Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 3 x^{18} - 35 x^{17} + 103 x^{16} + 501 x^{15} - 1437 x^{14} - 3775 x^{13} + 10450 x^{12} + 16076 x^{11} - 42255 x^{10} - 38701 x^{9} + 93907 x^{8} + 49522 x^{7} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.42761\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.42761 | 1.40158 | 0.700791 | − | 0.713367i | \(-0.252831\pi\) | ||||
0.700791 | + | 0.713367i | \(0.252831\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.44173 | 1.09197 | 0.545987 | − | 0.837794i | \(-0.316155\pi\) | ||||
0.545987 | + | 0.837794i | \(0.316155\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.41683 | 1.66941 | 0.834703 | − | 0.550701i | \(-0.185640\pi\) | ||||
0.834703 | + | 0.550701i | \(0.185640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.89329 | 0.964430 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.93135 | −1.78837 | −0.894184 | − | 0.447699i | \(-0.852243\pi\) | ||||
−0.894184 | + | 0.447699i | \(0.852243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.07880 | 1.13126 | 0.565628 | − | 0.824660i | \(-0.308634\pi\) | ||||
0.565628 | + | 0.824660i | \(0.308634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.92756 | 1.53049 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12648 | 0.515746 | 0.257873 | − | 0.966179i | \(-0.416978\pi\) | ||||
0.257873 | + | 0.966179i | \(0.416978\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.7223 | 2.33981 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.18265 | −1.08066 | −0.540328 | − | 0.841454i | \(-0.681700\pi\) | ||||
−0.540328 | + | 0.841454i | \(0.681700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.962033 | 0.192407 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.259048 | −0.0498538 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.70980 | 0.503198 | 0.251599 | − | 0.967832i | \(-0.419044\pi\) | ||||
0.251599 | + | 0.967832i | \(0.419044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.32365 | 0.596944 | 0.298472 | − | 0.954418i | \(-0.403523\pi\) | ||||
0.298472 | + | 0.954418i | \(0.403523\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.3990 | −2.50654 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.7847 | 1.82295 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.04829 | −1.15873 | −0.579365 | − | 0.815068i | \(-0.696700\pi\) | ||||
−0.579365 | + | 0.815068i | \(0.696700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.90174 | 1.58555 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.996946 | −0.155697 | −0.0778484 | − | 0.996965i | \(-0.524805\pi\) | ||||
−0.0778484 | + | 0.996965i | \(0.524805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.7651 | 1.94665 | 0.973327 | − | 0.229424i | \(-0.0736843\pi\) | ||||
0.973327 | + | 0.229424i | \(0.0736843\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.06463 | 1.05313 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.09666 | 0.889289 | 0.444644 | − | 0.895707i | \(-0.353330\pi\) | ||||
0.444644 | + | 0.895707i | \(0.353330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.5084 | 1.78691 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.16226 | 0.722860 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4827 | −1.95285 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.42761 | 0.321545 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2555 | −1.33515 | −0.667576 | − | 0.744542i | \(-0.732668\pi\) | ||||
−0.667576 | + | 0.744542i | \(0.732668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.30700 | −0.551454 | −0.275727 | − | 0.961236i | \(-0.588919\pi\) | ||||
−0.275727 | + | 0.961236i | \(0.588919\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.7792 | 1.61003 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.95932 | 1.23530 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7266 | 1.31047 | 0.655234 | − | 0.755426i | \(-0.272570\pi\) | ||||
0.655234 | + | 0.755426i | \(0.272570\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.5814 | −1.51463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.87319 | −0.340985 | −0.170492 | − | 0.985359i | \(-0.554536\pi\) | ||||
−0.170492 | + | 0.985359i | \(0.554536\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.21984 | −0.727977 | −0.363988 | − | 0.931404i | \(-0.618585\pi\) | ||||
−0.363988 | + | 0.931404i | \(0.618585\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.33544 | 0.269673 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −26.1978 | −2.98551 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.86596 | 0.322446 | 0.161223 | − | 0.986918i | \(-0.448456\pi\) | ||||
0.161223 | + | 0.986918i | \(0.448456\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.30874 | −1.03430 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7266 | 1.50669 | 0.753346 | − | 0.657625i | \(-0.228439\pi\) | ||||
0.753346 | + | 0.657625i | \(0.228439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.19228 | 0.563181 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.57834 | 0.705272 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.25663 | −0.451202 | −0.225601 | − | 0.974220i | \(-0.572435\pi\) | ||||
−0.225601 | + | 0.974220i | \(0.572435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.0154 | 1.88853 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.06851 | 0.836666 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.44173 | 0.250516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.67893 | −0.373539 | −0.186769 | − | 0.982404i | \(-0.559802\pi\) | ||||
−0.186769 | + | 0.982404i | \(0.559802\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.1611 | −1.72476 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.31667 | −0.529028 | −0.264514 | − | 0.964382i | \(-0.585212\pi\) | ||||
−0.264514 | + | 0.964382i | \(0.585212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.122603 | 0.0120804 | 0.00604020 | − | 0.999982i | \(-0.498077\pi\) | ||||
0.00604020 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 26.1810 | 2.55501 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.47416 | 0.529207 | 0.264603 | − | 0.964357i | \(-0.414759\pi\) | ||||
0.264603 | + | 0.964357i | \(0.414759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.58156 | −0.534617 | −0.267308 | − | 0.963611i | \(-0.586134\pi\) | ||||
−0.267308 | + | 0.963611i | \(0.586134\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.1105 | −1.62406 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.813631 | 0.0765400 | 0.0382700 | − | 0.999267i | \(-0.487815\pi\) | ||||
0.0382700 | + | 0.999267i | \(0.487815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6546 | −1.18005 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.8012 | 1.09102 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.39229 | 0.860990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.1809 | 2.19826 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.42020 | −0.218222 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.85962 | −0.881871 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.54992 | 0.315004 | 0.157502 | − | 0.987519i | \(-0.449656\pi\) | ||||
0.157502 | + | 0.987519i | \(0.449656\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 30.9886 | 2.72839 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.68249 | −0.409111 | −0.204556 | − | 0.978855i | \(-0.565575\pi\) | ||||
−0.204556 | + | 0.978855i | \(0.565575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.41683 | 0.382988 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.632524 | −0.0544390 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.80852 | 0.239948 | 0.119974 | − | 0.992777i | \(-0.461719\pi\) | ||||
0.119974 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5884 | −1.40701 | −0.703503 | − | 0.710692i | \(-0.748382\pi\) | ||||
−0.703503 | + | 0.710692i | \(0.748382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.8003 | 1.24641 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.1928 | −2.02310 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.61660 | 0.549478 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 30.3655 | 2.50451 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.80927 | −0.721684 | −0.360842 | − | 0.932627i | \(-0.617511\pi\) | ||||
−0.360842 | + | 0.932627i | \(0.617511\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.1537 | 1.31457 | 0.657286 | − | 0.753641i | \(-0.271704\pi\) | ||||
0.657286 | + | 0.753641i | \(0.271704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.15252 | 0.497401 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.11544 | 0.651847 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.77649 | 0.141779 | 0.0708897 | − | 0.997484i | \(-0.477416\pi\) | ||||
0.0708897 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.42761 | 0.192522 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.8909 | −1.80405 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.66129 | −0.600079 | −0.300039 | − | 0.953927i | \(-0.597000\pi\) | ||||
−0.300039 | + | 0.953927i | \(0.597000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −35.1584 | −2.73708 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4881 | −0.888979 | −0.444489 | − | 0.895784i | \(-0.646615\pi\) | ||||
−0.444489 | + | 0.895784i | \(0.646615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.63663 | 0.279741 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.89329 | 0.221255 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.21148 | 0.0921069 | 0.0460534 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460534 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.24914 | 0.321204 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.8964 | −1.87132 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.0305 | −1.04869 | −0.524345 | − | 0.851506i | \(-0.675690\pi\) | ||||
−0.524345 | + | 0.851506i | \(0.675690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.94037 | −0.515874 | −0.257937 | − | 0.966162i | \(-0.583043\pi\) | ||||
−0.257937 | + | 0.966162i | \(0.583043\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.4557 | −0.772908 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.2100 | −1.26530 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.6129 | −0.922344 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.14417 | −0.0832261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.2393 | −1.75389 | −0.876947 | − | 0.480586i | \(-0.840424\pi\) | ||||
−0.876947 | + | 0.480586i | \(0.840424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.7990 | 1.13724 | 0.568620 | − | 0.822600i | \(-0.307478\pi\) | ||||
0.568620 | + | 0.822600i | \(0.307478\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.1774 | 1.73138 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2980 | −0.876194 | −0.438097 | − | 0.898928i | \(-0.644347\pi\) | ||||
−0.438097 | + | 0.898928i | \(0.644347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.9880 | −1.06247 | −0.531236 | − | 0.847224i | \(-0.678272\pi\) | ||||
−0.531236 | + | 0.847224i | \(0.678272\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.0401 | 1.83673 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.9687 | 0.840041 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.43427 | −0.170017 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.9949 | −1.04222 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.93135 | −0.410280 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3066 | 0.984908 | 0.492454 | − | 0.870339i | \(-0.336100\pi\) | ||||
0.492454 | + | 0.870339i | \(0.336100\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.97498 | −0.477918 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.1688 | 2.12569 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.6800 | 0.996542 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.0993 | −1.02032 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.67348 | 0.583441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.9453 | −1.26867 | −0.634337 | − | 0.773057i | \(-0.718727\pi\) | ||||
−0.634337 | + | 0.773057i | \(0.718727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.78344 | 0.185563 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.85882 | 0.654353 | 0.327177 | − | 0.944963i | \(-0.393903\pi\) | ||||
0.327177 | + | 0.944963i | \(0.393903\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4970 | −0.759746 | −0.379873 | − | 0.925039i | \(-0.624032\pi\) | ||||
−0.379873 | + | 0.925039i | \(0.624032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −63.5979 | −4.18444 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.9156 | −1.17369 | −0.586844 | − | 0.809700i | \(-0.699630\pi\) | ||||
−0.586844 | + | 0.809700i | \(0.699630\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.8864 | 0.971080 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.95744 | 0.451934 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.1255 | 1.49586 | 0.747931 | − | 0.663776i | \(-0.231047\pi\) | ||||
0.747931 | + | 0.663776i | \(0.231047\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.7508 | −1.72317 | −0.861584 | − | 0.507615i | \(-0.830527\pi\) | ||||
−0.861584 | + | 0.507615i | \(0.830527\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.8208 | −1.39981 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 30.5421 | 1.95126 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.07880 | 0.259528 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 33.3229 | 2.11175 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.43342 | 0.0904765 | 0.0452382 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452382 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.7401 | 1.93261 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.6048 | 0.789345 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.4300 | −0.650609 | −0.325304 | − | 0.945609i | \(-0.605467\pi\) | ||||
−0.325304 | + | 0.945609i | \(0.605467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.1311 | −1.93439 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.84025 | 0.485299 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6721 | −0.904722 | −0.452361 | − | 0.891835i | \(-0.649418\pi\) | ||||
−0.452361 | + | 0.891835i | \(0.649418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.44173 | 0.149994 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3334 | −0.632396 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.0014 | −1.52436 | −0.762182 | − | 0.647363i | \(-0.775872\pi\) | ||||
−0.762182 | + | 0.647363i | \(0.775872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.4404 | 0.694952 | 0.347476 | − | 0.937689i | \(-0.387039\pi\) | ||||
0.347476 | + | 0.937689i | \(0.387039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 43.7343 | 2.64692 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.70615 | −0.344094 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.3604 | 1.94435 | 0.972173 | − | 0.234266i | \(-0.0752686\pi\) | ||||
0.972173 | + | 0.234266i | \(0.0752686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.61627 | 0.575711 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3855 | 1.75299 | 0.876496 | − | 0.481410i | \(-0.159875\pi\) | ||||
0.876496 | + | 0.481410i | \(0.159875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2416 | 1.44101 | 0.720506 | − | 0.693449i | \(-0.243910\pi\) | ||||
0.720506 | + | 0.693449i | \(0.243910\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.92756 | 0.351118 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.40334 | −0.259921 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.4781 | −0.734006 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.93100 | −0.523545 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.41460 | 0.257904 | 0.128952 | − | 0.991651i | \(-0.458839\pi\) | ||||
0.128952 | + | 0.991651i | \(0.458839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.0411 | −1.45795 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.53650 | 0.0891569 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.1390 | −1.22250 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 56.3811 | 3.24975 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9068 | −0.741476 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.5165 | −0.602174 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.78207 | −0.387073 | −0.193537 | − | 0.981093i | \(-0.561996\pi\) | ||||
−0.193537 | + | 0.981093i | \(0.561996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.297632 | 0.0169317 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.57129 | −0.0890997 | −0.0445499 | − | 0.999007i | \(-0.514185\pi\) | ||||
−0.0445499 | + | 0.999007i | \(0.514185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.4530 | −0.703888 | −0.351944 | − | 0.936021i | \(-0.614479\pi\) | ||||
−0.351944 | + | 0.936021i | \(0.614479\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 31.2033 | 1.75810 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.76645 | −0.492373 | −0.246186 | − | 0.969222i | \(-0.579178\pi\) | ||||
−0.246186 | + | 0.969222i | \(0.579178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0728 | −0.899903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.2891 | 0.741726 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.12648 | 0.118320 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.92394 | 0.217661 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.5499 | −0.749309 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.9279 | 1.48458 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.5910 | 1.90129 | 0.950647 | − | 0.310274i | \(-0.100421\pi\) | ||||
0.950647 | + | 0.310274i | \(0.100421\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.3927 | −1.11752 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.1915 | 1.43100 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.7342 | 1.40183 | 0.700916 | − | 0.713244i | \(-0.252775\pi\) | ||||
0.700916 | + | 0.713244i | \(0.252775\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.97518 | 0.107277 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.7137 | −1.06756 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.3297 | 1.31368 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.7205 | −1.65393 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.3008 | 0.821392 | 0.410696 | − | 0.911772i | \(-0.365286\pi\) | ||||
0.410696 | + | 0.911772i | \(0.365286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.14302 | 0.0611842 | 0.0305921 | − | 0.999532i | \(-0.490261\pi\) | ||||
0.0305921 | + | 0.999532i | \(0.490261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.05660 | −0.0563974 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.8086 | −1.48010 | −0.740051 | − | 0.672551i | \(-0.765199\pi\) | ||||
−0.740051 | + | 0.672551i | \(0.765199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.01554 | −0.372346 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.8008 | 1.20675 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.9728 | −1.42357 | −0.711786 | − | 0.702396i | \(-0.752113\pi\) | ||||
−0.711786 | + | 0.702396i | \(0.752113\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 58.7017 | 3.08104 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.1871 | −0.794931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2800 | 0.588814 | 0.294407 | − | 0.955680i | \(-0.404878\pi\) | ||||
0.294407 | + | 0.955680i | \(0.404878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.88445 | −0.150159 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.41683 | 0.229310 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.1386 | −1.45696 | −0.728482 | − | 0.685065i | \(-0.759774\pi\) | ||||
−0.728482 | + | 0.685065i | \(0.759774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.9353 | −1.23601 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.0527 | 0.569245 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3518 | −0.788567 | −0.394284 | − | 0.918989i | \(-0.629007\pi\) | ||||
−0.394284 | + | 0.918989i | \(0.629007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.61782 | 0.441504 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.5658 | −1.56184 | −0.780919 | − | 0.624632i | \(-0.785249\pi\) | ||||
−0.780919 | + | 0.624632i | \(0.785249\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −63.9678 | −3.26010 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 36.9330 | 1.87741 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.4912 | 1.44456 | 0.722280 | − | 0.691601i | \(-0.243094\pi\) | ||||
0.722280 | + | 0.691601i | \(0.243094\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0208 | −0.557345 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.3673 | −0.573403 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.99790 | 0.352103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.34029 | −0.468776 | −0.234388 | − | 0.972143i | \(-0.575309\pi\) | ||||
−0.234388 | + | 0.972143i | \(0.575309\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.7223 | 0.536789 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.8059 | −1.43850 | −0.719250 | − | 0.694752i | \(-0.755514\pi\) | ||||
−0.719250 | + | 0.694752i | \(0.755514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.5565 | 0.675297 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.7294 | −1.12943 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.8058 | 2.07224 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.8723 | 1.47709 | 0.738546 | − | 0.674203i | \(-0.235513\pi\) | ||||
0.738546 | + | 0.674203i | \(0.235513\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.81800 | 0.336307 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −45.2968 | −2.22891 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.5166 | 1.64527 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −40.2701 | −1.97203 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.4272 | 1.87729 | 0.938646 | − | 0.344881i | \(-0.112081\pi\) | ||||
0.938646 | + | 0.344881i | \(0.112081\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.10123 | −0.151145 | −0.0755724 | − | 0.997140i | \(-0.524078\pi\) | ||||
−0.0755724 | + | 0.997140i | \(0.524078\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.6394 | 0.857657 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.04574 | 0.0992330 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.0233 | −0.920601 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −58.7307 | −2.83554 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.5812 | 1.23221 | 0.616103 | − | 0.787666i | \(-0.288711\pi\) | ||||
0.616103 | + | 0.787666i | \(0.288711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.8557 | −1.33866 | −0.669329 | − | 0.742966i | \(-0.733418\pi\) | ||||
−0.669329 | + | 0.742966i | \(0.733418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.0625 | 0.770139 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.18265 | −0.247920 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.433274 | 0.0206790 | 0.0103395 | − | 0.999947i | \(-0.496709\pi\) | ||||
0.0103395 | + | 0.999947i | \(0.496709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 36.1904 | 1.72335 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8878 | 1.27748 | 0.638738 | − | 0.769424i | \(-0.279457\pi\) | ||||
0.638738 | + | 0.769424i | \(0.279457\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.3935 | −0.492700 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.3855 | −1.01150 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.1362 | 1.61099 | 0.805494 | − | 0.592604i | \(-0.201900\pi\) | ||||
0.805494 | + | 0.592604i | \(0.201900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.91323 | 0.278443 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 39.2149 | 1.84248 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.9887 | 2.06222 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.2474 | −0.900354 | −0.450177 | − | 0.892939i | \(-0.648639\pi\) | ||||
−0.450177 | + | 0.892939i | \(0.648639\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.550859 | −0.0257119 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.4602 | 1.46525 | 0.732623 | − | 0.680634i | \(-0.238296\pi\) | ||||
0.732623 | + | 0.680634i | \(0.238296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.9080 | 1.29699 | 0.648497 | − | 0.761217i | \(-0.275398\pi\) | ||||
0.648497 | + | 0.761217i | \(0.275398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.7011 | 0.913617 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.2738 | 1.40090 | 0.700451 | − | 0.713700i | \(-0.252982\pi\) | ||||
0.700451 | + | 0.713700i | \(0.252982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.3778 | 2.18770 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.31263 | 0.198715 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −75.7140 | −3.48133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.962033 | 0.0441411 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.89329 | 0.132475 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.9319 | 1.27624 | 0.638121 | − | 0.769936i | \(-0.279712\pi\) | ||||
0.638121 | + | 0.769936i | \(0.279712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.7486 | −1.31082 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −55.5701 | −2.52853 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.98294 | −0.407894 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.06821 | −0.410920 | −0.205460 | − | 0.978666i | \(-0.565869\pi\) | ||||
−0.205460 | + | 0.978666i | \(0.565869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.5986 | −0.841059 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.4672 | −1.10419 | −0.552094 | − | 0.833782i | \(-0.686171\pi\) | ||||
−0.552094 | + | 0.833782i | \(0.686171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.76233 | 0.259522 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −41.9028 | −1.88339 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.6904 | −0.569242 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2824 | −0.594602 | −0.297301 | − | 0.954784i | \(-0.596087\pi\) | ||||
−0.297301 | + | 0.954784i | \(0.596087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.8887 | −1.24598 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.4328 | 0.911052 | 0.455526 | − | 0.890222i | \(-0.349451\pi\) | ||||
0.455526 | + | 0.890222i | \(0.349451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9819 | −0.577685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.82832 | 0.392080 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.9047 | 1.68009 | 0.840047 | − | 0.542513i | \(-0.182527\pi\) | ||||
0.840047 | + | 0.542513i | \(0.182527\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.4720 | −1.21529 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.259048 | −0.0114372 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.299362 | 0.0131915 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.1614 | −1.59038 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.94099 | 0.129095 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.9888 | 1.27002 | 0.635011 | − | 0.772503i | \(-0.280996\pi\) | ||||
0.635011 | + | 0.772503i | \(0.280996\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.6227 | −1.86376 | −0.931880 | − | 0.362766i | \(-0.881832\pi\) | ||||
−0.931880 | + | 0.362766i | \(0.881832\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.3152 | 0.450194 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.06765 | 0.307872 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.85982 | 0.167818 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.6721 | −1.28766 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.06635 | −0.176133 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.3664 | 0.577880 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.0606 | −1.46983 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −74.1916 | −3.19566 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.2442 | 0.870368 | 0.435184 | − | 0.900342i | \(-0.356683\pi\) | ||||
0.435184 | + | 0.900342i | \(0.356683\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.8485 | −0.723039 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.6287 | −0.583787 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.8092 | −1.44558 | −0.722788 | − | 0.691070i | \(-0.757140\pi\) | ||||
−0.722788 | + | 0.691070i | \(0.757140\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.4614 | −0.531839 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.70980 | 0.115441 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.6585 | 0.538293 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −41.7791 | −1.77343 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.63096 | −0.196220 | −0.0981101 | − | 0.995176i | \(-0.531280\pi\) | ||||
−0.0981101 | + | 0.995176i | \(0.531280\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.0662 | 2.20216 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.6191 | −1.29274 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.58131 | 0.361659 | 0.180829 | − | 0.983514i | \(-0.442122\pi\) | ||||
0.180829 | + | 0.983514i | \(0.442122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.98667 | 0.0835797 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −41.1151 | −1.72667 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.0341 | −0.965641 | −0.482821 | − | 0.875719i | \(-0.660388\pi\) | ||||
−0.482821 | + | 0.875719i | \(0.660388\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.36276 | −0.0570299 | −0.0285149 | − | 0.999593i | \(-0.509078\pi\) | ||||
−0.0285149 | + | 0.999593i | \(0.509078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −58.8436 | −2.45823 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.98587 | −0.207925 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.5693 | −0.856312 | −0.428156 | − | 0.903705i | \(-0.640837\pi\) | ||||
−0.428156 | + | 0.903705i | \(0.640837\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38.3539 | 1.59393 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 60.6281 | 2.51528 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.93135 | −0.245651 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.8152 | 1.19136 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.0370 | −1.40486 | −0.702428 | − | 0.711754i | \(-0.747901\pi\) | ||||
−0.702428 | + | 0.711754i | \(0.747901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.32365 | 0.136948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.8547 | −1.22806 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.1137 | −0.497450 | −0.248725 | − | 0.968574i | \(-0.580011\pi\) | ||||
−0.248725 | + | 0.968574i | \(0.580011\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.9334 | 0.940178 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.3851 | −1.48914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.7127 | 0.601144 | 0.300572 | − | 0.953759i | \(-0.402822\pi\) | ||||
0.300572 | + | 0.953759i | \(0.402822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.49093 | 0.346352 | 0.173176 | − | 0.984891i | \(-0.444597\pi\) | ||||
0.173176 | + | 0.984891i | \(0.444597\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.0353 | 1.26385 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 59.0431 | 2.40044 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.8445 | −0.724285 | −0.362142 | − | 0.932123i | \(-0.617955\pi\) | ||||
−0.362142 | + | 0.932123i | \(0.617955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.0554 | 1.17739 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.8671 | 1.00601 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4422 | 0.542925 | 0.271463 | − | 0.962449i | \(-0.412493\pi\) | ||||
0.271463 | + | 0.962449i | \(0.412493\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.90946 | −0.238292 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.1603 | −0.690849 | −0.345425 | − | 0.938446i | \(-0.612265\pi\) | ||||
−0.345425 | + | 0.938446i | \(0.612265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.169156 | 0.00679897 | 0.00339949 | − | 0.999994i | \(-0.498918\pi\) | ||||
0.00339949 | + | 0.999994i | \(0.498918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.34255 | 0.0538748 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.8008 | −0.753238 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.8847 | −1.15539 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.3990 | −0.575041 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.9880 | −0.597611 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.91179 | −0.155726 | −0.0778629 | − | 0.996964i | \(-0.524810\pi\) | ||||
−0.0778629 | + | 0.996964i | \(0.524810\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.7309 | 1.38043 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.66794 | 0.343977 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51.0193 | 2.02146 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.31297 | −0.328856 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6148 | −0.498255 | −0.249127 | − | 0.968471i | \(-0.580144\pi\) | ||||
−0.249127 | + | 0.968471i | \(0.580144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.5038 | 1.51844 | 0.759220 | − | 0.650834i | \(-0.225581\pi\) | ||||
0.759220 | + | 0.650834i | \(0.225581\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 75.6657 | 2.97933 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.0194 | −1.45538 | −0.727692 | − | 0.685904i | \(-0.759407\pi\) | ||||
−0.727692 | + | 0.685904i | \(0.759407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 60.8289 | 2.38774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.6373 | 1.39673 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7482 | −0.577143 | −0.288572 | − | 0.957458i | \(-0.593180\pi\) | ||||
−0.288572 | + | 0.957458i | \(0.593180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.4334 | −0.446739 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.9958 | −0.702083 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.52104 | 0.137160 | 0.0685801 | − | 0.997646i | \(-0.478153\pi\) | ||||
0.0685801 | + | 0.997646i | \(0.478153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.9393 | −0.814443 | −0.407222 | − | 0.913329i | \(-0.633502\pi\) | ||||
−0.407222 | + | 0.913329i | \(0.633502\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.0558 | 0.817740 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.7847 | 0.418213 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.0439 | −0.543784 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −45.9919 | −1.77815 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.5463 | 0.986203 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.5325 | 0.444545 | 0.222273 | − | 0.974985i | \(-0.428653\pi\) | ||||
0.222273 | + | 0.974985i | \(0.428653\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.249212 | −0.00959219 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.31039 | 0.165662 | 0.0828309 | − | 0.996564i | \(-0.473604\pi\) | ||||
0.0828309 | + | 0.996564i | \(0.473604\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.2492 | −0.623587 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.9334 | 0.917129 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.7742 | 1.90456 | 0.952279 | − | 0.305230i | \(-0.0987334\pi\) | ||||
0.952279 | + | 0.305230i | \(0.0987334\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.85765 | 0.262017 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.9103 | −1.06485 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.07880 | 0.155390 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4006 | −0.966283 | −0.483142 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483142 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −75.7977 | −2.87932 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −40.5043 | −1.53641 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.11998 | −0.0803000 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −43.4920 | −1.64502 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.4730 | 0.811024 | 0.405512 | − | 0.914090i | \(-0.367093\pi\) | ||||
0.405512 | + | 0.914090i | \(0.367093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.04829 | −0.265831 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.1383 | 1.36105 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.4828 | −0.883162 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.6628 | 0.851121 | 0.425561 | − | 0.904930i | \(-0.360077\pi\) | ||||
0.425561 | + | 0.904930i | \(0.360077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.29206 | 0.310977 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.2253 | −0.645092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −59.0722 | −2.20918 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 56.1396 | 2.09657 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.3632 | 0.572950 | 0.286475 | − | 0.958088i | \(-0.407516\pi\) | ||||
0.286475 | + | 0.958088i | \(0.407516\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.541515 | 0.0201671 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −64.9404 | −2.41516 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.60692 | 0.0968185 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.7985 | 1.14225 | 0.571127 | − | 0.820862i | \(-0.306506\pi\) | ||||
0.571127 | + | 0.820862i | \(0.306506\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.0463 | −0.927641 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.1446 | 1.00398 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.5132 | 1.57026 | 0.785131 | − | 0.619329i | \(-0.212595\pi\) | ||||
0.785131 | + | 0.619329i | \(0.212595\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 74.1443 | 2.73485 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −63.6234 | −2.34360 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.0918 | 0.849445 | 0.424723 | − | 0.905324i | \(-0.360372\pi\) | ||||
0.424723 | + | 0.905324i | \(0.360372\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.90174 | 0.363750 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.49231 | −0.201493 | −0.100747 | − | 0.994912i | \(-0.532123\pi\) | ||||
−0.100747 | + | 0.994912i | \(0.532123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.5098 | −0.788059 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.7151 | 1.45310 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.1784 | 0.883461 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2136 | −0.482172 | −0.241086 | − | 0.970504i | \(-0.577504\pi\) | ||||
−0.241086 | + | 0.970504i | \(0.577504\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.47978 | 0.126810 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.4430 | 1.43548 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.2977 | −1.24657 | −0.623286 | − | 0.781994i | \(-0.714203\pi\) | ||||
−0.623286 | + | 0.781994i | \(0.714203\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 74.6249 | 2.70871 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.66171 | 0.0964868 | 0.0482434 | − | 0.998836i | \(-0.484638\pi\) | ||||
0.0482434 | + | 0.998836i | \(0.484638\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.6528 | −0.892492 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.0228 | 0.543149 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.8302 | −1.51040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.5865 | −0.670246 | −0.335123 | − | 0.942174i | \(-0.608778\pi\) | ||||
−0.335123 | + | 0.942174i | \(0.608778\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.3201 | −0.911881 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.8044 | −1.32376 | −0.661881 | − | 0.749609i | \(-0.730242\pi\) | ||||
−0.661881 | + | 0.749609i | \(0.730242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.19746 | 0.114856 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −75.5741 | −2.71121 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.996946 | −0.0357193 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.0419 | 0.609806 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.701968 | −0.0250863 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.33771 | 0.154819 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.0758 | −1.10773 | −0.553867 | − | 0.832605i | \(-0.686848\pi\) | ||||
−0.553867 | + | 0.832605i | \(0.686848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35.6182 | −1.26804 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.59367 | 0.127776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5674 | −0.623836 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.92756 | 0.210229 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.3939 | −0.474436 | −0.237218 | − | 0.971456i | \(-0.576236\pi\) | ||||
−0.237218 | + | 0.971456i | \(0.576236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9644 | 0.458647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.3157 | −0.435153 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.8920 | 1.30189 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −55.8933 | −1.96998 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −60.6937 | −2.13652 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.3412 | 1.45348 | 0.726740 | − | 0.686913i | \(-0.241035\pi\) | ||||
0.726740 | + | 0.686913i | \(0.241035\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.0952 | 1.40793 | 0.703966 | − | 0.710234i | \(-0.251411\pi\) | ||||
0.703966 | + | 0.710234i | \(0.251411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.7727 | 0.974032 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7068 | −0.655270 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.7651 | 0.446593 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 52.1237 | 1.82135 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.4412 | −0.957705 | −0.478852 | − | 0.877895i | \(-0.658947\pi\) | ||||
−0.478852 | + | 0.877895i | \(0.658947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.3157 | −1.05674 | −0.528370 | − | 0.849014i | \(-0.677197\pi\) | ||||
−0.528370 | + | 0.849014i | \(0.677197\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.8523 | −0.482275 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.9775 | −0.799006 | −0.399503 | − | 0.916732i | \(-0.630817\pi\) | ||||
−0.399503 | + | 0.916732i | \(0.630817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 55.9198 | 1.94218 | 0.971088 | − | 0.238724i | \(-0.0767290\pi\) | ||||
0.971088 | + | 0.238724i | \(0.0767290\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 78.5583 | 2.72516 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.5988 | 0.921594 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.0509 | −0.970741 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.860983 | −0.0297599 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.2795 | 1.28703 | 0.643515 | − | 0.765433i | \(-0.277475\pi\) | ||||
0.643515 | + | 0.765433i | \(0.277475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6570 | −0.746792 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 71.3365 | 2.45696 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.87966 | 0.305470 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 106.803 | 3.66979 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 58.8491 | 2.01969 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.5288 | 1.25219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.5559 | −1.52557 | −0.762783 | − | 0.646654i | \(-0.776168\pi\) | ||||
−0.762783 | + | 0.646654i | \(0.776168\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.06463 | 0.241605 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.2340 | 1.27189 | 0.635945 | − | 0.771735i | \(-0.280611\pi\) | ||||
0.635945 | + | 0.771735i | \(0.280611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.5366 | −1.79253 | −0.896263 | − | 0.443523i | \(-0.853729\pi\) | ||||
−0.896263 | + | 0.443523i | \(0.853729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.6896 | −0.364300 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.6678 | 1.62263 | 0.811316 | − | 0.584608i | \(-0.198752\pi\) | ||||
0.811316 | + | 0.584608i | \(0.198752\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.95810 | 0.100578 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.2920 | −1.02877 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.9990 | −0.576652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.7519 | 1.48248 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.6442 | −0.360252 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43.5483 | −1.47220 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.9010 | 1.44866 | 0.724332 | − | 0.689452i | \(-0.242148\pi\) | ||||
0.724332 | + | 0.689452i | \(0.242148\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.7169 | 0.361473 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.0745 | −1.85551 | −0.927753 | − | 0.373195i | \(-0.878262\pi\) | ||||
−0.927753 | + | 0.373195i | \(0.878262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.1137 | 0.374006 | 0.187003 | − | 0.982359i | \(-0.440123\pi\) | ||||
0.187003 | + | 0.982359i | \(0.440123\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −60.7901 | −2.04344 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.75241 | 0.193147 | 0.0965735 | − | 0.995326i | \(-0.469212\pi\) | ||||
0.0965735 | + | 0.995326i | \(0.469212\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.6794 | 0.525870 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 55.2134 | 1.84972 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.09666 | 0.204017 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.2587 | −1.14514 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −51.3172 | −1.71343 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00642 | 0.300381 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.12648 | 0.0708432 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 136.871 | 4.55479 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.9465 | −0.563320 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.42572 | 0.213362 | 0.106681 | − | 0.994293i | \(-0.465978\pi\) | ||||
0.106681 | + | 0.994293i | \(0.465978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.3827 | −0.510211 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.672625 | −0.0222850 | −0.0111425 | − | 0.999938i | \(-0.503547\pi\) | ||||
−0.0111425 | + | 0.999938i | \(0.503547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −81.4173 | −2.69452 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.5300 | −0.843995 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.6818 | −0.682973 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.9229 | −0.591223 | −0.295612 | − | 0.955308i | \(-0.595523\pi\) | ||||
−0.295612 | + | 0.955308i | \(0.595523\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.4642 | −0.542515 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.7192 | −0.385741 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.78068 | −0.222947 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.354725 | 0.0116507 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.10896 | 0.102002 | 0.0510008 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510008 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5084 | 0.409946 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.81448 | −0.124881 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.7972 | −1.00718 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.5833 | 1.06445 | 0.532225 | − | 0.846603i | \(-0.321356\pi\) | ||||
0.532225 | + | 0.846603i | \(0.321356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.2311 | −0.986556 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.9322 | −0.714968 | −0.357484 | − | 0.933919i | \(-0.616365\pi\) | ||||
−0.357484 | + | 0.933919i | \(0.616365\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.16682 | 0.168255 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.79375 | −0.0908807 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.4704 | −0.340241 | −0.170121 | − | 0.985423i | \(-0.554416\pi\) | ||||
−0.170121 | + | 0.985423i | \(0.554416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.3695 | −0.823528 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.2815 | −0.690101 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.67948 | −0.0867968 | −0.0433984 | − | 0.999058i | \(-0.513818\pi\) | ||||
−0.0433984 | + | 0.999058i | \(0.513818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59.1858 | −1.91521 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −39.0184 | −1.26129 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.4048 | 0.400571 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.9534 | −0.643657 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.8383 | 0.510383 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 38.5770 | 1.24184 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.3168 | 0.524714 | 0.262357 | − | 0.964971i | \(-0.415500\pi\) | ||||
0.262357 | + | 0.964971i | \(0.415500\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.16226 | 0.165836 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9928 | −0.898333 | −0.449166 | − | 0.893448i | \(-0.648279\pi\) | ||||
−0.449166 | + | 0.893448i | \(0.648279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −73.2680 | −2.34886 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.52580 | 0.305070 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.6814 | −0.565677 | −0.282838 | − | 0.959168i | \(-0.591276\pi\) | ||||
−0.282838 | + | 0.959168i | \(0.591276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.2475 | 0.806915 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.1491 | −0.515601 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.18277 | −0.229095 | −0.114547 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114547 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.0283 | −0.956780 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 65.3704 | 2.08076 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −66.1568 | −2.10366 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.5077 | 1.06441 | 0.532204 | − | 0.846616i | \(-0.321364\pi\) | ||||
0.532204 | + | 0.846616i | \(0.321364\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 83.9735 | 2.66482 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.5967 | −1.16019 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.9262 | −1.61285 | −0.806424 | − | 0.591338i | \(-0.798600\pi\) | ||||
−0.806424 | + | 0.591338i | \(0.798600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.82584 | 0.0577671 |
(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 | 4028.2.a.e.1.16 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.e.1.16 | ✓ | 19 | 1.1 | even | 1 | trivial |