Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16609.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} - x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.18109\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.60502 | 1.50401 | 0.752003 | − | 0.659159i | \(-0.229088\pi\) | ||||
0.752003 | + | 0.659159i | \(0.229088\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.78611 | 1.24599 | 0.622993 | − | 0.782227i | \(-0.285916\pi\) | ||||
0.622993 | + | 0.782227i | \(0.285916\pi\) | |||||||
\(6\) | −2.60502 | −1.06349 | ||||||||
\(7\) | −3.47175 | −1.31220 | −0.656100 | − | 0.754674i | \(-0.727795\pi\) | ||||
−0.656100 | + | 0.754674i | \(0.727795\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.78611 | 1.26204 | ||||||||
\(10\) | −2.78611 | −0.881046 | ||||||||
\(11\) | 0.290659 | 0.0876370 | 0.0438185 | − | 0.999040i | \(-0.486048\pi\) | ||||
0.0438185 | + | 0.999040i | \(0.486048\pi\) | |||||||
\(12\) | 2.60502 | 0.752003 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.47175 | 0.927865 | ||||||||
\(15\) | 7.25786 | 1.87397 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.54852 | −1.83079 | −0.915393 | − | 0.402562i | \(-0.868120\pi\) | ||||
−0.915393 | + | 0.402562i | \(0.868120\pi\) | |||||||
\(18\) | −3.78611 | −0.892395 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.78611 | 0.622993 | ||||||||
\(21\) | −9.04397 | −1.97356 | ||||||||
\(22\) | −0.290659 | −0.0619688 | ||||||||
\(23\) | −5.86288 | −1.22250 | −0.611248 | − | 0.791439i | \(-0.709332\pi\) | ||||
−0.611248 | + | 0.791439i | \(0.709332\pi\) | |||||||
\(24\) | −2.60502 | −0.531747 | ||||||||
\(25\) | 2.76241 | 0.552483 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.04783 | 0.394105 | ||||||||
\(28\) | −3.47175 | −0.656100 | ||||||||
\(29\) | 8.22507 | 1.52736 | 0.763678 | − | 0.645597i | \(-0.223391\pi\) | ||||
0.763678 | + | 0.645597i | \(0.223391\pi\) | |||||||
\(30\) | −7.25786 | −1.32510 | ||||||||
\(31\) | −5.41002 | −0.971668 | −0.485834 | − | 0.874051i | \(-0.661484\pi\) | ||||
−0.485834 | + | 0.874051i | \(0.661484\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.757172 | 0.131807 | ||||||||
\(34\) | 7.54852 | 1.29456 | ||||||||
\(35\) | −9.67269 | −1.63498 | ||||||||
\(36\) | 3.78611 | 0.631018 | ||||||||
\(37\) | −1.37609 | −0.226228 | −0.113114 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113114 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.78611 | −0.440523 | ||||||||
\(41\) | −4.80115 | −0.749813 | −0.374907 | − | 0.927063i | \(-0.622325\pi\) | ||||
−0.374907 | + | 0.927063i | \(0.622325\pi\) | |||||||
\(42\) | 9.04397 | 1.39552 | ||||||||
\(43\) | −8.94831 | −1.36460 | −0.682302 | − | 0.731070i | \(-0.739021\pi\) | ||||
−0.682302 | + | 0.731070i | \(0.739021\pi\) | |||||||
\(44\) | 0.290659 | 0.0438185 | ||||||||
\(45\) | 10.5485 | 1.57248 | ||||||||
\(46\) | 5.86288 | 0.864435 | ||||||||
\(47\) | 6.19613 | 0.903798 | 0.451899 | − | 0.892069i | \(-0.350747\pi\) | ||||
0.451899 | + | 0.892069i | \(0.350747\pi\) | |||||||
\(48\) | 2.60502 | 0.376002 | ||||||||
\(49\) | 5.05307 | 0.721867 | ||||||||
\(50\) | −2.76241 | −0.390664 | ||||||||
\(51\) | −19.6640 | −2.75351 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.8866 | −1.77011 | −0.885054 | − | 0.465489i | \(-0.845879\pi\) | ||||
−0.885054 | + | 0.465489i | \(0.845879\pi\) | |||||||
\(54\) | −2.04783 | −0.278675 | ||||||||
\(55\) | 0.809809 | 0.109195 | ||||||||
\(56\) | 3.47175 | 0.463933 | ||||||||
\(57\) | −2.60502 | −0.345043 | ||||||||
\(58\) | −8.22507 | −1.08000 | ||||||||
\(59\) | −5.57222 | −0.725441 | −0.362721 | − | 0.931898i | \(-0.618152\pi\) | ||||
−0.362721 | + | 0.931898i | \(0.618152\pi\) | |||||||
\(60\) | 7.25786 | 0.936986 | ||||||||
\(61\) | 1.41868 | 0.181644 | 0.0908218 | − | 0.995867i | \(-0.471051\pi\) | ||||
0.0908218 | + | 0.995867i | \(0.471051\pi\) | |||||||
\(62\) | 5.41002 | 0.687073 | ||||||||
\(63\) | −13.1444 | −1.65604 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.757172 | −0.0932014 | ||||||||
\(67\) | 8.72438 | 1.06585 | 0.532926 | − | 0.846162i | \(-0.321092\pi\) | ||||
0.532926 | + | 0.846162i | \(0.321092\pi\) | |||||||
\(68\) | −7.54852 | −0.915393 | ||||||||
\(69\) | −15.2729 | −1.83864 | ||||||||
\(70\) | 9.67269 | 1.15611 | ||||||||
\(71\) | −1.27177 | −0.150931 | −0.0754655 | − | 0.997148i | \(-0.524044\pi\) | ||||
−0.0754655 | + | 0.997148i | \(0.524044\pi\) | |||||||
\(72\) | −3.78611 | −0.446197 | ||||||||
\(73\) | −4.36219 | −0.510556 | −0.255278 | − | 0.966868i | \(-0.582167\pi\) | ||||
−0.255278 | + | 0.966868i | \(0.582167\pi\) | |||||||
\(74\) | 1.37609 | 0.159967 | ||||||||
\(75\) | 7.19613 | 0.830938 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −1.00910 | −0.114997 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.88701 | −1.11238 | −0.556188 | − | 0.831057i | \(-0.687737\pi\) | ||||
−0.556188 | + | 0.831057i | \(0.687737\pi\) | |||||||
\(80\) | 2.78611 | 0.311497 | ||||||||
\(81\) | −6.02370 | −0.669300 | ||||||||
\(82\) | 4.80115 | 0.530198 | ||||||||
\(83\) | 12.4968 | 1.37171 | 0.685853 | − | 0.727740i | \(-0.259429\pi\) | ||||
0.685853 | + | 0.727740i | \(0.259429\pi\) | |||||||
\(84\) | −9.04397 | −0.986779 | ||||||||
\(85\) | −21.0310 | −2.28113 | ||||||||
\(86\) | 8.94831 | 0.964921 | ||||||||
\(87\) | 21.4264 | 2.29716 | ||||||||
\(88\) | −0.290659 | −0.0309844 | ||||||||
\(89\) | −11.4351 | −1.21212 | −0.606059 | − | 0.795420i | \(-0.707251\pi\) | ||||
−0.606059 | + | 0.795420i | \(0.707251\pi\) | |||||||
\(90\) | −10.5485 | −1.11191 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.86288 | −0.611248 | ||||||||
\(93\) | −14.0932 | −1.46140 | ||||||||
\(94\) | −6.19613 | −0.639082 | ||||||||
\(95\) | −2.78611 | −0.285849 | ||||||||
\(96\) | −2.60502 | −0.265873 | ||||||||
\(97\) | 5.53848 | 0.562347 | 0.281174 | − | 0.959657i | \(-0.409276\pi\) | ||||
0.281174 | + | 0.959657i | \(0.409276\pi\) | |||||||
\(98\) | −5.05307 | −0.510437 | ||||||||
\(99\) | 1.10047 | 0.110601 | ||||||||
\(100\) | 2.76241 | 0.276241 | ||||||||
\(101\) | 4.48566 | 0.446339 | 0.223170 | − | 0.974780i | \(-0.428360\pi\) | ||||
0.223170 | + | 0.974780i | \(0.428360\pi\) | |||||||
\(102\) | 19.6640 | 1.94703 | ||||||||
\(103\) | 16.2492 | 1.60108 | 0.800541 | − | 0.599278i | \(-0.204546\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204546\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.1975 | −2.45903 | ||||||||
\(106\) | 12.8866 | 1.25166 | ||||||||
\(107\) | 8.04922 | 0.778147 | 0.389074 | − | 0.921207i | \(-0.372795\pi\) | ||||
0.389074 | + | 0.921207i | \(0.372795\pi\) | |||||||
\(108\) | 2.04783 | 0.197053 | ||||||||
\(109\) | −10.8248 | −1.03683 | −0.518416 | − | 0.855129i | \(-0.673478\pi\) | ||||
−0.518416 | + | 0.855129i | \(0.673478\pi\) | |||||||
\(110\) | −0.809809 | −0.0772122 | ||||||||
\(111\) | −3.58474 | −0.340248 | ||||||||
\(112\) | −3.47175 | −0.328050 | ||||||||
\(113\) | 0.847844 | 0.0797585 | 0.0398792 | − | 0.999205i | \(-0.487303\pi\) | ||||
0.0398792 | + | 0.999205i | \(0.487303\pi\) | |||||||
\(114\) | 2.60502 | 0.243982 | ||||||||
\(115\) | −16.3346 | −1.52321 | ||||||||
\(116\) | 8.22507 | 0.763678 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.57222 | 0.512965 | ||||||||
\(119\) | 26.2066 | 2.40236 | ||||||||
\(120\) | −7.25786 | −0.662549 | ||||||||
\(121\) | −10.9155 | −0.992320 | ||||||||
\(122\) | −1.41868 | −0.128441 | ||||||||
\(123\) | −12.5071 | −1.12772 | ||||||||
\(124\) | −5.41002 | −0.485834 | ||||||||
\(125\) | −6.23417 | −0.557601 | ||||||||
\(126\) | 13.1444 | 1.17100 | ||||||||
\(127\) | 7.83875 | 0.695576 | 0.347788 | − | 0.937573i | \(-0.386933\pi\) | ||||
0.347788 | + | 0.937573i | \(0.386933\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −23.3105 | −2.05238 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1396 | 1.32276 | 0.661378 | − | 0.750053i | \(-0.269972\pi\) | ||||
0.661378 | + | 0.750053i | \(0.269972\pi\) | |||||||
\(132\) | 0.757172 | 0.0659034 | ||||||||
\(133\) | 3.47175 | 0.301039 | ||||||||
\(134\) | −8.72438 | −0.753671 | ||||||||
\(135\) | 5.70548 | 0.491050 | ||||||||
\(136\) | 7.54852 | 0.647281 | ||||||||
\(137\) | 16.4501 | 1.40543 | 0.702715 | − | 0.711471i | \(-0.251971\pi\) | ||||
0.702715 | + | 0.711471i | \(0.251971\pi\) | |||||||
\(138\) | 15.2729 | 1.30012 | ||||||||
\(139\) | −12.7119 | −1.07821 | −0.539103 | − | 0.842240i | \(-0.681237\pi\) | ||||
−0.539103 | + | 0.842240i | \(0.681237\pi\) | |||||||
\(140\) | −9.67269 | −0.817491 | ||||||||
\(141\) | 16.1410 | 1.35932 | ||||||||
\(142\) | 1.27177 | 0.106724 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.78611 | 0.315509 | ||||||||
\(145\) | 22.9160 | 1.90307 | ||||||||
\(146\) | 4.36219 | 0.361017 | ||||||||
\(147\) | 13.1633 | 1.08569 | ||||||||
\(148\) | −1.37609 | −0.113114 | ||||||||
\(149\) | −13.7447 | −1.12601 | −0.563003 | − | 0.826455i | \(-0.690354\pi\) | ||||
−0.563003 | + | 0.826455i | \(0.690354\pi\) | |||||||
\(150\) | −7.19613 | −0.587562 | ||||||||
\(151\) | 1.69682 | 0.138085 | 0.0690427 | − | 0.997614i | \(-0.478006\pi\) | ||||
0.0690427 | + | 0.997614i | \(0.478006\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −28.5795 | −2.31052 | ||||||||
\(154\) | 1.00910 | 0.0813154 | ||||||||
\(155\) | −15.0729 | −1.21069 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.47656 | −0.596694 | −0.298347 | − | 0.954457i | \(-0.596435\pi\) | ||||
−0.298347 | + | 0.954457i | \(0.596435\pi\) | |||||||
\(158\) | 9.88701 | 0.786569 | ||||||||
\(159\) | −33.5697 | −2.66225 | ||||||||
\(160\) | −2.78611 | −0.220261 | ||||||||
\(161\) | 20.3545 | 1.60416 | ||||||||
\(162\) | 6.02370 | 0.473266 | ||||||||
\(163\) | 5.74465 | 0.449956 | 0.224978 | − | 0.974364i | \(-0.427769\pi\) | ||||
0.224978 | + | 0.974364i | \(0.427769\pi\) | |||||||
\(164\) | −4.80115 | −0.374907 | ||||||||
\(165\) | 2.10956 | 0.164229 | ||||||||
\(166\) | −12.4968 | −0.969943 | ||||||||
\(167\) | −21.4403 | −1.65910 | −0.829552 | − | 0.558430i | \(-0.811404\pi\) | ||||
−0.829552 | + | 0.558430i | \(0.811404\pi\) | |||||||
\(168\) | 9.04397 | 0.697758 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 21.0310 | 1.61301 | ||||||||
\(171\) | −3.78611 | −0.289531 | ||||||||
\(172\) | −8.94831 | −0.682302 | ||||||||
\(173\) | 2.17243 | 0.165167 | 0.0825835 | − | 0.996584i | \(-0.473683\pi\) | ||||
0.0825835 | + | 0.996584i | \(0.473683\pi\) | |||||||
\(174\) | −21.4264 | −1.62433 | ||||||||
\(175\) | −9.59042 | −0.724967 | ||||||||
\(176\) | 0.290659 | 0.0219093 | ||||||||
\(177\) | −14.5157 | −1.09107 | ||||||||
\(178\) | 11.4351 | 0.857097 | ||||||||
\(179\) | 7.35695 | 0.549884 | 0.274942 | − | 0.961461i | \(-0.411341\pi\) | ||||
0.274942 | + | 0.961461i | \(0.411341\pi\) | |||||||
\(180\) | 10.5485 | 0.786241 | ||||||||
\(181\) | 18.3734 | 1.36568 | 0.682841 | − | 0.730567i | \(-0.260744\pi\) | ||||
0.682841 | + | 0.730567i | \(0.260744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.69569 | 0.273193 | ||||||||
\(184\) | 5.86288 | 0.432217 | ||||||||
\(185\) | −3.83394 | −0.281877 | ||||||||
\(186\) | 14.0932 | 1.03336 | ||||||||
\(187\) | −2.19405 | −0.160445 | ||||||||
\(188\) | 6.19613 | 0.451899 | ||||||||
\(189\) | −7.10956 | −0.517145 | ||||||||
\(190\) | 2.78611 | 0.202126 | ||||||||
\(191\) | 18.1923 | 1.31635 | 0.658173 | − | 0.752866i | \(-0.271329\pi\) | ||||
0.658173 | + | 0.752866i | \(0.271329\pi\) | |||||||
\(192\) | 2.60502 | 0.188001 | ||||||||
\(193\) | 13.9734 | 1.00583 | 0.502913 | − | 0.864337i | \(-0.332261\pi\) | ||||
0.502913 | + | 0.864337i | \(0.332261\pi\) | |||||||
\(194\) | −5.53848 | −0.397639 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.05307 | 0.360934 | ||||||||
\(197\) | −27.2855 | −1.94401 | −0.972004 | − | 0.234963i | \(-0.924503\pi\) | ||||
−0.972004 | + | 0.234963i | \(0.924503\pi\) | |||||||
\(198\) | −1.10047 | −0.0782068 | ||||||||
\(199\) | 14.9773 | 1.06171 | 0.530855 | − | 0.847463i | \(-0.321871\pi\) | ||||
0.530855 | + | 0.847463i | \(0.321871\pi\) | |||||||
\(200\) | −2.76241 | −0.195332 | ||||||||
\(201\) | 22.7271 | 1.60305 | ||||||||
\(202\) | −4.48566 | −0.315610 | ||||||||
\(203\) | −28.5554 | −2.00420 | ||||||||
\(204\) | −19.6640 | −1.37676 | ||||||||
\(205\) | −13.3765 | −0.934257 | ||||||||
\(206\) | −16.2492 | −1.13214 | ||||||||
\(207\) | −22.1975 | −1.54283 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.290659 | −0.0201053 | ||||||||
\(210\) | 25.1975 | 1.73879 | ||||||||
\(211\) | −0.456717 | −0.0314417 | −0.0157209 | − | 0.999876i | \(-0.505004\pi\) | ||||
−0.0157209 | + | 0.999876i | \(0.505004\pi\) | |||||||
\(212\) | −12.8866 | −0.885054 | ||||||||
\(213\) | −3.31297 | −0.227001 | ||||||||
\(214\) | −8.04922 | −0.550233 | ||||||||
\(215\) | −24.9310 | −1.70028 | ||||||||
\(216\) | −2.04783 | −0.139337 | ||||||||
\(217\) | 18.7823 | 1.27502 | ||||||||
\(218\) | 10.8248 | 0.733151 | ||||||||
\(219\) | −11.3636 | −0.767879 | ||||||||
\(220\) | 0.809809 | 0.0545973 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.58474 | 0.240592 | ||||||||
\(223\) | −7.60640 | −0.509362 | −0.254681 | − | 0.967025i | \(-0.581971\pi\) | ||||
−0.254681 | + | 0.967025i | \(0.581971\pi\) | |||||||
\(224\) | 3.47175 | 0.231966 | ||||||||
\(225\) | 10.4588 | 0.697253 | ||||||||
\(226\) | −0.847844 | −0.0563978 | ||||||||
\(227\) | −23.9923 | −1.59242 | −0.796212 | − | 0.605018i | \(-0.793166\pi\) | ||||
−0.796212 | + | 0.605018i | \(0.793166\pi\) | |||||||
\(228\) | −2.60502 | −0.172521 | ||||||||
\(229\) | 7.00252 | 0.462739 | 0.231370 | − | 0.972866i | \(-0.425679\pi\) | ||||
0.231370 | + | 0.972866i | \(0.425679\pi\) | |||||||
\(230\) | 16.3346 | 1.07707 | ||||||||
\(231\) | −2.62871 | −0.172957 | ||||||||
\(232\) | −8.22507 | −0.540002 | ||||||||
\(233\) | −26.6731 | −1.74741 | −0.873707 | − | 0.486452i | \(-0.838291\pi\) | ||||
−0.873707 | + | 0.486452i | \(0.838291\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.2631 | 1.12612 | ||||||||
\(236\) | −5.57222 | −0.362721 | ||||||||
\(237\) | −25.7558 | −1.67302 | ||||||||
\(238\) | −26.2066 | −1.69872 | ||||||||
\(239\) | 2.88082 | 0.186345 | 0.0931725 | − | 0.995650i | \(-0.470299\pi\) | ||||
0.0931725 | + | 0.995650i | \(0.470299\pi\) | |||||||
\(240\) | 7.25786 | 0.468493 | ||||||||
\(241\) | −15.7344 | −1.01354 | −0.506772 | − | 0.862080i | \(-0.669161\pi\) | ||||
−0.506772 | + | 0.862080i | \(0.669161\pi\) | |||||||
\(242\) | 10.9155 | 0.701676 | ||||||||
\(243\) | −21.8353 | −1.40074 | ||||||||
\(244\) | 1.41868 | 0.0908218 | ||||||||
\(245\) | 14.0784 | 0.899437 | ||||||||
\(246\) | 12.5071 | 0.797421 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.41002 | 0.343537 | ||||||||
\(249\) | 32.5545 | 2.06306 | ||||||||
\(250\) | 6.23417 | 0.394283 | ||||||||
\(251\) | 14.0957 | 0.889710 | 0.444855 | − | 0.895603i | \(-0.353255\pi\) | ||||
0.444855 | + | 0.895603i | \(0.353255\pi\) | |||||||
\(252\) | −13.1444 | −0.828022 | ||||||||
\(253\) | −1.70410 | −0.107136 | ||||||||
\(254\) | −7.83875 | −0.491847 | ||||||||
\(255\) | −54.7862 | −3.43084 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.35738 | −0.396563 | −0.198281 | − | 0.980145i | \(-0.563536\pi\) | ||||
−0.198281 | + | 0.980145i | \(0.563536\pi\) | |||||||
\(258\) | 23.3105 | 1.45125 | ||||||||
\(259\) | 4.77745 | 0.296856 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.1410 | 1.92758 | ||||||||
\(262\) | −15.1396 | −0.935330 | ||||||||
\(263\) | −17.5360 | −1.08132 | −0.540658 | − | 0.841242i | \(-0.681825\pi\) | ||||
−0.540658 | + | 0.841242i | \(0.681825\pi\) | |||||||
\(264\) | −0.757172 | −0.0466007 | ||||||||
\(265\) | −35.9034 | −2.20553 | ||||||||
\(266\) | −3.47175 | −0.212867 | ||||||||
\(267\) | −29.7886 | −1.82303 | ||||||||
\(268\) | 8.72438 | 0.532926 | ||||||||
\(269\) | −21.8688 | −1.33337 | −0.666683 | − | 0.745342i | \(-0.732286\pi\) | ||||
−0.666683 | + | 0.745342i | \(0.732286\pi\) | |||||||
\(270\) | −5.70548 | −0.347225 | ||||||||
\(271\) | 27.7606 | 1.68634 | 0.843169 | − | 0.537648i | \(-0.180687\pi\) | ||||
0.843169 | + | 0.537648i | \(0.180687\pi\) | |||||||
\(272\) | −7.54852 | −0.457696 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4501 | −0.993789 | ||||||||
\(275\) | 0.802921 | 0.0484179 | ||||||||
\(276\) | −15.2729 | −0.919321 | ||||||||
\(277\) | 22.6693 | 1.36206 | 0.681032 | − | 0.732254i | \(-0.261531\pi\) | ||||
0.681032 | + | 0.732254i | \(0.261531\pi\) | |||||||
\(278\) | 12.7119 | 0.762407 | ||||||||
\(279\) | −20.4829 | −1.22628 | ||||||||
\(280\) | 9.67269 | 0.578054 | ||||||||
\(281\) | −14.3786 | −0.857756 | −0.428878 | − | 0.903362i | \(-0.641091\pi\) | ||||
−0.428878 | + | 0.903362i | \(0.641091\pi\) | |||||||
\(282\) | −16.1410 | −0.961184 | ||||||||
\(283\) | 1.33350 | 0.0792684 | 0.0396342 | − | 0.999214i | \(-0.487381\pi\) | ||||
0.0396342 | + | 0.999214i | \(0.487381\pi\) | |||||||
\(284\) | −1.27177 | −0.0754655 | ||||||||
\(285\) | −7.25786 | −0.429919 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.6684 | 0.983904 | ||||||||
\(288\) | −3.78611 | −0.223099 | ||||||||
\(289\) | 39.9802 | 2.35178 | ||||||||
\(290\) | −22.9160 | −1.34567 | ||||||||
\(291\) | 14.4278 | 0.845774 | ||||||||
\(292\) | −4.36219 | −0.255278 | ||||||||
\(293\) | −4.26172 | −0.248972 | −0.124486 | − | 0.992221i | \(-0.539728\pi\) | ||||
−0.124486 | + | 0.992221i | \(0.539728\pi\) | |||||||
\(294\) | −13.1633 | −0.767701 | ||||||||
\(295\) | −15.5248 | −0.903890 | ||||||||
\(296\) | 1.37609 | 0.0799837 | ||||||||
\(297\) | 0.595221 | 0.0345382 | ||||||||
\(298\) | 13.7447 | 0.796206 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.19613 | 0.415469 | ||||||||
\(301\) | 31.0663 | 1.79063 | ||||||||
\(302\) | −1.69682 | −0.0976412 | ||||||||
\(303\) | 11.6852 | 0.671298 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 3.95260 | 0.226325 | ||||||||
\(306\) | 28.5795 | 1.63378 | ||||||||
\(307\) | −15.7809 | −0.900662 | −0.450331 | − | 0.892862i | \(-0.648694\pi\) | ||||
−0.450331 | + | 0.892862i | \(0.648694\pi\) | |||||||
\(308\) | −1.00910 | −0.0574986 | ||||||||
\(309\) | 42.3294 | 2.40804 | ||||||||
\(310\) | 15.0729 | 0.856084 | ||||||||
\(311\) | 0.504549 | 0.0286103 | 0.0143052 | − | 0.999898i | \(-0.495446\pi\) | ||||
0.0143052 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.5871 | −1.16365 | −0.581825 | − | 0.813314i | \(-0.697661\pi\) | ||||
−0.581825 | + | 0.813314i | \(0.697661\pi\) | |||||||
\(314\) | 7.47656 | 0.421927 | ||||||||
\(315\) | −36.6219 | −2.06341 | ||||||||
\(316\) | −9.88701 | −0.556188 | ||||||||
\(317\) | −2.43826 | −0.136946 | −0.0684732 | − | 0.997653i | \(-0.521813\pi\) | ||||
−0.0684732 | + | 0.997653i | \(0.521813\pi\) | |||||||
\(318\) | 33.5697 | 1.88250 | ||||||||
\(319\) | 2.39069 | 0.133853 | ||||||||
\(320\) | 2.78611 | 0.155748 | ||||||||
\(321\) | 20.9683 | 1.17034 | ||||||||
\(322\) | −20.3545 | −1.13431 | ||||||||
\(323\) | 7.54852 | 0.420011 | ||||||||
\(324\) | −6.02370 | −0.334650 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.74465 | −0.318167 | ||||||||
\(327\) | −28.1989 | −1.55940 | ||||||||
\(328\) | 4.80115 | 0.265099 | ||||||||
\(329\) | −21.5114 | −1.18596 | ||||||||
\(330\) | −2.10956 | −0.116128 | ||||||||
\(331\) | 13.7558 | 0.756089 | 0.378044 | − | 0.925787i | \(-0.376597\pi\) | ||||
0.378044 | + | 0.925787i | \(0.376597\pi\) | |||||||
\(332\) | 12.4968 | 0.685853 | ||||||||
\(333\) | −5.21003 | −0.285508 | ||||||||
\(334\) | 21.4403 | 1.17316 | ||||||||
\(335\) | 24.3071 | 1.32804 | ||||||||
\(336\) | −9.04397 | −0.493389 | ||||||||
\(337\) | −10.0909 | −0.549684 | −0.274842 | − | 0.961489i | \(-0.588626\pi\) | ||||
−0.274842 | + | 0.961489i | \(0.588626\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.20865 | 0.119957 | ||||||||
\(340\) | −21.0310 | −1.14057 | ||||||||
\(341\) | −1.57247 | −0.0851541 | ||||||||
\(342\) | 3.78611 | 0.204729 | ||||||||
\(343\) | 6.75925 | 0.364965 | ||||||||
\(344\) | 8.94831 | 0.482461 | ||||||||
\(345\) | −42.5520 | −2.29092 | ||||||||
\(346\) | −2.17243 | −0.116791 | ||||||||
\(347\) | −10.6335 | −0.570837 | −0.285419 | − | 0.958403i | \(-0.592133\pi\) | ||||
−0.285419 | + | 0.958403i | \(0.592133\pi\) | |||||||
\(348\) | 21.4264 | 1.14858 | ||||||||
\(349\) | −11.7572 | −0.629347 | −0.314673 | − | 0.949200i | \(-0.601895\pi\) | ||||
−0.314673 | + | 0.949200i | \(0.601895\pi\) | |||||||
\(350\) | 9.59042 | 0.512629 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.290659 | −0.0154922 | ||||||||
\(353\) | 36.3071 | 1.93243 | 0.966215 | − | 0.257736i | \(-0.0829764\pi\) | ||||
0.966215 | + | 0.257736i | \(0.0829764\pi\) | |||||||
\(354\) | 14.5157 | 0.771502 | ||||||||
\(355\) | −3.54328 | −0.188058 | ||||||||
\(356\) | −11.4351 | −0.606059 | ||||||||
\(357\) | 68.2687 | 3.61316 | ||||||||
\(358\) | −7.35695 | −0.388827 | ||||||||
\(359\) | 18.5736 | 0.980277 | 0.490139 | − | 0.871644i | \(-0.336946\pi\) | ||||
0.490139 | + | 0.871644i | \(0.336946\pi\) | |||||||
\(360\) | −10.5485 | −0.555956 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −18.3734 | −0.965683 | ||||||||
\(363\) | −28.4351 | −1.49246 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.1535 | −0.636145 | ||||||||
\(366\) | −3.69569 | −0.193177 | ||||||||
\(367\) | 4.42873 | 0.231178 | 0.115589 | − | 0.993297i | \(-0.463124\pi\) | ||||
0.115589 | + | 0.993297i | \(0.463124\pi\) | |||||||
\(368\) | −5.86288 | −0.305624 | ||||||||
\(369\) | −18.1777 | −0.946292 | ||||||||
\(370\) | 3.83394 | 0.199317 | ||||||||
\(371\) | 44.7390 | 2.32273 | ||||||||
\(372\) | −14.0932 | −0.730698 | ||||||||
\(373\) | 22.8590 | 1.18360 | 0.591798 | − | 0.806087i | \(-0.298418\pi\) | ||||
0.591798 | + | 0.806087i | \(0.298418\pi\) | |||||||
\(374\) | 2.19405 | 0.113452 | ||||||||
\(375\) | −16.2401 | −0.838635 | ||||||||
\(376\) | −6.19613 | −0.319541 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 7.10956 | 0.365677 | ||||||||
\(379\) | 7.55263 | 0.387953 | 0.193976 | − | 0.981006i | \(-0.437862\pi\) | ||||
0.193976 | + | 0.981006i | \(0.437862\pi\) | |||||||
\(380\) | −2.78611 | −0.142924 | ||||||||
\(381\) | 20.4201 | 1.04615 | ||||||||
\(382\) | −18.1923 | −0.930798 | ||||||||
\(383\) | 13.8900 | 0.709746 | 0.354873 | − | 0.934915i | \(-0.384524\pi\) | ||||
0.354873 | + | 0.934915i | \(0.384524\pi\) | |||||||
\(384\) | −2.60502 | −0.132937 | ||||||||
\(385\) | −2.81146 | −0.143285 | ||||||||
\(386\) | −13.9734 | −0.711227 | ||||||||
\(387\) | −33.8793 | −1.72218 | ||||||||
\(388\) | 5.53848 | 0.281174 | ||||||||
\(389\) | −20.8952 | −1.05943 | −0.529715 | − | 0.848175i | \(-0.677701\pi\) | ||||
−0.529715 | + | 0.848175i | \(0.677701\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.2561 | 2.23813 | ||||||||
\(392\) | −5.05307 | −0.255219 | ||||||||
\(393\) | 39.4390 | 1.98943 | ||||||||
\(394\) | 27.2855 | 1.37462 | ||||||||
\(395\) | −27.5463 | −1.38601 | ||||||||
\(396\) | 1.10047 | 0.0553006 | ||||||||
\(397\) | 12.5175 | 0.628238 | 0.314119 | − | 0.949384i | \(-0.398291\pi\) | ||||
0.314119 | + | 0.949384i | \(0.398291\pi\) | |||||||
\(398\) | −14.9773 | −0.750742 | ||||||||
\(399\) | 9.04397 | 0.452765 | ||||||||
\(400\) | 2.76241 | 0.138121 | ||||||||
\(401\) | 12.1517 | 0.606828 | 0.303414 | − | 0.952859i | \(-0.401873\pi\) | ||||
0.303414 | + | 0.952859i | \(0.401873\pi\) | |||||||
\(402\) | −22.7271 | −1.13353 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.48566 | 0.223170 | ||||||||
\(405\) | −16.7827 | −0.833939 | ||||||||
\(406\) | 28.5554 | 1.41718 | ||||||||
\(407\) | −0.399974 | −0.0198260 | ||||||||
\(408\) | 19.6640 | 0.973514 | ||||||||
\(409\) | −27.5549 | −1.36250 | −0.681251 | − | 0.732050i | \(-0.738564\pi\) | ||||
−0.681251 | + | 0.732050i | \(0.738564\pi\) | |||||||
\(410\) | 13.3765 | 0.660620 | ||||||||
\(411\) | 42.8529 | 2.11378 | ||||||||
\(412\) | 16.2492 | 0.800541 | ||||||||
\(413\) | 19.3454 | 0.951924 | ||||||||
\(414\) | 22.1975 | 1.09095 | ||||||||
\(415\) | 34.8176 | 1.70913 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.1146 | −1.62163 | ||||||||
\(418\) | 0.290659 | 0.0142166 | ||||||||
\(419\) | 18.1109 | 0.884778 | 0.442389 | − | 0.896823i | \(-0.354131\pi\) | ||||
0.442389 | + | 0.896823i | \(0.354131\pi\) | |||||||
\(420\) | −25.1975 | −1.22951 | ||||||||
\(421\) | −10.8526 | −0.528926 | −0.264463 | − | 0.964396i | \(-0.585195\pi\) | ||||
−0.264463 | + | 0.964396i | \(0.585195\pi\) | |||||||
\(422\) | 0.456717 | 0.0222327 | ||||||||
\(423\) | 23.4592 | 1.14063 | ||||||||
\(424\) | 12.8866 | 0.625828 | ||||||||
\(425\) | −20.8521 | −1.01148 | ||||||||
\(426\) | 3.31297 | 0.160514 | ||||||||
\(427\) | −4.92531 | −0.238353 | ||||||||
\(428\) | 8.04922 | 0.389074 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.9310 | 1.20228 | ||||||||
\(431\) | 27.1681 | 1.30864 | 0.654322 | − | 0.756216i | \(-0.272954\pi\) | ||||
0.654322 | + | 0.756216i | \(0.272954\pi\) | |||||||
\(432\) | 2.04783 | 0.0985263 | ||||||||
\(433\) | 1.63490 | 0.0785685 | 0.0392842 | − | 0.999228i | \(-0.487492\pi\) | ||||
0.0392842 | + | 0.999228i | \(0.487492\pi\) | |||||||
\(434\) | −18.7823 | −0.901577 | ||||||||
\(435\) | 59.6964 | 2.86222 | ||||||||
\(436\) | −10.8248 | −0.518416 | ||||||||
\(437\) | 5.86288 | 0.280460 | ||||||||
\(438\) | 11.3636 | 0.542973 | ||||||||
\(439\) | −37.8206 | −1.80508 | −0.902538 | − | 0.430610i | \(-0.858299\pi\) | ||||
−0.902538 | + | 0.430610i | \(0.858299\pi\) | |||||||
\(440\) | −0.809809 | −0.0386061 | ||||||||
\(441\) | 19.1315 | 0.911023 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.70049 | 0.460884 | 0.230442 | − | 0.973086i | \(-0.425983\pi\) | ||||
0.230442 | + | 0.973086i | \(0.425983\pi\) | |||||||
\(444\) | −3.58474 | −0.170124 | ||||||||
\(445\) | −31.8595 | −1.51028 | ||||||||
\(446\) | 7.60640 | 0.360174 | ||||||||
\(447\) | −35.8050 | −1.69352 | ||||||||
\(448\) | −3.47175 | −0.164025 | ||||||||
\(449\) | 22.4381 | 1.05892 | 0.529459 | − | 0.848335i | \(-0.322395\pi\) | ||||
0.529459 | + | 0.848335i | \(0.322395\pi\) | |||||||
\(450\) | −10.4588 | −0.493033 | ||||||||
\(451\) | −1.39550 | −0.0657114 | ||||||||
\(452\) | 0.847844 | 0.0398792 | ||||||||
\(453\) | 4.42025 | 0.207681 | ||||||||
\(454\) | 23.9923 | 1.12601 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.60502 | 0.121991 | ||||||||
\(457\) | 2.85746 | 0.133666 | 0.0668331 | − | 0.997764i | \(-0.478711\pi\) | ||||
0.0668331 | + | 0.997764i | \(0.478711\pi\) | |||||||
\(458\) | −7.00252 | −0.327206 | ||||||||
\(459\) | −15.4581 | −0.721522 | ||||||||
\(460\) | −16.3346 | −0.761606 | ||||||||
\(461\) | −27.5356 | −1.28246 | −0.641230 | − | 0.767349i | \(-0.721575\pi\) | ||||
−0.641230 | + | 0.767349i | \(0.721575\pi\) | |||||||
\(462\) | 2.62871 | 0.122299 | ||||||||
\(463\) | −17.6784 | −0.821583 | −0.410792 | − | 0.911729i | \(-0.634748\pi\) | ||||
−0.410792 | + | 0.911729i | \(0.634748\pi\) | |||||||
\(464\) | 8.22507 | 0.381839 | ||||||||
\(465\) | −39.2652 | −1.82088 | ||||||||
\(466\) | 26.6731 | 1.23561 | ||||||||
\(467\) | 29.7663 | 1.37742 | 0.688710 | − | 0.725037i | \(-0.258177\pi\) | ||||
0.688710 | + | 0.725037i | \(0.258177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.2889 | −1.39861 | ||||||||
\(470\) | −17.2631 | −0.796288 | ||||||||
\(471\) | −19.4766 | −0.897432 | ||||||||
\(472\) | 5.57222 | 0.256482 | ||||||||
\(473\) | −2.60091 | −0.119590 | ||||||||
\(474\) | 25.7558 | 1.18300 | ||||||||
\(475\) | −2.76241 | −0.126748 | ||||||||
\(476\) | 26.2066 | 1.20118 | ||||||||
\(477\) | −48.7900 | −2.23394 | ||||||||
\(478\) | −2.88082 | −0.131766 | ||||||||
\(479\) | 29.1907 | 1.33376 | 0.666878 | − | 0.745167i | \(-0.267630\pi\) | ||||
0.666878 | + | 0.745167i | \(0.267630\pi\) | |||||||
\(480\) | −7.25786 | −0.331275 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.7344 | 0.716683 | ||||||||
\(483\) | 53.0237 | 2.41266 | ||||||||
\(484\) | −10.9155 | −0.496160 | ||||||||
\(485\) | 15.4308 | 0.700677 | ||||||||
\(486\) | 21.8353 | 0.990471 | ||||||||
\(487\) | −23.4246 | −1.06147 | −0.530735 | − | 0.847538i | \(-0.678084\pi\) | ||||
−0.530735 | + | 0.847538i | \(0.678084\pi\) | |||||||
\(488\) | −1.41868 | −0.0642207 | ||||||||
\(489\) | 14.9649 | 0.676737 | ||||||||
\(490\) | −14.0784 | −0.635998 | ||||||||
\(491\) | 26.5137 | 1.19655 | 0.598273 | − | 0.801292i | \(-0.295854\pi\) | ||||
0.598273 | + | 0.801292i | \(0.295854\pi\) | |||||||
\(492\) | −12.5071 | −0.563862 | ||||||||
\(493\) | −62.0871 | −2.79626 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.06603 | 0.137808 | ||||||||
\(496\) | −5.41002 | −0.242917 | ||||||||
\(497\) | 4.41526 | 0.198051 | ||||||||
\(498\) | −32.5545 | −1.45880 | ||||||||
\(499\) | 25.0203 | 1.12006 | 0.560031 | − | 0.828472i | \(-0.310789\pi\) | ||||
0.560031 | + | 0.828472i | \(0.310789\pi\) | |||||||
\(500\) | −6.23417 | −0.278800 | ||||||||
\(501\) | −55.8524 | −2.49530 | ||||||||
\(502\) | −14.0957 | −0.629120 | ||||||||
\(503\) | −23.4669 | −1.04634 | −0.523170 | − | 0.852229i | \(-0.675251\pi\) | ||||
−0.523170 | + | 0.852229i | \(0.675251\pi\) | |||||||
\(504\) | 13.1444 | 0.585500 | ||||||||
\(505\) | 12.4975 | 0.556133 | ||||||||
\(506\) | 1.70410 | 0.0757565 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.83875 | 0.347788 | ||||||||
\(509\) | 33.5449 | 1.48685 | 0.743426 | − | 0.668818i | \(-0.233199\pi\) | ||||
0.743426 | + | 0.668818i | \(0.233199\pi\) | |||||||
\(510\) | 54.7862 | 2.42597 | ||||||||
\(511\) | 15.1444 | 0.669951 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.04783 | −0.0904140 | ||||||||
\(514\) | 6.35738 | 0.280412 | ||||||||
\(515\) | 45.2721 | 1.99493 | ||||||||
\(516\) | −23.3105 | −1.02619 | ||||||||
\(517\) | 1.80096 | 0.0792062 | ||||||||
\(518\) | −4.77745 | −0.209909 | ||||||||
\(519\) | 5.65922 | 0.248412 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.6253 | 0.859800 | 0.429900 | − | 0.902877i | \(-0.358549\pi\) | ||||
0.429900 | + | 0.902877i | \(0.358549\pi\) | |||||||
\(522\) | −31.1410 | −1.36301 | ||||||||
\(523\) | 13.7276 | 0.600265 | 0.300133 | − | 0.953897i | \(-0.402969\pi\) | ||||
0.300133 | + | 0.953897i | \(0.402969\pi\) | |||||||
\(524\) | 15.1396 | 0.661378 | ||||||||
\(525\) | −24.9832 | −1.09036 | ||||||||
\(526\) | 17.5360 | 0.764606 | ||||||||
\(527\) | 40.8377 | 1.77892 | ||||||||
\(528\) | 0.757172 | 0.0329517 | ||||||||
\(529\) | 11.3734 | 0.494494 | ||||||||
\(530\) | 35.9034 | 1.55955 | ||||||||
\(531\) | −21.0970 | −0.915534 | ||||||||
\(532\) | 3.47175 | 0.150520 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 29.7886 | 1.28908 | ||||||||
\(535\) | 22.4260 | 0.969561 | ||||||||
\(536\) | −8.72438 | −0.376836 | ||||||||
\(537\) | 19.1650 | 0.827030 | ||||||||
\(538\) | 21.8688 | 0.942832 | ||||||||
\(539\) | 1.46872 | 0.0632623 | ||||||||
\(540\) | 5.70548 | 0.245525 | ||||||||
\(541\) | 13.1985 | 0.567446 | 0.283723 | − | 0.958906i | \(-0.408430\pi\) | ||||
0.283723 | + | 0.958906i | \(0.408430\pi\) | |||||||
\(542\) | −27.7606 | −1.19242 | ||||||||
\(543\) | 47.8629 | 2.05399 | ||||||||
\(544\) | 7.54852 | 0.323640 | ||||||||
\(545\) | −30.1592 | −1.29188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.7060 | 1.48392 | 0.741960 | − | 0.670444i | \(-0.233896\pi\) | ||||
0.741960 | + | 0.670444i | \(0.233896\pi\) | |||||||
\(548\) | 16.4501 | 0.702715 | ||||||||
\(549\) | 5.37129 | 0.229241 | ||||||||
\(550\) | −0.802921 | −0.0342367 | ||||||||
\(551\) | −8.22507 | −0.350400 | ||||||||
\(552\) | 15.2729 | 0.650058 | ||||||||
\(553\) | 34.3253 | 1.45966 | ||||||||
\(554\) | −22.6693 | −0.963125 | ||||||||
\(555\) | −9.98748 | −0.423945 | ||||||||
\(556\) | −12.7119 | −0.539103 | ||||||||
\(557\) | 18.3939 | 0.779374 | 0.389687 | − | 0.920947i | \(-0.372583\pi\) | ||||
0.389687 | + | 0.920947i | \(0.372583\pi\) | |||||||
\(558\) | 20.4829 | 0.867112 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −9.67269 | −0.408746 | ||||||||
\(561\) | −5.71553 | −0.241310 | ||||||||
\(562\) | 14.3786 | 0.606525 | ||||||||
\(563\) | −14.5543 | −0.613390 | −0.306695 | − | 0.951808i | \(-0.599223\pi\) | ||||
−0.306695 | + | 0.951808i | \(0.599223\pi\) | |||||||
\(564\) | 16.1410 | 0.679660 | ||||||||
\(565\) | 2.36219 | 0.0993780 | ||||||||
\(566\) | −1.33350 | −0.0560512 | ||||||||
\(567\) | 20.9128 | 0.878255 | ||||||||
\(568\) | 1.27177 | 0.0533621 | ||||||||
\(569\) | −1.47175 | −0.0616991 | −0.0308496 | − | 0.999524i | \(-0.509821\pi\) | ||||
−0.0308496 | + | 0.999524i | \(0.509821\pi\) | |||||||
\(570\) | 7.25786 | 0.303998 | ||||||||
\(571\) | −34.2772 | −1.43446 | −0.717229 | − | 0.696838i | \(-0.754590\pi\) | ||||
−0.717229 | + | 0.696838i | \(0.754590\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 47.3912 | 1.97979 | ||||||||
\(574\) | −16.6684 | −0.695725 | ||||||||
\(575\) | −16.1957 | −0.675407 | ||||||||
\(576\) | 3.78611 | 0.157755 | ||||||||
\(577\) | −13.1722 | −0.548368 | −0.274184 | − | 0.961677i | \(-0.588408\pi\) | ||||
−0.274184 | + | 0.961677i | \(0.588408\pi\) | |||||||
\(578\) | −39.9802 | −1.66296 | ||||||||
\(579\) | 36.4009 | 1.51277 | ||||||||
\(580\) | 22.9160 | 0.951533 | ||||||||
\(581\) | −43.3859 | −1.79995 | ||||||||
\(582\) | −14.4278 | −0.598053 | ||||||||
\(583\) | −3.74560 | −0.155127 | ||||||||
\(584\) | 4.36219 | 0.180509 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.26172 | 0.176050 | ||||||||
\(587\) | −44.4228 | −1.83353 | −0.916763 | − | 0.399431i | \(-0.869208\pi\) | ||||
−0.916763 | + | 0.399431i | \(0.869208\pi\) | |||||||
\(588\) | 13.1633 | 0.542847 | ||||||||
\(589\) | 5.41002 | 0.222916 | ||||||||
\(590\) | 15.5248 | 0.639147 | ||||||||
\(591\) | −71.0791 | −2.92380 | ||||||||
\(592\) | −1.37609 | −0.0565570 | ||||||||
\(593\) | 3.58955 | 0.147405 | 0.0737025 | − | 0.997280i | \(-0.476518\pi\) | ||||
0.0737025 | + | 0.997280i | \(0.476518\pi\) | |||||||
\(594\) | −0.595221 | −0.0244222 | ||||||||
\(595\) | 73.0145 | 2.99330 | ||||||||
\(596\) | −13.7447 | −0.563003 | ||||||||
\(597\) | 39.0160 | 1.59682 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.9253 | 0.773267 | 0.386634 | − | 0.922233i | \(-0.373638\pi\) | ||||
0.386634 | + | 0.922233i | \(0.373638\pi\) | |||||||
\(600\) | −7.19613 | −0.293781 | ||||||||
\(601\) | −38.5333 | −1.57181 | −0.785903 | − | 0.618350i | \(-0.787801\pi\) | ||||
−0.785903 | + | 0.618350i | \(0.787801\pi\) | |||||||
\(602\) | −31.0663 | −1.26617 | ||||||||
\(603\) | 33.0315 | 1.34514 | ||||||||
\(604\) | 1.69682 | 0.0690427 | ||||||||
\(605\) | −30.4118 | −1.23642 | ||||||||
\(606\) | −11.6852 | −0.474679 | ||||||||
\(607\) | −27.0515 | −1.09799 | −0.548994 | − | 0.835826i | \(-0.684989\pi\) | ||||
−0.548994 | + | 0.835826i | \(0.684989\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −74.3873 | −3.01433 | ||||||||
\(610\) | −3.95260 | −0.160036 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −28.5795 | −1.15526 | ||||||||
\(613\) | −13.6592 | −0.551691 | −0.275845 | − | 0.961202i | \(-0.588958\pi\) | ||||
−0.275845 | + | 0.961202i | \(0.588958\pi\) | |||||||
\(614\) | 15.7809 | 0.636864 | ||||||||
\(615\) | −34.8461 | −1.40513 | ||||||||
\(616\) | 1.00910 | 0.0406577 | ||||||||
\(617\) | −24.2233 | −0.975193 | −0.487597 | − | 0.873069i | \(-0.662126\pi\) | ||||
−0.487597 | + | 0.873069i | \(0.662126\pi\) | |||||||
\(618\) | −42.3294 | −1.70274 | ||||||||
\(619\) | 19.0506 | 0.765708 | 0.382854 | − | 0.923809i | \(-0.374941\pi\) | ||||
0.382854 | + | 0.923809i | \(0.374941\pi\) | |||||||
\(620\) | −15.0729 | −0.605343 | ||||||||
\(621\) | −12.0062 | −0.481792 | ||||||||
\(622\) | −0.504549 | −0.0202306 | ||||||||
\(623\) | 39.6999 | 1.59054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1811 | −1.24725 | ||||||||
\(626\) | 20.5871 | 0.822825 | ||||||||
\(627\) | −0.757172 | −0.0302385 | ||||||||
\(628\) | −7.47656 | −0.298347 | ||||||||
\(629\) | 10.3875 | 0.414175 | ||||||||
\(630\) | 36.6219 | 1.45905 | ||||||||
\(631\) | −22.6358 | −0.901116 | −0.450558 | − | 0.892747i | \(-0.648775\pi\) | ||||
−0.450558 | + | 0.892747i | \(0.648775\pi\) | |||||||
\(632\) | 9.88701 | 0.393284 | ||||||||
\(633\) | −1.18976 | −0.0472886 | ||||||||
\(634\) | 2.43826 | 0.0968357 | ||||||||
\(635\) | 21.8396 | 0.866679 | ||||||||
\(636\) | −33.5697 | −1.33113 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.39069 | −0.0946484 | ||||||||
\(639\) | −4.81505 | −0.190480 | ||||||||
\(640\) | −2.78611 | −0.110131 | ||||||||
\(641\) | 34.9057 | 1.37869 | 0.689347 | − | 0.724432i | \(-0.257898\pi\) | ||||
0.689347 | + | 0.724432i | \(0.257898\pi\) | |||||||
\(642\) | −20.9683 | −0.827554 | ||||||||
\(643\) | −15.7725 | −0.622005 | −0.311003 | − | 0.950409i | \(-0.600665\pi\) | ||||
−0.311003 | + | 0.950409i | \(0.600665\pi\) | |||||||
\(644\) | 20.3545 | 0.802079 | ||||||||
\(645\) | −64.9456 | −2.55723 | ||||||||
\(646\) | −7.54852 | −0.296993 | ||||||||
\(647\) | −38.6151 | −1.51812 | −0.759058 | − | 0.651023i | \(-0.774340\pi\) | ||||
−0.759058 | + | 0.651023i | \(0.774340\pi\) | |||||||
\(648\) | 6.02370 | 0.236633 | ||||||||
\(649\) | −1.61962 | −0.0635755 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.9281 | 1.91764 | ||||||||
\(652\) | 5.74465 | 0.224978 | ||||||||
\(653\) | −50.6059 | −1.98036 | −0.990182 | − | 0.139785i | \(-0.955359\pi\) | ||||
−0.990182 | + | 0.139785i | \(0.955359\pi\) | |||||||
\(654\) | 28.1989 | 1.10266 | ||||||||
\(655\) | 42.1807 | 1.64814 | ||||||||
\(656\) | −4.80115 | −0.187453 | ||||||||
\(657\) | −16.5157 | −0.644340 | ||||||||
\(658\) | 21.5114 | 0.838603 | ||||||||
\(659\) | −31.4982 | −1.22700 | −0.613498 | − | 0.789696i | \(-0.710238\pi\) | ||||
−0.613498 | + | 0.789696i | \(0.710238\pi\) | |||||||
\(660\) | 2.10956 | 0.0821147 | ||||||||
\(661\) | −20.2665 | −0.788277 | −0.394138 | − | 0.919051i | \(-0.628957\pi\) | ||||
−0.394138 | + | 0.919051i | \(0.628957\pi\) | |||||||
\(662\) | −13.7558 | −0.534636 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.4968 | −0.484971 | ||||||||
\(665\) | 9.67269 | 0.375091 | ||||||||
\(666\) | 5.21003 | 0.201885 | ||||||||
\(667\) | −48.2226 | −1.86719 | ||||||||
\(668\) | −21.4403 | −0.829552 | ||||||||
\(669\) | −19.8148 | −0.766084 | ||||||||
\(670\) | −24.3071 | −0.939064 | ||||||||
\(671\) | 0.412353 | 0.0159187 | ||||||||
\(672\) | 9.04397 | 0.348879 | ||||||||
\(673\) | −21.5018 | −0.828834 | −0.414417 | − | 0.910087i | \(-0.636015\pi\) | ||||
−0.414417 | + | 0.910087i | \(0.636015\pi\) | |||||||
\(674\) | 10.0909 | 0.388685 | ||||||||
\(675\) | 5.65695 | 0.217736 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.9882 | −0.691344 | −0.345672 | − | 0.938355i | \(-0.612349\pi\) | ||||
−0.345672 | + | 0.938355i | \(0.612349\pi\) | |||||||
\(678\) | −2.20865 | −0.0848226 | ||||||||
\(679\) | −19.2282 | −0.737912 | ||||||||
\(680\) | 21.0310 | 0.806503 | ||||||||
\(681\) | −62.5003 | −2.39502 | ||||||||
\(682\) | 1.57247 | 0.0602131 | ||||||||
\(683\) | 3.39909 | 0.130063 | 0.0650313 | − | 0.997883i | \(-0.479285\pi\) | ||||
0.0650313 | + | 0.997883i | \(0.479285\pi\) | |||||||
\(684\) | −3.78611 | −0.144766 | ||||||||
\(685\) | 45.8319 | 1.75115 | ||||||||
\(686\) | −6.75925 | −0.258070 | ||||||||
\(687\) | 18.2417 | 0.695963 | ||||||||
\(688\) | −8.94831 | −0.341151 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 42.5520 | 1.61993 | ||||||||
\(691\) | −3.51802 | −0.133832 | −0.0669158 | − | 0.997759i | \(-0.521316\pi\) | ||||
−0.0669158 | + | 0.997759i | \(0.521316\pi\) | |||||||
\(692\) | 2.17243 | 0.0825835 | ||||||||
\(693\) | −3.82055 | −0.145131 | ||||||||
\(694\) | 10.6335 | 0.403643 | ||||||||
\(695\) | −35.4166 | −1.34343 | ||||||||
\(696\) | −21.4264 | −0.812167 | ||||||||
\(697\) | 36.2416 | 1.37275 | ||||||||
\(698\) | 11.7572 | 0.445016 | ||||||||
\(699\) | −69.4839 | −2.62812 | ||||||||
\(700\) | −9.59042 | −0.362484 | ||||||||
\(701\) | −5.97219 | −0.225567 | −0.112783 | − | 0.993620i | \(-0.535977\pi\) | ||||
−0.112783 | + | 0.993620i | \(0.535977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.37609 | 0.0519003 | ||||||||
\(704\) | 0.290659 | 0.0109546 | ||||||||
\(705\) | 44.9707 | 1.69369 | ||||||||
\(706\) | −36.3071 | −1.36643 | ||||||||
\(707\) | −15.5731 | −0.585686 | ||||||||
\(708\) | −14.5157 | −0.545534 | ||||||||
\(709\) | −5.39138 | −0.202477 | −0.101239 | − | 0.994862i | \(-0.532281\pi\) | ||||
−0.101239 | + | 0.994862i | \(0.532281\pi\) | |||||||
\(710\) | 3.54328 | 0.132977 | ||||||||
\(711\) | −37.4333 | −1.40386 | ||||||||
\(712\) | 11.4351 | 0.428549 | ||||||||
\(713\) | 31.7183 | 1.18786 | ||||||||
\(714\) | −68.2687 | −2.55489 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.35695 | 0.274942 | ||||||||
\(717\) | 7.50459 | 0.280264 | ||||||||
\(718\) | −18.5736 | −0.693161 | ||||||||
\(719\) | 28.3167 | 1.05603 | 0.528017 | − | 0.849234i | \(-0.322936\pi\) | ||||
0.528017 | + | 0.849234i | \(0.322936\pi\) | |||||||
\(720\) | 10.5485 | 0.393120 | ||||||||
\(721\) | −56.4132 | −2.10094 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −40.9884 | −1.52438 | ||||||||
\(724\) | 18.3734 | 0.682841 | ||||||||
\(725\) | 22.7210 | 0.843838 | ||||||||
\(726\) | 28.4351 | 1.05533 | ||||||||
\(727\) | −28.8814 | −1.07115 | −0.535576 | − | 0.844487i | \(-0.679905\pi\) | ||||
−0.535576 | + | 0.844487i | \(0.679905\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.8103 | −1.43742 | ||||||||
\(730\) | 12.1535 | 0.449823 | ||||||||
\(731\) | 67.5465 | 2.49830 | ||||||||
\(732\) | 3.69569 | 0.136597 | ||||||||
\(733\) | −35.3948 | −1.30734 | −0.653668 | − | 0.756781i | \(-0.726771\pi\) | ||||
−0.653668 | + | 0.756781i | \(0.726771\pi\) | |||||||
\(734\) | −4.42873 | −0.163467 | ||||||||
\(735\) | 36.6745 | 1.35276 | ||||||||
\(736\) | 5.86288 | 0.216109 | ||||||||
\(737\) | 2.53582 | 0.0934081 | ||||||||
\(738\) | 18.1777 | 0.669129 | ||||||||
\(739\) | −35.6747 | −1.31231 | −0.656157 | − | 0.754624i | \(-0.727819\pi\) | ||||
−0.656157 | + | 0.754624i | \(0.727819\pi\) | |||||||
\(740\) | −3.83394 | −0.140939 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −44.7390 | −1.64242 | ||||||||
\(743\) | 4.75604 | 0.174482 | 0.0872411 | − | 0.996187i | \(-0.472195\pi\) | ||||
0.0872411 | + | 0.996187i | \(0.472195\pi\) | |||||||
\(744\) | 14.0932 | 0.516681 | ||||||||
\(745\) | −38.2941 | −1.40299 | ||||||||
\(746\) | −22.8590 | −0.836928 | ||||||||
\(747\) | 47.3144 | 1.73114 | ||||||||
\(748\) | −2.19405 | −0.0802223 | ||||||||
\(749\) | −27.9449 | −1.02108 | ||||||||
\(750\) | 16.2401 | 0.593005 | ||||||||
\(751\) | 7.69796 | 0.280902 | 0.140451 | − | 0.990088i | \(-0.455145\pi\) | ||||
0.140451 | + | 0.990088i | \(0.455145\pi\) | |||||||
\(752\) | 6.19613 | 0.225950 | ||||||||
\(753\) | 36.7194 | 1.33813 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.72753 | 0.172053 | ||||||||
\(756\) | −7.10956 | −0.258572 | ||||||||
\(757\) | −1.28610 | −0.0467443 | −0.0233721 | − | 0.999727i | \(-0.507440\pi\) | ||||
−0.0233721 | + | 0.999727i | \(0.507440\pi\) | |||||||
\(758\) | −7.55263 | −0.274324 | ||||||||
\(759\) | −4.43921 | −0.161133 | ||||||||
\(760\) | 2.78611 | 0.101063 | ||||||||
\(761\) | 9.65827 | 0.350112 | 0.175056 | − | 0.984558i | \(-0.443989\pi\) | ||||
0.175056 | + | 0.984558i | \(0.443989\pi\) | |||||||
\(762\) | −20.4201 | −0.739741 | ||||||||
\(763\) | 37.5812 | 1.36053 | ||||||||
\(764\) | 18.1923 | 0.658173 | ||||||||
\(765\) | −79.6258 | −2.87888 | ||||||||
\(766\) | −13.8900 | −0.501866 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.60502 | 0.0940004 | ||||||||
\(769\) | 21.6051 | 0.779098 | 0.389549 | − | 0.921006i | \(-0.372631\pi\) | ||||
0.389549 | + | 0.921006i | \(0.372631\pi\) | |||||||
\(770\) | 2.81146 | 0.101318 | ||||||||
\(771\) | −16.5611 | −0.596433 | ||||||||
\(772\) | 13.9734 | 0.502913 | ||||||||
\(773\) | −4.56376 | −0.164147 | −0.0820736 | − | 0.996626i | \(-0.526154\pi\) | ||||
−0.0820736 | + | 0.996626i | \(0.526154\pi\) | |||||||
\(774\) | 33.8793 | 1.21777 | ||||||||
\(775\) | −14.9447 | −0.536830 | ||||||||
\(776\) | −5.53848 | −0.198820 | ||||||||
\(777\) | 12.4453 | 0.446474 | ||||||||
\(778\) | 20.8952 | 0.749131 | ||||||||
\(779\) | 4.80115 | 0.172019 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.369651 | −0.0132271 | ||||||||
\(782\) | −44.2561 | −1.58259 | ||||||||
\(783\) | 16.8436 | 0.601939 | ||||||||
\(784\) | 5.05307 | 0.180467 | ||||||||
\(785\) | −20.8305 | −0.743473 | ||||||||
\(786\) | −39.4390 | −1.40674 | ||||||||
\(787\) | −0.533922 | −0.0190323 | −0.00951614 | − | 0.999955i | \(-0.503029\pi\) | ||||
−0.00951614 | + | 0.999955i | \(0.503029\pi\) | |||||||
\(788\) | −27.2855 | −0.972004 | ||||||||
\(789\) | −45.6816 | −1.62631 | ||||||||
\(790\) | 27.5463 | 0.980054 | ||||||||
\(791\) | −2.94351 | −0.104659 | ||||||||
\(792\) | −1.10047 | −0.0391034 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12.5175 | −0.444231 | ||||||||
\(795\) | −93.5290 | −3.31713 | ||||||||
\(796\) | 14.9773 | 0.530855 | ||||||||
\(797\) | 25.6716 | 0.909333 | 0.454667 | − | 0.890662i | \(-0.349758\pi\) | ||||
0.454667 | + | 0.890662i | \(0.349758\pi\) | |||||||
\(798\) | −9.04397 | −0.320153 | ||||||||
\(799\) | −46.7716 | −1.65466 | ||||||||
\(800\) | −2.76241 | −0.0976660 | ||||||||
\(801\) | −43.2946 | −1.52974 | ||||||||
\(802\) | −12.1517 | −0.429092 | ||||||||
\(803\) | −1.26791 | −0.0447436 | ||||||||
\(804\) | 22.7271 | 0.801525 | ||||||||
\(805\) | 56.7098 | 1.99876 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −56.9686 | −2.00539 | ||||||||
\(808\) | −4.48566 | −0.157805 | ||||||||
\(809\) | −12.2404 | −0.430348 | −0.215174 | − | 0.976576i | \(-0.569032\pi\) | ||||
−0.215174 | + | 0.976576i | \(0.569032\pi\) | |||||||
\(810\) | 16.7827 | 0.589684 | ||||||||
\(811\) | 13.6378 | 0.478888 | 0.239444 | − | 0.970910i | \(-0.423035\pi\) | ||||
0.239444 | + | 0.970910i | \(0.423035\pi\) | |||||||
\(812\) | −28.5554 | −1.00210 | ||||||||
\(813\) | 72.3169 | 2.53627 | ||||||||
\(814\) | 0.399974 | 0.0140191 | ||||||||
\(815\) | 16.0052 | 0.560639 | ||||||||
\(816\) | −19.6640 | −0.688379 | ||||||||
\(817\) | 8.94831 | 0.313062 | ||||||||
\(818\) | 27.5549 | 0.963434 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.3765 | −0.467129 | ||||||||
\(821\) | 1.60520 | 0.0560219 | 0.0280109 | − | 0.999608i | \(-0.491083\pi\) | ||||
0.0280109 | + | 0.999608i | \(0.491083\pi\) | |||||||
\(822\) | −42.8529 | −1.49467 | ||||||||
\(823\) | −56.3737 | −1.96506 | −0.982531 | − | 0.186098i | \(-0.940416\pi\) | ||||
−0.982531 | + | 0.186098i | \(0.940416\pi\) | |||||||
\(824\) | −16.2492 | −0.566068 | ||||||||
\(825\) | 2.09162 | 0.0728209 | ||||||||
\(826\) | −19.3454 | −0.673112 | ||||||||
\(827\) | 3.73537 | 0.129892 | 0.0649458 | − | 0.997889i | \(-0.479313\pi\) | ||||
0.0649458 | + | 0.997889i | \(0.479313\pi\) | |||||||
\(828\) | −22.1975 | −0.771417 | ||||||||
\(829\) | −13.3946 | −0.465213 | −0.232607 | − | 0.972571i | \(-0.574725\pi\) | ||||
−0.232607 | + | 0.972571i | \(0.574725\pi\) | |||||||
\(830\) | −34.8176 | −1.20854 | ||||||||
\(831\) | 59.0538 | 2.04855 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.1432 | −1.32158 | ||||||||
\(834\) | 33.1146 | 1.14666 | ||||||||
\(835\) | −59.7352 | −2.06722 | ||||||||
\(836\) | −0.290659 | −0.0100527 | ||||||||
\(837\) | −11.0788 | −0.382940 | ||||||||
\(838\) | −18.1109 | −0.625632 | ||||||||
\(839\) | 35.6369 | 1.23032 | 0.615161 | − | 0.788401i | \(-0.289091\pi\) | ||||
0.615161 | + | 0.788401i | \(0.289091\pi\) | |||||||
\(840\) | 25.1975 | 0.869397 | ||||||||
\(841\) | 38.6518 | 1.33282 | ||||||||
\(842\) | 10.8526 | 0.374007 | ||||||||
\(843\) | −37.4565 | −1.29007 | ||||||||
\(844\) | −0.456717 | −0.0157209 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.4592 | −0.806545 | ||||||||
\(847\) | 37.8960 | 1.30212 | ||||||||
\(848\) | −12.8866 | −0.442527 | ||||||||
\(849\) | 3.47379 | 0.119220 | ||||||||
\(850\) | 20.8521 | 0.715222 | ||||||||
\(851\) | 8.06786 | 0.276563 | ||||||||
\(852\) | −3.31297 | −0.113501 | ||||||||
\(853\) | 43.8953 | 1.50295 | 0.751473 | − | 0.659764i | \(-0.229344\pi\) | ||||
0.751473 | + | 0.659764i | \(0.229344\pi\) | |||||||
\(854\) | 4.92531 | 0.168541 | ||||||||
\(855\) | −10.5485 | −0.360752 | ||||||||
\(856\) | −8.04922 | −0.275117 | ||||||||
\(857\) | 48.5026 | 1.65682 | 0.828408 | − | 0.560125i | \(-0.189247\pi\) | ||||
0.828408 | + | 0.560125i | \(0.189247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.44787 | 0.0835203 | 0.0417601 | − | 0.999128i | \(-0.486703\pi\) | ||||
0.0417601 | + | 0.999128i | \(0.486703\pi\) | |||||||
\(860\) | −24.9310 | −0.850140 | ||||||||
\(861\) | 43.4214 | 1.47980 | ||||||||
\(862\) | −27.1681 | −0.925351 | ||||||||
\(863\) | −8.84127 | −0.300960 | −0.150480 | − | 0.988613i | \(-0.548082\pi\) | ||||
−0.150480 | + | 0.988613i | \(0.548082\pi\) | |||||||
\(864\) | −2.04783 | −0.0696686 | ||||||||
\(865\) | 6.05264 | 0.205796 | ||||||||
\(866\) | −1.63490 | −0.0555563 | ||||||||
\(867\) | 104.149 | 3.53709 | ||||||||
\(868\) | 18.7823 | 0.637511 | ||||||||
\(869\) | −2.87375 | −0.0974853 | ||||||||
\(870\) | −59.6964 | −2.02390 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.8248 | 0.366575 | ||||||||
\(873\) | 20.9693 | 0.709703 | ||||||||
\(874\) | −5.86288 | −0.198315 | ||||||||
\(875\) | 21.6435 | 0.731683 | ||||||||
\(876\) | −11.3636 | −0.383940 | ||||||||
\(877\) | −11.2932 | −0.381343 | −0.190672 | − | 0.981654i | \(-0.561067\pi\) | ||||
−0.190672 | + | 0.981654i | \(0.561067\pi\) | |||||||
\(878\) | 37.8206 | 1.27638 | ||||||||
\(879\) | −11.1019 | −0.374456 | ||||||||
\(880\) | 0.809809 | 0.0272986 | ||||||||
\(881\) | −13.5880 | −0.457790 | −0.228895 | − | 0.973451i | \(-0.573511\pi\) | ||||
−0.228895 | + | 0.973451i | \(0.573511\pi\) | |||||||
\(882\) | −19.1315 | −0.644191 | ||||||||
\(883\) | 17.5315 | 0.589983 | 0.294991 | − | 0.955500i | \(-0.404683\pi\) | ||||
0.294991 | + | 0.955500i | \(0.404683\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −40.4424 | −1.35946 | ||||||||
\(886\) | −9.70049 | −0.325894 | ||||||||
\(887\) | −30.0684 | −1.00960 | −0.504798 | − | 0.863237i | \(-0.668433\pi\) | ||||
−0.504798 | + | 0.863237i | \(0.668433\pi\) | |||||||
\(888\) | 3.58474 | 0.120296 | ||||||||
\(889\) | −27.2142 | −0.912735 | ||||||||
\(890\) | 31.8595 | 1.06793 | ||||||||
\(891\) | −1.75084 | −0.0586555 | ||||||||
\(892\) | −7.60640 | −0.254681 | ||||||||
\(893\) | −6.19613 | −0.207346 | ||||||||
\(894\) | 35.8050 | 1.19750 | ||||||||
\(895\) | 20.4973 | 0.685148 | ||||||||
\(896\) | 3.47175 | 0.115983 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.4381 | −0.748769 | ||||||||
\(899\) | −44.4978 | −1.48408 | ||||||||
\(900\) | 10.4588 | 0.348627 | ||||||||
\(901\) | 97.2746 | 3.24069 | ||||||||
\(902\) | 1.39550 | 0.0464650 | ||||||||
\(903\) | 80.9283 | 2.69313 | ||||||||
\(904\) | −0.847844 | −0.0281989 | ||||||||
\(905\) | 51.1902 | 1.70162 | ||||||||
\(906\) | −4.42025 | −0.146853 | ||||||||
\(907\) | −35.0422 | −1.16356 | −0.581778 | − | 0.813348i | \(-0.697643\pi\) | ||||
−0.581778 | + | 0.813348i | \(0.697643\pi\) | |||||||
\(908\) | −23.9923 | −0.796212 | ||||||||
\(909\) | 16.9832 | 0.563297 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.714766 | 0.0236813 | 0.0118406 | − | 0.999930i | \(-0.496231\pi\) | ||||
0.0118406 | + | 0.999930i | \(0.496231\pi\) | |||||||
\(912\) | −2.60502 | −0.0862607 | ||||||||
\(913\) | 3.63232 | 0.120212 | ||||||||
\(914\) | −2.85746 | −0.0945162 | ||||||||
\(915\) | 10.2966 | 0.340395 | ||||||||
\(916\) | 7.00252 | 0.231370 | ||||||||
\(917\) | −52.5611 | −1.73572 | ||||||||
\(918\) | 15.4581 | 0.510193 | ||||||||
\(919\) | 37.4522 | 1.23543 | 0.617717 | − | 0.786400i | \(-0.288058\pi\) | ||||
0.617717 | + | 0.786400i | \(0.288058\pi\) | |||||||
\(920\) | 16.3346 | 0.538537 | ||||||||
\(921\) | −41.1094 | −1.35460 | ||||||||
\(922\) | 27.5356 | 0.906836 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.62871 | −0.0864784 | ||||||||
\(925\) | −3.80133 | −0.124987 | ||||||||
\(926\) | 17.6784 | 0.580947 | ||||||||
\(927\) | 61.5213 | 2.02062 | ||||||||
\(928\) | −8.22507 | −0.270001 | ||||||||
\(929\) | −10.9426 | −0.359016 | −0.179508 | − | 0.983756i | \(-0.557451\pi\) | ||||
−0.179508 | + | 0.983756i | \(0.557451\pi\) | |||||||
\(930\) | 39.2652 | 1.28756 | ||||||||
\(931\) | −5.05307 | −0.165608 | ||||||||
\(932\) | −26.6731 | −0.873707 | ||||||||
\(933\) | 1.31436 | 0.0430301 | ||||||||
\(934\) | −29.7663 | −0.973984 | ||||||||
\(935\) | −6.11286 | −0.199912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.1216 | −0.592008 | −0.296004 | − | 0.955187i | \(-0.595654\pi\) | ||||
−0.296004 | + | 0.955187i | \(0.595654\pi\) | |||||||
\(938\) | 30.2889 | 0.988967 | ||||||||
\(939\) | −53.6297 | −1.75014 | ||||||||
\(940\) | 17.2631 | 0.563060 | ||||||||
\(941\) | 39.9721 | 1.30305 | 0.651526 | − | 0.758626i | \(-0.274129\pi\) | ||||
0.651526 | + | 0.758626i | \(0.274129\pi\) | |||||||
\(942\) | 19.4766 | 0.634581 | ||||||||
\(943\) | 28.1485 | 0.916643 | ||||||||
\(944\) | −5.57222 | −0.181360 | ||||||||
\(945\) | −19.8080 | −0.644355 | ||||||||
\(946\) | 2.60091 | 0.0845629 | ||||||||
\(947\) | −14.1216 | −0.458892 | −0.229446 | − | 0.973321i | \(-0.573691\pi\) | ||||
−0.229446 | + | 0.973321i | \(0.573691\pi\) | |||||||
\(948\) | −25.7558 | −0.836511 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.76241 | 0.0896245 | ||||||||
\(951\) | −6.35171 | −0.205968 | ||||||||
\(952\) | −26.2066 | −0.849361 | ||||||||
\(953\) | −60.3061 | −1.95351 | −0.976753 | − | 0.214370i | \(-0.931230\pi\) | ||||
−0.976753 | + | 0.214370i | \(0.931230\pi\) | |||||||
\(954\) | 48.7900 | 1.57963 | ||||||||
\(955\) | 50.6857 | 1.64015 | ||||||||
\(956\) | 2.88082 | 0.0931725 | ||||||||
\(957\) | 6.22779 | 0.201316 | ||||||||
\(958\) | −29.1907 | −0.943108 | ||||||||
\(959\) | −57.1108 | −1.84420 | ||||||||
\(960\) | 7.25786 | 0.234247 | ||||||||
\(961\) | −1.73169 | −0.0558609 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.4752 | 0.982050 | ||||||||
\(964\) | −15.7344 | −0.506772 | ||||||||
\(965\) | 38.9314 | 1.25325 | ||||||||
\(966\) | −53.0237 | −1.70601 | ||||||||
\(967\) | −1.06633 | −0.0342910 | −0.0171455 | − | 0.999853i | \(-0.505458\pi\) | ||||
−0.0171455 | + | 0.999853i | \(0.505458\pi\) | |||||||
\(968\) | 10.9155 | 0.350838 | ||||||||
\(969\) | 19.6640 | 0.631700 | ||||||||
\(970\) | −15.4308 | −0.495453 | ||||||||
\(971\) | 41.1051 | 1.31912 | 0.659562 | − | 0.751650i | \(-0.270742\pi\) | ||||
0.659562 | + | 0.751650i | \(0.270742\pi\) | |||||||
\(972\) | −21.8353 | −0.700368 | ||||||||
\(973\) | 44.1324 | 1.41482 | ||||||||
\(974\) | 23.4246 | 0.750573 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.41868 | 0.0454109 | ||||||||
\(977\) | −29.1331 | −0.932049 | −0.466025 | − | 0.884772i | \(-0.654314\pi\) | ||||
−0.466025 | + | 0.884772i | \(0.654314\pi\) | |||||||
\(978\) | −14.9649 | −0.478525 | ||||||||
\(979\) | −3.32372 | −0.106226 | ||||||||
\(980\) | 14.0784 | 0.449719 | ||||||||
\(981\) | −40.9841 | −1.30852 | ||||||||
\(982\) | −26.5137 | −0.846086 | ||||||||
\(983\) | −45.1403 | −1.43975 | −0.719877 | − | 0.694102i | \(-0.755802\pi\) | ||||
−0.719877 | + | 0.694102i | \(0.755802\pi\) | |||||||
\(984\) | 12.5071 | 0.398711 | ||||||||
\(985\) | −76.0203 | −2.42221 | ||||||||
\(986\) | 62.0871 | 1.97726 | ||||||||
\(987\) | −56.0376 | −1.78370 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.4629 | 1.66822 | ||||||||
\(990\) | −3.06603 | −0.0974447 | ||||||||
\(991\) | −26.4501 | −0.840216 | −0.420108 | − | 0.907474i | \(-0.638008\pi\) | ||||
−0.420108 | + | 0.907474i | \(0.638008\pi\) | |||||||
\(992\) | 5.41002 | 0.171768 | ||||||||
\(993\) | 35.8342 | 1.13716 | ||||||||
\(994\) | −4.41526 | −0.140044 | ||||||||
\(995\) | 41.7283 | 1.32288 | ||||||||
\(996\) | 32.5545 | 1.03153 | ||||||||
\(997\) | 49.1290 | 1.55593 | 0.777966 | − | 0.628307i | \(-0.216252\pi\) | ||||
0.777966 | + | 0.628307i | \(0.216252\pi\) | |||||||
\(998\) | −25.0203 | −0.792003 | ||||||||
\(999\) | −2.81800 | −0.0891576 |
(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 | 6422.2.a.ba.1.4 | 4 | ||
13.12 | even | 2 | 494.2.a.h.1.4 | ✓ | 4 | ||
39.38 | odd | 2 | 4446.2.a.bl.1.4 | 4 | |||
52.51 | odd | 2 | 3952.2.a.u.1.1 | 4 | |||
247.246 | odd | 2 | 9386.2.a.bf.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.a.h.1.4 | ✓ | 4 | 13.12 | even | 2 | ||
3952.2.a.u.1.1 | 4 | 52.51 | odd | 2 | |||
4446.2.a.bl.1.4 | 4 | 39.38 | odd | 2 | |||
6422.2.a.ba.1.4 | 4 | 1.1 | even | 1 | trivial | ||
9386.2.a.bf.1.1 | 4 | 247.246 | odd | 2 |