Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7497,2,Mod(1,7497)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7497, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7497.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7497 = 3^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7497.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: | \(59.8638463954\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.17314349056.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 40x^{4} - 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.391024\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7497.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.391024 | 0.276495 | 0.138248 | − | 0.990398i | \(-0.455853\pi\) | ||||
0.138248 | + | 0.990398i | \(0.455853\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.84710 | −0.923550 | ||||||||
\(5\) | 1.78339 | 0.797558 | 0.398779 | − | 0.917047i | \(-0.369434\pi\) | ||||
0.398779 | + | 0.917047i | \(0.369434\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.50431 | −0.531853 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.697349 | 0.220521 | ||||||||
\(11\) | −2.39447 | −0.721960 | −0.360980 | − | 0.932574i | \(-0.617558\pi\) | ||||
−0.360980 | + | 0.932574i | \(0.617558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.824980 | 0.228808 | 0.114404 | − | 0.993434i | \(-0.463504\pi\) | ||||
0.114404 | + | 0.993434i | \(0.463504\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.10598 | 0.776495 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.47917 | 0.568760 | 0.284380 | − | 0.958712i | \(-0.408212\pi\) | ||||
0.284380 | + | 0.958712i | \(0.408212\pi\) | |||||||
\(20\) | −3.29411 | −0.736585 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.936294 | −0.199619 | ||||||||
\(23\) | 6.42088 | 1.33885 | 0.669423 | − | 0.742882i | \(-0.266541\pi\) | ||||
0.669423 | + | 0.742882i | \(0.266541\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.81950 | −0.363901 | ||||||||
\(26\) | 0.322587 | 0.0632645 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.325841 | −0.0605071 | −0.0302535 | − | 0.999542i | \(-0.509631\pi\) | ||||
−0.0302535 | + | 0.999542i | \(0.509631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.36282 | −1.68161 | −0.840806 | − | 0.541337i | \(-0.817918\pi\) | ||||
−0.840806 | + | 0.541337i | \(0.817918\pi\) | |||||||
\(32\) | 4.22313 | 0.746550 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.391024 | 0.0670600 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.73648 | 0.943071 | 0.471536 | − | 0.881847i | \(-0.343700\pi\) | ||||
0.471536 | + | 0.881847i | \(0.343700\pi\) | |||||||
\(38\) | 0.969413 | 0.157260 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.68277 | −0.424184 | ||||||||
\(41\) | 3.20281 | 0.500194 | 0.250097 | − | 0.968221i | \(-0.419537\pi\) | ||||
0.250097 | + | 0.968221i | \(0.419537\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.52750 | 0.842936 | 0.421468 | − | 0.906843i | \(-0.361515\pi\) | ||||
0.421468 | + | 0.906843i | \(0.361515\pi\) | |||||||
\(44\) | 4.42283 | 0.666766 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.51071 | 0.370185 | ||||||||
\(47\) | −9.68339 | −1.41247 | −0.706234 | − | 0.707979i | \(-0.749607\pi\) | ||||
−0.706234 | + | 0.707979i | \(0.749607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.711468 | −0.100617 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.52382 | −0.211316 | ||||||||
\(53\) | −2.50798 | −0.344498 | −0.172249 | − | 0.985053i | \(-0.555103\pi\) | ||||
−0.172249 | + | 0.985053i | \(0.555103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.27029 | −0.575805 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.127411 | −0.0167299 | ||||||||
\(59\) | 2.90318 | 0.377961 | 0.188981 | − | 0.981981i | \(-0.439482\pi\) | ||||
0.188981 | + | 0.981981i | \(0.439482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.02319 | 0.131006 | 0.0655030 | − | 0.997852i | \(-0.479135\pi\) | ||||
0.0655030 | + | 0.997852i | \(0.479135\pi\) | |||||||
\(62\) | −3.66108 | −0.464958 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.56062 | −0.570078 | ||||||||
\(65\) | 1.47127 | 0.182488 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50773 | 0.184198 | 0.0920990 | − | 0.995750i | \(-0.470642\pi\) | ||||
0.0920990 | + | 0.995750i | \(0.470642\pi\) | |||||||
\(68\) | −1.84710 | −0.223994 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.16070 | −1.08718 | −0.543588 | − | 0.839352i | \(-0.682935\pi\) | ||||
−0.543588 | + | 0.839352i | \(0.682935\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0705787 | 0.00826062 | 0.00413031 | − | 0.999991i | \(-0.498685\pi\) | ||||
0.00413031 | + | 0.999991i | \(0.498685\pi\) | |||||||
\(74\) | 2.24310 | 0.260755 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.57927 | −0.525279 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.730309 | −0.0821662 | −0.0410831 | − | 0.999156i | \(-0.513081\pi\) | ||||
−0.0410831 | + | 0.999156i | \(0.513081\pi\) | |||||||
\(80\) | 5.53919 | 0.619300 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.25237 | 0.138301 | ||||||||
\(83\) | 5.53919 | 0.608005 | 0.304003 | − | 0.952671i | \(-0.401677\pi\) | ||||
0.304003 | + | 0.952671i | \(0.401677\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.78339 | 0.193436 | ||||||||
\(86\) | 2.16138 | 0.233068 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.60202 | 0.383976 | ||||||||
\(89\) | 0.313430 | 0.0332235 | 0.0166117 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166117 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −11.8600 | −1.23649 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.78643 | −0.390541 | ||||||||
\(95\) | 4.42134 | 0.453619 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.79755 | 0.791722 | 0.395861 | − | 0.918311i | \(-0.370446\pi\) | ||||
0.395861 | + | 0.918311i | \(0.370446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.36080 | 0.336080 | ||||||||
\(101\) | 10.0244 | 0.997467 | 0.498733 | − | 0.866755i | \(-0.333799\pi\) | ||||
0.498733 | + | 0.866755i | \(0.333799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.37989 | 0.431564 | 0.215782 | − | 0.976442i | \(-0.430770\pi\) | ||||
0.215782 | + | 0.976442i | \(0.430770\pi\) | |||||||
\(104\) | −1.24102 | −0.121692 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.980680 | −0.0952521 | ||||||||
\(107\) | 11.5552 | 1.11708 | 0.558540 | − | 0.829477i | \(-0.311362\pi\) | ||||
0.558540 | + | 0.829477i | \(0.311362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.27732 | 0.122345 | 0.0611726 | − | 0.998127i | \(-0.480516\pi\) | ||||
0.0611726 | + | 0.998127i | \(0.480516\pi\) | |||||||
\(110\) | −1.66978 | −0.159208 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.1510 | −1.51936 | −0.759678 | − | 0.650299i | \(-0.774643\pi\) | ||||
−0.759678 | + | 0.650299i | \(0.774643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4510 | 1.06781 | ||||||||
\(116\) | 0.601860 | 0.0558813 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.13521 | 0.104505 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.26651 | −0.478774 | ||||||||
\(122\) | 0.400091 | 0.0362226 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.2941 | 1.55305 | ||||||||
\(125\) | −12.1619 | −1.08779 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.3923 | 1.98699 | 0.993496 | − | 0.113864i | \(-0.0363228\pi\) | ||||
0.993496 | + | 0.113864i | \(0.0363228\pi\) | |||||||
\(128\) | −10.2296 | −0.904174 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.575300 | 0.0504571 | ||||||||
\(131\) | 13.9108 | 1.21539 | 0.607696 | − | 0.794169i | \(-0.292094\pi\) | ||||
0.607696 | + | 0.794169i | \(0.292094\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.589556 | 0.0509299 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50431 | −0.128993 | ||||||||
\(137\) | −4.04833 | −0.345873 | −0.172936 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172936 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50948 | 0.552127 | 0.276063 | − | 0.961139i | \(-0.410970\pi\) | ||||
0.276063 | + | 0.961139i | \(0.410970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.58205 | −0.300599 | ||||||||
\(143\) | −1.97539 | −0.165190 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.581102 | −0.0482579 | ||||||||
\(146\) | 0.0275979 | 0.00228402 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.5959 | −0.870974 | ||||||||
\(149\) | 10.4695 | 0.857698 | 0.428849 | − | 0.903376i | \(-0.358919\pi\) | ||||
0.428849 | + | 0.903376i | \(0.358919\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.60754 | 0.130820 | 0.0654098 | − | 0.997858i | \(-0.479165\pi\) | ||||
0.0654098 | + | 0.997858i | \(0.479165\pi\) | |||||||
\(152\) | −3.72943 | −0.302497 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6976 | −1.34118 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.35398 | −0.586911 | −0.293456 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293456 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(158\) | −0.285568 | −0.0227186 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.53150 | 0.595417 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2532 | 1.27305 | 0.636523 | − | 0.771258i | \(-0.280372\pi\) | ||||
0.636523 | + | 0.771258i | \(0.280372\pi\) | |||||||
\(164\) | −5.91591 | −0.461955 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.16595 | 0.168111 | ||||||||
\(167\) | 9.59527 | 0.742504 | 0.371252 | − | 0.928532i | \(-0.378929\pi\) | ||||
0.371252 | + | 0.928532i | \(0.378929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3194 | −0.947647 | ||||||||
\(170\) | 0.697349 | 0.0534843 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.2099 | −0.778494 | ||||||||
\(173\) | −10.4990 | −0.798226 | −0.399113 | − | 0.916902i | \(-0.630682\pi\) | ||||
−0.399113 | + | 0.916902i | \(0.630682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.43718 | −0.560599 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.122558 | 0.00918614 | ||||||||
\(179\) | 17.8730 | 1.33589 | 0.667946 | − | 0.744210i | \(-0.267174\pi\) | ||||
0.667946 | + | 0.744210i | \(0.267174\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7724 | 1.02370 | 0.511849 | − | 0.859076i | \(-0.328961\pi\) | ||||
0.511849 | + | 0.859076i | \(0.328961\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.65897 | −0.712069 | ||||||||
\(185\) | 10.2304 | 0.752154 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.39447 | −0.175101 | ||||||||
\(188\) | 17.8862 | 1.30449 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.72885 | 0.125424 | ||||||||
\(191\) | 18.9809 | 1.37341 | 0.686705 | − | 0.726936i | \(-0.259057\pi\) | ||||
0.686705 | + | 0.726936i | \(0.259057\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4445 | −1.18370 | −0.591850 | − | 0.806048i | \(-0.701602\pi\) | ||||
−0.591850 | + | 0.806048i | \(0.701602\pi\) | |||||||
\(194\) | 3.04903 | 0.218907 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.09504 | 0.434253 | 0.217127 | − | 0.976143i | \(-0.430332\pi\) | ||||
0.217127 | + | 0.976143i | \(0.430332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6917 | 1.25413 | 0.627064 | − | 0.778968i | \(-0.284256\pi\) | ||||
0.627064 | + | 0.778968i | \(0.284256\pi\) | |||||||
\(200\) | 2.73709 | 0.193542 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.91978 | 0.275795 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.71187 | 0.398934 | ||||||||
\(206\) | 1.71264 | 0.119325 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.56237 | 0.177669 | ||||||||
\(209\) | −5.93629 | −0.410622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.70125 | 0.254804 | 0.127402 | − | 0.991851i | \(-0.459336\pi\) | ||||
0.127402 | + | 0.991851i | \(0.459336\pi\) | |||||||
\(212\) | 4.63250 | 0.318161 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.51835 | 0.308868 | ||||||||
\(215\) | 9.85772 | 0.672291 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.499463 | 0.0338279 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.88765 | 0.531785 | ||||||||
\(221\) | 0.824980 | 0.0554942 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.8786 | −1.33117 | −0.665585 | − | 0.746322i | \(-0.731818\pi\) | ||||
−0.665585 | + | 0.746322i | \(0.731818\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.31541 | −0.420095 | ||||||||
\(227\) | 15.3302 | 1.01750 | 0.508751 | − | 0.860914i | \(-0.330107\pi\) | ||||
0.508751 | + | 0.860914i | \(0.330107\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5914 | −0.699903 | −0.349951 | − | 0.936768i | \(-0.613802\pi\) | ||||
−0.349951 | + | 0.936768i | \(0.613802\pi\) | |||||||
\(230\) | 4.47760 | 0.295244 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.490164 | 0.0321809 | ||||||||
\(233\) | −11.0326 | −0.722771 | −0.361385 | − | 0.932417i | \(-0.617696\pi\) | ||||
−0.361385 | + | 0.932417i | \(0.617696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.2693 | −1.12653 | ||||||||
\(236\) | −5.36246 | −0.349066 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.99978 | −0.323409 | −0.161704 | − | 0.986839i | \(-0.551699\pi\) | ||||
−0.161704 | + | 0.986839i | \(0.551699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6013 | 0.940554 | 0.470277 | − | 0.882519i | \(-0.344154\pi\) | ||||
0.470277 | + | 0.882519i | \(0.344154\pi\) | |||||||
\(242\) | −2.05933 | −0.132379 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.88993 | −0.120991 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.04526 | 0.130137 | ||||||||
\(248\) | 14.0846 | 0.894370 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.75558 | −0.300769 | ||||||||
\(251\) | 27.8108 | 1.75540 | 0.877701 | − | 0.479208i | \(-0.159076\pi\) | ||||
0.877701 | + | 0.479208i | \(0.159076\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.3746 | −0.966593 | ||||||||
\(254\) | 8.75591 | 0.549394 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.12124 | 0.320078 | ||||||||
\(257\) | 20.7172 | 1.29230 | 0.646150 | − | 0.763210i | \(-0.276378\pi\) | ||||
0.646150 | + | 0.763210i | \(0.276378\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.71758 | −0.168537 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.43945 | 0.336051 | ||||||||
\(263\) | 11.8435 | 0.730300 | 0.365150 | − | 0.930949i | \(-0.381018\pi\) | ||||
0.365150 | + | 0.930949i | \(0.381018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.47272 | −0.274757 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.78492 | −0.170116 | ||||||||
\(269\) | 30.1792 | 1.84006 | 0.920030 | − | 0.391847i | \(-0.128164\pi\) | ||||
0.920030 | + | 0.391847i | \(0.128164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.48089 | −0.0899576 | −0.0449788 | − | 0.998988i | \(-0.514322\pi\) | ||||
−0.0449788 | + | 0.998988i | \(0.514322\pi\) | |||||||
\(272\) | 3.10598 | 0.188328 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.58299 | −0.0956322 | ||||||||
\(275\) | 4.35675 | 0.262722 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6156 | 1.05842 | 0.529210 | − | 0.848491i | \(-0.322488\pi\) | ||||
0.529210 | + | 0.848491i | \(0.322488\pi\) | |||||||
\(278\) | 2.54536 | 0.152661 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6529 | −1.29170 | −0.645851 | − | 0.763463i | \(-0.723497\pi\) | ||||
−0.645851 | + | 0.763463i | \(0.723497\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.07601 | −0.539513 | −0.269756 | − | 0.962929i | \(-0.586943\pi\) | ||||
−0.269756 | + | 0.962929i | \(0.586943\pi\) | |||||||
\(284\) | 16.9207 | 1.00406 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.772424 | −0.0456744 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.227225 | −0.0133431 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.130366 | −0.00762909 | ||||||||
\(293\) | 20.2684 | 1.18409 | 0.592047 | − | 0.805903i | \(-0.298320\pi\) | ||||
0.592047 | + | 0.805903i | \(0.298320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.17751 | 0.301446 | ||||||||
\(296\) | −8.62942 | −0.501575 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.09384 | 0.237150 | ||||||||
\(299\) | 5.29710 | 0.306339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.628586 | 0.0361710 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.70025 | 0.441640 | ||||||||
\(305\) | 1.82475 | 0.104485 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.63815 | −0.493005 | −0.246503 | − | 0.969142i | \(-0.579281\pi\) | ||||
−0.246503 | + | 0.969142i | \(0.579281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.52916 | −0.370831 | ||||||||
\(311\) | 22.4944 | 1.27554 | 0.637770 | − | 0.770227i | \(-0.279857\pi\) | ||||
0.637770 | + | 0.770227i | \(0.279857\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4893 | −0.762460 | −0.381230 | − | 0.924480i | \(-0.624499\pi\) | ||||
−0.381230 | + | 0.924480i | \(0.624499\pi\) | |||||||
\(314\) | −2.87558 | −0.162278 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.34895 | 0.0758846 | ||||||||
\(317\) | 11.6200 | 0.652646 | 0.326323 | − | 0.945258i | \(-0.394190\pi\) | ||||
0.326323 | + | 0.945258i | \(0.394190\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.780216 | 0.0436837 | ||||||||
\(320\) | −8.13339 | −0.454670 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.47917 | 0.137945 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.50105 | −0.0832635 | ||||||||
\(326\) | 6.35537 | 0.351992 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.81800 | −0.266030 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8624 | −0.706979 | −0.353490 | − | 0.935438i | \(-0.615005\pi\) | ||||
−0.353490 | + | 0.935438i | \(0.615005\pi\) | |||||||
\(332\) | −10.2314 | −0.561523 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.75198 | 0.205299 | ||||||||
\(335\) | 2.68887 | 0.146909 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.40162 | −0.130824 | −0.0654122 | − | 0.997858i | \(-0.520836\pi\) | ||||
−0.0654122 | + | 0.997858i | \(0.520836\pi\) | |||||||
\(338\) | −4.81718 | −0.262020 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.29411 | −0.178648 | ||||||||
\(341\) | 22.4190 | 1.21406 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.31506 | −0.448318 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.10537 | −0.220706 | ||||||||
\(347\) | −25.5379 | −1.37094 | −0.685472 | − | 0.728099i | \(-0.740404\pi\) | ||||
−0.685472 | + | 0.728099i | \(0.740404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5107 | −0.616156 | −0.308078 | − | 0.951361i | \(-0.599686\pi\) | ||||
−0.308078 | + | 0.951361i | \(0.599686\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.1121 | −0.538979 | ||||||||
\(353\) | 11.1151 | 0.591599 | 0.295800 | − | 0.955250i | \(-0.404414\pi\) | ||||
0.295800 | + | 0.955250i | \(0.404414\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.3372 | −0.867086 | ||||||||
\(356\) | −0.578936 | −0.0306835 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.98877 | 0.369368 | ||||||||
\(359\) | −29.7631 | −1.57083 | −0.785417 | − | 0.618966i | \(-0.787552\pi\) | ||||
−0.785417 | + | 0.618966i | \(0.787552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8537 | −0.676512 | ||||||||
\(362\) | 5.38535 | 0.283048 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.125870 | 0.00658832 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.90853 | −0.0996247 | −0.0498123 | − | 0.998759i | \(-0.515862\pi\) | ||||
−0.0498123 | + | 0.998759i | \(0.515862\pi\) | |||||||
\(368\) | 19.9431 | 1.03961 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.00033 | 0.207967 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.3923 | 0.796982 | 0.398491 | − | 0.917172i | \(-0.369534\pi\) | ||||
0.398491 | + | 0.917172i | \(0.369534\pi\) | |||||||
\(374\) | −0.936294 | −0.0484146 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.5668 | 0.751225 | ||||||||
\(377\) | −0.268812 | −0.0138445 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.91721 | −0.201213 | −0.100607 | − | 0.994926i | \(-0.532078\pi\) | ||||
−0.100607 | + | 0.994926i | \(0.532078\pi\) | |||||||
\(380\) | −8.16665 | −0.418940 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.42198 | 0.379741 | ||||||||
\(383\) | 14.9720 | 0.765032 | 0.382516 | − | 0.923949i | \(-0.375058\pi\) | ||||
0.382516 | + | 0.923949i | \(0.375058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.43018 | −0.327287 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.4029 | −0.731195 | ||||||||
\(389\) | 20.8477 | 1.05702 | 0.528511 | − | 0.848926i | \(-0.322750\pi\) | ||||
0.528511 | + | 0.848926i | \(0.322750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.42088 | 0.324718 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.38330 | 0.120069 | ||||||||
\(395\) | −1.30243 | −0.0655323 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.21243 | −0.261604 | −0.130802 | − | 0.991408i | \(-0.541755\pi\) | ||||
−0.130802 | + | 0.991408i | \(0.541755\pi\) | |||||||
\(398\) | 6.91785 | 0.346761 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.65134 | −0.282567 | ||||||||
\(401\) | 0.841168 | 0.0420059 | 0.0210030 | − | 0.999779i | \(-0.493314\pi\) | ||||
0.0210030 | + | 0.999779i | \(0.493314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.72414 | −0.384767 | ||||||||
\(404\) | −18.5161 | −0.921211 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.7358 | −0.680860 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2234 | 1.19777 | 0.598885 | − | 0.800835i | \(-0.295611\pi\) | ||||
0.598885 | + | 0.800835i | \(0.295611\pi\) | |||||||
\(410\) | 2.23348 | 0.110303 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.09011 | −0.398571 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.87857 | 0.484920 | ||||||||
\(416\) | 3.48400 | 0.170817 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.32123 | −0.113535 | ||||||||
\(419\) | 2.89448 | 0.141404 | 0.0707022 | − | 0.997497i | \(-0.477476\pi\) | ||||
0.0707022 | + | 0.997497i | \(0.477476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.568900 | 0.0277265 | 0.0138632 | − | 0.999904i | \(-0.495587\pi\) | ||||
0.0138632 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(422\) | 1.44728 | 0.0704523 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.77278 | 0.183222 | ||||||||
\(425\) | −1.81950 | −0.0882588 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −21.3436 | −1.03168 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.85460 | 0.185885 | ||||||||
\(431\) | 19.4543 | 0.937080 | 0.468540 | − | 0.883442i | \(-0.344780\pi\) | ||||
0.468540 | + | 0.883442i | \(0.344780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5292 | −0.890458 | −0.445229 | − | 0.895417i | \(-0.646878\pi\) | ||||
−0.445229 | + | 0.895417i | \(0.646878\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.35934 | −0.112992 | ||||||||
\(437\) | 15.9184 | 0.761482 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6119 | 0.506477 | 0.253238 | − | 0.967404i | \(-0.418504\pi\) | ||||
0.253238 | + | 0.967404i | \(0.418504\pi\) | |||||||
\(440\) | 6.42382 | 0.306244 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.322587 | 0.0153439 | ||||||||
\(443\) | −2.45035 | −0.116420 | −0.0582099 | − | 0.998304i | \(-0.518539\pi\) | ||||
−0.0582099 | + | 0.998304i | \(0.518539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.558969 | 0.0264977 | ||||||||
\(446\) | −7.77301 | −0.368063 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.73433 | −0.459391 | −0.229696 | − | 0.973263i | \(-0.573773\pi\) | ||||
−0.229696 | + | 0.973263i | \(0.573773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.66902 | −0.361120 | ||||||||
\(452\) | 29.8325 | 1.40320 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.99448 | 0.281335 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.6570 | −1.48085 | −0.740427 | − | 0.672137i | \(-0.765376\pi\) | ||||
−0.740427 | + | 0.672137i | \(0.765376\pi\) | |||||||
\(458\) | −4.14151 | −0.193520 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.1511 | −0.986174 | ||||||||
\(461\) | 39.7798 | 1.85273 | 0.926365 | − | 0.376627i | \(-0.122916\pi\) | ||||
0.926365 | + | 0.376627i | \(0.122916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.42006 | −0.298365 | −0.149183 | − | 0.988810i | \(-0.547664\pi\) | ||||
−0.149183 | + | 0.988810i | \(0.547664\pi\) | |||||||
\(464\) | −1.01205 | −0.0469835 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.31401 | −0.199843 | ||||||||
\(467\) | −4.81379 | −0.222756 | −0.111378 | − | 0.993778i | \(-0.535526\pi\) | ||||
−0.111378 | + | 0.993778i | \(0.535526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.75271 | −0.311479 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.36727 | −0.201020 | ||||||||
\(473\) | −13.2354 | −0.608566 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.51085 | −0.206972 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.95503 | −0.0894210 | ||||||||
\(479\) | −0.688097 | −0.0314400 | −0.0157200 | − | 0.999876i | \(-0.505004\pi\) | ||||
−0.0157200 | + | 0.999876i | \(0.505004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.73248 | 0.215783 | ||||||||
\(482\) | 5.70946 | 0.260059 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.72778 | 0.442172 | ||||||||
\(485\) | 13.9061 | 0.631444 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.1222 | −1.50091 | −0.750454 | − | 0.660923i | \(-0.770165\pi\) | ||||
−0.750454 | + | 0.660923i | \(0.770165\pi\) | |||||||
\(488\) | −1.53919 | −0.0696759 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.46154 | 0.381864 | 0.190932 | − | 0.981603i | \(-0.438849\pi\) | ||||
0.190932 | + | 0.981603i | \(0.438849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.325841 | −0.0146751 | ||||||||
\(494\) | 0.799747 | 0.0359823 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.0807 | −1.30576 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.4753 | 1.14043 | 0.570215 | − | 0.821495i | \(-0.306860\pi\) | ||||
0.570215 | + | 0.821495i | \(0.306860\pi\) | |||||||
\(500\) | 22.4642 | 1.00463 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.8747 | 0.485361 | ||||||||
\(503\) | 33.0872 | 1.47529 | 0.737644 | − | 0.675190i | \(-0.235938\pi\) | ||||
0.737644 | + | 0.675190i | \(0.235938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.8775 | 0.795538 | ||||||||
\(506\) | −6.01183 | −0.267259 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −41.3608 | −1.83509 | ||||||||
\(509\) | −10.6821 | −0.473474 | −0.236737 | − | 0.971574i | \(-0.576078\pi\) | ||||
−0.236737 | + | 0.971574i | \(0.576078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.4617 | 0.992674 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.10090 | 0.357315 | ||||||||
\(515\) | 7.81108 | 0.344197 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.1866 | 1.01975 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.21324 | −0.0970568 | ||||||||
\(521\) | −0.0806199 | −0.00353202 | −0.00176601 | − | 0.999998i | \(-0.500562\pi\) | ||||
−0.00176601 | + | 0.999998i | \(0.500562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.9210 | 1.08972 | 0.544859 | − | 0.838528i | \(-0.316583\pi\) | ||||
0.544859 | + | 0.838528i | \(0.316583\pi\) | |||||||
\(524\) | −25.6947 | −1.12248 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.63108 | 0.201925 | ||||||||
\(527\) | −9.36282 | −0.407851 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.2277 | 0.792508 | ||||||||
\(530\) | −1.74894 | −0.0759691 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.64225 | 0.114449 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.6074 | 0.890937 | ||||||||
\(536\) | −2.26808 | −0.0979662 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.8008 | 0.508768 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.65299 | 0.0710678 | 0.0355339 | − | 0.999368i | \(-0.488687\pi\) | ||||
0.0355339 | + | 0.999368i | \(0.488687\pi\) | |||||||
\(542\) | −0.579062 | −0.0248729 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.22313 | 0.181065 | ||||||||
\(545\) | 2.27797 | 0.0975775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.78099 | 0.161663 | 0.0808317 | − | 0.996728i | \(-0.474242\pi\) | ||||
0.0808317 | + | 0.996728i | \(0.474242\pi\) | |||||||
\(548\) | 7.47768 | 0.319431 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.70359 | 0.0726413 | ||||||||
\(551\) | −0.807814 | −0.0344140 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.88813 | 0.292648 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0237 | −0.509917 | ||||||||
\(557\) | 13.9866 | 0.592631 | 0.296315 | − | 0.955090i | \(-0.404242\pi\) | ||||
0.296315 | + | 0.955090i | \(0.404242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.56008 | 0.192871 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.46679 | −0.357150 | ||||||||
\(563\) | 26.9628 | 1.13635 | 0.568174 | − | 0.822909i | \(-0.307650\pi\) | ||||
0.568174 | + | 0.822909i | \(0.307650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.8036 | −1.21178 | ||||||||
\(566\) | −3.54893 | −0.149173 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.7805 | 0.578217 | ||||||||
\(569\) | 21.7595 | 0.912206 | 0.456103 | − | 0.889927i | \(-0.349245\pi\) | ||||
0.456103 | + | 0.889927i | \(0.349245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5694 | 0.735255 | 0.367627 | − | 0.929973i | \(-0.380170\pi\) | ||||
0.367627 | + | 0.929973i | \(0.380170\pi\) | |||||||
\(572\) | 3.64875 | 0.152562 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.6828 | −0.487207 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.3313 | −1.42923 | −0.714615 | − | 0.699518i | \(-0.753398\pi\) | ||||
−0.714615 | + | 0.699518i | \(0.753398\pi\) | |||||||
\(578\) | 0.391024 | 0.0162644 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.07335 | 0.0445686 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00529 | 0.248714 | ||||||||
\(584\) | −0.106172 | −0.00439343 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.92543 | 0.327397 | ||||||||
\(587\) | 7.67741 | 0.316881 | 0.158440 | − | 0.987369i | \(-0.449353\pi\) | ||||
0.158440 | + | 0.987369i | \(0.449353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.2120 | −0.956434 | ||||||||
\(590\) | 2.02453 | 0.0833485 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.8174 | 0.732290 | ||||||||
\(593\) | 28.3378 | 1.16370 | 0.581848 | − | 0.813298i | \(-0.302330\pi\) | ||||
0.581848 | + | 0.813298i | \(0.302330\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.3383 | −0.792127 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.07129 | 0.0847014 | ||||||||
\(599\) | −31.0115 | −1.26710 | −0.633549 | − | 0.773703i | \(-0.718402\pi\) | ||||
−0.633549 | + | 0.773703i | \(0.718402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.1942 | 1.31323 | 0.656614 | − | 0.754227i | \(-0.271988\pi\) | ||||
0.656614 | + | 0.754227i | \(0.271988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.96929 | −0.120819 | ||||||||
\(605\) | −9.39227 | −0.381850 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.0667 | −0.692716 | −0.346358 | − | 0.938102i | \(-0.612582\pi\) | ||||
−0.346358 | + | 0.938102i | \(0.612582\pi\) | |||||||
\(608\) | 10.4698 | 0.424608 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.713521 | 0.0288896 | ||||||||
\(611\) | −7.98861 | −0.323184 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.8907 | 0.722599 | 0.361300 | − | 0.932450i | \(-0.382333\pi\) | ||||
0.361300 | + | 0.932450i | \(0.382333\pi\) | |||||||
\(614\) | −3.37772 | −0.136314 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.24625 | 0.130689 | 0.0653446 | − | 0.997863i | \(-0.479185\pi\) | ||||
0.0653446 | + | 0.997863i | \(0.479185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.6980 | −1.43482 | −0.717412 | − | 0.696649i | \(-0.754674\pi\) | ||||
−0.717412 | + | 0.696649i | \(0.754674\pi\) | |||||||
\(620\) | 30.8421 | 1.23865 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.79583 | 0.352681 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5919 | −0.503676 | ||||||||
\(626\) | −5.27463 | −0.210817 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.5835 | 0.542042 | ||||||||
\(629\) | 5.73648 | 0.228728 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.70037 | 0.147309 | 0.0736547 | − | 0.997284i | \(-0.476534\pi\) | ||||
0.0736547 | + | 0.997284i | \(0.476534\pi\) | |||||||
\(632\) | 1.09861 | 0.0437003 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.54371 | 0.180454 | ||||||||
\(635\) | 39.9343 | 1.58474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.305083 | 0.0120783 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.2433 | −0.721132 | ||||||||
\(641\) | −13.7758 | −0.544110 | −0.272055 | − | 0.962282i | \(-0.587703\pi\) | ||||
−0.272055 | + | 0.962282i | \(0.587703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.3825 | 0.764370 | 0.382185 | − | 0.924086i | \(-0.375172\pi\) | ||||
0.382185 | + | 0.924086i | \(0.375172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.969413 | 0.0381410 | ||||||||
\(647\) | 11.4980 | 0.452032 | 0.226016 | − | 0.974124i | \(-0.427430\pi\) | ||||
0.226016 | + | 0.974124i | \(0.427430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.95157 | −0.272873 | ||||||||
\(650\) | −0.586947 | −0.0230220 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.0212 | −1.17572 | ||||||||
\(653\) | 23.0275 | 0.901135 | 0.450568 | − | 0.892742i | \(-0.351222\pi\) | ||||
0.450568 | + | 0.892742i | \(0.351222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.8085 | 0.969347 | ||||||||
\(656\) | 9.94786 | 0.388399 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.8554 | 0.539730 | 0.269865 | − | 0.962898i | \(-0.413021\pi\) | ||||
0.269865 | + | 0.962898i | \(0.413021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.02000 | −0.117464 | −0.0587322 | − | 0.998274i | \(-0.518706\pi\) | ||||
−0.0587322 | + | 0.998274i | \(0.518706\pi\) | |||||||
\(662\) | −5.02949 | −0.195477 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.33264 | −0.323369 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.09218 | −0.0810096 | ||||||||
\(668\) | −17.7234 | −0.685740 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.05141 | 0.0406196 | ||||||||
\(671\) | −2.45000 | −0.0945811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.6955 | 1.45305 | 0.726527 | − | 0.687138i | \(-0.241133\pi\) | ||||
0.726527 | + | 0.687138i | \(0.241133\pi\) | |||||||
\(674\) | −0.939089 | −0.0361724 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.7552 | 0.875199 | ||||||||
\(677\) | −18.9072 | −0.726663 | −0.363331 | − | 0.931660i | \(-0.618361\pi\) | ||||
−0.363331 | + | 0.931660i | \(0.618361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.68277 | −0.102880 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.76635 | 0.335681 | ||||||||
\(683\) | −43.9211 | −1.68060 | −0.840298 | − | 0.542125i | \(-0.817620\pi\) | ||||
−0.840298 | + | 0.542125i | \(0.817620\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.21978 | −0.275854 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.1683 | 0.654536 | ||||||||
\(689\) | −2.06904 | −0.0788240 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.48739 | −0.132667 | −0.0663334 | − | 0.997798i | \(-0.521130\pi\) | ||||
−0.0663334 | + | 0.997798i | \(0.521130\pi\) | |||||||
\(692\) | 19.3928 | 0.737202 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.98591 | −0.379060 | ||||||||
\(695\) | 11.6090 | 0.440353 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.20281 | 0.121315 | ||||||||
\(698\) | −4.50097 | −0.170364 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.8246 | −1.54192 | −0.770961 | − | 0.636882i | \(-0.780224\pi\) | ||||
−0.770961 | + | 0.636882i | \(0.780224\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.2217 | 0.536381 | ||||||||
\(704\) | 10.9203 | 0.411573 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.34628 | 0.163574 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5408 | −0.508537 | −0.254269 | − | 0.967134i | \(-0.581835\pi\) | ||||
−0.254269 | + | 0.967134i | \(0.581835\pi\) | |||||||
\(710\) | −6.38821 | −0.239745 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.471494 | −0.0176700 | ||||||||
\(713\) | −60.1175 | −2.25142 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.52290 | −0.131749 | ||||||||
\(716\) | −33.0132 | −1.23376 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.6381 | −0.434329 | ||||||||
\(719\) | 1.76508 | 0.0658264 | 0.0329132 | − | 0.999458i | \(-0.489522\pi\) | ||||
0.0329132 | + | 0.999458i | \(0.489522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.02611 | −0.187052 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.4391 | −0.945436 | ||||||||
\(725\) | 0.592868 | 0.0220186 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.0693 | −0.855591 | −0.427796 | − | 0.903876i | \(-0.640710\pi\) | ||||
−0.427796 | + | 0.903876i | \(0.640710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0492180 | 0.00182164 | ||||||||
\(731\) | 5.52750 | 0.204442 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.41984 | −0.163251 | −0.0816253 | − | 0.996663i | \(-0.526011\pi\) | ||||
−0.0816253 | + | 0.996663i | \(0.526011\pi\) | |||||||
\(734\) | −0.746282 | −0.0275458 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.1162 | 0.999516 | ||||||||
\(737\) | −3.61020 | −0.132984 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0383 | 1.58319 | 0.791594 | − | 0.611048i | \(-0.209252\pi\) | ||||
0.791594 | + | 0.611048i | \(0.209252\pi\) | |||||||
\(740\) | −18.8966 | −0.694652 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.3270 | 0.892472 | 0.446236 | − | 0.894915i | \(-0.352764\pi\) | ||||
0.446236 | + | 0.894915i | \(0.352764\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6713 | 0.684064 | ||||||||
\(746\) | 6.01874 | 0.220362 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.42283 | 0.161715 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.8791 | −1.30925 | −0.654624 | − | 0.755954i | \(-0.727173\pi\) | ||||
−0.654624 | + | 0.755954i | \(0.727173\pi\) | |||||||
\(752\) | −30.0764 | −1.09677 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.105112 | −0.00382795 | ||||||||
\(755\) | 2.86688 | 0.104336 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.0527 | −1.05594 | −0.527969 | − | 0.849263i | \(-0.677046\pi\) | ||||
−0.527969 | + | 0.849263i | \(0.677046\pi\) | |||||||
\(758\) | −1.53172 | −0.0556346 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.65105 | −0.241259 | ||||||||
\(761\) | 42.4544 | 1.53897 | 0.769486 | − | 0.638663i | \(-0.220512\pi\) | ||||
0.769486 | + | 0.638663i | \(0.220512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −35.0596 | −1.26841 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.85440 | 0.211528 | ||||||||
\(767\) | 2.39506 | 0.0864807 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.1169 | 1.87938 | 0.939692 | − | 0.342021i | \(-0.111111\pi\) | ||||
0.939692 | + | 0.342021i | \(0.111111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 30.3746 | 1.09321 | ||||||||
\(773\) | 13.4872 | 0.485100 | 0.242550 | − | 0.970139i | \(-0.422016\pi\) | ||||
0.242550 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.0357 | 0.611939 | ||||||||
\(776\) | −11.7299 | −0.421079 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.15196 | 0.292262 | ||||||||
\(779\) | 7.94029 | 0.284491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.9350 | 0.784897 | ||||||||
\(782\) | 2.51071 | 0.0897830 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.1150 | −0.468096 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.06066 | −0.180393 | −0.0901965 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901965 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(788\) | −11.2581 | −0.401055 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.509280 | −0.0181194 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.844112 | 0.0299753 | ||||||||
\(794\) | −2.03818 | −0.0723324 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32.6783 | −1.15825 | ||||||||
\(797\) | −16.1134 | −0.570767 | −0.285383 | − | 0.958413i | \(-0.592121\pi\) | ||||
−0.285383 | + | 0.958413i | \(0.592121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.68339 | −0.342574 | ||||||||
\(800\) | −7.68399 | −0.271670 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.328916 | 0.0116144 | ||||||||
\(803\) | −0.168999 | −0.00596383 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.02032 | −0.106386 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.0798 | −0.530506 | ||||||||
\(809\) | −10.6143 | −0.373180 | −0.186590 | − | 0.982438i | \(-0.559744\pi\) | ||||
−0.186590 | + | 0.982438i | \(0.559744\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.5293 | −1.07203 | −0.536014 | − | 0.844209i | \(-0.680070\pi\) | ||||
−0.536014 | + | 0.844209i | \(0.680070\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.37103 | −0.188255 | ||||||||
\(815\) | 28.9858 | 1.01533 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.7036 | 0.479429 | ||||||||
\(818\) | 9.47191 | 0.331178 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.5504 | −0.368436 | ||||||||
\(821\) | 55.9025 | 1.95101 | 0.975505 | − | 0.219978i | \(-0.0705986\pi\) | ||||
0.975505 | + | 0.219978i | \(0.0705986\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.7906 | 0.445851 | 0.222926 | − | 0.974835i | \(-0.428439\pi\) | ||||
0.222926 | + | 0.974835i | \(0.428439\pi\) | |||||||
\(824\) | −6.58871 | −0.229528 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.8611 | 0.968826 | 0.484413 | − | 0.874840i | \(-0.339033\pi\) | ||||
0.484413 | + | 0.874840i | \(0.339033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.1069 | −0.663609 | −0.331804 | − | 0.943348i | \(-0.607657\pi\) | ||||
−0.331804 | + | 0.943348i | \(0.607657\pi\) | |||||||
\(830\) | 3.86275 | 0.134078 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.76242 | −0.130439 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.1121 | 0.592190 | ||||||||
\(836\) | 10.9649 | 0.379230 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.13181 | 0.0390977 | ||||||||
\(839\) | −20.9072 | −0.721797 | −0.360898 | − | 0.932605i | \(-0.617530\pi\) | ||||
−0.360898 | + | 0.932605i | \(0.617530\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8938 | −0.996339 | ||||||||
\(842\) | 0.222453 | 0.00766624 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.83658 | −0.235325 | ||||||||
\(845\) | −21.9704 | −0.755804 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.78975 | −0.267501 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.711468 | −0.0244032 | ||||||||
\(851\) | 36.8332 | 1.26263 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.1615 | −1.71750 | −0.858748 | − | 0.512397i | \(-0.828757\pi\) | ||||
−0.858748 | + | 0.512397i | \(0.828757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.3825 | −0.594123 | ||||||||
\(857\) | −20.9552 | −0.715816 | −0.357908 | − | 0.933757i | \(-0.616510\pi\) | ||||
−0.357908 | + | 0.933757i | \(0.616510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.3665 | 1.37729 | 0.688643 | − | 0.725100i | \(-0.258207\pi\) | ||||
0.688643 | + | 0.725100i | \(0.258207\pi\) | |||||||
\(860\) | −18.2082 | −0.620894 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.60708 | 0.259098 | ||||||||
\(863\) | −16.3915 | −0.557975 | −0.278987 | − | 0.960295i | \(-0.589999\pi\) | ||||
−0.278987 | + | 0.960295i | \(0.589999\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7239 | −0.636632 | ||||||||
\(866\) | −7.24537 | −0.246208 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.74870 | 0.0593207 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.24384 | 0.0421461 | ||||||||
\(872\) | −1.92148 | −0.0650697 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.22448 | 0.210546 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.4169 | 1.16218 | 0.581088 | − | 0.813841i | \(-0.302627\pi\) | ||||
0.581088 | + | 0.813841i | \(0.302627\pi\) | |||||||
\(878\) | 4.14949 | 0.140038 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.2634 | −0.447110 | ||||||||
\(881\) | −9.28729 | −0.312897 | −0.156448 | − | 0.987686i | \(-0.550005\pi\) | ||||
−0.156448 | + | 0.987686i | \(0.550005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.4528 | 0.654639 | 0.327319 | − | 0.944914i | \(-0.393855\pi\) | ||||
0.327319 | + | 0.944914i | \(0.393855\pi\) | |||||||
\(884\) | −1.52382 | −0.0512517 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.958146 | −0.0321895 | ||||||||
\(887\) | −20.2566 | −0.680151 | −0.340075 | − | 0.940398i | \(-0.610453\pi\) | ||||
−0.340075 | + | 0.940398i | \(0.610453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.218570 | 0.00732648 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.7178 | 1.22940 | ||||||||
\(893\) | −24.0068 | −0.803355 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.8746 | 1.06545 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.80635 | −0.127020 | ||||||||
\(899\) | 3.05079 | 0.101749 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.50798 | −0.0835530 | ||||||||
\(902\) | −2.99877 | −0.0998481 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.2960 | 0.808074 | ||||||||
\(905\) | 24.5617 | 0.816459 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.87681 | −0.327954 | −0.163977 | − | 0.986464i | \(-0.552432\pi\) | ||||
−0.163977 | + | 0.986464i | \(0.552432\pi\) | |||||||
\(908\) | −28.3165 | −0.939715 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.832714 | 0.0275890 | 0.0137945 | − | 0.999905i | \(-0.495609\pi\) | ||||
0.0137945 | + | 0.999905i | \(0.495609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.2634 | −0.438955 | ||||||||
\(914\) | −12.3786 | −0.409449 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.5635 | 0.646395 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.5390 | 0.644532 | 0.322266 | − | 0.946649i | \(-0.395555\pi\) | ||||
0.322266 | + | 0.946649i | \(0.395555\pi\) | |||||||
\(920\) | −17.2258 | −0.567917 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.5548 | 0.512271 | ||||||||
\(923\) | −7.55740 | −0.248755 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.4375 | −0.343184 | ||||||||
\(926\) | −2.51039 | −0.0824967 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.37607 | −0.0451716 | ||||||||
\(929\) | −58.7213 | −1.92658 | −0.963292 | − | 0.268457i | \(-0.913486\pi\) | ||||
−0.963292 | + | 0.268457i | \(0.913486\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.3784 | 0.667515 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.88231 | −0.0615909 | ||||||||
\(935\) | −4.27029 | −0.139653 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.2474 | −1.18415 | −0.592075 | − | 0.805883i | \(-0.701691\pi\) | ||||
−0.592075 | + | 0.805883i | \(0.701691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 31.8982 | 1.04040 | ||||||||
\(941\) | −1.30139 | −0.0424241 | −0.0212120 | − | 0.999775i | \(-0.506753\pi\) | ||||
−0.0212120 | + | 0.999775i | \(0.506753\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.5648 | 0.669683 | ||||||||
\(944\) | 9.01721 | 0.293485 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.17537 | −0.168266 | ||||||||
\(947\) | −28.8185 | −0.936477 | −0.468238 | − | 0.883602i | \(-0.655111\pi\) | ||||
−0.468238 | + | 0.883602i | \(0.655111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0582261 | 0.00189010 | ||||||||
\(950\) | −1.76385 | −0.0572268 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.4348 | 1.37460 | 0.687299 | − | 0.726375i | \(-0.258796\pi\) | ||||
0.687299 | + | 0.726375i | \(0.258796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.8504 | 1.09537 | ||||||||
\(956\) | 9.23509 | 0.298684 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.269062 | −0.00869300 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.6624 | 1.82782 | ||||||||
\(962\) | 1.85051 | 0.0596629 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.9701 | −0.868649 | ||||||||
\(965\) | −29.3270 | −0.944069 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.9540 | −1.28483 | −0.642417 | − | 0.766355i | \(-0.722068\pi\) | ||||
−0.642417 | + | 0.766355i | \(0.722068\pi\) | |||||||
\(968\) | 7.92245 | 0.254637 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.43762 | 0.174591 | ||||||||
\(971\) | −5.01507 | −0.160941 | −0.0804706 | − | 0.996757i | \(-0.525642\pi\) | ||||
−0.0804706 | + | 0.996757i | \(0.525642\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12.9515 | −0.414994 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.17801 | 0.101726 | ||||||||
\(977\) | −51.5778 | −1.65012 | −0.825060 | − | 0.565045i | \(-0.808859\pi\) | ||||
−0.825060 | + | 0.565045i | \(0.808859\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.750498 | −0.0239860 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.30866 | 0.105584 | ||||||||
\(983\) | 12.4383 | 0.396720 | 0.198360 | − | 0.980129i | \(-0.436438\pi\) | ||||
0.198360 | + | 0.980129i | \(0.436438\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.8699 | 0.346343 | ||||||||
\(986\) | −0.127411 | −0.00405760 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.77781 | −0.120188 | ||||||||
\(989\) | 35.4914 | 1.12856 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.7520 | 0.818038 | 0.409019 | − | 0.912526i | \(-0.365871\pi\) | ||||
0.409019 | + | 0.912526i | \(0.365871\pi\) | |||||||
\(992\) | −39.5404 | −1.25541 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.5512 | 1.00024 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.4501 | −1.69278 | −0.846391 | − | 0.532562i | \(-0.821229\pi\) | ||||
−0.846391 | + | 0.532562i | \(0.821229\pi\) | |||||||
\(998\) | 9.96144 | 0.315324 | ||||||||
\(999\) | 0 | 0 |
(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 | 7497.2.a.ce.1.5 | yes | 8 | |
3.2 | odd | 2 | 7497.2.a.cd.1.4 | ✓ | 8 | ||
7.6 | odd | 2 | 7497.2.a.cd.1.5 | yes | 8 | ||
21.20 | even | 2 | inner | 7497.2.a.ce.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7497.2.a.cd.1.4 | ✓ | 8 | 3.2 | odd | 2 | ||
7497.2.a.cd.1.5 | yes | 8 | 7.6 | odd | 2 | ||
7497.2.a.ce.1.4 | yes | 8 | 21.20 | even | 2 | inner | |
7497.2.a.ce.1.5 | yes | 8 | 1.1 | even | 1 | trivial |