Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(1,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, 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("775.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.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: | \(6.18840615665\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 155) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.89122\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 775.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.576713 | 0.407797 | 0.203899 | − | 0.978992i | \(-0.434639\pi\) | ||||
0.203899 | + | 0.978992i | \(0.434639\pi\) | |||||||
\(3\) | 1.89122 | 1.09190 | 0.545948 | − | 0.837819i | \(-0.316170\pi\) | ||||
0.545948 | + | 0.837819i | \(0.316170\pi\) | |||||||
\(4\) | −1.66740 | −0.833701 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.09069 | 0.445272 | ||||||||
\(7\) | −4.24412 | −1.60412 | −0.802062 | − | 0.597240i | \(-0.796264\pi\) | ||||
−0.802062 | + | 0.597240i | \(0.796264\pi\) | |||||||
\(8\) | −2.11504 | −0.747779 | ||||||||
\(9\) | 0.576713 | 0.192238 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09069 | 0.328855 | 0.164428 | − | 0.986389i | \(-0.447422\pi\) | ||||
0.164428 | + | 0.986389i | \(0.447422\pi\) | |||||||
\(12\) | −3.15343 | −0.910315 | ||||||||
\(13\) | −4.69175 | −1.30126 | −0.650629 | − | 0.759396i | \(-0.725495\pi\) | ||||
−0.650629 | + | 0.759396i | \(0.725495\pi\) | |||||||
\(14\) | −2.44763 | −0.654158 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.11504 | 0.528759 | ||||||||
\(17\) | −2.80053 | −0.679228 | −0.339614 | − | 0.940565i | \(-0.610296\pi\) | ||||
−0.339614 | + | 0.940565i | \(0.610296\pi\) | |||||||
\(18\) | 0.332597 | 0.0783939 | ||||||||
\(19\) | −4.20573 | −0.964860 | −0.482430 | − | 0.875935i | \(-0.660246\pi\) | ||||
−0.482430 | + | 0.875935i | \(0.660246\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.02655 | −1.75154 | ||||||||
\(22\) | 0.629015 | 0.134106 | ||||||||
\(23\) | 4.24412 | 0.884959 | 0.442480 | − | 0.896779i | \(-0.354099\pi\) | ||||
0.442480 | + | 0.896779i | \(0.354099\pi\) | |||||||
\(24\) | −4.00000 | −0.816497 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.70579 | −0.530649 | ||||||||
\(27\) | −4.58297 | −0.881993 | ||||||||
\(28\) | 7.07665 | 1.33736 | ||||||||
\(29\) | 6.02655 | 1.11910 | 0.559552 | − | 0.828796i | \(-0.310973\pi\) | ||||
0.559552 | + | 0.828796i | \(0.310973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 5.44984 | 0.963405 | ||||||||
\(33\) | 2.06273 | 0.359076 | ||||||||
\(34\) | −1.61510 | −0.276987 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.961612 | −0.160269 | ||||||||
\(37\) | −6.53428 | −1.07423 | −0.537114 | − | 0.843510i | \(-0.680486\pi\) | ||||
−0.537114 | + | 0.843510i | \(0.680486\pi\) | |||||||
\(38\) | −2.42550 | −0.393467 | ||||||||
\(39\) | −8.87313 | −1.42084 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.42189 | −1.15910 | −0.579552 | − | 0.814935i | \(-0.696772\pi\) | ||||
−0.579552 | + | 0.814935i | \(0.696772\pi\) | |||||||
\(42\) | −4.62901 | −0.714272 | ||||||||
\(43\) | −8.58297 | −1.30889 | −0.654445 | − | 0.756109i | \(-0.727098\pi\) | ||||
−0.654445 | + | 0.756109i | \(0.727098\pi\) | |||||||
\(44\) | −1.81862 | −0.274167 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.44763 | 0.360884 | ||||||||
\(47\) | 10.0893 | 1.47167 | 0.735837 | − | 0.677159i | \(-0.236789\pi\) | ||||
0.735837 | + | 0.677159i | \(0.236789\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 11.0125 | 1.57322 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.29642 | −0.741647 | ||||||||
\(52\) | 7.82304 | 1.08486 | ||||||||
\(53\) | 7.45610 | 1.02417 | 0.512087 | − | 0.858934i | \(-0.328873\pi\) | ||||
0.512087 | + | 0.858934i | \(0.328873\pi\) | |||||||
\(54\) | −2.64306 | −0.359674 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.97646 | 1.19953 | ||||||||
\(57\) | −7.95395 | −1.05353 | ||||||||
\(58\) | 3.47559 | 0.456367 | ||||||||
\(59\) | 0.716096 | 0.0932278 | 0.0466139 | − | 0.998913i | \(-0.485157\pi\) | ||||
0.0466139 | + | 0.998913i | \(0.485157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.78244 | 1.25251 | 0.626257 | − | 0.779617i | \(-0.284586\pi\) | ||||
0.626257 | + | 0.779617i | \(0.284586\pi\) | |||||||
\(62\) | −0.576713 | −0.0732426 | ||||||||
\(63\) | −2.44763 | −0.308373 | ||||||||
\(64\) | −1.08708 | −0.135885 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.18961 | 0.146430 | ||||||||
\(67\) | −3.27207 | −0.399747 | −0.199874 | − | 0.979822i | \(-0.564053\pi\) | ||||
−0.199874 | + | 0.979822i | \(0.564053\pi\) | |||||||
\(68\) | 4.66961 | 0.566273 | ||||||||
\(69\) | 8.02655 | 0.966284 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.42329 | −0.524948 | −0.262474 | − | 0.964939i | \(-0.584538\pi\) | ||||
−0.262474 | + | 0.964939i | \(0.584538\pi\) | |||||||
\(72\) | −1.21977 | −0.143751 | ||||||||
\(73\) | −2.50772 | −0.293507 | −0.146753 | − | 0.989173i | \(-0.546882\pi\) | ||||
−0.146753 | + | 0.989173i | \(0.546882\pi\) | |||||||
\(74\) | −3.76840 | −0.438067 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.01264 | 0.804405 | ||||||||
\(77\) | −4.62901 | −0.527525 | ||||||||
\(78\) | −5.11725 | −0.579414 | ||||||||
\(79\) | −17.1925 | −1.93431 | −0.967153 | − | 0.254194i | \(-0.918190\pi\) | ||||
−0.967153 | + | 0.254194i | \(0.918190\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3975 | −1.15528 | ||||||||
\(82\) | −4.28030 | −0.472680 | ||||||||
\(83\) | 5.55501 | 0.609742 | 0.304871 | − | 0.952394i | \(-0.401387\pi\) | ||||
0.304871 | + | 0.952394i | \(0.401387\pi\) | |||||||
\(84\) | 13.3835 | 1.46026 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.94991 | −0.533762 | ||||||||
\(87\) | 11.3975 | 1.22194 | ||||||||
\(88\) | −2.30685 | −0.245911 | ||||||||
\(89\) | 4.55097 | 0.482401 | 0.241201 | − | 0.970475i | \(-0.422459\pi\) | ||||
0.241201 | + | 0.970475i | \(0.422459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.9123 | 2.08738 | ||||||||
\(92\) | −7.07665 | −0.737792 | ||||||||
\(93\) | −1.89122 | −0.196110 | ||||||||
\(94\) | 5.81862 | 0.600145 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.3069 | 1.05194 | ||||||||
\(97\) | −3.42690 | −0.347949 | −0.173974 | − | 0.984750i | \(-0.555661\pi\) | ||||
−0.173974 | + | 0.984750i | \(0.555661\pi\) | |||||||
\(98\) | 6.35105 | 0.641553 | ||||||||
\(99\) | 0.629015 | 0.0632184 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.93226 | 0.391274 | 0.195637 | − | 0.980676i | \(-0.437323\pi\) | ||||
0.195637 | + | 0.980676i | \(0.437323\pi\) | |||||||
\(102\) | −3.05451 | −0.302442 | ||||||||
\(103\) | −2.44763 | −0.241173 | −0.120586 | − | 0.992703i | \(-0.538477\pi\) | ||||
−0.120586 | + | 0.992703i | \(0.538477\pi\) | |||||||
\(104\) | 9.92322 | 0.973052 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.30003 | 0.417655 | ||||||||
\(107\) | 20.1452 | 1.94751 | 0.973755 | − | 0.227599i | \(-0.0730874\pi\) | ||||
0.973755 | + | 0.227599i | \(0.0730874\pi\) | |||||||
\(108\) | 7.64166 | 0.735319 | ||||||||
\(109\) | −13.0495 | −1.24992 | −0.624958 | − | 0.780659i | \(-0.714884\pi\) | ||||
−0.624958 | + | 0.780659i | \(0.714884\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.3578 | −1.17295 | ||||||||
\(112\) | −8.97646 | −0.848196 | ||||||||
\(113\) | −18.5148 | −1.74172 | −0.870862 | − | 0.491527i | \(-0.836439\pi\) | ||||
−0.870862 | + | 0.491527i | \(0.836439\pi\) | |||||||
\(114\) | −4.58715 | −0.429626 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.0487 | −0.932998 | ||||||||
\(117\) | −2.70579 | −0.250150 | ||||||||
\(118\) | 0.412982 | 0.0380181 | ||||||||
\(119\) | 11.8858 | 1.08957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.81039 | −0.891854 | ||||||||
\(122\) | 5.64166 | 0.510771 | ||||||||
\(123\) | −14.0364 | −1.26562 | ||||||||
\(124\) | 1.66740 | 0.149737 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.41158 | −0.125754 | ||||||||
\(127\) | 11.9779 | 1.06286 | 0.531432 | − | 0.847101i | \(-0.321654\pi\) | ||||
0.531432 | + | 0.847101i | \(0.321654\pi\) | |||||||
\(128\) | −11.5266 | −1.01882 | ||||||||
\(129\) | −16.2323 | −1.42917 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.19321 | −0.191622 | −0.0958110 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958110 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(132\) | −3.43941 | −0.299362 | ||||||||
\(133\) | 17.8496 | 1.54776 | ||||||||
\(134\) | −1.88704 | −0.163016 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.92322 | 0.507912 | ||||||||
\(137\) | 9.10056 | 0.777513 | 0.388756 | − | 0.921341i | \(-0.372905\pi\) | ||||
0.388756 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(138\) | 4.62901 | 0.394048 | ||||||||
\(139\) | 4.11865 | 0.349339 | 0.174669 | − | 0.984627i | \(-0.444114\pi\) | ||||
0.174669 | + | 0.984627i | \(0.444114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.0811 | 1.60692 | ||||||||
\(142\) | −2.55097 | −0.214072 | ||||||||
\(143\) | −5.11725 | −0.427926 | ||||||||
\(144\) | 1.21977 | 0.101647 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.44623 | −0.119691 | ||||||||
\(147\) | 20.8271 | 1.71779 | ||||||||
\(148\) | 10.8953 | 0.895586 | ||||||||
\(149\) | −20.4137 | −1.67235 | −0.836176 | − | 0.548461i | \(-0.815214\pi\) | ||||
−0.836176 | + | 0.548461i | \(0.815214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.79648 | −0.797226 | −0.398613 | − | 0.917119i | \(-0.630508\pi\) | ||||
−0.398613 | + | 0.917119i | \(0.630508\pi\) | |||||||
\(152\) | 8.89527 | 0.721502 | ||||||||
\(153\) | −1.61510 | −0.130573 | ||||||||
\(154\) | −2.66961 | −0.215123 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.7951 | 1.18455 | ||||||||
\(157\) | 6.82444 | 0.544649 | 0.272325 | − | 0.962205i | \(-0.412208\pi\) | ||||
0.272325 | + | 0.962205i | \(0.412208\pi\) | |||||||
\(158\) | −9.91513 | −0.788805 | ||||||||
\(159\) | 14.1011 | 1.11829 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.0125 | −1.41958 | ||||||||
\(162\) | −5.99639 | −0.471121 | ||||||||
\(163\) | −21.2958 | −1.66802 | −0.834009 | − | 0.551751i | \(-0.813960\pi\) | ||||
−0.834009 | + | 0.551751i | \(0.813960\pi\) | |||||||
\(164\) | 12.3753 | 0.966347 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.20365 | 0.248651 | ||||||||
\(167\) | −11.3780 | −0.880460 | −0.440230 | − | 0.897885i | \(-0.645103\pi\) | ||||
−0.440230 | + | 0.897885i | \(0.645103\pi\) | |||||||
\(168\) | 16.9765 | 1.30976 | ||||||||
\(169\) | 9.01251 | 0.693270 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.42550 | −0.185482 | ||||||||
\(172\) | 14.3113 | 1.09122 | ||||||||
\(173\) | −9.56641 | −0.727320 | −0.363660 | − | 0.931532i | \(-0.618473\pi\) | ||||
−0.363660 | + | 0.931532i | \(0.618473\pi\) | |||||||
\(174\) | 6.57310 | 0.498306 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.30685 | 0.173885 | ||||||||
\(177\) | 1.35430 | 0.101795 | ||||||||
\(178\) | 2.62460 | 0.196722 | ||||||||
\(179\) | −3.44094 | −0.257188 | −0.128594 | − | 0.991697i | \(-0.541046\pi\) | ||||
−0.128594 | + | 0.991697i | \(0.541046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9890 | −0.965463 | −0.482731 | − | 0.875768i | \(-0.660355\pi\) | ||||
−0.482731 | + | 0.875768i | \(0.660355\pi\) | |||||||
\(182\) | 11.4837 | 0.851228 | ||||||||
\(183\) | 18.5007 | 1.36761 | ||||||||
\(184\) | −8.97646 | −0.661753 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.09069 | −0.0799733 | ||||||||
\(187\) | −3.05451 | −0.223368 | ||||||||
\(188\) | −16.8229 | −1.22694 | ||||||||
\(189\) | 19.4506 | 1.41483 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.5539 | 1.92137 | 0.960685 | − | 0.277642i | \(-0.0895528\pi\) | ||||
0.960685 | + | 0.277642i | \(0.0895528\pi\) | |||||||
\(192\) | −2.05591 | −0.148373 | ||||||||
\(193\) | 10.8510 | 0.781071 | 0.390536 | − | 0.920588i | \(-0.372290\pi\) | ||||
0.390536 | + | 0.920588i | \(0.372290\pi\) | |||||||
\(194\) | −1.97633 | −0.141892 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.3623 | −1.31159 | ||||||||
\(197\) | 15.0517 | 1.07239 | 0.536195 | − | 0.844094i | \(-0.319861\pi\) | ||||
0.536195 | + | 0.844094i | \(0.319861\pi\) | |||||||
\(198\) | 0.362761 | 0.0257803 | ||||||||
\(199\) | 2.64306 | 0.187361 | 0.0936806 | − | 0.995602i | \(-0.470137\pi\) | ||||
0.0936806 | + | 0.995602i | \(0.470137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.18820 | −0.436482 | ||||||||
\(202\) | 2.26778 | 0.159561 | ||||||||
\(203\) | −25.5774 | −1.79518 | ||||||||
\(204\) | 8.83126 | 0.618312 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.41158 | −0.0983495 | ||||||||
\(207\) | 2.44763 | 0.170122 | ||||||||
\(208\) | −9.92322 | −0.688052 | ||||||||
\(209\) | −4.58715 | −0.317299 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.93586 | 0.477485 | 0.238742 | − | 0.971083i | \(-0.423265\pi\) | ||||
0.238742 | + | 0.971083i | \(0.423265\pi\) | |||||||
\(212\) | −12.4323 | −0.853855 | ||||||||
\(213\) | −8.36541 | −0.573188 | ||||||||
\(214\) | 11.6180 | 0.794189 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.69315 | 0.659535 | ||||||||
\(217\) | 4.24412 | 0.288109 | ||||||||
\(218\) | −7.52581 | −0.509712 | ||||||||
\(219\) | −4.74265 | −0.320479 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.1394 | 0.883851 | ||||||||
\(222\) | −7.12687 | −0.478324 | ||||||||
\(223\) | 19.0616 | 1.27646 | 0.638229 | − | 0.769847i | \(-0.279667\pi\) | ||||
0.638229 | + | 0.769847i | \(0.279667\pi\) | |||||||
\(224\) | −23.1298 | −1.54542 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.6777 | −0.710271 | ||||||||
\(227\) | −17.8983 | −1.18795 | −0.593975 | − | 0.804483i | \(-0.702442\pi\) | ||||
−0.593975 | + | 0.804483i | \(0.702442\pi\) | |||||||
\(228\) | 13.2624 | 0.878327 | ||||||||
\(229\) | 28.3334 | 1.87232 | 0.936162 | − | 0.351569i | \(-0.114352\pi\) | ||||
0.936162 | + | 0.351569i | \(0.114352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.75448 | −0.576003 | ||||||||
\(232\) | −12.7464 | −0.836841 | ||||||||
\(233\) | −12.4742 | −0.817211 | −0.408606 | − | 0.912711i | \(-0.633985\pi\) | ||||
−0.408606 | + | 0.912711i | \(0.633985\pi\) | |||||||
\(234\) | −1.56046 | −0.102011 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.19402 | −0.0777242 | ||||||||
\(237\) | −32.5148 | −2.11206 | ||||||||
\(238\) | 6.85467 | 0.444322 | ||||||||
\(239\) | 12.4395 | 0.804647 | 0.402323 | − | 0.915498i | \(-0.368203\pi\) | ||||
0.402323 | + | 0.915498i | \(0.368203\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5229 | −0.806670 | −0.403335 | − | 0.915052i | \(-0.632149\pi\) | ||||
−0.403335 | + | 0.915052i | \(0.632149\pi\) | |||||||
\(242\) | −5.65778 | −0.363696 | ||||||||
\(243\) | −5.91513 | −0.379456 | ||||||||
\(244\) | −16.3113 | −1.04422 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.09498 | −0.516117 | ||||||||
\(247\) | 19.7322 | 1.25553 | ||||||||
\(248\) | 2.11504 | 0.134305 | ||||||||
\(249\) | 10.5058 | 0.665775 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.2273 | −1.27673 | −0.638367 | − | 0.769732i | \(-0.720390\pi\) | ||||
−0.638367 | + | 0.769732i | \(0.720390\pi\) | |||||||
\(252\) | 4.08119 | 0.257091 | ||||||||
\(253\) | 4.62901 | 0.291024 | ||||||||
\(254\) | 6.90778 | 0.433433 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.47338 | −0.279586 | ||||||||
\(257\) | 9.58702 | 0.598022 | 0.299011 | − | 0.954250i | \(-0.403343\pi\) | ||||
0.299011 | + | 0.954250i | \(0.403343\pi\) | |||||||
\(258\) | −9.36136 | −0.582813 | ||||||||
\(259\) | 27.7322 | 1.72320 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.47559 | 0.215134 | ||||||||
\(262\) | −1.26485 | −0.0781429 | ||||||||
\(263\) | 5.18985 | 0.320020 | 0.160010 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160010 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(264\) | −4.36276 | −0.268509 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.2941 | 0.631171 | ||||||||
\(267\) | 8.60688 | 0.526732 | ||||||||
\(268\) | 5.45586 | 0.333270 | ||||||||
\(269\) | 8.03907 | 0.490151 | 0.245075 | − | 0.969504i | \(-0.421187\pi\) | ||||
0.245075 | + | 0.969504i | \(0.421187\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.8215 | 1.32556 | 0.662781 | − | 0.748813i | \(-0.269376\pi\) | ||||
0.662781 | + | 0.748813i | \(0.269376\pi\) | |||||||
\(272\) | −5.92322 | −0.359148 | ||||||||
\(273\) | 37.6586 | 2.27920 | ||||||||
\(274\) | 5.24840 | 0.317068 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.3835 | −0.805592 | ||||||||
\(277\) | −20.7378 | −1.24601 | −0.623007 | − | 0.782217i | \(-0.714089\pi\) | ||||
−0.623007 | + | 0.782217i | \(0.714089\pi\) | |||||||
\(278\) | 2.37527 | 0.142459 | ||||||||
\(279\) | −0.576713 | −0.0345269 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.7986 | −1.47936 | −0.739679 | − | 0.672960i | \(-0.765023\pi\) | ||||
−0.739679 | + | 0.672960i | \(0.765023\pi\) | |||||||
\(282\) | 11.0043 | 0.655296 | ||||||||
\(283\) | −7.78244 | −0.462618 | −0.231309 | − | 0.972880i | \(-0.574301\pi\) | ||||
−0.231309 | + | 0.972880i | \(0.574301\pi\) | |||||||
\(284\) | 7.37540 | 0.437650 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.95118 | −0.174507 | ||||||||
\(287\) | 31.4993 | 1.85935 | ||||||||
\(288\) | 3.14299 | 0.185203 | ||||||||
\(289\) | −9.15703 | −0.538649 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.48101 | −0.379924 | ||||||||
\(292\) | 4.18138 | 0.244697 | ||||||||
\(293\) | 8.25663 | 0.482357 | 0.241179 | − | 0.970481i | \(-0.422466\pi\) | ||||
0.241179 | + | 0.970481i | \(0.422466\pi\) | |||||||
\(294\) | 12.0112 | 0.700510 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.8202 | 0.803285 | ||||||||
\(297\) | −4.99860 | −0.290048 | ||||||||
\(298\) | −11.7728 | −0.681981 | ||||||||
\(299\) | −19.9123 | −1.15156 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.4271 | 2.09962 | ||||||||
\(302\) | −5.64975 | −0.325107 | ||||||||
\(303\) | 7.43676 | 0.427231 | ||||||||
\(304\) | −8.89527 | −0.510179 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.931449 | −0.0532474 | ||||||||
\(307\) | −4.21603 | −0.240622 | −0.120311 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120311 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(308\) | 7.71843 | 0.439798 | ||||||||
\(309\) | −4.62901 | −0.263335 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.3452 | 0.586625 | 0.293312 | − | 0.956017i | \(-0.405242\pi\) | ||||
0.293312 | + | 0.956017i | \(0.405242\pi\) | |||||||
\(312\) | 18.7670 | 1.06247 | ||||||||
\(313\) | 10.9679 | 0.619941 | 0.309970 | − | 0.950746i | \(-0.399681\pi\) | ||||
0.309970 | + | 0.950746i | \(0.399681\pi\) | |||||||
\(314\) | 3.93574 | 0.222107 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.6668 | 1.61263 | ||||||||
\(317\) | 0.214760 | 0.0120621 | 0.00603105 | − | 0.999982i | \(-0.498080\pi\) | ||||
0.00603105 | + | 0.999982i | \(0.498080\pi\) | |||||||
\(318\) | 8.13229 | 0.456036 | ||||||||
\(319\) | 6.57310 | 0.368023 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.0990 | 2.12648 | ||||||||
\(322\) | −10.3880 | −0.578903 | ||||||||
\(323\) | 11.7783 | 0.655360 | ||||||||
\(324\) | 17.3369 | 0.963160 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.2816 | −0.680213 | ||||||||
\(327\) | −24.6795 | −1.36478 | ||||||||
\(328\) | 15.6976 | 0.866753 | ||||||||
\(329\) | −42.8201 | −2.36075 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.7130 | −0.588840 | −0.294420 | − | 0.955676i | \(-0.595126\pi\) | ||||
−0.294420 | + | 0.955676i | \(0.595126\pi\) | |||||||
\(332\) | −9.26245 | −0.508343 | ||||||||
\(333\) | −3.76840 | −0.206507 | ||||||||
\(334\) | −6.56186 | −0.359049 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −16.9765 | −0.926142 | ||||||||
\(337\) | 9.54692 | 0.520054 | 0.260027 | − | 0.965601i | \(-0.416269\pi\) | ||||
0.260027 | + | 0.965601i | \(0.416269\pi\) | |||||||
\(338\) | 5.19763 | 0.282714 | ||||||||
\(339\) | −35.0155 | −1.90178 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.09069 | −0.0590642 | ||||||||
\(342\) | −1.39881 | −0.0756392 | ||||||||
\(343\) | −17.0296 | −0.919510 | ||||||||
\(344\) | 18.1533 | 0.978760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.51707 | −0.296599 | ||||||||
\(347\) | −9.01391 | −0.483892 | −0.241946 | − | 0.970290i | \(-0.577786\pi\) | ||||
−0.241946 | + | 0.970290i | \(0.577786\pi\) | |||||||
\(348\) | −19.0043 | −1.01874 | ||||||||
\(349\) | −34.1933 | −1.83033 | −0.915163 | − | 0.403085i | \(-0.867938\pi\) | ||||
−0.915163 | + | 0.403085i | \(0.867938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.5021 | 1.14770 | ||||||||
\(352\) | 5.94409 | 0.316821 | ||||||||
\(353\) | −12.1312 | −0.645676 | −0.322838 | − | 0.946454i | \(-0.604637\pi\) | ||||
−0.322838 | + | 0.946454i | \(0.604637\pi\) | |||||||
\(354\) | 0.781039 | 0.0415118 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.58829 | −0.402179 | ||||||||
\(357\) | 22.4786 | 1.18969 | ||||||||
\(358\) | −1.98443 | −0.104880 | ||||||||
\(359\) | −28.2317 | −1.49001 | −0.745006 | − | 0.667058i | \(-0.767553\pi\) | ||||
−0.745006 | + | 0.667058i | \(0.767553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.31186 | −0.0690452 | ||||||||
\(362\) | −7.49090 | −0.393713 | ||||||||
\(363\) | −18.5536 | −0.973812 | ||||||||
\(364\) | −33.2019 | −1.74025 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.6696 | 0.557709 | ||||||||
\(367\) | 1.11989 | 0.0584580 | 0.0292290 | − | 0.999573i | \(-0.490695\pi\) | ||||
0.0292290 | + | 0.999573i | \(0.490695\pi\) | |||||||
\(368\) | 8.97646 | 0.467930 | ||||||||
\(369\) | −4.28030 | −0.222823 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.6445 | −1.64290 | ||||||||
\(372\) | 3.15343 | 0.163497 | ||||||||
\(373\) | −1.97786 | −0.102410 | −0.0512049 | − | 0.998688i | \(-0.516306\pi\) | ||||
−0.0512049 | + | 0.998688i | \(0.516306\pi\) | |||||||
\(374\) | −1.76157 | −0.0910888 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.3392 | −1.10049 | ||||||||
\(377\) | −28.2751 | −1.45624 | ||||||||
\(378\) | 11.2174 | 0.576963 | ||||||||
\(379\) | −30.4957 | −1.56646 | −0.783230 | − | 0.621732i | \(-0.786429\pi\) | ||||
−0.783230 | + | 0.621732i | \(0.786429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.6528 | 1.16054 | ||||||||
\(382\) | 15.3139 | 0.783529 | ||||||||
\(383\) | −26.7575 | −1.36725 | −0.683623 | − | 0.729835i | \(-0.739597\pi\) | ||||
−0.683623 | + | 0.729835i | \(0.739597\pi\) | |||||||
\(384\) | −21.7994 | −1.11244 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.25790 | 0.318519 | ||||||||
\(387\) | −4.94991 | −0.251618 | ||||||||
\(388\) | 5.71402 | 0.290085 | ||||||||
\(389\) | −26.7102 | −1.35426 | −0.677131 | − | 0.735863i | \(-0.736777\pi\) | ||||
−0.677131 | + | 0.735863i | \(0.736777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.8858 | −0.601089 | ||||||||
\(392\) | −23.2919 | −1.17642 | ||||||||
\(393\) | −4.14785 | −0.209231 | ||||||||
\(394\) | 8.68051 | 0.437318 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.04882 | −0.0527052 | ||||||||
\(397\) | 5.25523 | 0.263752 | 0.131876 | − | 0.991266i | \(-0.457900\pi\) | ||||
0.131876 | + | 0.991266i | \(0.457900\pi\) | |||||||
\(398\) | 1.52428 | 0.0764054 | ||||||||
\(399\) | 33.7575 | 1.68999 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.256629 | 0.0128154 | 0.00640772 | − | 0.999979i | \(-0.497960\pi\) | ||||
0.00640772 | + | 0.999979i | \(0.497960\pi\) | |||||||
\(402\) | −3.56882 | −0.177996 | ||||||||
\(403\) | 4.69175 | 0.233713 | ||||||||
\(404\) | −6.55665 | −0.326206 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.7508 | −0.732070 | ||||||||
\(407\) | −7.12687 | −0.353266 | ||||||||
\(408\) | 11.2021 | 0.554588 | ||||||||
\(409\) | 23.1285 | 1.14363 | 0.571815 | − | 0.820383i | \(-0.306240\pi\) | ||||
0.571815 | + | 0.820383i | \(0.306240\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.2112 | 0.848963 | ||||||||
\(412\) | 4.08119 | 0.201066 | ||||||||
\(413\) | −3.03920 | −0.149549 | ||||||||
\(414\) | 1.41158 | 0.0693754 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −25.5693 | −1.25364 | ||||||||
\(417\) | 7.78926 | 0.381442 | ||||||||
\(418\) | −2.64546 | −0.129394 | ||||||||
\(419\) | 25.7315 | 1.25707 | 0.628534 | − | 0.777782i | \(-0.283655\pi\) | ||||
0.628534 | + | 0.777782i | \(0.283655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8459 | −0.674806 | −0.337403 | − | 0.941360i | \(-0.609548\pi\) | ||||
−0.337403 | + | 0.941360i | \(0.609548\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | 5.81862 | 0.282911 | ||||||||
\(424\) | −15.7699 | −0.765855 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.82444 | −0.233745 | ||||||||
\(427\) | −41.5178 | −2.00919 | ||||||||
\(428\) | −33.5902 | −1.62364 | ||||||||
\(429\) | −9.67784 | −0.467250 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.1263 | −0.921280 | −0.460640 | − | 0.887587i | \(-0.652380\pi\) | ||||
−0.460640 | + | 0.887587i | \(0.652380\pi\) | |||||||
\(432\) | −9.69315 | −0.466362 | ||||||||
\(433\) | 9.00140 | 0.432580 | 0.216290 | − | 0.976329i | \(-0.430604\pi\) | ||||
0.216290 | + | 0.976329i | \(0.430604\pi\) | |||||||
\(434\) | 2.44763 | 0.117490 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.7588 | 1.04206 | ||||||||
\(437\) | −17.8496 | −0.853862 | ||||||||
\(438\) | −2.73515 | −0.130690 | ||||||||
\(439\) | 3.44972 | 0.164646 | 0.0823230 | − | 0.996606i | \(-0.473766\pi\) | ||||
0.0823230 | + | 0.996606i | \(0.473766\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.35105 | 0.302431 | ||||||||
\(442\) | 7.57765 | 0.360432 | ||||||||
\(443\) | 16.6053 | 0.788944 | 0.394472 | − | 0.918908i | \(-0.370928\pi\) | ||||
0.394472 | + | 0.918908i | \(0.370928\pi\) | |||||||
\(444\) | 20.6053 | 0.977887 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.9930 | 0.520536 | ||||||||
\(447\) | −38.6067 | −1.82604 | ||||||||
\(448\) | 4.61370 | 0.217977 | ||||||||
\(449\) | −4.15635 | −0.196150 | −0.0980752 | − | 0.995179i | \(-0.531269\pi\) | ||||
−0.0980752 | + | 0.995179i | \(0.531269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.09498 | −0.381178 | ||||||||
\(452\) | 30.8716 | 1.45208 | ||||||||
\(453\) | −18.5273 | −0.870488 | ||||||||
\(454\) | −10.3222 | −0.484443 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.8229 | 0.787805 | ||||||||
\(457\) | −31.0517 | −1.45254 | −0.726269 | − | 0.687411i | \(-0.758747\pi\) | ||||
−0.726269 | + | 0.687411i | \(0.758747\pi\) | |||||||
\(458\) | 16.3402 | 0.763529 | ||||||||
\(459\) | 12.8347 | 0.599074 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.666722 | 0.0310523 | 0.0155262 | − | 0.999879i | \(-0.495058\pi\) | ||||
0.0155262 | + | 0.999879i | \(0.495058\pi\) | |||||||
\(462\) | −5.04882 | −0.234892 | ||||||||
\(463\) | −2.06273 | −0.0958634 | −0.0479317 | − | 0.998851i | \(-0.515263\pi\) | ||||
−0.0479317 | + | 0.998851i | \(0.515263\pi\) | |||||||
\(464\) | 12.7464 | 0.591736 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.19402 | −0.333257 | ||||||||
\(467\) | −40.8173 | −1.88880 | −0.944400 | − | 0.328799i | \(-0.893356\pi\) | ||||
−0.944400 | + | 0.328799i | \(0.893356\pi\) | |||||||
\(468\) | 4.51164 | 0.208551 | ||||||||
\(469\) | 13.8870 | 0.641244 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.9065 | 0.594701 | ||||||||
\(472\) | −1.51457 | −0.0697138 | ||||||||
\(473\) | −9.36136 | −0.430436 | ||||||||
\(474\) | −18.7517 | −0.861293 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −19.8184 | −0.908373 | ||||||||
\(477\) | 4.30003 | 0.196885 | ||||||||
\(478\) | 7.17404 | 0.328133 | ||||||||
\(479\) | 27.4772 | 1.25547 | 0.627733 | − | 0.778429i | \(-0.283983\pi\) | ||||
0.627733 | + | 0.778429i | \(0.283983\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.6572 | 1.39785 | ||||||||
\(482\) | −7.22210 | −0.328958 | ||||||||
\(483\) | −34.0656 | −1.55004 | ||||||||
\(484\) | 16.3579 | 0.743540 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.41133 | −0.154741 | ||||||||
\(487\) | 37.8676 | 1.71594 | 0.857971 | − | 0.513698i | \(-0.171725\pi\) | ||||
0.857971 | + | 0.513698i | \(0.171725\pi\) | |||||||
\(488\) | −20.6902 | −0.936602 | ||||||||
\(489\) | −40.2751 | −1.82130 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.12827 | 0.276565 | 0.138282 | − | 0.990393i | \(-0.455842\pi\) | ||||
0.138282 | + | 0.990393i | \(0.455842\pi\) | |||||||
\(492\) | 23.4044 | 1.05515 | ||||||||
\(493\) | −16.8775 | −0.760126 | ||||||||
\(494\) | 11.3798 | 0.512002 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.11504 | −0.0949680 | ||||||||
\(497\) | 18.7729 | 0.842082 | ||||||||
\(498\) | 6.05880 | 0.271501 | ||||||||
\(499\) | −13.3767 | −0.598822 | −0.299411 | − | 0.954124i | \(-0.596790\pi\) | ||||
−0.299411 | + | 0.954124i | \(0.596790\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.5184 | −0.961371 | ||||||||
\(502\) | −11.6653 | −0.520649 | ||||||||
\(503\) | 9.11877 | 0.406586 | 0.203293 | − | 0.979118i | \(-0.434836\pi\) | ||||
0.203293 | + | 0.979118i | \(0.434836\pi\) | |||||||
\(504\) | 5.17684 | 0.230595 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.66961 | 0.118679 | ||||||||
\(507\) | 17.0446 | 0.756979 | ||||||||
\(508\) | −19.9719 | −0.886111 | ||||||||
\(509\) | 23.4853 | 1.04097 | 0.520484 | − | 0.853872i | \(-0.325752\pi\) | ||||
0.520484 | + | 0.853872i | \(0.325752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.6431 | 0.470821 | ||||||||
\(512\) | 20.4734 | 0.904804 | ||||||||
\(513\) | 19.2747 | 0.851000 | ||||||||
\(514\) | 5.52895 | 0.243872 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 27.0658 | 1.19150 | ||||||||
\(517\) | 11.0043 | 0.483968 | ||||||||
\(518\) | 15.9935 | 0.702715 | ||||||||
\(519\) | −18.0922 | −0.794158 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.0776 | −1.27391 | −0.636956 | − | 0.770900i | \(-0.719807\pi\) | ||||
−0.636956 | + | 0.770900i | \(0.719807\pi\) | |||||||
\(522\) | 2.00442 | 0.0877309 | ||||||||
\(523\) | 22.7741 | 0.995840 | 0.497920 | − | 0.867223i | \(-0.334097\pi\) | ||||
0.497920 | + | 0.867223i | \(0.334097\pi\) | |||||||
\(524\) | 3.65697 | 0.159755 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.99305 | 0.130503 | ||||||||
\(527\) | 2.80053 | 0.121993 | ||||||||
\(528\) | 4.36276 | 0.189865 | ||||||||
\(529\) | −4.98749 | −0.216847 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.412982 | 0.0179219 | ||||||||
\(532\) | −29.7625 | −1.29037 | ||||||||
\(533\) | 34.8216 | 1.50829 | ||||||||
\(534\) | 4.96369 | 0.214800 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.92055 | 0.298922 | ||||||||
\(537\) | −6.50757 | −0.280822 | ||||||||
\(538\) | 4.63623 | 0.199882 | ||||||||
\(539\) | 12.0112 | 0.517361 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8201 | −0.551179 | −0.275590 | − | 0.961275i | \(-0.588873\pi\) | ||||
−0.275590 | + | 0.961275i | \(0.588873\pi\) | |||||||
\(542\) | 12.5847 | 0.540561 | ||||||||
\(543\) | −24.5650 | −1.05419 | ||||||||
\(544\) | −15.2624 | −0.654372 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 21.7182 | 0.929452 | ||||||||
\(547\) | 29.9317 | 1.27979 | 0.639893 | − | 0.768464i | \(-0.278979\pi\) | ||||
0.639893 | + | 0.768464i | \(0.278979\pi\) | |||||||
\(548\) | −15.1743 | −0.648214 | ||||||||
\(549\) | 5.64166 | 0.240780 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.3460 | −1.07978 | ||||||||
\(552\) | −16.9765 | −0.722566 | ||||||||
\(553\) | 72.9669 | 3.10287 | ||||||||
\(554\) | −11.9597 | −0.508121 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.86744 | −0.291244 | ||||||||
\(557\) | −40.3195 | −1.70839 | −0.854195 | − | 0.519953i | \(-0.825950\pi\) | ||||
−0.854195 | + | 0.519953i | \(0.825950\pi\) | |||||||
\(558\) | −0.332597 | −0.0140800 | ||||||||
\(559\) | 40.2691 | 1.70320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.77675 | −0.243895 | ||||||||
\(562\) | −14.3016 | −0.603278 | ||||||||
\(563\) | 26.0825 | 1.09924 | 0.549622 | − | 0.835413i | \(-0.314772\pi\) | ||||
0.549622 | + | 0.835413i | \(0.314772\pi\) | |||||||
\(564\) | −31.8158 | −1.33969 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.48823 | −0.188654 | ||||||||
\(567\) | 44.1284 | 1.85322 | ||||||||
\(568\) | 9.35542 | 0.392545 | ||||||||
\(569\) | −29.1351 | −1.22141 | −0.610703 | − | 0.791860i | \(-0.709113\pi\) | ||||
−0.610703 | + | 0.791860i | \(0.709113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.58185 | 0.359139 | 0.179570 | − | 0.983745i | \(-0.442529\pi\) | ||||
0.179570 | + | 0.983745i | \(0.442529\pi\) | |||||||
\(572\) | 8.53251 | 0.356762 | ||||||||
\(573\) | 50.2192 | 2.09794 | ||||||||
\(574\) | 18.1661 | 0.758237 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.626934 | −0.0261222 | ||||||||
\(577\) | −0.522883 | −0.0217679 | −0.0108840 | − | 0.999941i | \(-0.503465\pi\) | ||||
−0.0108840 | + | 0.999941i | \(0.503465\pi\) | |||||||
\(578\) | −5.28098 | −0.219660 | ||||||||
\(579\) | 20.5216 | 0.852849 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.5761 | −0.978102 | ||||||||
\(582\) | −3.73768 | −0.154932 | ||||||||
\(583\) | 8.13229 | 0.336805 | ||||||||
\(584\) | 5.30392 | 0.219478 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.76170 | 0.196704 | ||||||||
\(587\) | 0.829733 | 0.0342467 | 0.0171234 | − | 0.999853i | \(-0.494549\pi\) | ||||
0.0171234 | + | 0.999853i | \(0.494549\pi\) | |||||||
\(588\) | −34.7271 | −1.43212 | ||||||||
\(589\) | 4.20573 | 0.173294 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.4661 | 1.17094 | ||||||||
\(592\) | −13.8202 | −0.568008 | ||||||||
\(593\) | 11.7950 | 0.484361 | 0.242180 | − | 0.970231i | \(-0.422137\pi\) | ||||
0.242180 | + | 0.970231i | \(0.422137\pi\) | |||||||
\(594\) | −2.88275 | −0.118281 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34.0378 | 1.39424 | ||||||||
\(597\) | 4.99860 | 0.204579 | ||||||||
\(598\) | −11.4837 | −0.469603 | ||||||||
\(599\) | 33.7841 | 1.38038 | 0.690190 | − | 0.723629i | \(-0.257527\pi\) | ||||
0.690190 | + | 0.723629i | \(0.257527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.98329 | −0.121691 | −0.0608454 | − | 0.998147i | \(-0.519380\pi\) | ||||
−0.0608454 | + | 0.998147i | \(0.519380\pi\) | |||||||
\(602\) | 21.0080 | 0.856221 | ||||||||
\(603\) | −1.88704 | −0.0768464 | ||||||||
\(604\) | 16.3347 | 0.664649 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.28887 | 0.174224 | ||||||||
\(607\) | −5.99567 | −0.243357 | −0.121678 | − | 0.992570i | \(-0.538828\pi\) | ||||
−0.121678 | + | 0.992570i | \(0.538828\pi\) | |||||||
\(608\) | −22.9206 | −0.929551 | ||||||||
\(609\) | −48.3725 | −1.96015 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −47.3364 | −1.91503 | ||||||||
\(612\) | 2.69302 | 0.108859 | ||||||||
\(613\) | −22.7615 | −0.919330 | −0.459665 | − | 0.888092i | \(-0.652031\pi\) | ||||
−0.459665 | + | 0.888092i | \(0.652031\pi\) | |||||||
\(614\) | −2.43144 | −0.0981249 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.79054 | 0.394472 | ||||||||
\(617\) | 9.98316 | 0.401907 | 0.200953 | − | 0.979601i | \(-0.435596\pi\) | ||||
0.200953 | + | 0.979601i | \(0.435596\pi\) | |||||||
\(618\) | −2.66961 | −0.107387 | ||||||||
\(619\) | 19.1144 | 0.768274 | 0.384137 | − | 0.923276i | \(-0.374499\pi\) | ||||
0.384137 | + | 0.923276i | \(0.374499\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.4506 | −0.780528 | ||||||||
\(622\) | 5.96623 | 0.239224 | ||||||||
\(623\) | −19.3148 | −0.773832 | ||||||||
\(624\) | −18.7670 | −0.751281 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.32531 | 0.252810 | ||||||||
\(627\) | −8.67530 | −0.346458 | ||||||||
\(628\) | −11.3791 | −0.454075 | ||||||||
\(629\) | 18.2994 | 0.729646 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.19932 | 0.206982 | 0.103491 | − | 0.994630i | \(-0.466999\pi\) | ||||
0.103491 | + | 0.994630i | \(0.466999\pi\) | |||||||
\(632\) | 36.3628 | 1.44643 | ||||||||
\(633\) | 13.1172 | 0.521364 | ||||||||
\(634\) | 0.123854 | 0.00491889 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −23.5122 | −0.932321 | ||||||||
\(637\) | −51.6680 | −2.04716 | ||||||||
\(638\) | 3.79079 | 0.150079 | ||||||||
\(639\) | −2.55097 | −0.100915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.96924 | 0.354264 | 0.177132 | − | 0.984187i | \(-0.443318\pi\) | ||||
0.177132 | + | 0.984187i | \(0.443318\pi\) | |||||||
\(642\) | 21.9722 | 0.867172 | ||||||||
\(643\) | −9.69580 | −0.382365 | −0.191182 | − | 0.981555i | \(-0.561232\pi\) | ||||
−0.191182 | + | 0.981555i | \(0.561232\pi\) | |||||||
\(644\) | 30.0341 | 1.18351 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.79267 | 0.267254 | ||||||||
\(647\) | −0.631663 | −0.0248332 | −0.0124166 | − | 0.999923i | \(-0.503952\pi\) | ||||
−0.0124166 | + | 0.999923i | \(0.503952\pi\) | |||||||
\(648\) | 21.9912 | 0.863895 | ||||||||
\(649\) | 0.781039 | 0.0306585 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.02655 | 0.314585 | ||||||||
\(652\) | 35.5087 | 1.39063 | ||||||||
\(653\) | 10.1074 | 0.395533 | 0.197767 | − | 0.980249i | \(-0.436631\pi\) | ||||
0.197767 | + | 0.980249i | \(0.436631\pi\) | |||||||
\(654\) | −14.2330 | −0.556553 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.6976 | −0.612887 | ||||||||
\(657\) | −1.44623 | −0.0564230 | ||||||||
\(658\) | −24.6949 | −0.962707 | ||||||||
\(659\) | 36.3066 | 1.41431 | 0.707153 | − | 0.707060i | \(-0.249979\pi\) | ||||
0.707153 | + | 0.707060i | \(0.249979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4456 | −0.522975 | −0.261487 | − | 0.965207i | \(-0.584213\pi\) | ||||
−0.261487 | + | 0.965207i | \(0.584213\pi\) | |||||||
\(662\) | −6.17833 | −0.240127 | ||||||||
\(663\) | 24.8495 | 0.965073 | ||||||||
\(664\) | −11.7491 | −0.455952 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.17328 | −0.0842130 | ||||||||
\(667\) | 25.5774 | 0.990361 | ||||||||
\(668\) | 18.9718 | 0.734041 | ||||||||
\(669\) | 36.0496 | 1.39376 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.6696 | 0.411896 | ||||||||
\(672\) | −43.7435 | −1.68744 | ||||||||
\(673\) | −21.1118 | −0.813800 | −0.406900 | − | 0.913473i | \(-0.633390\pi\) | ||||
−0.406900 | + | 0.913473i | \(0.633390\pi\) | |||||||
\(674\) | 5.50583 | 0.212077 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.0275 | −0.577980 | ||||||||
\(677\) | −19.7726 | −0.759922 | −0.379961 | − | 0.925003i | \(-0.624063\pi\) | ||||
−0.379961 | + | 0.925003i | \(0.624063\pi\) | |||||||
\(678\) | −20.1939 | −0.775542 | ||||||||
\(679\) | 14.5441 | 0.558153 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.8496 | −1.29712 | ||||||||
\(682\) | −0.629015 | −0.0240862 | ||||||||
\(683\) | 5.64293 | 0.215921 | 0.107960 | − | 0.994155i | \(-0.465568\pi\) | ||||
0.107960 | + | 0.994155i | \(0.465568\pi\) | |||||||
\(684\) | 4.04428 | 0.154637 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.82117 | −0.374974 | ||||||||
\(687\) | 53.5847 | 2.04438 | ||||||||
\(688\) | −18.1533 | −0.692088 | ||||||||
\(689\) | −34.9822 | −1.33271 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.97718 | 0.379550 | 0.189775 | − | 0.981828i | \(-0.439224\pi\) | ||||
0.189775 | + | 0.981828i | \(0.439224\pi\) | |||||||
\(692\) | 15.9511 | 0.606368 | ||||||||
\(693\) | −2.66961 | −0.101410 | ||||||||
\(694\) | −5.19844 | −0.197330 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −24.1062 | −0.913744 | ||||||||
\(697\) | 20.7852 | 0.787296 | ||||||||
\(698\) | −19.7197 | −0.746402 | ||||||||
\(699\) | −23.5914 | −0.892310 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.9600 | 1.24488 | 0.622441 | − | 0.782667i | \(-0.286141\pi\) | ||||
0.622441 | + | 0.782667i | \(0.286141\pi\) | |||||||
\(702\) | 12.4006 | 0.468029 | ||||||||
\(703\) | 27.4814 | 1.03648 | ||||||||
\(704\) | −1.18567 | −0.0446866 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.99619 | −0.263305 | ||||||||
\(707\) | −16.6889 | −0.627653 | ||||||||
\(708\) | −2.25816 | −0.0848667 | ||||||||
\(709\) | 26.2501 | 0.985842 | 0.492921 | − | 0.870074i | \(-0.335929\pi\) | ||||
0.492921 | + | 0.870074i | \(0.335929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.91513 | −0.371846 | ||||||||
\(712\) | −9.62546 | −0.360729 | ||||||||
\(713\) | −4.24412 | −0.158943 | ||||||||
\(714\) | 12.9637 | 0.485154 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.73743 | 0.214418 | ||||||||
\(717\) | 23.5259 | 0.878591 | ||||||||
\(718\) | −16.2816 | −0.607623 | ||||||||
\(719\) | −10.2635 | −0.382762 | −0.191381 | − | 0.981516i | \(-0.561297\pi\) | ||||
−0.191381 | + | 0.981516i | \(0.561297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.3880 | 0.386871 | ||||||||
\(722\) | −0.756565 | −0.0281564 | ||||||||
\(723\) | −23.6835 | −0.880800 | ||||||||
\(724\) | 21.6579 | 0.804908 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.7001 | −0.397118 | ||||||||
\(727\) | −11.7588 | −0.436109 | −0.218054 | − | 0.975937i | \(-0.569971\pi\) | ||||
−0.218054 | + | 0.975937i | \(0.569971\pi\) | |||||||
\(728\) | −42.1153 | −1.56090 | ||||||||
\(729\) | 20.0058 | 0.740956 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0369 | 0.889035 | ||||||||
\(732\) | −30.8482 | −1.14018 | ||||||||
\(733\) | −15.7669 | −0.582363 | −0.291181 | − | 0.956668i | \(-0.594048\pi\) | ||||
−0.291181 | + | 0.956668i | \(0.594048\pi\) | |||||||
\(734\) | 0.645857 | 0.0238390 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23.1298 | 0.852574 | ||||||||
\(737\) | −3.56882 | −0.131459 | ||||||||
\(738\) | −2.46850 | −0.0908667 | ||||||||
\(739\) | −6.39806 | −0.235356 | −0.117678 | − | 0.993052i | \(-0.537545\pi\) | ||||
−0.117678 | + | 0.993052i | \(0.537545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 37.3180 | 1.37091 | ||||||||
\(742\) | −18.2498 | −0.669971 | ||||||||
\(743\) | 4.17152 | 0.153038 | 0.0765190 | − | 0.997068i | \(-0.475619\pi\) | ||||
0.0765190 | + | 0.997068i | \(0.475619\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.14066 | −0.0417624 | ||||||||
\(747\) | 3.20365 | 0.117215 | ||||||||
\(748\) | 5.09310 | 0.186222 | ||||||||
\(749\) | −85.4986 | −3.12405 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9734 | 0.911293 | 0.455646 | − | 0.890161i | \(-0.349408\pi\) | ||||
0.455646 | + | 0.890161i | \(0.349408\pi\) | |||||||
\(752\) | 21.3392 | 0.778161 | ||||||||
\(753\) | −38.2542 | −1.39406 | ||||||||
\(754\) | −16.3066 | −0.593851 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −32.4321 | −1.17954 | ||||||||
\(757\) | −51.6338 | −1.87666 | −0.938331 | − | 0.345738i | \(-0.887629\pi\) | ||||
−0.938331 | + | 0.345738i | \(0.887629\pi\) | |||||||
\(758\) | −17.5873 | −0.638798 | ||||||||
\(759\) | 8.75448 | 0.317768 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.3238 | −0.954236 | −0.477118 | − | 0.878839i | \(-0.658319\pi\) | ||||
−0.477118 | + | 0.878839i | \(0.658319\pi\) | |||||||
\(762\) | 13.0641 | 0.473264 | ||||||||
\(763\) | 55.3836 | 2.00502 | ||||||||
\(764\) | −44.2760 | −1.60185 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.4314 | −0.557559 | ||||||||
\(767\) | −3.35974 | −0.121313 | ||||||||
\(768\) | −8.46015 | −0.305279 | ||||||||
\(769\) | 51.5996 | 1.86073 | 0.930364 | − | 0.366636i | \(-0.119491\pi\) | ||||
0.930364 | + | 0.366636i | \(0.119491\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.1312 | 0.652978 | ||||||||
\(772\) | −18.0930 | −0.651180 | ||||||||
\(773\) | 12.0627 | 0.433866 | 0.216933 | − | 0.976186i | \(-0.430395\pi\) | ||||
0.216933 | + | 0.976186i | \(0.430395\pi\) | |||||||
\(774\) | −2.85467 | −0.102609 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.24801 | 0.260188 | ||||||||
\(777\) | 52.4477 | 1.88155 | ||||||||
\(778\) | −15.4041 | −0.552264 | ||||||||
\(779\) | 31.2144 | 1.11837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.82444 | −0.172632 | ||||||||
\(782\) | −6.85467 | −0.245123 | ||||||||
\(783\) | −27.6195 | −0.987041 | ||||||||
\(784\) | 23.2919 | 0.831853 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.39212 | −0.0853240 | ||||||||
\(787\) | 33.6557 | 1.19970 | 0.599848 | − | 0.800114i | \(-0.295228\pi\) | ||||
0.599848 | + | 0.800114i | \(0.295228\pi\) | |||||||
\(788\) | −25.0973 | −0.894053 | ||||||||
\(789\) | 9.81514 | 0.349428 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 78.5789 | 2.79394 | ||||||||
\(792\) | −1.33039 | −0.0472733 | ||||||||
\(793\) | −45.8968 | −1.62984 | ||||||||
\(794\) | 3.03076 | 0.107558 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.40704 | −0.156203 | ||||||||
\(797\) | 44.8414 | 1.58836 | 0.794181 | − | 0.607681i | \(-0.207900\pi\) | ||||
0.794181 | + | 0.607681i | \(0.207900\pi\) | |||||||
\(798\) | 19.4684 | 0.689173 | ||||||||
\(799\) | −28.2554 | −0.999603 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.62460 | 0.0927356 | ||||||||
\(802\) | 0.148001 | 0.00522610 | ||||||||
\(803\) | −2.73515 | −0.0965212 | ||||||||
\(804\) | 10.3182 | 0.363896 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.70579 | 0.0953074 | ||||||||
\(807\) | 15.2036 | 0.535194 | ||||||||
\(808\) | −8.31687 | −0.292586 | ||||||||
\(809\) | 3.60700 | 0.126815 | 0.0634077 | − | 0.997988i | \(-0.479803\pi\) | ||||
0.0634077 | + | 0.997988i | \(0.479803\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5156 | 1.52804 | 0.764020 | − | 0.645193i | \(-0.223223\pi\) | ||||
0.764020 | + | 0.645193i | \(0.223223\pi\) | |||||||
\(812\) | 42.6478 | 1.49664 | ||||||||
\(813\) | 41.2693 | 1.44738 | ||||||||
\(814\) | −4.11016 | −0.144061 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −11.2021 | −0.392153 | ||||||||
\(817\) | 36.0976 | 1.26290 | ||||||||
\(818\) | 13.3385 | 0.466369 | ||||||||
\(819\) | 11.4837 | 0.401273 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7855 | 0.934819 | 0.467409 | − | 0.884041i | \(-0.345187\pi\) | ||||
0.467409 | + | 0.884041i | \(0.345187\pi\) | |||||||
\(822\) | 9.92589 | 0.346205 | ||||||||
\(823\) | 1.00125 | 0.0349013 | 0.0174507 | − | 0.999848i | \(-0.494445\pi\) | ||||
0.0174507 | + | 0.999848i | \(0.494445\pi\) | |||||||
\(824\) | 5.17684 | 0.180344 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.75274 | −0.0609857 | ||||||||
\(827\) | −4.95816 | −0.172412 | −0.0862060 | − | 0.996277i | \(-0.527474\pi\) | ||||
−0.0862060 | + | 0.996277i | \(0.527474\pi\) | |||||||
\(828\) | −4.08119 | −0.141831 | ||||||||
\(829\) | 42.6668 | 1.48188 | 0.740940 | − | 0.671571i | \(-0.234380\pi\) | ||||
0.740940 | + | 0.671571i | \(0.234380\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39.2197 | −1.36052 | ||||||||
\(832\) | 5.10032 | 0.176822 | ||||||||
\(833\) | −30.8409 | −1.06857 | ||||||||
\(834\) | 4.49217 | 0.155551 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.64862 | 0.264533 | ||||||||
\(837\) | 4.58297 | 0.158411 | ||||||||
\(838\) | 14.8397 | 0.512629 | ||||||||
\(839\) | 56.4093 | 1.94747 | 0.973733 | − | 0.227692i | \(-0.0731179\pi\) | ||||
0.973733 | + | 0.227692i | \(0.0731179\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.31936 | 0.252392 | ||||||||
\(842\) | −7.98508 | −0.275184 | ||||||||
\(843\) | −46.8995 | −1.61531 | ||||||||
\(844\) | −11.5649 | −0.398080 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.35567 | 0.115370 | ||||||||
\(847\) | 41.6364 | 1.43065 | ||||||||
\(848\) | 15.7699 | 0.541541 | ||||||||
\(849\) | −14.7183 | −0.505131 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7322 | −0.950648 | ||||||||
\(852\) | 13.9485 | 0.477868 | ||||||||
\(853\) | 1.39072 | 0.0476172 | 0.0238086 | − | 0.999717i | \(-0.492421\pi\) | ||||
0.0238086 | + | 0.999717i | \(0.492421\pi\) | |||||||
\(854\) | −23.9438 | −0.819341 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −42.6078 | −1.45631 | ||||||||
\(857\) | −44.5988 | −1.52347 | −0.761733 | − | 0.647892i | \(-0.775651\pi\) | ||||
−0.761733 | + | 0.647892i | \(0.775651\pi\) | |||||||
\(858\) | −5.58133 | −0.190543 | ||||||||
\(859\) | 4.63054 | 0.157992 | 0.0789960 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789960 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 59.5722 | 2.03021 | ||||||||
\(862\) | −11.0304 | −0.375696 | ||||||||
\(863\) | −5.29847 | −0.180362 | −0.0901811 | − | 0.995925i | \(-0.528745\pi\) | ||||
−0.0901811 | + | 0.995925i | \(0.528745\pi\) | |||||||
\(864\) | −24.9765 | −0.849716 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.19122 | 0.176405 | ||||||||
\(867\) | −17.3180 | −0.588149 | ||||||||
\(868\) | −7.07665 | −0.240197 | ||||||||
\(869\) | −18.7517 | −0.636107 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3517 | 0.520174 | ||||||||
\(872\) | 27.6002 | 0.934660 | ||||||||
\(873\) | −1.97633 | −0.0668888 | ||||||||
\(874\) | −10.2941 | −0.348203 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.90791 | 0.267183 | ||||||||
\(877\) | −29.4379 | −0.994047 | −0.497023 | − | 0.867737i | \(-0.665574\pi\) | ||||
−0.497023 | + | 0.867737i | \(0.665574\pi\) | |||||||
\(878\) | 1.98949 | 0.0671422 | ||||||||
\(879\) | 15.6151 | 0.526684 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.2360 | −0.412242 | −0.206121 | − | 0.978527i | \(-0.566084\pi\) | ||||
−0.206121 | + | 0.978527i | \(0.566084\pi\) | |||||||
\(882\) | 3.66273 | 0.123331 | ||||||||
\(883\) | 13.0166 | 0.438042 | 0.219021 | − | 0.975720i | \(-0.429714\pi\) | ||||
0.219021 | + | 0.975720i | \(0.429714\pi\) | |||||||
\(884\) | −21.9086 | −0.736867 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.57651 | 0.321729 | ||||||||
\(887\) | 42.6931 | 1.43349 | 0.716747 | − | 0.697333i | \(-0.245630\pi\) | ||||
0.716747 | + | 0.697333i | \(0.245630\pi\) | |||||||
\(888\) | 26.1371 | 0.877104 | ||||||||
\(889\) | −50.8354 | −1.70497 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.3405 | −0.379921 | ||||||||
\(892\) | −31.7833 | −1.06418 | ||||||||
\(893\) | −42.4328 | −1.41996 | ||||||||
\(894\) | −22.2650 | −0.744652 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 48.9203 | 1.63431 | ||||||||
\(897\) | −37.6586 | −1.25738 | ||||||||
\(898\) | −2.39702 | −0.0799896 | ||||||||
\(899\) | −6.02655 | −0.200997 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.8810 | −0.695648 | ||||||||
\(902\) | −4.66848 | −0.155443 | ||||||||
\(903\) | 68.8917 | 2.29257 | ||||||||
\(904\) | 39.1595 | 1.30242 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.6849 | −0.354983 | ||||||||
\(907\) | −2.96089 | −0.0983148 | −0.0491574 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491574 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(908\) | 29.8436 | 0.990396 | ||||||||
\(909\) | 2.26778 | 0.0752176 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.6094 | 1.67676 | 0.838382 | − | 0.545084i | \(-0.183502\pi\) | ||||
0.838382 | + | 0.545084i | \(0.183502\pi\) | |||||||
\(912\) | −16.8229 | −0.557062 | ||||||||
\(913\) | 6.05880 | 0.200517 | ||||||||
\(914\) | −17.9079 | −0.592341 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −47.2432 | −1.56096 | ||||||||
\(917\) | 9.30825 | 0.307386 | ||||||||
\(918\) | 7.40196 | 0.244301 | ||||||||
\(919\) | −53.7822 | −1.77411 | −0.887056 | − | 0.461661i | \(-0.847253\pi\) | ||||
−0.887056 | + | 0.461661i | \(0.847253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.97345 | −0.262734 | ||||||||
\(922\) | 0.384507 | 0.0126631 | ||||||||
\(923\) | 20.7530 | 0.683092 | ||||||||
\(924\) | 14.5973 | 0.480214 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.18961 | −0.0390928 | ||||||||
\(927\) | −1.41158 | −0.0463624 | ||||||||
\(928\) | 32.8438 | 1.07815 | ||||||||
\(929\) | −23.7699 | −0.779866 | −0.389933 | − | 0.920843i | \(-0.627502\pi\) | ||||
−0.389933 | + | 0.920843i | \(0.627502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.3156 | −1.51793 | ||||||||
\(932\) | 20.7995 | 0.681310 | ||||||||
\(933\) | 19.5651 | 0.640533 | ||||||||
\(934\) | −23.5399 | −0.770247 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.72285 | 0.187057 | ||||||||
\(937\) | 15.4351 | 0.504242 | 0.252121 | − | 0.967696i | \(-0.418872\pi\) | ||||
0.252121 | + | 0.967696i | \(0.418872\pi\) | |||||||
\(938\) | 8.00883 | 0.261498 | ||||||||
\(939\) | 20.7427 | 0.676911 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.8314 | −0.385692 | −0.192846 | − | 0.981229i | \(-0.561772\pi\) | ||||
−0.192846 | + | 0.981229i | \(0.561772\pi\) | |||||||
\(942\) | 7.44335 | 0.242517 | ||||||||
\(943\) | −31.4993 | −1.02576 | ||||||||
\(944\) | 1.51457 | 0.0492951 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.39881 | −0.175531 | ||||||||
\(947\) | −25.9237 | −0.842408 | −0.421204 | − | 0.906966i | \(-0.638392\pi\) | ||||
−0.421204 | + | 0.906966i | \(0.638392\pi\) | |||||||
\(948\) | 54.2152 | 1.76083 | ||||||||
\(949\) | 11.7656 | 0.381927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.406157 | 0.0131706 | ||||||||
\(952\) | −25.1388 | −0.814755 | ||||||||
\(953\) | −33.0212 | −1.06966 | −0.534831 | − | 0.844959i | \(-0.679625\pi\) | ||||
−0.534831 | + | 0.844959i | \(0.679625\pi\) | |||||||
\(954\) | 2.47988 | 0.0802890 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.7417 | −0.670835 | ||||||||
\(957\) | 12.4312 | 0.401843 | ||||||||
\(958\) | 15.8464 | 0.511975 | ||||||||
\(959\) | −38.6238 | −1.24723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 17.6804 | 0.570038 | ||||||||
\(963\) | 11.6180 | 0.374384 | ||||||||
\(964\) | 20.8807 | 0.672522 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −19.6461 | −0.632102 | ||||||||
\(967\) | 7.17998 | 0.230893 | 0.115446 | − | 0.993314i | \(-0.463170\pi\) | ||||
0.115446 | + | 0.993314i | \(0.463170\pi\) | |||||||
\(968\) | 20.7493 | 0.666909 | ||||||||
\(969\) | 22.2753 | 0.715585 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.1377 | 0.325334 | 0.162667 | − | 0.986681i | \(-0.447990\pi\) | ||||
0.162667 | + | 0.986681i | \(0.447990\pi\) | |||||||
\(972\) | 9.86290 | 0.316353 | ||||||||
\(973\) | −17.4800 | −0.560383 | ||||||||
\(974\) | 21.8387 | 0.699757 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.6902 | 0.662278 | ||||||||
\(977\) | −2.04187 | −0.0653252 | −0.0326626 | − | 0.999466i | \(-0.510399\pi\) | ||||
−0.0326626 | + | 0.999466i | \(0.510399\pi\) | |||||||
\(978\) | −23.2271 | −0.742722 | ||||||||
\(979\) | 4.96369 | 0.158640 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.52581 | −0.240281 | ||||||||
\(982\) | 3.53425 | 0.112782 | ||||||||
\(983\) | 38.5229 | 1.22869 | 0.614345 | − | 0.789038i | \(-0.289420\pi\) | ||||
0.614345 | + | 0.789038i | \(0.289420\pi\) | |||||||
\(984\) | 29.6875 | 0.946404 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.73349 | −0.309978 | ||||||||
\(987\) | −80.9822 | −2.57769 | ||||||||
\(988\) | −32.9016 | −1.04674 | ||||||||
\(989\) | −36.4271 | −1.15831 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.9389 | −1.39576 | −0.697882 | − | 0.716212i | \(-0.745874\pi\) | ||||
−0.697882 | + | 0.716212i | \(0.745874\pi\) | |||||||
\(992\) | −5.44984 | −0.173033 | ||||||||
\(993\) | −20.2607 | −0.642952 | ||||||||
\(994\) | 10.8266 | 0.343399 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −17.5173 | −0.555058 | ||||||||
\(997\) | −58.9278 | −1.86626 | −0.933131 | − | 0.359538i | \(-0.882934\pi\) | ||||
−0.933131 | + | 0.359538i | \(0.882934\pi\) | |||||||
\(998\) | −7.71450 | −0.244198 | ||||||||
\(999\) | 29.9464 | 0.947462 |
(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 | 775.2.a.e.1.3 | 4 | ||
3.2 | odd | 2 | 6975.2.a.bn.1.2 | 4 | |||
5.2 | odd | 4 | 775.2.b.f.249.5 | 8 | |||
5.3 | odd | 4 | 775.2.b.f.249.4 | 8 | |||
5.4 | even | 2 | 155.2.a.e.1.2 | ✓ | 4 | ||
15.14 | odd | 2 | 1395.2.a.l.1.3 | 4 | |||
20.19 | odd | 2 | 2480.2.a.x.1.4 | 4 | |||
35.34 | odd | 2 | 7595.2.a.s.1.2 | 4 | |||
40.19 | odd | 2 | 9920.2.a.cg.1.1 | 4 | |||
40.29 | even | 2 | 9920.2.a.cb.1.4 | 4 | |||
155.154 | odd | 2 | 4805.2.a.n.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
155.2.a.e.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
775.2.a.e.1.3 | 4 | 1.1 | even | 1 | trivial | ||
775.2.b.f.249.4 | 8 | 5.3 | odd | 4 | |||
775.2.b.f.249.5 | 8 | 5.2 | odd | 4 | |||
1395.2.a.l.1.3 | 4 | 15.14 | odd | 2 | |||
2480.2.a.x.1.4 | 4 | 20.19 | odd | 2 | |||
4805.2.a.n.1.2 | 4 | 155.154 | odd | 2 | |||
6975.2.a.bn.1.2 | 4 | 3.2 | odd | 2 | |||
7595.2.a.s.1.2 | 4 | 35.34 | odd | 2 | |||
9920.2.a.cb.1.4 | 4 | 40.29 | even | 2 | |||
9920.2.a.cg.1.1 | 4 | 40.19 | odd | 2 |