Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} + 70x^{4} - 105x^{2} + 45 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.856773\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.856773 | −0.605830 | −0.302915 | − | 0.953018i | \(-0.597960\pi\) | ||||
−0.302915 | + | 0.953018i | \(0.597960\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.26594 | −0.632970 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.647907 | 0.244886 | 0.122443 | − | 0.992476i | \(-0.460927\pi\) | ||||
0.122443 | + | 0.992476i | \(0.460927\pi\) | |||||||
\(8\) | 2.79817 | 0.989302 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.91382 | 1.78308 | 0.891542 | − | 0.452939i | \(-0.149624\pi\) | ||||
0.891542 | + | 0.452939i | \(0.149624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88397 | 0.799871 | 0.399935 | − | 0.916543i | \(-0.369033\pi\) | ||||
0.399935 | + | 0.916543i | \(0.369033\pi\) | |||||||
\(14\) | −0.555109 | −0.148359 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.134488 | 0.0336219 | ||||||||
\(17\) | −4.20027 | −1.01872 | −0.509358 | − | 0.860555i | \(-0.670117\pi\) | ||||
−0.509358 | + | 0.860555i | \(0.670117\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.64791 | −0.378056 | −0.189028 | − | 0.981972i | \(-0.560534\pi\) | ||||
−0.189028 | + | 0.981972i | \(0.560534\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.06680 | −1.08024 | ||||||||
\(23\) | −6.42752 | −1.34023 | −0.670115 | − | 0.742257i | \(-0.733755\pi\) | ||||
−0.670115 | + | 0.742257i | \(0.733755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.47091 | −0.484585 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.820212 | −0.155005 | ||||||||
\(29\) | −2.25888 | −0.419463 | −0.209732 | − | 0.977759i | \(-0.567259\pi\) | ||||
−0.209732 | + | 0.977759i | \(0.567259\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.28440 | −0.949107 | −0.474553 | − | 0.880227i | \(-0.657390\pi\) | ||||
−0.474553 | + | 0.880227i | \(0.657390\pi\) | |||||||
\(32\) | −5.71156 | −1.00967 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.59868 | 0.617168 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.71560 | −0.282042 | −0.141021 | − | 0.990007i | \(-0.545039\pi\) | ||||
−0.141021 | + | 0.990007i | \(0.545039\pi\) | |||||||
\(38\) | 1.41188 | 0.229037 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.176662 | 0.0275900 | 0.0137950 | − | 0.999905i | \(-0.495609\pi\) | ||||
0.0137950 | + | 0.999905i | \(0.495609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.95077 | 1.21248 | 0.606241 | − | 0.795281i | \(-0.292677\pi\) | ||||
0.606241 | + | 0.795281i | \(0.292677\pi\) | |||||||
\(44\) | −7.48654 | −1.12864 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.50692 | 0.811951 | ||||||||
\(47\) | −1.05903 | −0.154475 | −0.0772376 | − | 0.997013i | \(-0.524610\pi\) | ||||
−0.0772376 | + | 0.997013i | \(0.524610\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58022 | −0.940031 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.65094 | −0.506294 | ||||||||
\(53\) | 4.48612 | 0.616216 | 0.308108 | − | 0.951351i | \(-0.400304\pi\) | ||||
0.308108 | + | 0.951351i | \(0.400304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.81295 | 0.242266 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.93534 | 0.254123 | ||||||||
\(59\) | −9.74542 | −1.26875 | −0.634373 | − | 0.773027i | \(-0.718742\pi\) | ||||
−0.634373 | + | 0.773027i | \(0.718742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2844 | −1.44482 | −0.722410 | − | 0.691465i | \(-0.756966\pi\) | ||||
−0.722410 | + | 0.691465i | \(0.756966\pi\) | |||||||
\(62\) | 4.52753 | 0.574997 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.62453 | 0.578067 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6171 | −1.54143 | −0.770715 | − | 0.637181i | \(-0.780101\pi\) | ||||
−0.770715 | + | 0.637181i | \(0.780101\pi\) | |||||||
\(68\) | 5.31730 | 0.644817 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.09048 | 0.722807 | 0.361404 | − | 0.932409i | \(-0.382298\pi\) | ||||
0.361404 | + | 0.932409i | \(0.382298\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.08312 | −0.829016 | −0.414508 | − | 0.910046i | \(-0.636046\pi\) | ||||
−0.414508 | + | 0.910046i | \(0.636046\pi\) | |||||||
\(74\) | 1.46988 | 0.170870 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.08615 | 0.239298 | ||||||||
\(77\) | 3.83160 | 0.436652 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.58111 | 0.177889 | 0.0889443 | − | 0.996037i | \(-0.471651\pi\) | ||||
0.0889443 | + | 0.996037i | \(0.471651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.151359 | −0.0167149 | ||||||||
\(83\) | −11.5102 | −1.26340 | −0.631702 | − | 0.775211i | \(-0.717643\pi\) | ||||
−0.631702 | + | 0.775211i | \(0.717643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.81200 | −0.734557 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 16.5479 | 1.76401 | ||||||||
\(89\) | 15.5918 | 1.65272 | 0.826362 | − | 0.563140i | \(-0.190407\pi\) | ||||
0.826362 | + | 0.563140i | \(0.190407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.86855 | 0.195877 | ||||||||
\(92\) | 8.13685 | 0.848326 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.907347 | 0.0935857 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.55034 | −0.766621 | −0.383311 | − | 0.923619i | \(-0.625216\pi\) | ||||
−0.383311 | + | 0.923619i | \(0.625216\pi\) | |||||||
\(98\) | 5.63775 | 0.569499 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.1645 | 1.70793 | 0.853965 | − | 0.520330i | \(-0.174191\pi\) | ||||
0.853965 | + | 0.520330i | \(0.174191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.3561 | −1.71015 | −0.855074 | − | 0.518506i | \(-0.826489\pi\) | ||||
−0.855074 | + | 0.518506i | \(0.826489\pi\) | |||||||
\(104\) | 8.06985 | 0.791314 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.84358 | −0.373322 | ||||||||
\(107\) | 16.2046 | 1.56656 | 0.783278 | − | 0.621672i | \(-0.213546\pi\) | ||||
0.783278 | + | 0.621672i | \(0.213546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.12709 | 0.682652 | 0.341326 | − | 0.939945i | \(-0.389124\pi\) | ||||
0.341326 | + | 0.939945i | \(0.389124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0871355 | 0.00823353 | ||||||||
\(113\) | −14.9372 | −1.40518 | −0.702589 | − | 0.711596i | \(-0.747973\pi\) | ||||
−0.702589 | + | 0.711596i | \(0.747973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.85961 | 0.265508 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.34961 | 0.768644 | ||||||||
\(119\) | −2.72139 | −0.249469 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.9733 | 2.17939 | ||||||||
\(122\) | 9.66817 | 0.875315 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.68974 | 0.600757 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.30722 | −0.825883 | −0.412941 | − | 0.910758i | \(-0.635499\pi\) | ||||
−0.412941 | + | 0.910758i | \(0.635499\pi\) | |||||||
\(128\) | 7.46095 | 0.659461 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.47828 | 0.303899 | 0.151949 | − | 0.988388i | \(-0.451445\pi\) | ||||
0.151949 | + | 0.988388i | \(0.451445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.06769 | −0.0925805 | ||||||||
\(134\) | 10.8100 | 0.933844 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.7531 | −1.00782 | ||||||||
\(137\) | −8.17270 | −0.698241 | −0.349120 | − | 0.937078i | \(-0.613520\pi\) | ||||
−0.349120 | + | 0.937078i | \(0.613520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.93970 | 0.249342 | 0.124671 | − | 0.992198i | \(-0.460212\pi\) | ||||
0.124671 | + | 0.992198i | \(0.460212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.21816 | −0.437898 | ||||||||
\(143\) | 17.0553 | 1.42624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.06862 | 0.502243 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.17184 | 0.178524 | ||||||||
\(149\) | 15.4826 | 1.26838 | 0.634191 | − | 0.773176i | \(-0.281333\pi\) | ||||
0.634191 | + | 0.773176i | \(0.281333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8233 | 0.880791 | 0.440395 | − | 0.897804i | \(-0.354838\pi\) | ||||
0.440395 | + | 0.897804i | \(0.354838\pi\) | |||||||
\(152\) | −4.61112 | −0.374011 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.28281 | −0.264537 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.9086 | −1.34945 | −0.674726 | − | 0.738068i | \(-0.735738\pi\) | ||||
−0.674726 | + | 0.738068i | \(0.735738\pi\) | |||||||
\(158\) | −1.35465 | −0.107770 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.16443 | −0.328203 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.7750 | 1.31392 | 0.656960 | − | 0.753926i | \(-0.271842\pi\) | ||||
0.656960 | + | 0.753926i | \(0.271842\pi\) | |||||||
\(164\) | −0.223644 | −0.0174637 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.86159 | 0.765407 | ||||||||
\(167\) | 10.1916 | 0.788653 | 0.394326 | − | 0.918970i | \(-0.370978\pi\) | ||||
0.394326 | + | 0.918970i | \(0.370978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.68269 | −0.360207 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.0652 | −0.767465 | ||||||||
\(173\) | −14.3724 | −1.09271 | −0.546355 | − | 0.837554i | \(-0.683985\pi\) | ||||
−0.546355 | + | 0.837554i | \(0.683985\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.795336 | 0.0599507 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.3586 | −1.00127 | ||||||||
\(179\) | −7.59573 | −0.567731 | −0.283866 | − | 0.958864i | \(-0.591617\pi\) | ||||
−0.283866 | + | 0.958864i | \(0.591617\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8203 | −1.62189 | −0.810945 | − | 0.585122i | \(-0.801047\pi\) | ||||
−0.810945 | + | 0.585122i | \(0.801047\pi\) | |||||||
\(182\) | −1.60092 | −0.118668 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.9853 | −1.32589 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.8397 | −1.81646 | ||||||||
\(188\) | 1.34067 | 0.0977783 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.0283 | 1.37684 | 0.688421 | − | 0.725311i | \(-0.258304\pi\) | ||||
0.688421 | + | 0.725311i | \(0.258304\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.57675 | 0.617368 | 0.308684 | − | 0.951165i | \(-0.400111\pi\) | ||||
0.308684 | + | 0.951165i | \(0.400111\pi\) | |||||||
\(194\) | 6.46893 | 0.464442 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.33016 | 0.595012 | ||||||||
\(197\) | −18.5726 | −1.32325 | −0.661623 | − | 0.749837i | \(-0.730132\pi\) | ||||
−0.661623 | + | 0.749837i | \(0.730132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.32927 | −0.519558 | −0.259779 | − | 0.965668i | \(-0.583650\pi\) | ||||
−0.259779 | + | 0.965668i | \(0.583650\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.7061 | −1.03471 | ||||||||
\(203\) | −1.46354 | −0.102721 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.8702 | 1.03606 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.387859 | 0.0268932 | ||||||||
\(209\) | −9.74542 | −0.674105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5553 | −1.00203 | −0.501013 | − | 0.865440i | \(-0.667039\pi\) | ||||
−0.501013 | + | 0.865440i | \(0.667039\pi\) | |||||||
\(212\) | −5.67916 | −0.390046 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.8836 | −0.949066 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.42380 | −0.232423 | ||||||||
\(218\) | −6.10630 | −0.413571 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.1135 | −0.814841 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8711 | −1.79942 | −0.899712 | − | 0.436485i | \(-0.856223\pi\) | ||||
−0.899712 | + | 0.436485i | \(0.856223\pi\) | |||||||
\(224\) | −3.70056 | −0.247254 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.7978 | 0.851298 | ||||||||
\(227\) | 4.20027 | 0.278782 | 0.139391 | − | 0.990237i | \(-0.455486\pi\) | ||||
0.139391 | + | 0.990237i | \(0.455486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.30722 | 0.548957 | 0.274478 | − | 0.961593i | \(-0.411495\pi\) | ||||
0.274478 | + | 0.961593i | \(0.411495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.32072 | −0.414976 | ||||||||
\(233\) | 22.6158 | 1.48161 | 0.740805 | − | 0.671720i | \(-0.234444\pi\) | ||||
0.740805 | + | 0.671720i | \(0.234444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.3371 | 0.803079 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.33161 | 0.151136 | ||||||||
\(239\) | −1.28688 | −0.0832413 | −0.0416207 | − | 0.999133i | \(-0.513252\pi\) | ||||
−0.0416207 | + | 0.999133i | \(0.513252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.91599 | −0.316667 | −0.158333 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158333 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(242\) | −20.5396 | −1.32034 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.2854 | 0.914528 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.75252 | −0.302396 | ||||||||
\(248\) | −14.7867 | −0.938953 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9609 | −1.19680 | −0.598399 | − | 0.801198i | \(-0.704196\pi\) | ||||
−0.598399 | + | 0.801198i | \(0.704196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.0112 | −2.38974 | ||||||||
\(254\) | 7.97417 | 0.500344 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6414 | −0.977588 | ||||||||
\(257\) | −24.1690 | −1.50762 | −0.753810 | − | 0.657093i | \(-0.771786\pi\) | ||||
−0.753810 | + | 0.657093i | \(0.771786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.11155 | −0.0690682 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.98009 | −0.184111 | ||||||||
\(263\) | 17.6518 | 1.08846 | 0.544229 | − | 0.838937i | \(-0.316822\pi\) | ||||
0.544229 | + | 0.838937i | \(0.316822\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.914768 | 0.0560880 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.9726 | 0.975679 | ||||||||
\(269\) | −26.5149 | −1.61664 | −0.808320 | − | 0.588743i | \(-0.799623\pi\) | ||||
−0.808320 | + | 0.588743i | \(0.799623\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4180 | 1.24031 | 0.620153 | − | 0.784481i | \(-0.287071\pi\) | ||||
0.620153 | + | 0.784481i | \(0.287071\pi\) | |||||||
\(272\) | −0.564885 | −0.0342512 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.00214 | 0.423015 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0643 | 0.845043 | 0.422521 | − | 0.906353i | \(-0.361145\pi\) | ||||
0.422521 | + | 0.906353i | \(0.361145\pi\) | |||||||
\(278\) | −2.51866 | −0.151059 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.19966 | −0.369841 | −0.184920 | − | 0.982753i | \(-0.559203\pi\) | ||||
−0.184920 | + | 0.982753i | \(0.559203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9801 | −0.771586 | −0.385793 | − | 0.922585i | \(-0.626072\pi\) | ||||
−0.385793 | + | 0.922585i | \(0.626072\pi\) | |||||||
\(284\) | −7.71019 | −0.457516 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.6125 | −0.864056 | ||||||||
\(287\) | 0.114461 | 0.00675640 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.642299 | 0.0377823 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.96681 | 0.524743 | ||||||||
\(293\) | −18.5563 | −1.08407 | −0.542037 | − | 0.840355i | \(-0.682347\pi\) | ||||
−0.542037 | + | 0.840355i | \(0.682347\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.80053 | −0.279025 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.2650 | −0.768424 | ||||||||
\(299\) | −18.5368 | −1.07201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.15136 | 0.296919 | ||||||||
\(302\) | −9.27314 | −0.533609 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.221623 | −0.0127110 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0862 | −1.37467 | −0.687337 | − | 0.726338i | \(-0.741221\pi\) | ||||
−0.687337 | + | 0.726338i | \(0.741221\pi\) | |||||||
\(308\) | −4.85058 | −0.276388 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.3372 | 1.43674 | 0.718370 | − | 0.695661i | \(-0.244889\pi\) | ||||
0.718370 | + | 0.695661i | \(0.244889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.8224 | 1.23348 | 0.616739 | − | 0.787168i | \(-0.288454\pi\) | ||||
0.616739 | + | 0.787168i | \(0.288454\pi\) | |||||||
\(314\) | 14.4868 | 0.817539 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00159 | −0.112598 | ||||||||
\(317\) | −1.21940 | −0.0684884 | −0.0342442 | − | 0.999413i | \(-0.510902\pi\) | ||||
−0.0342442 | + | 0.999413i | \(0.510902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.3586 | −0.747938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.56797 | 0.198835 | ||||||||
\(323\) | 6.92166 | 0.385131 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.3724 | −0.796011 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.494331 | 0.0272949 | ||||||||
\(329\) | −0.686152 | −0.0378288 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.97470 | −0.328399 | −0.164200 | − | 0.986427i | \(-0.552504\pi\) | ||||
−0.164200 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(332\) | 14.5712 | 0.799697 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.73192 | −0.477789 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1718 | −1.48014 | −0.740072 | − | 0.672527i | \(-0.765209\pi\) | ||||
−0.740072 | + | 0.672527i | \(0.765209\pi\) | |||||||
\(338\) | 4.01200 | 0.218224 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.2510 | −1.69234 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.79871 | −0.475086 | ||||||||
\(344\) | 22.2476 | 1.19951 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3138 | 0.661996 | ||||||||
\(347\) | 12.4242 | 0.666964 | 0.333482 | − | 0.942757i | \(-0.391776\pi\) | ||||
0.333482 | + | 0.942757i | \(0.391776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2826 | 1.08570 | 0.542852 | − | 0.839828i | \(-0.317345\pi\) | ||||
0.542852 | + | 0.839828i | \(0.317345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −33.7771 | −1.80033 | ||||||||
\(353\) | 11.9880 | 0.638057 | 0.319029 | − | 0.947745i | \(-0.396643\pi\) | ||||
0.319029 | + | 0.947745i | \(0.396643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −19.7382 | −1.04613 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.50781 | 0.343949 | ||||||||
\(359\) | 3.54576 | 0.187138 | 0.0935690 | − | 0.995613i | \(-0.470172\pi\) | ||||
0.0935690 | + | 0.995613i | \(0.470172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2844 | −0.857074 | ||||||||
\(362\) | 18.6950 | 0.982589 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.36547 | −0.123984 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.3333 | −1.63558 | −0.817792 | − | 0.575514i | \(-0.804802\pi\) | ||||
−0.817792 | + | 0.575514i | \(0.804802\pi\) | |||||||
\(368\) | −0.864421 | −0.0450611 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.90659 | 0.150902 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.133595 | 0.00691730 | 0.00345865 | − | 0.999994i | \(-0.498899\pi\) | ||||
0.00345865 | + | 0.999994i | \(0.498899\pi\) | |||||||
\(374\) | 21.2819 | 1.10046 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.96334 | −0.152823 | ||||||||
\(377\) | −6.51455 | −0.335516 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.04343 | −0.413163 | −0.206582 | − | 0.978429i | \(-0.566234\pi\) | ||||
−0.206582 | + | 0.978429i | \(0.566234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.3030 | −0.834132 | ||||||||
\(383\) | −12.2322 | −0.625034 | −0.312517 | − | 0.949912i | \(-0.601172\pi\) | ||||
−0.312517 | + | 0.949912i | \(0.601172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.34832 | −0.374020 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.55829 | 0.485249 | ||||||||
\(389\) | −33.0004 | −1.67319 | −0.836593 | − | 0.547825i | \(-0.815456\pi\) | ||||
−0.836593 | + | 0.547825i | \(0.815456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.9973 | 1.36531 | ||||||||
\(392\) | −18.4126 | −0.929974 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.9125 | 0.801661 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9249 | 0.698872 | 0.349436 | − | 0.936960i | \(-0.386373\pi\) | ||||
0.349436 | + | 0.936960i | \(0.386373\pi\) | |||||||
\(398\) | 6.27952 | 0.314764 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.9494 | 1.39573 | 0.697863 | − | 0.716231i | \(-0.254134\pi\) | ||||
0.697863 | + | 0.716231i | \(0.254134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.2401 | −0.759163 | ||||||||
\(404\) | −21.7292 | −1.08107 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.25392 | 0.0622311 | ||||||||
\(407\) | −10.1457 | −0.502905 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9289 | 1.28210 | 0.641052 | − | 0.767498i | \(-0.278498\pi\) | ||||
0.641052 | + | 0.767498i | \(0.278498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.9718 | 1.08247 | ||||||||
\(413\) | −6.31413 | −0.310698 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.4720 | −0.807606 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.34961 | 0.408393 | ||||||||
\(419\) | 1.21614 | 0.0594123 | 0.0297061 | − | 0.999559i | \(-0.490543\pi\) | ||||
0.0297061 | + | 0.999559i | \(0.490543\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.4626 | 0.997286 | 0.498643 | − | 0.866807i | \(-0.333832\pi\) | ||||
0.498643 | + | 0.866807i | \(0.333832\pi\) | |||||||
\(422\) | 12.4705 | 0.607056 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.5529 | 0.609624 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.31124 | −0.353816 | ||||||||
\(428\) | −20.5140 | −0.991583 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.4381 | −1.03264 | −0.516319 | − | 0.856397i | \(-0.672698\pi\) | ||||
−0.516319 | + | 0.856397i | \(0.672698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.2844 | −1.11898 | −0.559489 | − | 0.828838i | \(-0.689002\pi\) | ||||
−0.559489 | + | 0.828838i | \(0.689002\pi\) | |||||||
\(434\) | 2.93342 | 0.140809 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.02248 | −0.432098 | ||||||||
\(437\) | 10.5919 | 0.506681 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5355 | −0.598285 | −0.299143 | − | 0.954208i | \(-0.596701\pi\) | ||||
−0.299143 | + | 0.954208i | \(0.596701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.3785 | 0.493655 | ||||||||
\(443\) | 13.3228 | 0.632986 | 0.316493 | − | 0.948595i | \(-0.397495\pi\) | ||||
0.316493 | + | 0.948595i | \(0.397495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23.0224 | 1.09014 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.99627 | 0.141560 | ||||||||
\(449\) | −30.2500 | −1.42758 | −0.713792 | − | 0.700358i | \(-0.753024\pi\) | ||||
−0.713792 | + | 0.700358i | \(0.753024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04475 | 0.0491953 | ||||||||
\(452\) | 18.9097 | 0.889436 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.59868 | −0.168894 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8391 | 0.600588 | 0.300294 | − | 0.953847i | \(-0.402915\pi\) | ||||
0.300294 | + | 0.953847i | \(0.402915\pi\) | |||||||
\(458\) | −7.11740 | −0.332574 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.8435 | −1.29680 | −0.648400 | − | 0.761300i | \(-0.724561\pi\) | ||||
−0.648400 | + | 0.761300i | \(0.724561\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.84616 | −0.178746 | −0.0893731 | − | 0.995998i | \(-0.528486\pi\) | ||||
−0.0893731 | + | 0.995998i | \(0.528486\pi\) | |||||||
\(464\) | −0.303791 | −0.0141031 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.3766 | −0.897603 | ||||||||
\(467\) | 40.6594 | 1.88149 | 0.940746 | − | 0.339112i | \(-0.110126\pi\) | ||||
0.940746 | + | 0.339112i | \(0.110126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.17473 | −0.377474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −27.2693 | −1.25517 | ||||||||
\(473\) | 47.0194 | 2.16196 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.44511 | 0.157907 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.10256 | 0.0504301 | ||||||||
\(479\) | 15.2642 | 0.697440 | 0.348720 | − | 0.937227i | \(-0.386616\pi\) | ||||
0.348720 | + | 0.937227i | \(0.386616\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.94774 | −0.225597 | ||||||||
\(482\) | 4.21189 | 0.191846 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −30.3487 | −1.37949 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.06466 | −0.365444 | −0.182722 | − | 0.983165i | \(-0.558491\pi\) | ||||
−0.182722 | + | 0.983165i | \(0.558491\pi\) | |||||||
\(488\) | −31.5757 | −1.42936 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.50128 | 0.428787 | 0.214393 | − | 0.976747i | \(-0.431223\pi\) | ||||
0.214393 | + | 0.976747i | \(0.431223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.48790 | 0.427314 | ||||||||
\(494\) | 4.07183 | 0.183200 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.710687 | −0.0319108 | ||||||||
\(497\) | 3.94606 | 0.177005 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.6405 | −0.879230 | −0.439615 | − | 0.898186i | \(-0.644885\pi\) | ||||
−0.439615 | + | 0.898186i | \(0.644885\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.2451 | 0.725056 | ||||||||
\(503\) | −20.6428 | −0.920415 | −0.460208 | − | 0.887811i | \(-0.652225\pi\) | ||||
−0.460208 | + | 0.887811i | \(0.652225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 32.5669 | 1.44778 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.7824 | 0.522759 | ||||||||
\(509\) | 31.9372 | 1.41559 | 0.707795 | − | 0.706418i | \(-0.249690\pi\) | ||||
0.707795 | + | 0.706418i | \(0.249690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.58920 | −0.203014 | ||||||||
\(512\) | −1.52077 | −0.0672093 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.7073 | 0.913360 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.26291 | −0.275442 | ||||||||
\(518\) | 0.952343 | 0.0418435 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.88261 | 0.389154 | 0.194577 | − | 0.980887i | \(-0.437667\pi\) | ||||
0.194577 | + | 0.980887i | \(0.437667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.3512 | −1.23971 | −0.619856 | − | 0.784716i | \(-0.712809\pi\) | ||||
−0.619856 | + | 0.784716i | \(0.712809\pi\) | |||||||
\(524\) | −4.40329 | −0.192359 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.1236 | −0.659420 | ||||||||
\(527\) | 22.1959 | 0.966870 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.3130 | 0.796215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.35163 | 0.0586007 | ||||||||
\(533\) | 0.509490 | 0.0220685 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −35.3049 | −1.52494 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.7172 | 0.979409 | ||||||||
\(539\) | −38.9142 | −1.67615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.8190 | −0.594124 | −0.297062 | − | 0.954858i | \(-0.596007\pi\) | ||||
−0.297062 | + | 0.954858i | \(0.596007\pi\) | |||||||
\(542\) | −17.4936 | −0.751414 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.9901 | 1.02857 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0831 | 0.516637 | 0.258318 | − | 0.966060i | \(-0.416832\pi\) | ||||
0.258318 | + | 0.966060i | \(0.416832\pi\) | |||||||
\(548\) | 10.3461 | 0.441966 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.72242 | 0.158580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.02441 | 0.0435624 | ||||||||
\(554\) | −12.0499 | −0.511952 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.72149 | −0.157826 | ||||||||
\(557\) | 15.5918 | 0.660644 | 0.330322 | − | 0.943868i | \(-0.392843\pi\) | ||||
0.330322 | + | 0.943868i | \(0.392843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.9298 | 0.969828 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.31170 | 0.224061 | ||||||||
\(563\) | 19.1854 | 0.808570 | 0.404285 | − | 0.914633i | \(-0.367520\pi\) | ||||
0.404285 | + | 0.914633i | \(0.367520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.1210 | 0.467450 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.0422 | 0.715074 | ||||||||
\(569\) | 30.1698 | 1.26478 | 0.632392 | − | 0.774648i | \(-0.282073\pi\) | ||||
0.632392 | + | 0.774648i | \(0.282073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.2616 | −1.05716 | −0.528582 | − | 0.848882i | \(-0.677276\pi\) | ||||
−0.528582 | + | 0.848882i | \(0.677276\pi\) | |||||||
\(572\) | −21.5910 | −0.902765 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.0980668 | −0.00409323 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.00948 | 0.375070 | 0.187535 | − | 0.982258i | \(-0.439950\pi\) | ||||
0.187535 | + | 0.982258i | \(0.439950\pi\) | |||||||
\(578\) | −0.550304 | −0.0228896 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.45751 | −0.309390 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.5301 | 1.09876 | ||||||||
\(584\) | −19.8198 | −0.820147 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.8986 | 0.656764 | ||||||||
\(587\) | −11.5059 | −0.474901 | −0.237451 | − | 0.971400i | \(-0.576312\pi\) | ||||
−0.237451 | + | 0.971400i | \(0.576312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.70820 | 0.358815 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.230727 | −0.00948280 | ||||||||
\(593\) | −23.0392 | −0.946107 | −0.473053 | − | 0.881034i | \(-0.656848\pi\) | ||||
−0.473053 | + | 0.881034i | \(0.656848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.6000 | −0.802848 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.8818 | 0.649456 | ||||||||
\(599\) | −2.07694 | −0.0848614 | −0.0424307 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424307 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.7922 | 1.17446 | 0.587230 | − | 0.809420i | \(-0.300218\pi\) | ||||
0.587230 | + | 0.809420i | \(0.300218\pi\) | |||||||
\(602\) | −4.41354 | −0.179883 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.7017 | −0.557514 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.99573 | 0.283948 | 0.141974 | − | 0.989870i | \(-0.454655\pi\) | ||||
0.141974 | + | 0.989870i | \(0.454655\pi\) | |||||||
\(608\) | 9.41212 | 0.381712 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.05421 | −0.123560 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.6552 | −1.39971 | −0.699855 | − | 0.714285i | \(-0.746752\pi\) | ||||
−0.699855 | + | 0.714285i | \(0.746752\pi\) | |||||||
\(614\) | 20.6364 | 0.832819 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.7215 | 0.431980 | ||||||||
\(617\) | 14.9852 | 0.603280 | 0.301640 | − | 0.953422i | \(-0.402466\pi\) | ||||
0.301640 | + | 0.953422i | \(0.402466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.8216 | −1.60056 | −0.800282 | − | 0.599624i | \(-0.795317\pi\) | ||||
−0.800282 | + | 0.599624i | \(0.795317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.7082 | −0.870420 | ||||||||
\(623\) | 10.1020 | 0.404728 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.6969 | −0.747277 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.4053 | 0.854164 | ||||||||
\(629\) | 7.20598 | 0.287321 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.66278 | 0.0661944 | 0.0330972 | − | 0.999452i | \(-0.489463\pi\) | ||||
0.0330972 | + | 0.999452i | \(0.489463\pi\) | |||||||
\(632\) | 4.42421 | 0.175986 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.04475 | 0.0414923 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.9772 | −0.751903 | ||||||||
\(638\) | 11.4453 | 0.453123 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.77663 | −0.267661 | −0.133830 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133830 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.2108 | −0.797035 | −0.398517 | − | 0.917161i | \(-0.630475\pi\) | ||||
−0.398517 | + | 0.917161i | \(0.630475\pi\) | |||||||
\(644\) | 5.27192 | 0.207743 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.93029 | −0.233324 | ||||||||
\(647\) | −5.05100 | −0.198575 | −0.0992877 | − | 0.995059i | \(-0.531656\pi\) | ||||
−0.0992877 | + | 0.995059i | \(0.531656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.6327 | −2.26228 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.2362 | −0.831672 | ||||||||
\(653\) | 9.64210 | 0.377325 | 0.188662 | − | 0.982042i | \(-0.439585\pi\) | ||||
0.188662 | + | 0.982042i | \(0.439585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.0237589 | 0.000927629 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.587876 | 0.0229178 | ||||||||
\(659\) | 26.7332 | 1.04138 | 0.520690 | − | 0.853746i | \(-0.325675\pi\) | ||||
0.520690 | + | 0.853746i | \(0.325675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00159 | −0.0778529 | −0.0389264 | − | 0.999242i | \(-0.512394\pi\) | ||||
−0.0389264 | + | 0.999242i | \(0.512394\pi\) | |||||||
\(662\) | 5.11896 | 0.198954 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.2074 | −1.24989 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.5190 | 0.562177 | ||||||||
\(668\) | −12.9020 | −0.499194 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −66.7339 | −2.57623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.2362 | 1.20407 | 0.602033 | − | 0.798471i | \(-0.294358\pi\) | ||||
0.602033 | + | 0.798471i | \(0.294358\pi\) | |||||||
\(674\) | 23.2801 | 0.896716 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.92801 | 0.228000 | ||||||||
\(677\) | −42.4874 | −1.63292 | −0.816462 | − | 0.577400i | \(-0.804067\pi\) | ||||
−0.816462 | + | 0.577400i | \(0.804067\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.89192 | −0.187735 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26.7750 | 1.02527 | ||||||||
\(683\) | 5.20811 | 0.199283 | 0.0996415 | − | 0.995023i | \(-0.468230\pi\) | ||||
0.0996415 | + | 0.995023i | \(0.468230\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.53850 | 0.287821 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.06928 | 0.0407659 | ||||||||
\(689\) | 12.9379 | 0.492893 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.07419 | 0.307157 | 0.153578 | − | 0.988136i | \(-0.450920\pi\) | ||||
0.153578 | + | 0.988136i | \(0.450920\pi\) | |||||||
\(692\) | 18.1946 | 0.691653 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.6447 | −0.404066 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.742030 | −0.0281064 | ||||||||
\(698\) | −17.3776 | −0.657752 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.7552 | −1.19938 | −0.599689 | − | 0.800233i | \(-0.704709\pi\) | ||||
−0.599689 | + | 0.800233i | \(0.704709\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.82714 | 0.106628 | ||||||||
\(704\) | 27.3487 | 1.03074 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.2710 | −0.386554 | ||||||||
\(707\) | 11.1210 | 0.418248 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.71630 | 0.364903 | 0.182452 | − | 0.983215i | \(-0.441597\pi\) | ||||
0.182452 | + | 0.983215i | \(0.441597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 43.6284 | 1.63504 | ||||||||
\(713\) | 33.9656 | 1.27202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.61574 | 0.359357 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.03791 | −0.113374 | ||||||||
\(719\) | 20.4661 | 0.763257 | 0.381628 | − | 0.924316i | \(-0.375363\pi\) | ||||
0.381628 | + | 0.924316i | \(0.375363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.2451 | −0.418791 | ||||||||
\(722\) | 13.9520 | 0.519241 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27.6232 | 1.02661 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.2337 | 1.86306 | 0.931532 | − | 0.363659i | \(-0.118473\pi\) | ||||
0.931532 | + | 0.363659i | \(0.118473\pi\) | |||||||
\(728\) | 5.22851 | 0.193781 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.3954 | −1.23517 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.8776 | −1.39904 | −0.699520 | − | 0.714613i | \(-0.746603\pi\) | ||||
−0.699520 | + | 0.714613i | \(0.746603\pi\) | |||||||
\(734\) | 26.8455 | 0.990886 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.7112 | 1.35319 | ||||||||
\(737\) | −74.6155 | −2.74850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.9709 | 1.65428 | 0.827141 | − | 0.561995i | \(-0.189966\pi\) | ||||
0.827141 | + | 0.561995i | \(0.189966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.49028 | −0.0914212 | ||||||||
\(743\) | −29.4546 | −1.08059 | −0.540293 | − | 0.841477i | \(-0.681687\pi\) | ||||
−0.540293 | + | 0.841477i | \(0.681687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.114461 | −0.00419071 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 31.4455 | 1.14976 | ||||||||
\(749\) | 10.4991 | 0.383627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.1341 | −1.24557 | −0.622786 | − | 0.782392i | \(-0.713999\pi\) | ||||
−0.622786 | + | 0.782392i | \(0.713999\pi\) | |||||||
\(752\) | −0.142426 | −0.00519375 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.58148 | 0.203266 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.2875 | 0.555635 | 0.277817 | − | 0.960634i | \(-0.410389\pi\) | ||||
0.277817 | + | 0.960634i | \(0.410389\pi\) | |||||||
\(758\) | 6.89139 | 0.250306 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0119 | 0.870429 | 0.435215 | − | 0.900327i | \(-0.356672\pi\) | ||||
0.435215 | + | 0.900327i | \(0.356672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.61769 | 0.167172 | ||||||||
\(764\) | −24.0887 | −0.871500 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.4802 | 0.378664 | ||||||||
\(767\) | −28.1056 | −1.01483 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.656954 | −0.0236904 | −0.0118452 | − | 0.999930i | \(-0.503771\pi\) | ||||
−0.0118452 | + | 0.999930i | \(0.503771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.8577 | −0.390776 | ||||||||
\(773\) | −28.1609 | −1.01288 | −0.506439 | − | 0.862276i | \(-0.669039\pi\) | ||||
−0.506439 | + | 0.862276i | \(0.669039\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −21.1271 | −0.758420 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.2738 | 1.01367 | ||||||||
\(779\) | −0.291123 | −0.0104306 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0180 | 1.28883 | ||||||||
\(782\) | −23.1306 | −0.827147 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.884958 | −0.0316056 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.66560 | −0.273249 | −0.136625 | − | 0.990623i | \(-0.543625\pi\) | ||||
−0.136625 | + | 0.990623i | \(0.543625\pi\) | |||||||
\(788\) | 23.5119 | 0.837575 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.67794 | −0.344108 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.5439 | −1.15567 | ||||||||
\(794\) | −11.9305 | −0.423397 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.27842 | 0.328865 | ||||||||
\(797\) | −34.7609 | −1.23129 | −0.615647 | − | 0.788022i | \(-0.711105\pi\) | ||||
−0.615647 | + | 0.788022i | \(0.711105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.44821 | 0.157366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.9463 | −0.845572 | ||||||||
\(803\) | −41.8883 | −1.47821 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.0573 | 0.459923 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 48.0291 | 1.68966 | ||||||||
\(809\) | −42.5017 | −1.49428 | −0.747140 | − | 0.664667i | \(-0.768573\pi\) | ||||
−0.747140 | + | 0.664667i | \(0.768573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.2810 | 1.37934 | 0.689672 | − | 0.724122i | \(-0.257755\pi\) | ||||
0.689672 | + | 0.724122i | \(0.257755\pi\) | |||||||
\(812\) | 1.85276 | 0.0650191 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.69258 | 0.304675 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.1021 | −0.458386 | ||||||||
\(818\) | −22.2152 | −0.776736 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.709911 | −0.0247761 | −0.0123880 | − | 0.999923i | \(-0.503943\pi\) | ||||
−0.0123880 | + | 0.999923i | \(0.503943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.6260 | −0.370398 | −0.185199 | − | 0.982701i | \(-0.559293\pi\) | ||||
−0.185199 | + | 0.982701i | \(0.559293\pi\) | |||||||
\(824\) | −48.5653 | −1.69185 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.40977 | 0.188230 | ||||||||
\(827\) | −11.0597 | −0.384585 | −0.192292 | − | 0.981338i | \(-0.561592\pi\) | ||||
−0.192292 | + | 0.981338i | \(0.561592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.64791 | −0.0572342 | −0.0286171 | − | 0.999590i | \(-0.509110\pi\) | ||||
−0.0286171 | + | 0.999590i | \(0.509110\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.3370 | 0.462379 | ||||||||
\(833\) | 27.6387 | 0.957625 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.3371 | 0.426688 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.04195 | −0.0359937 | ||||||||
\(839\) | 23.8789 | 0.824392 | 0.412196 | − | 0.911095i | \(-0.364762\pi\) | ||||
0.412196 | + | 0.911095i | \(0.364762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8975 | −0.824051 | ||||||||
\(842\) | −17.5318 | −0.604186 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.4261 | 0.634252 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.5324 | 0.533701 | ||||||||
\(848\) | 0.603328 | 0.0207184 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.0270 | 0.378002 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.3570 | 0.799729 | 0.399864 | − | 0.916574i | \(-0.369057\pi\) | ||||
0.399864 | + | 0.916574i | \(0.369057\pi\) | |||||||
\(854\) | 6.26407 | 0.214352 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 45.3431 | 1.54980 | ||||||||
\(857\) | 2.70183 | 0.0922929 | 0.0461464 | − | 0.998935i | \(-0.485306\pi\) | ||||
0.0461464 | + | 0.998935i | \(0.485306\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.5781 | 0.804474 | 0.402237 | − | 0.915536i | \(-0.368233\pi\) | ||||
0.402237 | + | 0.915536i | \(0.368233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.3676 | 0.625602 | ||||||||
\(863\) | −26.2965 | −0.895144 | −0.447572 | − | 0.894248i | \(-0.647711\pi\) | ||||
−0.447572 | + | 0.894248i | \(0.647711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.9494 | 0.677909 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.33433 | 0.147117 | ||||||||
\(869\) | 9.35039 | 0.317190 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.3875 | −1.23294 | ||||||||
\(872\) | 19.9428 | 0.675349 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.07489 | −0.306963 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.4164 | 1.12839 | 0.564196 | − | 0.825641i | \(-0.309186\pi\) | ||||
0.564196 | + | 0.825641i | \(0.309186\pi\) | |||||||
\(878\) | 10.7400 | 0.362459 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0398 | 0.708849 | 0.354425 | − | 0.935085i | \(-0.384677\pi\) | ||||
0.354425 | + | 0.935085i | \(0.384677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.5435 | 0.489428 | 0.244714 | − | 0.969595i | \(-0.421306\pi\) | ||||
0.244714 | + | 0.969595i | \(0.421306\pi\) | |||||||
\(884\) | 15.3350 | 0.515770 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.4146 | −0.383482 | ||||||||
\(887\) | 55.3525 | 1.85855 | 0.929277 | − | 0.369382i | \(-0.120431\pi\) | ||||
0.929277 | + | 0.369382i | \(0.120431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.03021 | −0.202247 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 34.0172 | 1.13898 | ||||||||
\(893\) | 1.74518 | 0.0584003 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.83400 | 0.161493 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.9173 | 0.864873 | ||||||||
\(899\) | 11.9368 | 0.398115 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.8429 | −0.627749 | ||||||||
\(902\) | −0.895112 | −0.0298040 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.7969 | −1.39015 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9003 | 0.860006 | 0.430003 | − | 0.902828i | \(-0.358513\pi\) | ||||
0.430003 | + | 0.902828i | \(0.358513\pi\) | |||||||
\(908\) | −5.31730 | −0.176461 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6499 | −0.352848 | −0.176424 | − | 0.984314i | \(-0.556453\pi\) | ||||
−0.176424 | + | 0.984314i | \(0.556453\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −68.0690 | −2.25275 | ||||||||
\(914\) | −11.0002 | −0.363854 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.5165 | −0.347473 | ||||||||
\(917\) | 2.25360 | 0.0744204 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.1958 | 0.369314 | 0.184657 | − | 0.982803i | \(-0.440883\pi\) | ||||
0.184657 | + | 0.982803i | \(0.440883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.8555 | 0.785640 | ||||||||
\(923\) | 17.5648 | 0.578152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.29528 | 0.108290 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.9017 | 0.423520 | ||||||||
\(929\) | −58.0987 | −1.90616 | −0.953078 | − | 0.302723i | \(-0.902104\pi\) | ||||
−0.953078 | + | 0.302723i | \(0.902104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.8436 | 0.355384 | ||||||||
\(932\) | −28.6303 | −0.937815 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.8359 | −1.13986 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7577 | 1.33150 | 0.665749 | − | 0.746176i | \(-0.268112\pi\) | ||||
0.665749 | + | 0.746176i | \(0.268112\pi\) | |||||||
\(938\) | 7.00389 | 0.228685 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.47724 | 0.0807559 | 0.0403779 | − | 0.999184i | \(-0.487144\pi\) | ||||
0.0403779 | + | 0.999184i | \(0.487144\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.13550 | −0.0369770 | ||||||||
\(944\) | −1.31064 | −0.0426577 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40.2850 | −1.30978 | ||||||||
\(947\) | −18.3448 | −0.596125 | −0.298063 | − | 0.954546i | \(-0.596340\pi\) | ||||
−0.298063 | + | 0.954546i | \(0.596340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.4275 | −0.663106 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.61490 | −0.246800 | ||||||||
\(953\) | −13.8466 | −0.448535 | −0.224267 | − | 0.974528i | \(-0.571999\pi\) | ||||
−0.224267 | + | 0.974528i | \(0.571999\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.62911 | 0.0526893 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.0780 | −0.422530 | ||||||||
\(959\) | −5.29515 | −0.170989 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.07508 | −0.0991962 | ||||||||
\(962\) | 4.23909 | 0.136674 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.22335 | 0.200441 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.61678 | −0.244939 | −0.122470 | − | 0.992472i | \(-0.539081\pi\) | ||||
−0.122470 | + | 0.992472i | \(0.539081\pi\) | |||||||
\(968\) | 67.0812 | 2.15607 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.9964 | 1.31564 | 0.657819 | − | 0.753176i | \(-0.271479\pi\) | ||||
0.657819 | + | 0.753176i | \(0.271479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.90465 | 0.0610604 | ||||||||
\(974\) | 6.90958 | 0.221397 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.51761 | −0.0485776 | ||||||||
\(977\) | 57.8650 | 1.85127 | 0.925633 | − | 0.378423i | \(-0.123534\pi\) | ||||
0.925633 | + | 0.378423i | \(0.123534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 92.2069 | 2.94694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.14044 | −0.259772 | ||||||||
\(983\) | 8.89795 | 0.283801 | 0.141900 | − | 0.989881i | \(-0.454679\pi\) | ||||
0.141900 | + | 0.989881i | \(0.454679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.12898 | −0.258879 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.01641 | 0.191408 | ||||||||
\(989\) | −51.1037 | −1.62500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.01945 | −0.222980 | −0.111490 | − | 0.993766i | \(-0.535562\pi\) | ||||
−0.111490 | + | 0.993766i | \(0.535562\pi\) | |||||||
\(992\) | 30.1822 | 0.958286 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.38088 | −0.107235 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.6542 | 1.57256 | 0.786281 | − | 0.617868i | \(-0.212004\pi\) | ||||
0.786281 | + | 0.617868i | \(0.212004\pi\) | |||||||
\(998\) | 16.8275 | 0.532664 | ||||||||
\(999\) | 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 | 5625.2.a.z.1.4 | ✓ | 8 | |
3.2 | odd | 2 | inner | 5625.2.a.z.1.5 | yes | 8 | |
5.4 | even | 2 | 5625.2.a.bb.1.5 | yes | 8 | ||
15.14 | odd | 2 | 5625.2.a.bb.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5625.2.a.z.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5625.2.a.z.1.5 | yes | 8 | 3.2 | odd | 2 | inner | |
5625.2.a.bb.1.4 | yes | 8 | 15.14 | odd | 2 | ||
5625.2.a.bb.1.5 | yes | 8 | 5.4 | even | 2 |