Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(2.36764\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 2.36764 | 1.36696 | 0.683480 | − | 0.729969i | \(-0.260466\pi\) | ||||
0.683480 | + | 0.729969i | \(0.260466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.42438 | 1.08422 | 0.542108 | − | 0.840309i | \(-0.317626\pi\) | ||||
0.542108 | + | 0.840309i | \(0.317626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.60574 | 0.868579 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.39480 | −1.62659 | −0.813297 | − | 0.581848i | \(-0.802330\pi\) | ||||
−0.813297 | + | 0.581848i | \(0.802330\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.20082 | 1.71980 | 0.859899 | − | 0.510464i | \(-0.170526\pi\) | ||||
0.859899 | + | 0.510464i | \(0.170526\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.74007 | 1.48208 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.01510 | −0.488734 | −0.244367 | − | 0.969683i | \(-0.578580\pi\) | ||||
−0.244367 | + | 0.969683i | \(0.578580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.62798 | 1.52056 | 0.760281 | − | 0.649594i | \(-0.225061\pi\) | ||||
0.760281 | + | 0.649594i | \(0.225061\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.84933 | 0.385611 | 0.192806 | − | 0.981237i | \(-0.438241\pi\) | ||||
0.192806 | + | 0.981237i | \(0.438241\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.877626 | 0.175525 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.933478 | −0.179648 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.47525 | 1.20242 | 0.601212 | − | 0.799090i | \(-0.294685\pi\) | ||||
0.601212 | + | 0.799090i | \(0.294685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.80856 | −1.58206 | −0.791032 | − | 0.611775i | \(-0.790456\pi\) | ||||
−0.791032 | + | 0.611775i | \(0.790456\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.7730 | −2.22349 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.09106 | 0.508167 | 0.254083 | − | 0.967182i | \(-0.418226\pi\) | ||||
0.254083 | + | 0.967182i | \(0.418226\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.6813 | 2.35089 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5582 | 1.61011 | 0.805055 | − | 0.593200i | \(-0.202136\pi\) | ||||
0.805055 | + | 0.593200i | \(0.202136\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.31730 | 0.941727 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.78617 | 0.552270 | 0.276135 | − | 0.961119i | \(-0.410946\pi\) | ||||
0.276135 | + | 0.961119i | \(0.410946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.77104 | −0.668080 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.87169 | −0.257097 | −0.128548 | − | 0.991703i | \(-0.541032\pi\) | ||||
−0.128548 | + | 0.991703i | \(0.541032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.0791 | −1.76358 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.6927 | 2.07855 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.79702 | 0.494330 | 0.247165 | − | 0.968973i | \(-0.420501\pi\) | ||||
0.247165 | + | 0.968973i | \(0.420501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.72660 | 0.861253 | 0.430627 | − | 0.902530i | \(-0.358293\pi\) | ||||
0.430627 | + | 0.902530i | \(0.358293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.0332 | 1.86463 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50663 | −0.428403 | −0.214201 | − | 0.976790i | \(-0.568715\pi\) | ||||
−0.214201 | + | 0.976790i | \(0.568715\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.37854 | 0.527115 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6539 | 1.50174 | 0.750871 | − | 0.660449i | \(-0.229634\pi\) | ||||
0.750871 | + | 0.660449i | \(0.229634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.71794 | 0.201070 | 0.100535 | − | 0.994934i | \(-0.467945\pi\) | ||||
0.100535 | + | 0.994934i | \(0.467945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.07790 | 0.239936 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.277292 | −0.0311978 | −0.0155989 | − | 0.999878i | \(-0.504965\pi\) | ||||
−0.0155989 | + | 0.999878i | \(0.504965\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0273 | −1.11415 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.38817 | −0.701193 | −0.350596 | − | 0.936527i | \(-0.614021\pi\) | ||||
−0.350596 | + | 0.936527i | \(0.614021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.88538 | −0.529894 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.3311 | 1.64366 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.19988 | −0.127187 | −0.0635936 | − | 0.997976i | \(-0.520256\pi\) | ||||
−0.0635936 | + | 0.997976i | \(0.520256\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.8555 | −2.16262 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.0687 | 1.64862 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.32529 | −0.946840 | −0.473420 | − | 0.880837i | \(-0.656981\pi\) | ||||
−0.473420 | + | 0.880837i | \(0.656981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.0574 | −1.41283 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.8284 | 1.77399 | 0.886996 | − | 0.461777i | \(-0.152788\pi\) | ||||
0.886996 | + | 0.461777i | \(0.152788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0560307 | −0.00552087 | −0.00276044 | − | 0.999996i | \(-0.500879\pi\) | ||||
−0.00276044 | + | 0.999996i | \(0.500879\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.65938 | 0.933808 | 0.466904 | − | 0.884308i | \(-0.345369\pi\) | ||||
0.466904 | + | 0.884308i | \(0.345369\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.1326 | 1.64101 | 0.820503 | − | 0.571643i | \(-0.193694\pi\) | ||||
0.820503 | + | 0.571643i | \(0.193694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.31852 | 0.694644 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8841 | −1.40018 | −0.700090 | − | 0.714055i | \(-0.746857\pi\) | ||||
−0.700090 | + | 0.714055i | \(0.746857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.48347 | 0.418086 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.1577 | 1.49378 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.1039 | 1.64581 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.36764 | −0.213483 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.99421 | −0.893909 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9367 | −1.14795 | −0.573974 | − | 0.818874i | \(-0.694599\pi\) | ||||
−0.573974 | + | 0.818874i | \(0.694599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.9980 | 2.20096 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.37469 | −0.469589 | −0.234794 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234794 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.26311 | −0.194777 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.20652 | −0.615695 | −0.307847 | − | 0.951436i | \(-0.599609\pi\) | ||||
−0.307847 | + | 0.951436i | \(0.599609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3439 | −1.21664 | −0.608319 | − | 0.793693i | \(-0.708156\pi\) | ||||
−0.608319 | + | 0.793693i | \(0.708156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.96431 | 0.754931 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −33.4522 | −2.79741 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.6985 | 1.30369 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.37448 | −0.276448 | −0.138224 | − | 0.990401i | \(-0.544139\pi\) | ||||
−0.138224 | + | 0.990401i | \(0.544139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.69407 | 0.381998 | 0.190999 | − | 0.981590i | \(-0.438827\pi\) | ||||
0.190999 | + | 0.981590i | \(0.438827\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.25082 | −0.424504 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.3553 | −1.71530 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5703 | 1.00322 | 0.501609 | − | 0.865095i | \(-0.332742\pi\) | ||||
0.501609 | + | 0.865095i | \(0.332742\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.43150 | −0.351441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.8637 | −1.24254 | −0.621272 | − | 0.783595i | \(-0.713384\pi\) | ||||
−0.621272 | + | 0.783595i | \(0.713384\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −30.9666 | −2.41074 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4327 | 0.962070 | 0.481035 | − | 0.876702i | \(-0.340261\pi\) | ||||
0.481035 | + | 0.876702i | \(0.340261\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.4502 | 1.95771 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.2708 | 1.32073 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8812 | −1.05536 | −0.527682 | − | 0.849442i | \(-0.676939\pi\) | ||||
−0.527682 | + | 0.849442i | \(0.676939\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.98999 | 0.675729 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.1352 | −1.13126 | −0.565628 | − | 0.824660i | \(-0.691366\pi\) | ||||
−0.565628 | + | 0.824660i | \(0.691366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.24711 | 0.0926968 | 0.0463484 | − | 0.998925i | \(-0.485242\pi\) | ||||
0.0463484 | + | 0.998925i | \(0.485242\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.9262 | 1.17730 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.49391 | 0.550963 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8711 | 0.794972 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.9998 | 1.80892 | 0.904460 | − | 0.426559i | \(-0.140274\pi\) | ||||
0.904460 | + | 0.426559i | \(0.140274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.6634 | 1.48739 | 0.743693 | − | 0.668522i | \(-0.233073\pi\) | ||||
0.743693 | + | 0.668522i | \(0.233073\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 35.5931 | 2.54888 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4928 | 0.818828 | 0.409414 | − | 0.912349i | \(-0.365733\pi\) | ||||
0.409414 | + | 0.912349i | \(0.365733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.57078 | 0.253126 | 0.126563 | − | 0.991959i | \(-0.459605\pi\) | ||||
0.126563 | + | 0.991959i | \(0.459605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.30244 | −0.585609 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.42438 | −0.169326 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.81885 | 0.334933 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35.7567 | −2.47334 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7479 | 1.08413 | 0.542064 | − | 0.840337i | \(-0.317643\pi\) | ||||
0.542064 | + | 0.840337i | \(0.317643\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.9599 | 2.05282 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.5971 | 1.74571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.06747 | 0.274854 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.4953 | −0.840524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.43674 | 0.364071 | 0.182035 | − | 0.983292i | \(-0.441731\pi\) | ||||
0.182035 | + | 0.983292i | \(0.441731\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.28686 | 0.152457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0641 | −1.33170 | −0.665852 | − | 0.746084i | \(-0.731932\pi\) | ||||
−0.665852 | + | 0.746084i | \(0.731932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3577 | 0.816617 | 0.408309 | − | 0.912844i | \(-0.366119\pi\) | ||||
0.408309 | + | 0.912844i | \(0.366119\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.65717 | 0.501638 | 0.250819 | − | 0.968034i | \(-0.419300\pi\) | ||||
0.250819 | + | 0.968034i | \(0.419300\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.17913 | 0.598780 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.656528 | −0.0426461 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.492584 | 0.0318626 | 0.0159313 | − | 0.999873i | \(-0.494929\pi\) | ||||
0.0159313 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.1779 | 1.55744 | 0.778719 | − | 0.627373i | \(-0.215870\pi\) | ||||
0.778719 | + | 0.627373i | \(0.215870\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.9408 | −1.34335 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.0989 | 2.61506 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.1249 | −0.958502 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9113 | −1.57239 | −0.786193 | − | 0.617981i | \(-0.787951\pi\) | ||||
−0.786193 | + | 0.617981i | \(0.787951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.97675 | −0.627233 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.5668 | −0.724343 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.95771 | −0.496388 | −0.248194 | − | 0.968710i | \(-0.579837\pi\) | ||||
−0.248194 | + | 0.968710i | \(0.579837\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.8728 | 1.04440 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.0497 | −0.989668 | −0.494834 | − | 0.868987i | \(-0.664771\pi\) | ||||
−0.494834 | + | 0.868987i | \(0.664771\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.53770 | −0.278749 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.84089 | −0.173860 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6584 | 1.01568 | 0.507840 | − | 0.861451i | \(-0.330444\pi\) | ||||
0.507840 | + | 0.861451i | \(0.330444\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.52867 | 0.153605 | 0.0768027 | − | 0.997046i | \(-0.475529\pi\) | ||||
0.0768027 | + | 0.997046i | \(0.475529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.73462 | −0.285508 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.883573 | 0.0530887 | 0.0265444 | − | 0.999648i | \(-0.491550\pi\) | ||||
0.0265444 | + | 0.999648i | \(0.491550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.9528 | −1.37415 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.76979 | −0.284542 | −0.142271 | − | 0.989828i | \(-0.545440\pi\) | ||||
−0.142271 | + | 0.989828i | \(0.545440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.6795 | −1.40760 | −0.703800 | − | 0.710398i | \(-0.748515\pi\) | ||||
−0.703800 | + | 0.710398i | \(0.748515\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 38.0451 | 2.25360 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9394 | −0.761139 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.0790 | −1.29429 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.2377 | 1.35756 | 0.678780 | − | 0.734342i | \(-0.262509\pi\) | ||||
0.678780 | + | 0.734342i | \(0.262509\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.20543 | 0.535961 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.03593 | 0.292214 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.4673 | 0.663173 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 42.2113 | 2.42498 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.3078 | 0.933785 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2175 | 1.49631 | 0.748155 | − | 0.663524i | \(-0.230940\pi\) | ||||
0.748155 | + | 0.663524i | \(0.230940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.132661 | −0.00754681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3994 | −1.15675 | −0.578373 | − | 0.815772i | \(-0.696312\pi\) | ||||
−0.578373 | + | 0.815772i | \(0.696312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.7718 | 0.665381 | 0.332691 | − | 0.943036i | \(-0.392044\pi\) | ||||
0.332691 | + | 0.943036i | \(0.392044\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.4111 | −1.03407 | −0.517036 | − | 0.855964i | \(-0.672965\pi\) | ||||
−0.517036 | + | 0.855964i | \(0.672965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.9327 | −1.95586 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.8700 | 1.27648 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.3561 | −0.743151 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.44200 | 0.301868 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 40.5639 | 2.24319 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.6689 | −1.79564 | −0.897822 | − | 0.440359i | \(-0.854851\pi\) | ||||
−0.897822 | + | 0.440359i | \(0.854851\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.05448 | 0.441383 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.50140 | −0.464481 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0008 | 1.47083 | 0.735413 | − | 0.677619i | \(-0.236988\pi\) | ||||
0.735413 | + | 0.677619i | \(0.236988\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −35.2403 | −1.91399 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 47.5205 | 2.57338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.6153 | 0.571506 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.9286 | −1.39192 | −0.695959 | − | 0.718082i | \(-0.745020\pi\) | ||||
−0.695959 | + | 0.718082i | \(0.745020\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.7455 | −1.80636 | −0.903178 | − | 0.429267i | \(-0.858772\pi\) | ||||
−0.903178 | + | 0.429267i | \(0.858772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.78833 | −0.308958 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −37.3762 | −1.98933 | −0.994667 | − | 0.103142i | \(-0.967110\pi\) | ||||
−0.994667 | + | 0.103142i | \(0.967110\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.6779 | 1.62821 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.3640 | −1.76089 | −0.880443 | − | 0.474153i | \(-0.842754\pi\) | ||||
−0.880443 | + | 0.474153i | \(0.842754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.9301 | 1.31211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 42.8636 | 2.24976 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.16494 | 0.218003 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1406 | 0.738132 | 0.369066 | − | 0.929403i | \(-0.379678\pi\) | ||||
0.369066 | + | 0.929403i | \(0.379678\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.60574 | −0.135649 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6001 | −0.548852 | −0.274426 | − | 0.961608i | \(-0.588488\pi\) | ||||
−0.274426 | + | 0.961608i | \(0.588488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.6627 | −1.22194 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.1519 | 2.06793 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.9849 | −0.975190 | −0.487595 | − | 0.873070i | \(-0.662126\pi\) | ||||
−0.487595 | + | 0.873070i | \(0.662126\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30.6295 | −1.56920 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.1555 | −0.774411 | −0.387205 | − | 0.921993i | \(-0.626560\pi\) | ||||
−0.387205 | + | 0.921993i | \(0.626560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.5119 | 1.39851 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.74145 | −0.392507 | −0.196254 | − | 0.980553i | \(-0.562878\pi\) | ||||
−0.196254 | + | 0.980553i | \(0.562878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.72658 | −0.188461 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.7254 | −0.641909 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.672261 | −0.0338251 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.9596 | 0.901368 | 0.450684 | − | 0.892683i | \(-0.351180\pi\) | ||||
0.450684 | + | 0.892683i | \(0.351180\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.3204 | 0.964817 | 0.482408 | − | 0.875947i | \(-0.339762\pi\) | ||||
0.482408 | + | 0.875947i | \(0.339762\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −54.6203 | −2.72083 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.3101 | −1.20798 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.6757 | −0.826582 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50740 | 0.420664 | 0.210332 | − | 0.977630i | \(-0.432545\pi\) | ||||
0.210332 | + | 0.977630i | \(0.432545\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0625 | −0.841630 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.4874 | −0.760245 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.9613 | −1.66309 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.9947 | −1.17222 | −0.586108 | − | 0.810233i | \(-0.699341\pi\) | ||||
−0.586108 | + | 0.810233i | \(0.699341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.7635 | −1.64553 | −0.822766 | − | 0.568380i | \(-0.807570\pi\) | ||||
−0.822766 | + | 0.568380i | \(0.807570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.86577 | 0.479690 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.76851 | −0.0857851 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −79.2029 | −3.82395 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.44247 | 0.454828 | 0.227414 | − | 0.973798i | \(-0.426973\pi\) | ||||
0.227414 | + | 0.973798i | \(0.426973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6428 | −0.559516 | −0.279758 | − | 0.960071i | \(-0.590254\pi\) | ||||
−0.279758 | + | 0.960071i | \(0.590254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 37.1684 | 1.78209 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.2573 | 0.586346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.9530 | −0.570486 | −0.285243 | − | 0.958455i | \(-0.592074\pi\) | ||||
−0.285243 | + | 0.958455i | \(0.592074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3873 | 1.15868 | 0.579339 | − | 0.815087i | \(-0.303311\pi\) | ||||
0.579339 | + | 0.815087i | \(0.303311\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.90897 | −0.137898 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.98957 | −0.377894 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.58128 | −0.310590 | −0.155295 | − | 0.987868i | \(-0.549633\pi\) | ||||
−0.155295 | + | 0.987868i | \(0.549633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.39480 | 0.254031 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1139 | 0.522175 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.5508 | −1.52266 | −0.761331 | − | 0.648364i | \(-0.775454\pi\) | ||||
−0.761331 | + | 0.648364i | \(0.775454\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.88105 | 0.0878001 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.6674 | 1.24203 | 0.621013 | − | 0.783801i | \(-0.286722\pi\) | ||||
0.621013 | + | 0.783801i | \(0.286722\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.9214 | 1.06525 | 0.532624 | − | 0.846352i | \(-0.321206\pi\) | ||||
0.532624 | + | 0.846352i | \(0.321206\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −50.5618 | −2.34475 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7685 | 0.683406 | 0.341703 | − | 0.939808i | \(-0.388996\pi\) | ||||
0.341703 | + | 0.939808i | \(0.388996\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.7619 | 1.37136 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −56.9594 | −2.61900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.81688 | 0.266897 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.87714 | −0.223309 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.8208 | −0.540105 | −0.270053 | − | 0.962846i | \(-0.587041\pi\) | ||||
−0.270053 | + | 0.962846i | \(0.587041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1671 | 0.873944 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.6081 | −1.02658 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4003 | 0.743167 | 0.371584 | − | 0.928399i | \(-0.378815\pi\) | ||||
0.371584 | + | 0.928399i | \(0.378815\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −37.5597 | −1.69851 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.3512 | 1.36973 | 0.684866 | − | 0.728669i | \(-0.259861\pi\) | ||||
0.684866 | + | 0.728669i | \(0.259861\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.0483 | −0.587666 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34.0806 | −1.53181 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.3568 | 0.956060 | 0.478030 | − | 0.878344i | \(-0.341351\pi\) | ||||
0.478030 | + | 0.878344i | \(0.341351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.4362 | 1.31511 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.7631 | 0.569079 | 0.284540 | − | 0.958664i | \(-0.408159\pi\) | ||||
0.284540 | + | 0.958664i | \(0.408159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.2229 | 1.92339 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 60.2569 | 2.67610 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.2326 | −0.763821 | −0.381911 | − | 0.924199i | \(-0.624734\pi\) | ||||
−0.381911 | + | 0.924199i | \(0.624734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.18707 | −0.273166 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.135840 | −0.00598582 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4257 | −0.898320 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.8656 | −1.44264 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.39754 | 0.236471 | 0.118235 | − | 0.992986i | \(-0.462276\pi\) | ||||
0.118235 | + | 0.992986i | \(0.462276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −44.8818 | −1.96254 | −0.981271 | − | 0.192633i | \(-0.938297\pi\) | ||||
−0.981271 | + | 0.192633i | \(0.938297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.7502 | 0.773209 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5800 | −0.851304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.89403 | 0.429364 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.20082 | −0.268587 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.4180 | 1.01245 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −35.8347 | −1.54638 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.3053 | −1.43191 | −0.715954 | − | 0.698147i | \(-0.754008\pi\) | ||||
−0.715954 | + | 0.698147i | \(0.754008\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.95271 | 0.126713 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.5360 | 1.77920 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1540 | −0.476913 | −0.238456 | − | 0.971153i | \(-0.576641\pi\) | ||||
−0.238456 | + | 0.971153i | \(0.576641\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.5277 | 0.748066 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.9178 | 1.82836 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.7429 | 0.753144 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.446080 | −0.0189010 | −0.00945050 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00945050 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 65.4695 | 2.76906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.7389 | 1.08670 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.2991 | −1.06623 | −0.533116 | − | 0.846042i | \(-0.678979\pi\) | ||||
−0.533116 | + | 0.846042i | \(0.678979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.0848 | −1.51810 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.4740 | −0.481014 | −0.240507 | − | 0.970647i | \(-0.577314\pi\) | ||||
−0.240507 | + | 0.970647i | \(0.577314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1564 | 1.09461 | 0.547305 | − | 0.836933i | \(-0.315654\pi\) | ||||
0.547305 | + | 0.836933i | \(0.315654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 59.1905 | 2.47272 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.62302 | 0.0676844 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5225 | −0.812733 | −0.406366 | − | 0.913710i | \(-0.633204\pi\) | ||||
−0.406366 | + | 0.913710i | \(0.633204\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 48.9236 | 2.03320 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0974 | 0.418193 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 39.1724 | 1.61958 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.2892 | −0.754875 | −0.377438 | − | 0.926035i | \(-0.623195\pi\) | ||||
−0.377438 | + | 0.926035i | \(0.623195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58.3829 | −2.40563 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.2109 | 1.11930 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.93664 | 0.243788 | 0.121894 | − | 0.992543i | \(-0.461103\pi\) | ||||
0.121894 | + | 0.992543i | \(0.461103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.45434 | 0.346013 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1101 | 0.453945 | 0.226972 | − | 0.973901i | \(-0.427117\pi\) | ||||
0.226972 | + | 0.973901i | \(0.427117\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.6877 | 1.86364 | 0.931820 | − | 0.362921i | \(-0.118220\pi\) | ||||
0.931820 | + | 0.362921i | \(0.118220\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.13734 | −0.372101 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 43.8908 | 1.78441 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3754 | −0.461713 | −0.230857 | − | 0.972988i | \(-0.574153\pi\) | ||||
−0.230857 | + | 0.972988i | \(0.574153\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.4774 | 0.949793 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.53763 | 0.385221 | 0.192611 | − | 0.981275i | \(-0.438305\pi\) | ||||
0.192611 | + | 0.981275i | \(0.438305\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.74007 | −0.231462 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5729 | −0.465907 | −0.232954 | − | 0.972488i | \(-0.574839\pi\) | ||||
−0.232954 | + | 0.972488i | \(0.574839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.1787 | 1.89627 | 0.948137 | − | 0.317863i | \(-0.102965\pi\) | ||||
0.948137 | + | 0.317863i | \(0.102965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.72630 | −0.0692742 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.6179 | −1.14472 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −84.6590 | −3.38095 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.22880 | −0.248359 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.0915 | −1.31735 | −0.658675 | − | 0.752427i | \(-0.728883\pi\) | ||||
−0.658675 | + | 0.752427i | \(0.728883\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.2853 | 1.48196 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.3635 | −1.24462 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.9727 | 1.30438 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.1502 | −0.558898 | −0.279449 | − | 0.960161i | \(-0.590152\pi\) | ||||
−0.279449 | + | 0.960161i | \(0.590152\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.23293 | 0.245803 | 0.122901 | − | 0.992419i | \(-0.460780\pi\) | ||||
0.122901 | + | 0.992419i | \(0.460780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 60.6048 | 2.38631 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.0471 | −1.81030 | −0.905149 | − | 0.425094i | \(-0.860241\pi\) | ||||
−0.905149 | + | 0.425094i | \(0.860241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.4842 | −0.804074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.07124 | 0.0810540 | 0.0405270 | − | 0.999178i | \(-0.487096\pi\) | ||||
0.0405270 | + | 0.999178i | \(0.487096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.0303 | −0.509136 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.47650 | 0.174645 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.83230 | 0.149285 | 0.0746427 | − | 0.997210i | \(-0.476218\pi\) | ||||
0.0746427 | + | 0.997210i | \(0.476218\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0169 | 0.739670 | 0.369835 | − | 0.929097i | \(-0.379414\pi\) | ||||
0.369835 | + | 0.929097i | \(0.379414\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29.5844 | −1.14896 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.9748 | 0.463668 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.8723 | 0.497670 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.2887 | −1.40091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.0308 | −1.04196 | −0.520981 | − | 0.853568i | \(-0.674434\pi\) | ||||
−0.520981 | + | 0.853568i | \(0.674434\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.819244 | −0.0315327 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.8341 | 0.839153 | 0.419577 | − | 0.907720i | \(-0.362179\pi\) | ||||
0.419577 | + | 0.907720i | \(0.362179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.5047 | −1.82038 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.52594 | −0.0583886 | −0.0291943 | − | 0.999574i | \(-0.509294\pi\) | ||||
−0.0291943 | + | 0.999574i | \(0.509294\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.4714 | −0.667546 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.2585 | 1.11628 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.6060 | −0.442155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.3213 | −0.811101 | −0.405551 | − | 0.914073i | \(-0.632920\pi\) | ||||
−0.405551 | + | 0.914073i | \(0.632920\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.7752 | −1.31910 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.01510 | 0.0763275 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.1294 | 0.685718 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5558 | −0.927460 | −0.463730 | − | 0.885977i | \(-0.653489\pi\) | ||||
−0.463730 | + | 0.885977i | \(0.653489\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.4875 | 0.772700 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.7329 | 0.818509 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.9389 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.722549 | −0.0270977 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.2899 | −0.610061 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −81.1009 | −3.03300 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.16626 | 0.0435549 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.1635 | 0.565501 | 0.282751 | − | 0.959193i | \(-0.408753\pi\) | ||||
0.282751 | + | 0.959193i | \(0.408753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 57.2448 | 2.12896 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.68285 | 0.211056 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2238 | 0.527533 | 0.263766 | − | 0.964587i | \(-0.415035\pi\) | ||||
0.263766 | + | 0.964587i | \(0.415035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4982 | −0.722155 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.2759 | −0.786916 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.49898 | −0.166174 | −0.0830869 | − | 0.996542i | \(-0.526478\pi\) | ||||
−0.0830869 | + | 0.996542i | \(0.526478\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.9176 | 0.696837 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.9630 | −1.58042 | −0.790210 | − | 0.612837i | \(-0.790028\pi\) | ||||
−0.790210 | + | 0.612837i | \(0.790028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 97.3075 | 3.57468 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.4336 | 1.37331 | 0.686654 | − | 0.726985i | \(-0.259079\pi\) | ||||
0.686654 | + | 0.726985i | \(0.259079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.18103 | −0.299730 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.6459 | −0.609041 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.7039 | −1.04742 | −0.523711 | − | 0.851896i | \(-0.675453\pi\) | ||||
−0.523711 | + | 0.851896i | \(0.675453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −58.9810 | −2.14939 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.3802 | 0.414168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8034 | 0.465348 | 0.232674 | − | 0.972555i | \(-0.425252\pi\) | ||||
0.232674 | + | 0.972555i | \(0.425252\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.6214 | −0.857402 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.2763 | −1.02501 | −0.512507 | − | 0.858683i | \(-0.671283\pi\) | ||||
−0.512507 | + | 0.858683i | \(0.671283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.7300 | −0.460254 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.5446 | 0.850148 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.7877 | 1.32660 | 0.663299 | − | 0.748354i | \(-0.269156\pi\) | ||||
0.663299 | + | 0.748354i | \(0.269156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.8410 | −0.678543 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2330 | −0.439991 | −0.219996 | − | 0.975501i | \(-0.570604\pi\) | ||||
−0.219996 | + | 0.975501i | \(0.570604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.73062 | −0.277692 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.62798 | −0.237472 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68.2654 | −2.44273 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.04450 | −0.216013 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.4752 | 1.08771 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3678 | 0.476511 | 0.238256 | − | 0.971202i | \(-0.423424\pi\) | ||||
0.238256 | + | 0.971202i | \(0.423424\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.0000 | −1.35284 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.7104 | 1.48118 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.7437 | −0.381038 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.5584 | −1.57834 | −0.789169 | − | 0.614176i | \(-0.789489\pi\) | ||||
−0.789169 | + | 0.614176i | \(0.789489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.62953 | −0.269913 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.12657 | −0.110472 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.26796 | −0.327059 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.4411 | 1.38839 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.8454 | −1.29542 | −0.647708 | − | 0.761888i | \(-0.724272\pi\) | ||||
−0.647708 | + | 0.761888i | \(0.724272\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.28194 | 0.115244 | 0.0576222 | − | 0.998338i | \(-0.481648\pi\) | ||||
0.0576222 | + | 0.998338i | \(0.481648\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.98698 | 0.209972 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.4598 | −1.34719 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 69.9795 | 2.44827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.0394 | 1.64169 | 0.820843 | − | 0.571154i | \(-0.193504\pi\) | ||||
0.820843 | + | 0.571154i | \(0.193504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.4688 | 0.504350 | 0.252175 | − | 0.967682i | \(-0.418854\pi\) | ||||
0.252175 | + | 0.967682i | \(0.418854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.2099 | −0.390278 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.2290 | −0.842526 | −0.421263 | − | 0.906939i | \(-0.638413\pi\) | ||||
−0.421263 | + | 0.906939i | \(0.638413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.50568 | 0.260683 | 0.130342 | − | 0.991469i | \(-0.458393\pi\) | ||||
0.130342 | + | 0.991469i | \(0.458393\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.09198 | 0.0725701 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.1416 | 1.04309 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.22259 | 0.284214 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.05557 | 0.0364424 | 0.0182212 | − | 0.999834i | \(-0.494200\pi\) | ||||
0.0182212 | + | 0.999834i | \(0.494200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9289 | 0.445823 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.2932 | −0.388957 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 61.7009 | 2.12258 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −56.0646 | −1.92413 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.71637 | 0.195955 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.6698 | −1.05011 | −0.525056 | − | 0.851067i | \(-0.675956\pi\) | ||||
−0.525056 | + | 0.851067i | \(0.675956\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 41.8709 | 1.43195 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.5630 | 0.702420 | 0.351210 | − | 0.936297i | \(-0.385770\pi\) | ||||
0.351210 | + | 0.936297i | \(0.385770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.90583 | 0.269743 | 0.134872 | − | 0.990863i | \(-0.456938\pi\) | ||||
0.134872 | + | 0.990863i | \(0.456938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.1040 | 0.650307 | 0.325153 | − | 0.945661i | \(-0.394584\pi\) | ||||
0.325153 | + | 0.945661i | \(0.394584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.6532 | −1.14424 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.6358 | −1.04045 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.49594 | 0.0507461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.7440 | −0.736766 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.2992 | −0.822405 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.798972 | 0.0269794 | 0.0134897 | − | 0.999909i | \(-0.495706\pi\) | ||||
0.0134897 | + | 0.999909i | \(0.495706\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 55.0185 | 1.85573 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.1673 | −1.52172 | −0.760862 | − | 0.648913i | \(-0.775224\pi\) | ||||
−0.760862 | + | 0.648913i | \(0.775224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.569815 | 0.0191758 | 0.00958790 | − | 0.999954i | \(-0.496948\pi\) | ||||
0.00958790 | + | 0.999954i | \(0.496948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.7952 | 0.732636 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.3283 | −0.581827 | −0.290913 | − | 0.956749i | \(-0.593959\pi\) | ||||
−0.290913 | + | 0.956749i | \(0.593959\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54.0956 | 1.81227 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.0947 | 0.839761 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.6935 | −1.22653 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.1506 | 0.906531 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.0376 | −1.90231 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.77166 | 0.125652 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.02347 | 0.100503 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.570307 | −0.0189367 | −0.00946836 | − | 0.999955i | \(-0.503014\pi\) | ||||
−0.00946836 | + | 0.999955i | \(0.503014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.4561 | 1.54085 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.0757389 | −0.00250934 | −0.00125467 | − | 0.999999i | \(-0.500399\pi\) | ||||
−0.00125467 | + | 0.999999i | \(0.500399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.4629 | 1.14056 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 38.6112 | 1.27645 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.78886 | 0.289918 | 0.144959 | − | 0.989438i | \(-0.453695\pi\) | ||||
0.144959 | + | 0.989438i | \(0.453695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 62.0736 | 2.04540 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 78.4646 | 2.58269 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.71279 | 0.0891961 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.146001 | −0.00479531 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.2132 | −0.761600 | −0.380800 | − | 0.924658i | \(-0.624351\pi\) | ||||
−0.380800 | + | 0.924658i | \(0.624351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.2986 | −1.58123 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.3557 | 0.861922 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.2589 | 1.24986 | 0.624931 | − | 0.780680i | \(-0.285127\pi\) | ||||
0.624931 | + | 0.780680i | \(0.285127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.8714 | 0.909549 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.504301 | 0.0164398 | 0.00821988 | − | 0.999966i | \(-0.497384\pi\) | ||||
0.00821988 | + | 0.999966i | \(0.497384\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.84933 | −0.0602223 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.1942 | 1.17615 | 0.588076 | − | 0.808805i | \(-0.299885\pi\) | ||||
0.588076 | + | 0.808805i | \(0.299885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.6526 | 0.345799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −43.5910 | −1.41353 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.7072 | 0.638378 | 0.319189 | − | 0.947691i | \(-0.396590\pi\) | ||||
0.319189 | + | 0.947691i | \(0.396590\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.6090 | 1.96126 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −82.7082 | −2.67358 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.5907 | 1.50293 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.1698 | 0.811085 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.0960 | 1.61265 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.6805 | −1.69409 | −0.847046 | − | 0.531520i | \(-0.821621\pi\) | ||||
−0.847046 | + | 0.531520i | \(0.821621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.6224 | −1.01586 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.1542 | 1.44907 | 0.724534 | − | 0.689239i | \(-0.242055\pi\) | ||||
0.724534 | + | 0.689239i | \(0.242055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.8847 | 0.412641 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5637 | 0.337962 | 0.168981 | − | 0.985619i | \(-0.445952\pi\) | ||||
0.168981 | + | 0.985619i | \(0.445952\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.47313 | 0.206882 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.6430 | 1.42534 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.1922 | −1.79225 | −0.896126 | − | 0.443799i | \(-0.853630\pi\) | ||||
−0.896126 | + | 0.443799i | \(0.853630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.8629 | 0.887787 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.5255 | 0.620876 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.796507 | −0.0253019 | −0.0126509 | − | 0.999920i | \(-0.504027\pi\) | ||||
−0.0126509 | + | 0.999920i | \(0.504027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −77.3482 | −2.45457 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.65694 | 0.274443 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.8484 | −0.850297 | −0.425148 | − | 0.905124i | \(-0.639778\pi\) | ||||
−0.425148 | + | 0.905124i | \(0.639778\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.88543 | −0.0912911 |
(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 | 8036.2.a.t.1.17 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.4 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.17 | yes | 20 | 1.1 | even | 1 | trivial |