Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8820,2,Mod(1,8820)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8820, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8820.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8820.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: | \(70.4280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2940) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8820.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843 | 0.784465 | 0.392232 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392232 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.82843 | 1.65614 | 0.828068 | − | 0.560627i | \(-0.189440\pi\) | ||||
0.828068 | + | 0.560627i | \(0.189440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.58579 | 0.593220 | 0.296610 | − | 0.954999i | \(-0.404144\pi\) | ||||
0.296610 | + | 0.954999i | \(0.404144\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.58579 | 0.956203 | 0.478101 | − | 0.878305i | \(-0.341325\pi\) | ||||
0.478101 | + | 0.878305i | \(0.341325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.65685 | 1.42184 | 0.710921 | − | 0.703272i | \(-0.248278\pi\) | ||||
0.710921 | + | 0.703272i | \(0.248278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.24264 | −0.762001 | −0.381000 | − | 0.924575i | \(-0.624420\pi\) | ||||
−0.381000 | + | 0.924575i | \(0.624420\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.48528 | 1.06617 | 0.533087 | − | 0.846061i | \(-0.321032\pi\) | ||||
0.533087 | + | 0.846061i | \(0.321032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.65685 | −1.47266 | −0.736328 | − | 0.676625i | \(-0.763442\pi\) | ||||
−0.736328 | + | 0.676625i | \(0.763442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.48528 | −0.945976 | −0.472988 | − | 0.881069i | \(-0.656825\pi\) | ||||
−0.472988 | + | 0.881069i | \(0.656825\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.41421 | 1.01842 | 0.509210 | − | 0.860642i | \(-0.329938\pi\) | ||||
0.509210 | + | 0.860642i | \(0.329938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843 | 0.368230 | 0.184115 | − | 0.982905i | \(-0.441058\pi\) | ||||
0.184115 | + | 0.982905i | \(0.441058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89949 | 1.26750 | 0.633750 | − | 0.773538i | \(-0.281515\pi\) | ||||
0.633750 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.82843 | 0.350823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.17157 | −0.143130 | −0.0715652 | − | 0.997436i | \(-0.522799\pi\) | ||||
−0.0715652 | + | 0.997436i | \(0.522799\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.48528 | −0.769661 | −0.384831 | − | 0.922987i | \(-0.625740\pi\) | ||||
−0.384831 | + | 0.922987i | \(0.625740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4853 | −1.46129 | −0.730646 | − | 0.682757i | \(-0.760781\pi\) | ||||
−0.730646 | + | 0.682757i | \(0.760781\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.828427 | −0.0909317 | −0.0454658 | − | 0.998966i | \(-0.514477\pi\) | ||||
−0.0454658 | + | 0.998966i | \(0.514477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.82843 | 0.740647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.828427 | −0.0878131 | −0.0439065 | − | 0.999036i | \(-0.513980\pi\) | ||||
−0.0439065 | + | 0.999036i | \(0.513980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.58579 | 0.265296 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000 | 0.406138 | 0.203069 | − | 0.979164i | \(-0.434908\pi\) | ||||
0.203069 | + | 0.979164i | \(0.434908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.343146 | −0.0341443 | −0.0170721 | − | 0.999854i | \(-0.505434\pi\) | ||||
−0.0170721 | + | 0.999854i | \(0.505434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82843 | −0.278693 | −0.139347 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139347 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.07107 | 0.876933 | 0.438467 | − | 0.898747i | \(-0.355522\pi\) | ||||
0.438467 | + | 0.898747i | \(0.355522\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6569 | −1.49965 | −0.749827 | − | 0.661634i | \(-0.769863\pi\) | ||||
−0.749827 | + | 0.661634i | \(0.769863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.24264 | −0.210970 | −0.105485 | − | 0.994421i | \(-0.533639\pi\) | ||||
−0.105485 | + | 0.994421i | \(0.533639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.58579 | 0.427627 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1421 | −1.25491 | −0.627456 | − | 0.778652i | \(-0.715904\pi\) | ||||
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3137 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.8995 | −1.01664 | −0.508321 | − | 0.861168i | \(-0.669734\pi\) | ||||
−0.508321 | + | 0.861168i | \(0.669734\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.5563 | 1.99802 | 0.999012 | − | 0.0444473i | \(-0.0141527\pi\) | ||||
0.999012 | + | 0.0444473i | \(0.0141527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.65685 | 0.635867 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.34315 | 0.683497 | 0.341749 | − | 0.939791i | \(-0.388981\pi\) | ||||
0.341749 | + | 0.939791i | \(0.388981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3137 | −1.40897 | −0.704485 | − | 0.709719i | \(-0.748822\pi\) | ||||
−0.704485 | + | 0.709719i | \(0.748822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.24264 | −0.340777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.1421 | −1.44790 | −0.723950 | − | 0.689852i | \(-0.757675\pi\) | ||||
−0.723950 | + | 0.689852i | \(0.757675\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1421 | 0.794393 | 0.397197 | − | 0.917734i | \(-0.369983\pi\) | ||||
0.397197 | + | 0.917734i | \(0.369983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0000 | 1.23812 | 0.619059 | − | 0.785345i | \(-0.287514\pi\) | ||||
0.619059 | + | 0.785345i | \(0.287514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1421 | −1.07521 | −0.537603 | − | 0.843198i | \(-0.680670\pi\) | ||||
−0.537603 | + | 0.843198i | \(0.680670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.48528 | −0.484733 | −0.242366 | − | 0.970185i | \(-0.577924\pi\) | ||||
−0.242366 | + | 0.970185i | \(0.577924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7574 | 1.17124 | 0.585618 | − | 0.810587i | \(-0.300852\pi\) | ||||
0.585618 | + | 0.810587i | \(0.300852\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.48528 | 0.476807 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6569 | 0.998688 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9706 | 1.37266 | 0.686331 | − | 0.727289i | \(-0.259220\pi\) | ||||
0.686331 | + | 0.727289i | \(0.259220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.17157 | 0.516221 | 0.258111 | − | 0.966115i | \(-0.416900\pi\) | ||||
0.258111 | + | 0.966115i | \(0.416900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.07107 | 0.0763104 | 0.0381552 | − | 0.999272i | \(-0.487852\pi\) | ||||
0.0381552 | + | 0.999272i | \(0.487852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.242641 | −0.0172003 | −0.00860017 | − | 0.999963i | \(-0.502738\pi\) | ||||
−0.00860017 | + | 0.999963i | \(0.502738\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.17157 | 0.357725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.34315 | −0.436680 | −0.218340 | − | 0.975873i | \(-0.570064\pi\) | ||||
−0.218340 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.65685 | −0.658592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.3137 | 1.29918 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8284 | 0.725125 | 0.362563 | − | 0.931959i | \(-0.381902\pi\) | ||||
0.362563 | + | 0.931959i | \(0.381902\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.00000 | 0.265489 | 0.132745 | − | 0.991150i | \(-0.457621\pi\) | ||||
0.132745 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.58579 | −0.170874 | −0.0854368 | − | 0.996344i | \(-0.527229\pi\) | ||||
−0.0854368 | + | 0.996344i | \(0.527229\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.7279 | 1.48896 | 0.744478 | − | 0.667647i | \(-0.232699\pi\) | ||||
0.744478 | + | 0.667647i | \(0.232699\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.48528 | −0.423053 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.34315 | 0.539673 | 0.269837 | − | 0.962906i | \(-0.413030\pi\) | ||||
0.269837 | + | 0.962906i | \(0.413030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.5858 | 1.71254 | 0.856271 | − | 0.516528i | \(-0.172776\pi\) | ||||
0.856271 | + | 0.516528i | \(0.172776\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.31371 | 0.465360 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.4853 | −1.79798 | −0.898988 | − | 0.437974i | \(-0.855696\pi\) | ||||
−0.898988 | + | 0.437974i | \(0.855696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.17157 | 0.576612 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.31371 | −0.0819469 | −0.0409734 | − | 0.999160i | \(-0.513046\pi\) | ||||
−0.0409734 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.92893 | 0.180606 | 0.0903028 | − | 0.995914i | \(-0.471217\pi\) | ||||
0.0903028 | + | 0.995914i | \(0.471217\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.41421 | 0.455452 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.8284 | 1.26993 | 0.634966 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634966 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.7574 | 0.714209 | 0.357104 | − | 0.934064i | \(-0.383764\pi\) | ||||
0.357104 | + | 0.934064i | \(0.383764\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.3137 | −1.04028 | −0.520140 | − | 0.854081i | \(-0.674120\pi\) | ||||
−0.520140 | + | 0.854081i | \(0.674120\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.9706 | −1.84755 | −0.923774 | − | 0.382937i | \(-0.874913\pi\) | ||||
−0.923774 | + | 0.382937i | \(0.874913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.65685 | −0.447318 | −0.223659 | − | 0.974667i | \(-0.571800\pi\) | ||||
−0.223659 | + | 0.974667i | \(0.571800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.82843 | 0.164677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9706 | 0.750107 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.89949 | 0.566843 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.65685 | −0.551146 | −0.275573 | − | 0.961280i | \(-0.588868\pi\) | ||||
−0.275573 | + | 0.961280i | \(0.588868\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.3137 | −1.77564 | −0.887819 | − | 0.460193i | \(-0.847780\pi\) | ||||
−0.887819 | + | 0.460193i | \(0.847780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5147 | 0.650850 | 0.325425 | − | 0.945568i | \(-0.394493\pi\) | ||||
0.325425 | + | 0.945568i | \(0.394493\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.8995 | −1.11767 | −0.558833 | − | 0.829280i | \(-0.688751\pi\) | ||||
−0.558833 | + | 0.829280i | \(0.688751\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.3137 | 0.857403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.6569 | 0.982454 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.82843 | 0.156893 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6274 | 0.584136 | 0.292068 | − | 0.956398i | \(-0.405657\pi\) | ||||
0.292068 | + | 0.956398i | \(0.405657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.17157 | −0.0640099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.79899 | −0.315891 | −0.157946 | − | 0.987448i | \(-0.550487\pi\) | ||||
−0.157946 | + | 0.987448i | \(0.550487\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.48528 | −0.459504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4142 | −0.827478 | −0.413739 | − | 0.910395i | \(-0.635777\pi\) | ||||
−0.413739 | + | 0.910395i | \(0.635777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.2132 | −0.707287 | −0.353643 | − | 0.935380i | \(-0.615057\pi\) | ||||
−0.353643 | + | 0.935380i | \(0.615057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.2843 | 1.39897 | 0.699485 | − | 0.714647i | \(-0.253413\pi\) | ||||
0.699485 | + | 0.714647i | \(0.253413\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.48528 | −0.344203 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.97056 | 0.367892 | 0.183946 | − | 0.982936i | \(-0.441113\pi\) | ||||
0.183946 | + | 0.982936i | \(0.441113\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3137 | −0.648090 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.4853 | −0.653509 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.1716 | −1.31395 | −0.656973 | − | 0.753914i | \(-0.728163\pi\) | ||||
−0.656973 | + | 0.753914i | \(0.728163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.3137 | 1.31069 | 0.655347 | − | 0.755328i | \(-0.272522\pi\) | ||||
0.655347 | + | 0.755328i | \(0.272522\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.6569 | 1.11538 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.9411 | −1.84617 | −0.923086 | − | 0.384594i | \(-0.874341\pi\) | ||||
−0.923086 | + | 0.384594i | \(0.874341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.1421 | 1.64239 | 0.821193 | − | 0.570650i | \(-0.193309\pi\) | ||||
0.821193 | + | 0.570650i | \(0.193309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.8284 | −0.650427 | −0.325214 | − | 0.945641i | \(-0.605436\pi\) | ||||
−0.325214 | + | 0.945641i | \(0.605436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.3137 | 1.58360 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.0000 | −0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.2843 | 1.41955 | 0.709773 | − | 0.704430i | \(-0.248797\pi\) | ||||
0.709773 | + | 0.704430i | \(0.248797\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5147 | −1.07439 | −0.537197 | − | 0.843457i | \(-0.680517\pi\) | ||||
−0.537197 | + | 0.843457i | \(0.680517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | −0.597763 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.9706 | 0.642927 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.727922 | 0.0359934 | 0.0179967 | − | 0.999838i | \(-0.494271\pi\) | ||||
0.0179967 | + | 0.999838i | \(0.494271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.828427 | −0.0406659 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.970563 | −0.0474151 | −0.0237075 | − | 0.999719i | \(-0.507547\pi\) | ||||
−0.0237075 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2843 | 1.18354 | 0.591771 | − | 0.806106i | \(-0.298429\pi\) | ||||
0.591771 | + | 0.806106i | \(0.298429\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.82843 | 0.331227 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.5147 | −1.03633 | −0.518164 | − | 0.855281i | \(-0.673384\pi\) | ||||
−0.518164 | + | 0.855281i | \(0.673384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.8284 | 0.904836 | 0.452418 | − | 0.891806i | \(-0.350561\pi\) | ||||
0.452418 | + | 0.891806i | \(0.350561\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.8579 | 0.567239 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.727922 | −0.0347418 | −0.0173709 | − | 0.999849i | \(-0.505530\pi\) | ||||
−0.0173709 | + | 0.999849i | \(0.505530\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.4142 | 1.11244 | 0.556221 | − | 0.831034i | \(-0.312251\pi\) | ||||
0.556221 | + | 0.831034i | \(0.312251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.828427 | −0.0392712 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.0000 | −1.03824 | −0.519122 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519122 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.4853 | 1.23893 | 0.619465 | − | 0.785025i | \(-0.287350\pi\) | ||||
0.619465 | + | 0.785025i | \(0.287350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.4558 | 1.83764 | 0.918821 | − | 0.394675i | \(-0.129143\pi\) | ||||
0.918821 | + | 0.394675i | \(0.129143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.1421 | −1.58672 | −0.793360 | − | 0.608753i | \(-0.791670\pi\) | ||||
−0.793360 | + | 0.608753i | \(0.791670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.9411 | 1.75571 | 0.877853 | − | 0.478930i | \(-0.158975\pi\) | ||||
0.877853 | + | 0.478930i | \(0.158975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.3137 | −0.888045 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.58579 | 0.118644 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.9411 | −1.55081 | −0.775405 | − | 0.631464i | \(-0.782454\pi\) | ||||
−0.775405 | + | 0.631464i | \(0.782454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.3431 | 0.836375 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.00000 | 0.181631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.2843 | 1.64420 | 0.822099 | − | 0.569345i | \(-0.192803\pi\) | ||||
0.822099 | + | 0.569345i | \(0.192803\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.1127 | −1.49436 | −0.747178 | − | 0.664624i | \(-0.768592\pi\) | ||||
−0.747178 | + | 0.664624i | \(0.768592\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.2843 | 2.35477 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.2843 | 1.17665 | 0.588323 | − | 0.808626i | \(-0.299788\pi\) | ||||
0.588323 | + | 0.808626i | \(0.299788\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.1716 | 1.21152 | 0.605760 | − | 0.795647i | \(-0.292869\pi\) | ||||
0.605760 | + | 0.795647i | \(0.292869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.343146 | −0.0152698 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.5147 | 0.953623 | 0.476812 | − | 0.879006i | \(-0.341792\pi\) | ||||
0.476812 | + | 0.879006i | \(0.341792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.82843 | −0.124635 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.9706 | −0.570445 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.1127 | −1.80118 | −0.900590 | − | 0.434670i | \(-0.856865\pi\) | ||||
−0.900590 | + | 0.434670i | \(0.856865\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.8284 | −0.823310 | −0.411655 | − | 0.911340i | \(-0.635049\pi\) | ||||
−0.411655 | + | 0.911340i | \(0.635049\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.9706 | −1.26198 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.97056 | −0.0856766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.65685 | 0.245026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.07107 | 0.392176 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.2843 | −0.872089 | −0.436044 | − | 0.899925i | \(-0.643621\pi\) | ||||
−0.436044 | + | 0.899925i | \(0.643621\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.6569 | −0.670666 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.1127 | −1.50131 | −0.750655 | − | 0.660694i | \(-0.770262\pi\) | ||||
−0.750655 | + | 0.660694i | \(0.770262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.7990 | 0.843465 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6985 | −1.17362 | −0.586811 | − | 0.809724i | \(-0.699617\pi\) | ||||
−0.586811 | + | 0.809724i | \(0.699617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.3137 | −1.15525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.5147 | 0.906737 | 0.453369 | − | 0.891323i | \(-0.350222\pi\) | ||||
0.453369 | + | 0.891323i | \(0.350222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.24264 | −0.0943486 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.5147 | −0.734255 | −0.367128 | − | 0.930171i | \(-0.619659\pi\) | ||||
−0.367128 | + | 0.930171i | \(0.619659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.2843 | −1.51845 | −0.759225 | − | 0.650829i | \(-0.774422\pi\) | ||||
−0.759225 | + | 0.650829i | \(0.774422\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.58579 | 0.191241 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.82843 | 0.117749 | 0.0588745 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588745 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.8284 | 0.614131 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.1716 | −0.461100 | −0.230550 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230550 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.9706 | −0.452034 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.9706 | −1.27181 | −0.635904 | − | 0.771768i | \(-0.719373\pi\) | ||||
−0.635904 | + | 0.771768i | \(0.719373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0000 | 0.572024 | 0.286012 | − | 0.958226i | \(-0.407670\pi\) | ||||
0.286012 | + | 0.958226i | \(0.407670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.2426 | 1.15204 | 0.576021 | − | 0.817435i | \(-0.304605\pi\) | ||||
0.576021 | + | 0.817435i | \(0.304605\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.4558 | −1.19558 | −0.597788 | − | 0.801654i | \(-0.703954\pi\) | ||||
−0.597788 | + | 0.801654i | \(0.703954\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.3431 | −0.742084 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6863 | 0.593174 | 0.296587 | − | 0.955006i | \(-0.404152\pi\) | ||||
0.296587 | + | 0.955006i | \(0.404152\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6985 | 0.954065 | 0.477033 | − | 0.878886i | \(-0.341712\pi\) | ||||
0.477033 | + | 0.878886i | \(0.341712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.8995 | −1.36254 | −0.681268 | − | 0.732034i | \(-0.738571\pi\) | ||||
−0.681268 | + | 0.732034i | \(0.738571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.2843 | 1.76573 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3137 | 1.16696 | 0.583480 | − | 0.812127i | \(-0.301691\pi\) | ||||
0.583480 | + | 0.812127i | \(0.301691\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.1421 | −0.561214 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.9706 | −1.69724 | −0.848618 | − | 0.529007i | \(-0.822565\pi\) | ||||
−0.848618 | + | 0.529007i | \(0.822565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2843 | −0.957678 | −0.478839 | − | 0.877903i | \(-0.658942\pi\) | ||||
−0.478839 | + | 0.877903i | \(0.658942\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.6863 | 0.498750 | 0.249375 | − | 0.968407i | \(-0.419775\pi\) | ||||
0.249375 | + | 0.968407i | \(0.419775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.65685 | 0.222051 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.4142 | −0.759737 | −0.379868 | − | 0.925041i | \(-0.624031\pi\) | ||||
−0.379868 | + | 0.925041i | \(0.624031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.3137 | 0.442063 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.7990 | 1.16080 | 0.580402 | − | 0.814330i | \(-0.302895\pi\) | ||||
0.580402 | + | 0.814330i | \(0.302895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.2426 | 1.72084 | 0.860420 | − | 0.509586i | \(-0.170201\pi\) | ||||
0.860420 | + | 0.509586i | \(0.170201\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.1127 | 1.35957 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.7990 | 0.764332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.1716 | 1.35576 | 0.677882 | − | 0.735170i | \(-0.262898\pi\) | ||||
0.677882 | + | 0.735170i | \(0.262898\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.02944 | −0.347029 | −0.173515 | − | 0.984831i | \(-0.555512\pi\) | ||||
−0.173515 | + | 0.984831i | \(0.555512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.5563 | 1.28400 | 0.641999 | − | 0.766705i | \(-0.278105\pi\) | ||||
0.641999 | + | 0.766705i | \(0.278105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.8995 | −0.454656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.9706 | 0.798915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.7279 | −1.70153 | −0.850765 | − | 0.525546i | \(-0.823861\pi\) | ||||
−0.850765 | + | 0.525546i | \(0.823861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.5563 | 0.893543 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.6569 | 0.517290 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.97056 | −0.112197 | −0.0560983 | − | 0.998425i | \(-0.517866\pi\) | ||||
−0.0560983 | + | 0.998425i | \(0.517866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7696 | 0.632476 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.3137 | 1.17601 | 0.588006 | − | 0.808857i | \(-0.299913\pi\) | ||||
0.588006 | + | 0.808857i | \(0.299913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.4558 | −0.728627 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685 | 0.211554 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.48528 | 0.167273 | 0.0836364 | − | 0.996496i | \(-0.473347\pi\) | ||||
0.0836364 | + | 0.996496i | \(0.473347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.65685 | 0.284368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.5980 | 1.32026 | 0.660128 | − | 0.751153i | \(-0.270502\pi\) | ||||
0.660128 | + | 0.751153i | \(0.270502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −65.9411 | −2.43892 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.51472 | 0.277562 | 0.138781 | − | 0.990323i | \(-0.455682\pi\) | ||||
0.138781 | + | 0.990323i | \(0.455682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.34315 | −0.0863109 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.6274 | 1.42093 | 0.710466 | − | 0.703731i | \(-0.248484\pi\) | ||||
0.710466 | + | 0.703731i | \(0.248484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.0416 | −1.10212 | −0.551060 | − | 0.834465i | \(-0.685777\pi\) | ||||
−0.551060 | + | 0.834465i | \(0.685777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.34315 | 0.305669 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.34315 | 0.0855026 | 0.0427513 | − | 0.999086i | \(-0.486388\pi\) | ||||
0.0427513 | + | 0.999086i | \(0.486388\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3137 | −0.630110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.82843 | −0.175492 | −0.0877461 | − | 0.996143i | \(-0.527966\pi\) | ||||
−0.0877461 | + | 0.996143i | \(0.527966\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.4853 | 0.380091 | 0.190046 | − | 0.981775i | \(-0.439136\pi\) | ||||
0.190046 | + | 0.981775i | \(0.439136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.00000 | 0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.2132 | 1.05346 | 0.526728 | − | 0.850034i | \(-0.323419\pi\) | ||||
0.526728 | + | 0.850034i | \(0.323419\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4558 | 0.483973 | 0.241987 | − | 0.970280i | \(-0.422201\pi\) | ||||
0.241987 | + | 0.970280i | \(0.422201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.24264 | −0.152400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.17157 | 0.185291 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.9706 | −0.464123 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.1421 | −0.647521 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.1127 | 0.823879 | 0.411939 | − | 0.911211i | \(-0.364852\pi\) | ||||
0.411939 | + | 0.911211i | \(0.364852\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.0000 | 0.994309 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.1127 | 1.66882 | 0.834409 | − | 0.551146i | \(-0.185809\pi\) | ||||
0.834409 | + | 0.551146i | \(0.185809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.2843 | −1.56666 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.9706 | −0.881192 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.4853 | −0.790540 | −0.395270 | − | 0.918565i | \(-0.629349\pi\) | ||||
−0.395270 | + | 0.918565i | \(0.629349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8995 | 0.628536 | 0.314268 | − | 0.949334i | \(-0.398241\pi\) | ||||
0.314268 | + | 0.949334i | \(0.398241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.1421 | 0.355264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.9706 | −0.873609 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.4264 | 1.55049 | 0.775246 | − | 0.631659i | \(-0.217626\pi\) | ||||
0.775246 | + | 0.631659i | \(0.217626\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4558 | −0.887335 | −0.443667 | − | 0.896191i | \(-0.646323\pi\) | ||||
−0.443667 | + | 0.896191i | \(0.646323\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.75736 | 0.200203 | 0.100101 | − | 0.994977i | \(-0.468083\pi\) | ||||
0.100101 | + | 0.994977i | \(0.468083\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0711 | −0.384514 | −0.192257 | − | 0.981345i | \(-0.561581\pi\) | ||||
−0.192257 | + | 0.981345i | \(0.561581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.5147 | −0.535628 | −0.267814 | − | 0.963471i | \(-0.586301\pi\) | ||||
−0.267814 | + | 0.963471i | \(0.586301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.00000 | −0.172005 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.7401 | 1.01948 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2843 | −0.557563 | −0.278781 | − | 0.960355i | \(-0.589930\pi\) | ||||
−0.278781 | + | 0.960355i | \(0.589930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.4558 | −0.869555 | −0.434778 | − | 0.900538i | \(-0.643173\pi\) | ||||
−0.434778 | + | 0.900538i | \(0.643173\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8995 | 1.02016 | 0.510079 | − | 0.860128i | \(-0.329616\pi\) | ||||
0.510079 | + | 0.860128i | \(0.329616\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.1005 | 0.548068 | 0.274034 | − | 0.961720i | \(-0.411642\pi\) | ||||
0.274034 | + | 0.961720i | \(0.411642\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1421 | −0.480847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.0000 | −0.678454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.31371 | −0.112281 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0294 | −0.439973 | −0.219986 | − | 0.975503i | \(-0.570601\pi\) | ||||
−0.219986 | + | 0.975503i | \(0.570601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.0000 | −1.54978 | −0.774890 | − | 0.632096i | \(-0.782195\pi\) | ||||
−0.774890 | + | 0.632096i | \(0.782195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.9706 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.8284 | 1.10227 | 0.551135 | − | 0.834416i | \(-0.314195\pi\) | ||||
0.551135 | + | 0.834416i | \(0.314195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.7696 | −0.561172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.48528 | −0.216779 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.4853 | −1.08344 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.6274 | 1.68664 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.7574 | 0.523792 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3431 | 0.741892 | 0.370946 | − | 0.928654i | \(-0.379033\pi\) | ||||
0.370946 | + | 0.928654i | \(0.379033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.9411 | −0.660679 | −0.330339 | − | 0.943862i | \(-0.607163\pi\) | ||||
−0.330339 | + | 0.943862i | \(0.607163\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.65685 | −0.0548339 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.2843 | −0.933012 | −0.466506 | − | 0.884518i | \(-0.654487\pi\) | ||||
−0.466506 | + | 0.884518i | \(0.654487\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.3431 | −0.603772 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.48528 | 0.213235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.8284 | −0.814594 | −0.407297 | − | 0.913296i | \(-0.633529\pi\) | ||||
−0.407297 | + | 0.913296i | \(0.633529\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.6569 | 0.446627 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.34315 | −0.207222 | −0.103611 | − | 0.994618i | \(-0.533040\pi\) | ||||
−0.103611 | + | 0.994618i | \(0.533040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.2548 | −1.27967 | −0.639836 | − | 0.768512i | \(-0.720998\pi\) | ||||
−0.639836 | + | 0.768512i | \(0.720998\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.17157 | 0.298668 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.0711 | −1.20465 | −0.602324 | − | 0.798252i | \(-0.705758\pi\) | ||||
−0.602324 | + | 0.798252i | \(0.705758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.3137 | −1.14633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.04163 | 0.0661349 | 0.0330675 | − | 0.999453i | \(-0.489472\pi\) | ||||
0.0330675 | + | 0.999453i | \(0.489472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.9706 | 0.613873 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0000 | −0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.17157 | 0.230861 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −59.7990 | −1.92301 | −0.961503 | − | 0.274795i | \(-0.911390\pi\) | ||||
−0.961503 | + | 0.274795i | \(0.911390\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.51472 | −0.112793 | −0.0563963 | − | 0.998408i | \(-0.517961\pi\) | ||||
−0.0563963 | + | 0.998408i | \(0.517961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0416 | 0.577203 | 0.288601 | − | 0.957449i | \(-0.406810\pi\) | ||||
0.288601 | + | 0.957449i | \(0.406810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.65685 | −0.0529533 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.5980 | 0.752659 | 0.376329 | − | 0.926486i | \(-0.377186\pi\) | ||||
0.376329 | + | 0.926486i | \(0.377186\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.07107 | 0.0341271 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.2843 | −1.40816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3137 | 0.359392 | 0.179696 | − | 0.983722i | \(-0.442489\pi\) | ||||
0.179696 | + | 0.983722i | \(0.442489\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.242641 | −0.00769223 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.3137 | −0.611671 | −0.305836 | − | 0.952084i | \(-0.598936\pi\) | ||||
−0.305836 | + | 0.952084i | \(0.598936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8820.2.a.bm.1.2 | 2 | ||
3.2 | odd | 2 | 2940.2.a.q.1.2 | yes | 2 | ||
7.6 | odd | 2 | 8820.2.a.bh.1.1 | 2 | |||
21.2 | odd | 6 | 2940.2.q.p.361.2 | 4 | |||
21.5 | even | 6 | 2940.2.q.r.361.1 | 4 | |||
21.11 | odd | 6 | 2940.2.q.p.961.2 | 4 | |||
21.17 | even | 6 | 2940.2.q.r.961.1 | 4 | |||
21.20 | even | 2 | 2940.2.a.o.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2940.2.a.o.1.1 | ✓ | 2 | 21.20 | even | 2 | ||
2940.2.a.q.1.2 | yes | 2 | 3.2 | odd | 2 | ||
2940.2.q.p.361.2 | 4 | 21.2 | odd | 6 | |||
2940.2.q.p.961.2 | 4 | 21.11 | odd | 6 | |||
2940.2.q.r.361.1 | 4 | 21.5 | even | 6 | |||
2940.2.q.r.961.1 | 4 | 21.17 | even | 6 | |||
8820.2.a.bh.1.1 | 2 | 7.6 | odd | 2 | |||
8820.2.a.bm.1.2 | 2 | 1.1 | even | 1 | trivial |