Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3640,2,Mod(1,3640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3640.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: | \(29.0655463357\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.75660\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3640.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.75660 | 1.01417 | 0.507086 | − | 0.861895i | \(-0.330723\pi\) | ||||
0.507086 | + | 0.861895i | \(0.330723\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0856374 | 0.0285458 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.23607 | −0.975711 | −0.487856 | − | 0.872924i | \(-0.662221\pi\) | ||||
−0.487856 | + | 0.872924i | \(0.662221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.75660 | 0.453552 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.59883 | −1.11538 | −0.557691 | − | 0.830049i | \(-0.688312\pi\) | ||||
−0.557691 | + | 0.830049i | \(0.688312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.150431 | 0.0345111 | 0.0172556 | − | 0.999851i | \(-0.494507\pi\) | ||||
0.0172556 | + | 0.999851i | \(0.494507\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.75660 | −0.383321 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.40734 | 0.293451 | 0.146726 | − | 0.989177i | \(-0.453127\pi\) | ||||
0.146726 | + | 0.989177i | \(0.453127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.11936 | −0.985222 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.67714 | −1.61130 | −0.805652 | − | 0.592389i | \(-0.798185\pi\) | ||||
−0.805652 | + | 0.592389i | \(0.798185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.96893 | −0.892447 | −0.446223 | − | 0.894922i | \(-0.647231\pi\) | ||||
−0.446223 | + | 0.894922i | \(0.647231\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.68447 | −0.989539 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.520530 | −0.0855747 | −0.0427873 | − | 0.999084i | \(-0.513624\pi\) | ||||
−0.0427873 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.75660 | 0.281281 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.55777 | 0.555631 | 0.277815 | − | 0.960634i | \(-0.410390\pi\) | ||||
0.277815 | + | 0.960634i | \(0.410390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.277129 | 0.0422617 | 0.0211309 | − | 0.999777i | \(-0.493273\pi\) | ||||
0.0211309 | + | 0.999777i | \(0.493273\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0856374 | 0.0127661 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.1155 | −1.62137 | −0.810685 | − | 0.585483i | \(-0.800905\pi\) | ||||
−0.810685 | + | 0.585483i | \(0.800905\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.07830 | −1.13119 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.171275 | 0.0235264 | 0.0117632 | − | 0.999931i | \(-0.496256\pi\) | ||||
0.0117632 | + | 0.999931i | \(0.496256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23607 | −0.436351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.264246 | 0.0350002 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.78362 | 1.01334 | 0.506670 | − | 0.862140i | \(-0.330876\pi\) | ||||
0.506670 | + | 0.862140i | \(0.330876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.68447 | 0.471748 | 0.235874 | − | 0.971784i | \(-0.424205\pi\) | ||||
0.235874 | + | 0.971784i | \(0.424205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0856374 | −0.0107893 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.95542 | −0.238893 | −0.119446 | − | 0.992841i | \(-0.538112\pi\) | ||||
−0.119446 | + | 0.992841i | \(0.538112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.47214 | 0.297610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.55160 | −0.184141 | −0.0920703 | − | 0.995753i | \(-0.529348\pi\) | ||||
−0.0920703 | + | 0.995753i | \(0.529348\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.85575 | 0.685363 | 0.342682 | − | 0.939452i | \(-0.388665\pi\) | ||||
0.342682 | + | 0.939452i | \(0.388665\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.75660 | 0.202834 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23607 | 0.368784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00352 | −0.562940 | −0.281470 | − | 0.959570i | \(-0.590822\pi\) | ||||
−0.281470 | + | 0.959570i | \(0.590822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.24958 | −1.02773 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.3279 | −1.13363 | −0.566816 | − | 0.823844i | \(-0.691825\pi\) | ||||
−0.566816 | + | 0.823844i | \(0.691825\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.59883 | −0.498814 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.2422 | −1.63414 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4918 | −1.64213 | −0.821065 | − | 0.570835i | \(-0.806620\pi\) | ||||
−0.821065 | + | 0.570835i | \(0.806620\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.72842 | −0.905095 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.150431 | 0.0154338 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.869786 | 0.0883134 | 0.0441567 | − | 0.999025i | \(-0.485940\pi\) | ||||
0.0441567 | + | 0.999025i | \(0.485940\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.277129 | −0.0278525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.08212 | −0.406186 | −0.203093 | − | 0.979159i | \(-0.565099\pi\) | ||||
−0.203093 | + | 0.979159i | \(0.565099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.41023 | 0.336020 | 0.168010 | − | 0.985785i | \(-0.446266\pi\) | ||||
0.168010 | + | 0.985785i | \(0.446266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.75660 | −0.171426 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.4067 | −1.00606 | −0.503028 | − | 0.864270i | \(-0.667781\pi\) | ||||
−0.503028 | + | 0.864270i | \(0.667781\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1566 | 0.972827 | 0.486413 | − | 0.873729i | \(-0.338305\pi\) | ||||
0.486413 | + | 0.873729i | \(0.338305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.914363 | −0.0867875 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.19767 | 0.677100 | 0.338550 | − | 0.940948i | \(-0.390064\pi\) | ||||
0.338550 | + | 0.940948i | \(0.390064\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.40734 | 0.131235 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0856374 | 0.00791718 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.59883 | 0.421574 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.24958 | 0.563506 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.23607 | −0.287155 | −0.143577 | − | 0.989639i | \(-0.545861\pi\) | ||||
−0.143577 | + | 0.989639i | \(0.545861\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.486803 | 0.0428607 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.3132 | 1.07581 | 0.537905 | − | 0.843005i | \(-0.319216\pi\) | ||||
0.537905 | + | 0.843005i | \(0.319216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.150431 | −0.0130440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.11936 | −0.440605 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.308823 | 0.0263845 | 0.0131923 | − | 0.999913i | \(-0.495801\pi\) | ||||
0.0131923 | + | 0.999913i | \(0.495801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.740199 | −0.0627829 | −0.0313914 | − | 0.999507i | \(-0.509994\pi\) | ||||
−0.0313914 | + | 0.999507i | \(0.509994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.5256 | −1.64435 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.23607 | −0.270614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.67714 | −0.720597 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.75660 | 0.144882 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.04809 | −0.413556 | −0.206778 | − | 0.978388i | \(-0.566298\pi\) | ||||
−0.206778 | + | 0.978388i | \(0.566298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.43436 | 0.605000 | 0.302500 | − | 0.953149i | \(-0.402179\pi\) | ||||
0.302500 | + | 0.953149i | \(0.402179\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.393832 | −0.0318395 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.96893 | −0.399114 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.3059 | −1.54078 | −0.770389 | − | 0.637575i | \(-0.779938\pi\) | ||||
−0.770389 | + | 0.637575i | \(0.779938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.300861 | 0.0238598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.40734 | −0.110914 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6361 | −1.38136 | −0.690682 | − | 0.723159i | \(-0.742690\pi\) | ||||
−0.690682 | + | 0.723159i | \(0.742690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.68447 | −0.442535 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5256 | 1.51093 | 0.755466 | − | 0.655188i | \(-0.227410\pi\) | ||||
0.755466 | + | 0.655188i | \(0.227410\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0128825 | 0.000985148 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.07479 | 0.0817146 | 0.0408573 | − | 0.999165i | \(-0.486991\pi\) | ||||
0.0408573 | + | 0.999165i | \(0.486991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.6727 | 1.02770 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.07160 | −0.304326 | −0.152163 | − | 0.988355i | \(-0.548624\pi\) | ||||
−0.152163 | + | 0.988355i | \(0.548624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.9907 | 1.93187 | 0.965935 | − | 0.258785i | \(-0.0833220\pi\) | ||||
0.965935 | + | 0.258785i | \(0.0833220\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.47214 | 0.478434 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.520530 | −0.0382701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.8821 | 1.08829 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.11936 | 0.372379 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9927 | −1.22955 | −0.614773 | − | 0.788704i | \(-0.710752\pi\) | ||||
−0.614773 | + | 0.788704i | \(0.710752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.4874 | 1.61868 | 0.809338 | − | 0.587343i | \(-0.199826\pi\) | ||||
0.809338 | + | 0.587343i | \(0.199826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.75660 | 0.125793 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.11585 | −0.150748 | −0.0753740 | − | 0.997155i | \(-0.524015\pi\) | ||||
−0.0753740 | + | 0.997155i | \(0.524015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.13491 | 0.576668 | 0.288334 | − | 0.957530i | \(-0.406899\pi\) | ||||
0.288334 | + | 0.957530i | \(0.406899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.43489 | −0.242279 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.67714 | 0.609016 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.55777 | 0.248486 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.120521 | 0.00837680 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.486803 | −0.0336729 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.6663 | −1.28504 | −0.642520 | − | 0.766269i | \(-0.722111\pi\) | ||||
−0.642520 | + | 0.766269i | \(0.722111\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.72553 | −0.186750 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.277129 | 0.0189000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.96893 | 0.337313 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.2862 | 0.695077 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.59883 | −0.309351 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8885 | 1.19791 | 0.598953 | − | 0.800784i | \(-0.295584\pi\) | ||||
0.598953 | + | 0.800784i | \(0.295584\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0856374 | 0.00570916 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.59532 | −0.636864 | −0.318432 | − | 0.947946i | \(-0.603156\pi\) | ||||
−0.318432 | + | 0.947946i | \(0.603156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9267 | 0.986385 | 0.493193 | − | 0.869920i | \(-0.335830\pi\) | ||||
0.493193 | + | 0.869920i | \(0.335830\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.68447 | 0.374011 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.64404 | −0.107705 | −0.0538523 | − | 0.998549i | \(-0.517150\pi\) | ||||
−0.0538523 | + | 0.998549i | \(0.517150\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.1155 | −0.725098 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.78917 | −0.570918 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.32459 | 0.538473 | 0.269237 | − | 0.963074i | \(-0.413229\pi\) | ||||
0.269237 | + | 0.963074i | \(0.413229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8446 | −1.08506 | −0.542528 | − | 0.840038i | \(-0.682533\pi\) | ||||
−0.542528 | + | 0.840038i | \(0.682533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.889701 | −0.0570743 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.150431 | 0.00957167 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.1419 | −1.14970 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.66277 | 0.357431 | 0.178715 | − | 0.983901i | \(-0.442806\pi\) | ||||
0.178715 | + | 0.983901i | \(0.442806\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.55426 | −0.286324 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.07830 | −0.505883 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2868 | 0.953566 | 0.476783 | − | 0.879021i | \(-0.341803\pi\) | ||||
0.476783 | + | 0.879021i | \(0.341803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.520530 | 0.0323442 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.743088 | −0.0459960 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6942 | −0.659430 | −0.329715 | − | 0.944080i | \(-0.606953\pi\) | ||||
−0.329715 | + | 0.944080i | \(0.606953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.171275 | 0.0105213 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.2129 | −1.66540 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.521459 | −0.0317939 | −0.0158970 | − | 0.999874i | \(-0.505060\pi\) | ||||
−0.0158970 | + | 0.999874i | \(0.505060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.29883 | −0.261135 | −0.130568 | − | 0.991439i | \(-0.541680\pi\) | ||||
−0.130568 | + | 0.991439i | \(0.541680\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.75660 | −0.106314 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.23607 | −0.195142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.58128 | −0.275262 | −0.137631 | − | 0.990484i | \(-0.543949\pi\) | ||||
−0.137631 | + | 0.990484i | \(0.543949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.425527 | −0.0254756 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.04809 | −0.301144 | −0.150572 | − | 0.988599i | \(-0.548112\pi\) | ||||
−0.150572 | + | 0.988599i | \(0.548112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.2777 | −1.68093 | −0.840467 | − | 0.541862i | \(-0.817720\pi\) | ||||
−0.840467 | + | 0.541862i | \(0.817720\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.264246 | 0.0156526 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.55777 | −0.210009 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.14927 | 0.244075 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.52786 | 0.0895650 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.7109 | 0.625735 | 0.312868 | − | 0.949797i | \(-0.398710\pi\) | ||||
0.312868 | + | 0.949797i | \(0.398710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.78362 | 0.453180 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.5666 | 0.961292 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.40734 | 0.0813887 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.277129 | −0.0159734 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.17065 | −0.411943 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.68447 | 0.210972 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.74660 | 0.213830 | 0.106915 | − | 0.994268i | \(-0.465903\pi\) | ||||
0.106915 | + | 0.994268i | \(0.465903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.99041 | 0.340782 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.01404 | −0.397730 | −0.198865 | − | 0.980027i | \(-0.563725\pi\) | ||||
−0.198865 | + | 0.980027i | \(0.563725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6778 | −0.660066 | −0.330033 | − | 0.943969i | \(-0.607060\pi\) | ||||
−0.330033 | + | 0.943969i | \(0.607060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0856374 | −0.00482512 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.6070 | 1.83139 | 0.915697 | − | 0.401869i | \(-0.131639\pi\) | ||||
0.915697 | + | 0.401869i | \(0.131639\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.0798 | 1.57217 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.2804 | −1.02031 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.691805 | −0.0384931 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.8411 | 0.986614 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.1155 | 0.612820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.2561 | −1.27827 | −0.639134 | − | 0.769095i | \(-0.720707\pi\) | ||||
−0.639134 | + | 0.769095i | \(0.720707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0445769 | −0.00244280 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.95542 | −0.106836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6575 | 0.743969 | 0.371984 | − | 0.928239i | \(-0.378677\pi\) | ||||
0.371984 | + | 0.928239i | \(0.378677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.6434 | 0.686696 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0798 | 0.870770 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.47214 | 0.133095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.87245 | −0.315249 | −0.157625 | − | 0.987499i | \(-0.550384\pi\) | ||||
−0.157625 | + | 0.987499i | \(0.550384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9576 | 0.800660 | 0.400330 | − | 0.916371i | \(-0.368896\pi\) | ||||
0.400330 | + | 0.916371i | \(0.368896\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.11936 | −0.273251 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.3343 | −1.02906 | −0.514530 | − | 0.857472i | \(-0.672034\pi\) | ||||
−0.514530 | + | 0.857472i | \(0.672034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.55160 | −0.0823502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.07830 | 0.427549 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.1863 | 1.11817 | 0.559085 | − | 0.829110i | \(-0.311153\pi\) | ||||
0.559085 | + | 0.829110i | \(0.311153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9774 | −0.998809 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.927245 | −0.0486677 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.85575 | 0.306504 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2765 | −0.693028 | −0.346514 | − | 0.938045i | \(-0.612635\pi\) | ||||
−0.346514 | + | 0.938045i | \(0.612635\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.304679 | 0.0158609 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.171275 | −0.00889215 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.1613 | 0.888578 | 0.444289 | − | 0.895883i | \(-0.353456\pi\) | ||||
0.444289 | + | 0.895883i | \(0.353456\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.75660 | 0.0907103 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.67714 | −0.446895 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.6167 | −1.21311 | −0.606555 | − | 0.795041i | \(-0.707449\pi\) | ||||
−0.606555 | + | 0.795041i | \(0.707449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.68447 | −0.291224 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.88151 | 0.402726 | 0.201363 | − | 0.979517i | \(-0.435463\pi\) | ||||
0.201363 | + | 0.979517i | \(0.435463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.23607 | 0.164925 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0237326 | 0.00120639 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.3865 | 0.678722 | 0.339361 | − | 0.940656i | \(-0.389789\pi\) | ||||
0.339361 | + | 0.940656i | \(0.389789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.47214 | −0.327310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.6294 | 1.09106 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.00352 | −0.251754 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.25108 | −0.414110 | −0.207055 | − | 0.978329i | \(-0.566388\pi\) | ||||
−0.207055 | + | 0.978329i | \(0.566388\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.264246 | −0.0132288 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8388 | 1.49008 | 0.745038 | − | 0.667022i | \(-0.232431\pi\) | ||||
0.745038 | + | 0.667022i | \(0.232431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.96893 | −0.247520 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.24958 | −0.459615 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.68447 | 0.0834961 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.1085 | −0.944855 | −0.472428 | − | 0.881369i | \(-0.656622\pi\) | ||||
−0.472428 | + | 0.881369i | \(0.656622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.542478 | 0.0267585 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.78362 | −0.383007 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.3279 | −0.506976 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.30023 | −0.0636727 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1560 | −0.642712 | −0.321356 | − | 0.946959i | \(-0.604139\pi\) | ||||
−0.321356 | + | 0.946959i | \(0.604139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.951907 | −0.0462833 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.59883 | −0.223076 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.68447 | −0.178304 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.68447 | −0.274449 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7463 | −1.24016 | −0.620078 | − | 0.784540i | \(-0.712899\pi\) | ||||
−0.620078 | + | 0.784540i | \(0.712899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.2182 | 1.50025 | 0.750126 | − | 0.661295i | \(-0.229993\pi\) | ||||
0.750126 | + | 0.661295i | \(0.229993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.2422 | −0.730810 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.211707 | 0.0101273 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.70554 | 0.129129 | 0.0645643 | − | 0.997914i | \(-0.479434\pi\) | ||||
0.0645643 | + | 0.997914i | \(0.479434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0856374 | 0.00407797 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.2144 | −0.912902 | −0.456451 | − | 0.889749i | \(-0.650880\pi\) | ||||
−0.456451 | + | 0.889749i | \(0.650880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.4918 | −0.734383 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.86747 | −0.419417 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.8287 | 0.558232 | 0.279116 | − | 0.960257i | \(-0.409959\pi\) | ||||
0.279116 | + | 0.960257i | \(0.409959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.5132 | −0.542135 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.0592 | 0.613574 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00000 | −0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.96627 | 0.185534 | 0.0927672 | − | 0.995688i | \(-0.470429\pi\) | ||||
0.0927672 | + | 0.995688i | \(0.470429\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.5431 | 1.09890 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.724603 | 0.0337481 | 0.0168741 | − | 0.999858i | \(-0.494629\pi\) | ||||
0.0168741 | + | 0.999858i | \(0.494629\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.6112 | −0.493144 | −0.246572 | − | 0.969125i | \(-0.579304\pi\) | ||||
−0.246572 | + | 0.969125i | \(0.579304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.72842 | −0.404771 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −42.4613 | −1.96488 | −0.982438 | − | 0.186589i | \(-0.940257\pi\) | ||||
−0.982438 | + | 0.186589i | \(0.940257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.95542 | 0.0902931 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.9127 | −1.56261 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.896807 | −0.0412352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.150431 | 0.00690223 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0146675 | 0.000671580 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.5349 | 1.02965 | 0.514823 | − | 0.857296i | \(-0.327858\pi\) | ||||
0.514823 | + | 0.857296i | \(0.327858\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.520530 | −0.0237341 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.47214 | −0.112486 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.869786 | 0.0394949 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.41671 | 0.381397 | 0.190699 | − | 0.981649i | \(-0.438925\pi\) | ||||
0.190699 | + | 0.981649i | \(0.438925\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.9795 | −1.40094 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.2909 | −1.68291 | −0.841457 | − | 0.540324i | \(-0.818302\pi\) | ||||
−0.841457 | + | 0.540324i | \(0.818302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.9047 | 1.79722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.277129 | −0.0124560 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.55160 | 0.0695986 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6250 | 0.833769 | 0.416885 | − | 0.908959i | \(-0.363122\pi\) | ||||
0.416885 | + | 0.908959i | \(0.363122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.2985 | 1.53235 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.0074 | −1.38255 | −0.691275 | − | 0.722591i | \(-0.742951\pi\) | ||||
−0.691275 | + | 0.722591i | \(0.742951\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.08212 | −0.181652 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.75660 | 0.0780133 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.15246 | −0.272703 | −0.136352 | − | 0.990661i | \(-0.543538\pi\) | ||||
−0.136352 | + | 0.990661i | \(0.543538\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.85575 | −0.259043 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.770109 | −0.0340011 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.41023 | 0.150273 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.9707 | 1.58199 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.88797 | 0.0828727 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.1690 | −1.84746 | −0.923728 | − | 0.383049i | \(-0.874874\pi\) | ||||
−0.923728 | + | 0.383049i | \(0.874874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.9599 | 1.00397 | 0.501983 | − | 0.864877i | \(-0.332604\pi\) | ||||
0.501983 | + | 0.864877i | \(0.332604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.75660 | −0.0766642 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.8513 | 0.995418 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0194 | −0.913886 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.666569 | 0.0289266 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.55777 | 0.154104 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.4067 | −0.449922 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.15216 | −0.308639 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.23607 | −0.139387 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.97830 | 0.429001 | 0.214500 | − | 0.976724i | \(-0.431188\pi\) | ||||
0.214500 | + | 0.976724i | \(0.431188\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.6551 | 1.95925 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.1566 | 0.435061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.3088 | −0.911100 | −0.455550 | − | 0.890210i | \(-0.650557\pi\) | ||||
−0.455550 | + | 0.890210i | \(0.650557\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.315529 | 0.0134664 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.30531 | −0.0556079 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.00352 | 0.212771 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.914363 | −0.0388125 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.0582 | 0.553292 | 0.276646 | − | 0.960972i | \(-0.410777\pi\) | ||||
0.276646 | + | 0.960972i | \(0.410777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.277129 | 0.0117213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.1419 | 1.10371 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.6413 | 0.743493 | 0.371747 | − | 0.928334i | \(-0.378759\pi\) | ||||
0.371747 | + | 0.928334i | \(0.378759\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.19767 | 0.302808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.24958 | 0.388446 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.3756 | −0.560736 | −0.280368 | − | 0.959893i | \(-0.590457\pi\) | ||||
−0.280368 | + | 0.959893i | \(0.590457\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.20563 | 0.301546 | 0.150773 | − | 0.988568i | \(-0.451824\pi\) | ||||
0.150773 | + | 0.988568i | \(0.451824\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.8493 | −1.24697 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.40734 | 0.0586903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.6622 | 1.23485 | 0.617426 | − | 0.786629i | \(-0.288175\pi\) | ||||
0.617426 | + | 0.786629i | \(0.288175\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.5013 | 1.64162 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3279 | 0.428473 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.554257 | −0.0229550 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0856374 | 0.00354067 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.5660 | 1.22032 | 0.610159 | − | 0.792279i | \(-0.291105\pi\) | ||||
0.610159 | + | 0.792279i | \(0.291105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.747479 | −0.0307994 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.71669 | −0.152884 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 48.3309 | 1.98471 | 0.992356 | − | 0.123409i | \(-0.0393828\pi\) | ||||
0.992356 | + | 0.123409i | \(0.0393828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.59883 | 0.188534 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2898 | 0.584841 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.0739 | 1.26964 | 0.634822 | − | 0.772659i | \(-0.281074\pi\) | ||||
0.634822 | + | 0.772659i | \(0.281074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9660 | −0.447311 | −0.223656 | − | 0.974668i | \(-0.571799\pi\) | ||||
−0.223656 | + | 0.974668i | \(0.571799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.167457 | −0.00681939 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.527864 | −0.0214607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5977 | 0.795445 | 0.397723 | − | 0.917506i | \(-0.369801\pi\) | ||||
0.397723 | + | 0.917506i | \(0.369801\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.2422 | 0.617647 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.1155 | −0.449687 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.7907 | −1.24362 | −0.621812 | − | 0.783167i | \(-0.713603\pi\) | ||||
−0.621812 | + | 0.783167i | \(0.713603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.24958 | 0.252007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.1725 | −0.771855 | −0.385927 | − | 0.922529i | \(-0.626118\pi\) | ||||
−0.385927 | + | 0.922529i | \(0.626118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.1590 | −0.890644 | −0.445322 | − | 0.895370i | \(-0.646911\pi\) | ||||
−0.445322 | + | 0.895370i | \(0.646911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.20470 | −0.289115 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.4918 | 0.620667 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.855118 | −0.0341501 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.39383 | 0.0954483 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.97627 | 0.317530 | 0.158765 | − | 0.987316i | \(-0.449249\pi\) | ||||
0.158765 | + | 0.987316i | \(0.449249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.7892 | −1.30325 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.23607 | −0.128419 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.132875 | −0.00525644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.27540 | −0.129370 | −0.0646852 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646852 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.97956 | 0.393555 | 0.196778 | − | 0.980448i | \(-0.436952\pi\) | ||||
0.196778 | + | 0.980448i | \(0.436952\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.486803 | 0.0191679 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.3238 | −1.62461 | −0.812304 | − | 0.583235i | \(-0.801787\pi\) | ||||
−0.812304 | + | 0.583235i | \(0.801787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.1883 | −0.988728 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.72842 | 0.342094 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.4715 | 0.683713 | 0.341856 | − | 0.939752i | \(-0.388944\pi\) | ||||
0.341856 | + | 0.939752i | \(0.388944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.3132 | 0.481117 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.501471 | 0.0195642 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.08270 | −0.236948 | −0.118474 | − | 0.992957i | \(-0.537800\pi\) | ||||
−0.118474 | + | 0.992957i | \(0.537800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.5825 | −1.22842 | −0.614208 | − | 0.789144i | \(-0.710524\pi\) | ||||
−0.614208 | + | 0.789144i | \(0.710524\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.07830 | −0.313735 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.150431 | −0.00583345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.2117 | −0.472839 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.4230 | 1.21488 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.9232 | −0.460290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.72490 | 0.374867 | 0.187434 | − | 0.982277i | \(-0.439983\pi\) | ||||
0.187434 | + | 0.982277i | \(0.439983\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.11936 | −0.197044 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.2592 | 0.394292 | 0.197146 | − | 0.980374i | \(-0.436833\pi\) | ||||
0.197146 | + | 0.980374i | \(0.436833\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.869786 | −0.0333793 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.8551 | −0.645890 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.6376 | −0.827939 | −0.413970 | − | 0.910291i | \(-0.635858\pi\) | ||||
−0.413970 | + | 0.910291i | \(0.635858\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.308823 | 0.0117995 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.2202 | 1.00036 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.171275 | 0.00652505 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6804 | −0.482386 | −0.241193 | − | 0.970477i | \(-0.577539\pi\) | ||||
−0.241193 | + | 0.970477i | \(0.577539\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.277129 | 0.0105272 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.740199 | −0.0280774 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.3616 | −0.619740 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.88792 | −0.109231 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.8446 | 1.39160 | 0.695801 | − | 0.718235i | \(-0.255050\pi\) | ||||
0.695801 | + | 0.718235i | \(0.255050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0783037 | −0.00295328 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.5256 | −0.735375 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.08212 | 0.153524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.89743 | −0.0712597 | −0.0356298 | − | 0.999365i | \(-0.511344\pi\) | ||||
−0.0356298 | + | 0.999365i | \(0.511344\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.428488 | −0.0160696 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.99299 | −0.261890 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.23607 | −0.121022 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.6230 | 0.546105 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.6558 | −1.06868 | −0.534340 | − | 0.845270i | \(-0.679440\pi\) | ||||
−0.534340 | + | 0.845270i | \(0.679440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.41023 | −0.127004 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.5892 | −1.10043 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.67714 | −0.322261 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.8504 | 1.36671 | 0.683354 | − | 0.730087i | \(-0.260521\pi\) | ||||
0.683354 | + | 0.730087i | \(0.260521\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.1859 | 0.969848 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.27447 | −0.0471379 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.2651 | 1.15480 | 0.577402 | − | 0.816460i | \(-0.304067\pi\) | ||||
0.577402 | + | 0.816460i | \(0.304067\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.75660 | 0.0647931 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.32788 | 0.233091 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.09287 | 0.113773 | 0.0568866 | − | 0.998381i | \(-0.481883\pi\) | ||||
0.0568866 | + | 0.998381i | \(0.481883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.264246 | 0.00970732 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.97355 | −0.365894 | −0.182947 | − | 0.983123i | \(-0.558564\pi\) | ||||
−0.182947 | + | 0.983123i | \(0.558564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.04809 | −0.184948 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.884453 | −0.0323605 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4067 | 0.380253 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.6672 | −1.00959 | −0.504795 | − | 0.863240i | \(-0.668432\pi\) | ||||
−0.504795 | + | 0.863240i | \(0.668432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.94721 | 0.362497 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.43436 | 0.270564 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.6164 | 0.603933 | 0.301966 | − | 0.953319i | \(-0.402357\pi\) | ||||
0.301966 | + | 0.953319i | \(0.402357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1623 | 0.803381 | 0.401691 | − | 0.915775i | \(-0.368423\pi\) | ||||
0.401691 | + | 0.915775i | \(0.368423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.1566 | −0.367694 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.393832 | −0.0142390 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.78362 | 0.281050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9443 | 0.394661 | 0.197330 | − | 0.980337i | \(-0.436773\pi\) | ||||
0.197330 | + | 0.980337i | \(0.436773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.8528 | 0.967080 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.6685 | −1.57065 | −0.785324 | − | 0.619085i | \(-0.787504\pi\) | ||||
−0.785324 | + | 0.619085i | \(0.787504\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.96893 | −0.178489 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.914363 | 0.0328026 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.535198 | 0.0191755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.02107 | 0.179668 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 44.4214 | 1.58749 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.3059 | −0.689056 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.71149 | −0.132300 | −0.0661502 | − | 0.997810i | \(-0.521072\pi\) | ||||
−0.0661502 | + | 0.997810i | \(0.521072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.7854 | −0.668776 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.19767 | −0.255920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.68447 | 0.130839 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.300861 | 0.0106704 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.9223 | 1.05990 | 0.529951 | − | 0.848029i | \(-0.322210\pi\) | ||||
0.529951 | + | 0.848029i | \(0.322210\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.1186 | 1.80844 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.32668 | −0.0468759 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.9496 | −0.668717 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.40734 | −0.0496023 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.915995 | −0.0322445 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.0546 | 0.916032 | 0.458016 | − | 0.888944i | \(-0.348560\pi\) | ||||
0.458016 | + | 0.888944i | \(0.348560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.2167 | 0.358757 | 0.179379 | − | 0.983780i | \(-0.442591\pi\) | ||||
0.179379 | + | 0.983780i | \(0.442591\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.55132 | −0.264836 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.6361 | −0.617765 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0416886 | 0.00145850 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0856374 | −0.00299241 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.8328 | −1.00627 | −0.503136 | − | 0.864207i | \(-0.667821\pi\) | ||||
−0.503136 | + | 0.864207i | \(0.667821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.6244 | −1.13721 | −0.568607 | − | 0.822609i | \(-0.692518\pi\) | ||||
−0.568607 | + | 0.822609i | \(0.692518\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.68447 | −0.197908 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.3379 | 1.26359 | 0.631797 | − | 0.775134i | \(-0.282318\pi\) | ||||
0.631797 | + | 0.775134i | \(0.282318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.7092 | −1.10131 | −0.550653 | − | 0.834734i | \(-0.685621\pi\) | ||||
−0.550653 | + | 0.834734i | \(0.685621\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.04747 | −0.279163 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.59883 | −0.159340 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5256 | 0.675710 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.4378 | 0.879258 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0127 | −0.725439 | −0.362719 | − | 0.931898i | \(-0.618152\pi\) | ||||
−0.362719 | + | 0.931898i | \(0.618152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.2927 | 1.59630 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.86747 | −0.305412 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.527864 | 0.0181376 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −49.6726 | −1.70476 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.732565 | −0.0251120 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.5864 | 1.01302 | 0.506510 | − | 0.862234i | \(-0.330935\pi\) | ||||
0.506510 | + | 0.862234i | \(0.330935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0128825 | 0.000440572 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.9633 | −0.784412 | −0.392206 | − | 0.919877i | \(-0.628288\pi\) | ||||
−0.392206 | + | 0.919877i | \(0.628288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2364 | −1.09989 | −0.549946 | − | 0.835200i | \(-0.685352\pi\) | ||||
−0.549946 | + | 0.835200i | \(0.685352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.24958 | −0.212985 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.48160 | 0.288717 | 0.144359 | − | 0.989525i | \(-0.453888\pi\) | ||||
0.144359 | + | 0.989525i | \(0.453888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.07479 | 0.0365439 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.28861 | 0.247534 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.1917 | 0.549266 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.95542 | −0.0662570 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0744862 | 0.00252098 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.5067 | 1.87433 | 0.937165 | − | 0.348887i | \(-0.113440\pi\) | ||||
0.937165 | + | 0.348887i | \(0.113440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.8147 | 0.634604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.2264 | −0.950971 | −0.475485 | − | 0.879724i | \(-0.657728\pi\) | ||||
−0.475485 | + | 0.879724i | \(0.657728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.2344 | 1.21938 | 0.609692 | − | 0.792638i | \(-0.291293\pi\) | ||||
0.609692 | + | 0.792638i | \(0.291293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.6727 | 0.459603 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50.4798 | −1.69495 | −0.847473 | − | 0.530838i | \(-0.821877\pi\) | ||||
−0.847473 | + | 0.530838i | \(0.821877\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.23607 | 0.108534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.9323 | 1.00277 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.67212 | −0.0559553 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.07160 | −0.136099 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.47214 | 0.0825422 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.1161 | 1.43800 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.787665 | −0.0262409 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.486803 | −0.0161998 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.9907 | 0.863959 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.25483 | −0.207688 | −0.103844 | − | 0.994594i | \(-0.533114\pi\) | ||||
−0.103844 | + | 0.994594i | \(0.533114\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.349582 | −0.0115949 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.07160 | −0.267424 | −0.133712 | − | 0.991020i | \(-0.542690\pi\) | ||||
−0.133712 | + | 0.991020i | \(0.542690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.4217 | 1.10610 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.47214 | 0.213962 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.3132 | −0.406618 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.1088 | 0.366447 | 0.183223 | − | 0.983071i | \(-0.441347\pi\) | ||||
0.183223 | + | 0.983071i | \(0.441347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.58128 | 0.216860 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.55160 | −0.0510714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.520530 | −0.0171149 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.292043 | 0.00959196 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.25947 | −0.106940 | −0.0534699 | − | 0.998569i | \(-0.517028\pi\) | ||||
−0.0534699 | + | 0.998569i | \(0.517028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.150431 | 0.00493016 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3208 | −0.403367 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.8821 | 0.486698 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.8799 | 0.714784 | 0.357392 | − | 0.933954i | \(-0.383666\pi\) | ||||
0.357392 | + | 0.933954i | \(0.383666\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.5131 | −0.669421 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.4393 | −1.02489 | −0.512446 | − | 0.858720i | \(-0.671260\pi\) | ||||
−0.512446 | + | 0.858720i | \(0.671260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.00701 | 0.163051 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.11936 | 0.166533 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.7425 | 0.511561 | 0.255781 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255781 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.85575 | 0.190086 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.2775 | 1.85735 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.5959 | −0.343236 | −0.171618 | − | 0.985164i | \(-0.554900\pi\) | ||||
−0.171618 | + | 0.985164i | \(0.554900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.9927 | −0.549870 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.3249 | 1.59445 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.308823 | −0.00997241 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.30970 | −0.203539 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.891204 | −0.0287187 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.4874 | 0.723894 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4020 | 0.334507 | 0.167254 | − | 0.985914i | \(-0.446510\pi\) | ||||
0.167254 | + | 0.985914i | \(0.446510\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.21522 | −0.0390386 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.73211 | 0.216044 | 0.108022 | − | 0.994149i | \(-0.465548\pi\) | ||||
0.108022 | + | 0.994149i | \(0.465548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.740199 | 0.0237297 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.75660 | 0.0562562 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.2059 | 0.486479 | 0.243240 | − | 0.969966i | \(-0.421790\pi\) | ||||
0.243240 | + | 0.969966i | \(0.421790\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.1326 | 1.60224 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.869786 | 0.0277701 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.1694 | −0.547619 | −0.273809 | − | 0.961784i | \(-0.588284\pi\) | ||||
−0.273809 | + | 0.961784i | \(0.588284\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.11585 | −0.0674165 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.5256 | 0.621505 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.390015 | 0.0124018 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.56481 | 0.240304 | 0.120152 | − | 0.992756i | \(-0.461662\pi\) | ||||
0.120152 | + | 0.992756i | \(0.461662\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.8515 | −1.29638 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.13491 | 0.257894 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.1931 | 0.702862 | 0.351431 | − | 0.936214i | \(-0.385695\pi\) | ||||
0.351431 | + | 0.936214i | \(0.385695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.66478 | 0.0843100 |
(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 | 3640.2.a.s.1.4 | ✓ | 4 | |
4.3 | odd | 2 | 7280.2.a.ca.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.s.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7280.2.a.ca.1.1 | 4 | 4.3 | odd | 2 |