Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 10x^{7} - x^{6} + 31x^{5} + 9x^{4} - 31x^{3} - 15x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.263492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.263492 | 0.186317 | 0.0931586 | − | 0.995651i | \(-0.470304\pi\) | ||||
0.0931586 | + | 0.995651i | \(0.470304\pi\) | |||||||
\(3\) | 1.72975 | 0.998670 | 0.499335 | − | 0.866409i | \(-0.333578\pi\) | ||||
0.499335 | + | 0.866409i | \(0.333578\pi\) | |||||||
\(4\) | −1.93057 | −0.965286 | ||||||||
\(5\) | −0.976450 | −0.436682 | −0.218341 | − | 0.975873i | \(-0.570064\pi\) | ||||
−0.218341 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(6\) | 0.455775 | 0.186069 | ||||||||
\(7\) | 0.775627 | 0.293159 | 0.146580 | − | 0.989199i | \(-0.453174\pi\) | ||||
0.146580 | + | 0.989199i | \(0.453174\pi\) | |||||||
\(8\) | −1.03568 | −0.366166 | ||||||||
\(9\) | −0.00797179 | −0.00265726 | ||||||||
\(10\) | −0.257287 | −0.0813613 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.33940 | −0.964003 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.204372 | 0.0546206 | ||||||||
\(15\) | −1.68901 | −0.436101 | ||||||||
\(16\) | 3.58825 | 0.897063 | ||||||||
\(17\) | −4.83237 | −1.17202 | −0.586010 | − | 0.810304i | \(-0.699302\pi\) | ||||
−0.586010 | + | 0.810304i | \(0.699302\pi\) | |||||||
\(18\) | −0.00210050 | −0.000495093 0 | ||||||||
\(19\) | 0.373766 | 0.0857478 | 0.0428739 | − | 0.999080i | \(-0.486349\pi\) | ||||
0.0428739 | + | 0.999080i | \(0.486349\pi\) | |||||||
\(20\) | 1.88511 | 0.421523 | ||||||||
\(21\) | 1.34164 | 0.292770 | ||||||||
\(22\) | 0.263492 | 0.0561767 | ||||||||
\(23\) | 0.0494328 | 0.0103074 | 0.00515372 | − | 0.999987i | \(-0.498360\pi\) | ||||
0.00515372 | + | 0.999987i | \(0.498360\pi\) | |||||||
\(24\) | −1.79146 | −0.365680 | ||||||||
\(25\) | −4.04654 | −0.809309 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.20303 | −1.00132 | ||||||||
\(28\) | −1.49740 | −0.282983 | ||||||||
\(29\) | −0.390176 | −0.0724539 | −0.0362270 | − | 0.999344i | \(-0.511534\pi\) | ||||
−0.0362270 | + | 0.999344i | \(0.511534\pi\) | |||||||
\(30\) | −0.445042 | −0.0812532 | ||||||||
\(31\) | −2.30297 | −0.413625 | −0.206813 | − | 0.978381i | \(-0.566309\pi\) | ||||
−0.206813 | + | 0.978381i | \(0.566309\pi\) | |||||||
\(32\) | 3.01683 | 0.533305 | ||||||||
\(33\) | 1.72975 | 0.301110 | ||||||||
\(34\) | −1.27329 | −0.218368 | ||||||||
\(35\) | −0.757361 | −0.128017 | ||||||||
\(36\) | 0.0153901 | 0.00256502 | ||||||||
\(37\) | 3.31853 | 0.545563 | 0.272782 | − | 0.962076i | \(-0.412056\pi\) | ||||
0.272782 | + | 0.962076i | \(0.412056\pi\) | |||||||
\(38\) | 0.0984844 | 0.0159763 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.01129 | 0.159898 | ||||||||
\(41\) | −2.78494 | −0.434934 | −0.217467 | − | 0.976068i | \(-0.569779\pi\) | ||||
−0.217467 | + | 0.976068i | \(0.569779\pi\) | |||||||
\(42\) | 0.353511 | 0.0545480 | ||||||||
\(43\) | −8.64863 | −1.31890 | −0.659452 | − | 0.751747i | \(-0.729212\pi\) | ||||
−0.659452 | + | 0.751747i | \(0.729212\pi\) | |||||||
\(44\) | −1.93057 | −0.291045 | ||||||||
\(45\) | 0.00778405 | 0.00116038 | ||||||||
\(46\) | 0.0130252 | 0.00192045 | ||||||||
\(47\) | −7.18602 | −1.04819 | −0.524094 | − | 0.851660i | \(-0.675596\pi\) | ||||
−0.524094 | + | 0.851660i | \(0.675596\pi\) | |||||||
\(48\) | 6.20677 | 0.895870 | ||||||||
\(49\) | −6.39840 | −0.914058 | ||||||||
\(50\) | −1.06623 | −0.150788 | ||||||||
\(51\) | −8.35877 | −1.17046 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.42786 | −0.470853 | −0.235426 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235426 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(54\) | −1.37096 | −0.186564 | ||||||||
\(55\) | −0.976450 | −0.131665 | ||||||||
\(56\) | −0.803297 | −0.107345 | ||||||||
\(57\) | 0.646521 | 0.0856338 | ||||||||
\(58\) | −0.102808 | −0.0134994 | ||||||||
\(59\) | 12.0408 | 1.56757 | 0.783787 | − | 0.621030i | \(-0.213285\pi\) | ||||
0.783787 | + | 0.621030i | \(0.213285\pi\) | |||||||
\(60\) | 3.26076 | 0.420962 | ||||||||
\(61\) | 1.31781 | 0.168729 | 0.0843645 | − | 0.996435i | \(-0.473114\pi\) | ||||
0.0843645 | + | 0.996435i | \(0.473114\pi\) | |||||||
\(62\) | −0.606814 | −0.0770655 | ||||||||
\(63\) | −0.00618313 | −0.000779001 0 | ||||||||
\(64\) | −6.38159 | −0.797699 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.455775 | 0.0561020 | ||||||||
\(67\) | −0.0855823 | −0.0104555 | −0.00522777 | − | 0.999986i | \(-0.501664\pi\) | ||||
−0.00522777 | + | 0.999986i | \(0.501664\pi\) | |||||||
\(68\) | 9.32923 | 1.13134 | ||||||||
\(69\) | 0.0855062 | 0.0102937 | ||||||||
\(70\) | −0.199559 | −0.0238518 | ||||||||
\(71\) | −5.84251 | −0.693378 | −0.346689 | − | 0.937980i | \(-0.612694\pi\) | ||||
−0.346689 | + | 0.937980i | \(0.612694\pi\) | |||||||
\(72\) | 0.00825618 | 0.000973000 0 | ||||||||
\(73\) | −7.94653 | −0.930071 | −0.465035 | − | 0.885292i | \(-0.653958\pi\) | ||||
−0.465035 | + | 0.885292i | \(0.653958\pi\) | |||||||
\(74\) | 0.874407 | 0.101648 | ||||||||
\(75\) | −6.99950 | −0.808233 | ||||||||
\(76\) | −0.721582 | −0.0827711 | ||||||||
\(77\) | 0.775627 | 0.0883909 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.1453 | −1.70398 | −0.851989 | − | 0.523559i | \(-0.824604\pi\) | ||||
−0.851989 | + | 0.523559i | \(0.824604\pi\) | |||||||
\(80\) | −3.50375 | −0.391731 | ||||||||
\(81\) | −8.97602 | −0.997336 | ||||||||
\(82\) | −0.733810 | −0.0810357 | ||||||||
\(83\) | 14.5887 | 1.60132 | 0.800658 | − | 0.599121i | \(-0.204483\pi\) | ||||
0.800658 | + | 0.599121i | \(0.204483\pi\) | |||||||
\(84\) | −2.59013 | −0.282606 | ||||||||
\(85\) | 4.71856 | 0.511800 | ||||||||
\(86\) | −2.27885 | −0.245734 | ||||||||
\(87\) | −0.674907 | −0.0723576 | ||||||||
\(88\) | −1.03568 | −0.110403 | ||||||||
\(89\) | −4.17837 | −0.442906 | −0.221453 | − | 0.975171i | \(-0.571080\pi\) | ||||
−0.221453 | + | 0.975171i | \(0.571080\pi\) | |||||||
\(90\) | 0.00205104 | 0.000216198 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0954335 | −0.00994963 | ||||||||
\(93\) | −3.98356 | −0.413075 | ||||||||
\(94\) | −1.89346 | −0.195296 | ||||||||
\(95\) | −0.364964 | −0.0374445 | ||||||||
\(96\) | 5.21835 | 0.532596 | ||||||||
\(97\) | −14.6583 | −1.48832 | −0.744161 | − | 0.668000i | \(-0.767151\pi\) | ||||
−0.744161 | + | 0.668000i | \(0.767151\pi\) | |||||||
\(98\) | −1.68593 | −0.170305 | ||||||||
\(99\) | −0.00797179 | −0.000801195 0 | ||||||||
\(100\) | 7.81215 | 0.781215 | ||||||||
\(101\) | −0.202281 | −0.0201277 | −0.0100639 | − | 0.999949i | \(-0.503203\pi\) | ||||
−0.0100639 | + | 0.999949i | \(0.503203\pi\) | |||||||
\(102\) | −2.20247 | −0.218077 | ||||||||
\(103\) | 11.5589 | 1.13893 | 0.569467 | − | 0.822014i | \(-0.307150\pi\) | ||||
0.569467 | + | 0.822014i | \(0.307150\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.31004 | −0.127847 | ||||||||
\(106\) | −0.903214 | −0.0877279 | ||||||||
\(107\) | −14.2165 | −1.37436 | −0.687179 | − | 0.726488i | \(-0.741151\pi\) | ||||
−0.687179 | + | 0.726488i | \(0.741151\pi\) | |||||||
\(108\) | 10.0448 | 0.966564 | ||||||||
\(109\) | 12.7076 | 1.21717 | 0.608586 | − | 0.793488i | \(-0.291737\pi\) | ||||
0.608586 | + | 0.793488i | \(0.291737\pi\) | |||||||
\(110\) | −0.257287 | −0.0245314 | ||||||||
\(111\) | 5.74022 | 0.544838 | ||||||||
\(112\) | 2.78314 | 0.262982 | ||||||||
\(113\) | 2.41619 | 0.227296 | 0.113648 | − | 0.993521i | \(-0.463746\pi\) | ||||
0.113648 | + | 0.993521i | \(0.463746\pi\) | |||||||
\(114\) | 0.170353 | 0.0159550 | ||||||||
\(115\) | −0.0482687 | −0.00450107 | ||||||||
\(116\) | 0.753264 | 0.0699388 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.17265 | 0.292066 | ||||||||
\(119\) | −3.74811 | −0.343589 | ||||||||
\(120\) | 1.74927 | 0.159686 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.347234 | 0.0314371 | ||||||||
\(123\) | −4.81724 | −0.434356 | ||||||||
\(124\) | 4.44605 | 0.399267 | ||||||||
\(125\) | 8.83350 | 0.790092 | ||||||||
\(126\) | −0.00162921 | −0.000145141 0 | ||||||||
\(127\) | 3.94265 | 0.349853 | 0.174927 | − | 0.984581i | \(-0.444031\pi\) | ||||
0.174927 | + | 0.984581i | \(0.444031\pi\) | |||||||
\(128\) | −7.71515 | −0.681930 | ||||||||
\(129\) | −14.9600 | −1.31715 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.8346 | −1.38347 | −0.691737 | − | 0.722150i | \(-0.743154\pi\) | ||||
−0.691737 | + | 0.722150i | \(0.743154\pi\) | |||||||
\(132\) | −3.33940 | −0.290658 | ||||||||
\(133\) | 0.289903 | 0.0251378 | ||||||||
\(134\) | −0.0225503 | −0.00194805 | ||||||||
\(135\) | 5.08050 | 0.437260 | ||||||||
\(136\) | 5.00476 | 0.429155 | ||||||||
\(137\) | 7.83512 | 0.669399 | 0.334700 | − | 0.942325i | \(-0.391365\pi\) | ||||
0.334700 | + | 0.942325i | \(0.391365\pi\) | |||||||
\(138\) | 0.0225302 | 0.00191790 | ||||||||
\(139\) | 1.29349 | 0.109712 | 0.0548561 | − | 0.998494i | \(-0.482530\pi\) | ||||
0.0548561 | + | 0.998494i | \(0.482530\pi\) | |||||||
\(140\) | 1.46214 | 0.123573 | ||||||||
\(141\) | −12.4300 | −1.04680 | ||||||||
\(142\) | −1.53946 | −0.129188 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.0286048 | −0.00238373 | ||||||||
\(145\) | 0.380988 | 0.0316393 | ||||||||
\(146\) | −2.09385 | −0.173288 | ||||||||
\(147\) | −11.0676 | −0.912842 | ||||||||
\(148\) | −6.40666 | −0.526624 | ||||||||
\(149\) | 13.4048 | 1.09816 | 0.549081 | − | 0.835769i | \(-0.314978\pi\) | ||||
0.549081 | + | 0.835769i | \(0.314978\pi\) | |||||||
\(150\) | −1.84431 | −0.150588 | ||||||||
\(151\) | −19.1366 | −1.55731 | −0.778656 | − | 0.627451i | \(-0.784098\pi\) | ||||
−0.778656 | + | 0.627451i | \(0.784098\pi\) | |||||||
\(152\) | −0.387100 | −0.0313980 | ||||||||
\(153\) | 0.0385226 | 0.00311437 | ||||||||
\(154\) | 0.204372 | 0.0164687 | ||||||||
\(155\) | 2.24873 | 0.180623 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.776709 | 0.0619881 | 0.0309940 | − | 0.999520i | \(-0.490133\pi\) | ||||
0.0309940 | + | 0.999520i | \(0.490133\pi\) | |||||||
\(158\) | −3.99067 | −0.317480 | ||||||||
\(159\) | −5.92933 | −0.470227 | ||||||||
\(160\) | −2.94578 | −0.232884 | ||||||||
\(161\) | 0.0383414 | 0.00302172 | ||||||||
\(162\) | −2.36511 | −0.185821 | ||||||||
\(163\) | 3.10254 | 0.243010 | 0.121505 | − | 0.992591i | \(-0.461228\pi\) | ||||
0.121505 | + | 0.992591i | \(0.461228\pi\) | |||||||
\(164\) | 5.37652 | 0.419836 | ||||||||
\(165\) | −1.68901 | −0.131489 | ||||||||
\(166\) | 3.84401 | 0.298353 | ||||||||
\(167\) | −20.0392 | −1.55068 | −0.775339 | − | 0.631545i | \(-0.782421\pi\) | ||||
−0.775339 | + | 0.631545i | \(0.782421\pi\) | |||||||
\(168\) | −1.38950 | −0.107202 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.24331 | 0.0953572 | ||||||||
\(171\) | −0.00297958 | −0.000227854 0 | ||||||||
\(172\) | 16.6968 | 1.27312 | ||||||||
\(173\) | 15.1318 | 1.15045 | 0.575223 | − | 0.817996i | \(-0.304915\pi\) | ||||
0.575223 | + | 0.817996i | \(0.304915\pi\) | |||||||
\(174\) | −0.177833 | −0.0134815 | ||||||||
\(175\) | −3.13861 | −0.237256 | ||||||||
\(176\) | 3.58825 | 0.270475 | ||||||||
\(177\) | 20.8275 | 1.56549 | ||||||||
\(178\) | −1.10097 | −0.0825210 | ||||||||
\(179\) | 5.59353 | 0.418080 | 0.209040 | − | 0.977907i | \(-0.432966\pi\) | ||||
0.209040 | + | 0.977907i | \(0.432966\pi\) | |||||||
\(180\) | −0.0150277 | −0.00112010 | ||||||||
\(181\) | 9.81461 | 0.729514 | 0.364757 | − | 0.931103i | \(-0.381152\pi\) | ||||
0.364757 | + | 0.931103i | \(0.381152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.27949 | 0.168505 | ||||||||
\(184\) | −0.0511963 | −0.00377424 | ||||||||
\(185\) | −3.24038 | −0.238238 | ||||||||
\(186\) | −1.04964 | −0.0769630 | ||||||||
\(187\) | −4.83237 | −0.353378 | ||||||||
\(188\) | 13.8731 | 1.01180 | ||||||||
\(189\) | −4.03561 | −0.293547 | ||||||||
\(190\) | −0.0961652 | −0.00697655 | ||||||||
\(191\) | −2.45366 | −0.177540 | −0.0887702 | − | 0.996052i | \(-0.528294\pi\) | ||||
−0.0887702 | + | 0.996052i | \(0.528294\pi\) | |||||||
\(192\) | −11.0385 | −0.796638 | ||||||||
\(193\) | 25.1495 | 1.81030 | 0.905149 | − | 0.425094i | \(-0.139759\pi\) | ||||
0.905149 | + | 0.425094i | \(0.139759\pi\) | |||||||
\(194\) | −3.86234 | −0.277300 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.3526 | 0.882327 | ||||||||
\(197\) | 23.2584 | 1.65710 | 0.828548 | − | 0.559918i | \(-0.189167\pi\) | ||||
0.828548 | + | 0.559918i | \(0.189167\pi\) | |||||||
\(198\) | −0.00210050 | −0.000149276 0 | ||||||||
\(199\) | −19.3989 | −1.37515 | −0.687577 | − | 0.726111i | \(-0.741326\pi\) | ||||
−0.687577 | + | 0.726111i | \(0.741326\pi\) | |||||||
\(200\) | 4.19091 | 0.296342 | ||||||||
\(201\) | −0.148036 | −0.0104416 | ||||||||
\(202\) | −0.0532996 | −0.00375014 | ||||||||
\(203\) | −0.302631 | −0.0212405 | ||||||||
\(204\) | 16.1372 | 1.12983 | ||||||||
\(205\) | 2.71935 | 0.189928 | ||||||||
\(206\) | 3.04568 | 0.212203 | ||||||||
\(207\) | −0.000394067 0 | −2.73896e−5 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.373766 | 0.0258539 | ||||||||
\(210\) | −0.345186 | −0.0238201 | ||||||||
\(211\) | 21.7549 | 1.49767 | 0.748835 | − | 0.662757i | \(-0.230614\pi\) | ||||
0.748835 | + | 0.662757i | \(0.230614\pi\) | |||||||
\(212\) | 6.61773 | 0.454507 | ||||||||
\(213\) | −10.1061 | −0.692457 | ||||||||
\(214\) | −3.74593 | −0.256066 | ||||||||
\(215\) | 8.44496 | 0.575941 | ||||||||
\(216\) | 5.38865 | 0.366651 | ||||||||
\(217\) | −1.78624 | −0.121258 | ||||||||
\(218\) | 3.34837 | 0.226780 | ||||||||
\(219\) | −13.7455 | −0.928834 | ||||||||
\(220\) | 1.88511 | 0.127094 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.51250 | 0.101513 | ||||||||
\(223\) | 16.0649 | 1.07578 | 0.537892 | − | 0.843014i | \(-0.319221\pi\) | ||||
0.537892 | + | 0.843014i | \(0.319221\pi\) | |||||||
\(224\) | 2.33993 | 0.156343 | ||||||||
\(225\) | 0.0322582 | 0.00215055 | ||||||||
\(226\) | 0.636648 | 0.0423492 | ||||||||
\(227\) | 2.71857 | 0.180438 | 0.0902190 | − | 0.995922i | \(-0.471243\pi\) | ||||
0.0902190 | + | 0.995922i | \(0.471243\pi\) | |||||||
\(228\) | −1.24816 | −0.0826611 | ||||||||
\(229\) | −24.2039 | −1.59944 | −0.799720 | − | 0.600373i | \(-0.795019\pi\) | ||||
−0.799720 | + | 0.600373i | \(0.795019\pi\) | |||||||
\(230\) | −0.0127184 | −0.000838627 0 | ||||||||
\(231\) | 1.34164 | 0.0882733 | ||||||||
\(232\) | 0.404096 | 0.0265302 | ||||||||
\(233\) | 17.8276 | 1.16792 | 0.583962 | − | 0.811781i | \(-0.301502\pi\) | ||||
0.583962 | + | 0.811781i | \(0.301502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.01679 | 0.457725 | ||||||||
\(236\) | −23.2456 | −1.51316 | ||||||||
\(237\) | −26.1975 | −1.70171 | ||||||||
\(238\) | −0.987598 | −0.0640165 | ||||||||
\(239\) | −8.54311 | −0.552608 | −0.276304 | − | 0.961070i | \(-0.589110\pi\) | ||||
−0.276304 | + | 0.961070i | \(0.589110\pi\) | |||||||
\(240\) | −6.06060 | −0.391210 | ||||||||
\(241\) | −21.6404 | −1.39398 | −0.696992 | − | 0.717079i | \(-0.745478\pi\) | ||||
−0.696992 | + | 0.717079i | \(0.745478\pi\) | |||||||
\(242\) | 0.263492 | 0.0169379 | ||||||||
\(243\) | 0.0828450 | 0.00531451 | ||||||||
\(244\) | −2.54414 | −0.162872 | ||||||||
\(245\) | 6.24772 | 0.399152 | ||||||||
\(246\) | −1.26931 | −0.0809280 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.38513 | 0.151456 | ||||||||
\(249\) | 25.2348 | 1.59919 | ||||||||
\(250\) | 2.32756 | 0.147208 | ||||||||
\(251\) | 20.2272 | 1.27673 | 0.638364 | − | 0.769735i | \(-0.279611\pi\) | ||||
0.638364 | + | 0.769735i | \(0.279611\pi\) | |||||||
\(252\) | 0.0119370 | 0.000751959 0 | ||||||||
\(253\) | 0.0494328 | 0.00310781 | ||||||||
\(254\) | 1.03886 | 0.0651837 | ||||||||
\(255\) | 8.16193 | 0.511120 | ||||||||
\(256\) | 10.7303 | 0.670644 | ||||||||
\(257\) | 6.67251 | 0.416220 | 0.208110 | − | 0.978105i | \(-0.433269\pi\) | ||||
0.208110 | + | 0.978105i | \(0.433269\pi\) | |||||||
\(258\) | −3.94183 | −0.245408 | ||||||||
\(259\) | 2.57394 | 0.159937 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.00311040 | 0.000192529 0 | ||||||||
\(262\) | −4.17229 | −0.257765 | ||||||||
\(263\) | 23.7582 | 1.46499 | 0.732496 | − | 0.680771i | \(-0.238355\pi\) | ||||
0.732496 | + | 0.680771i | \(0.238355\pi\) | |||||||
\(264\) | −1.79146 | −0.110257 | ||||||||
\(265\) | 3.34713 | 0.205613 | ||||||||
\(266\) | 0.0763871 | 0.00468360 | ||||||||
\(267\) | −7.22752 | −0.442317 | ||||||||
\(268\) | 0.165223 | 0.0100926 | ||||||||
\(269\) | −14.5009 | −0.884133 | −0.442066 | − | 0.896982i | \(-0.645754\pi\) | ||||
−0.442066 | + | 0.896982i | \(0.645754\pi\) | |||||||
\(270\) | 1.33867 | 0.0814691 | ||||||||
\(271\) | 19.4590 | 1.18205 | 0.591026 | − | 0.806652i | \(-0.298723\pi\) | ||||
0.591026 | + | 0.806652i | \(0.298723\pi\) | |||||||
\(272\) | −17.3397 | −1.05138 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.06449 | 0.124721 | ||||||||
\(275\) | −4.04654 | −0.244016 | ||||||||
\(276\) | −0.165076 | −0.00993640 | ||||||||
\(277\) | −19.6474 | −1.18050 | −0.590248 | − | 0.807222i | \(-0.700970\pi\) | ||||
−0.590248 | + | 0.807222i | \(0.700970\pi\) | |||||||
\(278\) | 0.340824 | 0.0204413 | ||||||||
\(279\) | 0.0183588 | 0.00109911 | ||||||||
\(280\) | 0.784380 | 0.0468757 | ||||||||
\(281\) | 9.71386 | 0.579480 | 0.289740 | − | 0.957105i | \(-0.406431\pi\) | ||||
0.289740 | + | 0.957105i | \(0.406431\pi\) | |||||||
\(282\) | −3.27521 | −0.195036 | ||||||||
\(283\) | −8.52020 | −0.506473 | −0.253237 | − | 0.967404i | \(-0.581495\pi\) | ||||
−0.253237 | + | 0.967404i | \(0.581495\pi\) | |||||||
\(284\) | 11.2794 | 0.669308 | ||||||||
\(285\) | −0.631296 | −0.0373947 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.16007 | −0.127505 | ||||||||
\(288\) | −0.0240495 | −0.00141713 | ||||||||
\(289\) | 6.35175 | 0.373633 | ||||||||
\(290\) | 0.100387 | 0.00589495 | ||||||||
\(291\) | −25.3551 | −1.48634 | ||||||||
\(292\) | 15.3413 | 0.897784 | ||||||||
\(293\) | −9.98789 | −0.583499 | −0.291749 | − | 0.956495i | \(-0.594237\pi\) | ||||
−0.291749 | + | 0.956495i | \(0.594237\pi\) | |||||||
\(294\) | −2.91623 | −0.170078 | ||||||||
\(295\) | −11.7572 | −0.684531 | ||||||||
\(296\) | −3.43692 | −0.199767 | ||||||||
\(297\) | −5.20303 | −0.301911 | ||||||||
\(298\) | 3.53205 | 0.204606 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 13.5130 | 0.780176 | ||||||||
\(301\) | −6.70811 | −0.386649 | ||||||||
\(302\) | −5.04234 | −0.290154 | ||||||||
\(303\) | −0.349896 | −0.0201010 | ||||||||
\(304\) | 1.34117 | 0.0769212 | ||||||||
\(305\) | −1.28678 | −0.0736809 | ||||||||
\(306\) | 0.0101504 | 0.000580260 0 | ||||||||
\(307\) | −0.878686 | −0.0501493 | −0.0250746 | − | 0.999686i | \(-0.507982\pi\) | ||||
−0.0250746 | + | 0.999686i | \(0.507982\pi\) | |||||||
\(308\) | −1.49740 | −0.0853224 | ||||||||
\(309\) | 19.9940 | 1.13742 | ||||||||
\(310\) | 0.592524 | 0.0336531 | ||||||||
\(311\) | −11.9408 | −0.677101 | −0.338551 | − | 0.940948i | \(-0.609937\pi\) | ||||
−0.338551 | + | 0.940948i | \(0.609937\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5562 | 1.10538 | 0.552691 | − | 0.833386i | \(-0.313601\pi\) | ||||
0.552691 | + | 0.833386i | \(0.313601\pi\) | |||||||
\(314\) | 0.204657 | 0.0115494 | ||||||||
\(315\) | 0.00603752 | 0.000340176 0 | ||||||||
\(316\) | 29.2391 | 1.64483 | ||||||||
\(317\) | −29.5494 | −1.65966 | −0.829830 | − | 0.558016i | \(-0.811563\pi\) | ||||
−0.829830 | + | 0.558016i | \(0.811563\pi\) | |||||||
\(318\) | −1.56233 | −0.0876113 | ||||||||
\(319\) | −0.390176 | −0.0218457 | ||||||||
\(320\) | 6.23131 | 0.348341 | ||||||||
\(321\) | −24.5909 | −1.37253 | ||||||||
\(322\) | 0.0101027 | 0.000562999 0 | ||||||||
\(323\) | −1.80617 | −0.100498 | ||||||||
\(324\) | 17.3289 | 0.962714 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.817495 | 0.0452769 | ||||||||
\(327\) | 21.9810 | 1.21555 | ||||||||
\(328\) | 2.88429 | 0.159258 | ||||||||
\(329\) | −5.57367 | −0.307286 | ||||||||
\(330\) | −0.445042 | −0.0244987 | ||||||||
\(331\) | 32.9803 | 1.81276 | 0.906379 | − | 0.422465i | \(-0.138835\pi\) | ||||
0.906379 | + | 0.422465i | \(0.138835\pi\) | |||||||
\(332\) | −28.1645 | −1.54573 | ||||||||
\(333\) | −0.0264546 | −0.00144970 | ||||||||
\(334\) | −5.28017 | −0.288918 | ||||||||
\(335\) | 0.0835668 | 0.00456574 | ||||||||
\(336\) | 4.81414 | 0.262633 | ||||||||
\(337\) | −8.43174 | −0.459306 | −0.229653 | − | 0.973273i | \(-0.573759\pi\) | ||||
−0.229653 | + | 0.973273i | \(0.573759\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.17940 | 0.226994 | ||||||||
\(340\) | −9.10953 | −0.494034 | ||||||||
\(341\) | −2.30297 | −0.124713 | ||||||||
\(342\) | −0.000785097 0 | −4.24532e−5 0 | ||||||||
\(343\) | −10.3922 | −0.561124 | ||||||||
\(344\) | 8.95717 | 0.482938 | ||||||||
\(345\) | −0.0834926 | −0.00449509 | ||||||||
\(346\) | 3.98710 | 0.214348 | ||||||||
\(347\) | −10.5456 | −0.566120 | −0.283060 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283060 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(348\) | 1.30296 | 0.0698458 | ||||||||
\(349\) | 35.6573 | 1.90869 | 0.954344 | − | 0.298708i | \(-0.0965558\pi\) | ||||
0.954344 | + | 0.298708i | \(0.0965558\pi\) | |||||||
\(350\) | −0.826999 | −0.0442049 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.01683 | 0.160797 | ||||||||
\(353\) | 17.7029 | 0.942229 | 0.471115 | − | 0.882072i | \(-0.343852\pi\) | ||||
0.471115 | + | 0.882072i | \(0.343852\pi\) | |||||||
\(354\) | 5.48788 | 0.291678 | ||||||||
\(355\) | 5.70492 | 0.302786 | ||||||||
\(356\) | 8.06663 | 0.427531 | ||||||||
\(357\) | −6.48329 | −0.343132 | ||||||||
\(358\) | 1.47385 | 0.0778955 | ||||||||
\(359\) | −17.9342 | −0.946533 | −0.473267 | − | 0.880919i | \(-0.656925\pi\) | ||||
−0.473267 | + | 0.880919i | \(0.656925\pi\) | |||||||
\(360\) | −0.00806175 | −0.000424892 0 | ||||||||
\(361\) | −18.8603 | −0.992647 | ||||||||
\(362\) | 2.58607 | 0.135921 | ||||||||
\(363\) | 1.72975 | 0.0907882 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.75939 | 0.406145 | ||||||||
\(366\) | 0.600627 | 0.0313953 | ||||||||
\(367\) | −7.54176 | −0.393676 | −0.196838 | − | 0.980436i | \(-0.563067\pi\) | ||||
−0.196838 | + | 0.980436i | \(0.563067\pi\) | |||||||
\(368\) | 0.177377 | 0.00924643 | ||||||||
\(369\) | 0.0222009 | 0.00115573 | ||||||||
\(370\) | −0.853815 | −0.0443877 | ||||||||
\(371\) | −2.65874 | −0.138035 | ||||||||
\(372\) | 7.69054 | 0.398736 | ||||||||
\(373\) | −23.5301 | −1.21834 | −0.609171 | − | 0.793039i | \(-0.708498\pi\) | ||||
−0.609171 | + | 0.793039i | \(0.708498\pi\) | |||||||
\(374\) | −1.27329 | −0.0658403 | ||||||||
\(375\) | 15.2797 | 0.789042 | ||||||||
\(376\) | 7.44238 | 0.383812 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.06335 | −0.0546929 | ||||||||
\(379\) | −30.4623 | −1.56475 | −0.782373 | − | 0.622811i | \(-0.785991\pi\) | ||||
−0.782373 | + | 0.622811i | \(0.785991\pi\) | |||||||
\(380\) | 0.704589 | 0.0361447 | ||||||||
\(381\) | 6.81979 | 0.349388 | ||||||||
\(382\) | −0.646520 | −0.0330788 | ||||||||
\(383\) | −31.1978 | −1.59413 | −0.797067 | − | 0.603891i | \(-0.793616\pi\) | ||||
−0.797067 | + | 0.603891i | \(0.793616\pi\) | |||||||
\(384\) | −13.3453 | −0.681023 | ||||||||
\(385\) | −0.757361 | −0.0385987 | ||||||||
\(386\) | 6.62669 | 0.337290 | ||||||||
\(387\) | 0.0689450 | 0.00350467 | ||||||||
\(388\) | 28.2989 | 1.43666 | ||||||||
\(389\) | 33.8085 | 1.71416 | 0.857079 | − | 0.515186i | \(-0.172277\pi\) | ||||
0.857079 | + | 0.515186i | \(0.172277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.238877 | −0.0120805 | ||||||||
\(392\) | 6.62667 | 0.334697 | ||||||||
\(393\) | −27.3898 | −1.38163 | ||||||||
\(394\) | 6.12842 | 0.308745 | ||||||||
\(395\) | 14.7886 | 0.744097 | ||||||||
\(396\) | 0.0153901 | 0.000773382 0 | ||||||||
\(397\) | −19.1080 | −0.959004 | −0.479502 | − | 0.877541i | \(-0.659183\pi\) | ||||
−0.479502 | + | 0.877541i | \(0.659183\pi\) | |||||||
\(398\) | −5.11147 | −0.256215 | ||||||||
\(399\) | 0.501459 | 0.0251043 | ||||||||
\(400\) | −14.5200 | −0.726001 | ||||||||
\(401\) | −21.8152 | −1.08940 | −0.544699 | − | 0.838632i | \(-0.683356\pi\) | ||||
−0.544699 | + | 0.838632i | \(0.683356\pi\) | |||||||
\(402\) | −0.0390063 | −0.00194546 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.390519 | 0.0194290 | ||||||||
\(405\) | 8.76464 | 0.435518 | ||||||||
\(406\) | −0.0797410 | −0.00395748 | ||||||||
\(407\) | 3.31853 | 0.164493 | ||||||||
\(408\) | 8.65698 | 0.428584 | ||||||||
\(409\) | −10.2357 | −0.506123 | −0.253062 | − | 0.967450i | \(-0.581438\pi\) | ||||
−0.253062 | + | 0.967450i | \(0.581438\pi\) | |||||||
\(410\) | 0.716529 | 0.0353868 | ||||||||
\(411\) | 13.5528 | 0.668510 | ||||||||
\(412\) | −22.3153 | −1.09940 | ||||||||
\(413\) | 9.33913 | 0.459549 | ||||||||
\(414\) | −0.000103834 0 | −5.10315e−6 0 | ||||||||
\(415\) | −14.2451 | −0.699266 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.23741 | 0.109566 | ||||||||
\(418\) | 0.0984844 | 0.00481703 | ||||||||
\(419\) | −4.54655 | −0.222113 | −0.111057 | − | 0.993814i | \(-0.535424\pi\) | ||||
−0.111057 | + | 0.993814i | \(0.535424\pi\) | |||||||
\(420\) | 2.52913 | 0.123409 | ||||||||
\(421\) | −2.57565 | −0.125529 | −0.0627647 | − | 0.998028i | \(-0.519992\pi\) | ||||
−0.0627647 | + | 0.998028i | \(0.519992\pi\) | |||||||
\(422\) | 5.73225 | 0.279042 | ||||||||
\(423\) | 0.0572854 | 0.00278531 | ||||||||
\(424\) | 3.55015 | 0.172410 | ||||||||
\(425\) | 19.5544 | 0.948527 | ||||||||
\(426\) | −2.66287 | −0.129017 | ||||||||
\(427\) | 1.02213 | 0.0494644 | ||||||||
\(428\) | 27.4459 | 1.32665 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.22518 | 0.107308 | ||||||||
\(431\) | −22.8922 | −1.10268 | −0.551340 | − | 0.834281i | \(-0.685883\pi\) | ||||
−0.551340 | + | 0.834281i | \(0.685883\pi\) | |||||||
\(432\) | −18.6698 | −0.898251 | ||||||||
\(433\) | −14.1020 | −0.677700 | −0.338850 | − | 0.940840i | \(-0.610038\pi\) | ||||
−0.338850 | + | 0.940840i | \(0.610038\pi\) | |||||||
\(434\) | −0.470661 | −0.0225925 | ||||||||
\(435\) | 0.659013 | 0.0315973 | ||||||||
\(436\) | −24.5330 | −1.17492 | ||||||||
\(437\) | 0.0184763 | 0.000883841 0 | ||||||||
\(438\) | −3.62183 | −0.173058 | ||||||||
\(439\) | 25.3673 | 1.21071 | 0.605357 | − | 0.795954i | \(-0.293030\pi\) | ||||
0.605357 | + | 0.795954i | \(0.293030\pi\) | |||||||
\(440\) | 1.01129 | 0.0482111 | ||||||||
\(441\) | 0.0510067 | 0.00242889 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.84745 | −0.372844 | −0.186422 | − | 0.982470i | \(-0.559689\pi\) | ||||
−0.186422 | + | 0.982470i | \(0.559689\pi\) | |||||||
\(444\) | −11.0819 | −0.525924 | ||||||||
\(445\) | 4.07997 | 0.193409 | ||||||||
\(446\) | 4.23297 | 0.200437 | ||||||||
\(447\) | 23.1869 | 1.09670 | ||||||||
\(448\) | −4.94973 | −0.233853 | ||||||||
\(449\) | −9.41851 | −0.444487 | −0.222244 | − | 0.974991i | \(-0.571338\pi\) | ||||
−0.222244 | + | 0.974991i | \(0.571338\pi\) | |||||||
\(450\) | 0.00849978 | 0.000400684 0 | ||||||||
\(451\) | −2.78494 | −0.131138 | ||||||||
\(452\) | −4.66463 | −0.219406 | ||||||||
\(453\) | −33.1014 | −1.55524 | ||||||||
\(454\) | 0.716323 | 0.0336187 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.669586 | −0.0313562 | ||||||||
\(457\) | 30.0349 | 1.40497 | 0.702487 | − | 0.711696i | \(-0.252073\pi\) | ||||
0.702487 | + | 0.711696i | \(0.252073\pi\) | |||||||
\(458\) | −6.37755 | −0.298003 | ||||||||
\(459\) | 25.1430 | 1.17357 | ||||||||
\(460\) | 0.0931861 | 0.00434482 | ||||||||
\(461\) | 5.52451 | 0.257302 | 0.128651 | − | 0.991690i | \(-0.458935\pi\) | ||||
0.128651 | + | 0.991690i | \(0.458935\pi\) | |||||||
\(462\) | 0.353511 | 0.0164468 | ||||||||
\(463\) | −12.9560 | −0.602116 | −0.301058 | − | 0.953606i | \(-0.597340\pi\) | ||||
−0.301058 | + | 0.953606i | \(0.597340\pi\) | |||||||
\(464\) | −1.40005 | −0.0649957 | ||||||||
\(465\) | 3.88974 | 0.180383 | ||||||||
\(466\) | 4.69743 | 0.217604 | ||||||||
\(467\) | 41.3398 | 1.91298 | 0.956490 | − | 0.291766i | \(-0.0942430\pi\) | ||||
0.956490 | + | 0.291766i | \(0.0942430\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0663799 | −0.00306514 | ||||||||
\(470\) | 1.84887 | 0.0852820 | ||||||||
\(471\) | 1.34351 | 0.0619057 | ||||||||
\(472\) | −12.4703 | −0.573993 | ||||||||
\(473\) | −8.64863 | −0.397664 | ||||||||
\(474\) | −6.90285 | −0.317058 | ||||||||
\(475\) | −1.51246 | −0.0693965 | ||||||||
\(476\) | 7.23600 | 0.331661 | ||||||||
\(477\) | 0.0273261 | 0.00125118 | ||||||||
\(478\) | −2.25104 | −0.102960 | ||||||||
\(479\) | 5.83127 | 0.266437 | 0.133219 | − | 0.991087i | \(-0.457469\pi\) | ||||
0.133219 | + | 0.991087i | \(0.457469\pi\) | |||||||
\(480\) | −5.09546 | −0.232575 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.70209 | −0.259723 | ||||||||
\(483\) | 0.0663209 | 0.00301771 | ||||||||
\(484\) | −1.93057 | −0.0877533 | ||||||||
\(485\) | 14.3131 | 0.649923 | ||||||||
\(486\) | 0.0218290 | 0.000990184 0 | ||||||||
\(487\) | −4.92176 | −0.223026 | −0.111513 | − | 0.993763i | \(-0.535570\pi\) | ||||
−0.111513 | + | 0.993763i | \(0.535570\pi\) | |||||||
\(488\) | −1.36483 | −0.0617829 | ||||||||
\(489\) | 5.36661 | 0.242687 | ||||||||
\(490\) | 1.64623 | 0.0743689 | ||||||||
\(491\) | 17.3615 | 0.783515 | 0.391758 | − | 0.920069i | \(-0.371867\pi\) | ||||
0.391758 | + | 0.920069i | \(0.371867\pi\) | |||||||
\(492\) | 9.30003 | 0.419278 | ||||||||
\(493\) | 1.88547 | 0.0849175 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.00778405 | 0.000349867 0 | ||||||||
\(496\) | −8.26363 | −0.371048 | ||||||||
\(497\) | −4.53161 | −0.203270 | ||||||||
\(498\) | 6.64916 | 0.297956 | ||||||||
\(499\) | −15.1483 | −0.678131 | −0.339066 | − | 0.940763i | \(-0.610111\pi\) | ||||
−0.339066 | + | 0.940763i | \(0.610111\pi\) | |||||||
\(500\) | −17.0537 | −0.762665 | ||||||||
\(501\) | −34.6627 | −1.54862 | ||||||||
\(502\) | 5.32970 | 0.237876 | ||||||||
\(503\) | 15.3714 | 0.685375 | 0.342687 | − | 0.939449i | \(-0.388663\pi\) | ||||
0.342687 | + | 0.939449i | \(0.388663\pi\) | |||||||
\(504\) | 0.00640371 | 0.000285244 0 | ||||||||
\(505\) | 0.197518 | 0.00878942 | ||||||||
\(506\) | 0.0130252 | 0.000579039 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.61157 | −0.337709 | ||||||||
\(509\) | 34.3660 | 1.52325 | 0.761624 | − | 0.648019i | \(-0.224402\pi\) | ||||
0.761624 | + | 0.648019i | \(0.224402\pi\) | |||||||
\(510\) | 2.15060 | 0.0952304 | ||||||||
\(511\) | −6.16354 | −0.272659 | ||||||||
\(512\) | 18.2577 | 0.806882 | ||||||||
\(513\) | −1.94472 | −0.0858613 | ||||||||
\(514\) | 1.75816 | 0.0775489 | ||||||||
\(515\) | −11.2867 | −0.497352 | ||||||||
\(516\) | 28.8813 | 1.27143 | ||||||||
\(517\) | −7.18602 | −0.316041 | ||||||||
\(518\) | 0.678213 | 0.0297990 | ||||||||
\(519\) | 26.1741 | 1.14892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.2698 | 1.15090 | 0.575451 | − | 0.817836i | \(-0.304826\pi\) | ||||
0.575451 | + | 0.817836i | \(0.304826\pi\) | |||||||
\(522\) | 0.000819567 0 | 3.58715e−5 0 | ||||||||
\(523\) | 8.63548 | 0.377603 | 0.188802 | − | 0.982015i | \(-0.439540\pi\) | ||||
0.188802 | + | 0.982015i | \(0.439540\pi\) | |||||||
\(524\) | 30.5698 | 1.33545 | ||||||||
\(525\) | −5.42900 | −0.236941 | ||||||||
\(526\) | 6.26010 | 0.272953 | ||||||||
\(527\) | 11.1288 | 0.484777 | ||||||||
\(528\) | 6.20677 | 0.270115 | ||||||||
\(529\) | −22.9976 | −0.999894 | ||||||||
\(530\) | 0.881944 | 0.0383092 | ||||||||
\(531\) | −0.0959864 | −0.00416545 | ||||||||
\(532\) | −0.559678 | −0.0242651 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.90440 | −0.0824112 | ||||||||
\(535\) | 13.8817 | 0.600157 | ||||||||
\(536\) | 0.0886354 | 0.00382847 | ||||||||
\(537\) | 9.67540 | 0.417524 | ||||||||
\(538\) | −3.82086 | −0.164729 | ||||||||
\(539\) | −6.39840 | −0.275599 | ||||||||
\(540\) | −9.80828 | −0.422081 | ||||||||
\(541\) | 44.0739 | 1.89489 | 0.947443 | − | 0.319925i | \(-0.103658\pi\) | ||||
0.947443 | + | 0.319925i | \(0.103658\pi\) | |||||||
\(542\) | 5.12730 | 0.220237 | ||||||||
\(543\) | 16.9768 | 0.728544 | ||||||||
\(544\) | −14.5784 | −0.625044 | ||||||||
\(545\) | −12.4084 | −0.531517 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.61458 | 0.240062 | 0.120031 | − | 0.992770i | \(-0.461701\pi\) | ||||
0.120031 | + | 0.992770i | \(0.461701\pi\) | |||||||
\(548\) | −15.1263 | −0.646162 | ||||||||
\(549\) | −0.0105053 | −0.000448357 0 | ||||||||
\(550\) | −1.06623 | −0.0454643 | ||||||||
\(551\) | −0.145835 | −0.00621277 | ||||||||
\(552\) | −0.0885567 | −0.00376922 | ||||||||
\(553\) | −11.7471 | −0.499537 | ||||||||
\(554\) | −5.17693 | −0.219947 | ||||||||
\(555\) | −5.60504 | −0.237921 | ||||||||
\(556\) | −2.49717 | −0.105904 | ||||||||
\(557\) | 2.68740 | 0.113869 | 0.0569345 | − | 0.998378i | \(-0.481867\pi\) | ||||
0.0569345 | + | 0.998378i | \(0.481867\pi\) | |||||||
\(558\) | 0.00483739 | 0.000204783 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.71760 | −0.114840 | ||||||||
\(561\) | −8.35877 | −0.352908 | ||||||||
\(562\) | 2.55953 | 0.107967 | ||||||||
\(563\) | −24.8840 | −1.04874 | −0.524368 | − | 0.851492i | \(-0.675698\pi\) | ||||
−0.524368 | + | 0.851492i | \(0.675698\pi\) | |||||||
\(564\) | 23.9970 | 1.01046 | ||||||||
\(565\) | −2.35929 | −0.0992561 | ||||||||
\(566\) | −2.24501 | −0.0943647 | ||||||||
\(567\) | −6.96204 | −0.292378 | ||||||||
\(568\) | 6.05094 | 0.253892 | ||||||||
\(569\) | 38.3160 | 1.60629 | 0.803146 | − | 0.595782i | \(-0.203158\pi\) | ||||
0.803146 | + | 0.595782i | \(0.203158\pi\) | |||||||
\(570\) | −0.166342 | −0.00696728 | ||||||||
\(571\) | −6.29021 | −0.263237 | −0.131618 | − | 0.991300i | \(-0.542017\pi\) | ||||
−0.131618 | + | 0.991300i | \(0.542017\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.24421 | −0.177304 | ||||||||
\(574\) | −0.569162 | −0.0237564 | ||||||||
\(575\) | −0.200032 | −0.00834191 | ||||||||
\(576\) | 0.0508727 | 0.00211969 | ||||||||
\(577\) | −31.2456 | −1.30077 | −0.650385 | − | 0.759605i | \(-0.725392\pi\) | ||||
−0.650385 | + | 0.759605i | \(0.725392\pi\) | |||||||
\(578\) | 1.67364 | 0.0696141 | ||||||||
\(579\) | 43.5022 | 1.80789 | ||||||||
\(580\) | −0.735524 | −0.0305410 | ||||||||
\(581\) | 11.3154 | 0.469441 | ||||||||
\(582\) | −6.68088 | −0.276931 | ||||||||
\(583\) | −3.42786 | −0.141967 | ||||||||
\(584\) | 8.23002 | 0.340561 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.63173 | −0.108716 | ||||||||
\(587\) | −8.59755 | −0.354859 | −0.177429 | − | 0.984134i | \(-0.556778\pi\) | ||||
−0.177429 | + | 0.984134i | \(0.556778\pi\) | |||||||
\(588\) | 21.3668 | 0.881154 | ||||||||
\(589\) | −0.860771 | −0.0354675 | ||||||||
\(590\) | −3.09793 | −0.127540 | ||||||||
\(591\) | 40.2312 | 1.65489 | ||||||||
\(592\) | 11.9077 | 0.489404 | ||||||||
\(593\) | 29.9426 | 1.22959 | 0.614797 | − | 0.788685i | \(-0.289238\pi\) | ||||
0.614797 | + | 0.788685i | \(0.289238\pi\) | |||||||
\(594\) | −1.37096 | −0.0562511 | ||||||||
\(595\) | 3.65984 | 0.150039 | ||||||||
\(596\) | −25.8789 | −1.06004 | ||||||||
\(597\) | −33.5553 | −1.37333 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.2184 | −1.11211 | −0.556057 | − | 0.831144i | \(-0.687687\pi\) | ||||
−0.556057 | + | 0.831144i | \(0.687687\pi\) | |||||||
\(600\) | 7.24921 | 0.295948 | ||||||||
\(601\) | −26.1539 | −1.06684 | −0.533419 | − | 0.845851i | \(-0.679093\pi\) | ||||
−0.533419 | + | 0.845851i | \(0.679093\pi\) | |||||||
\(602\) | −1.76753 | −0.0720393 | ||||||||
\(603\) | 0.000682243 0 | 2.77831e−5 0 | ||||||||
\(604\) | 36.9445 | 1.50325 | ||||||||
\(605\) | −0.976450 | −0.0396984 | ||||||||
\(606\) | −0.0921948 | −0.00374516 | ||||||||
\(607\) | −14.4023 | −0.584573 | −0.292286 | − | 0.956331i | \(-0.594416\pi\) | ||||
−0.292286 | + | 0.956331i | \(0.594416\pi\) | |||||||
\(608\) | 1.12759 | 0.0457297 | ||||||||
\(609\) | −0.523476 | −0.0212123 | ||||||||
\(610\) | −0.339057 | −0.0137280 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.0743706 | −0.00300625 | ||||||||
\(613\) | 23.2677 | 0.939774 | 0.469887 | − | 0.882726i | \(-0.344295\pi\) | ||||
0.469887 | + | 0.882726i | \(0.344295\pi\) | |||||||
\(614\) | −0.231527 | −0.00934367 | ||||||||
\(615\) | 4.70380 | 0.189675 | ||||||||
\(616\) | −0.803297 | −0.0323658 | ||||||||
\(617\) | −23.7698 | −0.956934 | −0.478467 | − | 0.878105i | \(-0.658807\pi\) | ||||
−0.478467 | + | 0.878105i | \(0.658807\pi\) | |||||||
\(618\) | 5.26827 | 0.211921 | ||||||||
\(619\) | −37.3418 | −1.50090 | −0.750448 | − | 0.660930i | \(-0.770162\pi\) | ||||
−0.750448 | + | 0.660930i | \(0.770162\pi\) | |||||||
\(620\) | −4.34134 | −0.174353 | ||||||||
\(621\) | −0.257200 | −0.0103211 | ||||||||
\(622\) | −3.14631 | −0.126156 | ||||||||
\(623\) | −3.24085 | −0.129842 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.6072 | 0.464290 | ||||||||
\(626\) | 5.15291 | 0.205952 | ||||||||
\(627\) | 0.646521 | 0.0258196 | ||||||||
\(628\) | −1.49949 | −0.0598362 | ||||||||
\(629\) | −16.0364 | −0.639411 | ||||||||
\(630\) | 0.00159084 | 6.33806e−5 0 | ||||||||
\(631\) | 6.86579 | 0.273323 | 0.136661 | − | 0.990618i | \(-0.456363\pi\) | ||||
0.136661 | + | 0.990618i | \(0.456363\pi\) | |||||||
\(632\) | 15.6856 | 0.623940 | ||||||||
\(633\) | 37.6305 | 1.49568 | ||||||||
\(634\) | −7.78604 | −0.309223 | ||||||||
\(635\) | −3.84980 | −0.152775 | ||||||||
\(636\) | 11.4470 | 0.453903 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.102808 | −0.00407023 | ||||||||
\(639\) | 0.0465752 | 0.00184249 | ||||||||
\(640\) | 7.53346 | 0.297786 | ||||||||
\(641\) | 18.3310 | 0.724031 | 0.362016 | − | 0.932172i | \(-0.382089\pi\) | ||||
0.362016 | + | 0.932172i | \(0.382089\pi\) | |||||||
\(642\) | −6.47951 | −0.255726 | ||||||||
\(643\) | −17.7938 | −0.701720 | −0.350860 | − | 0.936428i | \(-0.614111\pi\) | ||||
−0.350860 | + | 0.936428i | \(0.614111\pi\) | |||||||
\(644\) | −0.0740208 | −0.00291683 | ||||||||
\(645\) | 14.6077 | 0.575176 | ||||||||
\(646\) | −0.475913 | −0.0187245 | ||||||||
\(647\) | 8.89493 | 0.349696 | 0.174848 | − | 0.984595i | \(-0.444057\pi\) | ||||
0.174848 | + | 0.984595i | \(0.444057\pi\) | |||||||
\(648\) | 9.29624 | 0.365191 | ||||||||
\(649\) | 12.0408 | 0.472641 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.08975 | −0.121097 | ||||||||
\(652\) | −5.98968 | −0.234574 | ||||||||
\(653\) | 3.84991 | 0.150659 | 0.0753293 | − | 0.997159i | \(-0.475999\pi\) | ||||
0.0753293 | + | 0.997159i | \(0.475999\pi\) | |||||||
\(654\) | 5.79183 | 0.226478 | ||||||||
\(655\) | 15.4617 | 0.604138 | ||||||||
\(656\) | −9.99306 | −0.390163 | ||||||||
\(657\) | 0.0633480 | 0.00247144 | ||||||||
\(658\) | −1.46862 | −0.0572527 | ||||||||
\(659\) | 7.26528 | 0.283015 | 0.141508 | − | 0.989937i | \(-0.454805\pi\) | ||||
0.141508 | + | 0.989937i | \(0.454805\pi\) | |||||||
\(660\) | 3.26076 | 0.126925 | ||||||||
\(661\) | −12.0382 | −0.468230 | −0.234115 | − | 0.972209i | \(-0.575219\pi\) | ||||
−0.234115 | + | 0.972209i | \(0.575219\pi\) | |||||||
\(662\) | 8.69004 | 0.337748 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.1091 | −0.586348 | ||||||||
\(665\) | −0.283076 | −0.0109772 | ||||||||
\(666\) | −0.00697059 | −0.000270105 0 | ||||||||
\(667\) | −0.0192875 | −0.000746815 0 | ||||||||
\(668\) | 38.6871 | 1.49685 | ||||||||
\(669\) | 27.7882 | 1.07435 | ||||||||
\(670\) | 0.0220192 | 0.000850676 0 | ||||||||
\(671\) | 1.31781 | 0.0508737 | ||||||||
\(672\) | 4.04749 | 0.156135 | ||||||||
\(673\) | −19.1151 | −0.736832 | −0.368416 | − | 0.929661i | \(-0.620100\pi\) | ||||
−0.368416 | + | 0.929661i | \(0.620100\pi\) | |||||||
\(674\) | −2.22170 | −0.0855766 | ||||||||
\(675\) | 21.0543 | 0.810381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.8824 | 0.648844 | 0.324422 | − | 0.945912i | \(-0.394830\pi\) | ||||
0.324422 | + | 0.945912i | \(0.394830\pi\) | |||||||
\(678\) | 1.10124 | 0.0422929 | ||||||||
\(679\) | −11.3693 | −0.436316 | ||||||||
\(680\) | −4.88690 | −0.187404 | ||||||||
\(681\) | 4.70245 | 0.180198 | ||||||||
\(682\) | −0.606814 | −0.0232361 | ||||||||
\(683\) | 16.5802 | 0.634423 | 0.317212 | − | 0.948355i | \(-0.397253\pi\) | ||||
0.317212 | + | 0.948355i | \(0.397253\pi\) | |||||||
\(684\) | 0.00575230 | 0.000219945 0 | ||||||||
\(685\) | −7.65061 | −0.292315 | ||||||||
\(686\) | −2.73825 | −0.104547 | ||||||||
\(687\) | −41.8667 | −1.59731 | ||||||||
\(688\) | −31.0335 | −1.18314 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.0219997 | −0.000837513 0 | ||||||||
\(691\) | −18.5861 | −0.707047 | −0.353523 | − | 0.935426i | \(-0.615017\pi\) | ||||
−0.353523 | + | 0.935426i | \(0.615017\pi\) | |||||||
\(692\) | −29.2130 | −1.11051 | ||||||||
\(693\) | −0.00618313 | −0.000234878 0 | ||||||||
\(694\) | −2.77870 | −0.105478 | ||||||||
\(695\) | −1.26303 | −0.0479093 | ||||||||
\(696\) | 0.698984 | 0.0264949 | ||||||||
\(697\) | 13.4578 | 0.509752 | ||||||||
\(698\) | 9.39541 | 0.355621 | ||||||||
\(699\) | 30.8372 | 1.16637 | ||||||||
\(700\) | 6.05931 | 0.229020 | ||||||||
\(701\) | −51.0772 | −1.92916 | −0.964579 | − | 0.263793i | \(-0.915026\pi\) | ||||
−0.964579 | + | 0.263793i | \(0.915026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.24035 | 0.0467808 | ||||||||
\(704\) | −6.38159 | −0.240515 | ||||||||
\(705\) | 12.1373 | 0.457117 | ||||||||
\(706\) | 4.66457 | 0.175553 | ||||||||
\(707\) | −0.156895 | −0.00590064 | ||||||||
\(708\) | −40.2090 | −1.51115 | ||||||||
\(709\) | 6.26174 | 0.235165 | 0.117582 | − | 0.993063i | \(-0.462486\pi\) | ||||
0.117582 | + | 0.993063i | \(0.462486\pi\) | |||||||
\(710\) | 1.50320 | 0.0564142 | ||||||||
\(711\) | 0.120735 | 0.00452792 | ||||||||
\(712\) | 4.32743 | 0.162177 | ||||||||
\(713\) | −0.113842 | −0.00426342 | ||||||||
\(714\) | −1.70830 | −0.0639314 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.7987 | −0.403567 | ||||||||
\(717\) | −14.7774 | −0.551873 | ||||||||
\(718\) | −4.72554 | −0.176355 | ||||||||
\(719\) | 2.84647 | 0.106155 | 0.0530776 | − | 0.998590i | \(-0.483097\pi\) | ||||
0.0530776 | + | 0.998590i | \(0.483097\pi\) | |||||||
\(720\) | 0.0279311 | 0.00104093 | ||||||||
\(721\) | 8.96540 | 0.333889 | ||||||||
\(722\) | −4.96954 | −0.184947 | ||||||||
\(723\) | −37.4325 | −1.39213 | ||||||||
\(724\) | −18.9478 | −0.704190 | ||||||||
\(725\) | 1.57887 | 0.0586376 | ||||||||
\(726\) | 0.455775 | 0.0169154 | ||||||||
\(727\) | −24.5240 | −0.909545 | −0.454772 | − | 0.890608i | \(-0.650279\pi\) | ||||
−0.454772 | + | 0.890608i | \(0.650279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0714 | 1.00264 | ||||||||
\(730\) | 2.04454 | 0.0756718 | ||||||||
\(731\) | 41.7933 | 1.54578 | ||||||||
\(732\) | −4.40071 | −0.162655 | ||||||||
\(733\) | −3.78597 | −0.139838 | −0.0699191 | − | 0.997553i | \(-0.522274\pi\) | ||||
−0.0699191 | + | 0.997553i | \(0.522274\pi\) | |||||||
\(734\) | −1.98719 | −0.0733487 | ||||||||
\(735\) | 10.8070 | 0.398622 | ||||||||
\(736\) | 0.149130 | 0.00549701 | ||||||||
\(737\) | −0.0855823 | −0.00315246 | ||||||||
\(738\) | 0.00584977 | 0.000215333 0 | ||||||||
\(739\) | 33.0302 | 1.21503 | 0.607517 | − | 0.794307i | \(-0.292166\pi\) | ||||
0.607517 | + | 0.794307i | \(0.292166\pi\) | |||||||
\(740\) | 6.25579 | 0.229967 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.700557 | −0.0257183 | ||||||||
\(743\) | 42.2022 | 1.54825 | 0.774125 | − | 0.633033i | \(-0.218190\pi\) | ||||
0.774125 | + | 0.633033i | \(0.218190\pi\) | |||||||
\(744\) | 4.12567 | 0.151254 | ||||||||
\(745\) | −13.0891 | −0.479547 | ||||||||
\(746\) | −6.20000 | −0.226998 | ||||||||
\(747\) | −0.116298 | −0.00425512 | ||||||||
\(748\) | 9.32923 | 0.341110 | ||||||||
\(749\) | −11.0267 | −0.402906 | ||||||||
\(750\) | 4.02609 | 0.147012 | ||||||||
\(751\) | −1.51083 | −0.0551311 | −0.0275655 | − | 0.999620i | \(-0.508775\pi\) | ||||
−0.0275655 | + | 0.999620i | \(0.508775\pi\) | |||||||
\(752\) | −25.7853 | −0.940291 | ||||||||
\(753\) | 34.9879 | 1.27503 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.6859 | 0.680050 | ||||||||
\(756\) | 7.79104 | 0.283357 | ||||||||
\(757\) | −6.97665 | −0.253571 | −0.126785 | − | 0.991930i | \(-0.540466\pi\) | ||||
−0.126785 | + | 0.991930i | \(0.540466\pi\) | |||||||
\(758\) | −8.02659 | −0.291539 | ||||||||
\(759\) | 0.0855062 | 0.00310368 | ||||||||
\(760\) | 0.377984 | 0.0137109 | ||||||||
\(761\) | 39.9612 | 1.44859 | 0.724296 | − | 0.689489i | \(-0.242165\pi\) | ||||
0.724296 | + | 0.689489i | \(0.242165\pi\) | |||||||
\(762\) | 1.79696 | 0.0650970 | ||||||||
\(763\) | 9.85639 | 0.356825 | ||||||||
\(764\) | 4.73696 | 0.171377 | ||||||||
\(765\) | −0.0376154 | −0.00135999 | ||||||||
\(766\) | −8.22038 | −0.297015 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 18.5607 | 0.669752 | ||||||||
\(769\) | −19.8747 | −0.716702 | −0.358351 | − | 0.933587i | \(-0.616661\pi\) | ||||
−0.358351 | + | 0.933587i | \(0.616661\pi\) | |||||||
\(770\) | −0.199559 | −0.00719160 | ||||||||
\(771\) | 11.5418 | 0.415667 | ||||||||
\(772\) | −48.5529 | −1.74746 | ||||||||
\(773\) | −30.3791 | −1.09266 | −0.546330 | − | 0.837570i | \(-0.683976\pi\) | ||||
−0.546330 | + | 0.837570i | \(0.683976\pi\) | |||||||
\(774\) | 0.0181665 | 0.000652981 0 | ||||||||
\(775\) | 9.31906 | 0.334751 | ||||||||
\(776\) | 15.1812 | 0.544974 | ||||||||
\(777\) | 4.45227 | 0.159724 | ||||||||
\(778\) | 8.90827 | 0.319377 | ||||||||
\(779\) | −1.04091 | −0.0372946 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.84251 | −0.209061 | ||||||||
\(782\) | −0.0629423 | −0.00225081 | ||||||||
\(783\) | 2.03010 | 0.0725499 | ||||||||
\(784\) | −22.9591 | −0.819967 | ||||||||
\(785\) | −0.758417 | −0.0270691 | ||||||||
\(786\) | −7.21701 | −0.257422 | ||||||||
\(787\) | 13.9900 | 0.498690 | 0.249345 | − | 0.968415i | \(-0.419785\pi\) | ||||
0.249345 | + | 0.968415i | \(0.419785\pi\) | |||||||
\(788\) | −44.9021 | −1.59957 | ||||||||
\(789\) | 41.0957 | 1.46304 | ||||||||
\(790\) | 3.89669 | 0.138638 | ||||||||
\(791\) | 1.87406 | 0.0666340 | ||||||||
\(792\) | 0.00825618 | 0.000293371 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.03481 | −0.178679 | ||||||||
\(795\) | 5.78970 | 0.205339 | ||||||||
\(796\) | 37.4511 | 1.32742 | ||||||||
\(797\) | −30.6940 | −1.08724 | −0.543619 | − | 0.839332i | \(-0.682946\pi\) | ||||
−0.543619 | + | 0.839332i | \(0.682946\pi\) | |||||||
\(798\) | 0.132131 | 0.00467737 | ||||||||
\(799\) | 34.7255 | 1.22850 | ||||||||
\(800\) | −12.2077 | −0.431608 | ||||||||
\(801\) | 0.0333090 | 0.00117692 | ||||||||
\(802\) | −5.74813 | −0.202973 | ||||||||
\(803\) | −7.94653 | −0.280427 | ||||||||
\(804\) | 0.285794 | 0.0100792 | ||||||||
\(805\) | −0.0374384 | −0.00131953 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.0828 | −0.882957 | ||||||||
\(808\) | 0.209498 | 0.00737011 | ||||||||
\(809\) | 15.6130 | 0.548922 | 0.274461 | − | 0.961598i | \(-0.411501\pi\) | ||||
0.274461 | + | 0.961598i | \(0.411501\pi\) | |||||||
\(810\) | 2.30941 | 0.0811446 | ||||||||
\(811\) | 26.9841 | 0.947541 | 0.473770 | − | 0.880648i | \(-0.342893\pi\) | ||||
0.473770 | + | 0.880648i | \(0.342893\pi\) | |||||||
\(812\) | 0.584251 | 0.0205032 | ||||||||
\(813\) | 33.6592 | 1.18048 | ||||||||
\(814\) | 0.874407 | 0.0306480 | ||||||||
\(815\) | −3.02948 | −0.106118 | ||||||||
\(816\) | −29.9934 | −1.04998 | ||||||||
\(817\) | −3.23256 | −0.113093 | ||||||||
\(818\) | −2.69703 | −0.0942994 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.24991 | −0.183335 | ||||||||
\(821\) | −50.1848 | −1.75146 | −0.875731 | − | 0.482799i | \(-0.839620\pi\) | ||||
−0.875731 | + | 0.482799i | \(0.839620\pi\) | |||||||
\(822\) | 3.57105 | 0.124555 | ||||||||
\(823\) | −46.8136 | −1.63182 | −0.815910 | − | 0.578179i | \(-0.803764\pi\) | ||||
−0.815910 | + | 0.578179i | \(0.803764\pi\) | |||||||
\(824\) | −11.9713 | −0.417039 | ||||||||
\(825\) | −6.99950 | −0.243691 | ||||||||
\(826\) | 2.46079 | 0.0856218 | ||||||||
\(827\) | 20.8413 | 0.724723 | 0.362362 | − | 0.932038i | \(-0.381971\pi\) | ||||
0.362362 | + | 0.932038i | \(0.381971\pi\) | |||||||
\(828\) | 0.000760776 0 | 2.64388e−5 0 | ||||||||
\(829\) | −53.2741 | −1.85029 | −0.925144 | − | 0.379617i | \(-0.876056\pi\) | ||||
−0.925144 | + | 0.379617i | \(0.876056\pi\) | |||||||
\(830\) | −3.75348 | −0.130285 | ||||||||
\(831\) | −33.9850 | −1.17893 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.9194 | 1.07129 | ||||||||
\(834\) | 0.589539 | 0.0204141 | ||||||||
\(835\) | 19.5673 | 0.677153 | ||||||||
\(836\) | −0.721582 | −0.0249564 | ||||||||
\(837\) | 11.9824 | 0.414173 | ||||||||
\(838\) | −1.19798 | −0.0413835 | ||||||||
\(839\) | 0.119197 | 0.00411514 | 0.00205757 | − | 0.999998i | \(-0.499345\pi\) | ||||
0.00205757 | + | 0.999998i | \(0.499345\pi\) | |||||||
\(840\) | 1.35678 | 0.0468133 | ||||||||
\(841\) | −28.8478 | −0.994750 | ||||||||
\(842\) | −0.678663 | −0.0233883 | ||||||||
\(843\) | 16.8025 | 0.578710 | ||||||||
\(844\) | −41.9994 | −1.44568 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.0150943 | 0.000518951 0 | ||||||||
\(847\) | 0.775627 | 0.0266508 | ||||||||
\(848\) | −12.3000 | −0.422384 | ||||||||
\(849\) | −14.7378 | −0.505800 | ||||||||
\(850\) | 5.15243 | 0.176727 | ||||||||
\(851\) | 0.164044 | 0.00562336 | ||||||||
\(852\) | 19.5105 | 0.668419 | ||||||||
\(853\) | −35.2244 | −1.20606 | −0.603030 | − | 0.797718i | \(-0.706040\pi\) | ||||
−0.603030 | + | 0.797718i | \(0.706040\pi\) | |||||||
\(854\) | 0.269324 | 0.00921608 | ||||||||
\(855\) | 0.00290941 | 9.94999e−5 0 | ||||||||
\(856\) | 14.7236 | 0.503244 | ||||||||
\(857\) | −10.9308 | −0.373388 | −0.186694 | − | 0.982418i | \(-0.559777\pi\) | ||||
−0.186694 | + | 0.982418i | \(0.559777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.6770 | −0.637252 | −0.318626 | − | 0.947880i | \(-0.603221\pi\) | ||||
−0.318626 | + | 0.947880i | \(0.603221\pi\) | |||||||
\(860\) | −16.3036 | −0.555948 | ||||||||
\(861\) | −3.73638 | −0.127335 | ||||||||
\(862\) | −6.03192 | −0.205448 | ||||||||
\(863\) | −32.8465 | −1.11811 | −0.559054 | − | 0.829131i | \(-0.688836\pi\) | ||||
−0.559054 | + | 0.829131i | \(0.688836\pi\) | |||||||
\(864\) | −15.6967 | −0.534011 | ||||||||
\(865\) | −14.7754 | −0.502379 | ||||||||
\(866\) | −3.71578 | −0.126267 | ||||||||
\(867\) | 10.9869 | 0.373136 | ||||||||
\(868\) | 3.44847 | 0.117049 | ||||||||
\(869\) | −15.1453 | −0.513769 | ||||||||
\(870\) | 0.173645 | 0.00588711 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −13.1610 | −0.445687 | ||||||||
\(873\) | 0.116853 | 0.00395486 | ||||||||
\(874\) | 0.00486836 | 0.000164675 0 | ||||||||
\(875\) | 6.85150 | 0.231623 | ||||||||
\(876\) | 26.5367 | 0.896591 | ||||||||
\(877\) | 35.5874 | 1.20170 | 0.600850 | − | 0.799362i | \(-0.294829\pi\) | ||||
0.600850 | + | 0.799362i | \(0.294829\pi\) | |||||||
\(878\) | 6.68408 | 0.225577 | ||||||||
\(879\) | −17.2765 | −0.582723 | ||||||||
\(880\) | −3.50375 | −0.118111 | ||||||||
\(881\) | −46.3588 | −1.56187 | −0.780933 | − | 0.624614i | \(-0.785256\pi\) | ||||
−0.780933 | + | 0.624614i | \(0.785256\pi\) | |||||||
\(882\) | 0.0134399 | 0.000452544 0 | ||||||||
\(883\) | −30.5731 | −1.02887 | −0.514434 | − | 0.857530i | \(-0.671998\pi\) | ||||
−0.514434 | + | 0.857530i | \(0.671998\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.3370 | −0.683621 | ||||||||
\(886\) | −2.06774 | −0.0694672 | ||||||||
\(887\) | −43.8421 | −1.47207 | −0.736036 | − | 0.676942i | \(-0.763305\pi\) | ||||
−0.736036 | + | 0.676942i | \(0.763305\pi\) | |||||||
\(888\) | −5.94501 | −0.199501 | ||||||||
\(889\) | 3.05802 | 0.102563 | ||||||||
\(890\) | 1.07504 | 0.0360354 | ||||||||
\(891\) | −8.97602 | −0.300708 | ||||||||
\(892\) | −31.0144 | −1.03844 | ||||||||
\(893\) | −2.68589 | −0.0898799 | ||||||||
\(894\) | 6.10956 | 0.204334 | ||||||||
\(895\) | −5.46181 | −0.182568 | ||||||||
\(896\) | −5.98408 | −0.199914 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.48170 | −0.0828156 | ||||||||
\(899\) | 0.898564 | 0.0299688 | ||||||||
\(900\) | −0.0622767 | −0.00207589 | ||||||||
\(901\) | 16.5647 | 0.551849 | ||||||||
\(902\) | −0.733810 | −0.0244332 | ||||||||
\(903\) | −11.6033 | −0.386135 | ||||||||
\(904\) | −2.50239 | −0.0832282 | ||||||||
\(905\) | −9.58348 | −0.318566 | ||||||||
\(906\) | −8.72197 | −0.289768 | ||||||||
\(907\) | −45.3727 | −1.50658 | −0.753289 | − | 0.657690i | \(-0.771534\pi\) | ||||
−0.753289 | + | 0.657690i | \(0.771534\pi\) | |||||||
\(908\) | −5.24840 | −0.174174 | ||||||||
\(909\) | 0.00161254 | 5.34847e−5 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.2313 | −1.53171 | −0.765856 | − | 0.643013i | \(-0.777684\pi\) | ||||
−0.765856 | + | 0.643013i | \(0.777684\pi\) | |||||||
\(912\) | 2.31988 | 0.0768189 | ||||||||
\(913\) | 14.5887 | 0.482815 | ||||||||
\(914\) | 7.91397 | 0.261771 | ||||||||
\(915\) | −2.22581 | −0.0735829 | ||||||||
\(916\) | 46.7274 | 1.54392 | ||||||||
\(917\) | −12.2817 | −0.405578 | ||||||||
\(918\) | 6.62497 | 0.218657 | ||||||||
\(919\) | −48.2463 | −1.59150 | −0.795750 | − | 0.605625i | \(-0.792923\pi\) | ||||
−0.795750 | + | 0.605625i | \(0.792923\pi\) | |||||||
\(920\) | 0.0499906 | 0.00164814 | ||||||||
\(921\) | −1.51991 | −0.0500826 | ||||||||
\(922\) | 1.45567 | 0.0479398 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.59013 | −0.0852090 | ||||||||
\(925\) | −13.4286 | −0.441529 | ||||||||
\(926\) | −3.41381 | −0.112185 | ||||||||
\(927\) | −0.0921452 | −0.00302645 | ||||||||
\(928\) | −1.17709 | −0.0386400 | ||||||||
\(929\) | −3.40932 | −0.111856 | −0.0559280 | − | 0.998435i | \(-0.517812\pi\) | ||||
−0.0559280 | + | 0.998435i | \(0.517812\pi\) | |||||||
\(930\) | 1.02492 | 0.0336084 | ||||||||
\(931\) | −2.39151 | −0.0783784 | ||||||||
\(932\) | −34.4174 | −1.12738 | ||||||||
\(933\) | −20.6546 | −0.676201 | ||||||||
\(934\) | 10.8927 | 0.356421 | ||||||||
\(935\) | 4.71856 | 0.154314 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.6118 | −1.13072 | −0.565360 | − | 0.824844i | \(-0.691263\pi\) | ||||
−0.565360 | + | 0.824844i | \(0.691263\pi\) | |||||||
\(938\) | −0.0174906 | −0.000571088 0 | ||||||||
\(939\) | 33.8273 | 1.10391 | ||||||||
\(940\) | −13.5464 | −0.441836 | ||||||||
\(941\) | 32.9559 | 1.07433 | 0.537165 | − | 0.843477i | \(-0.319495\pi\) | ||||
0.537165 | + | 0.843477i | \(0.319495\pi\) | |||||||
\(942\) | 0.354005 | 0.0115341 | ||||||||
\(943\) | −0.137667 | −0.00448306 | ||||||||
\(944\) | 43.2053 | 1.40621 | ||||||||
\(945\) | 3.94057 | 0.128187 | ||||||||
\(946\) | −2.27885 | −0.0740917 | ||||||||
\(947\) | 13.5265 | 0.439552 | 0.219776 | − | 0.975550i | \(-0.429467\pi\) | ||||
0.219776 | + | 0.975550i | \(0.429467\pi\) | |||||||
\(948\) | 50.5762 | 1.64264 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.398522 | −0.0129298 | ||||||||
\(951\) | −51.1130 | −1.65745 | ||||||||
\(952\) | 3.88183 | 0.125811 | ||||||||
\(953\) | −35.2197 | −1.14088 | −0.570440 | − | 0.821340i | \(-0.693227\pi\) | ||||
−0.570440 | + | 0.821340i | \(0.693227\pi\) | |||||||
\(954\) | 0.00720023 | 0.000233116 0 | ||||||||
\(955\) | 2.39588 | 0.0775287 | ||||||||
\(956\) | 16.4931 | 0.533424 | ||||||||
\(957\) | −0.674907 | −0.0218166 | ||||||||
\(958\) | 1.53649 | 0.0496419 | ||||||||
\(959\) | 6.07713 | 0.196241 | ||||||||
\(960\) | 10.7786 | 0.347878 | ||||||||
\(961\) | −25.6963 | −0.828914 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.113331 | 0.00365203 | ||||||||
\(964\) | 41.7784 | 1.34559 | ||||||||
\(965\) | −24.5572 | −0.790525 | ||||||||
\(966\) | 0.0174750 | 0.000562250 0 | ||||||||
\(967\) | −23.4856 | −0.755244 | −0.377622 | − | 0.925960i | \(-0.623258\pi\) | ||||
−0.377622 | + | 0.925960i | \(0.623258\pi\) | |||||||
\(968\) | −1.03568 | −0.0332879 | ||||||||
\(969\) | −3.12423 | −0.100365 | ||||||||
\(970\) | 3.77139 | 0.121092 | ||||||||
\(971\) | 48.6664 | 1.56178 | 0.780890 | − | 0.624668i | \(-0.214766\pi\) | ||||
0.780890 | + | 0.624668i | \(0.214766\pi\) | |||||||
\(972\) | −0.159938 | −0.00513002 | ||||||||
\(973\) | 1.00326 | 0.0321631 | ||||||||
\(974\) | −1.29685 | −0.0415536 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.72865 | 0.151360 | ||||||||
\(977\) | 15.1199 | 0.483729 | 0.241865 | − | 0.970310i | \(-0.422241\pi\) | ||||
0.241865 | + | 0.970310i | \(0.422241\pi\) | |||||||
\(978\) | 1.41406 | 0.0452167 | ||||||||
\(979\) | −4.17837 | −0.133541 | ||||||||
\(980\) | −12.0617 | −0.385296 | ||||||||
\(981\) | −0.101303 | −0.00323434 | ||||||||
\(982\) | 4.57463 | 0.145982 | ||||||||
\(983\) | −34.0595 | −1.08633 | −0.543165 | − | 0.839626i | \(-0.682774\pi\) | ||||
−0.543165 | + | 0.839626i | \(0.682774\pi\) | |||||||
\(984\) | 4.98910 | 0.159047 | ||||||||
\(985\) | −22.7107 | −0.723624 | ||||||||
\(986\) | 0.496808 | 0.0158216 | ||||||||
\(987\) | −9.64104 | −0.306878 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.427526 | −0.0135945 | ||||||||
\(990\) | 0.00205104 | 6.51863e−5 0 | ||||||||
\(991\) | −9.72217 | −0.308835 | −0.154418 | − | 0.988006i | \(-0.549350\pi\) | ||||
−0.154418 | + | 0.988006i | \(0.549350\pi\) | |||||||
\(992\) | −6.94766 | −0.220588 | ||||||||
\(993\) | 57.0475 | 1.81035 | ||||||||
\(994\) | −1.19404 | −0.0378727 | ||||||||
\(995\) | 18.9421 | 0.600505 | ||||||||
\(996\) | −48.7175 | −1.54367 | ||||||||
\(997\) | 12.5275 | 0.396749 | 0.198375 | − | 0.980126i | \(-0.436434\pi\) | ||||
0.198375 | + | 0.980126i | \(0.436434\pi\) | |||||||
\(998\) | −3.99146 | −0.126347 | ||||||||
\(999\) | −17.2664 | −0.546286 |
(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 | 1859.2.a.q.1.6 | ✓ | 9 | |
13.12 | even | 2 | 1859.2.a.r.1.4 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.q.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial | |
1859.2.a.r.1.4 | yes | 9 | 13.12 | even | 2 |