Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(1,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.1 |
$q$-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 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56155 | 0.772337 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.56155 | 1.26515 | 0.632574 | − | 0.774500i | \(-0.281999\pi\) | ||||
0.632574 | + | 0.774500i | \(0.281999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.56155 | 1.10634 | 0.553170 | − | 0.833069i | \(-0.313418\pi\) | ||||
0.553170 | + | 0.833069i | \(0.313418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.12311 | −0.257658 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.12311 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.68466 | 1.05561 | 0.527807 | − | 0.849364i | \(-0.323014\pi\) | ||||
0.527807 | + | 0.849364i | \(0.323014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.12311 | 0.487747 | 0.243874 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243874 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.12311 | −1.39126 | −0.695630 | − | 0.718400i | \(-0.744875\pi\) | ||||
−0.695630 | + | 0.718400i | \(0.744875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.68466 | 0.537463 | 0.268731 | − | 0.963215i | \(-0.413396\pi\) | ||||
0.268731 | + | 0.963215i | \(0.413396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.12311 | −0.428992 | −0.214496 | − | 0.976725i | \(-0.568811\pi\) | ||||
−0.214496 | + | 0.976725i | \(0.568811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.56155 | −0.345400 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.36932 | −1.19962 | −0.599809 | − | 0.800143i | \(-0.704757\pi\) | ||||
−0.599809 | + | 0.800143i | \(0.704757\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.56155 | −0.565791 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.24621 | 0.763096 | 0.381548 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381548 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24621 | 0.496981 | 0.248491 | − | 0.968634i | \(-0.420065\pi\) | ||||
0.248491 | + | 0.968634i | \(0.420065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.56155 | 0.291916 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.56155 | 0.738232 | 0.369116 | − | 0.929383i | \(-0.379660\pi\) | ||||
0.369116 | + | 0.929383i | \(0.379660\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.56155 | −0.494770 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.12311 | −0.755048 | −0.377524 | − | 0.926000i | \(-0.623224\pi\) | ||||
−0.377524 | + | 0.926000i | \(0.623224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.56155 | 0.478181 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.12311 | 0.115228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.8078 | −1.50350 | −0.751750 | − | 0.659448i | \(-0.770790\pi\) | ||||
−0.751750 | + | 0.659448i | \(0.770790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.246211 | −0.0244989 | −0.0122495 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122495 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.43845 | −0.141734 | −0.0708672 | − | 0.997486i | \(-0.522577\pi\) | ||||
−0.0708672 | + | 0.997486i | \(0.522577\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3693 | −1.09911 | −0.549557 | − | 0.835456i | \(-0.685203\pi\) | ||||
−0.549557 | + | 0.835456i | \(0.685203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6847 | 1.69388 | 0.846942 | − | 0.531686i | \(-0.178441\pi\) | ||||
0.846942 | + | 0.531686i | \(0.178441\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.12311 | 0.477732 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.56155 | 0.418157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2462 | −0.909204 | −0.454602 | − | 0.890695i | \(-0.650219\pi\) | ||||
−0.454602 | + | 0.890695i | \(0.650219\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.12311 | −0.797089 | −0.398545 | − | 0.917149i | \(-0.630485\pi\) | ||||
−0.398545 | + | 0.917149i | \(0.630485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.12311 | −0.0973856 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.87689 | 0.758404 | 0.379202 | − | 0.925314i | \(-0.376199\pi\) | ||||
0.379202 | + | 0.925314i | \(0.376199\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.87689 | 0.583291 | 0.291645 | − | 0.956527i | \(-0.405797\pi\) | ||||
0.291645 | + | 0.956527i | \(0.405797\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.6847 | 0.977120 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.68466 | −0.472085 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24621 | 0.347863 | 0.173932 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173932 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.9309 | −1.78471 | −0.892354 | − | 0.451335i | \(-0.850948\pi\) | ||||
−0.892354 | + | 0.451335i | \(0.850948\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.75379 | 0.299585 | 0.149792 | − | 0.988717i | \(-0.452139\pi\) | ||||
0.149792 | + | 0.988717i | \(0.452139\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.12311 | −0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.12311 | −0.0879684 | −0.0439842 | − | 0.999032i | \(-0.514005\pi\) | ||||
−0.0439842 | + | 0.999032i | \(0.514005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.9309 | 1.69706 | 0.848531 | − | 0.529146i | \(-0.177488\pi\) | ||||
0.848531 | + | 0.529146i | \(0.177488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.56155 | 0.650923 | 0.325461 | − | 0.945555i | \(-0.394480\pi\) | ||||
0.325461 | + | 0.945555i | \(0.394480\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.0000 | 1.49487 | 0.747435 | − | 0.664335i | \(-0.231285\pi\) | ||||
0.747435 | + | 0.664335i | \(0.231285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6155 | 1.75533 | 0.877664 | − | 0.479276i | \(-0.159101\pi\) | ||||
0.877664 | + | 0.479276i | \(0.159101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.6847 | 0.854467 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.43845 | −0.682942 | −0.341471 | − | 0.939892i | \(-0.610925\pi\) | ||||
−0.341471 | + | 0.939892i | \(0.610925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.36932 | −0.386492 | −0.193246 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193246 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.12311 | 0.507500 | 0.253750 | − | 0.967270i | \(-0.418336\pi\) | ||||
0.253750 | + | 0.967270i | \(0.418336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.2462 | 1.29344 | 0.646720 | − | 0.762728i | \(-0.276140\pi\) | ||||
0.646720 | + | 0.762728i | \(0.276140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.68466 | 0.398985 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.12311 | −0.218127 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.87689 | −0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0540 | 1.58710 | 0.793551 | − | 0.608504i | \(-0.208230\pi\) | ||||
0.793551 | + | 0.608504i | \(0.208230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.12311 | 0.622191 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.8078 | 1.39968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.56155 | 0.439394 | 0.219697 | − | 0.975568i | \(-0.429493\pi\) | ||||
0.219697 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.6847 | 1.57201 | 0.786003 | − | 0.618223i | \(-0.212147\pi\) | ||||
0.786003 | + | 0.618223i | \(0.212147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1231 | 1.26369 | 0.631845 | − | 0.775095i | \(-0.282298\pi\) | ||||
0.631845 | + | 0.775095i | \(0.282298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.12311 | 0.204601 | 0.102301 | − | 0.994754i | \(-0.467380\pi\) | ||||
0.102301 | + | 0.994754i | \(0.467380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.68466 | −0.240361 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.807764 | −0.0522499 | −0.0261250 | − | 0.999659i | \(-0.508317\pi\) | ||||
−0.0261250 | + | 0.999659i | \(0.508317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2462 | 0.788848 | 0.394424 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394424 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.12311 | −0.325975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.1231 | −1.08080 | −0.540400 | − | 0.841408i | \(-0.681727\pi\) | ||||
−0.540400 | + | 0.841408i | \(0.681727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1231 | −0.825043 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.4924 | −1.40304 | −0.701519 | − | 0.712650i | \(-0.747495\pi\) | ||||
−0.701519 | + | 0.712650i | \(0.747495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.1231 | −1.30251 | −0.651253 | − | 0.758860i | \(-0.725756\pi\) | ||||
−0.651253 | + | 0.758860i | \(0.725756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.12311 | 0.191851 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.7386 | −1.75223 | −0.876113 | − | 0.482106i | \(-0.839872\pi\) | ||||
−0.876113 | + | 0.482106i | \(0.839872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.56155 | 0.154467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.2462 | 0.976140 | 0.488070 | − | 0.872804i | \(-0.337701\pi\) | ||||
0.488070 | + | 0.872804i | \(0.337701\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.5616 | −0.987979 | −0.493990 | − | 0.869468i | \(-0.664462\pi\) | ||||
−0.493990 | + | 0.869468i | \(0.664462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6847 | 1.40791 | 0.703953 | − | 0.710246i | \(-0.251416\pi\) | ||||
0.703953 | + | 0.710246i | \(0.251416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.12311 | 0.184351 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.80776 | 0.223986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.68466 | −0.565784 | −0.282892 | − | 0.959152i | \(-0.591294\pi\) | ||||
−0.282892 | + | 0.959152i | \(0.591294\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.3693 | −1.35148 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.12311 | −0.525847 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.36932 | 0.536486 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.6847 | 1.80834 | 0.904169 | − | 0.427174i | \(-0.140491\pi\) | ||||
0.904169 | + | 0.427174i | \(0.140491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.61553 | −0.545247 | −0.272623 | − | 0.962121i | \(-0.587891\pi\) | ||||
−0.272623 | + | 0.962121i | \(0.587891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.3002 | 1.76919 | 0.884596 | − | 0.466359i | \(-0.154434\pi\) | ||||
0.884596 | + | 0.466359i | \(0.154434\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4924 | 1.26330 | 0.631650 | − | 0.775254i | \(-0.282378\pi\) | ||||
0.631650 | + | 0.775254i | \(0.282378\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.5616 | 0.815290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.12311 | −0.285057 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.56155 | 0.253029 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.68466 | 0.203142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.24621 | −0.341267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.4924 | −1.87892 | −0.939461 | − | 0.342656i | \(-0.888674\pi\) | ||||
−0.939461 | + | 0.342656i | \(0.888674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.12311 | −0.0602915 | −0.0301457 | − | 0.999546i | \(-0.509597\pi\) | ||||
−0.0301457 | + | 0.999546i | \(0.509597\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.4924 | −1.20399 | −0.601996 | − | 0.798499i | \(-0.705628\pi\) | ||||
−0.601996 | + | 0.798499i | \(0.705628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.8078 | 0.788138 | 0.394069 | − | 0.919081i | \(-0.371067\pi\) | ||||
0.394069 | + | 0.919081i | \(0.371067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00000 | 0.422224 | 0.211112 | − | 0.977462i | \(-0.432292\pi\) | ||||
0.211112 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.24621 | −0.222257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.68466 | −0.192338 | −0.0961688 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961688 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.12311 | −0.162144 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3693 | 1.52069 | 0.760343 | − | 0.649522i | \(-0.225031\pi\) | ||||
0.760343 | + | 0.649522i | \(0.225031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.9309 | 1.33551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4924 | −0.847159 | −0.423579 | − | 0.905859i | \(-0.639227\pi\) | ||||
−0.423579 | + | 0.905859i | \(0.639227\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.2462 | −0.523557 | −0.261778 | − | 0.965128i | \(-0.584309\pi\) | ||||
−0.261778 | + | 0.965128i | \(0.584309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.56155 | −0.130549 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.93087 | −0.199303 | −0.0996515 | − | 0.995022i | \(-0.531773\pi\) | ||||
−0.0996515 | + | 0.995022i | \(0.531773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.3693 | −1.18184 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.56155 | −0.330148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4384 | 1.17634 | 0.588171 | − | 0.808737i | \(-0.299848\pi\) | ||||
0.588171 | + | 0.808737i | \(0.299848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.4384 | −1.37021 | −0.685105 | − | 0.728444i | \(-0.740244\pi\) | ||||
−0.685105 | + | 0.728444i | \(0.740244\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.3693 | 0.761829 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.4924 | −1.30997 | −0.654983 | − | 0.755644i | \(-0.727324\pi\) | ||||
−0.654983 | + | 0.755644i | \(0.727324\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.75379 | 0.476504 | 0.238252 | − | 0.971203i | \(-0.423426\pi\) | ||||
0.238252 | + | 0.971203i | \(0.423426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.68466 | 0.472001 | 0.236001 | − | 0.971753i | \(-0.424163\pi\) | ||||
0.236001 | + | 0.971753i | \(0.424163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.56155 | 0.221268 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.36932 | −0.453413 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.807764 | 0.0389086 | 0.0194543 | − | 0.999811i | \(-0.493807\pi\) | ||||
0.0194543 | + | 0.999811i | \(0.493807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.24621 | −0.396288 | −0.198144 | − | 0.980173i | \(-0.563491\pi\) | ||||
−0.198144 | + | 0.980173i | \(0.563491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.75379 | 0.275241 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3693 | 0.733537 | 0.366769 | − | 0.930312i | \(-0.380464\pi\) | ||||
0.366769 | + | 0.930312i | \(0.380464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.3693 | −1.30036 | −0.650178 | − | 0.759782i | \(-0.725306\pi\) | ||||
−0.650178 | + | 0.759782i | \(0.725306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.12311 | 0.337668 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.8078 | −0.887593 | −0.443797 | − | 0.896128i | \(-0.646369\pi\) | ||||
−0.443797 | + | 0.896128i | \(0.646369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.56155 | −0.213849 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.87689 | −0.415244 | −0.207622 | − | 0.978209i | \(-0.566572\pi\) | ||||
−0.207622 | + | 0.978209i | \(0.566572\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.87689 | 0.227140 | 0.113570 | − | 0.993530i | \(-0.463771\pi\) | ||||
0.113570 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4924 | 0.952364 | 0.476182 | − | 0.879347i | \(-0.342020\pi\) | ||||
0.476182 | + | 0.879347i | \(0.342020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.5616 | 1.22912 | 0.614561 | − | 0.788869i | \(-0.289333\pi\) | ||||
0.614561 | + | 0.788869i | \(0.289333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.24621 | 0.288423 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.3693 | −1.07452 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.12311 | −0.0515316 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.1231 | 0.599610 | 0.299805 | − | 0.954001i | \(-0.403078\pi\) | ||||
0.299805 | + | 0.954001i | \(0.403078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3693 | 1.24793 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.8078 | 0.672386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.12311 | −0.232150 | −0.116075 | − | 0.993240i | \(-0.537031\pi\) | ||||
−0.116075 | + | 0.993240i | \(0.537031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.17708 | 0.188509 | 0.0942545 | − | 0.995548i | \(-0.469953\pi\) | ||||
0.0942545 | + | 0.995548i | \(0.469953\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.9309 | 1.16787 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.17708 | 0.186992 | 0.0934959 | − | 0.995620i | \(-0.470196\pi\) | ||||
0.0934959 | + | 0.995620i | \(0.470196\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0691 | 0.448960 | 0.224480 | − | 0.974479i | \(-0.427932\pi\) | ||||
0.224480 | + | 0.974479i | \(0.427932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.246211 | 0.0109563 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2462 | 1.25199 | 0.625996 | − | 0.779827i | \(-0.284693\pi\) | ||||
0.625996 | + | 0.779827i | \(0.284693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.24621 | 0.187841 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.43845 | 0.0633856 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.43845 | 0.415102 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.50758 | −0.328283 | −0.164142 | − | 0.986437i | \(-0.552485\pi\) | ||||
−0.164142 | + | 0.986437i | \(0.552485\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.2462 | 0.617072 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3693 | 0.491538 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.56155 | 0.110334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.1922 | −0.739152 | −0.369576 | − | 0.929201i | \(-0.620497\pi\) | ||||
−0.369576 | + | 0.929201i | \(0.620497\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.6847 | −0.757528 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2462 | −0.609124 | −0.304562 | − | 0.952493i | \(-0.598510\pi\) | ||||
−0.304562 | + | 0.952493i | \(0.598510\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.38447 | −0.271988 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.56155 | 0.279026 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.87689 | 0.206641 | 0.103320 | − | 0.994648i | \(-0.467053\pi\) | ||||
0.103320 | + | 0.994648i | \(0.467053\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.6155 | −1.76015 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.0000 | −1.18006 | −0.590030 | − | 0.807382i | \(-0.700884\pi\) | ||||
−0.590030 | + | 0.807382i | \(0.700884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | −0.588984 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.9848 | −1.46664 | −0.733320 | − | 0.679883i | \(-0.762031\pi\) | ||||
−0.733320 | + | 0.679883i | \(0.762031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.50758 | −0.314182 | −0.157091 | − | 0.987584i | \(-0.550212\pi\) | ||||
−0.157091 | + | 0.987584i | \(0.550212\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.12311 | −0.213648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.0540 | 0.543444 | 0.271722 | − | 0.962376i | \(-0.412407\pi\) | ||||
0.271722 | + | 0.962376i | \(0.412407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00000 | 0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.75379 | −0.402582 | −0.201291 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.4384 | 0.962502 | 0.481251 | − | 0.876583i | \(-0.340183\pi\) | ||||
0.481251 | + | 0.876583i | \(0.340183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.56155 | −0.187005 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.80776 | 0.359875 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.4924 | −1.08065 | −0.540324 | − | 0.841457i | \(-0.681698\pi\) | ||||
−0.540324 | + | 0.841457i | \(0.681698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.43845 | 0.180449 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.94602 | 0.200753 | 0.100376 | − | 0.994950i | \(-0.467995\pi\) | ||||
0.100376 | + | 0.994950i | \(0.467995\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.8078 | 0.679969 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.73863 | −0.352950 | −0.176475 | − | 0.984305i | \(-0.556469\pi\) | ||||
−0.176475 | + | 0.984305i | \(0.556469\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.7538 | −0.634224 | −0.317112 | − | 0.948388i | \(-0.602713\pi\) | ||||
−0.317112 | + | 0.948388i | \(0.602713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.1080 | 1.69246 | 0.846231 | − | 0.532817i | \(-0.178866\pi\) | ||||
0.846231 | + | 0.532817i | \(0.178866\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.12311 | −0.285381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.3693 | 1.09129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.80776 | −0.350632 | −0.175316 | − | 0.984512i | \(-0.556095\pi\) | ||||
−0.175316 | + | 0.984512i | \(0.556095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.2462 | 0.406608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.56155 | 0.180735 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.56155 | 0.101018 | 0.0505089 | − | 0.998724i | \(-0.483916\pi\) | ||||
0.0505089 | + | 0.998724i | \(0.483916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.50758 | 0.137897 | 0.0689486 | − | 0.997620i | \(-0.478036\pi\) | ||||
0.0689486 | + | 0.997620i | \(0.478036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2462 | −0.402199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −49.2311 | −1.92656 | −0.963280 | − | 0.268499i | \(-0.913473\pi\) | ||||
−0.963280 | + | 0.268499i | \(0.913473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.12311 | 0.356469 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.1771 | −1.40926 | −0.704629 | − | 0.709575i | \(-0.748887\pi\) | ||||
−0.704629 | + | 0.709575i | \(0.748887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.12311 | 0.121475 | 0.0607374 | − | 0.998154i | \(-0.480655\pi\) | ||||
0.0607374 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.12311 | 0.0435522 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.1231 | −1.12765 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8617 | −0.996897 | −0.498448 | − | 0.866919i | \(-0.666097\pi\) | ||||
−0.498448 | + | 0.866919i | \(0.666097\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.9309 | 0.919738 | 0.459869 | − | 0.887987i | \(-0.347896\pi\) | ||||
0.459869 | + | 0.887987i | \(0.347896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.8078 | −0.568270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.7386 | 1.63535 | 0.817674 | − | 0.575681i | \(-0.195263\pi\) | ||||
0.817674 | + | 0.575681i | \(0.195263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.87689 | −0.339169 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.2462 | −0.542737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.49242 | −0.323067 | −0.161533 | − | 0.986867i | \(-0.551644\pi\) | ||||
−0.161533 | + | 0.986867i | \(0.551644\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.87689 | −0.260855 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.2462 | 0.539614 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0691303 | −0.00261102 | −0.00130551 | − | 0.999999i | \(-0.500416\pi\) | ||||
−0.00130551 | + | 0.999999i | \(0.500416\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.73863 | −0.254152 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.246211 | −0.00925973 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.1771 | −0.682655 | −0.341327 | − | 0.939945i | \(-0.610876\pi\) | ||||
−0.341327 | + | 0.939945i | \(0.610876\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.6847 | −0.436981 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.6155 | 1.85035 | 0.925173 | − | 0.379544i | \(-0.123919\pi\) | ||||
0.925173 | + | 0.379544i | \(0.123919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.43845 | −0.0535706 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.68466 | 0.211123 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5076 | −0.723496 | −0.361748 | − | 0.932276i | \(-0.617820\pi\) | ||||
−0.361748 | + | 0.932276i | \(0.617820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.6155 | −1.53921 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.68466 | −0.209968 | −0.104984 | − | 0.994474i | \(-0.533479\pi\) | ||||
−0.104984 | + | 0.994474i | \(0.533479\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.06913 | −0.223257 | −0.111628 | − | 0.993750i | \(-0.535607\pi\) | ||||
−0.111628 | + | 0.993750i | \(0.535607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.9848 | 1.21010 | 0.605048 | − | 0.796189i | \(-0.293154\pi\) | ||||
0.605048 | + | 0.796189i | \(0.293154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.24621 | −0.155569 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.3693 | −0.415426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.9309 | −1.67604 | −0.838021 | − | 0.545639i | \(-0.816287\pi\) | ||||
−0.838021 | + | 0.545639i | \(0.816287\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.9309 | 0.798146 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6307 | 0.531761 | 0.265881 | − | 0.964006i | \(-0.414337\pi\) | ||||
0.265881 | + | 0.964006i | \(0.414337\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.7538 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6847 | 0.640228 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.2462 | −0.658833 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.50758 | −0.342852 | −0.171426 | − | 0.985197i | \(-0.554837\pi\) | ||||
−0.171426 | + | 0.985197i | \(0.554837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.06913 | −0.290226 | −0.145113 | − | 0.989415i | \(-0.546355\pi\) | ||||
−0.145113 | + | 0.989415i | \(0.546355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.50758 | −0.125672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.4924 | 0.733277 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.75379 | −0.133978 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.82292 | 0.136272 | 0.0681362 | − | 0.997676i | \(-0.478295\pi\) | ||||
0.0681362 | + | 0.997676i | \(0.478295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0000 | 0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.7386 | −1.51769 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.0540 | 0.462396 | 0.231198 | − | 0.972907i | \(-0.425736\pi\) | ||||
0.231198 | + | 0.972907i | \(0.425736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8078 | 0.594616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.8769 | 0.383837 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.12311 | 0.180566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.5464 | 1.88259 | 0.941296 | − | 0.337584i | \(-0.109610\pi\) | ||||
0.941296 | + | 0.337584i | \(0.109610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.6155 | 0.759024 | 0.379512 | − | 0.925187i | \(-0.376092\pi\) | ||||
0.379512 | + | 0.925187i | \(0.376092\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.12311 | 0.0393407 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2462 | 0.358470 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.4233 | −1.41078 | −0.705391 | − | 0.708818i | \(-0.749229\pi\) | ||||
−0.705391 | + | 0.708818i | \(0.749229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.50758 | 0.122266 | 0.0611332 | − | 0.998130i | \(-0.480529\pi\) | ||||
0.0611332 | + | 0.998130i | \(0.480529\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.3693 | 0.673537 | 0.336769 | − | 0.941587i | \(-0.390666\pi\) | ||||
0.336769 | + | 0.941587i | \(0.390666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.1231 | 1.49773 | 0.748864 | − | 0.662724i | \(-0.230600\pi\) | ||||
0.748864 | + | 0.662724i | \(0.230600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.56155 | 0.158048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.9309 | −0.758949 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.1231 | −1.28163 | −0.640816 | − | 0.767695i | \(-0.721404\pi\) | ||||
−0.640816 | + | 0.767695i | \(0.721404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.80776 | −0.268595 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.43845 | −0.152507 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.7386 | −1.05371 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −56.7386 | −1.94269 | −0.971347 | − | 0.237666i | \(-0.923618\pi\) | ||||
−0.971347 | + | 0.237666i | \(0.923618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.2462 | 1.10151 | 0.550755 | − | 0.834667i | \(-0.314340\pi\) | ||||
0.550755 | + | 0.834667i | \(0.314340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.4924 | −0.562714 | −0.281357 | − | 0.959603i | \(-0.590785\pi\) | ||||
−0.281357 | + | 0.959603i | \(0.590785\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.2462 | −1.43808 | −0.719039 | − | 0.694970i | \(-0.755418\pi\) | ||||
−0.719039 | + | 0.694970i | \(0.755418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.56155 | −0.291102 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.8078 | 0.570164 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.4924 | 0.965429 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.7538 | −0.802108 | −0.401054 | − | 0.916054i | \(-0.631356\pi\) | ||||
−0.401054 | + | 0.916054i | \(0.631356\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.8617 | −1.54512 | −0.772561 | − | 0.634941i | \(-0.781024\pi\) | ||||
−0.772561 | + | 0.634941i | \(0.781024\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4924 | −0.824236 | −0.412118 | − | 0.911131i | \(-0.635211\pi\) | ||||
−0.412118 | + | 0.911131i | \(0.635211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.4924 | −0.419454 | −0.209727 | − | 0.977760i | \(-0.567258\pi\) | ||||
−0.209727 | + | 0.977760i | \(0.567258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2462 | −0.343647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.13826 | −0.138482 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2462 | −0.474610 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.6155 | −0.785007 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.1080 | −1.66381 | −0.831904 | − | 0.554920i | \(-0.812749\pi\) | ||||
−0.831904 | + | 0.554920i | \(0.812749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.49242 | 0.148841 | 0.0744203 | − | 0.997227i | \(-0.476289\pi\) | ||||
0.0744203 | + | 0.997227i | \(0.476289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.2462 | 0.339100 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.12311 | −0.301271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.3002 | 0.438733 | 0.219366 | − | 0.975643i | \(-0.429601\pi\) | ||||
0.219366 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.4924 | 1.20116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.1080 | 1.70961 | 0.854803 | − | 0.518952i | \(-0.173678\pi\) | ||||
0.854803 | + | 0.518952i | \(0.173678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12311 | −0.0368083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.6847 | −0.382129 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6695 | 0.740580 | 0.370290 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370290 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8617 | 0.451880 | 0.225940 | − | 0.974141i | \(-0.427455\pi\) | ||||
0.225940 | + | 0.974141i | \(0.427455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.3693 | 0.628755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.8769 | 0.805842 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.43845 | 0.305421 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.87689 | 0.286650 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.36932 | 0.172844 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.8769 | 0.864303 | 0.432151 | − | 0.901801i | \(-0.357755\pi\) | ||||
0.432151 | + | 0.901801i | \(0.357755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4773 | −1.58780 | −0.793901 | − | 0.608048i | \(-0.791953\pi\) | ||||
−0.793901 | + | 0.608048i | \(0.791953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.87689 | 0.220463 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.2311 | 1.57504 | 0.787521 | − | 0.616288i | \(-0.211364\pi\) | ||||
0.787521 | + | 0.616288i | \(0.211364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.2462 | −0.583151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4233 | −0.332451 | −0.166226 | − | 0.986088i | \(-0.553158\pi\) | ||||
−0.166226 | + | 0.986088i | \(0.553158\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.12311 | −0.226961 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.7386 | 1.48620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4924 | 0.650963 | 0.325482 | − | 0.945548i | \(-0.394474\pi\) | ||||
0.325482 | + | 0.945548i | \(0.394474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.2462 | −0.578444 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.68466 | 0.306716 | 0.153358 | − | 0.988171i | \(-0.450991\pi\) | ||||
0.153358 | + | 0.988171i | \(0.450991\pi\) | |||||||
\(998\) | 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 | 5040.2.a.bt.1.2 | 2 | ||
3.2 | odd | 2 | 560.2.a.i.1.2 | 2 | |||
4.3 | odd | 2 | 315.2.a.e.1.1 | 2 | |||
12.11 | even | 2 | 35.2.a.b.1.2 | ✓ | 2 | ||
15.2 | even | 4 | 2800.2.g.t.449.1 | 4 | |||
15.8 | even | 4 | 2800.2.g.t.449.4 | 4 | |||
15.14 | odd | 2 | 2800.2.a.bi.1.1 | 2 | |||
20.3 | even | 4 | 1575.2.d.e.1324.3 | 4 | |||
20.7 | even | 4 | 1575.2.d.e.1324.2 | 4 | |||
20.19 | odd | 2 | 1575.2.a.p.1.2 | 2 | |||
21.20 | even | 2 | 3920.2.a.bs.1.1 | 2 | |||
24.5 | odd | 2 | 2240.2.a.bd.1.1 | 2 | |||
24.11 | even | 2 | 2240.2.a.bh.1.2 | 2 | |||
28.27 | even | 2 | 2205.2.a.x.1.1 | 2 | |||
60.23 | odd | 4 | 175.2.b.b.99.2 | 4 | |||
60.47 | odd | 4 | 175.2.b.b.99.3 | 4 | |||
60.59 | even | 2 | 175.2.a.f.1.1 | 2 | |||
84.11 | even | 6 | 245.2.e.i.226.1 | 4 | |||
84.23 | even | 6 | 245.2.e.i.116.1 | 4 | |||
84.47 | odd | 6 | 245.2.e.h.116.1 | 4 | |||
84.59 | odd | 6 | 245.2.e.h.226.1 | 4 | |||
84.83 | odd | 2 | 245.2.a.d.1.2 | 2 | |||
132.131 | odd | 2 | 4235.2.a.m.1.1 | 2 | |||
156.155 | even | 2 | 5915.2.a.l.1.1 | 2 | |||
420.83 | even | 4 | 1225.2.b.f.99.2 | 4 | |||
420.167 | even | 4 | 1225.2.b.f.99.3 | 4 | |||
420.419 | odd | 2 | 1225.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
175.2.a.f.1.1 | 2 | 60.59 | even | 2 | |||
175.2.b.b.99.2 | 4 | 60.23 | odd | 4 | |||
175.2.b.b.99.3 | 4 | 60.47 | odd | 4 | |||
245.2.a.d.1.2 | 2 | 84.83 | odd | 2 | |||
245.2.e.h.116.1 | 4 | 84.47 | odd | 6 | |||
245.2.e.h.226.1 | 4 | 84.59 | odd | 6 | |||
245.2.e.i.116.1 | 4 | 84.23 | even | 6 | |||
245.2.e.i.226.1 | 4 | 84.11 | even | 6 | |||
315.2.a.e.1.1 | 2 | 4.3 | odd | 2 | |||
560.2.a.i.1.2 | 2 | 3.2 | odd | 2 | |||
1225.2.a.s.1.1 | 2 | 420.419 | odd | 2 | |||
1225.2.b.f.99.2 | 4 | 420.83 | even | 4 | |||
1225.2.b.f.99.3 | 4 | 420.167 | even | 4 | |||
1575.2.a.p.1.2 | 2 | 20.19 | odd | 2 | |||
1575.2.d.e.1324.2 | 4 | 20.7 | even | 4 | |||
1575.2.d.e.1324.3 | 4 | 20.3 | even | 4 | |||
2205.2.a.x.1.1 | 2 | 28.27 | even | 2 | |||
2240.2.a.bd.1.1 | 2 | 24.5 | odd | 2 | |||
2240.2.a.bh.1.2 | 2 | 24.11 | even | 2 | |||
2800.2.a.bi.1.1 | 2 | 15.14 | odd | 2 | |||
2800.2.g.t.449.1 | 4 | 15.2 | even | 4 | |||
2800.2.g.t.449.4 | 4 | 15.8 | even | 4 | |||
3920.2.a.bs.1.1 | 2 | 21.20 | even | 2 | |||
4235.2.a.m.1.1 | 2 | 132.131 | odd | 2 | |||
5040.2.a.bt.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5915.2.a.l.1.1 | 2 | 156.155 | even | 2 |