Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(12.5764383184\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.23607 | −1.27722 | −0.638611 | − | 0.769529i | \(-0.720491\pi\) | ||||
−0.638611 | + | 0.769529i | \(0.720491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23607 | 0.897524 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(14\) | −1.61803 | −0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −6.47214 | −1.56972 | −0.784862 | − | 0.619671i | \(-0.787266\pi\) | ||||
−0.784862 | + | 0.619671i | \(0.787266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.85410 | −1.46130 | ||||||||
\(23\) | 1.76393 | 0.367805 | 0.183903 | − | 0.982944i | \(-0.441127\pi\) | ||||
0.183903 | + | 0.982944i | \(0.441127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.23607 | 1.02688 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.618034 | −0.116797 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.70820 | −1.74364 | −0.871822 | − | 0.489822i | \(-0.837062\pi\) | ||||
−0.871822 | + | 0.489822i | \(0.837062\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.4721 | −1.79596 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | −0.493197 | −0.246598 | − | 0.969118i | \(-0.579313\pi\) | ||||
−0.246598 | + | 0.969118i | \(0.579313\pi\) | |||||||
\(38\) | 7.23607 | 1.17385 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.23607 | −1.44243 | −0.721216 | − | 0.692711i | \(-0.756416\pi\) | ||||
−0.721216 | + | 0.692711i | \(0.756416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.23607 | −0.950991 | −0.475496 | − | 0.879718i | \(-0.657731\pi\) | ||||
−0.475496 | + | 0.879718i | \(0.657731\pi\) | |||||||
\(44\) | −2.61803 | −0.394683 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.85410 | 0.420814 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.09017 | −1.06229 | ||||||||
\(59\) | 1.70820 | 0.222389 | 0.111195 | − | 0.993799i | \(-0.464532\pi\) | ||||
0.111195 | + | 0.993799i | \(0.464532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.70820 | 0.474787 | 0.237393 | − | 0.971414i | \(-0.423707\pi\) | ||||
0.237393 | + | 0.971414i | \(0.423707\pi\) | |||||||
\(62\) | −15.7082 | −1.99494 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.236068 | −0.0288403 | −0.0144201 | − | 0.999896i | \(-0.504590\pi\) | ||||
−0.0144201 | + | 0.999896i | \(0.504590\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.70820 | 0.558761 | 0.279381 | − | 0.960180i | \(-0.409871\pi\) | ||||
0.279381 | + | 0.960180i | \(0.409871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2361 | 1.54916 | 0.774582 | − | 0.632473i | \(-0.217960\pi\) | ||||
0.774582 | + | 0.632473i | \(0.217960\pi\) | |||||||
\(74\) | −4.85410 | −0.564278 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.76393 | 0.317045 | ||||||||
\(77\) | 4.23607 | 0.482745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1803 | 1.25789 | 0.628943 | − | 0.777451i | \(-0.283488\pi\) | ||||
0.628943 | + | 0.777451i | \(0.283488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.9443 | −1.65032 | ||||||||
\(83\) | 5.70820 | 0.626557 | 0.313278 | − | 0.949661i | \(-0.398573\pi\) | ||||
0.313278 | + | 0.949661i | \(0.398573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.0902 | −1.08805 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.47214 | 1.00973 | ||||||||
\(89\) | −12.7639 | −1.35297 | −0.676487 | − | 0.736455i | \(-0.736499\pi\) | ||||
−0.676487 | + | 0.736455i | \(0.736499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23607 | −0.339232 | ||||||||
\(92\) | 1.09017 | 0.113658 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.23607 | −0.333775 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.763932 | −0.0775655 | −0.0387828 | − | 0.999248i | \(-0.512348\pi\) | ||||
−0.0387828 | + | 0.999248i | \(0.512348\pi\) | |||||||
\(98\) | 1.61803 | 0.163446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.23607 | −0.919023 | −0.459512 | − | 0.888172i | \(-0.651976\pi\) | ||||
−0.459512 | + | 0.888172i | \(0.651976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.472136 | 0.0465209 | 0.0232605 | − | 0.999729i | \(-0.492595\pi\) | ||||
0.0232605 | + | 0.999729i | \(0.492595\pi\) | |||||||
\(104\) | −7.23607 | −0.709555 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.763932 | −0.0741996 | ||||||||
\(107\) | 8.00000 | 0.773389 | 0.386695 | − | 0.922208i | \(-0.373617\pi\) | ||||
0.386695 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.4164 | −1.76397 | −0.881986 | − | 0.471276i | \(-0.843794\pi\) | ||||
−0.881986 | + | 0.471276i | \(0.843794\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.85410 | 0.458670 | ||||||||
\(113\) | 12.4164 | 1.16804 | 0.584019 | − | 0.811740i | \(-0.301479\pi\) | ||||
0.584019 | + | 0.811740i | \(0.301479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.09017 | −0.286915 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.76393 | 0.254441 | ||||||||
\(119\) | 6.47214 | 0.593300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.94427 | 0.631297 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6525 | 1.56640 | 0.783202 | − | 0.621767i | \(-0.213585\pi\) | ||||
0.783202 | + | 0.621767i | \(0.213585\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.944272 | −0.0825014 | −0.0412507 | − | 0.999149i | \(-0.513134\pi\) | ||||
−0.0412507 | + | 0.999149i | \(0.513134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.47214 | −0.387783 | ||||||||
\(134\) | −0.381966 | −0.0329968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.4721 | 1.24098 | ||||||||
\(137\) | 6.94427 | 0.593289 | 0.296645 | − | 0.954988i | \(-0.404132\pi\) | ||||
0.296645 | + | 0.954988i | \(0.404132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.6525 | −1.75172 | −0.875860 | − | 0.482565i | \(-0.839705\pi\) | ||||
−0.875860 | + | 0.482565i | \(0.839705\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.61803 | 0.639291 | ||||||||
\(143\) | −13.7082 | −1.14634 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 21.4164 | 1.77243 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.85410 | −0.152406 | ||||||||
\(149\) | 13.9443 | 1.14236 | 0.571180 | − | 0.820825i | \(-0.306486\pi\) | ||||
0.571180 | + | 0.820825i | \(0.306486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7639 | −1.28285 | −0.641425 | − | 0.767185i | \(-0.721657\pi\) | ||||
−0.641425 | + | 0.767185i | \(0.721657\pi\) | |||||||
\(152\) | −10.0000 | −0.811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.85410 | 0.552319 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.23607 | −0.417884 | −0.208942 | − | 0.977928i | \(-0.567002\pi\) | ||||
−0.208942 | + | 0.977928i | \(0.567002\pi\) | |||||||
\(158\) | 18.0902 | 1.43918 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.76393 | −0.139017 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4721 | 0.820241 | 0.410120 | − | 0.912031i | \(-0.365487\pi\) | ||||
0.410120 | + | 0.912031i | \(0.365487\pi\) | |||||||
\(164\) | −5.70820 | −0.445736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.23607 | 0.716858 | ||||||||
\(167\) | 0.763932 | 0.0591148 | 0.0295574 | − | 0.999563i | \(-0.490590\pi\) | ||||
0.0295574 | + | 0.999563i | \(0.490590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.85410 | −0.293873 | ||||||||
\(173\) | −20.4721 | −1.55647 | −0.778234 | − | 0.627975i | \(-0.783884\pi\) | ||||
−0.778234 | + | 0.627975i | \(0.783884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.5623 | 1.54994 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.6525 | −1.54797 | ||||||||
\(179\) | −3.41641 | −0.255354 | −0.127677 | − | 0.991816i | \(-0.540752\pi\) | ||||
−0.127677 | + | 0.991816i | \(0.540752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1803 | −1.05402 | −0.527008 | − | 0.849860i | \(-0.676686\pi\) | ||||
−0.527008 | + | 0.849860i | \(0.676686\pi\) | |||||||
\(182\) | −5.23607 | −0.388123 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.94427 | −0.290776 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.4164 | 2.00489 | ||||||||
\(188\) | −1.23607 | −0.0901495 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.47214 | 0.178877 | 0.0894387 | − | 0.995992i | \(-0.471493\pi\) | ||||
0.0894387 | + | 0.995992i | \(0.471493\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4164 | 1.03772 | 0.518858 | − | 0.854861i | \(-0.326357\pi\) | ||||
0.518858 | + | 0.854861i | \(0.326357\pi\) | |||||||
\(194\) | −1.23607 | −0.0887445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | 7.47214 | 0.532368 | 0.266184 | − | 0.963922i | \(-0.414237\pi\) | ||||
0.266184 | + | 0.963922i | \(0.414237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.76393 | 0.195930 | 0.0979650 | − | 0.995190i | \(-0.468767\pi\) | ||||
0.0979650 | + | 0.995190i | \(0.468767\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.9443 | −1.05148 | ||||||||
\(203\) | 5.00000 | 0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.763932 | 0.0532257 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.7082 | −1.08917 | ||||||||
\(209\) | −18.9443 | −1.31040 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | −0.291796 | −0.0200406 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.9443 | 0.884852 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.70820 | 0.659036 | ||||||||
\(218\) | −29.7984 | −2.01820 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.9443 | −1.40886 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.18034 | 0.146006 | 0.0730032 | − | 0.997332i | \(-0.476742\pi\) | ||||
0.0730032 | + | 0.997332i | \(0.476742\pi\) | |||||||
\(224\) | 3.38197 | 0.225967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0902 | 1.33638 | ||||||||
\(227\) | −5.41641 | −0.359500 | −0.179750 | − | 0.983712i | \(-0.557529\pi\) | ||||
−0.179750 | + | 0.983712i | \(0.557529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.47214 | 0.295527 | 0.147764 | − | 0.989023i | \(-0.452793\pi\) | ||||
0.147764 | + | 0.989023i | \(0.452793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.1803 | 0.734025 | ||||||||
\(233\) | −9.94427 | −0.651471 | −0.325735 | − | 0.945461i | \(-0.605612\pi\) | ||||
−0.325735 | + | 0.945461i | \(0.605612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.05573 | 0.0687220 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.4721 | 0.678808 | ||||||||
\(239\) | 14.4721 | 0.936125 | 0.468062 | − | 0.883695i | \(-0.344952\pi\) | ||||
0.468062 | + | 0.883695i | \(0.344952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4721 | −0.803401 | −0.401700 | − | 0.915771i | \(-0.631581\pi\) | ||||
−0.401700 | + | 0.915771i | \(0.631581\pi\) | |||||||
\(242\) | 11.2361 | 0.722282 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.29180 | 0.146717 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4721 | 0.920840 | ||||||||
\(248\) | 21.7082 | 1.37847 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.47214 | 0.156040 | 0.0780199 | − | 0.996952i | \(-0.475140\pi\) | ||||
0.0780199 | + | 0.996952i | \(0.475140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.47214 | −0.469769 | ||||||||
\(254\) | 28.5623 | 1.79216 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 18.6525 | 1.16351 | 0.581755 | − | 0.813364i | \(-0.302366\pi\) | ||||
0.581755 | + | 0.813364i | \(0.302366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | 0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.52786 | −0.0943918 | ||||||||
\(263\) | 11.7639 | 0.725395 | 0.362698 | − | 0.931907i | \(-0.381856\pi\) | ||||
0.362698 | + | 0.931907i | \(0.381856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.23607 | −0.443672 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.145898 | −0.00891214 | ||||||||
\(269\) | −1.70820 | −0.104151 | −0.0520755 | − | 0.998643i | \(-0.516584\pi\) | ||||
−0.0520755 | + | 0.998643i | \(0.516584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2918 | 0.625182 | 0.312591 | − | 0.949888i | \(-0.398803\pi\) | ||||
0.312591 | + | 0.949888i | \(0.398803\pi\) | |||||||
\(272\) | 31.4164 | 1.90490 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2361 | 0.678796 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8885 | −0.954650 | −0.477325 | − | 0.878727i | \(-0.658394\pi\) | ||||
−0.477325 | + | 0.878727i | \(0.658394\pi\) | |||||||
\(278\) | −33.4164 | −2.00418 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.3607 | −1.75151 | −0.875756 | − | 0.482755i | \(-0.839636\pi\) | ||||
−0.875756 | + | 0.482755i | \(0.839636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.41641 | 0.559747 | 0.279874 | − | 0.960037i | \(-0.409707\pi\) | ||||
0.279874 | + | 0.960037i | \(0.409707\pi\) | |||||||
\(284\) | 2.90983 | 0.172667 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.1803 | −1.31155 | ||||||||
\(287\) | 9.23607 | 0.545188 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.18034 | 0.478718 | ||||||||
\(293\) | 9.12461 | 0.533066 | 0.266533 | − | 0.963826i | \(-0.414122\pi\) | ||||
0.266533 | + | 0.963826i | \(0.414122\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.70820 | 0.389906 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.5623 | 1.30700 | ||||||||
\(299\) | 5.70820 | 0.330114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.23607 | 0.359441 | ||||||||
\(302\) | −25.5066 | −1.46774 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.7082 | −1.24505 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.4164 | −1.79303 | −0.896515 | − | 0.443014i | \(-0.853909\pi\) | ||||
−0.896515 | + | 0.443014i | \(0.853909\pi\) | |||||||
\(308\) | 2.61803 | 0.149176 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3607 | 1.15455 | 0.577274 | − | 0.816550i | \(-0.304116\pi\) | ||||
0.577274 | + | 0.816550i | \(0.304116\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.4721 | −1.60934 | −0.804670 | − | 0.593722i | \(-0.797658\pi\) | ||||
−0.804670 | + | 0.593722i | \(0.797658\pi\) | |||||||
\(314\) | −8.47214 | −0.478110 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.90983 | 0.388708 | ||||||||
\(317\) | −19.3607 | −1.08740 | −0.543702 | − | 0.839278i | \(-0.682978\pi\) | ||||
−0.543702 | + | 0.839278i | \(0.682978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.1803 | 1.18587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.85410 | −0.159053 | ||||||||
\(323\) | −28.9443 | −1.61050 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.9443 | 0.938456 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.6525 | 1.14034 | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.2918 | −0.620653 | −0.310327 | − | 0.950630i | \(-0.600438\pi\) | ||||
−0.310327 | + | 0.950630i | \(0.600438\pi\) | |||||||
\(332\) | 3.52786 | 0.193617 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.23607 | 0.0676346 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.52786 | 0.410069 | 0.205034 | − | 0.978755i | \(-0.434269\pi\) | ||||
0.205034 | + | 0.978755i | \(0.434269\pi\) | |||||||
\(338\) | −4.09017 | −0.222476 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.1246 | 2.22702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 13.9443 | 0.751825 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.1246 | −1.78079 | ||||||||
\(347\) | 15.7639 | 0.846252 | 0.423126 | − | 0.906071i | \(-0.360933\pi\) | ||||
0.423126 | + | 0.906071i | \(0.360933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.47214 | −0.239388 | −0.119694 | − | 0.992811i | \(-0.538191\pi\) | ||||
−0.119694 | + | 0.992811i | \(0.538191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.3262 | 0.763591 | ||||||||
\(353\) | 20.1803 | 1.07409 | 0.537046 | − | 0.843553i | \(-0.319540\pi\) | ||||
0.537046 | + | 0.843553i | \(0.319540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.88854 | −0.418092 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.52786 | −0.292157 | ||||||||
\(359\) | −10.1246 | −0.534357 | −0.267178 | − | 0.963647i | \(-0.586091\pi\) | ||||
−0.267178 | + | 0.963647i | \(0.586091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −22.9443 | −1.20592 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.12461 | −0.163103 | −0.0815517 | − | 0.996669i | \(-0.525988\pi\) | ||||
−0.0815517 | + | 0.996669i | \(0.525988\pi\) | |||||||
\(368\) | −8.56231 | −0.446341 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.472136 | 0.0245121 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.8328 | −0.819792 | −0.409896 | − | 0.912132i | \(-0.634435\pi\) | ||||
−0.409896 | + | 0.912132i | \(0.634435\pi\) | |||||||
\(374\) | 44.3607 | 2.29384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.47214 | 0.230633 | ||||||||
\(377\) | −16.1803 | −0.833330 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1803 | 0.574295 | 0.287148 | − | 0.957886i | \(-0.407293\pi\) | ||||
0.287148 | + | 0.957886i | \(0.407293\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.00000 | 0.204658 | ||||||||
\(383\) | −28.7639 | −1.46977 | −0.734884 | − | 0.678193i | \(-0.762763\pi\) | ||||
−0.734884 | + | 0.678193i | \(0.762763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.3262 | 1.18727 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.472136 | −0.0239691 | ||||||||
\(389\) | 32.8885 | 1.66752 | 0.833758 | − | 0.552131i | \(-0.186185\pi\) | ||||
0.833758 | + | 0.552131i | \(0.186185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4164 | −0.577353 | ||||||||
\(392\) | −2.23607 | −0.112938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0902 | 0.609094 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.9443 | −1.35229 | −0.676147 | − | 0.736767i | \(-0.736352\pi\) | ||||
−0.676147 | + | 0.736767i | \(0.736352\pi\) | |||||||
\(398\) | 4.47214 | 0.224168 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.4721 | −0.572891 | −0.286446 | − | 0.958097i | \(-0.592474\pi\) | ||||
−0.286446 | + | 0.958097i | \(0.592474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.4164 | −1.56496 | ||||||||
\(404\) | −5.70820 | −0.283994 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.09017 | 0.401508 | ||||||||
\(407\) | 12.7082 | 0.629922 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5279 | 0.767803 | 0.383902 | − | 0.923374i | \(-0.374580\pi\) | ||||
0.383902 | + | 0.923374i | \(0.374580\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.291796 | 0.0143758 | ||||||||
\(413\) | −1.70820 | −0.0840552 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.9443 | −0.536587 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −30.6525 | −1.49926 | ||||||||
\(419\) | 3.81966 | 0.186603 | 0.0933013 | − | 0.995638i | \(-0.470258\pi\) | ||||
0.0933013 | + | 0.995638i | \(0.470258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(422\) | 19.4164 | 0.945176 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.05573 | 0.0512707 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.70820 | −0.179453 | ||||||||
\(428\) | 4.94427 | 0.238990 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.4721 | −1.27512 | −0.637559 | − | 0.770402i | \(-0.720056\pi\) | ||||
−0.637559 | + | 0.770402i | \(0.720056\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.3607 | −0.786244 | −0.393122 | − | 0.919486i | \(-0.628605\pi\) | ||||
−0.393122 | + | 0.919486i | \(0.628605\pi\) | |||||||
\(434\) | 15.7082 | 0.754018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.3820 | −0.545097 | ||||||||
\(437\) | 7.88854 | 0.377360 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.7082 | −1.03608 | −0.518038 | − | 0.855358i | \(-0.673337\pi\) | ||||
−0.518038 | + | 0.855358i | \(0.673337\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −33.8885 | −1.61191 | ||||||||
\(443\) | 7.41641 | 0.352364 | 0.176182 | − | 0.984358i | \(-0.443625\pi\) | ||||
0.176182 | + | 0.984358i | \(0.443625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.52786 | 0.167049 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.23607 | −0.200135 | ||||||||
\(449\) | −29.4721 | −1.39088 | −0.695438 | − | 0.718586i | \(-0.744790\pi\) | ||||
−0.695438 | + | 0.718586i | \(0.744790\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.1246 | 1.84231 | ||||||||
\(452\) | 7.67376 | 0.360943 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.76393 | −0.411312 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4721 | 1.00442 | 0.502212 | − | 0.864744i | \(-0.332520\pi\) | ||||
0.502212 | + | 0.864744i | \(0.332520\pi\) | |||||||
\(458\) | 7.23607 | 0.338119 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.18034 | −0.380996 | −0.190498 | − | 0.981688i | \(-0.561010\pi\) | ||||
−0.190498 | + | 0.981688i | \(0.561010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.8885 | −1.01725 | −0.508623 | − | 0.860989i | \(-0.669845\pi\) | ||||
−0.508623 | + | 0.860989i | \(0.669845\pi\) | |||||||
\(464\) | 24.2705 | 1.12673 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.0902 | −0.745363 | ||||||||
\(467\) | −10.9443 | −0.506441 | −0.253220 | − | 0.967409i | \(-0.581490\pi\) | ||||
−0.253220 | + | 0.967409i | \(0.581490\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.236068 | 0.0109006 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.81966 | −0.175814 | ||||||||
\(473\) | 26.4164 | 1.21463 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.4164 | 1.07104 | ||||||||
\(479\) | 3.81966 | 0.174525 | 0.0872624 | − | 0.996185i | \(-0.472188\pi\) | ||||
0.0872624 | + | 0.996185i | \(0.472188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.70820 | −0.442656 | ||||||||
\(482\) | −20.1803 | −0.919189 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.29180 | 0.195082 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.2361 | −0.463841 | −0.231920 | − | 0.972735i | \(-0.574501\pi\) | ||||
−0.231920 | + | 0.972735i | \(0.574501\pi\) | |||||||
\(488\) | −8.29180 | −0.375352 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2361 | 0.461947 | 0.230974 | − | 0.972960i | \(-0.425809\pi\) | ||||
0.230974 | + | 0.972960i | \(0.425809\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.3607 | 1.45745 | ||||||||
\(494\) | 23.4164 | 1.05355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 47.1246 | 2.11596 | ||||||||
\(497\) | −4.70820 | −0.211192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.9443 | 1.29572 | 0.647862 | − | 0.761758i | \(-0.275663\pi\) | ||||
0.647862 | + | 0.761758i | \(0.275663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.00000 | 0.178529 | ||||||||
\(503\) | −43.8885 | −1.95689 | −0.978447 | − | 0.206499i | \(-0.933793\pi\) | ||||
−0.978447 | + | 0.206499i | \(0.933793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.0902 | −0.537474 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.9098 | 0.484045 | ||||||||
\(509\) | −9.34752 | −0.414322 | −0.207161 | − | 0.978307i | \(-0.566422\pi\) | ||||
−0.207161 | + | 0.978307i | \(0.566422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.2361 | −0.585529 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.1803 | 1.33120 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.47214 | 0.372604 | ||||||||
\(518\) | 4.85410 | 0.213277 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3607 | 1.24013 | 0.620063 | − | 0.784552i | \(-0.287107\pi\) | ||||
0.620063 | + | 0.784552i | \(0.287107\pi\) | |||||||
\(524\) | −0.583592 | −0.0254943 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.0344 | 0.829941 | ||||||||
\(527\) | 62.8328 | 2.73704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8885 | −0.864719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.76393 | −0.119832 | ||||||||
\(533\) | −29.8885 | −1.29462 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.527864 | 0.0228003 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.76393 | −0.119162 | ||||||||
\(539\) | −4.23607 | −0.182460 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.94427 | −0.0835908 | −0.0417954 | − | 0.999126i | \(-0.513308\pi\) | ||||
−0.0417954 | + | 0.999126i | \(0.513308\pi\) | |||||||
\(542\) | 16.6525 | 0.715285 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.8885 | 0.938464 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2361 | 0.608690 | 0.304345 | − | 0.952562i | \(-0.401562\pi\) | ||||
0.304345 | + | 0.952562i | \(0.401562\pi\) | |||||||
\(548\) | 4.29180 | 0.183336 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.3607 | −0.952597 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1803 | −0.475436 | ||||||||
\(554\) | −25.7082 | −1.09224 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.7639 | −0.541311 | ||||||||
\(557\) | −44.8885 | −1.90199 | −0.950994 | − | 0.309208i | \(-0.899936\pi\) | ||||
−0.950994 | + | 0.309208i | \(0.899936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.1803 | −0.853537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −47.5066 | −2.00394 | ||||||||
\(563\) | −9.41641 | −0.396854 | −0.198427 | − | 0.980116i | \(-0.563583\pi\) | ||||
−0.198427 | + | 0.980116i | \(0.563583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.2361 | 0.640420 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.5279 | −0.441739 | ||||||||
\(569\) | −13.9443 | −0.584574 | −0.292287 | − | 0.956331i | \(-0.594416\pi\) | ||||
−0.292287 | + | 0.956331i | \(0.594416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5967 | −0.527157 | −0.263579 | − | 0.964638i | \(-0.584903\pi\) | ||||
−0.263579 | + | 0.964638i | \(0.584903\pi\) | |||||||
\(572\) | −8.47214 | −0.354238 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.9443 | 0.623762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 40.2705 | 1.67503 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.70820 | −0.236816 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | 0.0828315 | ||||||||
\(584\) | −29.5967 | −1.22472 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7639 | 0.609892 | ||||||||
\(587\) | −29.2361 | −1.20670 | −0.603351 | − | 0.797476i | \(-0.706168\pi\) | ||||
−0.603351 | + | 0.797476i | \(0.706168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.4164 | −1.78894 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.5623 | 0.598507 | ||||||||
\(593\) | 25.3050 | 1.03915 | 0.519575 | − | 0.854425i | \(-0.326090\pi\) | ||||
0.519575 | + | 0.854425i | \(0.326090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.61803 | 0.353008 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.23607 | 0.377691 | ||||||||
\(599\) | −11.1803 | −0.456816 | −0.228408 | − | 0.973565i | \(-0.573352\pi\) | ||||
−0.228408 | + | 0.973565i | \(0.573352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0557 | −0.777299 | −0.388650 | − | 0.921386i | \(-0.627058\pi\) | ||||
−0.388650 | + | 0.921386i | \(0.627058\pi\) | |||||||
\(602\) | 10.0902 | 0.411245 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.74265 | −0.396423 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.1246 | −1.34449 | −0.672243 | − | 0.740330i | \(-0.734669\pi\) | ||||
−0.672243 | + | 0.740330i | \(0.734669\pi\) | |||||||
\(608\) | −15.1246 | −0.613384 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.47214 | −0.261835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.5836 | 0.710195 | 0.355097 | − | 0.934829i | \(-0.384448\pi\) | ||||
0.355097 | + | 0.934829i | \(0.384448\pi\) | |||||||
\(614\) | −50.8328 | −2.05145 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.47214 | −0.381643 | ||||||||
\(617\) | 11.9443 | 0.480858 | 0.240429 | − | 0.970667i | \(-0.422712\pi\) | ||||
0.240429 | + | 0.970667i | \(0.422712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.70820 | 0.0686585 | 0.0343293 | − | 0.999411i | \(-0.489071\pi\) | ||||
0.0343293 | + | 0.999411i | \(0.489071\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.9443 | 1.32094 | ||||||||
\(623\) | 12.7639 | 0.511376 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −46.0689 | −1.84128 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.23607 | −0.129133 | ||||||||
\(629\) | 19.4164 | 0.774183 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.65248 | −0.145403 | −0.0727014 | − | 0.997354i | \(-0.523162\pi\) | ||||
−0.0727014 | + | 0.997354i | \(0.523162\pi\) | |||||||
\(632\) | −25.0000 | −0.994447 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −31.3262 | −1.24412 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23607 | 0.128218 | ||||||||
\(638\) | 34.2705 | 1.35678 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.83282 | 0.388373 | 0.194186 | − | 0.980965i | \(-0.437793\pi\) | ||||
0.194186 | + | 0.980965i | \(0.437793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.52786 | −0.375742 | −0.187871 | − | 0.982194i | \(-0.560159\pi\) | ||||
−0.187871 | + | 0.982194i | \(0.560159\pi\) | |||||||
\(644\) | −1.09017 | −0.0429587 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −46.8328 | −1.84261 | ||||||||
\(647\) | 15.8885 | 0.624643 | 0.312322 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312322 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.23607 | −0.284041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.47214 | 0.253468 | ||||||||
\(653\) | 42.9443 | 1.68054 | 0.840270 | − | 0.542169i | \(-0.182397\pi\) | ||||
0.840270 | + | 0.542169i | \(0.182397\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 44.8328 | 1.75043 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.23607 | 0.126155 | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.7214 | 1.81725 | 0.908625 | − | 0.417613i | \(-0.137133\pi\) | ||||
0.908625 | + | 0.417613i | \(0.137133\pi\) | |||||||
\(662\) | −18.2705 | −0.710104 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.7639 | −0.495337 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.81966 | −0.341499 | ||||||||
\(668\) | 0.472136 | 0.0182675 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.7082 | −0.606408 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4721 | −1.09752 | −0.548760 | − | 0.835980i | \(-0.684900\pi\) | ||||
−0.548760 | + | 0.835980i | \(0.684900\pi\) | |||||||
\(674\) | 12.1803 | 0.469169 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.56231 | −0.0600887 | ||||||||
\(677\) | 30.3607 | 1.16686 | 0.583428 | − | 0.812165i | \(-0.301711\pi\) | ||||
0.583428 | + | 0.812165i | \(0.301711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.763932 | 0.0293170 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 66.5410 | 2.54799 | ||||||||
\(683\) | −26.1246 | −0.999630 | −0.499815 | − | 0.866132i | \(-0.666599\pi\) | ||||
−0.499815 | + | 0.866132i | \(0.666599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.61803 | −0.0617768 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.2705 | 1.15405 | ||||||||
\(689\) | −1.52786 | −0.0582070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1803 | 0.691613 | 0.345806 | − | 0.938306i | \(-0.387605\pi\) | ||||
0.345806 | + | 0.938306i | \(0.387605\pi\) | |||||||
\(692\) | −12.6525 | −0.480975 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.5066 | 0.968216 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 59.7771 | 2.26422 | ||||||||
\(698\) | −7.23607 | −0.273889 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.9443 | 1.77306 | 0.886530 | − | 0.462670i | \(-0.153109\pi\) | ||||
0.886530 | + | 0.462670i | \(0.153109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.4164 | −0.506009 | ||||||||
\(704\) | −17.9443 | −0.676300 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.6525 | 1.22889 | ||||||||
\(707\) | 9.23607 | 0.347358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.8885 | −1.79849 | −0.899246 | − | 0.437443i | \(-0.855884\pi\) | ||||
−0.899246 | + | 0.437443i | \(0.855884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28.5410 | 1.06962 | ||||||||
\(713\) | −17.1246 | −0.641322 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.11146 | −0.0789088 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.3820 | −0.611370 | ||||||||
\(719\) | 6.18034 | 0.230488 | 0.115244 | − | 0.993337i | \(-0.463235\pi\) | ||||
0.115244 | + | 0.993337i | \(0.463235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.472136 | −0.0175833 | ||||||||
\(722\) | 1.61803 | 0.0602170 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.76393 | −0.325709 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.9443 | 0.776780 | 0.388390 | − | 0.921495i | \(-0.373031\pi\) | ||||
0.388390 | + | 0.921495i | \(0.373031\pi\) | |||||||
\(728\) | 7.23607 | 0.268187 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.3607 | 1.49279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.00000 | −0.147743 | −0.0738717 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738717 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(734\) | −5.05573 | −0.186610 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.96556 | −0.219893 | ||||||||
\(737\) | 1.00000 | 0.0368355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.65248 | −0.207930 | −0.103965 | − | 0.994581i | \(-0.533153\pi\) | ||||
−0.103965 | + | 0.994581i | \(0.533153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.763932 | 0.0280448 | ||||||||
\(743\) | −1.52786 | −0.0560519 | −0.0280259 | − | 0.999607i | \(-0.508922\pi\) | ||||
−0.0280259 | + | 0.999607i | \(0.508922\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25.6180 | −0.937943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.9443 | 0.619544 | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9443 | 0.764267 | 0.382134 | − | 0.924107i | \(-0.375189\pi\) | ||||
0.382134 | + | 0.924107i | \(0.375189\pi\) | |||||||
\(752\) | 9.70820 | 0.354022 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −26.1803 | −0.953432 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.4164 | −1.68703 | −0.843517 | − | 0.537103i | \(-0.819519\pi\) | ||||
−0.843517 | + | 0.537103i | \(0.819519\pi\) | |||||||
\(758\) | 18.0902 | 0.657065 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.7771 | 1.58692 | 0.793459 | − | 0.608624i | \(-0.208278\pi\) | ||||
0.793459 | + | 0.608624i | \(0.208278\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.4164 | 0.666719 | ||||||||
\(764\) | 1.52786 | 0.0552762 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −46.5410 | −1.68160 | ||||||||
\(767\) | 5.52786 | 0.199600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.0132 | 1.19048 | 0.595242 | − | 0.803546i | \(-0.297056\pi\) | ||||
0.595242 | + | 0.803546i | \(0.297056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.90983 | 0.320672 | ||||||||
\(773\) | 27.8197 | 1.00060 | 0.500302 | − | 0.865851i | \(-0.333222\pi\) | ||||
0.500302 | + | 0.865851i | \(0.333222\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.70820 | 0.0613209 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 53.2148 | 1.90784 | ||||||||
\(779\) | −41.3050 | −1.47990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.9443 | −0.713662 | ||||||||
\(782\) | −18.4721 | −0.660562 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.2361 | −1.61249 | −0.806246 | − | 0.591581i | \(-0.798504\pi\) | ||||
−0.806246 | + | 0.591581i | \(0.798504\pi\) | |||||||
\(788\) | 4.61803 | 0.164511 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.4164 | −0.441477 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | −43.5967 | −1.54719 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.70820 | 0.0605457 | ||||||||
\(797\) | −8.58359 | −0.304046 | −0.152023 | − | 0.988377i | \(-0.548579\pi\) | ||||
−0.152023 | + | 0.988377i | \(0.548579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9443 | 0.457935 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.5623 | −0.655458 | ||||||||
\(803\) | −56.0689 | −1.97863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −50.8328 | −1.79051 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.6525 | 0.726552 | ||||||||
\(809\) | −20.5279 | −0.721721 | −0.360861 | − | 0.932620i | \(-0.617517\pi\) | ||||
−0.360861 | + | 0.932620i | \(0.617517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.7214 | 1.64061 | 0.820304 | − | 0.571927i | \(-0.193804\pi\) | ||||
0.820304 | + | 0.571927i | \(0.193804\pi\) | |||||||
\(812\) | 3.09017 | 0.108444 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.5623 | 0.720708 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.8885 | −0.975697 | ||||||||
\(818\) | 25.1246 | 0.878461 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8328 | 0.866671 | 0.433336 | − | 0.901233i | \(-0.357336\pi\) | ||||
0.433336 | + | 0.901233i | \(0.357336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.347524 | 0.0121139 | 0.00605697 | − | 0.999982i | \(-0.498072\pi\) | ||||
0.00605697 | + | 0.999982i | \(0.498072\pi\) | |||||||
\(824\) | −1.05573 | −0.0367780 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.76393 | −0.0961695 | ||||||||
\(827\) | −25.5410 | −0.888148 | −0.444074 | − | 0.895990i | \(-0.646467\pi\) | ||||
−0.444074 | + | 0.895990i | \(0.646467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.3607 | −1.81856 | −0.909281 | − | 0.416183i | \(-0.863368\pi\) | ||||
−0.909281 | + | 0.416183i | \(0.863368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.7082 | 0.475246 | ||||||||
\(833\) | −6.47214 | −0.224246 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.7082 | −0.404937 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.18034 | 0.213496 | ||||||||
\(839\) | −0.652476 | −0.0225260 | −0.0112630 | − | 0.999937i | \(-0.503585\pi\) | ||||
−0.0112630 | + | 0.999937i | \(0.503585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −21.0344 | −0.724895 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.41641 | 0.255283 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.94427 | −0.238608 | ||||||||
\(848\) | 2.29180 | 0.0787006 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.29180 | −0.181400 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.583592 | −0.0199818 | −0.00999091 | − | 0.999950i | \(-0.503180\pi\) | ||||
−0.00999091 | + | 0.999950i | \(0.503180\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.8885 | −0.611418 | ||||||||
\(857\) | −38.1803 | −1.30422 | −0.652108 | − | 0.758126i | \(-0.726115\pi\) | ||||
−0.652108 | + | 0.758126i | \(0.726115\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.3607 | −0.762937 | −0.381468 | − | 0.924382i | \(-0.624581\pi\) | ||||
−0.381468 | + | 0.924382i | \(0.624581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42.8328 | −1.45889 | ||||||||
\(863\) | 49.6525 | 1.69019 | 0.845095 | − | 0.534616i | \(-0.179544\pi\) | ||||
0.845095 | + | 0.534616i | \(0.179544\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26.4721 | −0.899560 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.00000 | 0.203653 | ||||||||
\(869\) | −47.3607 | −1.60660 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.763932 | −0.0258848 | ||||||||
\(872\) | 41.1803 | 1.39454 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.7639 | 0.431746 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3607 | 0.484926 | 0.242463 | − | 0.970161i | \(-0.422045\pi\) | ||||
0.242463 | + | 0.970161i | \(0.422045\pi\) | |||||||
\(878\) | −35.1246 | −1.18540 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.1803 | −0.949420 | −0.474710 | − | 0.880142i | \(-0.657447\pi\) | ||||
−0.474710 | + | 0.880142i | \(0.657447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.5967 | 1.70272 | 0.851358 | − | 0.524585i | \(-0.175780\pi\) | ||||
0.851358 | + | 0.524585i | \(0.175780\pi\) | |||||||
\(884\) | −12.9443 | −0.435363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | −52.6525 | −1.76790 | −0.883949 | − | 0.467584i | \(-0.845124\pi\) | ||||
−0.883949 | + | 0.467584i | \(0.845124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.6525 | −0.592045 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.34752 | 0.0451184 | ||||||||
\(893\) | −8.94427 | −0.299309 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.6180 | −0.454947 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47.6869 | −1.59133 | ||||||||
\(899\) | 48.5410 | 1.61893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.05573 | 0.101801 | ||||||||
\(902\) | 63.3050 | 2.10782 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.7639 | −0.923415 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.8328 | 0.625333 | 0.312667 | − | 0.949863i | \(-0.398778\pi\) | ||||
0.312667 | + | 0.949863i | \(0.398778\pi\) | |||||||
\(908\) | −3.34752 | −0.111091 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.1803 | −0.767999 | −0.383999 | − | 0.923333i | \(-0.625454\pi\) | ||||
−0.383999 | + | 0.923333i | \(0.625454\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.1803 | −0.800252 | ||||||||
\(914\) | 34.7426 | 1.14918 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.76393 | 0.0913229 | ||||||||
\(917\) | 0.944272 | 0.0311826 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.2361 | −1.06337 | −0.531685 | − | 0.846942i | \(-0.678441\pi\) | ||||
−0.531685 | + | 0.846942i | \(0.678441\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.2361 | −0.435907 | ||||||||
\(923\) | 15.2361 | 0.501501 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −35.4164 | −1.16386 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.9098 | 0.555092 | ||||||||
\(929\) | −51.7082 | −1.69649 | −0.848246 | − | 0.529603i | \(-0.822341\pi\) | ||||
−0.848246 | + | 0.529603i | \(0.822341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.47214 | 0.146568 | ||||||||
\(932\) | −6.14590 | −0.201316 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.7082 | −0.579430 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.7639 | −1.00501 | −0.502507 | − | 0.864573i | \(-0.667589\pi\) | ||||
−0.502507 | + | 0.864573i | \(0.667589\pi\) | |||||||
\(938\) | 0.381966 | 0.0124716 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.763932 | 0.0249035 | 0.0124517 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124517 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.2918 | −0.530534 | ||||||||
\(944\) | −8.29180 | −0.269875 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42.7426 | 1.38968 | ||||||||
\(947\) | −18.8328 | −0.611984 | −0.305992 | − | 0.952034i | \(-0.598988\pi\) | ||||
−0.305992 | + | 0.952034i | \(0.598988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.8328 | 1.39041 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.4721 | −0.469045 | ||||||||
\(953\) | −5.47214 | −0.177260 | −0.0886299 | − | 0.996065i | \(-0.528249\pi\) | ||||
−0.0886299 | + | 0.996065i | \(0.528249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.94427 | 0.289278 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.18034 | 0.199678 | ||||||||
\(959\) | −6.94427 | −0.224242 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.2492 | 2.04030 | ||||||||
\(962\) | −15.7082 | −0.506453 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.70820 | −0.248265 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.8885 | 1.60431 | 0.802154 | − | 0.597118i | \(-0.203687\pi\) | ||||
0.802154 | + | 0.597118i | \(0.203687\pi\) | |||||||
\(968\) | −15.5279 | −0.499084 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | 0.577647 | 0.288824 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288824 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.6525 | 0.662088 | ||||||||
\(974\) | −16.5623 | −0.530691 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.0000 | −0.576166 | ||||||||
\(977\) | −2.52786 | −0.0808735 | −0.0404368 | − | 0.999182i | \(-0.512875\pi\) | ||||
−0.0404368 | + | 0.999182i | \(0.512875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.0689 | 1.72805 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.5623 | 0.528524 | ||||||||
\(983\) | 32.5410 | 1.03790 | 0.518949 | − | 0.854805i | \(-0.326324\pi\) | ||||
0.518949 | + | 0.854805i | \(0.326324\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 52.3607 | 1.66750 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.94427 | 0.284555 | ||||||||
\(989\) | −11.0000 | −0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.18034 | −0.291623 | −0.145812 | − | 0.989312i | \(-0.546579\pi\) | ||||
−0.145812 | + | 0.989312i | \(0.546579\pi\) | |||||||
\(992\) | 32.8328 | 1.04244 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.61803 | −0.241629 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.5836 | 0.588548 | 0.294274 | − | 0.955721i | \(-0.404922\pi\) | ||||
0.294274 | + | 0.955721i | \(0.404922\pi\) | |||||||
\(998\) | 46.8328 | 1.48247 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.2.a.s.1.2 | 2 | ||
3.2 | odd | 2 | 175.2.a.d.1.1 | ✓ | 2 | ||
5.2 | odd | 4 | 1575.2.d.k.1324.4 | 4 | |||
5.3 | odd | 4 | 1575.2.d.k.1324.1 | 4 | |||
5.4 | even | 2 | 1575.2.a.n.1.1 | 2 | |||
12.11 | even | 2 | 2800.2.a.bh.1.2 | 2 | |||
15.2 | even | 4 | 175.2.b.c.99.1 | 4 | |||
15.8 | even | 4 | 175.2.b.c.99.4 | 4 | |||
15.14 | odd | 2 | 175.2.a.e.1.2 | yes | 2 | ||
21.20 | even | 2 | 1225.2.a.n.1.1 | 2 | |||
60.23 | odd | 4 | 2800.2.g.s.449.3 | 4 | |||
60.47 | odd | 4 | 2800.2.g.s.449.2 | 4 | |||
60.59 | even | 2 | 2800.2.a.bp.1.1 | 2 | |||
105.62 | odd | 4 | 1225.2.b.k.99.1 | 4 | |||
105.83 | odd | 4 | 1225.2.b.k.99.4 | 4 | |||
105.104 | even | 2 | 1225.2.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.a.d.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
175.2.a.e.1.2 | yes | 2 | 15.14 | odd | 2 | ||
175.2.b.c.99.1 | 4 | 15.2 | even | 4 | |||
175.2.b.c.99.4 | 4 | 15.8 | even | 4 | |||
1225.2.a.n.1.1 | 2 | 21.20 | even | 2 | |||
1225.2.a.u.1.2 | 2 | 105.104 | even | 2 | |||
1225.2.b.k.99.1 | 4 | 105.62 | odd | 4 | |||
1225.2.b.k.99.4 | 4 | 105.83 | odd | 4 | |||
1575.2.a.n.1.1 | 2 | 5.4 | even | 2 | |||
1575.2.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1575.2.d.k.1324.1 | 4 | 5.3 | odd | 4 | |||
1575.2.d.k.1324.4 | 4 | 5.2 | odd | 4 | |||
2800.2.a.bh.1.2 | 2 | 12.11 | even | 2 | |||
2800.2.a.bp.1.1 | 2 | 60.59 | even | 2 | |||
2800.2.g.s.449.2 | 4 | 60.47 | odd | 4 | |||
2800.2.g.s.449.3 | 4 | 60.23 | odd | 4 |