Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 1.61803 | 0.934172 | 0.467086 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.23607 | 0.467190 | 0.233595 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233595 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.61803 | 1.09088 | 0.545439 | − | 0.838150i | \(-0.316363\pi\) | ||||
0.545439 | + | 0.838150i | \(0.316363\pi\) | |||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | 0.381966 | 0.105938 | 0.0529692 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529692 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(14\) | −1.23607 | −0.330353 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.85410 | 0.934757 | 0.467379 | − | 0.884057i | \(-0.345199\pi\) | ||||
0.467379 | + | 0.884057i | \(0.345199\pi\) | |||||||
\(18\) | 0.381966 | 0.0900303 | ||||||||
\(19\) | 0.618034 | 0.141787 | 0.0708934 | − | 0.997484i | \(-0.477415\pi\) | ||||
0.0708934 | + | 0.997484i | \(0.477415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | −3.61803 | −0.771367 | ||||||||
\(23\) | −8.47214 | −1.76656 | −0.883281 | − | 0.468844i | \(-0.844671\pi\) | ||||
−0.883281 | + | 0.468844i | \(0.844671\pi\) | |||||||
\(24\) | 4.85410 | 0.990839 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.381966 | −0.0749097 | ||||||||
\(27\) | −5.47214 | −1.05311 | ||||||||
\(28\) | −1.23607 | −0.233595 | ||||||||
\(29\) | −7.09017 | −1.31661 | −0.658306 | − | 0.752751i | \(-0.728727\pi\) | ||||
−0.658306 | + | 0.752751i | \(0.728727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.52786 | −0.274412 | −0.137206 | − | 0.990543i | \(-0.543812\pi\) | ||||
−0.137206 | + | 0.990543i | \(0.543812\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 5.85410 | 1.01907 | ||||||||
\(34\) | −3.85410 | −0.660973 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.381966 | 0.0636610 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | −0.618034 | −0.100258 | ||||||||
\(39\) | 0.618034 | 0.0989646 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.09017 | −0.638777 | −0.319389 | − | 0.947624i | \(-0.603478\pi\) | ||||
−0.319389 | + | 0.947624i | \(0.603478\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | −6.47214 | −0.986991 | −0.493496 | − | 0.869748i | \(-0.664281\pi\) | ||||
−0.493496 | + | 0.869748i | \(0.664281\pi\) | |||||||
\(44\) | −3.61803 | −0.545439 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.47214 | 1.24915 | ||||||||
\(47\) | −7.85410 | −1.14564 | −0.572819 | − | 0.819682i | \(-0.694150\pi\) | ||||
−0.572819 | + | 0.819682i | \(0.694150\pi\) | |||||||
\(48\) | −1.61803 | −0.233543 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.23607 | 0.873224 | ||||||||
\(52\) | −0.381966 | −0.0529692 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 5.47214 | 0.744663 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.70820 | 0.495530 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 7.09017 | 0.930985 | ||||||||
\(59\) | −2.76393 | −0.359833 | −0.179917 | − | 0.983682i | \(-0.557583\pi\) | ||||
−0.179917 | + | 0.983682i | \(0.557583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.85410 | 0.621504 | 0.310752 | − | 0.950491i | \(-0.399419\pi\) | ||||
0.310752 | + | 0.950491i | \(0.399419\pi\) | |||||||
\(62\) | 1.52786 | 0.194039 | ||||||||
\(63\) | −0.472136 | −0.0594835 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.85410 | −0.720590 | ||||||||
\(67\) | −12.7984 | −1.56357 | −0.781785 | − | 0.623548i | \(-0.785691\pi\) | ||||
−0.781785 | + | 0.623548i | \(0.785691\pi\) | |||||||
\(68\) | −3.85410 | −0.467379 | ||||||||
\(69\) | −13.7082 | −1.65027 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.7984 | −1.75624 | −0.878122 | − | 0.478437i | \(-0.841204\pi\) | ||||
−0.878122 | + | 0.478437i | \(0.841204\pi\) | |||||||
\(72\) | −1.14590 | −0.135045 | ||||||||
\(73\) | 1.09017 | 0.127595 | 0.0637974 | − | 0.997963i | \(-0.479679\pi\) | ||||
0.0637974 | + | 0.997963i | \(0.479679\pi\) | |||||||
\(74\) | 4.47214 | 0.519875 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.618034 | −0.0708934 | ||||||||
\(77\) | 4.47214 | 0.509647 | ||||||||
\(78\) | −0.618034 | −0.0699786 | ||||||||
\(79\) | 14.6525 | 1.64853 | 0.824266 | − | 0.566203i | \(-0.191588\pi\) | ||||
0.824266 | + | 0.566203i | \(0.191588\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 4.09017 | 0.451684 | ||||||||
\(83\) | 13.3820 | 1.46886 | 0.734431 | − | 0.678684i | \(-0.237449\pi\) | ||||
0.734431 | + | 0.678684i | \(0.237449\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.47214 | 0.697908 | ||||||||
\(87\) | −11.4721 | −1.22994 | ||||||||
\(88\) | 10.8541 | 1.15705 | ||||||||
\(89\) | 16.4721 | 1.74604 | 0.873021 | − | 0.487682i | \(-0.162157\pi\) | ||||
0.873021 | + | 0.487682i | \(0.162157\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.472136 | 0.0494933 | ||||||||
\(92\) | 8.47214 | 0.883281 | ||||||||
\(93\) | −2.47214 | −0.256349 | ||||||||
\(94\) | 7.85410 | 0.810089 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.09017 | −0.825700 | ||||||||
\(97\) | 12.7639 | 1.29598 | 0.647990 | − | 0.761648i | \(-0.275610\pi\) | ||||
0.647990 | + | 0.761648i | \(0.275610\pi\) | |||||||
\(98\) | 5.47214 | 0.552769 | ||||||||
\(99\) | −1.38197 | −0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.76393 | 0.275022 | 0.137511 | − | 0.990500i | \(-0.456090\pi\) | ||||
0.137511 | + | 0.990500i | \(0.456090\pi\) | |||||||
\(102\) | −6.23607 | −0.617463 | ||||||||
\(103\) | −18.6525 | −1.83788 | −0.918942 | − | 0.394394i | \(-0.870955\pi\) | ||||
−0.918942 | + | 0.394394i | \(0.870955\pi\) | |||||||
\(104\) | 1.14590 | 0.112365 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −8.09017 | −0.782106 | −0.391053 | − | 0.920368i | \(-0.627889\pi\) | ||||
−0.391053 | + | 0.920368i | \(0.627889\pi\) | |||||||
\(108\) | 5.47214 | 0.526557 | ||||||||
\(109\) | −14.4721 | −1.38618 | −0.693090 | − | 0.720851i | \(-0.743751\pi\) | ||||
−0.693090 | + | 0.720851i | \(0.743751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.23607 | −0.686817 | ||||||||
\(112\) | −1.23607 | −0.116797 | ||||||||
\(113\) | 21.1246 | 1.98724 | 0.993618 | − | 0.112796i | \(-0.0359807\pi\) | ||||
0.993618 | + | 0.112796i | \(0.0359807\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.09017 | 0.658306 | ||||||||
\(117\) | −0.145898 | −0.0134883 | ||||||||
\(118\) | 2.76393 | 0.254441 | ||||||||
\(119\) | 4.76393 | 0.436709 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.09017 | 0.190015 | ||||||||
\(122\) | −4.85410 | −0.439470 | ||||||||
\(123\) | −6.61803 | −0.596728 | ||||||||
\(124\) | 1.52786 | 0.137206 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.472136 | 0.0420612 | ||||||||
\(127\) | 10.0000 | 0.887357 | 0.443678 | − | 0.896186i | \(-0.353673\pi\) | ||||
0.443678 | + | 0.896186i | \(0.353673\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | −10.4721 | −0.922020 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3820 | −1.34393 | −0.671964 | − | 0.740584i | \(-0.734549\pi\) | ||||
−0.671964 | + | 0.740584i | \(0.734549\pi\) | |||||||
\(132\) | −5.85410 | −0.509534 | ||||||||
\(133\) | 0.763932 | 0.0662413 | ||||||||
\(134\) | 12.7984 | 1.10561 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.5623 | 0.991460 | ||||||||
\(137\) | 1.90983 | 0.163168 | 0.0815839 | − | 0.996666i | \(-0.474002\pi\) | ||||
0.0815839 | + | 0.996666i | \(0.474002\pi\) | |||||||
\(138\) | 13.7082 | 1.16692 | ||||||||
\(139\) | 1.90983 | 0.161990 | 0.0809948 | − | 0.996715i | \(-0.474190\pi\) | ||||
0.0809948 | + | 0.996715i | \(0.474190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.7082 | −1.07022 | ||||||||
\(142\) | 14.7984 | 1.24185 | ||||||||
\(143\) | 1.38197 | 0.115566 | ||||||||
\(144\) | 0.381966 | 0.0318305 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.09017 | −0.0902231 | ||||||||
\(147\) | −8.85410 | −0.730274 | ||||||||
\(148\) | 4.47214 | 0.367607 | ||||||||
\(149\) | −4.94427 | −0.405051 | −0.202525 | − | 0.979277i | \(-0.564915\pi\) | ||||
−0.202525 | + | 0.979277i | \(0.564915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.9443 | −0.890632 | −0.445316 | − | 0.895373i | \(-0.646909\pi\) | ||||
−0.445316 | + | 0.895373i | \(0.646909\pi\) | |||||||
\(152\) | 1.85410 | 0.150388 | ||||||||
\(153\) | −1.47214 | −0.119015 | ||||||||
\(154\) | −4.47214 | −0.360375 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.618034 | −0.0494823 | ||||||||
\(157\) | 10.3262 | 0.824124 | 0.412062 | − | 0.911156i | \(-0.364809\pi\) | ||||
0.412062 | + | 0.911156i | \(0.364809\pi\) | |||||||
\(158\) | −14.6525 | −1.16569 | ||||||||
\(159\) | 6.47214 | 0.513274 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4721 | −0.825320 | ||||||||
\(162\) | 7.70820 | 0.605614 | ||||||||
\(163\) | 21.8885 | 1.71444 | 0.857222 | − | 0.514948i | \(-0.172189\pi\) | ||||
0.857222 | + | 0.514948i | \(0.172189\pi\) | |||||||
\(164\) | 4.09017 | 0.319389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.3820 | −1.03864 | ||||||||
\(167\) | −17.7082 | −1.37030 | −0.685151 | − | 0.728401i | \(-0.740264\pi\) | ||||
−0.685151 | + | 0.728401i | \(0.740264\pi\) | |||||||
\(168\) | 6.00000 | 0.462910 | ||||||||
\(169\) | −12.8541 | −0.988777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.236068 | −0.0180526 | ||||||||
\(172\) | 6.47214 | 0.493496 | ||||||||
\(173\) | −9.32624 | −0.709061 | −0.354530 | − | 0.935045i | \(-0.615359\pi\) | ||||
−0.354530 | + | 0.935045i | \(0.615359\pi\) | |||||||
\(174\) | 11.4721 | 0.869700 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.61803 | −0.272720 | ||||||||
\(177\) | −4.47214 | −0.336146 | ||||||||
\(178\) | −16.4721 | −1.23464 | ||||||||
\(179\) | −12.9443 | −0.967500 | −0.483750 | − | 0.875206i | \(-0.660726\pi\) | ||||
−0.483750 | + | 0.875206i | \(0.660726\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.61803 | −0.417585 | −0.208793 | − | 0.977960i | \(-0.566953\pi\) | ||||
−0.208793 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(182\) | −0.472136 | −0.0349970 | ||||||||
\(183\) | 7.85410 | 0.580592 | ||||||||
\(184\) | −25.4164 | −1.87372 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.47214 | 0.181266 | ||||||||
\(187\) | 13.9443 | 1.01971 | ||||||||
\(188\) | 7.85410 | 0.572819 | ||||||||
\(189\) | −6.76393 | −0.492004 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6525 | 0.770786 | 0.385393 | − | 0.922753i | \(-0.374066\pi\) | ||||
0.385393 | + | 0.922753i | \(0.374066\pi\) | |||||||
\(192\) | 11.3262 | 0.817401 | ||||||||
\(193\) | −8.47214 | −0.609838 | −0.304919 | − | 0.952378i | \(-0.598629\pi\) | ||||
−0.304919 | + | 0.952378i | \(0.598629\pi\) | |||||||
\(194\) | −12.7639 | −0.916397 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.47214 | 0.390867 | ||||||||
\(197\) | −2.94427 | −0.209771 | −0.104885 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104885 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(198\) | 1.38197 | 0.0982120 | ||||||||
\(199\) | −17.1459 | −1.21544 | −0.607720 | − | 0.794151i | \(-0.707916\pi\) | ||||
−0.607720 | + | 0.794151i | \(0.707916\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.7082 | −1.46064 | ||||||||
\(202\) | −2.76393 | −0.194470 | ||||||||
\(203\) | −8.76393 | −0.615107 | ||||||||
\(204\) | −6.23607 | −0.436612 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.6525 | 1.29958 | ||||||||
\(207\) | 3.23607 | 0.224922 | ||||||||
\(208\) | −0.381966 | −0.0264846 | ||||||||
\(209\) | 2.23607 | 0.154672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.7639 | −0.741020 | −0.370510 | − | 0.928829i | \(-0.620817\pi\) | ||||
−0.370510 | + | 0.928829i | \(0.620817\pi\) | |||||||
\(212\) | −4.00000 | −0.274721 | ||||||||
\(213\) | −23.9443 | −1.64063 | ||||||||
\(214\) | 8.09017 | 0.553033 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −16.4164 | −1.11700 | ||||||||
\(217\) | −1.88854 | −0.128203 | ||||||||
\(218\) | 14.4721 | 0.980177 | ||||||||
\(219\) | 1.76393 | 0.119195 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.47214 | 0.0990266 | ||||||||
\(222\) | 7.23607 | 0.485653 | ||||||||
\(223\) | −6.61803 | −0.443176 | −0.221588 | − | 0.975140i | \(-0.571124\pi\) | ||||
−0.221588 | + | 0.975140i | \(0.571124\pi\) | |||||||
\(224\) | −6.18034 | −0.412941 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.1246 | −1.40519 | ||||||||
\(227\) | 27.5967 | 1.83166 | 0.915830 | − | 0.401566i | \(-0.131534\pi\) | ||||
0.915830 | + | 0.401566i | \(0.131534\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | 25.0344 | 1.65432 | 0.827161 | − | 0.561965i | \(-0.189954\pi\) | ||||
0.827161 | + | 0.561965i | \(0.189954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.23607 | 0.476098 | ||||||||
\(232\) | −21.2705 | −1.39648 | ||||||||
\(233\) | −14.9443 | −0.979032 | −0.489516 | − | 0.871994i | \(-0.662826\pi\) | ||||
−0.489516 | + | 0.871994i | \(0.662826\pi\) | |||||||
\(234\) | 0.145898 | 0.00953765 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.76393 | 0.179917 | ||||||||
\(237\) | 23.7082 | 1.54001 | ||||||||
\(238\) | −4.76393 | −0.308800 | ||||||||
\(239\) | −10.4721 | −0.677386 | −0.338693 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338693 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −2.09017 | −0.134361 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | −4.85410 | −0.310752 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.61803 | 0.421950 | ||||||||
\(247\) | 0.236068 | 0.0150206 | ||||||||
\(248\) | −4.58359 | −0.291058 | ||||||||
\(249\) | 21.6525 | 1.37217 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.70820 | 0.486538 | 0.243269 | − | 0.969959i | \(-0.421780\pi\) | ||||
0.243269 | + | 0.969959i | \(0.421780\pi\) | |||||||
\(252\) | 0.472136 | 0.0297418 | ||||||||
\(253\) | −30.6525 | −1.92710 | ||||||||
\(254\) | −10.0000 | −0.627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −9.12461 | −0.569178 | −0.284589 | − | 0.958650i | \(-0.591857\pi\) | ||||
−0.284589 | + | 0.958650i | \(0.591857\pi\) | |||||||
\(258\) | 10.4721 | 0.651967 | ||||||||
\(259\) | −5.52786 | −0.343485 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.70820 | 0.167634 | ||||||||
\(262\) | 15.3820 | 0.950301 | ||||||||
\(263\) | 14.4721 | 0.892390 | 0.446195 | − | 0.894936i | \(-0.352779\pi\) | ||||
0.446195 | + | 0.894936i | \(0.352779\pi\) | |||||||
\(264\) | 17.5623 | 1.08089 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.763932 | −0.0468397 | ||||||||
\(267\) | 26.6525 | 1.63111 | ||||||||
\(268\) | 12.7984 | 0.781785 | ||||||||
\(269\) | 1.70820 | 0.104151 | 0.0520755 | − | 0.998643i | \(-0.483416\pi\) | ||||
0.0520755 | + | 0.998643i | \(0.483416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.81966 | −0.353519 | −0.176760 | − | 0.984254i | \(-0.556562\pi\) | ||||
−0.176760 | + | 0.984254i | \(0.556562\pi\) | |||||||
\(272\) | −3.85410 | −0.233689 | ||||||||
\(273\) | 0.763932 | 0.0462353 | ||||||||
\(274\) | −1.90983 | −0.115377 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.7082 | 0.825137 | ||||||||
\(277\) | 8.00000 | 0.480673 | 0.240337 | − | 0.970690i | \(-0.422742\pi\) | ||||
0.240337 | + | 0.970690i | \(0.422742\pi\) | |||||||
\(278\) | −1.90983 | −0.114544 | ||||||||
\(279\) | 0.583592 | 0.0349387 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.03444 | −0.538950 | −0.269475 | − | 0.963007i | \(-0.586850\pi\) | ||||
−0.269475 | + | 0.963007i | \(0.586850\pi\) | |||||||
\(282\) | 12.7082 | 0.756763 | ||||||||
\(283\) | −6.76393 | −0.402074 | −0.201037 | − | 0.979584i | \(-0.564431\pi\) | ||||
−0.201037 | + | 0.979584i | \(0.564431\pi\) | |||||||
\(284\) | 14.7984 | 0.878122 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.38197 | −0.0817174 | ||||||||
\(287\) | −5.05573 | −0.298430 | ||||||||
\(288\) | 1.90983 | 0.112538 | ||||||||
\(289\) | −2.14590 | −0.126229 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.6525 | 1.21067 | ||||||||
\(292\) | −1.09017 | −0.0637974 | ||||||||
\(293\) | −5.67376 | −0.331465 | −0.165732 | − | 0.986171i | \(-0.552999\pi\) | ||||
−0.165732 | + | 0.986171i | \(0.552999\pi\) | |||||||
\(294\) | 8.85410 | 0.516382 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.4164 | −0.779813 | ||||||||
\(297\) | −19.7984 | −1.14882 | ||||||||
\(298\) | 4.94427 | 0.286414 | ||||||||
\(299\) | −3.23607 | −0.187147 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 10.9443 | 0.629772 | ||||||||
\(303\) | 4.47214 | 0.256917 | ||||||||
\(304\) | −0.618034 | −0.0354467 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.47214 | 0.0841564 | ||||||||
\(307\) | −29.7082 | −1.69554 | −0.847768 | − | 0.530367i | \(-0.822054\pi\) | ||||
−0.847768 | + | 0.530367i | \(0.822054\pi\) | |||||||
\(308\) | −4.47214 | −0.254824 | ||||||||
\(309\) | −30.1803 | −1.71690 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.2148 | −1.71332 | −0.856662 | − | 0.515879i | \(-0.827465\pi\) | ||||
−0.856662 | + | 0.515879i | \(0.827465\pi\) | |||||||
\(312\) | 1.85410 | 0.104968 | ||||||||
\(313\) | −12.2918 | −0.694773 | −0.347387 | − | 0.937722i | \(-0.612931\pi\) | ||||
−0.347387 | + | 0.937722i | \(0.612931\pi\) | |||||||
\(314\) | −10.3262 | −0.582743 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.6525 | −0.824266 | ||||||||
\(317\) | 15.0344 | 0.844418 | 0.422209 | − | 0.906498i | \(-0.361255\pi\) | ||||
0.422209 | + | 0.906498i | \(0.361255\pi\) | |||||||
\(318\) | −6.47214 | −0.362939 | ||||||||
\(319\) | −25.6525 | −1.43626 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.0902 | −0.730622 | ||||||||
\(322\) | 10.4721 | 0.583589 | ||||||||
\(323\) | 2.38197 | 0.132536 | ||||||||
\(324\) | 7.70820 | 0.428234 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.8885 | −1.21229 | ||||||||
\(327\) | −23.4164 | −1.29493 | ||||||||
\(328\) | −12.2705 | −0.677526 | ||||||||
\(329\) | −9.70820 | −0.535231 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1803 | −0.779422 | −0.389711 | − | 0.920937i | \(-0.627425\pi\) | ||||
−0.389711 | + | 0.920937i | \(0.627425\pi\) | |||||||
\(332\) | −13.3820 | −0.734431 | ||||||||
\(333\) | 1.70820 | 0.0936090 | ||||||||
\(334\) | 17.7082 | 0.968950 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | −0.109109 | ||||||||
\(337\) | 26.6525 | 1.45185 | 0.725926 | − | 0.687772i | \(-0.241411\pi\) | ||||
0.725926 | + | 0.687772i | \(0.241411\pi\) | |||||||
\(338\) | 12.8541 | 0.699171 | ||||||||
\(339\) | 34.1803 | 1.85642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.52786 | −0.299351 | ||||||||
\(342\) | 0.236068 | 0.0127651 | ||||||||
\(343\) | −15.4164 | −0.832408 | ||||||||
\(344\) | −19.4164 | −1.04686 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.32624 | 0.501382 | ||||||||
\(347\) | 12.7984 | 0.687053 | 0.343526 | − | 0.939143i | \(-0.388379\pi\) | ||||
0.343526 | + | 0.939143i | \(0.388379\pi\) | |||||||
\(348\) | 11.4721 | 0.614971 | ||||||||
\(349\) | −14.5066 | −0.776519 | −0.388260 | − | 0.921550i | \(-0.626924\pi\) | ||||
−0.388260 | + | 0.921550i | \(0.626924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.09017 | −0.111565 | ||||||||
\(352\) | −18.0902 | −0.964209 | ||||||||
\(353\) | 14.6738 | 0.781006 | 0.390503 | − | 0.920602i | \(-0.372301\pi\) | ||||
0.390503 | + | 0.920602i | \(0.372301\pi\) | |||||||
\(354\) | 4.47214 | 0.237691 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16.4721 | −0.873021 | ||||||||
\(357\) | 7.70820 | 0.407961 | ||||||||
\(358\) | 12.9443 | 0.684126 | ||||||||
\(359\) | 17.7082 | 0.934603 | 0.467302 | − | 0.884098i | \(-0.345226\pi\) | ||||
0.467302 | + | 0.884098i | \(0.345226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6180 | −0.979897 | ||||||||
\(362\) | 5.61803 | 0.295277 | ||||||||
\(363\) | 3.38197 | 0.177507 | ||||||||
\(364\) | −0.472136 | −0.0247466 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.85410 | −0.410540 | ||||||||
\(367\) | −6.18034 | −0.322611 | −0.161306 | − | 0.986905i | \(-0.551570\pi\) | ||||
−0.161306 | + | 0.986905i | \(0.551570\pi\) | |||||||
\(368\) | 8.47214 | 0.441641 | ||||||||
\(369\) | 1.56231 | 0.0813304 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.94427 | 0.256694 | ||||||||
\(372\) | 2.47214 | 0.128174 | ||||||||
\(373\) | −8.14590 | −0.421779 | −0.210889 | − | 0.977510i | \(-0.567636\pi\) | ||||
−0.210889 | + | 0.977510i | \(0.567636\pi\) | |||||||
\(374\) | −13.9443 | −0.721041 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.5623 | −1.21513 | ||||||||
\(377\) | −2.70820 | −0.139480 | ||||||||
\(378\) | 6.76393 | 0.347899 | ||||||||
\(379\) | −36.7426 | −1.88734 | −0.943671 | − | 0.330884i | \(-0.892653\pi\) | ||||
−0.943671 | + | 0.330884i | \(0.892653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.1803 | 0.828944 | ||||||||
\(382\) | −10.6525 | −0.545028 | ||||||||
\(383\) | 15.5279 | 0.793437 | 0.396718 | − | 0.917940i | \(-0.370149\pi\) | ||||
0.396718 | + | 0.917940i | \(0.370149\pi\) | |||||||
\(384\) | 4.85410 | 0.247710 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.47214 | 0.431220 | ||||||||
\(387\) | 2.47214 | 0.125666 | ||||||||
\(388\) | −12.7639 | −0.647990 | ||||||||
\(389\) | −23.7082 | −1.20205 | −0.601027 | − | 0.799229i | \(-0.705242\pi\) | ||||
−0.601027 | + | 0.799229i | \(0.705242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.6525 | −1.65131 | ||||||||
\(392\) | −16.4164 | −0.829154 | ||||||||
\(393\) | −24.8885 | −1.25546 | ||||||||
\(394\) | 2.94427 | 0.148330 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.38197 | 0.0694464 | ||||||||
\(397\) | 31.3050 | 1.57115 | 0.785575 | − | 0.618766i | \(-0.212367\pi\) | ||||
0.785575 | + | 0.618766i | \(0.212367\pi\) | |||||||
\(398\) | 17.1459 | 0.859446 | ||||||||
\(399\) | 1.23607 | 0.0618808 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.79837 | 0.339495 | 0.169747 | − | 0.985488i | \(-0.445705\pi\) | ||||
0.169747 | + | 0.985488i | \(0.445705\pi\) | |||||||
\(402\) | 20.7082 | 1.03283 | ||||||||
\(403\) | −0.583592 | −0.0290708 | ||||||||
\(404\) | −2.76393 | −0.137511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.76393 | 0.434947 | ||||||||
\(407\) | −16.1803 | −0.802030 | ||||||||
\(408\) | 18.7082 | 0.926194 | ||||||||
\(409\) | 15.0557 | 0.744458 | 0.372229 | − | 0.928141i | \(-0.378594\pi\) | ||||
0.372229 | + | 0.928141i | \(0.378594\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.09017 | 0.152427 | ||||||||
\(412\) | 18.6525 | 0.918942 | ||||||||
\(413\) | −3.41641 | −0.168110 | ||||||||
\(414\) | −3.23607 | −0.159044 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.90983 | −0.0936371 | ||||||||
\(417\) | 3.09017 | 0.151326 | ||||||||
\(418\) | −2.23607 | −0.109370 | ||||||||
\(419\) | 27.7984 | 1.35804 | 0.679020 | − | 0.734120i | \(-0.262405\pi\) | ||||
0.679020 | + | 0.734120i | \(0.262405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.3607 | 1.67464 | 0.837319 | − | 0.546715i | \(-0.184122\pi\) | ||||
0.837319 | + | 0.546715i | \(0.184122\pi\) | |||||||
\(422\) | 10.7639 | 0.523980 | ||||||||
\(423\) | 3.00000 | 0.145865 | ||||||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23.9443 | 1.16010 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 8.09017 | 0.391053 | ||||||||
\(429\) | 2.23607 | 0.107958 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.4508 | 1.08142 | 0.540710 | − | 0.841209i | \(-0.318156\pi\) | ||||
0.540710 | + | 0.841209i | \(0.318156\pi\) | |||||||
\(432\) | 5.47214 | 0.263278 | ||||||||
\(433\) | 18.6525 | 0.896381 | 0.448190 | − | 0.893938i | \(-0.352069\pi\) | ||||
0.448190 | + | 0.893938i | \(0.352069\pi\) | |||||||
\(434\) | 1.88854 | 0.0906530 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.4721 | 0.693090 | ||||||||
\(437\) | −5.23607 | −0.250475 | ||||||||
\(438\) | −1.76393 | −0.0842839 | ||||||||
\(439\) | 10.8541 | 0.518038 | 0.259019 | − | 0.965872i | \(-0.416601\pi\) | ||||
0.259019 | + | 0.965872i | \(0.416601\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.09017 | 0.0995319 | ||||||||
\(442\) | −1.47214 | −0.0700224 | ||||||||
\(443\) | 14.9443 | 0.710024 | 0.355012 | − | 0.934862i | \(-0.384477\pi\) | ||||
0.355012 | + | 0.934862i | \(0.384477\pi\) | |||||||
\(444\) | 7.23607 | 0.343409 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.61803 | 0.313373 | ||||||||
\(447\) | −8.00000 | −0.378387 | ||||||||
\(448\) | 8.65248 | 0.408791 | ||||||||
\(449\) | −13.2361 | −0.624649 | −0.312324 | − | 0.949976i | \(-0.601108\pi\) | ||||
−0.312324 | + | 0.949976i | \(0.601108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.7984 | −0.696828 | ||||||||
\(452\) | −21.1246 | −0.993618 | ||||||||
\(453\) | −17.7082 | −0.832004 | ||||||||
\(454\) | −27.5967 | −1.29518 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | 0.140488 | ||||||||
\(457\) | 24.6525 | 1.15319 | 0.576597 | − | 0.817029i | \(-0.304380\pi\) | ||||
0.576597 | + | 0.817029i | \(0.304380\pi\) | |||||||
\(458\) | −25.0344 | −1.16978 | ||||||||
\(459\) | −21.0902 | −0.984405 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.0000 | −1.67669 | −0.838344 | − | 0.545142i | \(-0.816476\pi\) | ||||
−0.838344 | + | 0.545142i | \(0.816476\pi\) | |||||||
\(462\) | −7.23607 | −0.336652 | ||||||||
\(463\) | −4.29180 | −0.199457 | −0.0997283 | − | 0.995015i | \(-0.531797\pi\) | ||||
−0.0997283 | + | 0.995015i | \(0.531797\pi\) | |||||||
\(464\) | 7.09017 | 0.329153 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.9443 | 0.692280 | ||||||||
\(467\) | −8.67376 | −0.401374 | −0.200687 | − | 0.979655i | \(-0.564317\pi\) | ||||
−0.200687 | + | 0.979655i | \(0.564317\pi\) | |||||||
\(468\) | 0.145898 | 0.00674414 | ||||||||
\(469\) | −15.8197 | −0.730484 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.7082 | 0.769873 | ||||||||
\(472\) | −8.29180 | −0.381661 | ||||||||
\(473\) | −23.4164 | −1.07669 | ||||||||
\(474\) | −23.7082 | −1.08895 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.76393 | −0.218354 | ||||||||
\(477\) | −1.52786 | −0.0699561 | ||||||||
\(478\) | 10.4721 | 0.478984 | ||||||||
\(479\) | −38.9443 | −1.77941 | −0.889705 | − | 0.456537i | \(-0.849090\pi\) | ||||
−0.889705 | + | 0.456537i | \(0.849090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70820 | −0.0778874 | ||||||||
\(482\) | −1.00000 | −0.0455488 | ||||||||
\(483\) | −16.9443 | −0.770991 | ||||||||
\(484\) | −2.09017 | −0.0950077 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.94427 | −0.178916 | ||||||||
\(487\) | 7.32624 | 0.331984 | 0.165992 | − | 0.986127i | \(-0.446917\pi\) | ||||
0.165992 | + | 0.986127i | \(0.446917\pi\) | |||||||
\(488\) | 14.5623 | 0.659205 | ||||||||
\(489\) | 35.4164 | 1.60159 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.41641 | −0.154180 | −0.0770902 | − | 0.997024i | \(-0.524563\pi\) | ||||
−0.0770902 | + | 0.997024i | \(0.524563\pi\) | |||||||
\(492\) | 6.61803 | 0.298364 | ||||||||
\(493\) | −27.3262 | −1.23071 | ||||||||
\(494\) | −0.236068 | −0.0106212 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.52786 | 0.0686031 | ||||||||
\(497\) | −18.2918 | −0.820499 | ||||||||
\(498\) | −21.6525 | −0.970271 | ||||||||
\(499\) | 41.3050 | 1.84906 | 0.924532 | − | 0.381105i | \(-0.124456\pi\) | ||||
0.924532 | + | 0.381105i | \(0.124456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.6525 | −1.28010 | ||||||||
\(502\) | −7.70820 | −0.344034 | ||||||||
\(503\) | −26.6525 | −1.18838 | −0.594188 | − | 0.804327i | \(-0.702526\pi\) | ||||
−0.594188 | + | 0.804327i | \(0.702526\pi\) | |||||||
\(504\) | −1.41641 | −0.0630918 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30.6525 | 1.36267 | ||||||||
\(507\) | −20.7984 | −0.923688 | ||||||||
\(508\) | −10.0000 | −0.443678 | ||||||||
\(509\) | 2.96556 | 0.131446 | 0.0657230 | − | 0.997838i | \(-0.479065\pi\) | ||||
0.0657230 | + | 0.997838i | \(0.479065\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.34752 | 0.0596110 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | −3.38197 | −0.149317 | ||||||||
\(514\) | 9.12461 | 0.402469 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.4721 | 0.461010 | ||||||||
\(517\) | −28.4164 | −1.24975 | ||||||||
\(518\) | 5.52786 | 0.242880 | ||||||||
\(519\) | −15.0902 | −0.662385 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.23607 | 0.141775 | 0.0708874 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708874 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(522\) | −2.70820 | −0.118535 | ||||||||
\(523\) | 6.56231 | 0.286950 | 0.143475 | − | 0.989654i | \(-0.454172\pi\) | ||||
0.143475 | + | 0.989654i | \(0.454172\pi\) | |||||||
\(524\) | 15.3820 | 0.671964 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.4721 | −0.631015 | ||||||||
\(527\) | −5.88854 | −0.256509 | ||||||||
\(528\) | −5.85410 | −0.254767 | ||||||||
\(529\) | 48.7771 | 2.12074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.05573 | 0.0458147 | ||||||||
\(532\) | −0.763932 | −0.0331207 | ||||||||
\(533\) | −1.56231 | −0.0676710 | ||||||||
\(534\) | −26.6525 | −1.15337 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −38.3951 | −1.65842 | ||||||||
\(537\) | −20.9443 | −0.903812 | ||||||||
\(538\) | −1.70820 | −0.0736459 | ||||||||
\(539\) | −19.7984 | −0.852776 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.7984 | 1.49610 | 0.748049 | − | 0.663643i | \(-0.230991\pi\) | ||||
0.748049 | + | 0.663643i | \(0.230991\pi\) | |||||||
\(542\) | 5.81966 | 0.249976 | ||||||||
\(543\) | −9.09017 | −0.390097 | ||||||||
\(544\) | −19.2705 | −0.826216 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.763932 | −0.0326933 | ||||||||
\(547\) | 9.70820 | 0.415093 | 0.207546 | − | 0.978225i | \(-0.433452\pi\) | ||||
0.207546 | + | 0.978225i | \(0.433452\pi\) | |||||||
\(548\) | −1.90983 | −0.0815839 | ||||||||
\(549\) | −1.85410 | −0.0791311 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.38197 | −0.186678 | ||||||||
\(552\) | −41.1246 | −1.75038 | ||||||||
\(553\) | 18.1115 | 0.770177 | ||||||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.90983 | −0.0809948 | ||||||||
\(557\) | −45.8885 | −1.94436 | −0.972180 | − | 0.234235i | \(-0.924741\pi\) | ||||
−0.972180 | + | 0.234235i | \(0.924741\pi\) | |||||||
\(558\) | −0.583592 | −0.0247054 | ||||||||
\(559\) | −2.47214 | −0.104560 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.5623 | 0.952581 | ||||||||
\(562\) | 9.03444 | 0.381095 | ||||||||
\(563\) | 7.72949 | 0.325759 | 0.162880 | − | 0.986646i | \(-0.447922\pi\) | ||||
0.162880 | + | 0.986646i | \(0.447922\pi\) | |||||||
\(564\) | 12.7082 | 0.535112 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.76393 | 0.284309 | ||||||||
\(567\) | −9.52786 | −0.400133 | ||||||||
\(568\) | −44.3951 | −1.86278 | ||||||||
\(569\) | 23.5066 | 0.985447 | 0.492724 | − | 0.870186i | \(-0.336001\pi\) | ||||
0.492724 | + | 0.870186i | \(0.336001\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.326238 | 0.0136526 | 0.00682632 | − | 0.999977i | \(-0.497827\pi\) | ||||
0.00682632 | + | 0.999977i | \(0.497827\pi\) | |||||||
\(572\) | −1.38197 | −0.0577829 | ||||||||
\(573\) | 17.2361 | 0.720047 | ||||||||
\(574\) | 5.05573 | 0.211022 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.67376 | −0.111407 | ||||||||
\(577\) | 22.8541 | 0.951429 | 0.475714 | − | 0.879600i | \(-0.342190\pi\) | ||||
0.475714 | + | 0.879600i | \(0.342190\pi\) | |||||||
\(578\) | 2.14590 | 0.0892576 | ||||||||
\(579\) | −13.7082 | −0.569694 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5410 | 0.686237 | ||||||||
\(582\) | −20.6525 | −0.856073 | ||||||||
\(583\) | 14.4721 | 0.599375 | ||||||||
\(584\) | 3.27051 | 0.135335 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.67376 | 0.234381 | ||||||||
\(587\) | −20.4721 | −0.844975 | −0.422488 | − | 0.906369i | \(-0.638843\pi\) | ||||
−0.422488 | + | 0.906369i | \(0.638843\pi\) | |||||||
\(588\) | 8.85410 | 0.365137 | ||||||||
\(589\) | −0.944272 | −0.0389080 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.76393 | −0.195962 | ||||||||
\(592\) | 4.47214 | 0.183804 | ||||||||
\(593\) | −40.8328 | −1.67680 | −0.838401 | − | 0.545053i | \(-0.816509\pi\) | ||||
−0.838401 | + | 0.545053i | \(0.816509\pi\) | |||||||
\(594\) | 19.7984 | 0.812337 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.94427 | 0.202525 | ||||||||
\(597\) | −27.7426 | −1.13543 | ||||||||
\(598\) | 3.23607 | 0.132333 | ||||||||
\(599\) | 19.4508 | 0.794740 | 0.397370 | − | 0.917658i | \(-0.369923\pi\) | ||||
0.397370 | + | 0.917658i | \(0.369923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.7426 | 1.58035 | 0.790173 | − | 0.612884i | \(-0.209991\pi\) | ||||
0.790173 | + | 0.612884i | \(0.209991\pi\) | |||||||
\(602\) | 8.00000 | 0.326056 | ||||||||
\(603\) | 4.88854 | 0.199077 | ||||||||
\(604\) | 10.9443 | 0.445316 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.47214 | −0.181668 | ||||||||
\(607\) | 44.3607 | 1.80054 | 0.900272 | − | 0.435327i | \(-0.143367\pi\) | ||||
0.900272 | + | 0.435327i | \(0.143367\pi\) | |||||||
\(608\) | −3.09017 | −0.125323 | ||||||||
\(609\) | −14.1803 | −0.574616 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | −0.121367 | ||||||||
\(612\) | 1.47214 | 0.0595076 | ||||||||
\(613\) | 26.6869 | 1.07787 | 0.538937 | − | 0.842346i | \(-0.318826\pi\) | ||||
0.538937 | + | 0.842346i | \(0.318826\pi\) | |||||||
\(614\) | 29.7082 | 1.19893 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.4164 | 0.540562 | ||||||||
\(617\) | −19.0557 | −0.767155 | −0.383577 | − | 0.923509i | \(-0.625308\pi\) | ||||
−0.383577 | + | 0.923509i | \(0.625308\pi\) | |||||||
\(618\) | 30.1803 | 1.21403 | ||||||||
\(619\) | 11.9656 | 0.480936 | 0.240468 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240468 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 46.3607 | 1.86039 | ||||||||
\(622\) | 30.2148 | 1.21150 | ||||||||
\(623\) | 20.3607 | 0.815733 | ||||||||
\(624\) | −0.618034 | −0.0247412 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.2918 | 0.491279 | ||||||||
\(627\) | 3.61803 | 0.144490 | ||||||||
\(628\) | −10.3262 | −0.412062 | ||||||||
\(629\) | −17.2361 | −0.687247 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.9098 | 0.673170 | 0.336585 | − | 0.941653i | \(-0.390728\pi\) | ||||
0.336585 | + | 0.941653i | \(0.390728\pi\) | |||||||
\(632\) | 43.9574 | 1.74853 | ||||||||
\(633\) | −17.4164 | −0.692240 | ||||||||
\(634\) | −15.0344 | −0.597094 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.47214 | −0.256637 | ||||||||
\(637\) | −2.09017 | −0.0828155 | ||||||||
\(638\) | 25.6525 | 1.01559 | ||||||||
\(639\) | 5.65248 | 0.223608 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.1459 | −0.558729 | −0.279365 | − | 0.960185i | \(-0.590124\pi\) | ||||
−0.279365 | + | 0.960185i | \(0.590124\pi\) | |||||||
\(642\) | 13.0902 | 0.516628 | ||||||||
\(643\) | 12.0000 | 0.473234 | 0.236617 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236617 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(644\) | 10.4721 | 0.412660 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.38197 | −0.0937172 | ||||||||
\(647\) | −3.81966 | −0.150166 | −0.0750832 | − | 0.997177i | \(-0.523922\pi\) | ||||
−0.0750832 | + | 0.997177i | \(0.523922\pi\) | |||||||
\(648\) | −23.1246 | −0.908421 | ||||||||
\(649\) | −10.0000 | −0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.05573 | −0.119763 | ||||||||
\(652\) | −21.8885 | −0.857222 | ||||||||
\(653\) | 18.3262 | 0.717161 | 0.358581 | − | 0.933499i | \(-0.383261\pi\) | ||||
0.358581 | + | 0.933499i | \(0.383261\pi\) | |||||||
\(654\) | 23.4164 | 0.915654 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.09017 | 0.159694 | ||||||||
\(657\) | −0.416408 | −0.0162456 | ||||||||
\(658\) | 9.70820 | 0.378465 | ||||||||
\(659\) | −14.7639 | −0.575121 | −0.287561 | − | 0.957762i | \(-0.592844\pi\) | ||||
−0.287561 | + | 0.957762i | \(0.592844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.0689 | −1.55850 | −0.779249 | − | 0.626714i | \(-0.784399\pi\) | ||||
−0.779249 | + | 0.626714i | \(0.784399\pi\) | |||||||
\(662\) | 14.1803 | 0.551135 | ||||||||
\(663\) | 2.38197 | 0.0925079 | ||||||||
\(664\) | 40.1459 | 1.55796 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.70820 | −0.0661916 | ||||||||
\(667\) | 60.0689 | 2.32588 | ||||||||
\(668\) | 17.7082 | 0.685151 | ||||||||
\(669\) | −10.7082 | −0.414003 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.5623 | 0.677985 | ||||||||
\(672\) | −10.0000 | −0.385758 | ||||||||
\(673\) | −5.34752 | −0.206132 | −0.103066 | − | 0.994675i | \(-0.532865\pi\) | ||||
−0.103066 | + | 0.994675i | \(0.532865\pi\) | |||||||
\(674\) | −26.6525 | −1.02662 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.8541 | 0.494389 | ||||||||
\(677\) | −12.3820 | −0.475878 | −0.237939 | − | 0.971280i | \(-0.576472\pi\) | ||||
−0.237939 | + | 0.971280i | \(0.576472\pi\) | |||||||
\(678\) | −34.1803 | −1.31269 | ||||||||
\(679\) | 15.7771 | 0.605469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 44.6525 | 1.71109 | ||||||||
\(682\) | 5.52786 | 0.211673 | ||||||||
\(683\) | 16.3607 | 0.626024 | 0.313012 | − | 0.949749i | \(-0.398662\pi\) | ||||
0.313012 | + | 0.949749i | \(0.398662\pi\) | |||||||
\(684\) | 0.236068 | 0.00902628 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.4164 | 0.588601 | ||||||||
\(687\) | 40.5066 | 1.54542 | ||||||||
\(688\) | 6.47214 | 0.246748 | ||||||||
\(689\) | 1.52786 | 0.0582070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.1803 | −1.07203 | −0.536015 | − | 0.844208i | \(-0.680071\pi\) | ||||
−0.536015 | + | 0.844208i | \(0.680071\pi\) | |||||||
\(692\) | 9.32624 | 0.354530 | ||||||||
\(693\) | −1.70820 | −0.0648893 | ||||||||
\(694\) | −12.7984 | −0.485820 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −34.4164 | −1.30455 | ||||||||
\(697\) | −15.7639 | −0.597102 | ||||||||
\(698\) | 14.5066 | 0.549082 | ||||||||
\(699\) | −24.1803 | −0.914584 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.1803 | −1.29097 | −0.645487 | − | 0.763771i | \(-0.723345\pi\) | ||||
−0.645487 | + | 0.763771i | \(0.723345\pi\) | |||||||
\(702\) | 2.09017 | 0.0788884 | ||||||||
\(703\) | −2.76393 | −0.104244 | ||||||||
\(704\) | 25.3262 | 0.954519 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.6738 | −0.552254 | ||||||||
\(707\) | 3.41641 | 0.128487 | ||||||||
\(708\) | 4.47214 | 0.168073 | ||||||||
\(709\) | −18.4721 | −0.693736 | −0.346868 | − | 0.937914i | \(-0.612755\pi\) | ||||
−0.346868 | + | 0.937914i | \(0.612755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.59675 | −0.209894 | ||||||||
\(712\) | 49.4164 | 1.85196 | ||||||||
\(713\) | 12.9443 | 0.484767 | ||||||||
\(714\) | −7.70820 | −0.288472 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.9443 | 0.483750 | ||||||||
\(717\) | −16.9443 | −0.632795 | ||||||||
\(718\) | −17.7082 | −0.660864 | ||||||||
\(719\) | 15.5967 | 0.581661 | 0.290830 | − | 0.956775i | \(-0.406069\pi\) | ||||
0.290830 | + | 0.956775i | \(0.406069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.0557 | −0.858640 | ||||||||
\(722\) | 18.6180 | 0.692891 | ||||||||
\(723\) | 1.61803 | 0.0601753 | ||||||||
\(724\) | 5.61803 | 0.208793 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.38197 | −0.125517 | ||||||||
\(727\) | −44.7984 | −1.66148 | −0.830740 | − | 0.556661i | \(-0.812082\pi\) | ||||
−0.830740 | + | 0.556661i | \(0.812082\pi\) | |||||||
\(728\) | 1.41641 | 0.0524956 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.9443 | −0.922597 | ||||||||
\(732\) | −7.85410 | −0.290296 | ||||||||
\(733\) | −18.1803 | −0.671506 | −0.335753 | − | 0.941950i | \(-0.608991\pi\) | ||||
−0.335753 | + | 0.941950i | \(0.608991\pi\) | |||||||
\(734\) | 6.18034 | 0.228121 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 42.3607 | 1.56144 | ||||||||
\(737\) | −46.3050 | −1.70566 | ||||||||
\(738\) | −1.56231 | −0.0575093 | ||||||||
\(739\) | −7.23607 | −0.266183 | −0.133092 | − | 0.991104i | \(-0.542490\pi\) | ||||
−0.133092 | + | 0.991104i | \(0.542490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.381966 | 0.0140319 | ||||||||
\(742\) | −4.94427 | −0.181510 | ||||||||
\(743\) | 18.9230 | 0.694217 | 0.347109 | − | 0.937825i | \(-0.387164\pi\) | ||||
0.347109 | + | 0.937825i | \(0.387164\pi\) | |||||||
\(744\) | −7.41641 | −0.271899 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.14590 | 0.298243 | ||||||||
\(747\) | −5.11146 | −0.187018 | ||||||||
\(748\) | −13.9443 | −0.509853 | ||||||||
\(749\) | −10.0000 | −0.365392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.14590 | 0.333739 | 0.166869 | − | 0.985979i | \(-0.446634\pi\) | ||||
0.166869 | + | 0.985979i | \(0.446634\pi\) | |||||||
\(752\) | 7.85410 | 0.286410 | ||||||||
\(753\) | 12.4721 | 0.454510 | ||||||||
\(754\) | 2.70820 | 0.0986270 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.76393 | 0.246002 | ||||||||
\(757\) | −7.85410 | −0.285462 | −0.142731 | − | 0.989762i | \(-0.545588\pi\) | ||||
−0.142731 | + | 0.989762i | \(0.545588\pi\) | |||||||
\(758\) | 36.7426 | 1.33455 | ||||||||
\(759\) | −49.5967 | −1.80025 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8328 | −0.900189 | −0.450094 | − | 0.892981i | \(-0.648610\pi\) | ||||
−0.450094 | + | 0.892981i | \(0.648610\pi\) | |||||||
\(762\) | −16.1803 | −0.586152 | ||||||||
\(763\) | −17.8885 | −0.647609 | ||||||||
\(764\) | −10.6525 | −0.385393 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.5279 | −0.561045 | ||||||||
\(767\) | −1.05573 | −0.0381201 | ||||||||
\(768\) | −27.5066 | −0.992558 | ||||||||
\(769\) | −3.41641 | −0.123199 | −0.0615994 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615994 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7639 | −0.531710 | ||||||||
\(772\) | 8.47214 | 0.304919 | ||||||||
\(773\) | 37.0132 | 1.33127 | 0.665635 | − | 0.746277i | \(-0.268161\pi\) | ||||
0.665635 | + | 0.746277i | \(0.268161\pi\) | |||||||
\(774\) | −2.47214 | −0.0888591 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 38.2918 | 1.37460 | ||||||||
\(777\) | −8.94427 | −0.320874 | ||||||||
\(778\) | 23.7082 | 0.849980 | ||||||||
\(779\) | −2.52786 | −0.0905701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.5410 | −1.91585 | ||||||||
\(782\) | 32.6525 | 1.16765 | ||||||||
\(783\) | 38.7984 | 1.38654 | ||||||||
\(784\) | 5.47214 | 0.195433 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.8885 | 0.887745 | ||||||||
\(787\) | 6.96556 | 0.248295 | 0.124148 | − | 0.992264i | \(-0.460380\pi\) | ||||
0.124148 | + | 0.992264i | \(0.460380\pi\) | |||||||
\(788\) | 2.94427 | 0.104885 | ||||||||
\(789\) | 23.4164 | 0.833646 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.1115 | 0.928417 | ||||||||
\(792\) | −4.14590 | −0.147318 | ||||||||
\(793\) | 1.85410 | 0.0658411 | ||||||||
\(794\) | −31.3050 | −1.11097 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.1459 | 0.607720 | ||||||||
\(797\) | −34.0344 | −1.20556 | −0.602781 | − | 0.797907i | \(-0.705941\pi\) | ||||
−0.602781 | + | 0.797907i | \(0.705941\pi\) | |||||||
\(798\) | −1.23607 | −0.0437563 | ||||||||
\(799\) | −30.2705 | −1.07089 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.29180 | −0.222310 | ||||||||
\(802\) | −6.79837 | −0.240059 | ||||||||
\(803\) | 3.94427 | 0.139190 | ||||||||
\(804\) | 20.7082 | 0.730322 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.583592 | 0.0205562 | ||||||||
\(807\) | 2.76393 | 0.0972950 | ||||||||
\(808\) | 8.29180 | 0.291704 | ||||||||
\(809\) | −33.8885 | −1.19146 | −0.595729 | − | 0.803186i | \(-0.703137\pi\) | ||||
−0.595729 | + | 0.803186i | \(0.703137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.5066 | −0.895657 | −0.447829 | − | 0.894119i | \(-0.647803\pi\) | ||||
−0.447829 | + | 0.894119i | \(0.647803\pi\) | |||||||
\(812\) | 8.76393 | 0.307554 | ||||||||
\(813\) | −9.41641 | −0.330248 | ||||||||
\(814\) | 16.1803 | 0.567121 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.23607 | −0.218306 | ||||||||
\(817\) | −4.00000 | −0.139942 | ||||||||
\(818\) | −15.0557 | −0.526411 | ||||||||
\(819\) | −0.180340 | −0.00630159 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.45085 | 0.294937 | 0.147468 | − | 0.989067i | \(-0.452888\pi\) | ||||
0.147468 | + | 0.989067i | \(0.452888\pi\) | |||||||
\(822\) | −3.09017 | −0.107782 | ||||||||
\(823\) | 39.4164 | 1.37397 | 0.686985 | − | 0.726672i | \(-0.258934\pi\) | ||||
0.686985 | + | 0.726672i | \(0.258934\pi\) | |||||||
\(824\) | −55.9574 | −1.94937 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.41641 | 0.118872 | ||||||||
\(827\) | 10.9443 | 0.380570 | 0.190285 | − | 0.981729i | \(-0.439059\pi\) | ||||
0.190285 | + | 0.981729i | \(0.439059\pi\) | |||||||
\(828\) | −3.23607 | −0.112461 | ||||||||
\(829\) | −10.7984 | −0.375043 | −0.187522 | − | 0.982260i | \(-0.560045\pi\) | ||||
−0.187522 | + | 0.982260i | \(0.560045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.9443 | 0.449032 | ||||||||
\(832\) | 2.67376 | 0.0926960 | ||||||||
\(833\) | −21.0902 | −0.730731 | ||||||||
\(834\) | −3.09017 | −0.107004 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.23607 | −0.0773360 | ||||||||
\(837\) | 8.36068 | 0.288987 | ||||||||
\(838\) | −27.7984 | −0.960279 | ||||||||
\(839\) | −23.8885 | −0.824724 | −0.412362 | − | 0.911020i | \(-0.635296\pi\) | ||||
−0.412362 | + | 0.911020i | \(0.635296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2705 | 0.733466 | ||||||||
\(842\) | −34.3607 | −1.18415 | ||||||||
\(843\) | −14.6180 | −0.503472 | ||||||||
\(844\) | 10.7639 | 0.370510 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 2.58359 | 0.0887733 | ||||||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | −10.9443 | −0.375606 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.8885 | 1.29880 | ||||||||
\(852\) | 23.9443 | 0.820317 | ||||||||
\(853\) | −19.9787 | −0.684058 | −0.342029 | − | 0.939689i | \(-0.611114\pi\) | ||||
−0.342029 | + | 0.939689i | \(0.611114\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.2705 | −0.829549 | ||||||||
\(857\) | 20.2918 | 0.693155 | 0.346577 | − | 0.938021i | \(-0.387344\pi\) | ||||
0.346577 | + | 0.938021i | \(0.387344\pi\) | |||||||
\(858\) | −2.23607 | −0.0763381 | ||||||||
\(859\) | 47.7426 | 1.62896 | 0.814479 | − | 0.580193i | \(-0.197023\pi\) | ||||
0.814479 | + | 0.580193i | \(0.197023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.18034 | −0.278785 | ||||||||
\(862\) | −22.4508 | −0.764679 | ||||||||
\(863\) | 23.2361 | 0.790965 | 0.395482 | − | 0.918474i | \(-0.370577\pi\) | ||||
0.395482 | + | 0.918474i | \(0.370577\pi\) | |||||||
\(864\) | 27.3607 | 0.930829 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.6525 | −0.633837 | ||||||||
\(867\) | −3.47214 | −0.117920 | ||||||||
\(868\) | 1.88854 | 0.0641014 | ||||||||
\(869\) | 53.0132 | 1.79835 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.88854 | −0.165642 | ||||||||
\(872\) | −43.4164 | −1.47027 | ||||||||
\(873\) | −4.87539 | −0.165007 | ||||||||
\(874\) | 5.23607 | 0.177113 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.76393 | −0.0595977 | ||||||||
\(877\) | 32.5410 | 1.09883 | 0.549416 | − | 0.835549i | \(-0.314850\pi\) | ||||
0.549416 | + | 0.835549i | \(0.314850\pi\) | |||||||
\(878\) | −10.8541 | −0.366308 | ||||||||
\(879\) | −9.18034 | −0.309645 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.20163 | 0.175247 | 0.0876236 | − | 0.996154i | \(-0.472073\pi\) | ||||
0.0876236 | + | 0.996154i | \(0.472073\pi\) | |||||||
\(882\) | −2.09017 | −0.0703797 | ||||||||
\(883\) | −17.4377 | −0.586825 | −0.293413 | − | 0.955986i | \(-0.594791\pi\) | ||||
−0.293413 | + | 0.955986i | \(0.594791\pi\) | |||||||
\(884\) | −1.47214 | −0.0495133 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.9443 | −0.502063 | ||||||||
\(887\) | −41.9787 | −1.40951 | −0.704754 | − | 0.709452i | \(-0.748942\pi\) | ||||
−0.704754 | + | 0.709452i | \(0.748942\pi\) | |||||||
\(888\) | −21.7082 | −0.728480 | ||||||||
\(889\) | 12.3607 | 0.414564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.8885 | −0.934301 | ||||||||
\(892\) | 6.61803 | 0.221588 | ||||||||
\(893\) | −4.85410 | −0.162436 | ||||||||
\(894\) | 8.00000 | 0.267560 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.70820 | 0.123882 | ||||||||
\(897\) | −5.23607 | −0.174827 | ||||||||
\(898\) | 13.2361 | 0.441693 | ||||||||
\(899\) | 10.8328 | 0.361295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4164 | 0.513595 | ||||||||
\(902\) | 14.7984 | 0.492732 | ||||||||
\(903\) | −12.9443 | −0.430758 | ||||||||
\(904\) | 63.3738 | 2.10778 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.7082 | 0.588316 | ||||||||
\(907\) | −28.1803 | −0.935713 | −0.467856 | − | 0.883804i | \(-0.654974\pi\) | ||||
−0.467856 | + | 0.883804i | \(0.654974\pi\) | |||||||
\(908\) | −27.5967 | −0.915830 | ||||||||
\(909\) | −1.05573 | −0.0350163 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.6525 | 1.08182 | 0.540912 | − | 0.841079i | \(-0.318079\pi\) | ||||
0.540912 | + | 0.841079i | \(0.318079\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | 48.4164 | 1.60235 | ||||||||
\(914\) | −24.6525 | −0.815431 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.0344 | −0.827161 | ||||||||
\(917\) | −19.0132 | −0.627870 | ||||||||
\(918\) | 21.0902 | 0.696079 | ||||||||
\(919\) | −14.9443 | −0.492966 | −0.246483 | − | 0.969147i | \(-0.579275\pi\) | ||||
−0.246483 | + | 0.969147i | \(0.579275\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.0689 | −1.58392 | ||||||||
\(922\) | 36.0000 | 1.18560 | ||||||||
\(923\) | −5.65248 | −0.186054 | ||||||||
\(924\) | −7.23607 | −0.238049 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.29180 | 0.141037 | ||||||||
\(927\) | 7.12461 | 0.234003 | ||||||||
\(928\) | 35.4508 | 1.16373 | ||||||||
\(929\) | 11.2361 | 0.368643 | 0.184322 | − | 0.982866i | \(-0.440991\pi\) | ||||
0.184322 | + | 0.982866i | \(0.440991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.38197 | −0.110839 | ||||||||
\(932\) | 14.9443 | 0.489516 | ||||||||
\(933\) | −48.8885 | −1.60054 | ||||||||
\(934\) | 8.67376 | 0.283814 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.437694 | −0.0143065 | ||||||||
\(937\) | −24.3607 | −0.795829 | −0.397914 | − | 0.917423i | \(-0.630266\pi\) | ||||
−0.397914 | + | 0.917423i | \(0.630266\pi\) | |||||||
\(938\) | 15.8197 | 0.516530 | ||||||||
\(939\) | −19.8885 | −0.649038 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.6525 | −0.803648 | −0.401824 | − | 0.915717i | \(-0.631624\pi\) | ||||
−0.401824 | + | 0.915717i | \(0.631624\pi\) | |||||||
\(942\) | −16.7082 | −0.544383 | ||||||||
\(943\) | 34.6525 | 1.12844 | ||||||||
\(944\) | 2.76393 | 0.0899583 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.4164 | 0.761333 | ||||||||
\(947\) | 3.12461 | 0.101536 | 0.0507681 | − | 0.998710i | \(-0.483833\pi\) | ||||
0.0507681 | + | 0.998710i | \(0.483833\pi\) | |||||||
\(948\) | −23.7082 | −0.770007 | ||||||||
\(949\) | 0.416408 | 0.0135172 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.3262 | 0.788832 | ||||||||
\(952\) | 14.2918 | 0.463200 | ||||||||
\(953\) | −27.6180 | −0.894636 | −0.447318 | − | 0.894375i | \(-0.647621\pi\) | ||||
−0.447318 | + | 0.894375i | \(0.647621\pi\) | |||||||
\(954\) | 1.52786 | 0.0494664 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.4721 | 0.338693 | ||||||||
\(957\) | −41.5066 | −1.34172 | ||||||||
\(958\) | 38.9443 | 1.25823 | ||||||||
\(959\) | 2.36068 | 0.0762303 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6656 | −0.924698 | ||||||||
\(962\) | 1.70820 | 0.0550747 | ||||||||
\(963\) | 3.09017 | 0.0995793 | ||||||||
\(964\) | −1.00000 | −0.0322078 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.9443 | 0.545173 | ||||||||
\(967\) | 24.9443 | 0.802154 | 0.401077 | − | 0.916044i | \(-0.368636\pi\) | ||||
0.401077 | + | 0.916044i | \(0.368636\pi\) | |||||||
\(968\) | 6.27051 | 0.201542 | ||||||||
\(969\) | 3.85410 | 0.123812 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.7214 | −1.17844 | −0.589222 | − | 0.807971i | \(-0.700566\pi\) | ||||
−0.589222 | + | 0.807971i | \(0.700566\pi\) | |||||||
\(972\) | −3.94427 | −0.126513 | ||||||||
\(973\) | 2.36068 | 0.0756799 | ||||||||
\(974\) | −7.32624 | −0.234748 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.85410 | −0.155376 | ||||||||
\(977\) | −22.9443 | −0.734052 | −0.367026 | − | 0.930211i | \(-0.619624\pi\) | ||||
−0.367026 | + | 0.930211i | \(0.619624\pi\) | |||||||
\(978\) | −35.4164 | −1.13249 | ||||||||
\(979\) | 59.5967 | 1.90472 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.52786 | 0.176491 | ||||||||
\(982\) | 3.41641 | 0.109022 | ||||||||
\(983\) | −49.5967 | −1.58189 | −0.790945 | − | 0.611887i | \(-0.790411\pi\) | ||||
−0.790945 | + | 0.611887i | \(0.790411\pi\) | |||||||
\(984\) | −19.8541 | −0.632926 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 27.3262 | 0.870245 | ||||||||
\(987\) | −15.7082 | −0.499998 | ||||||||
\(988\) | −0.236068 | −0.00751032 | ||||||||
\(989\) | 54.8328 | 1.74358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.5836 | 0.780924 | 0.390462 | − | 0.920619i | \(-0.372315\pi\) | ||||
0.390462 | + | 0.920619i | \(0.372315\pi\) | |||||||
\(992\) | 7.63932 | 0.242549 | ||||||||
\(993\) | −22.9443 | −0.728114 | ||||||||
\(994\) | 18.2918 | 0.580181 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.6525 | −0.686085 | ||||||||
\(997\) | −21.1459 | −0.669697 | −0.334849 | − | 0.942272i | \(-0.608685\pi\) | ||||
−0.334849 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(998\) | −41.3050 | −1.30749 | ||||||||
\(999\) | 24.4721 | 0.774264 |
(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 | 6025.2.a.a.1.2 | 2 | ||
5.2 | odd | 4 | 1205.2.b.b.724.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1205.2.b.b.724.4 | yes | 4 | ||
5.4 | even | 2 | 6025.2.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.b.724.1 | ✓ | 4 | 5.2 | odd | 4 | ||
1205.2.b.b.724.4 | yes | 4 | 5.3 | odd | 4 | ||
6025.2.a.a.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6025.2.a.d.1.1 | 2 | 5.4 | even | 2 |