Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.09529\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09529 | 0.774490 | 0.387245 | − | 0.921977i | \(-0.373427\pi\) | ||||
0.387245 | + | 0.921977i | \(0.373427\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.800331 | −0.400166 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.09529 | 0.447152 | ||||||||
\(7\) | −0.705037 | −0.266479 | −0.133239 | − | 0.991084i | \(-0.542538\pi\) | ||||
−0.133239 | + | 0.991084i | \(0.542538\pi\) | |||||||
\(8\) | −3.06719 | −1.08441 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.09529 | 0.346362 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.800331 | −0.231036 | ||||||||
\(13\) | −4.71333 | −1.30724 | −0.653621 | − | 0.756822i | \(-0.726751\pi\) | ||||
−0.653621 | + | 0.756822i | \(0.726751\pi\) | |||||||
\(14\) | −0.772223 | −0.206385 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −1.75881 | −0.439702 | ||||||||
\(17\) | −7.78051 | −1.88705 | −0.943526 | − | 0.331299i | \(-0.892513\pi\) | ||||
−0.943526 | + | 0.331299i | \(0.892513\pi\) | |||||||
\(18\) | 1.09529 | 0.258163 | ||||||||
\(19\) | −1.19967 | −0.275223 | −0.137611 | − | 0.990486i | \(-0.543943\pi\) | ||||
−0.137611 | + | 0.990486i | \(0.543943\pi\) | |||||||
\(20\) | −0.800331 | −0.178959 | ||||||||
\(21\) | −0.705037 | −0.153852 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.89318 | −1.43733 | −0.718664 | − | 0.695358i | \(-0.755246\pi\) | ||||
−0.718664 | + | 0.695358i | \(0.755246\pi\) | |||||||
\(24\) | −3.06719 | −0.626087 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.16248 | −1.01245 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.564263 | 0.106636 | ||||||||
\(29\) | 1.32741 | 0.246493 | 0.123246 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123246 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(30\) | 1.09529 | 0.199972 | ||||||||
\(31\) | −7.68126 | −1.37960 | −0.689798 | − | 0.724002i | \(-0.742301\pi\) | ||||
−0.689798 | + | 0.724002i | \(0.742301\pi\) | |||||||
\(32\) | 4.20796 | 0.743869 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.52195 | −1.46150 | ||||||||
\(35\) | −0.705037 | −0.119173 | ||||||||
\(36\) | −0.800331 | −0.133389 | ||||||||
\(37\) | 8.43763 | 1.38714 | 0.693569 | − | 0.720391i | \(-0.256037\pi\) | ||||
0.693569 | + | 0.720391i | \(0.256037\pi\) | |||||||
\(38\) | −1.31399 | −0.213157 | ||||||||
\(39\) | −4.71333 | −0.754737 | ||||||||
\(40\) | −3.06719 | −0.484965 | ||||||||
\(41\) | −0.232901 | −0.0363730 | −0.0181865 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181865 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(42\) | −0.772223 | −0.119157 | ||||||||
\(43\) | 7.32892 | 1.11765 | 0.558825 | − | 0.829286i | \(-0.311252\pi\) | ||||
0.558825 | + | 0.829286i | \(0.311252\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −7.55006 | −1.11320 | ||||||||
\(47\) | 8.32228 | 1.21393 | 0.606965 | − | 0.794729i | \(-0.292387\pi\) | ||||
0.606965 | + | 0.794729i | \(0.292387\pi\) | |||||||
\(48\) | −1.75881 | −0.253862 | ||||||||
\(49\) | −6.50292 | −0.928989 | ||||||||
\(50\) | 1.09529 | 0.154898 | ||||||||
\(51\) | −7.78051 | −1.08949 | ||||||||
\(52\) | 3.77222 | 0.523113 | ||||||||
\(53\) | 6.82332 | 0.937254 | 0.468627 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468627 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(54\) | 1.09529 | 0.149051 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.16248 | 0.288974 | ||||||||
\(57\) | −1.19967 | −0.158900 | ||||||||
\(58\) | 1.45390 | 0.190906 | ||||||||
\(59\) | −3.54011 | −0.460883 | −0.230442 | − | 0.973086i | \(-0.574017\pi\) | ||||
−0.230442 | + | 0.973086i | \(0.574017\pi\) | |||||||
\(60\) | −0.800331 | −0.103322 | ||||||||
\(61\) | −10.8719 | −1.39200 | −0.695999 | − | 0.718043i | \(-0.745038\pi\) | ||||
−0.695999 | + | 0.718043i | \(0.745038\pi\) | |||||||
\(62\) | −8.41324 | −1.06848 | ||||||||
\(63\) | −0.705037 | −0.0888263 | ||||||||
\(64\) | 8.12657 | 1.01582 | ||||||||
\(65\) | −4.71333 | −0.584616 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.04036 | −0.249269 | −0.124635 | − | 0.992203i | \(-0.539776\pi\) | ||||
−0.124635 | + | 0.992203i | \(0.539776\pi\) | |||||||
\(68\) | 6.22699 | 0.755133 | ||||||||
\(69\) | −6.89318 | −0.829841 | ||||||||
\(70\) | −0.772223 | −0.0922983 | ||||||||
\(71\) | 0.670527 | 0.0795769 | 0.0397884 | − | 0.999208i | \(-0.487332\pi\) | ||||
0.0397884 | + | 0.999208i | \(0.487332\pi\) | |||||||
\(72\) | −3.06719 | −0.361471 | ||||||||
\(73\) | −5.00433 | −0.585713 | −0.292856 | − | 0.956156i | \(-0.594606\pi\) | ||||
−0.292856 | + | 0.956156i | \(0.594606\pi\) | |||||||
\(74\) | 9.24168 | 1.07432 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.960132 | 0.110135 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.16248 | −0.584536 | ||||||||
\(79\) | 2.28027 | 0.256550 | 0.128275 | − | 0.991739i | \(-0.459056\pi\) | ||||
0.128275 | + | 0.991739i | \(0.459056\pi\) | |||||||
\(80\) | −1.75881 | −0.196641 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.255095 | −0.0281706 | ||||||||
\(83\) | −2.10999 | −0.231601 | −0.115801 | − | 0.993272i | \(-0.536943\pi\) | ||||
−0.115801 | + | 0.993272i | \(0.536943\pi\) | |||||||
\(84\) | 0.564263 | 0.0615662 | ||||||||
\(85\) | −7.78051 | −0.843915 | ||||||||
\(86\) | 8.02732 | 0.865608 | ||||||||
\(87\) | 1.32741 | 0.142313 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.34722 | −0.354805 | −0.177402 | − | 0.984138i | \(-0.556769\pi\) | ||||
−0.177402 | + | 0.984138i | \(0.556769\pi\) | |||||||
\(90\) | 1.09529 | 0.115454 | ||||||||
\(91\) | 3.32307 | 0.348353 | ||||||||
\(92\) | 5.51683 | 0.575169 | ||||||||
\(93\) | −7.68126 | −0.796510 | ||||||||
\(94\) | 9.11534 | 0.940176 | ||||||||
\(95\) | −1.19967 | −0.123083 | ||||||||
\(96\) | 4.20796 | 0.429473 | ||||||||
\(97\) | 3.32228 | 0.337327 | 0.168663 | − | 0.985674i | \(-0.446055\pi\) | ||||
0.168663 | + | 0.985674i | \(0.446055\pi\) | |||||||
\(98\) | −7.12261 | −0.719492 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.800331 | −0.0800331 | ||||||||
\(101\) | −18.9218 | −1.88279 | −0.941394 | − | 0.337310i | \(-0.890483\pi\) | ||||
−0.941394 | + | 0.337310i | \(0.890483\pi\) | |||||||
\(102\) | −8.52195 | −0.843799 | ||||||||
\(103\) | −18.0964 | −1.78309 | −0.891545 | − | 0.452932i | \(-0.850378\pi\) | ||||
−0.891545 | + | 0.452932i | \(0.850378\pi\) | |||||||
\(104\) | 14.4567 | 1.41759 | ||||||||
\(105\) | −0.705037 | −0.0688046 | ||||||||
\(106\) | 7.47354 | 0.725894 | ||||||||
\(107\) | −6.11945 | −0.591589 | −0.295795 | − | 0.955252i | \(-0.595584\pi\) | ||||
−0.295795 | + | 0.955252i | \(0.595584\pi\) | |||||||
\(108\) | −0.800331 | −0.0770119 | ||||||||
\(109\) | 9.03128 | 0.865039 | 0.432520 | − | 0.901625i | \(-0.357625\pi\) | ||||
0.432520 | + | 0.901625i | \(0.357625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.43763 | 0.800864 | ||||||||
\(112\) | 1.24002 | 0.117171 | ||||||||
\(113\) | 3.91684 | 0.368466 | 0.184233 | − | 0.982883i | \(-0.441020\pi\) | ||||
0.184233 | + | 0.982883i | \(0.441020\pi\) | |||||||
\(114\) | −1.31399 | −0.123066 | ||||||||
\(115\) | −6.89318 | −0.642792 | ||||||||
\(116\) | −1.06236 | −0.0986380 | ||||||||
\(117\) | −4.71333 | −0.435747 | ||||||||
\(118\) | −3.87746 | −0.356949 | ||||||||
\(119\) | 5.48555 | 0.502860 | ||||||||
\(120\) | −3.06719 | −0.279994 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.9079 | −1.07809 | ||||||||
\(123\) | −0.232901 | −0.0210000 | ||||||||
\(124\) | 6.14755 | 0.552067 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.772223 | −0.0687951 | ||||||||
\(127\) | 10.8675 | 0.964336 | 0.482168 | − | 0.876079i | \(-0.339849\pi\) | ||||
0.482168 | + | 0.876079i | \(0.339849\pi\) | |||||||
\(128\) | 0.485063 | 0.0428739 | ||||||||
\(129\) | 7.32892 | 0.645275 | ||||||||
\(130\) | −5.16248 | −0.452779 | ||||||||
\(131\) | −11.7094 | −1.02305 | −0.511526 | − | 0.859268i | \(-0.670920\pi\) | ||||
−0.511526 | + | 0.859268i | \(0.670920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.845811 | 0.0733411 | ||||||||
\(134\) | −2.23479 | −0.193056 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 23.8643 | 2.04635 | ||||||||
\(137\) | 20.4302 | 1.74547 | 0.872735 | − | 0.488194i | \(-0.162344\pi\) | ||||
0.872735 | + | 0.488194i | \(0.162344\pi\) | |||||||
\(138\) | −7.55006 | −0.642704 | ||||||||
\(139\) | −8.17100 | −0.693055 | −0.346528 | − | 0.938040i | \(-0.612639\pi\) | ||||
−0.346528 | + | 0.938040i | \(0.612639\pi\) | |||||||
\(140\) | 0.564263 | 0.0476889 | ||||||||
\(141\) | 8.32228 | 0.700862 | ||||||||
\(142\) | 0.734424 | 0.0616315 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.75881 | −0.146567 | ||||||||
\(145\) | 1.32741 | 0.110235 | ||||||||
\(146\) | −5.48122 | −0.453629 | ||||||||
\(147\) | −6.50292 | −0.536352 | ||||||||
\(148\) | −6.75289 | −0.555084 | ||||||||
\(149\) | −9.60217 | −0.786641 | −0.393320 | − | 0.919401i | \(-0.628674\pi\) | ||||
−0.393320 | + | 0.919401i | \(0.628674\pi\) | |||||||
\(150\) | 1.09529 | 0.0894304 | ||||||||
\(151\) | 6.90776 | 0.562146 | 0.281073 | − | 0.959686i | \(-0.409310\pi\) | ||||
0.281073 | + | 0.959686i | \(0.409310\pi\) | |||||||
\(152\) | 3.67961 | 0.298456 | ||||||||
\(153\) | −7.78051 | −0.629017 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.68126 | −0.616974 | ||||||||
\(156\) | 3.77222 | 0.302020 | ||||||||
\(157\) | 11.3519 | 0.905980 | 0.452990 | − | 0.891516i | \(-0.350357\pi\) | ||||
0.452990 | + | 0.891516i | \(0.350357\pi\) | |||||||
\(158\) | 2.49757 | 0.198696 | ||||||||
\(159\) | 6.82332 | 0.541124 | ||||||||
\(160\) | 4.20796 | 0.332668 | ||||||||
\(161\) | 4.85995 | 0.383018 | ||||||||
\(162\) | 1.09529 | 0.0860544 | ||||||||
\(163\) | −1.79253 | −0.140402 | −0.0702008 | − | 0.997533i | \(-0.522364\pi\) | ||||
−0.0702008 | + | 0.997533i | \(0.522364\pi\) | |||||||
\(164\) | 0.186398 | 0.0145552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.31106 | −0.179373 | ||||||||
\(167\) | 6.02450 | 0.466189 | 0.233095 | − | 0.972454i | \(-0.425115\pi\) | ||||
0.233095 | + | 0.972454i | \(0.425115\pi\) | |||||||
\(168\) | 2.16248 | 0.166839 | ||||||||
\(169\) | 9.21546 | 0.708882 | ||||||||
\(170\) | −8.52195 | −0.653604 | ||||||||
\(171\) | −1.19967 | −0.0917410 | ||||||||
\(172\) | −5.86556 | −0.447245 | ||||||||
\(173\) | 4.18674 | 0.318312 | 0.159156 | − | 0.987253i | \(-0.449123\pi\) | ||||
0.159156 | + | 0.987253i | \(0.449123\pi\) | |||||||
\(174\) | 1.45390 | 0.110220 | ||||||||
\(175\) | −0.705037 | −0.0532958 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.54011 | −0.266091 | ||||||||
\(178\) | −3.66619 | −0.274793 | ||||||||
\(179\) | 4.85166 | 0.362630 | 0.181315 | − | 0.983425i | \(-0.441965\pi\) | ||||
0.181315 | + | 0.983425i | \(0.441965\pi\) | |||||||
\(180\) | −0.800331 | −0.0596532 | ||||||||
\(181\) | −23.0877 | −1.71610 | −0.858049 | − | 0.513569i | \(-0.828323\pi\) | ||||
−0.858049 | + | 0.513569i | \(0.828323\pi\) | |||||||
\(182\) | 3.63974 | 0.269795 | ||||||||
\(183\) | −10.8719 | −0.803670 | ||||||||
\(184\) | 21.1427 | 1.55866 | ||||||||
\(185\) | 8.43763 | 0.620347 | ||||||||
\(186\) | −8.41324 | −0.616889 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.66058 | −0.485773 | ||||||||
\(189\) | −0.705037 | −0.0512839 | ||||||||
\(190\) | −1.31399 | −0.0953269 | ||||||||
\(191\) | 6.22571 | 0.450476 | 0.225238 | − | 0.974304i | \(-0.427684\pi\) | ||||
0.225238 | + | 0.974304i | \(0.427684\pi\) | |||||||
\(192\) | 8.12657 | 0.586485 | ||||||||
\(193\) | 19.0868 | 1.37390 | 0.686950 | − | 0.726705i | \(-0.258949\pi\) | ||||
0.686950 | + | 0.726705i | \(0.258949\pi\) | |||||||
\(194\) | 3.63887 | 0.261256 | ||||||||
\(195\) | −4.71333 | −0.337528 | ||||||||
\(196\) | 5.20449 | 0.371749 | ||||||||
\(197\) | 6.80056 | 0.484520 | 0.242260 | − | 0.970211i | \(-0.422111\pi\) | ||||
0.242260 | + | 0.970211i | \(0.422111\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2972 | 1.50972 | 0.754860 | − | 0.655886i | \(-0.227705\pi\) | ||||
0.754860 | + | 0.655886i | \(0.227705\pi\) | |||||||
\(200\) | −3.06719 | −0.216883 | ||||||||
\(201\) | −2.04036 | −0.143916 | ||||||||
\(202\) | −20.7249 | −1.45820 | ||||||||
\(203\) | −0.935870 | −0.0656852 | ||||||||
\(204\) | 6.22699 | 0.435976 | ||||||||
\(205\) | −0.232901 | −0.0162665 | ||||||||
\(206\) | −19.8209 | −1.38099 | ||||||||
\(207\) | −6.89318 | −0.479109 | ||||||||
\(208\) | 8.28984 | 0.574797 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.772223 | −0.0532884 | ||||||||
\(211\) | −8.89073 | −0.612063 | −0.306032 | − | 0.952021i | \(-0.599001\pi\) | ||||
−0.306032 | + | 0.952021i | \(0.599001\pi\) | |||||||
\(212\) | −5.46091 | −0.375057 | ||||||||
\(213\) | 0.670527 | 0.0459437 | ||||||||
\(214\) | −6.70259 | −0.458180 | ||||||||
\(215\) | 7.32892 | 0.499828 | ||||||||
\(216\) | −3.06719 | −0.208696 | ||||||||
\(217\) | 5.41558 | 0.367633 | ||||||||
\(218\) | 9.89190 | 0.669964 | ||||||||
\(219\) | −5.00433 | −0.338162 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.6721 | 2.46683 | ||||||||
\(222\) | 9.24168 | 0.620261 | ||||||||
\(223\) | 5.41720 | 0.362762 | 0.181381 | − | 0.983413i | \(-0.441943\pi\) | ||||
0.181381 | + | 0.983413i | \(0.441943\pi\) | |||||||
\(224\) | −2.96677 | −0.198226 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 4.29009 | 0.285373 | ||||||||
\(227\) | −8.43842 | −0.560077 | −0.280039 | − | 0.959989i | \(-0.590347\pi\) | ||||
−0.280039 | + | 0.959989i | \(0.590347\pi\) | |||||||
\(228\) | 0.960132 | 0.0635863 | ||||||||
\(229\) | −11.2053 | −0.740466 | −0.370233 | − | 0.928939i | \(-0.620722\pi\) | ||||
−0.370233 | + | 0.928939i | \(0.620722\pi\) | |||||||
\(230\) | −7.55006 | −0.497836 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.07140 | −0.267300 | ||||||||
\(233\) | 5.83979 | 0.382577 | 0.191289 | − | 0.981534i | \(-0.438733\pi\) | ||||
0.191289 | + | 0.981534i | \(0.438733\pi\) | |||||||
\(234\) | −5.16248 | −0.337482 | ||||||||
\(235\) | 8.32228 | 0.542886 | ||||||||
\(236\) | 2.83326 | 0.184430 | ||||||||
\(237\) | 2.28027 | 0.148119 | ||||||||
\(238\) | 6.00829 | 0.389460 | ||||||||
\(239\) | −16.5261 | −1.06899 | −0.534494 | − | 0.845173i | \(-0.679498\pi\) | ||||
−0.534494 | + | 0.845173i | \(0.679498\pi\) | |||||||
\(240\) | −1.75881 | −0.113531 | ||||||||
\(241\) | −3.29180 | −0.212043 | −0.106022 | − | 0.994364i | \(-0.533811\pi\) | ||||
−0.106022 | + | 0.994364i | \(0.533811\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.70108 | 0.557030 | ||||||||
\(245\) | −6.50292 | −0.415456 | ||||||||
\(246\) | −0.255095 | −0.0162643 | ||||||||
\(247\) | 5.65443 | 0.359783 | ||||||||
\(248\) | 23.5599 | 1.49605 | ||||||||
\(249\) | −2.10999 | −0.133715 | ||||||||
\(250\) | 1.09529 | 0.0692725 | ||||||||
\(251\) | −7.39934 | −0.467042 | −0.233521 | − | 0.972352i | \(-0.575025\pi\) | ||||
−0.233521 | + | 0.972352i | \(0.575025\pi\) | |||||||
\(252\) | 0.564263 | 0.0355452 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 11.9031 | 0.746869 | ||||||||
\(255\) | −7.78051 | −0.487235 | ||||||||
\(256\) | −15.7219 | −0.982616 | ||||||||
\(257\) | −18.6991 | −1.16642 | −0.583210 | − | 0.812322i | \(-0.698203\pi\) | ||||
−0.583210 | + | 0.812322i | \(0.698203\pi\) | |||||||
\(258\) | 8.02732 | 0.499759 | ||||||||
\(259\) | −5.94884 | −0.369643 | ||||||||
\(260\) | 3.77222 | 0.233943 | ||||||||
\(261\) | 1.32741 | 0.0821643 | ||||||||
\(262\) | −12.8252 | −0.792344 | ||||||||
\(263\) | 3.99020 | 0.246046 | 0.123023 | − | 0.992404i | \(-0.460741\pi\) | ||||
0.123023 | + | 0.992404i | \(0.460741\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.82332 | 0.419153 | ||||||||
\(266\) | 0.926412 | 0.0568020 | ||||||||
\(267\) | −3.34722 | −0.204847 | ||||||||
\(268\) | 1.63296 | 0.0997489 | ||||||||
\(269\) | −12.7150 | −0.775246 | −0.387623 | − | 0.921818i | \(-0.626704\pi\) | ||||
−0.387623 | + | 0.921818i | \(0.626704\pi\) | |||||||
\(270\) | 1.09529 | 0.0666575 | ||||||||
\(271\) | 23.8280 | 1.44745 | 0.723724 | − | 0.690090i | \(-0.242429\pi\) | ||||
0.723724 | + | 0.690090i | \(0.242429\pi\) | |||||||
\(272\) | 13.6844 | 0.829740 | ||||||||
\(273\) | 3.32307 | 0.201121 | ||||||||
\(274\) | 22.3771 | 1.35185 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.51683 | 0.332074 | ||||||||
\(277\) | 7.41252 | 0.445375 | 0.222688 | − | 0.974890i | \(-0.428517\pi\) | ||||
0.222688 | + | 0.974890i | \(0.428517\pi\) | |||||||
\(278\) | −8.94965 | −0.536764 | ||||||||
\(279\) | −7.68126 | −0.459865 | ||||||||
\(280\) | 2.16248 | 0.129233 | ||||||||
\(281\) | −29.0815 | −1.73485 | −0.867427 | − | 0.497564i | \(-0.834228\pi\) | ||||
−0.867427 | + | 0.497564i | \(0.834228\pi\) | |||||||
\(282\) | 9.11534 | 0.542811 | ||||||||
\(283\) | −21.6729 | −1.28832 | −0.644160 | − | 0.764891i | \(-0.722793\pi\) | ||||
−0.644160 | + | 0.764891i | \(0.722793\pi\) | |||||||
\(284\) | −0.536643 | −0.0318439 | ||||||||
\(285\) | −1.19967 | −0.0710623 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.164204 | 0.00969265 | ||||||||
\(288\) | 4.20796 | 0.247956 | ||||||||
\(289\) | 43.5364 | 2.56096 | ||||||||
\(290\) | 1.45390 | 0.0853759 | ||||||||
\(291\) | 3.32228 | 0.194756 | ||||||||
\(292\) | 4.00512 | 0.234382 | ||||||||
\(293\) | −8.41220 | −0.491446 | −0.245723 | − | 0.969340i | \(-0.579025\pi\) | ||||
−0.245723 | + | 0.969340i | \(0.579025\pi\) | |||||||
\(294\) | −7.12261 | −0.415399 | ||||||||
\(295\) | −3.54011 | −0.206113 | ||||||||
\(296\) | −25.8798 | −1.50423 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.5172 | −0.609245 | ||||||||
\(299\) | 32.4898 | 1.87893 | ||||||||
\(300\) | −0.800331 | −0.0462071 | ||||||||
\(301\) | −5.16716 | −0.297830 | ||||||||
\(302\) | 7.56603 | 0.435376 | ||||||||
\(303\) | −18.9218 | −1.08703 | ||||||||
\(304\) | 2.10999 | 0.121016 | ||||||||
\(305\) | −10.8719 | −0.622520 | ||||||||
\(306\) | −8.52195 | −0.487167 | ||||||||
\(307\) | 23.7431 | 1.35509 | 0.677545 | − | 0.735481i | \(-0.263044\pi\) | ||||
0.677545 | + | 0.735481i | \(0.263044\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.0964 | −1.02947 | ||||||||
\(310\) | −8.41324 | −0.477840 | ||||||||
\(311\) | 23.0471 | 1.30688 | 0.653440 | − | 0.756979i | \(-0.273325\pi\) | ||||
0.653440 | + | 0.756979i | \(0.273325\pi\) | |||||||
\(312\) | 14.4567 | 0.818447 | ||||||||
\(313\) | −17.3638 | −0.981460 | −0.490730 | − | 0.871312i | \(-0.663270\pi\) | ||||
−0.490730 | + | 0.871312i | \(0.663270\pi\) | |||||||
\(314\) | 12.4337 | 0.701673 | ||||||||
\(315\) | −0.705037 | −0.0397243 | ||||||||
\(316\) | −1.82497 | −0.102663 | ||||||||
\(317\) | −6.15095 | −0.345472 | −0.172736 | − | 0.984968i | \(-0.555261\pi\) | ||||
−0.172736 | + | 0.984968i | \(0.555261\pi\) | |||||||
\(318\) | 7.47354 | 0.419095 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.12657 | 0.454289 | ||||||||
\(321\) | −6.11945 | −0.341554 | ||||||||
\(322\) | 5.32307 | 0.296643 | ||||||||
\(323\) | 9.33404 | 0.519360 | ||||||||
\(324\) | −0.800331 | −0.0444628 | ||||||||
\(325\) | −4.71333 | −0.261448 | ||||||||
\(326\) | −1.96335 | −0.108740 | ||||||||
\(327\) | 9.03128 | 0.499431 | ||||||||
\(328\) | 0.714351 | 0.0394434 | ||||||||
\(329\) | −5.86752 | −0.323487 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.4191 | 1.06737 | 0.533685 | − | 0.845683i | \(-0.320807\pi\) | ||||
0.533685 | + | 0.845683i | \(0.320807\pi\) | |||||||
\(332\) | 1.68869 | 0.0926788 | ||||||||
\(333\) | 8.43763 | 0.462379 | ||||||||
\(334\) | 6.59859 | 0.361059 | ||||||||
\(335\) | −2.04036 | −0.111477 | ||||||||
\(336\) | 1.24002 | 0.0676489 | ||||||||
\(337\) | 31.6868 | 1.72609 | 0.863045 | − | 0.505127i | \(-0.168554\pi\) | ||||
0.863045 | + | 0.505127i | \(0.168554\pi\) | |||||||
\(338\) | 10.0936 | 0.549022 | ||||||||
\(339\) | 3.91684 | 0.212734 | ||||||||
\(340\) | 6.22699 | 0.337706 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.31399 | −0.0710524 | ||||||||
\(343\) | 9.52006 | 0.514035 | ||||||||
\(344\) | −22.4791 | −1.21199 | ||||||||
\(345\) | −6.89318 | −0.371116 | ||||||||
\(346\) | 4.58571 | 0.246529 | ||||||||
\(347\) | −27.9434 | −1.50008 | −0.750041 | − | 0.661392i | \(-0.769966\pi\) | ||||
−0.750041 | + | 0.661392i | \(0.769966\pi\) | |||||||
\(348\) | −1.06236 | −0.0569487 | ||||||||
\(349\) | −0.683331 | −0.0365779 | −0.0182889 | − | 0.999833i | \(-0.505822\pi\) | ||||
−0.0182889 | + | 0.999833i | \(0.505822\pi\) | |||||||
\(350\) | −0.772223 | −0.0412771 | ||||||||
\(351\) | −4.71333 | −0.251579 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.55900 | 0.0829769 | 0.0414885 | − | 0.999139i | \(-0.486790\pi\) | ||||
0.0414885 | + | 0.999139i | \(0.486790\pi\) | |||||||
\(354\) | −3.87746 | −0.206085 | ||||||||
\(355\) | 0.670527 | 0.0355879 | ||||||||
\(356\) | 2.67889 | 0.141981 | ||||||||
\(357\) | 5.48555 | 0.290326 | ||||||||
\(358\) | 5.31399 | 0.280853 | ||||||||
\(359\) | 15.8404 | 0.836022 | 0.418011 | − | 0.908442i | \(-0.362727\pi\) | ||||
0.418011 | + | 0.908442i | \(0.362727\pi\) | |||||||
\(360\) | −3.06719 | −0.161655 | ||||||||
\(361\) | −17.5608 | −0.924252 | ||||||||
\(362\) | −25.2878 | −1.32910 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.65956 | −0.139399 | ||||||||
\(365\) | −5.00433 | −0.261939 | ||||||||
\(366\) | −11.9079 | −0.622434 | ||||||||
\(367\) | 15.7361 | 0.821419 | 0.410710 | − | 0.911766i | \(-0.365281\pi\) | ||||
0.410710 | + | 0.911766i | \(0.365281\pi\) | |||||||
\(368\) | 12.1238 | 0.631996 | ||||||||
\(369\) | −0.232901 | −0.0121243 | ||||||||
\(370\) | 9.24168 | 0.480452 | ||||||||
\(371\) | −4.81069 | −0.249759 | ||||||||
\(372\) | 6.14755 | 0.318736 | ||||||||
\(373\) | −5.27703 | −0.273234 | −0.136617 | − | 0.990624i | \(-0.543623\pi\) | ||||
−0.136617 | + | 0.990624i | \(0.543623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −25.5260 | −1.31640 | ||||||||
\(377\) | −6.25650 | −0.322226 | ||||||||
\(378\) | −0.772223 | −0.0397189 | ||||||||
\(379\) | 33.5093 | 1.72125 | 0.860627 | − | 0.509235i | \(-0.170072\pi\) | ||||
0.860627 | + | 0.509235i | \(0.170072\pi\) | |||||||
\(380\) | 0.960132 | 0.0492537 | ||||||||
\(381\) | 10.8675 | 0.556760 | ||||||||
\(382\) | 6.81898 | 0.348889 | ||||||||
\(383\) | −20.2323 | −1.03382 | −0.516910 | − | 0.856039i | \(-0.672918\pi\) | ||||
−0.516910 | + | 0.856039i | \(0.672918\pi\) | |||||||
\(384\) | 0.485063 | 0.0247532 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.9057 | 1.06407 | ||||||||
\(387\) | 7.32892 | 0.372550 | ||||||||
\(388\) | −2.65892 | −0.134986 | ||||||||
\(389\) | −27.5729 | −1.39800 | −0.699000 | − | 0.715122i | \(-0.746371\pi\) | ||||
−0.699000 | + | 0.715122i | \(0.746371\pi\) | |||||||
\(390\) | −5.16248 | −0.261412 | ||||||||
\(391\) | 53.6325 | 2.71231 | ||||||||
\(392\) | 19.9457 | 1.00741 | ||||||||
\(393\) | −11.7094 | −0.590660 | ||||||||
\(394\) | 7.44862 | 0.375256 | ||||||||
\(395\) | 2.28027 | 0.114733 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7601 | 0.590222 | 0.295111 | − | 0.955463i | \(-0.404643\pi\) | ||||
0.295111 | + | 0.955463i | \(0.404643\pi\) | |||||||
\(398\) | 23.3267 | 1.16926 | ||||||||
\(399\) | 0.845811 | 0.0423435 | ||||||||
\(400\) | −1.75881 | −0.0879404 | ||||||||
\(401\) | −7.72406 | −0.385721 | −0.192861 | − | 0.981226i | \(-0.561777\pi\) | ||||
−0.192861 | + | 0.981226i | \(0.561777\pi\) | |||||||
\(402\) | −2.23479 | −0.111461 | ||||||||
\(403\) | 36.2043 | 1.80347 | ||||||||
\(404\) | 15.1437 | 0.753427 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −1.02505 | −0.0508725 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 23.8643 | 1.18146 | ||||||||
\(409\) | 16.7409 | 0.827783 | 0.413892 | − | 0.910326i | \(-0.364169\pi\) | ||||
0.413892 | + | 0.910326i | \(0.364169\pi\) | |||||||
\(410\) | −0.255095 | −0.0125983 | ||||||||
\(411\) | 20.4302 | 1.00775 | ||||||||
\(412\) | 14.4831 | 0.713531 | ||||||||
\(413\) | 2.49591 | 0.122816 | ||||||||
\(414\) | −7.55006 | −0.371065 | ||||||||
\(415\) | −2.10999 | −0.103575 | ||||||||
\(416\) | −19.8335 | −0.972417 | ||||||||
\(417\) | −8.17100 | −0.400136 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.0968 | −1.86115 | −0.930576 | − | 0.366100i | \(-0.880693\pi\) | ||||
−0.930576 | + | 0.366100i | \(0.880693\pi\) | |||||||
\(420\) | 0.564263 | 0.0275332 | ||||||||
\(421\) | −22.6633 | −1.10454 | −0.552272 | − | 0.833664i | \(-0.686239\pi\) | ||||
−0.552272 | + | 0.833664i | \(0.686239\pi\) | |||||||
\(422\) | −9.73797 | −0.474037 | ||||||||
\(423\) | 8.32228 | 0.404643 | ||||||||
\(424\) | −20.9284 | −1.01637 | ||||||||
\(425\) | −7.78051 | −0.377410 | ||||||||
\(426\) | 0.734424 | 0.0355829 | ||||||||
\(427\) | 7.66506 | 0.370938 | ||||||||
\(428\) | 4.89758 | 0.236734 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.02732 | 0.387112 | ||||||||
\(431\) | −33.9766 | −1.63660 | −0.818299 | − | 0.574793i | \(-0.805082\pi\) | ||||
−0.818299 | + | 0.574793i | \(0.805082\pi\) | |||||||
\(432\) | −1.75881 | −0.0846207 | ||||||||
\(433\) | −36.6753 | −1.76250 | −0.881251 | − | 0.472649i | \(-0.843298\pi\) | ||||
−0.881251 | + | 0.472649i | \(0.843298\pi\) | |||||||
\(434\) | 5.93165 | 0.284728 | ||||||||
\(435\) | 1.32741 | 0.0636442 | ||||||||
\(436\) | −7.22801 | −0.346159 | ||||||||
\(437\) | 8.26953 | 0.395585 | ||||||||
\(438\) | −5.48122 | −0.261903 | ||||||||
\(439\) | 1.05012 | 0.0501193 | 0.0250596 | − | 0.999686i | \(-0.492022\pi\) | ||||
0.0250596 | + | 0.999686i | \(0.492022\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50292 | −0.309663 | ||||||||
\(442\) | 40.1667 | 1.91054 | ||||||||
\(443\) | −30.5206 | −1.45008 | −0.725039 | − | 0.688708i | \(-0.758178\pi\) | ||||
−0.725039 | + | 0.688708i | \(0.758178\pi\) | |||||||
\(444\) | −6.75289 | −0.320478 | ||||||||
\(445\) | −3.34722 | −0.158674 | ||||||||
\(446\) | 5.93342 | 0.280956 | ||||||||
\(447\) | −9.60217 | −0.454167 | ||||||||
\(448\) | −5.72953 | −0.270695 | ||||||||
\(449\) | −36.5695 | −1.72582 | −0.862910 | − | 0.505357i | \(-0.831361\pi\) | ||||
−0.862910 | + | 0.505357i | \(0.831361\pi\) | |||||||
\(450\) | 1.09529 | 0.0516327 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.13477 | −0.147447 | ||||||||
\(453\) | 6.90776 | 0.324555 | ||||||||
\(454\) | −9.24255 | −0.433774 | ||||||||
\(455\) | 3.32307 | 0.155788 | ||||||||
\(456\) | 3.67961 | 0.172313 | ||||||||
\(457\) | −2.38409 | −0.111523 | −0.0557615 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557615 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(458\) | −12.2731 | −0.573483 | ||||||||
\(459\) | −7.78051 | −0.363163 | ||||||||
\(460\) | 5.51683 | 0.257223 | ||||||||
\(461\) | 28.5962 | 1.33186 | 0.665929 | − | 0.746015i | \(-0.268035\pi\) | ||||
0.665929 | + | 0.746015i | \(0.268035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.5806 | −1.42120 | −0.710600 | − | 0.703596i | \(-0.751577\pi\) | ||||
−0.710600 | + | 0.703596i | \(0.751577\pi\) | |||||||
\(464\) | −2.33465 | −0.108383 | ||||||||
\(465\) | −7.68126 | −0.356210 | ||||||||
\(466\) | 6.39628 | 0.296302 | ||||||||
\(467\) | −3.74219 | −0.173168 | −0.0865840 | − | 0.996245i | \(-0.527595\pi\) | ||||
−0.0865840 | + | 0.996245i | \(0.527595\pi\) | |||||||
\(468\) | 3.77222 | 0.174371 | ||||||||
\(469\) | 1.43853 | 0.0664250 | ||||||||
\(470\) | 9.11534 | 0.420459 | ||||||||
\(471\) | 11.3519 | 0.523068 | ||||||||
\(472\) | 10.8582 | 0.499788 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.49757 | 0.114717 | ||||||||
\(475\) | −1.19967 | −0.0550446 | ||||||||
\(476\) | −4.39026 | −0.201227 | ||||||||
\(477\) | 6.82332 | 0.312418 | ||||||||
\(478\) | −18.1010 | −0.827920 | ||||||||
\(479\) | −0.944951 | −0.0431759 | −0.0215880 | − | 0.999767i | \(-0.506872\pi\) | ||||
−0.0215880 | + | 0.999767i | \(0.506872\pi\) | |||||||
\(480\) | 4.20796 | 0.192066 | ||||||||
\(481\) | −39.7693 | −1.81332 | ||||||||
\(482\) | −3.60548 | −0.164225 | ||||||||
\(483\) | 4.85995 | 0.221135 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.32228 | 0.150857 | ||||||||
\(486\) | 1.09529 | 0.0496835 | ||||||||
\(487\) | −13.3873 | −0.606638 | −0.303319 | − | 0.952889i | \(-0.598095\pi\) | ||||
−0.303319 | + | 0.952889i | \(0.598095\pi\) | |||||||
\(488\) | 33.3460 | 1.50950 | ||||||||
\(489\) | −1.79253 | −0.0810609 | ||||||||
\(490\) | −7.12261 | −0.321767 | ||||||||
\(491\) | −2.78887 | −0.125860 | −0.0629300 | − | 0.998018i | \(-0.520045\pi\) | ||||
−0.0629300 | + | 0.998018i | \(0.520045\pi\) | |||||||
\(492\) | 0.186398 | 0.00840347 | ||||||||
\(493\) | −10.3279 | −0.465145 | ||||||||
\(494\) | 6.19327 | 0.278648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.5099 | 0.606611 | ||||||||
\(497\) | −0.472746 | −0.0212056 | ||||||||
\(498\) | −2.31106 | −0.103561 | ||||||||
\(499\) | 17.7790 | 0.795899 | 0.397950 | − | 0.917407i | \(-0.369722\pi\) | ||||
0.397950 | + | 0.917407i | \(0.369722\pi\) | |||||||
\(500\) | −0.800331 | −0.0357919 | ||||||||
\(501\) | 6.02450 | 0.269155 | ||||||||
\(502\) | −8.10445 | −0.361719 | ||||||||
\(503\) | 25.7838 | 1.14964 | 0.574822 | − | 0.818279i | \(-0.305071\pi\) | ||||
0.574822 | + | 0.818279i | \(0.305071\pi\) | |||||||
\(504\) | 2.16248 | 0.0963245 | ||||||||
\(505\) | −18.9218 | −0.842008 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.21546 | 0.409273 | ||||||||
\(508\) | −8.69761 | −0.385894 | ||||||||
\(509\) | −28.2301 | −1.25128 | −0.625639 | − | 0.780113i | \(-0.715162\pi\) | ||||
−0.625639 | + | 0.780113i | \(0.715162\pi\) | |||||||
\(510\) | −8.52195 | −0.377358 | ||||||||
\(511\) | 3.52824 | 0.156080 | ||||||||
\(512\) | −18.1902 | −0.803900 | ||||||||
\(513\) | −1.19967 | −0.0529667 | ||||||||
\(514\) | −20.4810 | −0.903380 | ||||||||
\(515\) | −18.0964 | −0.797422 | ||||||||
\(516\) | −5.86556 | −0.258217 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6.51573 | −0.286285 | ||||||||
\(519\) | 4.18674 | 0.183778 | ||||||||
\(520\) | 14.4567 | 0.633966 | ||||||||
\(521\) | 11.6955 | 0.512388 | 0.256194 | − | 0.966625i | \(-0.417531\pi\) | ||||
0.256194 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(522\) | 1.45390 | 0.0636354 | ||||||||
\(523\) | −19.6871 | −0.860857 | −0.430429 | − | 0.902625i | \(-0.641638\pi\) | ||||
−0.430429 | + | 0.902625i | \(0.641638\pi\) | |||||||
\(524\) | 9.37137 | 0.409390 | ||||||||
\(525\) | −0.705037 | −0.0307703 | ||||||||
\(526\) | 4.37044 | 0.190560 | ||||||||
\(527\) | 59.7642 | 2.60337 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.5159 | 1.06591 | ||||||||
\(530\) | 7.47354 | 0.324630 | ||||||||
\(531\) | −3.54011 | −0.153628 | ||||||||
\(532\) | −0.676929 | −0.0293486 | ||||||||
\(533\) | 1.09774 | 0.0475484 | ||||||||
\(534\) | −3.66619 | −0.158652 | ||||||||
\(535\) | −6.11945 | −0.264567 | ||||||||
\(536\) | 6.25815 | 0.270311 | ||||||||
\(537\) | 4.85166 | 0.209364 | ||||||||
\(538\) | −13.9266 | −0.600420 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.800331 | −0.0344408 | ||||||||
\(541\) | −5.45092 | −0.234353 | −0.117177 | − | 0.993111i | \(-0.537384\pi\) | ||||
−0.117177 | + | 0.993111i | \(0.537384\pi\) | |||||||
\(542\) | 26.0987 | 1.12103 | ||||||||
\(543\) | −23.0877 | −0.990789 | ||||||||
\(544\) | −32.7401 | −1.40372 | ||||||||
\(545\) | 9.03128 | 0.386857 | ||||||||
\(546\) | 3.63974 | 0.155766 | ||||||||
\(547\) | 12.7892 | 0.546827 | 0.273414 | − | 0.961897i | \(-0.411847\pi\) | ||||
0.273414 | + | 0.961897i | \(0.411847\pi\) | |||||||
\(548\) | −16.3509 | −0.698477 | ||||||||
\(549\) | −10.8719 | −0.463999 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.59245 | −0.0678405 | ||||||||
\(552\) | 21.1427 | 0.899891 | ||||||||
\(553\) | −1.60767 | −0.0683653 | ||||||||
\(554\) | 8.11889 | 0.344939 | ||||||||
\(555\) | 8.43763 | 0.358157 | ||||||||
\(556\) | 6.53951 | 0.277337 | ||||||||
\(557\) | −0.354468 | −0.0150193 | −0.00750964 | − | 0.999972i | \(-0.502390\pi\) | ||||
−0.00750964 | + | 0.999972i | \(0.502390\pi\) | |||||||
\(558\) | −8.41324 | −0.356161 | ||||||||
\(559\) | −34.5436 | −1.46104 | ||||||||
\(560\) | 1.24002 | 0.0524006 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.8528 | −1.34363 | ||||||||
\(563\) | 35.0818 | 1.47852 | 0.739261 | − | 0.673419i | \(-0.235175\pi\) | ||||
0.739261 | + | 0.673419i | \(0.235175\pi\) | |||||||
\(564\) | −6.66058 | −0.280461 | ||||||||
\(565\) | 3.91684 | 0.164783 | ||||||||
\(566\) | −23.7382 | −0.997791 | ||||||||
\(567\) | −0.705037 | −0.0296088 | ||||||||
\(568\) | −2.05663 | −0.0862943 | ||||||||
\(569\) | −16.3179 | −0.684084 | −0.342042 | − | 0.939685i | \(-0.611119\pi\) | ||||
−0.342042 | + | 0.939685i | \(0.611119\pi\) | |||||||
\(570\) | −1.31399 | −0.0550370 | ||||||||
\(571\) | −14.4160 | −0.603291 | −0.301645 | − | 0.953420i | \(-0.597536\pi\) | ||||
−0.301645 | + | 0.953420i | \(0.597536\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.22571 | 0.260083 | ||||||||
\(574\) | 0.179852 | 0.00750686 | ||||||||
\(575\) | −6.89318 | −0.287465 | ||||||||
\(576\) | 8.12657 | 0.338607 | ||||||||
\(577\) | 8.90863 | 0.370871 | 0.185435 | − | 0.982656i | \(-0.440630\pi\) | ||||
0.185435 | + | 0.982656i | \(0.440630\pi\) | |||||||
\(578\) | 47.6852 | 1.98344 | ||||||||
\(579\) | 19.0868 | 0.793221 | ||||||||
\(580\) | −1.06236 | −0.0441122 | ||||||||
\(581\) | 1.48762 | 0.0617168 | ||||||||
\(582\) | 3.63887 | 0.150836 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 15.3492 | 0.635155 | ||||||||
\(585\) | −4.71333 | −0.194872 | ||||||||
\(586\) | −9.21383 | −0.380620 | ||||||||
\(587\) | −13.8014 | −0.569644 | −0.284822 | − | 0.958580i | \(-0.591934\pi\) | ||||
−0.284822 | + | 0.958580i | \(0.591934\pi\) | |||||||
\(588\) | 5.20449 | 0.214630 | ||||||||
\(589\) | 9.21497 | 0.379696 | ||||||||
\(590\) | −3.87746 | −0.159633 | ||||||||
\(591\) | 6.80056 | 0.279738 | ||||||||
\(592\) | −14.8402 | −0.609927 | ||||||||
\(593\) | −16.4676 | −0.676242 | −0.338121 | − | 0.941103i | \(-0.609791\pi\) | ||||
−0.338121 | + | 0.941103i | \(0.609791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.48555 | 0.224886 | ||||||||
\(596\) | 7.68492 | 0.314787 | ||||||||
\(597\) | 21.2972 | 0.871638 | ||||||||
\(598\) | 35.5859 | 1.45522 | ||||||||
\(599\) | 37.8599 | 1.54692 | 0.773458 | − | 0.633848i | \(-0.218525\pi\) | ||||
0.773458 | + | 0.633848i | \(0.218525\pi\) | |||||||
\(600\) | −3.06719 | −0.125217 | ||||||||
\(601\) | 1.56441 | 0.0638135 | 0.0319067 | − | 0.999491i | \(-0.489842\pi\) | ||||
0.0319067 | + | 0.999491i | \(0.489842\pi\) | |||||||
\(602\) | −5.65956 | −0.230666 | ||||||||
\(603\) | −2.04036 | −0.0830897 | ||||||||
\(604\) | −5.52850 | −0.224951 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.7249 | −0.841892 | ||||||||
\(607\) | 18.8523 | 0.765191 | 0.382595 | − | 0.923916i | \(-0.375030\pi\) | ||||
0.382595 | + | 0.923916i | \(0.375030\pi\) | |||||||
\(608\) | −5.04816 | −0.204730 | ||||||||
\(609\) | −0.935870 | −0.0379234 | ||||||||
\(610\) | −11.9079 | −0.482136 | ||||||||
\(611\) | −39.2256 | −1.58690 | ||||||||
\(612\) | 6.22699 | 0.251711 | ||||||||
\(613\) | 32.6700 | 1.31953 | 0.659765 | − | 0.751472i | \(-0.270656\pi\) | ||||
0.659765 | + | 0.751472i | \(0.270656\pi\) | |||||||
\(614\) | 26.0057 | 1.04950 | ||||||||
\(615\) | −0.232901 | −0.00939148 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6559 | −1.35493 | −0.677467 | − | 0.735553i | \(-0.736922\pi\) | ||||
−0.677467 | + | 0.735553i | \(0.736922\pi\) | |||||||
\(618\) | −19.8209 | −0.797312 | ||||||||
\(619\) | −8.94001 | −0.359329 | −0.179665 | − | 0.983728i | \(-0.557501\pi\) | ||||
−0.179665 | + | 0.983728i | \(0.557501\pi\) | |||||||
\(620\) | 6.14755 | 0.246892 | ||||||||
\(621\) | −6.89318 | −0.276614 | ||||||||
\(622\) | 25.2433 | 1.01216 | ||||||||
\(623\) | 2.35992 | 0.0945480 | ||||||||
\(624\) | 8.28984 | 0.331859 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −19.0185 | −0.760131 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.08528 | −0.362542 | ||||||||
\(629\) | −65.6491 | −2.61760 | ||||||||
\(630\) | −0.772223 | −0.0307661 | ||||||||
\(631\) | −19.2577 | −0.766638 | −0.383319 | − | 0.923616i | \(-0.625219\pi\) | ||||
−0.383319 | + | 0.923616i | \(0.625219\pi\) | |||||||
\(632\) | −6.99401 | −0.278207 | ||||||||
\(633\) | −8.89073 | −0.353375 | ||||||||
\(634\) | −6.73710 | −0.267565 | ||||||||
\(635\) | 10.8675 | 0.431264 | ||||||||
\(636\) | −5.46091 | −0.216539 | ||||||||
\(637\) | 30.6504 | 1.21441 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.670527 | 0.0265256 | ||||||||
\(640\) | 0.485063 | 0.0191738 | ||||||||
\(641\) | −14.8928 | −0.588229 | −0.294114 | − | 0.955770i | \(-0.595025\pi\) | ||||
−0.294114 | + | 0.955770i | \(0.595025\pi\) | |||||||
\(642\) | −6.70259 | −0.264530 | ||||||||
\(643\) | 35.3193 | 1.39286 | 0.696429 | − | 0.717626i | \(-0.254771\pi\) | ||||
0.696429 | + | 0.717626i | \(0.254771\pi\) | |||||||
\(644\) | −3.88957 | −0.153270 | ||||||||
\(645\) | 7.32892 | 0.288576 | ||||||||
\(646\) | 10.2235 | 0.402239 | ||||||||
\(647\) | 31.1428 | 1.22435 | 0.612175 | − | 0.790722i | \(-0.290295\pi\) | ||||
0.612175 | + | 0.790722i | \(0.290295\pi\) | |||||||
\(648\) | −3.06719 | −0.120490 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.16248 | −0.202489 | ||||||||
\(651\) | 5.41558 | 0.212253 | ||||||||
\(652\) | 1.43462 | 0.0561839 | ||||||||
\(653\) | 5.05494 | 0.197815 | 0.0989075 | − | 0.995097i | \(-0.468465\pi\) | ||||
0.0989075 | + | 0.995097i | \(0.468465\pi\) | |||||||
\(654\) | 9.89190 | 0.386804 | ||||||||
\(655\) | −11.7094 | −0.457523 | ||||||||
\(656\) | 0.409628 | 0.0159933 | ||||||||
\(657\) | −5.00433 | −0.195238 | ||||||||
\(658\) | −6.42666 | −0.250537 | ||||||||
\(659\) | −14.4486 | −0.562837 | −0.281419 | − | 0.959585i | \(-0.590805\pi\) | ||||
−0.281419 | + | 0.959585i | \(0.590805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.8696 | 0.578361 | 0.289181 | − | 0.957275i | \(-0.406617\pi\) | ||||
0.289181 | + | 0.957275i | \(0.406617\pi\) | |||||||
\(662\) | 21.2696 | 0.826667 | ||||||||
\(663\) | 36.6721 | 1.42423 | ||||||||
\(664\) | 6.47172 | 0.251152 | ||||||||
\(665\) | 0.845811 | 0.0327991 | ||||||||
\(666\) | 9.24168 | 0.358108 | ||||||||
\(667\) | −9.15004 | −0.354291 | ||||||||
\(668\) | −4.82159 | −0.186553 | ||||||||
\(669\) | 5.41720 | 0.209441 | ||||||||
\(670\) | −2.23479 | −0.0863375 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.96677 | −0.114446 | ||||||||
\(673\) | −41.6153 | −1.60415 | −0.802075 | − | 0.597223i | \(-0.796271\pi\) | ||||
−0.802075 | + | 0.597223i | \(0.796271\pi\) | |||||||
\(674\) | 34.7064 | 1.33684 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −7.37542 | −0.283670 | ||||||||
\(677\) | 44.2366 | 1.70015 | 0.850076 | − | 0.526660i | \(-0.176556\pi\) | ||||
0.850076 | + | 0.526660i | \(0.176556\pi\) | |||||||
\(678\) | 4.29009 | 0.164760 | ||||||||
\(679\) | −2.34233 | −0.0898904 | ||||||||
\(680\) | 23.8643 | 0.915153 | ||||||||
\(681\) | −8.43842 | −0.323361 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.5318 | 0.938683 | 0.469342 | − | 0.883017i | \(-0.344491\pi\) | ||||
0.469342 | + | 0.883017i | \(0.344491\pi\) | |||||||
\(684\) | 0.960132 | 0.0367116 | ||||||||
\(685\) | 20.4302 | 0.780598 | ||||||||
\(686\) | 10.4273 | 0.398115 | ||||||||
\(687\) | −11.2053 | −0.427508 | ||||||||
\(688\) | −12.8902 | −0.491433 | ||||||||
\(689\) | −32.1605 | −1.22522 | ||||||||
\(690\) | −7.55006 | −0.287426 | ||||||||
\(691\) | 23.7670 | 0.904139 | 0.452069 | − | 0.891983i | \(-0.350686\pi\) | ||||
0.452069 | + | 0.891983i | \(0.350686\pi\) | |||||||
\(692\) | −3.35078 | −0.127378 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.6063 | −1.16180 | ||||||||
\(695\) | −8.17100 | −0.309944 | ||||||||
\(696\) | −4.07140 | −0.154326 | ||||||||
\(697\) | 1.81209 | 0.0686378 | ||||||||
\(698\) | −0.748449 | −0.0283292 | ||||||||
\(699\) | 5.83979 | 0.220881 | ||||||||
\(700\) | 0.564263 | 0.0213271 | ||||||||
\(701\) | −32.6939 | −1.23483 | −0.617416 | − | 0.786637i | \(-0.711820\pi\) | ||||
−0.617416 | + | 0.786637i | \(0.711820\pi\) | |||||||
\(702\) | −5.16248 | −0.194845 | ||||||||
\(703\) | −10.1224 | −0.381772 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.32228 | 0.313435 | ||||||||
\(706\) | 1.70756 | 0.0642648 | ||||||||
\(707\) | 13.3406 | 0.501723 | ||||||||
\(708\) | 2.83326 | 0.106480 | ||||||||
\(709\) | 23.8264 | 0.894821 | 0.447410 | − | 0.894329i | \(-0.352346\pi\) | ||||
0.447410 | + | 0.894329i | \(0.352346\pi\) | |||||||
\(710\) | 0.734424 | 0.0275624 | ||||||||
\(711\) | 2.28027 | 0.0855168 | ||||||||
\(712\) | 10.2666 | 0.384755 | ||||||||
\(713\) | 52.9483 | 1.98293 | ||||||||
\(714\) | 6.00829 | 0.224855 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.88293 | −0.145112 | ||||||||
\(717\) | −16.5261 | −0.617180 | ||||||||
\(718\) | 17.3499 | 0.647491 | ||||||||
\(719\) | −2.84680 | −0.106168 | −0.0530838 | − | 0.998590i | \(-0.516905\pi\) | ||||
−0.0530838 | + | 0.998590i | \(0.516905\pi\) | |||||||
\(720\) | −1.75881 | −0.0655469 | ||||||||
\(721\) | 12.7586 | 0.475156 | ||||||||
\(722\) | −19.2342 | −0.715824 | ||||||||
\(723\) | −3.29180 | −0.122423 | ||||||||
\(724\) | 18.4778 | 0.686723 | ||||||||
\(725\) | 1.32741 | 0.0492986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.5192 | −0.501399 | −0.250700 | − | 0.968065i | \(-0.580661\pi\) | ||||
−0.250700 | + | 0.968065i | \(0.580661\pi\) | |||||||
\(728\) | −10.1925 | −0.377758 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.48122 | −0.202869 | ||||||||
\(731\) | −57.0227 | −2.10906 | ||||||||
\(732\) | 8.70108 | 0.321601 | ||||||||
\(733\) | 32.8352 | 1.21280 | 0.606399 | − | 0.795161i | \(-0.292614\pi\) | ||||
0.606399 | + | 0.795161i | \(0.292614\pi\) | |||||||
\(734\) | 17.2357 | 0.636181 | ||||||||
\(735\) | −6.50292 | −0.239864 | ||||||||
\(736\) | −29.0062 | −1.06918 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.255095 | −0.00939018 | ||||||||
\(739\) | 50.8927 | 1.87212 | 0.936058 | − | 0.351844i | \(-0.114445\pi\) | ||||
0.936058 | + | 0.351844i | \(0.114445\pi\) | |||||||
\(740\) | −6.75289 | −0.248241 | ||||||||
\(741\) | 5.65443 | 0.207721 | ||||||||
\(742\) | −5.26912 | −0.193435 | ||||||||
\(743\) | −15.4855 | −0.568107 | −0.284054 | − | 0.958808i | \(-0.591679\pi\) | ||||
−0.284054 | + | 0.958808i | \(0.591679\pi\) | |||||||
\(744\) | 23.5599 | 0.863746 | ||||||||
\(745\) | −9.60217 | −0.351796 | ||||||||
\(746\) | −5.77990 | −0.211617 | ||||||||
\(747\) | −2.10999 | −0.0772004 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.31444 | 0.157646 | ||||||||
\(750\) | 1.09529 | 0.0399945 | ||||||||
\(751\) | 11.0575 | 0.403494 | 0.201747 | − | 0.979438i | \(-0.435338\pi\) | ||||
0.201747 | + | 0.979438i | \(0.435338\pi\) | |||||||
\(752\) | −14.6373 | −0.533767 | ||||||||
\(753\) | −7.39934 | −0.269647 | ||||||||
\(754\) | −6.85270 | −0.249561 | ||||||||
\(755\) | 6.90776 | 0.251399 | ||||||||
\(756\) | 0.564263 | 0.0205221 | ||||||||
\(757\) | 9.00282 | 0.327213 | 0.163607 | − | 0.986526i | \(-0.447687\pi\) | ||||
0.163607 | + | 0.986526i | \(0.447687\pi\) | |||||||
\(758\) | 36.7025 | 1.33309 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.67961 | 0.133473 | ||||||||
\(761\) | 8.29644 | 0.300746 | 0.150373 | − | 0.988629i | \(-0.451953\pi\) | ||||
0.150373 | + | 0.988629i | \(0.451953\pi\) | |||||||
\(762\) | 11.9031 | 0.431205 | ||||||||
\(763\) | −6.36738 | −0.230515 | ||||||||
\(764\) | −4.98263 | −0.180265 | ||||||||
\(765\) | −7.78051 | −0.281305 | ||||||||
\(766\) | −22.1603 | −0.800684 | ||||||||
\(767\) | 16.6857 | 0.602486 | ||||||||
\(768\) | −15.7219 | −0.567313 | ||||||||
\(769\) | 2.89088 | 0.104248 | 0.0521239 | − | 0.998641i | \(-0.483401\pi\) | ||||
0.0521239 | + | 0.998641i | \(0.483401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.6991 | −0.673432 | ||||||||
\(772\) | −15.2758 | −0.549787 | ||||||||
\(773\) | −27.8477 | −1.00161 | −0.500807 | − | 0.865559i | \(-0.666963\pi\) | ||||
−0.500807 | + | 0.865559i | \(0.666963\pi\) | |||||||
\(774\) | 8.02732 | 0.288536 | ||||||||
\(775\) | −7.68126 | −0.275919 | ||||||||
\(776\) | −10.1901 | −0.365802 | ||||||||
\(777\) | −5.94884 | −0.213413 | ||||||||
\(778\) | −30.2004 | −1.08274 | ||||||||
\(779\) | 0.279404 | 0.0100107 | ||||||||
\(780\) | 3.77222 | 0.135067 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 58.7433 | 2.10066 | ||||||||
\(783\) | 1.32741 | 0.0474376 | ||||||||
\(784\) | 11.4374 | 0.408478 | ||||||||
\(785\) | 11.3519 | 0.405167 | ||||||||
\(786\) | −12.8252 | −0.457460 | ||||||||
\(787\) | −24.8356 | −0.885292 | −0.442646 | − | 0.896696i | \(-0.645960\pi\) | ||||
−0.442646 | + | 0.896696i | \(0.645960\pi\) | |||||||
\(788\) | −5.44270 | −0.193888 | ||||||||
\(789\) | 3.99020 | 0.142055 | ||||||||
\(790\) | 2.49757 | 0.0888594 | ||||||||
\(791\) | −2.76152 | −0.0981883 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.2426 | 1.81968 | ||||||||
\(794\) | 12.8808 | 0.457121 | ||||||||
\(795\) | 6.82332 | 0.241998 | ||||||||
\(796\) | −17.0448 | −0.604138 | ||||||||
\(797\) | −2.81107 | −0.0995731 | −0.0497866 | − | 0.998760i | \(-0.515854\pi\) | ||||
−0.0497866 | + | 0.998760i | \(0.515854\pi\) | |||||||
\(798\) | 0.926412 | 0.0327946 | ||||||||
\(799\) | −64.7516 | −2.29075 | ||||||||
\(800\) | 4.20796 | 0.148774 | ||||||||
\(801\) | −3.34722 | −0.118268 | ||||||||
\(802\) | −8.46012 | −0.298737 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.63296 | 0.0575901 | ||||||||
\(805\) | 4.85995 | 0.171291 | ||||||||
\(806\) | 39.6544 | 1.39677 | ||||||||
\(807\) | −12.7150 | −0.447589 | ||||||||
\(808\) | 58.0366 | 2.04172 | ||||||||
\(809\) | 11.6766 | 0.410526 | 0.205263 | − | 0.978707i | \(-0.434195\pi\) | ||||
0.205263 | + | 0.978707i | \(0.434195\pi\) | |||||||
\(810\) | 1.09529 | 0.0384847 | ||||||||
\(811\) | 24.0690 | 0.845175 | 0.422588 | − | 0.906322i | \(-0.361122\pi\) | ||||
0.422588 | + | 0.906322i | \(0.361122\pi\) | |||||||
\(812\) | 0.749006 | 0.0262849 | ||||||||
\(813\) | 23.8280 | 0.835684 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.79253 | −0.0627895 | ||||||||
\(816\) | 13.6844 | 0.479051 | ||||||||
\(817\) | −8.79227 | −0.307603 | ||||||||
\(818\) | 18.3362 | 0.641110 | ||||||||
\(819\) | 3.32307 | 0.116118 | ||||||||
\(820\) | 0.186398 | 0.00650930 | ||||||||
\(821\) | 4.85561 | 0.169462 | 0.0847310 | − | 0.996404i | \(-0.472997\pi\) | ||||
0.0847310 | + | 0.996404i | \(0.472997\pi\) | |||||||
\(822\) | 22.3771 | 0.780490 | ||||||||
\(823\) | 26.0601 | 0.908397 | 0.454198 | − | 0.890901i | \(-0.349926\pi\) | ||||
0.454198 | + | 0.890901i | \(0.349926\pi\) | |||||||
\(824\) | 55.5050 | 1.93361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.73376 | 0.0951195 | ||||||||
\(827\) | −16.2843 | −0.566260 | −0.283130 | − | 0.959081i | \(-0.591373\pi\) | ||||
−0.283130 | + | 0.959081i | \(0.591373\pi\) | |||||||
\(828\) | 5.51683 | 0.191723 | ||||||||
\(829\) | −10.0141 | −0.347805 | −0.173903 | − | 0.984763i | \(-0.555638\pi\) | ||||
−0.173903 | + | 0.984763i | \(0.555638\pi\) | |||||||
\(830\) | −2.31106 | −0.0802179 | ||||||||
\(831\) | 7.41252 | 0.257137 | ||||||||
\(832\) | −38.3032 | −1.32792 | ||||||||
\(833\) | 50.5961 | 1.75305 | ||||||||
\(834\) | −8.94965 | −0.309901 | ||||||||
\(835\) | 6.02450 | 0.208486 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.68126 | −0.265503 | ||||||||
\(838\) | −41.7272 | −1.44144 | ||||||||
\(839\) | 11.7532 | 0.405766 | 0.202883 | − | 0.979203i | \(-0.434969\pi\) | ||||
0.202883 | + | 0.979203i | \(0.434969\pi\) | |||||||
\(840\) | 2.16248 | 0.0746126 | ||||||||
\(841\) | −27.2380 | −0.939241 | ||||||||
\(842\) | −24.8230 | −0.855458 | ||||||||
\(843\) | −29.0815 | −1.00162 | ||||||||
\(844\) | 7.11553 | 0.244927 | ||||||||
\(845\) | 9.21546 | 0.317021 | ||||||||
\(846\) | 9.11534 | 0.313392 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.0009 | −0.412113 | ||||||||
\(849\) | −21.6729 | −0.743812 | ||||||||
\(850\) | −8.52195 | −0.292300 | ||||||||
\(851\) | −58.1621 | −1.99377 | ||||||||
\(852\) | −0.536643 | −0.0183851 | ||||||||
\(853\) | −45.6353 | −1.56252 | −0.781262 | − | 0.624203i | \(-0.785424\pi\) | ||||
−0.781262 | + | 0.624203i | \(0.785424\pi\) | |||||||
\(854\) | 8.39549 | 0.287288 | ||||||||
\(855\) | −1.19967 | −0.0410278 | ||||||||
\(856\) | 18.7695 | 0.641527 | ||||||||
\(857\) | −8.41558 | −0.287471 | −0.143735 | − | 0.989616i | \(-0.545911\pi\) | ||||
−0.143735 | + | 0.989616i | \(0.545911\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.3009 | −1.54565 | −0.772823 | − | 0.634622i | \(-0.781156\pi\) | ||||
−0.772823 | + | 0.634622i | \(0.781156\pi\) | |||||||
\(860\) | −5.86556 | −0.200014 | ||||||||
\(861\) | 0.164204 | 0.00559606 | ||||||||
\(862\) | −37.2144 | −1.26753 | ||||||||
\(863\) | −12.0590 | −0.410493 | −0.205247 | − | 0.978710i | \(-0.565800\pi\) | ||||
−0.205247 | + | 0.978710i | \(0.565800\pi\) | |||||||
\(864\) | 4.20796 | 0.143158 | ||||||||
\(865\) | 4.18674 | 0.142354 | ||||||||
\(866\) | −40.1702 | −1.36504 | ||||||||
\(867\) | 43.5364 | 1.47857 | ||||||||
\(868\) | −4.33425 | −0.147114 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.45390 | 0.0492918 | ||||||||
\(871\) | 9.61687 | 0.325855 | ||||||||
\(872\) | −27.7006 | −0.938061 | ||||||||
\(873\) | 3.32228 | 0.112442 | ||||||||
\(874\) | 9.05757 | 0.306377 | ||||||||
\(875\) | −0.705037 | −0.0238346 | ||||||||
\(876\) | 4.00512 | 0.135321 | ||||||||
\(877\) | −21.1439 | −0.713979 | −0.356989 | − | 0.934108i | \(-0.616197\pi\) | ||||
−0.356989 | + | 0.934108i | \(0.616197\pi\) | |||||||
\(878\) | 1.15019 | 0.0388169 | ||||||||
\(879\) | −8.41220 | −0.283736 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.1669 | −0.443605 | −0.221803 | − | 0.975092i | \(-0.571194\pi\) | ||||
−0.221803 | + | 0.975092i | \(0.571194\pi\) | |||||||
\(882\) | −7.12261 | −0.239831 | ||||||||
\(883\) | −34.7697 | −1.17009 | −0.585047 | − | 0.810999i | \(-0.698924\pi\) | ||||
−0.585047 | + | 0.810999i | \(0.698924\pi\) | |||||||
\(884\) | −29.3498 | −0.987142 | ||||||||
\(885\) | −3.54011 | −0.119000 | ||||||||
\(886\) | −33.4290 | −1.12307 | ||||||||
\(887\) | −20.9565 | −0.703651 | −0.351826 | − | 0.936066i | \(-0.614439\pi\) | ||||
−0.351826 | + | 0.936066i | \(0.614439\pi\) | |||||||
\(888\) | −25.8798 | −0.868468 | ||||||||
\(889\) | −7.66200 | −0.256975 | ||||||||
\(890\) | −3.66619 | −0.122891 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.33555 | −0.145165 | ||||||||
\(893\) | −9.98398 | −0.334101 | ||||||||
\(894\) | −10.5172 | −0.351748 | ||||||||
\(895\) | 4.85166 | 0.162173 | ||||||||
\(896\) | −0.341987 | −0.0114250 | ||||||||
\(897\) | 32.4898 | 1.08480 | ||||||||
\(898\) | −40.0543 | −1.33663 | ||||||||
\(899\) | −10.1961 | −0.340061 | ||||||||
\(900\) | −0.800331 | −0.0266777 | ||||||||
\(901\) | −53.0889 | −1.76865 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.16716 | −0.171952 | ||||||||
\(904\) | −12.0137 | −0.399569 | ||||||||
\(905\) | −23.0877 | −0.767462 | ||||||||
\(906\) | 7.56603 | 0.251365 | ||||||||
\(907\) | 26.2408 | 0.871312 | 0.435656 | − | 0.900113i | \(-0.356516\pi\) | ||||
0.435656 | + | 0.900113i | \(0.356516\pi\) | |||||||
\(908\) | 6.75353 | 0.224124 | ||||||||
\(909\) | −18.9218 | −0.627596 | ||||||||
\(910\) | 3.63974 | 0.120656 | ||||||||
\(911\) | −39.6599 | −1.31399 | −0.656995 | − | 0.753895i | \(-0.728173\pi\) | ||||
−0.656995 | + | 0.753895i | \(0.728173\pi\) | |||||||
\(912\) | 2.10999 | 0.0698687 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.61128 | −0.0863734 | ||||||||
\(915\) | −10.8719 | −0.359412 | ||||||||
\(916\) | 8.96793 | 0.296309 | ||||||||
\(917\) | 8.25554 | 0.272622 | ||||||||
\(918\) | −8.52195 | −0.281266 | ||||||||
\(919\) | 14.9758 | 0.494005 | 0.247003 | − | 0.969015i | \(-0.420554\pi\) | ||||
0.247003 | + | 0.969015i | \(0.420554\pi\) | |||||||
\(920\) | 21.1427 | 0.697053 | ||||||||
\(921\) | 23.7431 | 0.782361 | ||||||||
\(922\) | 31.3213 | 1.03151 | ||||||||
\(923\) | −3.16041 | −0.104026 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.43763 | 0.277427 | ||||||||
\(926\) | −33.4947 | −1.10071 | ||||||||
\(927\) | −18.0964 | −0.594364 | ||||||||
\(928\) | 5.58567 | 0.183359 | ||||||||
\(929\) | −49.6461 | −1.62884 | −0.814418 | − | 0.580279i | \(-0.802943\pi\) | ||||
−0.814418 | + | 0.580279i | \(0.802943\pi\) | |||||||
\(930\) | −8.41324 | −0.275881 | ||||||||
\(931\) | 7.80135 | 0.255679 | ||||||||
\(932\) | −4.67376 | −0.153094 | ||||||||
\(933\) | 23.0471 | 0.754527 | ||||||||
\(934\) | −4.09880 | −0.134117 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.4567 | 0.472530 | ||||||||
\(937\) | −54.2914 | −1.77362 | −0.886811 | − | 0.462132i | \(-0.847085\pi\) | ||||
−0.886811 | + | 0.462132i | \(0.847085\pi\) | |||||||
\(938\) | 1.57561 | 0.0514455 | ||||||||
\(939\) | −17.3638 | −0.566646 | ||||||||
\(940\) | −6.66058 | −0.217244 | ||||||||
\(941\) | 6.66066 | 0.217131 | 0.108566 | − | 0.994089i | \(-0.465374\pi\) | ||||
0.108566 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(942\) | 12.4337 | 0.405111 | ||||||||
\(943\) | 1.60543 | 0.0522800 | ||||||||
\(944\) | 6.22638 | 0.202651 | ||||||||
\(945\) | −0.705037 | −0.0229349 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.6250 | −1.38513 | −0.692563 | − | 0.721358i | \(-0.743518\pi\) | ||||
−0.692563 | + | 0.721358i | \(0.743518\pi\) | |||||||
\(948\) | −1.82497 | −0.0592723 | ||||||||
\(949\) | 23.5871 | 0.765669 | ||||||||
\(950\) | −1.31399 | −0.0426315 | ||||||||
\(951\) | −6.15095 | −0.199458 | ||||||||
\(952\) | −16.8252 | −0.545308 | ||||||||
\(953\) | −16.7539 | −0.542713 | −0.271357 | − | 0.962479i | \(-0.587472\pi\) | ||||
−0.271357 | + | 0.962479i | \(0.587472\pi\) | |||||||
\(954\) | 7.47354 | 0.241965 | ||||||||
\(955\) | 6.22571 | 0.201459 | ||||||||
\(956\) | 13.2264 | 0.427772 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.03500 | −0.0334393 | ||||||||
\(959\) | −14.4040 | −0.465131 | ||||||||
\(960\) | 8.12657 | 0.262284 | ||||||||
\(961\) | 28.0018 | 0.903284 | ||||||||
\(962\) | −43.5591 | −1.40440 | ||||||||
\(963\) | −6.11945 | −0.197196 | ||||||||
\(964\) | 2.63453 | 0.0848524 | ||||||||
\(965\) | 19.0868 | 0.614427 | ||||||||
\(966\) | 5.32307 | 0.171267 | ||||||||
\(967\) | −50.1233 | −1.61186 | −0.805928 | − | 0.592014i | \(-0.798333\pi\) | ||||
−0.805928 | + | 0.592014i | \(0.798333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.33404 | 0.299853 | ||||||||
\(970\) | 3.63887 | 0.116837 | ||||||||
\(971\) | 40.1230 | 1.28761 | 0.643804 | − | 0.765190i | \(-0.277355\pi\) | ||||
0.643804 | + | 0.765190i | \(0.277355\pi\) | |||||||
\(972\) | −0.800331 | −0.0256706 | ||||||||
\(973\) | 5.76086 | 0.184685 | ||||||||
\(974\) | −14.6631 | −0.469835 | ||||||||
\(975\) | −4.71333 | −0.150947 | ||||||||
\(976\) | 19.1215 | 0.612064 | ||||||||
\(977\) | −24.1682 | −0.773209 | −0.386604 | − | 0.922246i | \(-0.626352\pi\) | ||||
−0.386604 | + | 0.922246i | \(0.626352\pi\) | |||||||
\(978\) | −1.96335 | −0.0627809 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.20449 | 0.166251 | ||||||||
\(981\) | 9.03128 | 0.288346 | ||||||||
\(982\) | −3.05464 | −0.0974774 | ||||||||
\(983\) | 23.3021 | 0.743220 | 0.371610 | − | 0.928389i | \(-0.378806\pi\) | ||||
0.371610 | + | 0.928389i | \(0.378806\pi\) | |||||||
\(984\) | 0.714351 | 0.0227727 | ||||||||
\(985\) | 6.80056 | 0.216684 | ||||||||
\(986\) | −11.3121 | −0.360250 | ||||||||
\(987\) | −5.86752 | −0.186765 | ||||||||
\(988\) | −4.52542 | −0.143973 | ||||||||
\(989\) | −50.5195 | −1.60643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.0689 | −1.71756 | −0.858778 | − | 0.512348i | \(-0.828776\pi\) | ||||
−0.858778 | + | 0.512348i | \(0.828776\pi\) | |||||||
\(992\) | −32.3224 | −1.02624 | ||||||||
\(993\) | 19.4191 | 0.616246 | ||||||||
\(994\) | −0.517796 | −0.0164235 | ||||||||
\(995\) | 21.2972 | 0.675168 | ||||||||
\(996\) | 1.68869 | 0.0535081 | ||||||||
\(997\) | 50.7109 | 1.60603 | 0.803015 | − | 0.595959i | \(-0.203228\pi\) | ||||
0.803015 | + | 0.595959i | \(0.203228\pi\) | |||||||
\(998\) | 19.4733 | 0.616416 | ||||||||
\(999\) | 8.43763 | 0.266955 |
(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 | 1815.2.a.p.1.4 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bt.1.1 | 4 | |||
5.4 | even | 2 | 9075.2.a.di.1.1 | 4 | |||
11.3 | even | 5 | 165.2.m.d.31.2 | yes | 8 | ||
11.4 | even | 5 | 165.2.m.d.16.2 | ✓ | 8 | ||
11.10 | odd | 2 | 1815.2.a.w.1.1 | 4 | |||
33.14 | odd | 10 | 495.2.n.a.361.1 | 8 | |||
33.26 | odd | 10 | 495.2.n.a.181.1 | 8 | |||
33.32 | even | 2 | 5445.2.a.bf.1.4 | 4 | |||
55.3 | odd | 20 | 825.2.bx.f.724.2 | 16 | |||
55.4 | even | 10 | 825.2.n.g.676.1 | 8 | |||
55.14 | even | 10 | 825.2.n.g.526.1 | 8 | |||
55.37 | odd | 20 | 825.2.bx.f.49.2 | 16 | |||
55.47 | odd | 20 | 825.2.bx.f.724.3 | 16 | |||
55.48 | odd | 20 | 825.2.bx.f.49.3 | 16 | |||
55.54 | odd | 2 | 9075.2.a.cm.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.16.2 | ✓ | 8 | 11.4 | even | 5 | ||
165.2.m.d.31.2 | yes | 8 | 11.3 | even | 5 | ||
495.2.n.a.181.1 | 8 | 33.26 | odd | 10 | |||
495.2.n.a.361.1 | 8 | 33.14 | odd | 10 | |||
825.2.n.g.526.1 | 8 | 55.14 | even | 10 | |||
825.2.n.g.676.1 | 8 | 55.4 | even | 10 | |||
825.2.bx.f.49.2 | 16 | 55.37 | odd | 20 | |||
825.2.bx.f.49.3 | 16 | 55.48 | odd | 20 | |||
825.2.bx.f.724.2 | 16 | 55.3 | odd | 20 | |||
825.2.bx.f.724.3 | 16 | 55.47 | odd | 20 | |||
1815.2.a.p.1.4 | 4 | 1.1 | even | 1 | trivial | ||
1815.2.a.w.1.1 | 4 | 11.10 | odd | 2 | |||
5445.2.a.bf.1.4 | 4 | 33.32 | even | 2 | |||
5445.2.a.bt.1.1 | 4 | 3.2 | odd | 2 | |||
9075.2.a.cm.1.4 | 4 | 55.54 | odd | 2 | |||
9075.2.a.di.1.1 | 4 | 5.4 | even | 2 |