Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10000,2,Mod(1,10000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10000, 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("10000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.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: | \(79.8504020213\) |
Analytic rank: | \(0\) |
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 25) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10000.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.618034 | 0.233595 | 0.116797 | − | 0.993156i | \(-0.462737\pi\) | ||||
0.116797 | + | 0.993156i | \(0.462737\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23607 | 1.57873 | 0.789367 | − | 0.613922i | \(-0.210409\pi\) | ||||
0.789367 | + | 0.613922i | \(0.210409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.85410 | −0.514235 | −0.257118 | − | 0.966380i | \(-0.582773\pi\) | ||||
−0.257118 | + | 0.966380i | \(0.582773\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.23607 | 1.26993 | 0.634967 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634967 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.854102 | −0.195944 | −0.0979722 | − | 0.995189i | \(-0.531236\pi\) | ||||
−0.0979722 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.618034 | 0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.76393 | 0.784834 | 0.392417 | − | 0.919787i | \(-0.371639\pi\) | ||||
0.392417 | + | 0.919787i | \(0.371639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.61803 | −0.671852 | −0.335926 | − | 0.941888i | \(-0.609049\pi\) | ||||
−0.335926 | + | 0.941888i | \(0.609049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.23607 | 0.911482 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.236068 | 0.0388093 | 0.0194047 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194047 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.85410 | −0.296894 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.763932 | −0.119306 | −0.0596531 | − | 0.998219i | \(-0.518999\pi\) | ||||
−0.0596531 | + | 0.998219i | \(0.518999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.85410 | −0.740244 | −0.370122 | − | 0.928983i | \(-0.620684\pi\) | ||||
−0.370122 | + | 0.928983i | \(0.620684\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.618034 | 0.0901495 | 0.0450748 | − | 0.998984i | \(-0.485647\pi\) | ||||
0.0450748 | + | 0.998984i | \(0.485647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23607 | 0.733196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.47214 | 0.476935 | 0.238467 | − | 0.971151i | \(-0.423355\pi\) | ||||
0.238467 | + | 0.971151i | \(0.423355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.854102 | −0.113129 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8541 | 1.41308 | 0.706542 | − | 0.707671i | \(-0.250254\pi\) | ||||
0.706542 | + | 0.707671i | \(0.250254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.70820 | 1.11497 | 0.557486 | − | 0.830187i | \(-0.311766\pi\) | ||||
0.557486 | + | 0.830187i | \(0.311766\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.23607 | −0.155730 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.76393 | 0.582007 | 0.291003 | − | 0.956722i | \(-0.406011\pi\) | ||||
0.291003 | + | 0.956722i | \(0.406011\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.76393 | 0.453124 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.61803 | 0.785416 | 0.392708 | − | 0.919663i | \(-0.371538\pi\) | ||||
0.392708 | + | 0.919663i | \(0.371538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23607 | 0.368784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.09017 | 0.910215 | 0.455108 | − | 0.890436i | \(-0.349601\pi\) | ||||
0.455108 | + | 0.890436i | \(0.349601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.23607 | −0.684497 | −0.342249 | − | 0.939609i | \(-0.611189\pi\) | ||||
−0.342249 | + | 0.939609i | \(0.611189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.61803 | −0.387894 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.94427 | −0.948091 | −0.474045 | − | 0.880500i | \(-0.657207\pi\) | ||||
−0.474045 | + | 0.880500i | \(0.657207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.14590 | −0.120123 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.00000 | 0.311086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.85410 | 0.391325 | 0.195662 | − | 0.980671i | \(-0.437314\pi\) | ||||
0.195662 | + | 0.980671i | \(0.437314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.4721 | −1.05249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.47214 | 0.146483 | 0.0732415 | − | 0.997314i | \(-0.476666\pi\) | ||||
0.0732415 | + | 0.997314i | \(0.476666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.56231 | 0.843669 | 0.421835 | − | 0.906673i | \(-0.361386\pi\) | ||||
0.421835 | + | 0.906673i | \(0.361386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.4164 | −1.58703 | −0.793517 | − | 0.608548i | \(-0.791752\pi\) | ||||
−0.793517 | + | 0.608548i | \(0.791752\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.236068 | 0.0224066 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.8541 | −1.58550 | −0.792750 | − | 0.609547i | \(-0.791352\pi\) | ||||
−0.792750 | + | 0.609547i | \(0.791352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.70820 | 0.342824 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.23607 | 0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.763932 | −0.0688814 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8885 | 1.76482 | 0.882411 | − | 0.470479i | \(-0.155919\pi\) | ||||
0.882411 | + | 0.470479i | \(0.155919\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.85410 | −0.427380 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.79837 | −0.593977 | −0.296988 | − | 0.954881i | \(-0.595982\pi\) | ||||
−0.296988 | + | 0.954881i | \(0.595982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.527864 | −0.0457716 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9443 | 1.02047 | 0.510234 | − | 0.860036i | \(-0.329559\pi\) | ||||
0.510234 | + | 0.860036i | \(0.329559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.618034 | 0.0520479 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.70820 | −0.811841 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.61803 | −0.545846 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.94427 | −0.323127 | −0.161564 | − | 0.986862i | \(-0.551654\pi\) | ||||
−0.161564 | + | 0.986862i | \(0.551654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5623 | −1.18506 | −0.592532 | − | 0.805547i | \(-0.701872\pi\) | ||||
−0.592532 | + | 0.805547i | \(0.701872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.4721 | −0.846622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1803 | −1.05191 | −0.525953 | − | 0.850514i | \(-0.676291\pi\) | ||||
−0.525953 | + | 0.850514i | \(0.676291\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.47214 | 0.275358 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.32624 | 0.183333 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5623 | 1.12687 | 0.563433 | − | 0.826162i | \(-0.309480\pi\) | ||||
0.563433 | + | 0.826162i | \(0.309480\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.56231 | −0.735562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.70820 | 0.130630 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8885 | −1.43607 | −0.718035 | − | 0.696007i | \(-0.754958\pi\) | ||||
−0.718035 | + | 0.696007i | \(0.754958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.8541 | 0.815844 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.527864 | 0.0394544 | 0.0197272 | − | 0.999805i | \(-0.493720\pi\) | ||||
0.0197272 | + | 0.999805i | \(0.493720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.291796 | 0.0216890 | 0.0108445 | − | 0.999941i | \(-0.496548\pi\) | ||||
0.0108445 | + | 0.999941i | \(0.496548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.70820 | 0.643729 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.4164 | 2.00489 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.09017 | −0.224777 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.81966 | 0.131666 | 0.0658330 | − | 0.997831i | \(-0.479030\pi\) | ||||
0.0658330 | + | 0.997831i | \(0.479030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.70820 | −0.554849 | −0.277424 | − | 0.960747i | \(-0.589481\pi\) | ||||
−0.277424 | + | 0.960747i | \(0.589481\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.70820 | −0.264199 | −0.132099 | − | 0.991236i | \(-0.542172\pi\) | ||||
−0.132099 | + | 0.991236i | \(0.542172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.5623 | 1.24496 | 0.622479 | − | 0.782636i | \(-0.286125\pi\) | ||||
0.622479 | + | 0.782636i | \(0.286125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.76393 | 0.336022 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.23607 | −0.156941 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.52786 | −0.523223 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.47214 | −0.309344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.18034 | 0.632001 | 0.316000 | − | 0.948759i | \(-0.397660\pi\) | ||||
0.316000 | + | 0.948759i | \(0.397660\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.61803 | 0.453460 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.85410 | 0.125865 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.00000 | 0.608164 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.70820 | −0.653044 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.180340 | −0.0120765 | −0.00603823 | − | 0.999982i | \(-0.501922\pi\) | ||||
−0.00603823 | + | 0.999982i | \(0.501922\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.7639 | 0.979917 | 0.489958 | − | 0.871746i | \(-0.337012\pi\) | ||||
0.489958 | + | 0.871746i | \(0.337012\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.7082 | 1.43452 | 0.717259 | − | 0.696806i | \(-0.245396\pi\) | ||||
0.717259 | + | 0.696806i | \(0.245396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.23607 | 0.212918 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.94427 | 0.192886 | 0.0964428 | − | 0.995339i | \(-0.469254\pi\) | ||||
0.0964428 | + | 0.995339i | \(0.469254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.09017 | 0.525513 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.5279 | 1.32784 | 0.663919 | − | 0.747805i | \(-0.268892\pi\) | ||||
0.663919 | + | 0.747805i | \(0.268892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.52786 | 0.162834 | 0.0814170 | − | 0.996680i | \(-0.474055\pi\) | ||||
0.0814170 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.58359 | 0.100762 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.23607 | −0.395195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.1803 | 1.84185 | 0.920923 | − | 0.389744i | \(-0.127436\pi\) | ||||
0.920923 | + | 0.389744i | \(0.127436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.7082 | 1.23904 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.8541 | −1.42560 | −0.712800 | − | 0.701367i | \(-0.752573\pi\) | ||||
−0.712800 | + | 0.701367i | \(0.752573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.145898 | 0.00906566 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.23607 | 0.447901 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9098 | −0.672729 | −0.336364 | − | 0.941732i | \(-0.609197\pi\) | ||||
−0.336364 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.94427 | −0.547381 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7639 | −0.778231 | −0.389115 | − | 0.921189i | \(-0.627219\pi\) | ||||
−0.389115 | + | 0.921189i | \(0.627219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.14590 | −0.0693529 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.7082 | 1.48457 | 0.742286 | − | 0.670083i | \(-0.233742\pi\) | ||||
0.742286 | + | 0.670083i | \(0.233742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0902 | 0.601929 | 0.300965 | − | 0.953635i | \(-0.402691\pi\) | ||||
0.300965 | + | 0.953635i | \(0.402691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.8541 | −1.77464 | −0.887321 | − | 0.461152i | \(-0.847436\pi\) | ||||
−0.887321 | + | 0.461152i | \(0.847436\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.472136 | −0.0278693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.85410 | 0.225931 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.5279 | 1.14083 | 0.570415 | − | 0.821357i | \(-0.306782\pi\) | ||||
0.570415 | + | 0.821357i | \(0.306782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.1803 | −1.51914 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.97871 | −0.403589 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.47214 | 0.0845720 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.23607 | 0.527130 | 0.263565 | − | 0.964642i | \(-0.415102\pi\) | ||||
0.263565 | + | 0.964642i | \(0.415102\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.56231 | 0.487093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.50658 | −0.482364 | −0.241182 | − | 0.970480i | \(-0.577535\pi\) | ||||
−0.241182 | + | 0.970480i | \(0.577535\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7639 | 0.947553 | 0.473777 | − | 0.880645i | \(-0.342890\pi\) | ||||
0.473777 | + | 0.880645i | \(0.342890\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.65248 | −0.429806 | −0.214903 | − | 0.976635i | \(-0.568944\pi\) | ||||
−0.214903 | + | 0.976635i | \(0.568944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.9443 | −1.06068 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.4164 | −0.916275 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.47214 | −0.248836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0000 | 0.553001 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.381966 | 0.0210585 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.1246 | 1.27104 | 0.635522 | − | 0.772083i | \(-0.280785\pi\) | ||||
0.635522 | + | 0.772083i | \(0.280785\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.472136 | −0.0258729 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.85410 | −0.427840 | −0.213920 | − | 0.976851i | \(-0.568623\pi\) | ||||
−0.213920 | + | 0.976851i | \(0.568623\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.8541 | −0.915389 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7082 | 0.850647 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.41641 | −0.454443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.9098 | −1.06882 | −0.534408 | − | 0.845227i | \(-0.679465\pi\) | ||||
−0.534408 | + | 0.845227i | \(0.679465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7082 | 1.16201 | 0.581007 | − | 0.813899i | \(-0.302659\pi\) | ||||
0.581007 | + | 0.813899i | \(0.302659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.27051 | 0.494823 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9098 | −0.687121 | −0.343560 | − | 0.939131i | \(-0.611633\pi\) | ||||
−0.343560 | + | 0.939131i | \(0.611633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.23607 | 0.171271 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.7426 | −0.725309 | −0.362655 | − | 0.931924i | \(-0.618130\pi\) | ||||
−0.362655 | + | 0.931924i | \(0.618130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2705 | −0.961606 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.4164 | 0.861638 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.5623 | −1.33434 | −0.667171 | − | 0.744905i | \(-0.732495\pi\) | ||||
−0.667171 | + | 0.744905i | \(0.732495\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.52786 | 0.0795374 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.14590 | 0.111409 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2705 | 1.46379 | 0.731896 | − | 0.681417i | \(-0.238636\pi\) | ||||
0.731896 | + | 0.681417i | \(0.238636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.70820 | 0.345490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5967 | −0.749785 | −0.374892 | − | 0.927068i | \(-0.622320\pi\) | ||||
−0.374892 | + | 0.927068i | \(0.622320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.8885 | 1.01892 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.3607 | 1.70465 | 0.852326 | − | 0.523012i | \(-0.175192\pi\) | ||||
0.852326 | + | 0.523012i | \(0.175192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.70820 | 0.493496 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | 0.760530 | 0.380265 | − | 0.924878i | \(-0.375833\pi\) | ||||
0.380265 | + | 0.924878i | \(0.375833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.7082 | 0.996687 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.79837 | −0.342933 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.0344 | −1.45720 | −0.728598 | − | 0.684941i | \(-0.759828\pi\) | ||||
−0.728598 | + | 0.684941i | \(0.759828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.527864 | −0.0264263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5967 | 1.32818 | 0.664089 | − | 0.747653i | \(-0.268820\pi\) | ||||
0.664089 | + | 0.747653i | \(0.268820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.56231 | −0.277078 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.23607 | 0.0612696 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.58359 | 0.0783036 | 0.0391518 | − | 0.999233i | \(-0.487534\pi\) | ||||
0.0391518 | + | 0.999233i | \(0.487534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9443 | 0.589167 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.70820 | 0.330089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.00000 | −0.244851 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.47214 | 0.462744 | 0.231372 | − | 0.972865i | \(-0.425679\pi\) | ||||
0.231372 | + | 0.972865i | \(0.425679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.23607 | −0.0600997 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.38197 | 0.260452 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.70820 | −0.468717 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.8328 | 1.43700 | 0.718498 | − | 0.695529i | \(-0.244830\pi\) | ||||
0.718498 | + | 0.695529i | \(0.244830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.8541 | −1.29053 | −0.645263 | − | 0.763961i | \(-0.723252\pi\) | ||||
−0.645263 | + | 0.763961i | \(0.723252\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.21478 | −0.153784 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.9787 | 1.95581 | 0.977904 | − | 0.209056i | \(-0.0670391\pi\) | ||||
0.977904 | + | 0.209056i | \(0.0670391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.2361 | 0.630289 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.9443 | 1.42270 | 0.711348 | − | 0.702840i | \(-0.248085\pi\) | ||||
0.711348 | + | 0.702840i | \(0.248085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.94427 | −0.186558 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.67376 | 0.220568 | 0.110284 | − | 0.993900i | \(-0.464824\pi\) | ||||
0.110284 | + | 0.993900i | \(0.464824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | −0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.5623 | −0.684197 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4164 | 1.00182 | 0.500909 | − | 0.865500i | \(-0.332999\pi\) | ||||
0.500909 | + | 0.865500i | \(0.332999\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.1803 | −1.22199 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.819660 | 0.0381754 | 0.0190877 | − | 0.999818i | \(-0.493924\pi\) | ||||
0.0190877 | + | 0.999818i | \(0.493924\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.1246 | −1.12117 | −0.560583 | − | 0.828098i | \(-0.689423\pi\) | ||||
−0.560583 | + | 0.828098i | \(0.689423\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.4508 | 1.27027 | 0.635137 | − | 0.772400i | \(-0.280944\pi\) | ||||
0.635137 | + | 0.772400i | \(0.280944\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.94427 | 0.135954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1803 | −0.607318 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.4164 | −1.16865 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.94427 | −0.317956 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.8541 | 0.495937 | 0.247968 | − | 0.968768i | \(-0.420237\pi\) | ||||
0.247968 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.437694 | −0.0199571 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.32624 | 0.105847 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.4164 | −1.65018 | −0.825092 | − | 0.564998i | \(-0.808877\pi\) | ||||
−0.825092 | + | 0.564998i | \(0.808877\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.0000 | 0.497437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.2492 | 1.95181 | 0.975905 | − | 0.218196i | \(-0.0700171\pi\) | ||||
0.975905 | + | 0.218196i | \(0.0700171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.9443 | −0.853207 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.09017 | 0.183469 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.56231 | −0.338535 | −0.169268 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169268 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5623 | 0.650596 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.4164 | −1.66832 | −0.834158 | − | 0.551526i | \(-0.814046\pi\) | ||||
−0.834158 | + | 0.551526i | \(0.814046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.56231 | −0.424677 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3262 | −0.900945 | −0.450472 | − | 0.892790i | \(-0.648744\pi\) | ||||
−0.450472 | + | 0.892790i | \(0.648744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.56231 | 0.246062 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.27051 | 0.188548 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.23607 | 0.142322 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8885 | −0.829115 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3607 | 1.28631 | 0.643157 | − | 0.765734i | \(-0.277624\pi\) | ||||
0.643157 | + | 0.765734i | \(0.277624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.1459 | −0.574830 | −0.287415 | − | 0.957806i | \(-0.592796\pi\) | ||||
−0.287415 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.7082 | 0.684260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.7082 | −0.942056 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.41641 | 0.0613514 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.527864 | 0.0227790 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.6525 | −1.49259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1246 | 1.16618 | 0.583089 | − | 0.812408i | \(-0.301844\pi\) | ||||
0.583089 | + | 0.812408i | \(0.301844\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.291796 | 0.0125222 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2918 | −0.910371 | −0.455186 | − | 0.890397i | \(-0.650427\pi\) | ||||
−0.455186 | + | 0.890397i | \(0.650427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.4164 | −0.743314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.09017 | 0.131646 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.00000 | 0.212622 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.76393 | −0.201854 | −0.100927 | − | 0.994894i | \(-0.532181\pi\) | ||||
−0.100927 | + | 0.994894i | \(0.532181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.00000 | 0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.4164 | 1.15752 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.38197 | 0.311113 | 0.155556 | − | 0.987827i | \(-0.450283\pi\) | ||||
0.155556 | + | 0.987827i | \(0.450283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.618034 | 0.0259550 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.5279 | 0.860573 | 0.430286 | − | 0.902692i | \(-0.358413\pi\) | ||||
0.430286 | + | 0.902692i | \(0.358413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.12461 | 0.340004 | 0.170002 | − | 0.985444i | \(-0.445623\pi\) | ||||
0.170002 | + | 0.985444i | \(0.445623\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.81966 | 0.0760174 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7771 | 1.40616 | 0.703079 | − | 0.711111i | \(-0.251808\pi\) | ||||
0.703079 | + | 0.711111i | \(0.251808\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.70820 | −0.320342 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.85410 | −0.159895 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.1803 | 0.752953 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.29180 | 0.218416 | 0.109208 | − | 0.994019i | \(-0.465169\pi\) | ||||
0.109208 | + | 0.994019i | \(0.465169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.56231 | −0.105578 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.70820 | −0.152535 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9098 | 0.448013 | 0.224007 | − | 0.974588i | \(-0.428086\pi\) | ||||
0.224007 | + | 0.974588i | \(0.428086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.5623 | 0.718777 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.47214 | 0.387021 | 0.193510 | − | 0.981098i | \(-0.438013\pi\) | ||||
0.193510 | + | 0.981098i | \(0.438013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.72949 | 0.111338 | 0.0556691 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556691 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.52786 | −0.388005 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.5623 | −1.44343 | −0.721715 | − | 0.692191i | \(-0.756646\pi\) | ||||
−0.721715 | + | 0.692191i | \(0.756646\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.23607 | −0.0906100 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.14590 | −0.0463581 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.9787 | 0.604985 | 0.302492 | − | 0.953152i | \(-0.402181\pi\) | ||||
0.302492 | + | 0.953152i | \(0.402181\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.2361 | −0.573123 | −0.286561 | − | 0.958062i | \(-0.592512\pi\) | ||||
−0.286561 | + | 0.958062i | \(0.592512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.5279 | −1.22702 | −0.613509 | − | 0.789688i | \(-0.710243\pi\) | ||||
−0.613509 | + | 0.789688i | \(0.710243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.8197 | −0.755207 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.52786 | −0.221469 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.47214 | −0.178600 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.23607 | 0.0492853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2361 | 0.407491 | 0.203746 | − | 0.979024i | \(-0.434688\pi\) | ||||
0.203746 | + | 0.979024i | \(0.434688\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.18034 | 0.364886 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.2705 | 0.486175 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.2361 | −0.523611 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.09017 | −0.0430591 | −0.0215296 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215296 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.8328 | −1.21593 | −0.607964 | − | 0.793965i | \(-0.708013\pi\) | ||||
−0.607964 | + | 0.793965i | \(0.708013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.5410 | −1.43658 | −0.718288 | − | 0.695746i | \(-0.755074\pi\) | ||||
−0.718288 | + | 0.695746i | \(0.755074\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.8328 | 2.23088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.85410 | 0.0726680 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.0902 | −0.747056 | −0.373528 | − | 0.927619i | \(-0.621852\pi\) | ||||
−0.373528 | + | 0.927619i | \(0.621852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.0000 | −0.702247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5279 | −0.604880 | −0.302440 | − | 0.953168i | \(-0.597801\pi\) | ||||
−0.302440 | + | 0.953168i | \(0.597801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.6869 | 0.765732 | 0.382866 | − | 0.923804i | \(-0.374937\pi\) | ||||
0.382866 | + | 0.923804i | \(0.374937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.70820 | −0.377035 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.6180 | −0.527292 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.180340 | −0.00697234 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.5967 | 1.76024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.1803 | −0.469518 | −0.234759 | − | 0.972054i | \(-0.575430\pi\) | ||||
−0.234759 | + | 0.972054i | \(0.575430\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.6180 | −0.408084 | −0.204042 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204042 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.38197 | 0.0914115 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.7639 | 0.565755 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.4721 | −0.515497 | −0.257748 | − | 0.966212i | \(-0.582981\pi\) | ||||
−0.257748 | + | 0.966212i | \(0.582981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.7082 | 0.828220 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.43769 | −0.245257 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.2705 | −1.37980 | −0.689898 | − | 0.723907i | \(-0.742344\pi\) | ||||
−0.689898 | + | 0.723907i | \(0.742344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.47214 | −0.245856 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.94427 | 0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.0132 | −1.54905 | −0.774523 | − | 0.632546i | \(-0.782010\pi\) | ||||
−0.774523 | + | 0.632546i | \(0.782010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.201626 | −0.00760447 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.909830 | 0.0342177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.5410 | −1.25966 | −0.629830 | − | 0.776733i | \(-0.716875\pi\) | ||||
−0.629830 | + | 0.776733i | \(0.716875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.1803 | −0.606810 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.2918 | 0.422881 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.5279 | 0.766627 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.2918 | 0.868637 | 0.434319 | − | 0.900759i | \(-0.356989\pi\) | ||||
0.434319 | + | 0.900759i | \(0.356989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.29180 | 0.197077 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.52786 | 0.0940123 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5623 | 0.910966 | 0.455483 | − | 0.890245i | \(-0.349467\pi\) | ||||
0.455483 | + | 0.890245i | \(0.349467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.4164 | −0.940060 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.9787 | 0.737931 | 0.368965 | − | 0.929443i | \(-0.379712\pi\) | ||||
0.368965 | + | 0.929443i | \(0.379712\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.9443 | 0.918834 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9787 | −0.587786 | −0.293893 | − | 0.955838i | \(-0.594951\pi\) | ||||
−0.293893 | + | 0.955838i | \(0.594951\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.58359 | 0.0581747 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.3607 | 1.04045 | 0.520226 | − | 0.854029i | \(-0.325848\pi\) | ||||
0.520226 | + | 0.854029i | \(0.325848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.4721 | 0.456332 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1459 | −0.370723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.11146 | 0.186520 | 0.0932598 | − | 0.995642i | \(-0.470271\pi\) | ||||
0.0932598 | + | 0.995642i | \(0.470271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.1803 | 1.06339 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.4164 | −1.10550 | −0.552752 | − | 0.833346i | \(-0.686422\pi\) | ||||
−0.552752 | + | 0.833346i | \(0.686422\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.7082 | 0.715362 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.4508 | −0.668843 | −0.334421 | − | 0.942424i | \(-0.608541\pi\) | ||||
−0.334421 | + | 0.942424i | \(0.608541\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.18034 | 0.223743 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.1246 | −0.726658 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.4164 | 0.483808 | 0.241904 | − | 0.970300i | \(-0.422228\pi\) | ||||
0.241904 | + | 0.970300i | \(0.422228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.8541 | −0.823070 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.1591 | 1.30055 | 0.650275 | − | 0.759699i | \(-0.274654\pi\) | ||||
0.650275 | + | 0.759699i | \(0.274654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.145898 | 0.00523406 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.652476 | 0.0233774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.6525 | 1.23996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.0902 | 0.646490 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.8197 | −0.421325 | −0.210663 | − | 0.977559i | \(-0.567562\pi\) | ||||
−0.210663 | + | 0.977559i | \(0.567562\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.9098 | −0.388400 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.4164 | −0.370365 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.1459 | −0.573358 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.76393 | −0.345856 | −0.172928 | − | 0.984934i | \(-0.555323\pi\) | ||||
−0.172928 | + | 0.984934i | \(0.555323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.23607 | 0.114484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8885 | 0.632061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 47.1246 | 1.66299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.7639 | −0.449312 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.9787 | 1.08915 | 0.544577 | − | 0.838711i | \(-0.316690\pi\) | ||||
0.544577 | + | 0.838711i | \(0.316690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.7082 | 0.516475 | 0.258237 | − | 0.966081i | \(-0.416858\pi\) | ||||
0.258237 | + | 0.966081i | \(0.416858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.14590 | 0.145047 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.29180 | 0.0800818 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.6869 | −1.41998 | −0.709992 | − | 0.704210i | \(-0.751301\pi\) | ||||
−0.709992 | + | 0.704210i | \(0.751301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.7082 | 1.66300 | 0.831502 | − | 0.555522i | \(-0.187482\pi\) | ||||
0.831502 | + | 0.555522i | \(0.187482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.965558 | −0.0335757 | −0.0167879 | − | 0.999859i | \(-0.505344\pi\) | ||||
−0.0167879 | + | 0.999859i | \(0.505344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.8541 | −1.24526 | −0.622632 | − | 0.782515i | \(-0.713937\pi\) | ||||
−0.622632 | + | 0.782515i | \(0.713937\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.7082 | 0.857118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.6525 | −1.20064 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.0000 | −0.518476 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.8541 | −0.374725 | −0.187363 | − | 0.982291i | \(-0.559994\pi\) | ||||
−0.187363 | + | 0.982291i | \(0.559994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0902 | 0.347524 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.1459 | 0.348617 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.8541 | −1.02459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.888544 | 0.0304589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.3050 | 0.524032 | 0.262016 | − | 0.965064i | \(-0.415613\pi\) | ||||
0.262016 | + | 0.965064i | \(0.415613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.6869 | −0.672492 | −0.336246 | − | 0.941774i | \(-0.609157\pi\) | ||||
−0.336246 | + | 0.941774i | \(0.609157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.58359 | 0.0540315 | 0.0270157 | − | 0.999635i | \(-0.491400\pi\) | ||||
0.0270157 | + | 0.999635i | \(0.491400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.472136 | −0.0160904 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.4377 | −0.729748 | −0.364874 | − | 0.931057i | \(-0.618888\pi\) | ||||
−0.364874 | + | 0.931057i | \(0.618888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.4164 | 0.353760 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.3607 | 1.43699 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.83282 | −0.299289 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.70820 | −0.260883 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.5410 | 1.23390 | 0.616951 | − | 0.787001i | \(-0.288368\pi\) | ||||
0.616951 | + | 0.787001i | \(0.288368\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.5279 | 0.658659 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.3607 | −1.35979 | −0.679893 | − | 0.733311i | \(-0.737974\pi\) | ||||
−0.679893 | + | 0.733311i | \(0.737974\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.5836 | −0.692693 | −0.346347 | − | 0.938107i | \(-0.612578\pi\) | ||||
−0.346347 | + | 0.938107i | \(0.612578\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.8885 | 1.00356 | 0.501780 | − | 0.864996i | \(-0.332679\pi\) | ||||
0.501780 | + | 0.864996i | \(0.332679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.2918 | 0.412254 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.23607 | 0.175415 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.527864 | −0.0176643 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.97871 | −0.233012 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.8541 | −0.362005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1803 | 0.605675 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.00000 | −0.0998337 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.2492 | −1.10402 | −0.552011 | − | 0.833837i | \(-0.686139\pi\) | ||||
−0.552011 | + | 0.833837i | \(0.686139\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.94427 | −0.0976553 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.2361 | 1.33308 | 0.666540 | − | 0.745469i | \(-0.267774\pi\) | ||||
0.666540 | + | 0.745469i | \(0.267774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.6525 | −1.08064 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.20163 | −0.138750 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.2148 | 1.75539 | 0.877697 | − | 0.479216i | \(-0.159079\pi\) | ||||
0.877697 | + | 0.479216i | \(0.159079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.23607 | 0.304339 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.2705 | −0.403889 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.1246 | −0.562446 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.6312 | 1.36588 | 0.682938 | − | 0.730477i | \(-0.260702\pi\) | ||||
0.682938 | + | 0.730477i | \(0.260702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.65248 | 0.185252 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.50658 | −0.278493 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.7295 | −0.579197 | −0.289599 | − | 0.957148i | \(-0.593522\pi\) | ||||
−0.289599 | + | 0.957148i | \(0.593522\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.7639 | 0.547070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.4164 | −1.51313 | −0.756566 | − | 0.653918i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653918i | \(0.773124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.87539 | −0.0936355 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.65248 | 0.0861939 | 0.0430969 | − | 0.999071i | \(-0.486278\pi\) | ||||
0.0430969 | + | 0.999071i | \(0.486278\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.6869 | −0.541680 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.65248 | −0.248149 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.74265 | 0.250809 | 0.125404 | − | 0.992106i | \(-0.459977\pi\) | ||||
0.125404 | + | 0.992106i | \(0.459977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.9443 | −0.612381 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.38197 | 0.238376 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32.8328 | 1.05802 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.11146 | 0.132216 | 0.0661078 | − | 0.997812i | \(-0.478942\pi\) | ||||
0.0661078 | + | 0.997812i | \(0.478942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.47214 | −0.143666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.61803 | −0.180291 | −0.0901456 | − | 0.995929i | \(-0.528733\pi\) | ||||
−0.0901456 | + | 0.995929i | \(0.528733\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.09017 | −0.0990663 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.34752 | 0.0751040 | 0.0375520 | − | 0.999295i | \(-0.488044\pi\) | ||||
0.0375520 | + | 0.999295i | \(0.488044\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.8328 | −1.49678 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.0000 | −0.638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.61803 | 0.306768 | 0.153384 | − | 0.988167i | \(-0.450983\pi\) | ||||
0.153384 | + | 0.988167i | \(0.450983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.381966 | 0.0121581 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.2705 | −0.580968 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.3607 | 0.487948 | 0.243974 | − | 0.969782i | \(-0.421549\pi\) | ||||
0.243974 | + | 0.969782i | \(0.421549\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.1246 | 0.733837 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.8885 | −0.788228 | −0.394114 | − | 0.919062i | \(-0.628949\pi\) | ||||
−0.394114 | + | 0.919062i | \(0.628949\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.18034 | −0.0373443 |
(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 | 10000.2.a.l.1.2 | 2 | ||
4.3 | odd | 2 | 625.2.a.c.1.2 | 2 | |||
5.4 | even | 2 | 10000.2.a.c.1.1 | 2 | |||
12.11 | even | 2 | 5625.2.a.d.1.1 | 2 | |||
20.3 | even | 4 | 625.2.b.a.624.1 | 4 | |||
20.7 | even | 4 | 625.2.b.a.624.4 | 4 | |||
20.19 | odd | 2 | 625.2.a.b.1.1 | 2 | |||
25.9 | even | 10 | 400.2.u.b.81.1 | 4 | |||
25.14 | even | 10 | 400.2.u.b.321.1 | 4 | |||
60.59 | even | 2 | 5625.2.a.f.1.2 | 2 | |||
100.3 | even | 20 | 625.2.e.c.249.1 | 8 | |||
100.11 | odd | 10 | 125.2.d.a.101.1 | 4 | |||
100.19 | odd | 10 | 625.2.d.h.251.1 | 4 | |||
100.23 | even | 20 | 125.2.e.a.24.1 | 8 | |||
100.27 | even | 20 | 125.2.e.a.24.2 | 8 | |||
100.31 | odd | 10 | 625.2.d.b.251.1 | 4 | |||
100.39 | odd | 10 | 25.2.d.a.21.1 | yes | 4 | ||
100.47 | even | 20 | 625.2.e.c.249.2 | 8 | |||
100.59 | odd | 10 | 25.2.d.a.6.1 | ✓ | 4 | ||
100.63 | even | 20 | 125.2.e.a.99.2 | 8 | |||
100.67 | even | 20 | 625.2.e.c.374.1 | 8 | |||
100.71 | odd | 10 | 625.2.d.b.376.1 | 4 | |||
100.79 | odd | 10 | 625.2.d.h.376.1 | 4 | |||
100.83 | even | 20 | 625.2.e.c.374.2 | 8 | |||
100.87 | even | 20 | 125.2.e.a.99.1 | 8 | |||
100.91 | odd | 10 | 125.2.d.a.26.1 | 4 | |||
300.59 | even | 10 | 225.2.h.b.181.1 | 4 | |||
300.239 | even | 10 | 225.2.h.b.46.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.6.1 | ✓ | 4 | 100.59 | odd | 10 | ||
25.2.d.a.21.1 | yes | 4 | 100.39 | odd | 10 | ||
125.2.d.a.26.1 | 4 | 100.91 | odd | 10 | |||
125.2.d.a.101.1 | 4 | 100.11 | odd | 10 | |||
125.2.e.a.24.1 | 8 | 100.23 | even | 20 | |||
125.2.e.a.24.2 | 8 | 100.27 | even | 20 | |||
125.2.e.a.99.1 | 8 | 100.87 | even | 20 | |||
125.2.e.a.99.2 | 8 | 100.63 | even | 20 | |||
225.2.h.b.46.1 | 4 | 300.239 | even | 10 | |||
225.2.h.b.181.1 | 4 | 300.59 | even | 10 | |||
400.2.u.b.81.1 | 4 | 25.9 | even | 10 | |||
400.2.u.b.321.1 | 4 | 25.14 | even | 10 | |||
625.2.a.b.1.1 | 2 | 20.19 | odd | 2 | |||
625.2.a.c.1.2 | 2 | 4.3 | odd | 2 | |||
625.2.b.a.624.1 | 4 | 20.3 | even | 4 | |||
625.2.b.a.624.4 | 4 | 20.7 | even | 4 | |||
625.2.d.b.251.1 | 4 | 100.31 | odd | 10 | |||
625.2.d.b.376.1 | 4 | 100.71 | odd | 10 | |||
625.2.d.h.251.1 | 4 | 100.19 | odd | 10 | |||
625.2.d.h.376.1 | 4 | 100.79 | odd | 10 | |||
625.2.e.c.249.1 | 8 | 100.3 | even | 20 | |||
625.2.e.c.249.2 | 8 | 100.47 | even | 20 | |||
625.2.e.c.374.1 | 8 | 100.67 | even | 20 | |||
625.2.e.c.374.2 | 8 | 100.83 | even | 20 | |||
5625.2.a.d.1.1 | 2 | 12.11 | even | 2 | |||
5625.2.a.f.1.2 | 2 | 60.59 | even | 2 | |||
10000.2.a.c.1.1 | 2 | 5.4 | even | 2 | |||
10000.2.a.l.1.2 | 2 | 1.1 | even | 1 | trivial |