Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73205 | −1.93185 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.46410 | 2.73205 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46410 | 0.931343 | 0.465671 | − | 0.884958i | \(-0.345813\pi\) | ||||
0.465671 | + | 0.884958i | \(0.345813\pi\) | |||||||
\(8\) | −9.46410 | −3.34607 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.73205 | 0.863950 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −6.73205 | −1.79922 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.9282 | 3.73205 | ||||||||
\(17\) | 3.26795 | 0.792594 | 0.396297 | − | 0.918122i | \(-0.370295\pi\) | ||||
0.396297 | + | 0.918122i | \(0.370295\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.46410 | −0.335888 | −0.167944 | − | 0.985797i | \(-0.553713\pi\) | ||||
−0.167944 | + | 0.985797i | \(0.553713\pi\) | |||||||
\(20\) | −5.46410 | −1.22181 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.46410 | −2.01775 | ||||||||
\(23\) | 7.46410 | 1.55637 | 0.778186 | − | 0.628033i | \(-0.216140\pi\) | ||||
0.778186 | + | 0.628033i | \(0.216140\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.4641 | 2.54448 | ||||||||
\(29\) | −0.732051 | −0.135938 | −0.0679692 | − | 0.997687i | \(-0.521652\pi\) | ||||
−0.0679692 | + | 0.997687i | \(0.521652\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.19615 | −1.29247 | −0.646234 | − | 0.763140i | \(-0.723657\pi\) | ||||
−0.646234 | + | 0.763140i | \(0.723657\pi\) | |||||||
\(32\) | −21.8564 | −3.86370 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.92820 | −1.53117 | ||||||||
\(35\) | −2.46410 | −0.416509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.46410 | 1.49641 | ||||||||
\(41\) | −8.73205 | −1.36372 | −0.681859 | − | 0.731484i | \(-0.738828\pi\) | ||||
−0.681859 | + | 0.731484i | \(0.738828\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.73205 | −0.569132 | −0.284566 | − | 0.958656i | \(-0.591850\pi\) | ||||
−0.284566 | + | 0.958656i | \(0.591850\pi\) | |||||||
\(44\) | 18.9282 | 2.85353 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.3923 | −3.00668 | ||||||||
\(47\) | 10.1962 | 1.48726 | 0.743631 | − | 0.668590i | \(-0.233102\pi\) | ||||
0.743631 | + | 0.668590i | \(0.233102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.928203 | −0.132600 | ||||||||
\(50\) | −2.73205 | −0.386370 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.92820 | −0.951662 | −0.475831 | − | 0.879537i | \(-0.657853\pi\) | ||||
−0.475831 | + | 0.879537i | \(0.657853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | −23.3205 | −3.11633 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −10.7321 | −1.39719 | −0.698597 | − | 0.715515i | \(-0.746192\pi\) | ||||
−0.698597 | + | 0.715515i | \(0.746192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46410 | −0.315496 | −0.157748 | − | 0.987479i | \(-0.550423\pi\) | ||||
−0.157748 | + | 0.987479i | \(0.550423\pi\) | |||||||
\(62\) | 19.6603 | 2.49685 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.53590 | −0.676318 | −0.338159 | − | 0.941089i | \(-0.609804\pi\) | ||||
−0.338159 | + | 0.941089i | \(0.609804\pi\) | |||||||
\(68\) | 17.8564 | 2.16541 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.73205 | 0.804634 | ||||||||
\(71\) | −9.26795 | −1.09990 | −0.549952 | − | 0.835197i | \(-0.685354\pi\) | ||||
−0.549952 | + | 0.835197i | \(0.685354\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.39230 | −0.631122 | −0.315561 | − | 0.948905i | \(-0.602193\pi\) | ||||
−0.315561 | + | 0.948905i | \(0.602193\pi\) | |||||||
\(74\) | 10.9282 | 1.27038 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 8.53590 | 0.972756 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9282 | −1.34203 | −0.671014 | − | 0.741445i | \(-0.734141\pi\) | ||||
−0.671014 | + | 0.741445i | \(0.734141\pi\) | |||||||
\(80\) | −14.9282 | −1.66902 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 23.8564 | 2.63450 | ||||||||
\(83\) | −9.46410 | −1.03882 | −0.519410 | − | 0.854525i | \(-0.673848\pi\) | ||||
−0.519410 | + | 0.854525i | \(0.673848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.26795 | −0.354459 | ||||||||
\(86\) | 10.1962 | 1.09948 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −32.7846 | −3.49485 | ||||||||
\(89\) | −4.73205 | −0.501596 | −0.250798 | − | 0.968039i | \(-0.580693\pi\) | ||||
−0.250798 | + | 0.968039i | \(0.580693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 40.7846 | 4.25209 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −27.8564 | −2.87317 | ||||||||
\(95\) | 1.46410 | 0.150214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.53590 | 0.968224 | 0.484112 | − | 0.875006i | \(-0.339143\pi\) | ||||
0.484112 | + | 0.875006i | \(0.339143\pi\) | |||||||
\(98\) | 2.53590 | 0.256164 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.46410 | 0.546410 | ||||||||
\(101\) | −8.92820 | −0.888389 | −0.444195 | − | 0.895930i | \(-0.646510\pi\) | ||||
−0.444195 | + | 0.895930i | \(0.646510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.19615 | 0.709058 | 0.354529 | − | 0.935045i | \(-0.384641\pi\) | ||||
0.354529 | + | 0.935045i | \(0.384641\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.9282 | 1.83847 | ||||||||
\(107\) | 7.12436 | 0.688737 | 0.344369 | − | 0.938834i | \(-0.388093\pi\) | ||||
0.344369 | + | 0.938834i | \(0.388093\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7321 | 1.12373 | 0.561863 | − | 0.827230i | \(-0.310085\pi\) | ||||
0.561863 | + | 0.827230i | \(0.310085\pi\) | |||||||
\(110\) | 9.46410 | 0.902367 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 36.7846 | 3.47582 | ||||||||
\(113\) | −12.5359 | −1.17928 | −0.589639 | − | 0.807667i | \(-0.700730\pi\) | ||||
−0.589639 | + | 0.807667i | \(0.700730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.46410 | −0.696031 | ||||||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 29.3205 | 2.69917 | ||||||||
\(119\) | 8.05256 | 0.738177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.73205 | 0.609491 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −39.3205 | −3.53109 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.66025 | −0.236059 | −0.118030 | − | 0.993010i | \(-0.537658\pi\) | ||||
−0.118030 | + | 0.993010i | \(0.537658\pi\) | |||||||
\(128\) | −37.8564 | −3.34607 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.73205 | −0.413441 | −0.206721 | − | 0.978400i | \(-0.566279\pi\) | ||||
−0.206721 | + | 0.978400i | \(0.566279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.60770 | −0.312827 | ||||||||
\(134\) | 15.1244 | 1.30655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.9282 | −2.65207 | ||||||||
\(137\) | −15.1244 | −1.29216 | −0.646080 | − | 0.763269i | \(-0.723593\pi\) | ||||
−0.646080 | + | 0.763269i | \(0.723593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.07180 | −0.345365 | −0.172683 | − | 0.984978i | \(-0.555244\pi\) | ||||
−0.172683 | + | 0.984978i | \(0.555244\pi\) | |||||||
\(140\) | −13.4641 | −1.13792 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.3205 | 2.12485 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.732051 | 0.0607935 | ||||||||
\(146\) | 14.7321 | 1.21923 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.8564 | −1.79659 | ||||||||
\(149\) | −4.00000 | −0.327693 | −0.163846 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163846 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.85641 | −0.802103 | −0.401051 | − | 0.916056i | \(-0.631355\pi\) | ||||
−0.401051 | + | 0.916056i | \(0.631355\pi\) | |||||||
\(152\) | 13.8564 | 1.12390 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −23.3205 | −1.87922 | ||||||||
\(155\) | 7.19615 | 0.578009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.26795 | 0.500237 | 0.250118 | − | 0.968215i | \(-0.419530\pi\) | ||||
0.250118 | + | 0.968215i | \(0.419530\pi\) | |||||||
\(158\) | 32.5885 | 2.59260 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 21.8564 | 1.72790 | ||||||||
\(161\) | 18.3923 | 1.44952 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4641 | 0.976264 | 0.488132 | − | 0.872770i | \(-0.337678\pi\) | ||||
0.488132 | + | 0.872770i | \(0.337678\pi\) | |||||||
\(164\) | −47.7128 | −3.72574 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.8564 | 2.00685 | ||||||||
\(167\) | −10.5359 | −0.815292 | −0.407646 | − | 0.913140i | \(-0.633650\pi\) | ||||
−0.407646 | + | 0.913140i | \(0.633650\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.92820 | 0.684762 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20.3923 | −1.55490 | ||||||||
\(173\) | −6.73205 | −0.511828 | −0.255914 | − | 0.966700i | \(-0.582376\pi\) | ||||
−0.255914 | + | 0.966700i | \(0.582376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.46410 | 0.186269 | ||||||||
\(176\) | 51.7128 | 3.89800 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.9282 | 0.969010 | ||||||||
\(179\) | 15.1244 | 1.13045 | 0.565224 | − | 0.824938i | \(-0.308790\pi\) | ||||
0.565224 | + | 0.824938i | \(0.308790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4641 | −1.59541 | −0.797707 | − | 0.603045i | \(-0.793954\pi\) | ||||
−0.797707 | + | 0.603045i | \(0.793954\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −70.6410 | −5.20772 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3205 | 0.827838 | ||||||||
\(188\) | 55.7128 | 4.06327 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −17.5167 | −1.26746 | −0.633731 | − | 0.773554i | \(-0.718477\pi\) | ||||
−0.633731 | + | 0.773554i | \(0.718477\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.9282 | −1.43446 | −0.717232 | − | 0.696835i | \(-0.754591\pi\) | ||||
−0.717232 | + | 0.696835i | \(0.754591\pi\) | |||||||
\(194\) | −26.0526 | −1.87046 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.07180 | −0.362271 | ||||||||
\(197\) | −10.9282 | −0.778602 | −0.389301 | − | 0.921111i | \(-0.627283\pi\) | ||||
−0.389301 | + | 0.921111i | \(0.627283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.0000 | −1.06332 | −0.531661 | − | 0.846957i | \(-0.678432\pi\) | ||||
−0.531661 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(200\) | −9.46410 | −0.669213 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.3923 | 1.71624 | ||||||||
\(203\) | −1.80385 | −0.126605 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.73205 | 0.609873 | ||||||||
\(206\) | −19.6603 | −1.36979 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.07180 | −0.350824 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4641 | 1.27112 | 0.635561 | − | 0.772051i | \(-0.280769\pi\) | ||||
0.635561 | + | 0.772051i | \(0.280769\pi\) | |||||||
\(212\) | −37.8564 | −2.59999 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.4641 | −1.33054 | ||||||||
\(215\) | 3.73205 | 0.254524 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.7321 | −1.20373 | ||||||||
\(218\) | −32.0526 | −2.17087 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.9282 | −1.27614 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.8564 | 1.06182 | 0.530912 | − | 0.847427i | \(-0.321850\pi\) | ||||
0.530912 | + | 0.847427i | \(0.321850\pi\) | |||||||
\(224\) | −53.8564 | −3.59843 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 34.2487 | 2.27819 | ||||||||
\(227\) | −5.66025 | −0.375684 | −0.187842 | − | 0.982199i | \(-0.560149\pi\) | ||||
−0.187842 | + | 0.982199i | \(0.560149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.39230 | 0.158088 | 0.0790440 | − | 0.996871i | \(-0.474813\pi\) | ||||
0.0790440 | + | 0.996871i | \(0.474813\pi\) | |||||||
\(230\) | 20.3923 | 1.34463 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.92820 | 0.454859 | ||||||||
\(233\) | 3.85641 | 0.252642 | 0.126321 | − | 0.991989i | \(-0.459683\pi\) | ||||
0.126321 | + | 0.991989i | \(0.459683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1962 | −0.665124 | ||||||||
\(236\) | −58.6410 | −3.81721 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.0000 | −1.42605 | ||||||||
\(239\) | 1.46410 | 0.0947049 | 0.0473524 | − | 0.998878i | \(-0.484922\pi\) | ||||
0.0473524 | + | 0.998878i | \(0.484922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3923 | 1.44242 | 0.721208 | − | 0.692719i | \(-0.243587\pi\) | ||||
0.721208 | + | 0.692719i | \(0.243587\pi\) | |||||||
\(242\) | −2.73205 | −0.175623 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.4641 | −0.861951 | ||||||||
\(245\) | 0.928203 | 0.0593007 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 68.1051 | 4.32468 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.73205 | 0.172790 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.8564 | 1.62558 | ||||||||
\(254\) | 7.26795 | 0.456032 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 43.7128 | 2.73205 | ||||||||
\(257\) | −7.26795 | −0.453362 | −0.226681 | − | 0.973969i | \(-0.572788\pi\) | ||||
−0.226681 | + | 0.973969i | \(0.572788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.85641 | −0.612447 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.9282 | 0.798707 | ||||||||
\(263\) | 23.6603 | 1.45895 | 0.729477 | − | 0.684005i | \(-0.239764\pi\) | ||||
0.729477 | + | 0.684005i | \(0.239764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92820 | 0.425596 | ||||||||
\(266\) | 9.85641 | 0.604335 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −30.2487 | −1.84773 | ||||||||
\(269\) | 1.66025 | 0.101227 | 0.0506137 | − | 0.998718i | \(-0.483882\pi\) | ||||
0.0506137 | + | 0.998718i | \(0.483882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.267949 | 0.0162768 | 0.00813838 | − | 0.999967i | \(-0.497409\pi\) | ||||
0.00813838 | + | 0.999967i | \(0.497409\pi\) | |||||||
\(272\) | 48.7846 | 2.95800 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 41.3205 | 2.49626 | ||||||||
\(275\) | 3.46410 | 0.208893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.2487 | −1.69730 | −0.848650 | − | 0.528954i | \(-0.822584\pi\) | ||||
−0.848650 | + | 0.528954i | \(0.822584\pi\) | |||||||
\(278\) | 11.1244 | 0.667195 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 23.3205 | 1.39367 | ||||||||
\(281\) | 3.12436 | 0.186383 | 0.0931917 | − | 0.995648i | \(-0.470293\pi\) | ||||
0.0931917 | + | 0.995648i | \(0.470293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.73205 | −0.221847 | −0.110924 | − | 0.993829i | \(-0.535381\pi\) | ||||
−0.110924 | + | 0.993829i | \(0.535381\pi\) | |||||||
\(284\) | −50.6410 | −3.00499 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.5167 | −1.27009 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.32051 | −0.371795 | ||||||||
\(290\) | −2.00000 | −0.117444 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.4641 | −1.72426 | ||||||||
\(293\) | 6.58846 | 0.384902 | 0.192451 | − | 0.981307i | \(-0.438356\pi\) | ||||
0.192451 | + | 0.981307i | \(0.438356\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7321 | 0.624844 | ||||||||
\(296\) | 37.8564 | 2.20036 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.9282 | 0.633054 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.19615 | −0.530057 | ||||||||
\(302\) | 26.9282 | 1.54954 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.8564 | −1.25355 | ||||||||
\(305\) | 2.46410 | 0.141094 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.9282 | 1.47980 | 0.739900 | − | 0.672716i | \(-0.234873\pi\) | ||||
0.739900 | + | 0.672716i | \(0.234873\pi\) | |||||||
\(308\) | 46.6410 | 2.65762 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.6603 | −1.11663 | ||||||||
\(311\) | 0.196152 | 0.0111228 | 0.00556139 | − | 0.999985i | \(-0.498230\pi\) | ||||
0.00556139 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.1962 | −1.19808 | −0.599039 | − | 0.800720i | \(-0.704450\pi\) | ||||
−0.599039 | + | 0.800720i | \(0.704450\pi\) | |||||||
\(314\) | −17.1244 | −0.966383 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −65.1769 | −3.66649 | ||||||||
\(317\) | 10.5359 | 0.591755 | 0.295878 | − | 0.955226i | \(-0.404388\pi\) | ||||
0.295878 | + | 0.955226i | \(0.404388\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.53590 | −0.141983 | ||||||||
\(320\) | −29.8564 | −1.66902 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −50.2487 | −2.80025 | ||||||||
\(323\) | −4.78461 | −0.266223 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −34.0526 | −1.88600 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 82.6410 | 4.56309 | ||||||||
\(329\) | 25.1244 | 1.38515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.1244 | 0.886275 | 0.443137 | − | 0.896454i | \(-0.353865\pi\) | ||||
0.443137 | + | 0.896454i | \(0.353865\pi\) | |||||||
\(332\) | −51.7128 | −2.83811 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.7846 | 1.57502 | ||||||||
\(335\) | 5.53590 | 0.302458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.05256 | −0.384177 | −0.192089 | − | 0.981378i | \(-0.561526\pi\) | ||||
−0.192089 | + | 0.981378i | \(0.561526\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −17.8564 | −0.968400 | ||||||||
\(341\) | −24.9282 | −1.34994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5359 | −1.05484 | ||||||||
\(344\) | 35.3205 | 1.90435 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.3923 | 0.988776 | ||||||||
\(347\) | −13.4641 | −0.722791 | −0.361395 | − | 0.932413i | \(-0.617700\pi\) | ||||
−0.361395 | + | 0.932413i | \(0.617700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.9808 | 1.17660 | 0.588302 | − | 0.808642i | \(-0.299797\pi\) | ||||
0.588302 | + | 0.808642i | \(0.299797\pi\) | |||||||
\(350\) | −6.73205 | −0.359843 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −75.7128 | −4.03551 | ||||||||
\(353\) | 23.0718 | 1.22799 | 0.613994 | − | 0.789311i | \(-0.289562\pi\) | ||||
0.613994 | + | 0.789311i | \(0.289562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.26795 | 0.491892 | ||||||||
\(356\) | −25.8564 | −1.37039 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.3205 | −2.18386 | ||||||||
\(359\) | 16.3397 | 0.862379 | 0.431189 | − | 0.902261i | \(-0.358094\pi\) | ||||
0.431189 | + | 0.902261i | \(0.358094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8564 | −0.887179 | ||||||||
\(362\) | 58.6410 | 3.08210 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.39230 | 0.282246 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.12436 | 0.319689 | 0.159844 | − | 0.987142i | \(-0.448901\pi\) | ||||
0.159844 | + | 0.987142i | \(0.448901\pi\) | |||||||
\(368\) | 111.426 | 5.80846 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.9282 | −0.568130 | ||||||||
\(371\) | −17.0718 | −0.886324 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.1244 | −1.35267 | −0.676334 | − | 0.736595i | \(-0.736432\pi\) | ||||
−0.676334 | + | 0.736595i | \(0.736432\pi\) | |||||||
\(374\) | −30.9282 | −1.59926 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −96.4974 | −4.97647 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.2679 | −0.835628 | −0.417814 | − | 0.908532i | \(-0.637204\pi\) | ||||
−0.417814 | + | 0.908532i | \(0.637204\pi\) | |||||||
\(380\) | 8.00000 | 0.410391 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 47.8564 | 2.44855 | ||||||||
\(383\) | 25.6603 | 1.31118 | 0.655589 | − | 0.755118i | \(-0.272420\pi\) | ||||
0.655589 | + | 0.755118i | \(0.272420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.53590 | −0.435030 | ||||||||
\(386\) | 54.4449 | 2.77117 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.1051 | 2.64524 | ||||||||
\(389\) | −10.5359 | −0.534191 | −0.267096 | − | 0.963670i | \(-0.586064\pi\) | ||||
−0.267096 | + | 0.963670i | \(0.586064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.3923 | 1.23357 | ||||||||
\(392\) | 8.78461 | 0.443690 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 29.8564 | 1.50414 | ||||||||
\(395\) | 11.9282 | 0.600173 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3205 | −0.517971 | −0.258986 | − | 0.965881i | \(-0.583388\pi\) | ||||
−0.258986 | + | 0.965881i | \(0.583388\pi\) | |||||||
\(398\) | 40.9808 | 2.05418 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.9282 | 0.746410 | ||||||||
\(401\) | 19.3205 | 0.964820 | 0.482410 | − | 0.875946i | \(-0.339762\pi\) | ||||
0.482410 | + | 0.875946i | \(0.339762\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −48.7846 | −2.42713 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.92820 | 0.244583 | ||||||||
\(407\) | −13.8564 | −0.686837 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6603 | 0.724903 | 0.362451 | − | 0.932003i | \(-0.381940\pi\) | ||||
0.362451 | + | 0.932003i | \(0.381940\pi\) | |||||||
\(410\) | −23.8564 | −1.17818 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 39.3205 | 1.93718 | ||||||||
\(413\) | −26.4449 | −1.30127 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.46410 | 0.464574 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.8564 | 0.677739 | ||||||||
\(419\) | 38.4449 | 1.87815 | 0.939077 | − | 0.343706i | \(-0.111682\pi\) | ||||
0.939077 | + | 0.343706i | \(0.111682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.58846 | −0.369839 | −0.184919 | − | 0.982754i | \(-0.559202\pi\) | ||||
−0.184919 | + | 0.982754i | \(0.559202\pi\) | |||||||
\(422\) | −50.4449 | −2.45562 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 65.5692 | 3.18432 | ||||||||
\(425\) | 3.26795 | 0.158519 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.07180 | −0.293835 | ||||||||
\(428\) | 38.9282 | 1.88167 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.1962 | −0.491702 | ||||||||
\(431\) | −11.3205 | −0.545290 | −0.272645 | − | 0.962115i | \(-0.587898\pi\) | ||||
−0.272645 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.1962 | 0.730280 | 0.365140 | − | 0.930953i | \(-0.381021\pi\) | ||||
0.365140 | + | 0.930953i | \(0.381021\pi\) | |||||||
\(434\) | 48.4449 | 2.32543 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 64.1051 | 3.07008 | ||||||||
\(437\) | −10.9282 | −0.522767 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.39230 | −0.257361 | −0.128680 | − | 0.991686i | \(-0.541074\pi\) | ||||
−0.128680 | + | 0.991686i | \(0.541074\pi\) | |||||||
\(440\) | 32.7846 | 1.56294 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.1244 | 1.00365 | 0.501824 | − | 0.864970i | \(-0.332662\pi\) | ||||
0.501824 | + | 0.864970i | \(0.332662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.73205 | 0.224321 | ||||||||
\(446\) | −43.3205 | −2.05129 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 73.5692 | 3.47582 | ||||||||
\(449\) | −24.9282 | −1.17643 | −0.588217 | − | 0.808703i | \(-0.700170\pi\) | ||||
−0.588217 | + | 0.808703i | \(0.700170\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.2487 | −1.42436 | ||||||||
\(452\) | −68.4974 | −3.22185 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.4641 | 0.725766 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3923 | 0.720022 | 0.360011 | − | 0.932948i | \(-0.382773\pi\) | ||||
0.360011 | + | 0.932948i | \(0.382773\pi\) | |||||||
\(458\) | −6.53590 | −0.305402 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −40.7846 | −1.90159 | ||||||||
\(461\) | −33.5167 | −1.56103 | −0.780513 | − | 0.625139i | \(-0.785042\pi\) | ||||
−0.780513 | + | 0.625139i | \(0.785042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.7846 | 1.84895 | 0.924474 | − | 0.381246i | \(-0.124505\pi\) | ||||
0.924474 | + | 0.381246i | \(0.124505\pi\) | |||||||
\(464\) | −10.9282 | −0.507329 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.5359 | −0.488066 | ||||||||
\(467\) | 6.33975 | 0.293368 | 0.146684 | − | 0.989183i | \(-0.453140\pi\) | ||||
0.146684 | + | 0.989183i | \(0.453140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.6410 | −0.629884 | ||||||||
\(470\) | 27.8564 | 1.28492 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 101.569 | 4.67510 | ||||||||
\(473\) | −12.9282 | −0.594439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.46410 | −0.0671776 | ||||||||
\(476\) | 44.0000 | 2.01674 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.00000 | −0.182956 | ||||||||
\(479\) | 29.9090 | 1.36658 | 0.683288 | − | 0.730149i | \(-0.260549\pi\) | ||||
0.683288 | + | 0.730149i | \(0.260549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −61.1769 | −2.78653 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.46410 | 0.248368 | ||||||||
\(485\) | −9.53590 | −0.433003 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.7846 | 0.941841 | 0.470920 | − | 0.882176i | \(-0.343922\pi\) | ||||
0.470920 | + | 0.882176i | \(0.343922\pi\) | |||||||
\(488\) | 23.3205 | 1.05567 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.53590 | −0.114560 | ||||||||
\(491\) | 17.1244 | 0.772811 | 0.386406 | − | 0.922329i | \(-0.373716\pi\) | ||||
0.386406 | + | 0.922329i | \(0.373716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.39230 | −0.107744 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −107.426 | −4.82355 | ||||||||
\(497\) | −22.8372 | −1.02439 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3923 | −0.912885 | −0.456442 | − | 0.889753i | \(-0.650877\pi\) | ||||
−0.456442 | + | 0.889753i | \(0.650877\pi\) | |||||||
\(500\) | −5.46410 | −0.244362 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.7846 | −0.480862 | −0.240431 | − | 0.970666i | \(-0.577289\pi\) | ||||
−0.240431 | + | 0.970666i | \(0.577289\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.92820 | 0.397300 | ||||||||
\(506\) | −70.6410 | −3.14038 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.5359 | −0.644926 | ||||||||
\(509\) | 0.928203 | 0.0411419 | 0.0205709 | − | 0.999788i | \(-0.493452\pi\) | ||||
0.0205709 | + | 0.999788i | \(0.493452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.2872 | −0.587791 | ||||||||
\(512\) | −43.7128 | −1.93185 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.8564 | 0.875829 | ||||||||
\(515\) | −7.19615 | −0.317100 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.3205 | 1.55339 | ||||||||
\(518\) | 26.9282 | 1.18316 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.26795 | 0.406036 | 0.203018 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203018 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.5359 | −1.33524 | −0.667621 | − | 0.744501i | \(-0.732687\pi\) | ||||
−0.667621 | + | 0.744501i | \(0.732687\pi\) | |||||||
\(524\) | −25.8564 | −1.12954 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −64.6410 | −2.81848 | ||||||||
\(527\) | −23.5167 | −1.02440 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.7128 | 1.42230 | ||||||||
\(530\) | −18.9282 | −0.822189 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.7128 | −0.854659 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.12436 | −0.308013 | ||||||||
\(536\) | 52.3923 | 2.26300 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.53590 | −0.195556 | ||||||||
\(539\) | −3.21539 | −0.138497 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5885 | −0.584213 | −0.292107 | − | 0.956386i | \(-0.594356\pi\) | ||||
−0.292107 | + | 0.956386i | \(0.594356\pi\) | |||||||
\(542\) | −0.732051 | −0.0314443 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −71.4256 | −3.06235 | ||||||||
\(545\) | −11.7321 | −0.502546 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.33975 | −0.313825 | −0.156912 | − | 0.987613i | \(-0.550154\pi\) | ||||
−0.156912 | + | 0.987613i | \(0.550154\pi\) | |||||||
\(548\) | −82.6410 | −3.53025 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.46410 | −0.403551 | ||||||||
\(551\) | 1.07180 | 0.0456601 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.3923 | −1.24989 | ||||||||
\(554\) | 77.1769 | 3.27893 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.2487 | −0.943556 | ||||||||
\(557\) | −14.5359 | −0.615906 | −0.307953 | − | 0.951402i | \(-0.599644\pi\) | ||||
−0.307953 | + | 0.951402i | \(0.599644\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −36.7846 | −1.55443 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.53590 | −0.360065 | ||||||||
\(563\) | −3.46410 | −0.145994 | −0.0729972 | − | 0.997332i | \(-0.523256\pi\) | ||||
−0.0729972 | + | 0.997332i | \(0.523256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.5359 | 0.527389 | ||||||||
\(566\) | 10.1962 | 0.428576 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 87.7128 | 3.68035 | ||||||||
\(569\) | 33.8038 | 1.41713 | 0.708566 | − | 0.705645i | \(-0.249343\pi\) | ||||
0.708566 | + | 0.705645i | \(0.249343\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.8564 | 0.998360 | 0.499180 | − | 0.866498i | \(-0.333635\pi\) | ||||
0.499180 | + | 0.866498i | \(0.333635\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 58.7846 | 2.45362 | ||||||||
\(575\) | 7.46410 | 0.311275 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.7128 | 1.81979 | 0.909894 | − | 0.414841i | \(-0.136163\pi\) | ||||
0.909894 | + | 0.414841i | \(0.136163\pi\) | |||||||
\(578\) | 17.2679 | 0.718252 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.00000 | 0.166091 | ||||||||
\(581\) | −23.3205 | −0.967498 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.0000 | −0.993978 | ||||||||
\(584\) | 51.0333 | 2.11177 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 8.33975 | 0.344218 | 0.172109 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172109 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5359 | 0.434124 | ||||||||
\(590\) | −29.3205 | −1.20711 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −59.7128 | −2.45418 | ||||||||
\(593\) | 13.3205 | 0.547008 | 0.273504 | − | 0.961871i | \(-0.411817\pi\) | ||||
0.273504 | + | 0.961871i | \(0.411817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.05256 | −0.330123 | ||||||||
\(596\) | −21.8564 | −0.895273 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.12436 | −0.0459399 | −0.0229700 | − | 0.999736i | \(-0.507312\pi\) | ||||
−0.0229700 | + | 0.999736i | \(0.507312\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.2487 | 1.07071 | 0.535354 | − | 0.844628i | \(-0.320178\pi\) | ||||
0.535354 | + | 0.844628i | \(0.320178\pi\) | |||||||
\(602\) | 25.1244 | 1.02399 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −53.8564 | −2.19139 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.3923 | 1.55830 | 0.779148 | − | 0.626840i | \(-0.215652\pi\) | ||||
0.779148 | + | 0.626840i | \(0.215652\pi\) | |||||||
\(608\) | 32.0000 | 1.29777 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.73205 | −0.272573 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.7846 | −1.76844 | −0.884222 | − | 0.467067i | \(-0.845311\pi\) | ||||
−0.884222 | + | 0.467067i | \(0.845311\pi\) | |||||||
\(614\) | −70.8372 | −2.85876 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −80.7846 | −3.25490 | ||||||||
\(617\) | 44.6410 | 1.79718 | 0.898590 | − | 0.438790i | \(-0.144593\pi\) | ||||
0.898590 | + | 0.438790i | \(0.144593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.5885 | 0.787327 | 0.393663 | − | 0.919255i | \(-0.371208\pi\) | ||||
0.393663 | + | 0.919255i | \(0.371208\pi\) | |||||||
\(620\) | 39.3205 | 1.57915 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.535898 | −0.0214876 | ||||||||
\(623\) | −11.6603 | −0.467158 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 57.9090 | 2.31451 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 34.2487 | 1.36667 | ||||||||
\(629\) | −13.0718 | −0.521207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.5885 | −1.65561 | −0.827805 | − | 0.561016i | \(-0.810411\pi\) | ||||
−0.827805 | + | 0.561016i | \(0.810411\pi\) | |||||||
\(632\) | 112.890 | 4.49051 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.7846 | −1.14318 | ||||||||
\(635\) | 2.66025 | 0.105569 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.92820 | 0.274290 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 37.8564 | 1.49641 | ||||||||
\(641\) | 2.78461 | 0.109985 | 0.0549927 | − | 0.998487i | \(-0.482486\pi\) | ||||
0.0549927 | + | 0.998487i | \(0.482486\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.7846 | −1.49008 | −0.745040 | − | 0.667020i | \(-0.767570\pi\) | ||||
−0.745040 | + | 0.667020i | \(0.767570\pi\) | |||||||
\(644\) | 100.497 | 3.96015 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.0718 | 0.514303 | ||||||||
\(647\) | −2.00000 | −0.0786281 | −0.0393141 | − | 0.999227i | \(-0.512517\pi\) | ||||
−0.0393141 | + | 0.999227i | \(0.512517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.1769 | −1.45932 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 68.1051 | 2.66720 | ||||||||
\(653\) | 45.5167 | 1.78120 | 0.890602 | − | 0.454783i | \(-0.150283\pi\) | ||||
0.890602 | + | 0.454783i | \(0.150283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.73205 | 0.184897 | ||||||||
\(656\) | −130.354 | −5.08946 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −68.6410 | −2.67591 | ||||||||
\(659\) | −25.1769 | −0.980753 | −0.490377 | − | 0.871511i | \(-0.663141\pi\) | ||||
−0.490377 | + | 0.871511i | \(0.663141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0526 | 0.663268 | 0.331634 | − | 0.943408i | \(-0.392400\pi\) | ||||
0.331634 | + | 0.943408i | \(0.392400\pi\) | |||||||
\(662\) | −44.0526 | −1.71215 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 89.5692 | 3.47596 | ||||||||
\(665\) | 3.60770 | 0.139900 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.46410 | −0.211571 | ||||||||
\(668\) | −57.5692 | −2.22742 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −15.1244 | −0.584305 | ||||||||
\(671\) | −8.53590 | −0.329525 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.33975 | −0.0516434 | −0.0258217 | − | 0.999667i | \(-0.508220\pi\) | ||||
−0.0258217 | + | 0.999667i | \(0.508220\pi\) | |||||||
\(674\) | 19.2679 | 0.742174 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.78461 | 0.337620 | 0.168810 | − | 0.985649i | \(-0.446008\pi\) | ||||
0.168810 | + | 0.985649i | \(0.446008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.4974 | 0.901748 | ||||||||
\(680\) | 30.9282 | 1.18604 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 68.1051 | 2.60788 | ||||||||
\(683\) | −44.7321 | −1.71162 | −0.855812 | − | 0.517287i | \(-0.826942\pi\) | ||||
−0.855812 | + | 0.517287i | \(0.826942\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.1244 | 0.577872 | ||||||||
\(686\) | 53.3731 | 2.03779 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −55.7128 | −2.12403 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.4115 | −0.472157 | −0.236079 | − | 0.971734i | \(-0.575862\pi\) | ||||
−0.236079 | + | 0.971734i | \(0.575862\pi\) | |||||||
\(692\) | −36.7846 | −1.39834 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.7846 | 1.39632 | ||||||||
\(695\) | 4.07180 | 0.154452 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.5359 | −1.08087 | ||||||||
\(698\) | −60.0526 | −2.27302 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.4641 | 0.508895 | ||||||||
\(701\) | −32.7846 | −1.23826 | −0.619129 | − | 0.785289i | \(-0.712514\pi\) | ||||
−0.619129 | + | 0.785289i | \(0.712514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.85641 | 0.220879 | ||||||||
\(704\) | 103.426 | 3.89800 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −63.0333 | −2.37229 | ||||||||
\(707\) | −22.0000 | −0.827395 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.3397 | −0.500985 | −0.250492 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250492 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(710\) | −25.3205 | −0.950262 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 44.7846 | 1.67837 | ||||||||
\(713\) | −53.7128 | −2.01156 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 82.6410 | 3.08844 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −44.6410 | −1.66599 | ||||||||
\(719\) | −31.2679 | −1.16610 | −0.583049 | − | 0.812437i | \(-0.698140\pi\) | ||||
−0.583049 | + | 0.812437i | \(0.698140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.7321 | 0.660376 | ||||||||
\(722\) | 46.0526 | 1.71390 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −117.282 | −4.35875 | ||||||||
\(725\) | −0.732051 | −0.0271877 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.73205 | −0.360942 | −0.180471 | − | 0.983580i | \(-0.557762\pi\) | ||||
−0.180471 | + | 0.983580i | \(0.557762\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.7321 | −0.545258 | ||||||||
\(731\) | −12.1962 | −0.451091 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.3205 | 1.19379 | 0.596893 | − | 0.802321i | \(-0.296402\pi\) | ||||
0.596893 | + | 0.802321i | \(0.296402\pi\) | |||||||
\(734\) | −16.7321 | −0.617591 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −163.138 | −6.01336 | ||||||||
\(737\) | −19.1769 | −0.706391 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3923 | 0.382287 | 0.191144 | − | 0.981562i | \(-0.438780\pi\) | ||||
0.191144 | + | 0.981562i | \(0.438780\pi\) | |||||||
\(740\) | 21.8564 | 0.803457 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 46.6410 | 1.71225 | ||||||||
\(743\) | 25.9090 | 0.950508 | 0.475254 | − | 0.879849i | \(-0.342356\pi\) | ||||
0.475254 | + | 0.879849i | \(0.342356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | 0.146549 | ||||||||
\(746\) | 71.3731 | 2.61315 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 61.8564 | 2.26169 | ||||||||
\(749\) | 17.5551 | 0.641451 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3205 | 0.486072 | 0.243036 | − | 0.970017i | \(-0.421857\pi\) | ||||
0.243036 | + | 0.970017i | \(0.421857\pi\) | |||||||
\(752\) | 152.210 | 5.55054 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.85641 | 0.358711 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.0718 | 0.475103 | 0.237551 | − | 0.971375i | \(-0.423655\pi\) | ||||
0.237551 | + | 0.971375i | \(0.423655\pi\) | |||||||
\(758\) | 44.4449 | 1.61431 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.8564 | −0.502625 | ||||||||
\(761\) | −21.8564 | −0.792294 | −0.396147 | − | 0.918187i | \(-0.629653\pi\) | ||||
−0.396147 | + | 0.918187i | \(0.629653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.9090 | 1.04657 | ||||||||
\(764\) | −95.7128 | −3.46277 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −70.1051 | −2.53300 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.6077 | 1.06768 | 0.533840 | − | 0.845585i | \(-0.320748\pi\) | ||||
0.533840 | + | 0.845585i | \(0.320748\pi\) | |||||||
\(770\) | 23.3205 | 0.840413 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −108.890 | −3.91903 | ||||||||
\(773\) | −19.8564 | −0.714185 | −0.357093 | − | 0.934069i | \(-0.616232\pi\) | ||||
−0.357093 | + | 0.934069i | \(0.616232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.19615 | −0.258493 | ||||||||
\(776\) | −90.2487 | −3.23974 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.7846 | 1.03198 | ||||||||
\(779\) | 12.7846 | 0.458056 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.1051 | −1.14881 | ||||||||
\(782\) | −66.6410 | −2.38308 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.8564 | −0.494872 | ||||||||
\(785\) | −6.26795 | −0.223713 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.4641 | −1.01464 | −0.507318 | − | 0.861759i | \(-0.669363\pi\) | ||||
−0.507318 | + | 0.861759i | \(0.669363\pi\) | |||||||
\(788\) | −59.7128 | −2.12718 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.5885 | −1.15945 | ||||||||
\(791\) | −30.8897 | −1.09831 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 28.1962 | 1.00064 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −81.9615 | −2.90505 | ||||||||
\(797\) | −28.4449 | −1.00757 | −0.503784 | − | 0.863829i | \(-0.668059\pi\) | ||||
−0.503784 | + | 0.863829i | \(0.668059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.3205 | 1.17879 | ||||||||
\(800\) | −21.8564 | −0.772741 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −52.7846 | −1.86389 | ||||||||
\(803\) | −18.6795 | −0.659185 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.3923 | −0.648244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 84.4974 | 2.97261 | ||||||||
\(809\) | −36.0000 | −1.26569 | −0.632846 | − | 0.774277i | \(-0.718114\pi\) | ||||
−0.632846 | + | 0.774277i | \(0.718114\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.0526 | −1.37132 | −0.685660 | − | 0.727922i | \(-0.740486\pi\) | ||||
−0.685660 | + | 0.727922i | \(0.740486\pi\) | |||||||
\(812\) | −9.85641 | −0.345892 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 37.8564 | 1.32687 | ||||||||
\(815\) | −12.4641 | −0.436598 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.46410 | 0.191165 | ||||||||
\(818\) | −40.0526 | −1.40040 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 47.7128 | 1.66620 | ||||||||
\(821\) | −12.9282 | −0.451197 | −0.225599 | − | 0.974220i | \(-0.572434\pi\) | ||||
−0.225599 | + | 0.974220i | \(0.572434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.1769 | 1.71420 | 0.857100 | − | 0.515150i | \(-0.172264\pi\) | ||||
0.857100 | + | 0.515150i | \(0.172264\pi\) | |||||||
\(824\) | −68.1051 | −2.37255 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 72.2487 | 2.51385 | ||||||||
\(827\) | −28.5885 | −0.994118 | −0.497059 | − | 0.867717i | \(-0.665587\pi\) | ||||
−0.497059 | + | 0.867717i | \(0.665587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1769 | 0.839699 | 0.419849 | − | 0.907594i | \(-0.362083\pi\) | ||||
0.419849 | + | 0.907594i | \(0.362083\pi\) | |||||||
\(830\) | −25.8564 | −0.897489 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.03332 | −0.105098 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5359 | 0.364610 | ||||||||
\(836\) | −27.7128 | −0.958468 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −105.033 | −3.62832 | ||||||||
\(839\) | 27.4641 | 0.948166 | 0.474083 | − | 0.880480i | \(-0.342780\pi\) | ||||
0.474083 | + | 0.880480i | \(0.342780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4641 | −0.981521 | ||||||||
\(842\) | 20.7321 | 0.714474 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 100.890 | 3.47277 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.46410 | 0.0846675 | ||||||||
\(848\) | −103.426 | −3.55165 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.92820 | −0.306235 | ||||||||
\(851\) | −29.8564 | −1.02346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.3923 | −1.28029 | −0.640144 | − | 0.768255i | \(-0.721125\pi\) | ||||
−0.640144 | + | 0.768255i | \(0.721125\pi\) | |||||||
\(854\) | 16.5885 | 0.567645 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −67.4256 | −2.30456 | ||||||||
\(857\) | −7.12436 | −0.243363 | −0.121682 | − | 0.992569i | \(-0.538829\pi\) | ||||
−0.121682 | + | 0.992569i | \(0.538829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.7846 | −1.15272 | −0.576358 | − | 0.817197i | \(-0.695527\pi\) | ||||
−0.576358 | + | 0.817197i | \(0.695527\pi\) | |||||||
\(860\) | 20.3923 | 0.695372 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.9282 | 1.05342 | ||||||||
\(863\) | −13.6077 | −0.463211 | −0.231606 | − | 0.972810i | \(-0.574398\pi\) | ||||
−0.231606 | + | 0.972810i | \(0.574398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.73205 | 0.228897 | ||||||||
\(866\) | −41.5167 | −1.41079 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −96.8897 | −3.28865 | ||||||||
\(869\) | −41.3205 | −1.40170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −111.033 | −3.76006 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.8564 | 1.00991 | ||||||||
\(875\) | −2.46410 | −0.0833018 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.6410 | −1.71003 | −0.855013 | − | 0.518607i | \(-0.826451\pi\) | ||||
−0.855013 | + | 0.518607i | \(0.826451\pi\) | |||||||
\(878\) | 14.7321 | 0.497183 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −51.7128 | −1.74324 | ||||||||
\(881\) | −37.1769 | −1.25252 | −0.626261 | − | 0.779613i | \(-0.715416\pi\) | ||||
−0.626261 | + | 0.779613i | \(0.715416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.6603 | 0.560662 | 0.280331 | − | 0.959903i | \(-0.409556\pi\) | ||||
0.280331 | + | 0.959903i | \(0.409556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −57.7128 | −1.93890 | ||||||||
\(887\) | −48.9808 | −1.64461 | −0.822307 | − | 0.569045i | \(-0.807313\pi\) | ||||
−0.822307 | + | 0.569045i | \(0.807313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.55514 | −0.219852 | ||||||||
\(890\) | −12.9282 | −0.433354 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 86.6410 | 2.90096 | ||||||||
\(893\) | −14.9282 | −0.499553 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.1244 | −0.505551 | ||||||||
\(896\) | −93.2820 | −3.11633 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 68.1051 | 2.27270 | ||||||||
\(899\) | 5.26795 | 0.175696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.6410 | −0.754282 | ||||||||
\(902\) | 82.6410 | 2.75164 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 118.641 | 3.94594 | ||||||||
\(905\) | 21.4641 | 0.713491 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.4641 | −1.04475 | −0.522374 | − | 0.852716i | \(-0.674954\pi\) | ||||
−0.522374 | + | 0.852716i | \(0.674954\pi\) | |||||||
\(908\) | −30.9282 | −1.02639 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.7128 | −1.58080 | −0.790398 | − | 0.612594i | \(-0.790126\pi\) | ||||
−0.790398 | + | 0.612594i | \(0.790126\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.7846 | −1.08501 | ||||||||
\(914\) | −42.0526 | −1.39098 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.0718 | 0.431904 | ||||||||
\(917\) | −11.6603 | −0.385056 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.9282 | −1.08620 | −0.543101 | − | 0.839668i | \(-0.682750\pi\) | ||||
−0.543101 | + | 0.839668i | \(0.682750\pi\) | |||||||
\(920\) | 70.6410 | 2.32897 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 91.5692 | 3.01567 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | −108.694 | −3.57189 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.0000 | 0.525226 | ||||||||
\(929\) | 19.3205 | 0.633885 | 0.316943 | − | 0.948445i | \(-0.397344\pi\) | ||||
0.316943 | + | 0.948445i | \(0.397344\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.35898 | 0.0445389 | ||||||||
\(932\) | 21.0718 | 0.690230 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.3205 | −0.566744 | ||||||||
\(935\) | −11.3205 | −0.370220 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.2487 | −0.530822 | −0.265411 | − | 0.964135i | \(-0.585508\pi\) | ||||
−0.265411 | + | 0.964135i | \(0.585508\pi\) | |||||||
\(938\) | 37.2679 | 1.21684 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −55.7128 | −1.81715 | ||||||||
\(941\) | 40.5885 | 1.32315 | 0.661573 | − | 0.749881i | \(-0.269889\pi\) | ||||
0.661573 | + | 0.749881i | \(0.269889\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −65.1769 | −2.12245 | ||||||||
\(944\) | −160.210 | −5.21440 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.3205 | 1.14837 | ||||||||
\(947\) | −36.5885 | −1.18897 | −0.594483 | − | 0.804109i | \(-0.702643\pi\) | ||||
−0.594483 | + | 0.804109i | \(0.702643\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −76.2102 | −2.46999 | ||||||||
\(953\) | 24.2487 | 0.785493 | 0.392746 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392746 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.5167 | 0.566826 | ||||||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −81.7128 | −2.64002 | ||||||||
\(959\) | −37.2679 | −1.20344 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.7846 | 0.670471 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 122.354 | 3.94075 | ||||||||
\(965\) | 19.9282 | 0.641512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.2487 | −1.03705 | −0.518524 | − | 0.855063i | \(-0.673518\pi\) | ||||
−0.518524 | + | 0.855063i | \(0.673518\pi\) | |||||||
\(968\) | −9.46410 | −0.304188 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 26.0526 | 0.836497 | ||||||||
\(971\) | 1.17691 | 0.0377690 | 0.0188845 | − | 0.999822i | \(-0.493989\pi\) | ||||
0.0188845 | + | 0.999822i | \(0.493989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0333 | −0.321654 | ||||||||
\(974\) | −56.7846 | −1.81950 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.7846 | −1.17745 | ||||||||
\(977\) | 1.07180 | 0.0342898 | 0.0171449 | − | 0.999853i | \(-0.494542\pi\) | ||||
0.0171449 | + | 0.999853i | \(0.494542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.3923 | −0.523900 | ||||||||
\(980\) | 5.07180 | 0.162013 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −46.7846 | −1.49296 | ||||||||
\(983\) | −23.8564 | −0.760901 | −0.380451 | − | 0.924801i | \(-0.624231\pi\) | ||||
−0.380451 | + | 0.924801i | \(0.624231\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.9282 | 0.348202 | ||||||||
\(986\) | 6.53590 | 0.208145 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.8564 | −0.885782 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9282 | 0.918935 | 0.459467 | − | 0.888195i | \(-0.348040\pi\) | ||||
0.459467 | + | 0.888195i | \(0.348040\pi\) | |||||||
\(992\) | 157.282 | 4.99371 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 62.3923 | 1.97896 | ||||||||
\(995\) | 15.0000 | 0.475532 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.5885 | −1.82384 | −0.911922 | − | 0.410363i | \(-0.865402\pi\) | ||||
−0.911922 | + | 0.410363i | \(0.865402\pi\) | |||||||
\(998\) | 55.7128 | 1.76356 | ||||||||
\(999\) | 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 | 7605.2.a.y.1.1 | 2 | ||
3.2 | odd | 2 | 2535.2.a.s.1.2 | 2 | |||
13.6 | odd | 12 | 585.2.bu.a.361.2 | 4 | |||
13.11 | odd | 12 | 585.2.bu.a.316.2 | 4 | |||
13.12 | even | 2 | 7605.2.a.bk.1.2 | 2 | |||
39.11 | even | 12 | 195.2.bb.a.121.1 | ✓ | 4 | ||
39.32 | even | 12 | 195.2.bb.a.166.1 | yes | 4 | ||
39.38 | odd | 2 | 2535.2.a.n.1.1 | 2 | |||
195.32 | odd | 12 | 975.2.w.a.49.1 | 4 | |||
195.89 | even | 12 | 975.2.bc.h.901.2 | 4 | |||
195.128 | odd | 12 | 975.2.w.a.199.1 | 4 | |||
195.149 | even | 12 | 975.2.bc.h.751.2 | 4 | |||
195.167 | odd | 12 | 975.2.w.f.199.2 | 4 | |||
195.188 | odd | 12 | 975.2.w.f.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.bb.a.121.1 | ✓ | 4 | 39.11 | even | 12 | ||
195.2.bb.a.166.1 | yes | 4 | 39.32 | even | 12 | ||
585.2.bu.a.316.2 | 4 | 13.11 | odd | 12 | |||
585.2.bu.a.361.2 | 4 | 13.6 | odd | 12 | |||
975.2.w.a.49.1 | 4 | 195.32 | odd | 12 | |||
975.2.w.a.199.1 | 4 | 195.128 | odd | 12 | |||
975.2.w.f.49.2 | 4 | 195.188 | odd | 12 | |||
975.2.w.f.199.2 | 4 | 195.167 | odd | 12 | |||
975.2.bc.h.751.2 | 4 | 195.149 | even | 12 | |||
975.2.bc.h.901.2 | 4 | 195.89 | even | 12 | |||
2535.2.a.n.1.1 | 2 | 39.38 | odd | 2 | |||
2535.2.a.s.1.2 | 2 | 3.2 | odd | 2 | |||
7605.2.a.y.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7605.2.a.bk.1.2 | 2 | 13.12 | even | 2 |