Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, 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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 567) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.18890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.456850 | −0.323042 | −0.161521 | − | 0.986869i | \(-0.551640\pi\) | ||||
−0.161521 | + | 0.986869i | \(0.551640\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.79129 | −0.895644 | ||||||||
\(5\) | 4.37780 | 1.95781 | 0.978906 | − | 0.204310i | \(-0.0654949\pi\) | ||||
0.978906 | + | 0.204310i | \(0.0654949\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −2.64575 | −0.797724 | −0.398862 | − | 0.917011i | \(-0.630595\pi\) | ||||
−0.398862 | + | 0.917011i | \(0.630595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.58258 | 0.821899 | 0.410950 | − | 0.911658i | \(-0.365197\pi\) | ||||
0.410950 | + | 0.911658i | \(0.365197\pi\) | |||||||
\(20\) | −7.84190 | −1.75350 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.20871 | 0.257698 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.1652 | 2.83303 | ||||||||
\(26\) | 1.82740 | 0.358383 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.82740 | 0.339340 | 0.169670 | − | 0.985501i | \(-0.445730\pi\) | ||||
0.169670 | + | 0.985501i | \(0.445730\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.16515 | −1.64611 | −0.823055 | − | 0.567962i | \(-0.807732\pi\) | ||||
−0.823055 | + | 0.567962i | \(0.807732\pi\) | |||||||
\(32\) | −4.73930 | −0.837798 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.58258 | 0.271409 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | −1.63670 | −0.265508 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.58258 | 1.19891 | ||||||||
\(41\) | −4.37780 | −0.683698 | −0.341849 | − | 0.939755i | \(-0.611053\pi\) | ||||
−0.341849 | + | 0.939755i | \(0.611053\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.58258 | −1.30883 | −0.654415 | − | 0.756135i | \(-0.727085\pi\) | ||||
−0.654415 | + | 0.756135i | \(0.727085\pi\) | |||||||
\(44\) | 4.73930 | 0.714477 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.58258 | 0.233338 | ||||||||
\(47\) | −2.74110 | −0.399831 | −0.199915 | − | 0.979813i | \(-0.564067\pi\) | ||||
−0.199915 | + | 0.979813i | \(0.564067\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.47135 | −0.915188 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.16515 | 0.993628 | ||||||||
\(53\) | −8.66025 | −1.18958 | −0.594789 | − | 0.803882i | \(-0.702764\pi\) | ||||
−0.594789 | + | 0.803882i | \(0.702764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.5826 | −1.56179 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.834849 | −0.109621 | ||||||||
\(59\) | −3.46410 | −0.450988 | −0.225494 | − | 0.974245i | \(-0.572400\pi\) | ||||
−0.225494 | + | 0.974245i | \(0.572400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.41742 | −0.309519 | −0.154760 | − | 0.987952i | \(-0.549460\pi\) | ||||
−0.154760 | + | 0.987952i | \(0.549460\pi\) | |||||||
\(62\) | 4.18710 | 0.531762 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.41742 | −0.427178 | ||||||||
\(65\) | −17.5112 | −2.17200 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.582576 | −0.0711729 | −0.0355865 | − | 0.999367i | \(-0.511330\pi\) | ||||
−0.0355865 | + | 0.999367i | \(0.511330\pi\) | |||||||
\(68\) | 6.20520 | 0.752491 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4014 | 1.35309 | 0.676546 | − | 0.736400i | \(-0.263476\pi\) | ||||
0.676546 | + | 0.736400i | \(0.263476\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.16515 | 0.370453 | 0.185226 | − | 0.982696i | \(-0.440698\pi\) | ||||
0.185226 | + | 0.982696i | \(0.440698\pi\) | |||||||
\(74\) | −1.37055 | −0.159323 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.41742 | −0.736129 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.58258 | −0.965615 | −0.482808 | − | 0.875726i | \(-0.660383\pi\) | ||||
−0.482808 | + | 0.875726i | \(0.660383\pi\) | |||||||
\(80\) | 12.2197 | 1.36620 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | −6.20520 | −0.681110 | −0.340555 | − | 0.940225i | \(-0.610615\pi\) | ||||
−0.340555 | + | 0.940225i | \(0.610615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.1652 | −1.64489 | ||||||||
\(86\) | 3.92095 | 0.422807 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.58258 | −0.488504 | ||||||||
\(89\) | −8.75560 | −0.928092 | −0.464046 | − | 0.885811i | \(-0.653603\pi\) | ||||
−0.464046 | + | 0.885811i | \(0.653603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.20520 | 0.646937 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.25227 | 0.129162 | ||||||||
\(95\) | 15.6838 | 1.60912 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.58258 | −0.769894 | −0.384947 | − | 0.922939i | \(-0.625780\pi\) | ||||
−0.384947 | + | 0.922939i | \(0.625780\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.3739 | −2.53739 | ||||||||
\(101\) | 1.82740 | 0.181833 | 0.0909166 | − | 0.995859i | \(-0.471020\pi\) | ||||
0.0909166 | + | 0.995859i | \(0.471020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.58258 | −0.353002 | −0.176501 | − | 0.984300i | \(-0.556478\pi\) | ||||
−0.176501 | + | 0.984300i | \(0.556478\pi\) | |||||||
\(104\) | −6.92820 | −0.679366 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.95644 | 0.384283 | ||||||||
\(107\) | 11.2107 | 1.08377 | 0.541887 | − | 0.840451i | \(-0.317710\pi\) | ||||
0.541887 | + | 0.840451i | \(0.317710\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 5.29150 | 0.504525 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.9518 | 1.31247 | 0.656235 | − | 0.754556i | \(-0.272148\pi\) | ||||
0.656235 | + | 0.754556i | \(0.272148\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.1652 | −1.41416 | ||||||||
\(116\) | −3.27340 | −0.303928 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.58258 | 0.145688 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | −0.363636 | ||||||||
\(122\) | 1.10440 | 0.0999878 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.4174 | 1.47433 | ||||||||
\(125\) | 40.1232 | 3.58873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.41742 | −0.658190 | −0.329095 | − | 0.944297i | \(-0.606744\pi\) | ||||
−0.329095 | + | 0.944297i | \(0.606744\pi\) | |||||||
\(128\) | 11.0399 | 0.975795 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.00000 | 0.701646 | ||||||||
\(131\) | −18.4249 | −1.60979 | −0.804896 | − | 0.593416i | \(-0.797779\pi\) | ||||
−0.804896 | + | 0.593416i | \(0.797779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.266150 | 0.0229918 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 17.6066 | 1.50423 | 0.752115 | − | 0.659032i | \(-0.229034\pi\) | ||||
0.752115 | + | 0.659032i | \(0.229034\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.58258 | 0.643146 | 0.321573 | − | 0.946885i | \(-0.395788\pi\) | ||||
0.321573 | + | 0.946885i | \(0.395788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.20871 | −0.437105 | ||||||||
\(143\) | 10.5830 | 0.884995 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | −1.44600 | −0.119672 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.37386 | −0.441729 | ||||||||
\(149\) | −10.6784 | −0.874805 | −0.437402 | − | 0.899266i | \(-0.644101\pi\) | ||||
−0.437402 | + | 0.899266i | \(0.644101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.5826 | −1.67499 | −0.837493 | − | 0.546448i | \(-0.815980\pi\) | ||||
−0.837493 | + | 0.546448i | \(0.815980\pi\) | |||||||
\(152\) | 6.20520 | 0.503308 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −40.1232 | −3.22277 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.834849 | −0.0666282 | −0.0333141 | − | 0.999445i | \(-0.510606\pi\) | ||||
−0.0333141 | + | 0.999445i | \(0.510606\pi\) | |||||||
\(158\) | 3.92095 | 0.311934 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20.7477 | −1.64025 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5826 | 1.14220 | 0.571098 | − | 0.820882i | \(-0.306518\pi\) | ||||
0.571098 | + | 0.820882i | \(0.306518\pi\) | |||||||
\(164\) | 7.84190 | 0.612350 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.83485 | 0.220027 | ||||||||
\(167\) | −2.55040 | −0.197356 | −0.0986780 | − | 0.995119i | \(-0.531461\pi\) | ||||
−0.0986780 | + | 0.995119i | \(0.531461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 6.92820 | 0.531369 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.3739 | 1.17225 | ||||||||
\(173\) | 11.4967 | 0.874078 | 0.437039 | − | 0.899442i | \(-0.356027\pi\) | ||||
0.437039 | + | 0.899442i | \(0.356027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.38505 | −0.556669 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.00000 | 0.299813 | ||||||||
\(179\) | 1.63670 | 0.122333 | 0.0611664 | − | 0.998128i | \(-0.480518\pi\) | ||||
0.0611664 | + | 0.998128i | \(0.480518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.1652 | −0.978558 | −0.489279 | − | 0.872127i | \(-0.662740\pi\) | ||||
−0.489279 | + | 0.872127i | \(0.662740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 13.1334 | 0.965587 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.16515 | 0.670222 | ||||||||
\(188\) | 4.91010 | 0.358106 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.16515 | −0.519815 | ||||||||
\(191\) | −6.10985 | −0.442093 | −0.221047 | − | 0.975263i | \(-0.570947\pi\) | ||||
−0.221047 | + | 0.975263i | \(0.570947\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 3.46410 | 0.248708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0953502 | 0.00679342 | 0.00339671 | − | 0.999994i | \(-0.498919\pi\) | ||||
0.00339671 | + | 0.999994i | \(0.498919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7477 | 1.18721 | 0.593607 | − | 0.804755i | \(-0.297703\pi\) | ||||
0.593607 | + | 0.804755i | \(0.297703\pi\) | |||||||
\(200\) | 24.5348 | 1.73487 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.834849 | −0.0587397 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.1652 | −1.33855 | ||||||||
\(206\) | 1.63670 | 0.114034 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.1652 | −0.774164 | ||||||||
\(209\) | −9.47860 | −0.655649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7477 | 0.808747 | 0.404373 | − | 0.914594i | \(-0.367490\pi\) | ||||
0.404373 | + | 0.914594i | \(0.367490\pi\) | |||||||
\(212\) | 15.5130 | 1.06544 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.12159 | −0.350105 | ||||||||
\(215\) | −37.5728 | −2.56244 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.74110 | −0.185651 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.7477 | 1.39881 | ||||||||
\(221\) | 13.8564 | 0.932083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.0000 | −1.47323 | −0.736614 | − | 0.676313i | \(-0.763577\pi\) | ||||
−0.736614 | + | 0.676313i | \(0.763577\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.37386 | −0.423983 | ||||||||
\(227\) | −13.1334 | −0.871695 | −0.435847 | − | 0.900021i | \(-0.643551\pi\) | ||||
−0.435847 | + | 0.900021i | \(0.643551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.9129 | −1.44804 | −0.724022 | − | 0.689777i | \(-0.757709\pi\) | ||||
−0.724022 | + | 0.689777i | \(0.757709\pi\) | |||||||
\(230\) | 6.92820 | 0.456832 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.16515 | 0.207802 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | 6.20520 | 0.403924 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.2578 | −1.63379 | −0.816894 | − | 0.576787i | \(-0.804306\pi\) | ||||
−0.816894 | + | 0.576787i | \(0.804306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.4174 | −1.18637 | −0.593185 | − | 0.805066i | \(-0.702130\pi\) | ||||
−0.593185 | + | 0.805066i | \(0.702130\pi\) | |||||||
\(242\) | 1.82740 | 0.117470 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.33030 | 0.277219 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.3303 | −0.911815 | ||||||||
\(248\) | −15.8745 | −1.00803 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.3303 | −1.15931 | ||||||||
\(251\) | 7.84190 | 0.494977 | 0.247488 | − | 0.968891i | \(-0.420395\pi\) | ||||
0.247488 | + | 0.968891i | \(0.420395\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.16515 | 0.576208 | ||||||||
\(254\) | 3.38865 | 0.212623 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.79129 | 0.111955 | ||||||||
\(257\) | 10.2016 | 0.636359 | 0.318179 | − | 0.948031i | \(-0.396929\pi\) | ||||
0.318179 | + | 0.948031i | \(0.396929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 31.3676 | 1.94534 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.41742 | 0.520030 | ||||||||
\(263\) | 4.28245 | 0.264067 | 0.132034 | − | 0.991245i | \(-0.457849\pi\) | ||||
0.132034 | + | 0.991245i | \(0.457849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.9129 | −2.32897 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.04356 | 0.0637456 | ||||||||
\(269\) | −6.92820 | −0.422420 | −0.211210 | − | 0.977441i | \(-0.567740\pi\) | ||||
−0.211210 | + | 0.977441i | \(0.567740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.74773 | −0.531387 | −0.265693 | − | 0.964058i | \(-0.585601\pi\) | ||||
−0.265693 | + | 0.964058i | \(0.585601\pi\) | |||||||
\(272\) | −9.66930 | −0.586288 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.04356 | −0.485929 | ||||||||
\(275\) | −37.4775 | −2.25998 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00000 | 0.420589 | 0.210295 | − | 0.977638i | \(-0.432558\pi\) | ||||
0.210295 | + | 0.977638i | \(0.432558\pi\) | |||||||
\(278\) | −3.46410 | −0.207763 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.6356 | 1.76791 | 0.883955 | − | 0.467572i | \(-0.154871\pi\) | ||||
0.883955 | + | 0.467572i | \(0.154871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.5826 | −1.04518 | −0.522588 | − | 0.852585i | \(-0.675033\pi\) | ||||
−0.522588 | + | 0.852585i | \(0.675033\pi\) | |||||||
\(284\) | −20.4231 | −1.21189 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.83485 | −0.285891 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −3.65480 | −0.214617 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.66970 | −0.331794 | ||||||||
\(293\) | −21.6983 | −1.26763 | −0.633814 | − | 0.773485i | \(-0.718512\pi\) | ||||
−0.633814 | + | 0.773485i | \(0.718512\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.1652 | −0.882949 | ||||||||
\(296\) | 5.19615 | 0.302020 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.87841 | 0.282599 | ||||||||
\(299\) | 13.8564 | 0.801337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.40315 | 0.541091 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.0000 | 0.573539 | ||||||||
\(305\) | −10.5830 | −0.605981 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3303 | −0.932020 | −0.466010 | − | 0.884780i | \(-0.654309\pi\) | ||||
−0.466010 | + | 0.884780i | \(0.654309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.3303 | 1.04109 | ||||||||
\(311\) | 18.0435 | 1.02315 | 0.511577 | − | 0.859238i | \(-0.329062\pi\) | ||||
0.511577 | + | 0.859238i | \(0.329062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.16515 | 0.0658583 | 0.0329291 | − | 0.999458i | \(-0.489516\pi\) | ||||
0.0329291 | + | 0.999458i | \(0.489516\pi\) | |||||||
\(314\) | 0.381401 | 0.0215237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3739 | 0.864847 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.83485 | −0.270700 | ||||||||
\(320\) | −14.9608 | −0.836335 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.4104 | −0.690533 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −56.6606 | −3.14296 | ||||||||
\(326\) | −6.66205 | −0.368977 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.58258 | −0.418678 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3303 | 0.787665 | 0.393832 | − | 0.919182i | \(-0.371149\pi\) | ||||
0.393832 | + | 0.919182i | \(0.371149\pi\) | |||||||
\(332\) | 11.1153 | 0.610032 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.16515 | 0.0637542 | ||||||||
\(335\) | −2.55040 | −0.139343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1652 | −1.09847 | −0.549233 | − | 0.835669i | \(-0.685080\pi\) | ||||
−0.549233 | + | 0.835669i | \(0.685080\pi\) | |||||||
\(338\) | −1.37055 | −0.0745481 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 27.1652 | 1.47324 | ||||||||
\(341\) | 24.2487 | 1.31314 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −14.8655 | −0.801492 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.25227 | −0.282364 | ||||||||
\(347\) | −36.0315 | −1.93427 | −0.967135 | − | 0.254262i | \(-0.918167\pi\) | ||||
−0.967135 | + | 0.254262i | \(0.918167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.7477 | 1.32472 | 0.662358 | − | 0.749188i | \(-0.269556\pi\) | ||||
0.662358 | + | 0.749188i | \(0.269556\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.5390 | 0.668332 | ||||||||
\(353\) | −35.7454 | −1.90254 | −0.951268 | − | 0.308364i | \(-0.900218\pi\) | ||||
−0.951268 | + | 0.308364i | \(0.900218\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.9129 | 2.64910 | ||||||||
\(356\) | 15.6838 | 0.831240 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.747727 | −0.0395186 | ||||||||
\(359\) | 30.3586 | 1.60226 | 0.801132 | − | 0.598488i | \(-0.204232\pi\) | ||||
0.801132 | + | 0.598488i | \(0.204232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.16515 | −0.324482 | ||||||||
\(362\) | 6.01450 | 0.316115 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.8564 | 0.725277 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.83485 | 0.461175 | 0.230588 | − | 0.973052i | \(-0.425935\pi\) | ||||
0.230588 | + | 0.973052i | \(0.425935\pi\) | |||||||
\(368\) | −9.66930 | −0.504047 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.33030 | −0.379549 | −0.189774 | − | 0.981828i | \(-0.560776\pi\) | ||||
−0.189774 | + | 0.981828i | \(0.560776\pi\) | |||||||
\(374\) | −4.18710 | −0.216510 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.74773 | −0.244845 | ||||||||
\(377\) | −7.30960 | −0.376464 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.9129 | −1.48515 | −0.742577 | − | 0.669760i | \(-0.766397\pi\) | ||||
−0.742577 | + | 0.669760i | \(0.766397\pi\) | |||||||
\(380\) | −28.0942 | −1.44120 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.79129 | 0.142815 | ||||||||
\(383\) | 19.3386 | 0.988157 | 0.494078 | − | 0.869417i | \(-0.335506\pi\) | ||||
0.494078 | + | 0.869417i | \(0.335506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.39590 | −0.325543 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.5826 | 0.689551 | ||||||||
\(389\) | −31.7490 | −1.60974 | −0.804869 | − | 0.593452i | \(-0.797765\pi\) | ||||
−0.804869 | + | 0.593452i | \(0.797765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.0435608 | −0.00219456 | ||||||||
\(395\) | −37.5728 | −1.89049 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.58258 | 0.0794272 | 0.0397136 | − | 0.999211i | \(-0.487355\pi\) | ||||
0.0397136 | + | 0.999211i | \(0.487355\pi\) | |||||||
\(398\) | −7.65120 | −0.383520 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 39.5390 | 1.97695 | ||||||||
\(401\) | 14.1425 | 0.706241 | 0.353120 | − | 0.935578i | \(-0.385121\pi\) | ||||
0.353120 | + | 0.935578i | \(0.385121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.6606 | 1.82619 | ||||||||
\(404\) | −3.27340 | −0.162858 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.93725 | −0.393435 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.25227 | −0.457495 | −0.228748 | − | 0.973486i | \(-0.573463\pi\) | ||||
−0.228748 | + | 0.973486i | \(0.573463\pi\) | |||||||
\(410\) | 8.75560 | 0.432408 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.41742 | 0.316164 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.1652 | −1.33348 | ||||||||
\(416\) | 18.9572 | 0.929454 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.33030 | 0.211802 | ||||||||
\(419\) | −18.6156 | −0.909432 | −0.454716 | − | 0.890636i | \(-0.650259\pi\) | ||||
−0.454716 | + | 0.890636i | \(0.650259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.1652 | −0.787841 | −0.393921 | − | 0.919144i | \(-0.628882\pi\) | ||||
−0.393921 | + | 0.919144i | \(0.628882\pi\) | |||||||
\(422\) | −5.36695 | −0.261259 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.0000 | −0.728464 | ||||||||
\(425\) | −49.0695 | −2.38022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −20.0815 | −0.970676 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.1652 | 0.827777 | ||||||||
\(431\) | −36.6591 | −1.76581 | −0.882904 | − | 0.469554i | \(-0.844415\pi\) | ||||
−0.882904 | + | 0.469554i | \(0.844415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.9129 | 1.05307 | 0.526533 | − | 0.850155i | \(-0.323492\pi\) | ||||
0.526533 | + | 0.850155i | \(0.323492\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.7477 | −0.514723 | ||||||||
\(437\) | −12.4104 | −0.593670 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.5826 | −1.22099 | −0.610495 | − | 0.792020i | \(-0.709029\pi\) | ||||
−0.610495 | + | 0.792020i | \(0.709029\pi\) | |||||||
\(440\) | −20.0616 | −0.956400 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.33030 | −0.301102 | ||||||||
\(443\) | 17.3205 | 0.822922 | 0.411461 | − | 0.911427i | \(-0.365019\pi\) | ||||
0.411461 | + | 0.911427i | \(0.365019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.3303 | −1.81703 | ||||||||
\(446\) | 10.0507 | 0.475915 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.5529 | 1.25311 | 0.626554 | − | 0.779378i | \(-0.284465\pi\) | ||||
0.626554 | + | 0.779378i | \(0.284465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.5826 | 0.545402 | ||||||||
\(452\) | −24.9916 | −1.17551 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.3303 | 1.46557 | 0.732785 | − | 0.680460i | \(-0.238220\pi\) | ||||
0.732785 | + | 0.680460i | \(0.238220\pi\) | |||||||
\(458\) | 10.0109 | 0.467779 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 27.1652 | 1.26658 | ||||||||
\(461\) | −13.3241 | −0.620566 | −0.310283 | − | 0.950644i | \(-0.600424\pi\) | ||||
−0.310283 | + | 0.950644i | \(0.600424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.9129 | 0.971904 | 0.485952 | − | 0.873986i | \(-0.338473\pi\) | ||||
0.485952 | + | 0.873986i | \(0.338473\pi\) | |||||||
\(464\) | 5.10080 | 0.236799 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.20520 | 0.287143 | 0.143571 | − | 0.989640i | \(-0.454141\pi\) | ||||
0.143571 | + | 0.989640i | \(0.454141\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.48220 | 0.252875 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.00000 | −0.276172 | ||||||||
\(473\) | 22.7074 | 1.04409 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 50.7477 | 2.32847 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.5390 | 0.527782 | ||||||||
\(479\) | 24.6301 | 1.12538 | 0.562689 | − | 0.826668i | \(-0.309767\pi\) | ||||
0.562689 | + | 0.826668i | \(0.309767\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 8.41400 | 0.383247 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.16515 | 0.325689 | ||||||||
\(485\) | −33.1950 | −1.50731 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.58258 | −0.298285 | −0.149142 | − | 0.988816i | \(-0.547651\pi\) | ||||
−0.149142 | + | 0.988816i | \(0.547651\pi\) | |||||||
\(488\) | −4.18710 | −0.189541 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.4213 | 1.01186 | 0.505930 | − | 0.862575i | \(-0.331149\pi\) | ||||
0.505930 | + | 0.862575i | \(0.331149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.33030 | −0.285102 | ||||||||
\(494\) | 6.54680 | 0.294555 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.5826 | −1.14869 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | −71.8722 | −3.21422 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.58258 | −0.159898 | ||||||||
\(503\) | 5.48220 | 0.244439 | 0.122220 | − | 0.992503i | \(-0.460999\pi\) | ||||
0.122220 | + | 0.992503i | \(0.460999\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | −4.18710 | −0.186139 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.2867 | 0.589504 | ||||||||
\(509\) | 19.1479 | 0.848716 | 0.424358 | − | 0.905494i | \(-0.360500\pi\) | ||||
0.424358 | + | 0.905494i | \(0.360500\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.8981 | −1.01196 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.66061 | −0.205570 | ||||||||
\(515\) | −15.6838 | −0.691111 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.25227 | 0.318955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −30.3303 | −1.33007 | ||||||||
\(521\) | −3.46410 | −0.151765 | −0.0758825 | − | 0.997117i | \(-0.524177\pi\) | ||||
−0.0758825 | + | 0.997117i | \(0.524177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.41742 | 0.280614 | 0.140307 | − | 0.990108i | \(-0.455191\pi\) | ||||
0.140307 | + | 0.990108i | \(0.455191\pi\) | |||||||
\(524\) | 33.0043 | 1.44180 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.95644 | −0.0853048 | ||||||||
\(527\) | 31.7490 | 1.38301 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 17.3205 | 0.752355 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.5112 | 0.758495 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.0780 | 2.12183 | ||||||||
\(536\) | −1.00905 | −0.0435844 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.16515 | 0.136459 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0000 | 0.472927 | 0.236463 | − | 0.971640i | \(-0.424012\pi\) | ||||
0.236463 | + | 0.971640i | \(0.424012\pi\) | |||||||
\(542\) | 3.99640 | 0.171660 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.4174 | 0.703891 | ||||||||
\(545\) | 26.2668 | 1.12515 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9129 | −0.552115 | −0.276057 | − | 0.961141i | \(-0.589028\pi\) | ||||
−0.276057 | + | 0.961141i | \(0.589028\pi\) | |||||||
\(548\) | −31.5384 | −1.34725 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.1216 | 0.730067 | ||||||||
\(551\) | 6.54680 | 0.278903 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.19795 | −0.135868 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.5826 | −0.576030 | ||||||||
\(557\) | 12.5058 | 0.529886 | 0.264943 | − | 0.964264i | \(-0.414647\pi\) | ||||
0.264943 | + | 0.964264i | \(0.414647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.3303 | 1.45202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5390 | −0.571109 | ||||||||
\(563\) | 41.7599 | 1.75997 | 0.879985 | − | 0.475001i | \(-0.157552\pi\) | ||||
0.879985 | + | 0.475001i | \(0.157552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.0780 | 2.56957 | ||||||||
\(566\) | 8.03260 | 0.337636 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.7477 | 0.828596 | ||||||||
\(569\) | 11.9337 | 0.500285 | 0.250142 | − | 0.968209i | \(-0.419523\pi\) | ||||
0.250142 | + | 0.968209i | \(0.419523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.834849 | −0.0349373 | −0.0174687 | − | 0.999847i | \(-0.505561\pi\) | ||||
−0.0174687 | + | 0.999847i | \(0.505561\pi\) | |||||||
\(572\) | −18.9572 | −0.792641 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −49.0695 | −2.04634 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.7477 | −1.36331 | −0.681653 | − | 0.731676i | \(-0.738739\pi\) | ||||
−0.681653 | + | 0.731676i | \(0.738739\pi\) | |||||||
\(578\) | 2.28425 | 0.0950123 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.3303 | −0.595033 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.9129 | 0.948954 | ||||||||
\(584\) | 5.48220 | 0.226855 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.91288 | 0.409497 | ||||||||
\(587\) | 8.56490 | 0.353511 | 0.176756 | − | 0.984255i | \(-0.443440\pi\) | ||||
0.176756 | + | 0.984255i | \(0.443440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.8348 | −1.35294 | ||||||||
\(590\) | 6.92820 | 0.285230 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.37386 | 0.344164 | ||||||||
\(593\) | 43.5873 | 1.78992 | 0.894958 | − | 0.446150i | \(-0.147205\pi\) | ||||
0.894958 | + | 0.446150i | \(0.147205\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.1280 | 0.783514 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.33030 | −0.258865 | ||||||||
\(599\) | 4.47315 | 0.182768 | 0.0913840 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913840 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.41742 | −0.180190 | −0.0900952 | − | 0.995933i | \(-0.528717\pi\) | ||||
−0.0900952 | + | 0.995933i | \(0.528717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.8693 | 1.50019 | ||||||||
\(605\) | −17.5112 | −0.711932 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.5826 | −0.876010 | −0.438005 | − | 0.898973i | \(-0.644315\pi\) | ||||
−0.438005 | + | 0.898973i | \(0.644315\pi\) | |||||||
\(608\) | −16.9789 | −0.688586 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.83485 | 0.195757 | ||||||||
\(611\) | 10.9644 | 0.443572 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00000 | 0.0403896 | 0.0201948 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201948 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(614\) | 7.46050 | 0.301081 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.8208 | 0.999248 | 0.499624 | − | 0.866242i | \(-0.333471\pi\) | ||||
0.499624 | + | 0.866242i | \(0.333471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.9129 | 1.12191 | 0.560957 | − | 0.827845i | \(-0.310433\pi\) | ||||
0.560957 | + | 0.827845i | \(0.310433\pi\) | |||||||
\(620\) | 71.8722 | 2.88646 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.24318 | −0.330521 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 104.826 | 4.19303 | ||||||||
\(626\) | −0.532300 | −0.0212750 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.49545 | 0.0596751 | ||||||||
\(629\) | −10.3923 | −0.414368 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1652 | −1.24067 | −0.620333 | − | 0.784339i | \(-0.713002\pi\) | ||||
−0.620333 | + | 0.784339i | \(0.713002\pi\) | |||||||
\(632\) | −14.8655 | −0.591316 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.4720 | −1.28861 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.20880 | 0.0874473 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.3303 | 1.91042 | ||||||||
\(641\) | 12.1244 | 0.478883 | 0.239442 | − | 0.970911i | \(-0.423036\pi\) | ||||
0.239442 | + | 0.970911i | \(0.423036\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.3303 | 1.35385 | 0.676927 | − | 0.736050i | \(-0.263311\pi\) | ||||
0.676927 | + | 0.736050i | \(0.263311\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.66970 | 0.223071 | ||||||||
\(647\) | −11.3060 | −0.444485 | −0.222242 | − | 0.974991i | \(-0.571338\pi\) | ||||
−0.222242 | + | 0.974991i | \(0.571338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.16515 | 0.359764 | ||||||||
\(650\) | 25.8854 | 1.01531 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −26.1216 | −1.02300 | ||||||||
\(653\) | 12.1244 | 0.474463 | 0.237231 | − | 0.971453i | \(-0.423760\pi\) | ||||
0.237231 | + | 0.971453i | \(0.423760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −80.6606 | −3.15167 | ||||||||
\(656\) | −12.2197 | −0.477099 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.49125 | 0.252863 | 0.126432 | − | 0.991975i | \(-0.459648\pi\) | ||||
0.126432 | + | 0.991975i | \(0.459648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | 0.311164 | 0.155582 | − | 0.987823i | \(-0.450275\pi\) | ||||
0.155582 | + | 0.987823i | \(0.450275\pi\) | |||||||
\(662\) | −6.54680 | −0.254449 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.7477 | −0.417093 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.33030 | −0.245110 | ||||||||
\(668\) | 4.56850 | 0.176761 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.16515 | 0.0450137 | ||||||||
\(671\) | 6.39590 | 0.246911 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.4955 | 1.09842 | 0.549210 | − | 0.835685i | \(-0.314929\pi\) | ||||
0.549210 | + | 0.835685i | \(0.314929\pi\) | |||||||
\(674\) | 9.21245 | 0.354850 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.37386 | −0.206687 | ||||||||
\(677\) | −11.8383 | −0.454983 | −0.227492 | − | 0.973780i | \(-0.573052\pi\) | ||||
−0.227492 | + | 0.973780i | \(0.573052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −26.2668 | −1.00729 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.0780 | −0.424200 | ||||||||
\(683\) | 4.47315 | 0.171160 | 0.0855802 | − | 0.996331i | \(-0.472726\pi\) | ||||
0.0855802 | + | 0.996331i | \(0.472726\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 77.0780 | 2.94500 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −23.9564 | −0.913331 | ||||||||
\(689\) | 34.6410 | 1.31972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8348 | −0.412177 | −0.206089 | − | 0.978533i | \(-0.566073\pi\) | ||||
−0.206089 | + | 0.978533i | \(0.566073\pi\) | |||||||
\(692\) | −20.5939 | −0.782863 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.4610 | 0.624850 | ||||||||
\(695\) | 33.1950 | 1.25916 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.1652 | 0.574421 | ||||||||
\(698\) | −11.3060 | −0.427939 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.4449 | −1.11212 | −0.556059 | − | 0.831143i | \(-0.687687\pi\) | ||||
−0.556059 | + | 0.831143i | \(0.687687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7477 | 0.405358 | ||||||||
\(704\) | 9.04165 | 0.340770 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.3303 | 0.614599 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0000 | 0.563337 | 0.281668 | − | 0.959512i | \(-0.409112\pi\) | ||||
0.281668 | + | 0.959512i | \(0.409112\pi\) | |||||||
\(710\) | −22.8027 | −0.855770 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.1652 | −0.568338 | ||||||||
\(713\) | 31.7490 | 1.18901 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.3303 | 1.73266 | ||||||||
\(716\) | −2.93180 | −0.109567 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.8693 | −0.517598 | ||||||||
\(719\) | −49.0695 | −1.82998 | −0.914992 | − | 0.403471i | \(-0.867803\pi\) | ||||
−0.914992 | + | 0.403471i | \(0.867803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.81655 | 0.104821 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.5826 | 0.876440 | ||||||||
\(725\) | 25.8854 | 0.961360 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.2432 | −1.71506 | −0.857532 | − | 0.514430i | \(-0.828004\pi\) | ||||
−0.857532 | + | 0.514430i | \(0.828004\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.33030 | −0.234295 | ||||||||
\(731\) | 29.7309 | 1.09964 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.7477 | −0.396976 | −0.198488 | − | 0.980103i | \(-0.563603\pi\) | ||||
−0.198488 | + | 0.980103i | \(0.563603\pi\) | |||||||
\(734\) | −4.03620 | −0.148979 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.4174 | 0.605154 | ||||||||
\(737\) | 1.54135 | 0.0567764 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.4174 | −0.714281 | −0.357141 | − | 0.934051i | \(-0.616248\pi\) | ||||
−0.357141 | + | 0.934051i | \(0.616248\pi\) | |||||||
\(740\) | −23.5257 | −0.864822 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.4195 | −0.492312 | −0.246156 | − | 0.969230i | \(-0.579168\pi\) | ||||
−0.246156 | + | 0.969230i | \(0.579168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.7477 | −1.71270 | ||||||||
\(746\) | 3.34885 | 0.122610 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.4174 | −0.600280 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.41742 | −0.343647 | −0.171823 | − | 0.985128i | \(-0.554966\pi\) | ||||
−0.171823 | + | 0.985128i | \(0.554966\pi\) | |||||||
\(752\) | −7.65120 | −0.279011 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.33939 | 0.121614 | ||||||||
\(755\) | −90.1064 | −3.27931 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.83485 | −0.248417 | −0.124208 | − | 0.992256i | \(-0.539639\pi\) | ||||
−0.124208 | + | 0.992256i | \(0.539639\pi\) | |||||||
\(758\) | 13.2089 | 0.479767 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.1652 | 0.985384 | ||||||||
\(761\) | 30.4539 | 1.10395 | 0.551977 | − | 0.833859i | \(-0.313874\pi\) | ||||
0.551977 | + | 0.833859i | \(0.313874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.9445 | 0.395958 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.83485 | −0.319216 | ||||||||
\(767\) | 13.8564 | 0.500326 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.0780 | 1.62556 | 0.812778 | − | 0.582574i | \(-0.197954\pi\) | ||||
0.812778 | + | 0.582574i | \(0.197954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.0780 | −0.902578 | ||||||||
\(773\) | 31.5583 | 1.13507 | 0.567537 | − | 0.823348i | \(-0.307896\pi\) | ||||
0.567537 | + | 0.823348i | \(0.307896\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −129.826 | −4.66348 | ||||||||
\(776\) | −13.1334 | −0.471462 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.5045 | 0.520013 | ||||||||
\(779\) | −15.6838 | −0.561931 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.1652 | −1.07939 | ||||||||
\(782\) | −5.48220 | −0.196043 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.65480 | −0.130445 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.9129 | −1.92179 | −0.960893 | − | 0.276919i | \(-0.910687\pi\) | ||||
−0.960893 | + | 0.276919i | \(0.910687\pi\) | |||||||
\(788\) | −0.170800 | −0.00608449 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.1652 | 0.610709 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.66970 | 0.343381 | ||||||||
\(794\) | −0.723000 | −0.0256583 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.0000 | −1.06332 | ||||||||
\(797\) | 50.7062 | 1.79611 | 0.898053 | − | 0.439887i | \(-0.144981\pi\) | ||||
0.898053 | + | 0.439887i | \(0.144981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.49545 | 0.335925 | ||||||||
\(800\) | −67.1329 | −2.37351 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.46099 | −0.228145 | ||||||||
\(803\) | −8.37420 | −0.295519 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.7484 | −0.589937 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.16515 | 0.111350 | ||||||||
\(809\) | 10.1063 | 0.355317 | 0.177658 | − | 0.984092i | \(-0.443148\pi\) | ||||
0.177658 | + | 0.984092i | \(0.443148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.62614 | 0.127096 | ||||||||
\(815\) | 63.8396 | 2.23620 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.7477 | −1.07573 | ||||||||
\(818\) | 4.22690 | 0.147790 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 34.3303 | 1.19887 | ||||||||
\(821\) | 33.6718 | 1.17515 | 0.587576 | − | 0.809169i | \(-0.300082\pi\) | ||||
0.587576 | + | 0.809169i | \(0.300082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0000 | 0.418294 | 0.209147 | − | 0.977884i | \(-0.432931\pi\) | ||||
0.209147 | + | 0.977884i | \(0.432931\pi\) | |||||||
\(824\) | −6.20520 | −0.216168 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2578 | −0.878298 | −0.439149 | − | 0.898414i | \(-0.644720\pi\) | ||||
−0.439149 | + | 0.898414i | \(0.644720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3303 | 0.358786 | 0.179393 | − | 0.983777i | \(-0.442587\pi\) | ||||
0.179393 | + | 0.983777i | \(0.442587\pi\) | |||||||
\(830\) | 12.4104 | 0.430771 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.6697 | 0.473911 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.1652 | −0.386386 | ||||||||
\(836\) | 16.9789 | 0.587228 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.50455 | 0.293785 | ||||||||
\(839\) | 39.0188 | 1.34708 | 0.673540 | − | 0.739151i | \(-0.264773\pi\) | ||||
0.673540 | + | 0.739151i | \(0.264773\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6606 | −0.884848 | ||||||||
\(842\) | 7.38505 | 0.254506 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.0436 | −0.724349 | ||||||||
\(845\) | 13.1334 | 0.451803 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.1733 | −0.830113 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.4174 | 0.768911 | ||||||||
\(851\) | −10.3923 | −0.356244 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.7477 | −0.436474 | −0.218237 | − | 0.975896i | \(-0.570031\pi\) | ||||
−0.218237 | + | 0.975896i | \(0.570031\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.4174 | 0.663674 | ||||||||
\(857\) | 40.3139 | 1.37710 | 0.688549 | − | 0.725190i | \(-0.258248\pi\) | ||||
0.688549 | + | 0.725190i | \(0.258248\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.3303 | −0.898378 | −0.449189 | − | 0.893437i | \(-0.648287\pi\) | ||||
−0.449189 | + | 0.893437i | \(0.648287\pi\) | |||||||
\(860\) | 67.3037 | 2.29504 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.7477 | 0.570430 | ||||||||
\(863\) | 2.45505 | 0.0835709 | 0.0417855 | − | 0.999127i | \(-0.486695\pi\) | ||||
0.0417855 | + | 0.999127i | \(0.486695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.3303 | 1.71128 | ||||||||
\(866\) | −10.0109 | −0.340184 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.7074 | 0.770294 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.33030 | 0.0789593 | ||||||||
\(872\) | 10.3923 | 0.351928 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.66970 | 0.191780 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.0000 | 0.438979 | 0.219489 | − | 0.975615i | \(-0.429561\pi\) | ||||
0.219489 | + | 0.975615i | \(0.429561\pi\) | |||||||
\(878\) | 11.6874 | 0.394431 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −32.3303 | −1.08985 | ||||||||
\(881\) | −21.5076 | −0.724610 | −0.362305 | − | 0.932060i | \(-0.618010\pi\) | ||||
−0.362305 | + | 0.932060i | \(0.618010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.9129 | 1.64605 | 0.823025 | − | 0.568006i | \(-0.192285\pi\) | ||||
0.823025 | + | 0.568006i | \(0.192285\pi\) | |||||||
\(884\) | −24.8208 | −0.834814 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.91288 | −0.265838 | ||||||||
\(887\) | −22.9934 | −0.772043 | −0.386022 | − | 0.922490i | \(-0.626151\pi\) | ||||
−0.386022 | + | 0.922490i | \(0.626151\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 17.5112 | 0.586977 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 39.4083 | 1.31949 | ||||||||
\(893\) | −9.82020 | −0.328621 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.16515 | 0.239505 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.1307 | −0.404806 | ||||||||
\(899\) | −16.7484 | −0.558591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.0000 | 0.999445 | ||||||||
\(902\) | −5.29150 | −0.176188 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.1652 | 0.803721 | ||||||||
\(905\) | −57.6344 | −1.91583 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5826 | 0.617024 | 0.308512 | − | 0.951220i | \(-0.400169\pi\) | ||||
0.308512 | + | 0.951220i | \(0.400169\pi\) | |||||||
\(908\) | 23.5257 | 0.780728 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.94630 | 0.296404 | 0.148202 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148202 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.4174 | 0.543337 | ||||||||
\(914\) | −14.3133 | −0.473440 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39.2523 | 1.29693 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0780 | 0.530365 | 0.265183 | − | 0.964198i | \(-0.414568\pi\) | ||||
0.265183 | + | 0.964198i | \(0.414568\pi\) | |||||||
\(920\) | −26.2668 | −0.865991 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.08712 | 0.200469 | ||||||||
\(923\) | −45.6054 | −1.50112 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.4955 | 1.39724 | ||||||||
\(926\) | −9.55405 | −0.313966 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.66061 | −0.284298 | ||||||||
\(929\) | −2.35970 | −0.0774193 | −0.0387096 | − | 0.999251i | \(-0.512325\pi\) | ||||
−0.0387096 | + | 0.999251i | \(0.512325\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.83485 | −0.0927591 | ||||||||
\(935\) | 40.1232 | 1.31217 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.4955 | −1.09425 | −0.547124 | − | 0.837051i | \(-0.684278\pi\) | ||||
−0.547124 | + | 0.837051i | \(0.684278\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.4955 | 0.701104 | ||||||||
\(941\) | −32.8136 | −1.06969 | −0.534847 | − | 0.844949i | \(-0.679631\pi\) | ||||
−0.534847 | + | 0.844949i | \(0.679631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.1652 | 0.493845 | ||||||||
\(944\) | −9.66930 | −0.314709 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.3739 | −0.337283 | ||||||||
\(947\) | 41.7599 | 1.35702 | 0.678508 | − | 0.734593i | \(-0.262627\pi\) | ||||
0.678508 | + | 0.734593i | \(0.262627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6606 | −0.410981 | ||||||||
\(950\) | −23.1841 | −0.752192 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.65480 | 0.118391 | 0.0591953 | − | 0.998246i | \(-0.481147\pi\) | ||||
0.0591953 | + | 0.998246i | \(0.481147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.7477 | −0.865536 | ||||||||
\(956\) | 45.2439 | 1.46329 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.2523 | −0.363544 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.0000 | 1.70968 | ||||||||
\(962\) | 5.48220 | 0.176753 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.9909 | 1.06257 | ||||||||
\(965\) | 61.2892 | 1.97297 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.00000 | 0.128631 | 0.0643157 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643157 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(968\) | −6.92820 | −0.222681 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.1652 | 0.486924 | ||||||||
\(971\) | 35.2131 | 1.13004 | 0.565021 | − | 0.825076i | \(-0.308868\pi\) | ||||
0.565021 | + | 0.825076i | \(0.308868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.00725 | 0.0963585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.74773 | −0.215989 | ||||||||
\(977\) | −24.8208 | −0.794088 | −0.397044 | − | 0.917800i | \(-0.629964\pi\) | ||||
−0.397044 | + | 0.917800i | \(0.629964\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.1652 | 0.740361 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.2432 | −0.326873 | ||||||||
\(983\) | −44.3103 | −1.41328 | −0.706640 | − | 0.707573i | \(-0.749790\pi\) | ||||
−0.706640 | + | 0.707573i | \(0.749790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.417424 | 0.0133002 | ||||||||
\(986\) | 2.89200 | 0.0921001 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.6697 | 0.816662 | ||||||||
\(989\) | 29.7309 | 0.945388 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.7477 | −1.13556 | −0.567782 | − | 0.823179i | \(-0.692198\pi\) | ||||
−0.567782 | + | 0.823179i | \(0.692198\pi\) | |||||||
\(992\) | 43.4364 | 1.37911 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 73.3182 | 2.32434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.83485 | −0.216462 | −0.108231 | − | 0.994126i | \(-0.534519\pi\) | ||||
−0.108231 | + | 0.994126i | \(0.534519\pi\) | |||||||
\(998\) | 9.13701 | 0.289227 | ||||||||
\(999\) | 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 | 3969.2.a.u.1.2 | 4 | ||
3.2 | odd | 2 | inner | 3969.2.a.u.1.3 | 4 | ||
7.6 | odd | 2 | 567.2.a.i.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 567.2.a.i.1.3 | yes | 4 | ||
28.27 | even | 2 | 9072.2.a.ci.1.1 | 4 | |||
63.13 | odd | 6 | 567.2.f.n.379.3 | 8 | |||
63.20 | even | 6 | 567.2.f.n.190.2 | 8 | |||
63.34 | odd | 6 | 567.2.f.n.190.3 | 8 | |||
63.41 | even | 6 | 567.2.f.n.379.2 | 8 | |||
84.83 | odd | 2 | 9072.2.a.ci.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.a.i.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
567.2.a.i.1.3 | yes | 4 | 21.20 | even | 2 | ||
567.2.f.n.190.2 | 8 | 63.20 | even | 6 | |||
567.2.f.n.190.3 | 8 | 63.34 | odd | 6 | |||
567.2.f.n.379.2 | 8 | 63.41 | even | 6 | |||
567.2.f.n.379.3 | 8 | 63.13 | odd | 6 | |||
3969.2.a.u.1.2 | 4 | 1.1 | even | 1 | trivial | ||
3969.2.a.u.1.3 | 4 | 3.2 | odd | 2 | inner | ||
9072.2.a.ci.1.1 | 4 | 28.27 | even | 2 | |||
9072.2.a.ci.1.4 | 4 | 84.83 | odd | 2 |