | \(-0.275010\pi\) | ||||
0.649423 | + | 0.760427i | \(0.275010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.14590 | −0.836364 | −0.418182 | − | 0.908363i | \(-0.637333\pi\) | ||||
−0.418182 | + | 0.908363i | \(0.637333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.47214 | −0.862808 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.94427 | 0.331256 | 0.165628 | − | 0.986188i | \(-0.447035\pi\) | ||||
0.165628 | + | 0.986188i | \(0.447035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.4164 | −1.69217 | −0.846085 | − | 0.533048i | \(-0.821047\pi\) | ||||
−0.846085 | + | 0.533048i | \(0.821047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.618034 | 0.0670352 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.23607 | −0.990210 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.2361 | −1.06143 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.23607 | −0.537209 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.0902 | −1.53217 | −0.766087 | − | 0.642737i | \(-0.777799\pi\) | ||||
−0.766087 | + | 0.642737i | \(0.777799\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.291796 | 0.0293266 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.472136 | 0.0469793 | 0.0234896 | − | 0.999724i | \(-0.492522\pi\) | ||||
0.0234896 | + | 0.999724i | \(0.492522\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.4164 | −1.51902 | −0.759512 | − | 0.650493i | \(-0.774562\pi\) | ||||
−0.759512 | + | 0.650493i | \(0.774562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.7639 | 1.04059 | 0.520294 | − | 0.853987i | \(-0.325822\pi\) | ||||
0.520294 | + | 0.853987i | \(0.325822\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.52786 | −0.337908 | −0.168954 | − | 0.985624i | \(-0.554039\pi\) | ||||
−0.168954 | + | 0.985624i | \(0.554039\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.763932 | 0.0725092 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.76393 | 0.444239 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.472136 | 0.0436490 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.145898 | 0.0131552 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.94427 | 0.531672 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.85410 | −0.696939 | −0.348469 | − | 0.937320i | \(-0.613298\pi\) | ||||
−0.348469 | + | 0.937320i | \(0.613298\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.5623 | −1.72236 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.38197 | 0.291073 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.38197 | 0.203505 | 0.101753 | − | 0.994810i | \(-0.467555\pi\) | ||||
0.101753 | + | 0.994810i | \(0.467555\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0344 | 1.19039 | 0.595193 | − | 0.803583i | \(-0.297076\pi\) | ||||
0.595193 | + | 0.803583i | \(0.297076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.7082 | 1.15444 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.944272 | 0.0789640 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.52786 | 0.292973 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.6180 | −1.11563 | −0.557816 | − | 0.829964i | \(-0.688361\pi\) | ||||
−0.557816 | + | 0.829964i | \(0.688361\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.1459 | −1.23256 | −0.616278 | − | 0.787529i | \(-0.711360\pi\) | ||||
−0.616278 | + | 0.787529i | \(0.711360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.381966 | 0.0308801 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.90983 | 0.314045 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.18034 | 0.174010 | 0.0870050 | − | 0.996208i | \(-0.472270\pi\) | ||||
0.0870050 | + | 0.996208i | \(0.472270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.4721 | 1.38563 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.70820 | 0.447101 | 0.223551 | − | 0.974692i | \(-0.428235\pi\) | ||||
0.223551 | + | 0.974692i | \(0.428235\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.763932 | 0.0594720 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.3820 | −1.11291 | −0.556455 | − | 0.830878i | \(-0.687839\pi\) | ||||
−0.556455 | + | 0.830878i | \(0.687839\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.23607 | −0.247468 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.9098 | 0.905488 | 0.452744 | − | 0.891641i | \(-0.350445\pi\) | ||||
0.452744 | + | 0.891641i | \(0.350445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.3820 | −1.37393 | −0.686966 | − | 0.726689i | \(-0.741058\pi\) | ||||
−0.686966 | + | 0.726689i | \(0.741058\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.4721 | 0.927047 | 0.463523 | − | 0.886085i | \(-0.346585\pi\) | ||||
0.463523 | + | 0.886085i | \(0.346585\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8541 | 0.876280 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.291796 | −0.0214533 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.763932 | 0.0558642 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.7984 | 1.50492 | 0.752459 | − | 0.658639i | \(-0.228868\pi\) | ||||
0.752459 | + | 0.658639i | \(0.228868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1803 | −1.02072 | −0.510362 | − | 0.859960i | \(-0.670488\pi\) | ||||
−0.510362 | + | 0.859960i | \(0.670488\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.23607 | 0.0885167 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.70820 | 0.691681 | 0.345840 | − | 0.938293i | \(-0.387594\pi\) | ||||
0.345840 | + | 0.938293i | \(0.387594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0902 | 0.857049 | 0.428525 | − | 0.903530i | \(-0.359033\pi\) | ||||
0.428525 | + | 0.903530i | \(0.359033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.1803 | −1.49395 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0557281 | −0.00389222 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.94427 | 0.204641 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.47214 | −0.447687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.29180 | −0.157774 | −0.0788869 | − | 0.996884i | \(-0.525137\pi\) | ||||
−0.0788869 | + | 0.996884i | \(0.525137\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.7082 | 1.21335 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.47214 | 0.509595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.5623 | −0.781308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.23607 | 0.0831469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.94427 | −0.197163 | −0.0985815 | − | 0.995129i | \(-0.531431\pi\) | ||||
−0.0985815 | + | 0.995129i | \(0.531431\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.76393 | 0.117595 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.7426 | −1.70860 | −0.854300 | − | 0.519781i | \(-0.826014\pi\) | ||||
−0.854300 | + | 0.519781i | \(0.826014\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2361 | 1.27116 | 0.635578 | − | 0.772037i | \(-0.280762\pi\) | ||||
0.635578 | + | 0.772037i | \(0.280762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.47214 | 0.424004 | 0.212002 | − | 0.977269i | \(-0.432002\pi\) | ||||
0.212002 | + | 0.977269i | \(0.432002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.23607 | −0.341563 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.76393 | 0.309451 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.9098 | 0.770383 | 0.385191 | − | 0.922837i | \(-0.374135\pi\) | ||||
0.385191 | + | 0.922837i | \(0.374135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.03444 | −0.259881 | −0.129941 | − | 0.991522i | \(-0.541479\pi\) | ||||
−0.129941 | + | 0.991522i | \(0.541479\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4721 | −0.666326 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.9443 | −1.58078 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4164 | 1.09931 | 0.549657 | − | 0.835390i | \(-0.314758\pi\) | ||||
0.549657 | + | 0.835390i | \(0.314758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.88854 | 0.370210 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.00000 | 0.0626224 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.7082 | −1.60363 | −0.801817 | − | 0.597570i | \(-0.796133\pi\) | ||||
−0.801817 | + | 0.597570i | \(0.796133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.18034 | 0.134960 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.9443 | −1.04483 | −0.522414 | − | 0.852692i | \(-0.674969\pi\) | ||||
−0.522414 | + | 0.852692i | \(0.674969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.67376 | −0.409966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.23607 | −0.198044 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.70820 | −0.225257 | −0.112629 | − | 0.993637i | \(-0.535927\pi\) | ||||
−0.112629 | + | 0.993637i | \(0.535927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.52786 | 0.212738 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.76393 | 0.166069 | 0.0830343 | − | 0.996547i | \(-0.473539\pi\) | ||||
0.0830343 | + | 0.996547i | \(0.473539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.41641 | 0.144667 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.90983 | −0.531516 | −0.265758 | − | 0.964040i | \(-0.585622\pi\) | ||||
−0.265758 | + | 0.964040i | \(0.585622\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.43769 | 0.263794 | 0.131897 | − | 0.991263i | \(-0.457893\pi\) | ||||
0.131897 | + | 0.991263i | \(0.457893\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.47214 | −0.501846 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.4164 | −1.43132 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.29180 | 0.367571 | 0.183785 | − | 0.982966i | \(-0.441165\pi\) | ||||
0.183785 | + | 0.982966i | \(0.441165\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.18034 | 0.242568 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.52786 | 0.551011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.763932 | 0.0438867 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.52786 | −0.259265 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.05573 | −0.0602536 | −0.0301268 | − | 0.999546i | \(-0.509591\pi\) | ||||
−0.0301268 | + | 0.999546i | \(0.509591\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.9443 | −1.41903 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.6180 | −1.50937 | −0.754685 | − | 0.656087i | \(-0.772210\pi\) | ||||
−0.754685 | + | 0.656087i | \(0.772210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.27051 | 0.0718135 | 0.0359067 | − | 0.999355i | \(-0.488568\pi\) | ||||
0.0359067 | + | 0.999355i | \(0.488568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.1803 | −1.58277 | −0.791383 | − | 0.611321i | \(-0.790638\pi\) | ||||
−0.791383 | + | 0.611321i | \(0.790638\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.36068 | 0.244151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.4164 | 0.972089 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.47214 | −0.471402 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.70820 | 0.316634 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.70820 | −0.315664 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0344 | 0.991263 | 0.495631 | − | 0.868533i | \(-0.334937\pi\) | ||||
0.495631 | + | 0.868533i | \(0.334937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.180340 | −0.00988256 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.09017 | 0.442013 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.52786 | 0.519016 | 0.259508 | − | 0.965741i | \(-0.416440\pi\) | ||||
0.259508 | + | 0.965741i | \(0.416440\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.70820 | 0.527277 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.83282 | 0.261712 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.70820 | 0.414996 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.9443 | 1.66118 | 0.830588 | − | 0.556888i | \(-0.188005\pi\) | ||||
0.830588 | + | 0.556888i | \(0.188005\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5279 | 0.831188 | 0.415594 | − | 0.909550i | \(-0.363574\pi\) | ||||
0.415594 | + | 0.909550i | \(0.363574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.76393 | 0.361032 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7639 | 0.679356 | 0.339678 | − | 0.940542i | \(-0.389682\pi\) | ||||
0.339678 | + | 0.940542i | \(0.389682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.76393 | −0.358992 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.5623 | 1.03246 | 0.516230 | − | 0.856450i | \(-0.327335\pi\) | ||||
0.516230 | + | 0.856450i | \(0.327335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.7771 | 2.77774 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.8541 | −0.884611 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.41641 | 0.231165 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.5066 | 1.01824 | 0.509118 | − | 0.860697i | \(-0.329972\pi\) | ||||
0.509118 | + | 0.860697i | \(0.329972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0344419 | −0.00179297 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.8541 | −0.872672 | −0.436336 | − | 0.899784i | \(-0.643724\pi\) | ||||
−0.436336 | + | 0.899784i | \(0.643724\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.61803 | 0.496673 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.05573 | 0.363388 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.6525 | 0.547181 | 0.273590 | − | 0.961846i | \(-0.411789\pi\) | ||||
0.273590 | + | 0.961846i | \(0.411789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.7082 | −0.651061 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.6525 | 1.56627 | 0.783134 | − | 0.621853i | \(-0.213620\pi\) | ||||
0.783134 | + | 0.621853i | \(0.213620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.61803 | 0.234748 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.5623 | −1.09325 | −0.546626 | − | 0.837377i | \(-0.684088\pi\) | ||||
−0.546626 | + | 0.837377i | \(0.684088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.70820 | 0.389821 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.9443 | 0.652952 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.81966 | −0.0915570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.79837 | 0.341201 | 0.170600 | − | 0.985340i | \(-0.445429\pi\) | ||||
0.170600 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4721 | −0.522954 | −0.261477 | − | 0.965210i | \(-0.584209\pi\) | ||||
−0.261477 | + | 0.965210i | \(0.584209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.81966 | 0.389525 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.76393 | 0.236722 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.360680 | −0.0178782 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.18034 | 0.404492 | 0.202246 | − | 0.979335i | \(-0.435176\pi\) | ||||
0.202246 | + | 0.979335i | \(0.435176\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.85410 | 0.190109 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.52786 | 0.467704 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.7082 | 1.11203 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.4508 | −1.82959 | −0.914797 | − | 0.403914i | \(-0.867649\pi\) | ||||
−0.914797 | + | 0.403914i | \(0.867649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.2148 | −1.42384 | −0.711921 | − | 0.702260i | \(-0.752174\pi\) | ||||
−0.711921 | + | 0.702260i | \(0.752174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.23607 | −0.157343 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.61803 | 0.224008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.52786 | 0.0737660 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.05573 | 0.243526 | 0.121763 | − | 0.992559i | \(-0.461145\pi\) | ||||
0.121763 | + | 0.992559i | \(0.461145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.9443 | −0.814290 | −0.407145 | − | 0.913364i | \(-0.633476\pi\) | ||||
−0.407145 | + | 0.913364i | \(0.633476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.70820 | 0.273687 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −65.3050 | −3.12396 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.32624 | 0.158753 | 0.0793763 | − | 0.996845i | \(-0.474707\pi\) | ||||
0.0793763 | + | 0.996845i | \(0.474707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.8885 | 1.23000 | 0.615001 | − | 0.788526i | \(-0.289156\pi\) | ||||
0.615001 | + | 0.788526i | \(0.289156\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.23607 | 0.0585952 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.0344 | −1.04219 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.7082 | 0.835702 | 0.417851 | − | 0.908516i | \(-0.362783\pi\) | ||||
0.417851 | + | 0.908516i | \(0.362783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0688837 | −0.00324361 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.5066 | −1.15142 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.618034 | 0.0289104 | 0.0144552 | − | 0.999896i | \(-0.495399\pi\) | ||||
0.0144552 | + | 0.999896i | \(0.495399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.47214 | 0.255417 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9443 | 0.602875 | 0.301437 | − | 0.953486i | \(-0.402534\pi\) | ||||
0.301437 | + | 0.953486i | \(0.402534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0344 | −0.605762 | −0.302881 | − | 0.953028i | \(-0.597948\pi\) | ||||
−0.302881 | + | 0.953028i | \(0.597948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.32624 | 0.293372 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.4721 | −0.484593 | −0.242296 | − | 0.970202i | \(-0.577901\pi\) | ||||
−0.242296 | + | 0.970202i | \(0.577901\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.52786 | 0.162555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.23607 | 0.424675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.1246 | −1.79516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.12461 | −0.188853 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.2705 | 1.10895 | 0.554474 | − | 0.832201i | \(-0.312920\pi\) | ||||
0.554474 | + | 0.832201i | \(0.312920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.583592 | −0.0266095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.32624 | 0.423483 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3607 | −1.01326 | −0.506630 | − | 0.862164i | \(-0.669109\pi\) | ||||
−0.506630 | + | 0.862164i | \(0.669109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.23607 | 0.417669 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.09017 | −0.0491987 | −0.0245993 | − | 0.999697i | \(-0.507831\pi\) | ||||
−0.0245993 | + | 0.999697i | \(0.507831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.70820 | 0.257085 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.180340 | −0.00810568 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0557 | 0.763519 | 0.381760 | − | 0.924262i | \(-0.375318\pi\) | ||||
0.381760 | + | 0.924262i | \(0.375318\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.2705 | −1.03965 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.6180 | 0.473435 | 0.236717 | − | 0.971579i | \(-0.423928\pi\) | ||||
0.236717 | + | 0.971579i | \(0.423928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.291796 | −0.0129848 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.5623 | −0.824381 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.763932 | 0.0338607 | 0.0169303 | − | 0.999857i | \(-0.494611\pi\) | ||||
0.0169303 | + | 0.999857i | \(0.494611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.3607 | −2.04687 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.52786 | 0.419848 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.47214 | −0.284644 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.2705 | 0.845881 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7426 | 1.17162 | 0.585808 | − | 0.810450i | \(-0.300777\pi\) | ||||
0.585808 | + | 0.810450i | \(0.300777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.1803 | −1.49460 | −0.747301 | − | 0.664486i | \(-0.768651\pi\) | ||||
−0.747301 | + | 0.664486i | \(0.768651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.32624 | 0.275575 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.4164 | 1.58332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.111456 | −0.00482770 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.65248 | −0.287612 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.7426 | −1.28349 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.23607 | −0.225116 | −0.112558 | − | 0.993645i | \(-0.535904\pi\) | ||||
−0.112558 | + | 0.993645i | \(0.535904\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.1803 | 0.866021 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.18034 | 0.0933955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.6525 | −1.73817 | −0.869087 | − | 0.494659i | \(-0.835293\pi\) | ||||
−0.869087 | + | 0.494659i | \(0.835293\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.79837 | −0.119432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.3607 | −2.06023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.472136 | −0.0200411 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.3607 | 1.45591 | 0.727954 | − | 0.685626i | \(-0.240471\pi\) | ||||
0.727954 | + | 0.685626i | \(0.240471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.9443 | 0.632075 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.23607 | 0.0521868 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.1246 | 1.22746 | 0.613728 | − | 0.789518i | \(-0.289669\pi\) | ||||
0.613728 | + | 0.789518i | \(0.289669\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.70820 | −0.156005 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.5066 | −1.82389 | −0.911945 | − | 0.410312i | \(-0.865420\pi\) | ||||
−0.911945 | + | 0.410312i | \(0.865420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.47214 | 0.354548 | 0.177274 | − | 0.984162i | \(-0.443272\pi\) | ||||
0.177274 | + | 0.984162i | \(0.443272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.6525 | 1.40585 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 35.5967 | 1.48449 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.1246 | −0.712907 | −0.356453 | − | 0.934313i | \(-0.616014\pi\) | ||||
−0.356453 | + | 0.934313i | \(0.616014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.9443 | −0.953531 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.24922 | −0.341648 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.291796 | −0.0120643 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.8328 | 1.76790 | 0.883950 | − | 0.467582i | \(-0.154875\pi\) | ||||
0.883950 | + | 0.467582i | \(0.154875\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.5967 | −2.20842 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.7082 | 0.646149 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.3607 | 0.918243 | 0.459122 | − | 0.888373i | \(-0.348164\pi\) | ||||
0.459122 | + | 0.888373i | \(0.348164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.5623 | 0.800632 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0902 | 1.47460 | 0.737302 | − | 0.675563i | \(-0.236099\pi\) | ||||
0.737302 | + | 0.675563i | \(0.236099\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.2492 | −1.96813 | −0.984063 | − | 0.177818i | \(-0.943096\pi\) | ||||
−0.984063 | + | 0.177818i | \(0.943096\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.00000 | 0.203616 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.43769 | 0.261729 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.8541 | 1.61763 | 0.808814 | − | 0.588064i | \(-0.200110\pi\) | ||||
0.808814 | + | 0.588064i | \(0.200110\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.4721 | −0.423657 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.5623 | −0.709335 | −0.354667 | − | 0.934993i | \(-0.615406\pi\) | ||||
−0.354667 | + | 0.934993i | \(0.615406\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0901699 | −0.00363600 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.0132 | −1.40958 | −0.704788 | − | 0.709418i | \(-0.748958\pi\) | ||||
−0.704788 | + | 0.709418i | \(0.748958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.0000 | 1.28619 | 0.643094 | − | 0.765787i | \(-0.277650\pi\) | ||||
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 42.1803 | 1.69264 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4164 | 0.776656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.4721 | −0.418217 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.472136 | −0.0188253 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0902 | −1.47654 | −0.738268 | − | 0.674507i | \(-0.764356\pi\) | ||||
−0.738268 | + | 0.674507i | \(0.764356\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.70820 | −0.147388 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.85410 | 0.192629 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.18034 | −0.165372 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.0557 | 0.831651 | 0.415826 | − | 0.909444i | \(-0.363493\pi\) | ||||
0.415826 | + | 0.909444i | \(0.363493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.14590 | −0.124062 | −0.0620311 | − | 0.998074i | \(-0.519758\pi\) | ||||
−0.0620311 | + | 0.998074i | \(0.519758\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0902 | 0.476050 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7639 | 0.816314 | 0.408157 | − | 0.912912i | \(-0.366172\pi\) | ||||
0.408157 | + | 0.912912i | \(0.366172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.4721 | −1.27073 | −0.635366 | − | 0.772211i | \(-0.719151\pi\) | ||||
−0.635366 | + | 0.772211i | \(0.719151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.94427 | −0.193189 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.72949 | 0.106488 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.74265 | 0.0678838 | 0.0339419 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339419 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8328 | −1.19926 | −0.599629 | − | 0.800278i | \(-0.704685\pi\) | ||||
−0.599629 | + | 0.800278i | \(0.704685\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.00000 | 0.0776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.0000 | 1.70369 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.76393 | −0.184184 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.59675 | −0.216060 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4721 | −0.557860 | −0.278930 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278930 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.2705 | 0.972662 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.7771 | 1.29816 | 0.649079 | − | 0.760721i | \(-0.275154\pi\) | ||||
0.649079 | + | 0.760721i | \(0.275154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.6525 | −1.59613 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.1803 | 1.07829 | 0.539145 | − | 0.842213i | \(-0.318747\pi\) | ||||
0.539145 | + | 0.842213i | \(0.318747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.47214 | −0.0562474 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.1246 | 1.18748 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.3475 | −0.508500 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.49342 | −0.323105 | −0.161553 | − | 0.986864i | \(-0.551650\pi\) | ||||
−0.161553 | + | 0.986864i | \(0.551650\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.67376 | −0.329015 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0901699 | −0.00341543 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.4721 | 0.396093 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.4164 | −1.71535 | −0.857677 | − | 0.514189i | \(-0.828093\pi\) | ||||
−0.857677 | + | 0.514189i | \(0.828093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.47214 | −0.319079 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.6525 | 1.52674 | 0.763368 | − | 0.645964i | \(-0.223544\pi\) | ||||
0.763368 | + | 0.645964i | \(0.223544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.12461 | −0.0421762 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.7639 | 1.82622 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.583592 | −0.0218251 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.2705 | 0.719670 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.1459 | 1.45990 | 0.729948 | − | 0.683503i | \(-0.239544\pi\) | ||||
0.729948 | + | 0.683503i | \(0.239544\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.52786 | −0.242774 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.3607 | 0.979011 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4721 | −0.610918 | −0.305459 | − | 0.952205i | \(-0.598810\pi\) | ||||
−0.305459 | + | 0.952205i | \(0.598810\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0902 | 0.447171 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.0000 | −1.32969 | −0.664845 | − | 0.746981i | \(-0.731502\pi\) | ||||
−0.664845 | + | 0.746981i | \(0.731502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0000 | 0.368355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.43769 | −0.0528864 | −0.0264432 | − | 0.999650i | \(-0.508418\pi\) | ||||
−0.0264432 | + | 0.999650i | \(0.508418\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9443 | −0.622463 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.65248 | 0.170683 | 0.0853414 | − | 0.996352i | \(-0.472802\pi\) | ||||
0.0853414 | + | 0.996352i | \(0.472802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.41641 | 0.308353 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.88854 | 0.215451 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9443 | 0.399362 | 0.199681 | − | 0.979861i | \(-0.436009\pi\) | ||||
0.199681 | + | 0.979861i | \(0.436009\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.1803 | 1.02695 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.36068 | 0.340670 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.43769 | −0.343019 | −0.171509 | − | 0.985182i | \(-0.554864\pi\) | ||||
−0.171509 | + | 0.985182i | \(0.554864\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.52786 | 0.345840 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.1803 | −1.09404 | −0.547018 | − | 0.837121i | \(-0.684237\pi\) | ||||
−0.547018 | + | 0.837121i | \(0.684237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.236068 | −0.00853506 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.12461 | 0.256920 | 0.128460 | − | 0.991715i | \(-0.458997\pi\) | ||||
0.128460 | + | 0.991715i | \(0.458997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.5967 | −1.49807 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.41641 | −0.194815 | −0.0974073 | − | 0.995245i | \(-0.531055\pi\) | ||||
−0.0974073 | + | 0.995245i | \(0.531055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.2148 | 1.04943 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.763932 | 0.0273707 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.36068 | −0.299169 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 31.2361 | 1.11629 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.34752 | −0.0480952 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0000 | 0.427754 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.4164 | −0.976050 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.05573 | −0.321578 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.7984 | −0.382979 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.4164 | −0.546077 | −0.273039 | − | 0.962003i | \(-0.588029\pi\) | ||||
−0.273039 | + | 0.962003i | \(0.588029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.47214 | −0.299723 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.763932 | 0.0269922 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.45898 | 0.192643 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.1803 | 0.569575 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.4853 | −1.88044 | −0.940221 | − | 0.340564i | \(-0.889382\pi\) | ||||
−0.940221 | + | 0.340564i | \(0.889382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.96556 | 0.104135 | 0.0520674 | − | 0.998644i | \(-0.483419\pi\) | ||||
0.0520674 | + | 0.998644i | \(0.483419\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.00000 | −0.210429 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.52786 | −0.123576 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −102.430 | −3.58356 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.3607 | 0.501191 | 0.250596 | − | 0.968092i | \(-0.419374\pi\) | ||||
0.250596 | + | 0.968092i | \(0.419374\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.4853 | 1.65523 | 0.827617 | − | 0.561294i | \(-0.189696\pi\) | ||||
0.827617 | + | 0.561294i | \(0.189696\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.70820 | 0.198734 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.5279 | 0.957238 | 0.478619 | − | 0.878023i | \(-0.341138\pi\) | ||||
0.478619 | + | 0.878023i | \(0.341138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.18034 | 0.214652 | 0.107326 | − | 0.994224i | \(-0.465771\pi\) | ||||
0.107326 | + | 0.994224i | \(0.465771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.47214 | 0.155137 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.88854 | 0.307601 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.6180 | 1.19657 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.5279 | 0.467034 | 0.233517 | − | 0.972353i | \(-0.424977\pi\) | ||||
0.233517 | + | 0.972353i | \(0.424977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.58359 | 0.123572 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4164 | −0.496527 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.09017 | 0.243909 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.18034 | 0.246429 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.63932 | −0.124754 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.3607 | 1.31344 | 0.656722 | − | 0.754132i | \(-0.271942\pi\) | ||||
0.656722 | + | 0.754132i | \(0.271942\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | 0.0683986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.0902 | 0.515470 | 0.257735 | − | 0.966216i | \(-0.417024\pi\) | ||||
0.257735 | + | 0.966216i | \(0.417024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.9443 | −0.509892 | −0.254946 | − | 0.966955i | \(-0.582058\pi\) | ||||
−0.254946 | + | 0.966955i | \(0.582058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.3262 | −1.57696 | −0.788482 | − | 0.615058i | \(-0.789133\pi\) | ||||
−0.788482 | + | 0.615058i | \(0.789133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.36068 | −0.250271 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.61803 | 0.0549513 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.24922 | −0.0762997 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1803 | 0.548250 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.76393 | 0.195080 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.2918 | 0.617670 | 0.308835 | − | 0.951116i | \(-0.400061\pi\) | ||||
0.308835 | + | 0.951116i | \(0.400061\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.1803 | 0.343374 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.6738 | 0.662826 | 0.331413 | − | 0.943486i | \(-0.392475\pi\) | ||||
0.331413 | + | 0.943486i | \(0.392475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9787 | 0.504074 | 0.252037 | − | 0.967718i | \(-0.418900\pi\) | ||||
0.252037 | + | 0.967718i | \(0.418900\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.5066 | 0.554237 | 0.277118 | − | 0.960836i | \(-0.410621\pi\) | ||||
0.277118 | + | 0.960836i | \(0.410621\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.88854 | 0.197274 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 71.7771 | 2.40193 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3607 | 0.379746 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4164 | 0.514739 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.1115 | 1.20438 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7984 | −0.359746 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.70820 | −0.256229 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.3050 | −1.03946 | −0.519732 | − | 0.854329i | \(-0.673968\pi\) | ||||
−0.519732 | + | 0.854329i | \(0.673968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.180340 | −0.00598150 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4721 | −0.479483 | −0.239742 | − | 0.970837i | \(-0.577063\pi\) | ||||
−0.239742 | + | 0.970837i | \(0.577063\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7771 | 0.389765 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.32624 | −0.242198 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.1591 | −0.994855 | −0.497428 | − | 0.867505i | \(-0.665722\pi\) | ||||
−0.497428 | + | 0.867505i | \(0.665722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.70820 | −0.0562872 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.5279 | −0.445275 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.18034 | −0.0716891 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.88854 | 0.193405 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.2705 | −0.697863 | −0.348931 | − | 0.937148i | \(-0.613455\pi\) | ||||
−0.348931 | + | 0.937148i | \(0.613455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −43.0689 | −1.41001 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.472136 | −0.0154405 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.30495 | 0.173305 | 0.0866526 | − | 0.996239i | \(-0.472383\pi\) | ||||
0.0866526 | + | 0.996239i | \(0.472383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.05573 | 0.0670862 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.9787 | −1.49886 | −0.749432 | − | 0.662082i | \(-0.769673\pi\) | ||||
−0.749432 | + | 0.662082i | \(0.769673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.695048 | −0.0226339 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.87539 | 0.223420 | 0.111710 | − | 0.993741i | \(-0.464367\pi\) | ||||
0.111710 | + | 0.993741i | \(0.464367\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.83282 | 0.286725 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.5967 | −1.47858 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3262 | 1.04715 | 0.523575 | − | 0.851980i | \(-0.324598\pi\) | ||||
0.523575 | + | 0.851980i | \(0.324598\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.8541 | −0.415949 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.05573 | 0.228079 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.02129 | 0.291009 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.11146 | −0.132490 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.76393 | 0.282121 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.7984 | 1.21551 | 0.607757 | − | 0.794123i | \(-0.292070\pi\) | ||||
0.607757 | + | 0.794123i | \(0.292070\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.7082 | −0.440371 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.1246 | −0.677921 | −0.338961 | − | 0.940801i | \(-0.610075\pi\) | ||||
−0.338961 | + | 0.940801i | \(0.610075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.23607 | 0.295791 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.21478 | −0.0708571 | −0.0354286 | − | 0.999372i | \(-0.511280\pi\) | ||||
−0.0354286 | + | 0.999372i | \(0.511280\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.52786 | 0.0488307 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.34752 | 0.0430231 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.90983 | −0.220389 | −0.110195 | − | 0.993910i | \(-0.535147\pi\) | ||||
−0.110195 | + | 0.993910i | \(0.535147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 93.1935 | 2.96338 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.2492 | −0.897366 | −0.448683 | − | 0.893691i | \(-0.648107\pi\) | ||||
−0.448683 | + | 0.893691i | \(0.648107\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.1803 | 0.926010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.47214 | −0.236883 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0344 | −0.919530 | −0.459765 | − | 0.888041i | \(-0.652066\pi\) | ||||
−0.459765 | + | 0.888041i | \(0.652066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.58359 | −0.0817412 |
(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 | 3332.2.a.l.1.2 | 2 | ||
7.6 | odd | 2 | 476.2.a.b.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 4284.2.a.m.1.1 | 2 | |||
28.27 | even | 2 | 1904.2.a.j.1.2 | 2 | |||
56.13 | odd | 2 | 7616.2.a.u.1.2 | 2 | |||
56.27 | even | 2 | 7616.2.a.p.1.1 | 2 | |||
119.118 | odd | 2 | 8092.2.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.a.b.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1904.2.a.j.1.2 | 2 | 28.27 | even | 2 | |||
3332.2.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4284.2.a.m.1.1 | 2 | 21.20 | even | 2 | |||
7616.2.a.p.1.1 | 2 | 56.27 | even | 2 | |||
7616.2.a.u.1.2 | 2 | 56.13 | odd | 2 | |||
8092.2.a.m.1.2 | 2 | 119.118 | odd | 2 |