Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3100,3,Mod(1301,3100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3100.1301");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3100.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(84.4688819517\) |
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: | \( x^{20} + 114 x^{18} + 5280 x^{16} + 128422 x^{14} + 1776819 x^{12} + 14249420 x^{10} + 65297060 x^{8} + \cdots + 20793600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 620) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.11 | ||
Root | \(0.693074i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3100.1301 |
Dual form | 3100.3.d.e.1301.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).
\(n\) | \(1551\) | \(1801\) | \(2977\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.693074i | 0.231025i | 0.993306 | + | 0.115512i | \(0.0368510\pi\) | ||||
−0.993306 | + | 0.115512i | \(0.963149\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.01983 | 1.28855 | 0.644274 | − | 0.764795i | \(-0.277160\pi\) | ||||
0.644274 | + | 0.764795i | \(0.277160\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.51965 | 0.946628 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.32398i | − | 0.665817i | −0.942959 | − | 0.332908i | \(-0.891970\pi\) | ||
0.942959 | − | 0.332908i | \(-0.108030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.20530i | 0.0927156i | 0.998925 | + | 0.0463578i | \(0.0147614\pi\) | ||||
−0.998925 | + | 0.0463578i | \(0.985239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.61928i | − | 0.154075i | −0.997028 | − | 0.0770377i | \(-0.975454\pi\) | ||
0.997028 | − | 0.0770377i | \(-0.0245462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −15.5460 | −0.818211 | −0.409105 | − | 0.912487i | \(-0.634159\pi\) | ||||
−0.409105 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.25141i | 0.297686i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 39.1974i | 1.70424i | 0.523350 | + | 0.852118i | \(0.324682\pi\) | ||||
−0.523350 | + | 0.852118i | \(0.675318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.1424i | 0.449719i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.8559i | 1.30538i | 0.757627 | + | 0.652688i | \(0.226359\pi\) | ||||
−0.757627 | + | 0.652688i | \(0.773641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.3467 | − | 28.8488i | 0.366024 | − | 0.930605i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.07606 | 0.153820 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 72.7141i | 1.96525i | 0.185613 | + | 0.982623i | \(0.440573\pi\) | ||||
−0.185613 | + | 0.982623i | \(0.559427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.835364 | −0.0214196 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −54.6523 | −1.33298 | −0.666491 | − | 0.745513i | \(-0.732205\pi\) | ||||
−0.666491 | + | 0.745513i | \(0.732205\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 53.8375i | 1.25204i | 0.779809 | + | 0.626018i | \(0.215316\pi\) | ||||
−0.779809 | + | 0.626018i | \(0.784684\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.08458 | −0.108183 | −0.0540913 | − | 0.998536i | \(-0.517226\pi\) | ||||
−0.0540913 | + | 0.998536i | \(0.517226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 32.3573 | 0.660354 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.81536 | 0.0355952 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 34.0833i | − | 0.643081i | −0.946896 | − | 0.321540i | \(-0.895799\pi\) | ||
0.946896 | − | 0.321540i | \(-0.104201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 10.7745i | − | 0.189027i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 23.0023 | 0.389870 | 0.194935 | − | 0.980816i | \(-0.437550\pi\) | ||||
0.194935 | + | 0.980816i | \(0.437550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.49235i | 0.0244647i | 0.999925 | + | 0.0122323i | \(0.00389377\pi\) | ||||
−0.999925 | + | 0.0122323i | \(0.996106\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 76.8458 | 1.21977 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 96.1191 | 1.43461 | 0.717306 | − | 0.696758i | \(-0.245375\pi\) | ||||
0.717306 | + | 0.696758i | \(0.245375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −27.1667 | −0.393721 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.02664 | 0.0707978 | 0.0353989 | − | 0.999373i | \(-0.488730\pi\) | ||||
0.0353989 | + | 0.999373i | \(0.488730\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 76.6699i | 1.05027i | 0.851018 | + | 0.525136i | \(0.175986\pi\) | ||||
−0.851018 | + | 0.525136i | \(0.824014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 66.0611i | − | 0.857936i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 50.4131i | 0.638141i | 0.947731 | + | 0.319070i | \(0.103371\pi\) | ||||
−0.947731 | + | 0.319070i | \(0.896629\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 68.2612 | 0.842731 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 113.505i | 1.36753i | 0.729703 | + | 0.683764i | \(0.239658\pi\) | ||||
−0.729703 | + | 0.683764i | \(0.760342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −26.2369 | −0.301574 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 145.171i | − | 1.63114i | −0.578661 | − | 0.815568i | \(-0.696424\pi\) | ||
0.578661 | − | 0.815568i | \(-0.303576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8716i | 0.119468i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.9943 | + | 7.86413i | 0.214993 | + | 0.0845606i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.3814 | 0.179190 | 0.0895949 | − | 0.995978i | \(-0.471443\pi\) | ||||
0.0895949 | + | 0.995978i | \(0.471443\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 62.3978i | − | 0.630280i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 123.598 | 1.22374 | 0.611869 | − | 0.790959i | \(-0.290418\pi\) | ||||
0.611869 | + | 0.790959i | \(0.290418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −34.2866 | −0.332879 | −0.166440 | − | 0.986052i | \(-0.553227\pi\) | ||||
−0.166440 | + | 0.986052i | \(0.553227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −122.332 | −1.14329 | −0.571646 | − | 0.820501i | \(-0.693695\pi\) | ||||
−0.571646 | + | 0.820501i | \(0.693695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −193.649 | −1.77659 | −0.888297 | − | 0.459269i | \(-0.848111\pi\) | ||||
−0.888297 | + | 0.459269i | \(0.848111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −50.3963 | −0.454020 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 189.325 | 1.67544 | 0.837721 | − | 0.546098i | \(-0.183888\pi\) | ||||
0.837721 | + | 0.546098i | \(0.183888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.2688i | 0.0877672i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 23.6255i | − | 0.198533i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 67.3593 | 0.556688 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 37.8781i | − | 0.307952i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 190.990i | − | 1.50386i | −0.659244 | − | 0.751929i | \(-0.729124\pi\) | ||
0.659244 | − | 0.751929i | \(-0.270876\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −37.3134 | −0.289251 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 61.2275 | 0.467385 | 0.233693 | − | 0.972311i | \(-0.424919\pi\) | ||||
0.233693 | + | 0.972311i | \(0.424919\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −140.222 | −1.05430 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 66.3248i | − | 0.484123i | −0.970261 | − | 0.242061i | \(-0.922176\pi\) | ||
0.970261 | − | 0.242061i | \(-0.0778235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 81.0932i | − | 0.583404i | −0.956509 | − | 0.291702i | \(-0.905778\pi\) | ||
0.956509 | − | 0.291702i | \(-0.0942216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 3.52399i | − | 0.0249929i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.82762 | 0.0617316 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.4260i | 0.152558i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 115.602 | 0.775850 | 0.387925 | − | 0.921691i | \(-0.373192\pi\) | ||||
0.387925 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 203.042i | 1.34465i | 0.740258 | + | 0.672323i | \(0.234703\pi\) | ||||
−0.740258 | + | 0.672323i | \(0.765297\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 22.3154i | − | 0.145852i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −144.573 | −0.920847 | −0.460423 | − | 0.887699i | \(-0.652302\pi\) | ||||
−0.460423 | + | 0.887699i | \(0.652302\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.6222 | 0.148567 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 353.554i | 2.19599i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 49.2890 | 0.302386 | 0.151193 | − | 0.988504i | \(-0.451688\pi\) | ||||
0.151193 | + | 0.988504i | \(0.451688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 225.149i | − | 1.34820i | −0.738642 | − | 0.674098i | \(-0.764532\pi\) | ||
0.738642 | − | 0.674098i | \(-0.235468\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 167.547 | 0.991404 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −132.446 | −0.774541 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −83.1425 | −0.480592 | −0.240296 | − | 0.970700i | \(-0.577245\pi\) | ||||
−0.240296 | + | 0.970700i | \(0.577245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.9423i | 0.0900696i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 221.904i | 1.23969i | 0.784725 | + | 0.619844i | \(0.212804\pi\) | ||||
−0.784725 | + | 0.619844i | \(0.787196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 310.184i | 1.71372i | 0.515547 | + | 0.856862i | \(0.327589\pi\) | ||||
−0.515547 | + | 0.856862i | \(0.672411\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.03431 | −0.00565195 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.1836 | −0.102586 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 109.523i | 0.579484i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −102.675 | −0.537564 | −0.268782 | − | 0.963201i | \(-0.586621\pi\) | ||||
−0.268782 | + | 0.963201i | \(0.586621\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −231.065 | −1.19723 | −0.598613 | − | 0.801039i | \(-0.704281\pi\) | ||||
−0.598613 | + | 0.801039i | \(0.704281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 67.7244i | − | 0.343778i | −0.985116 | − | 0.171889i | \(-0.945013\pi\) | ||
0.985116 | − | 0.171889i | \(-0.0549871\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 67.6929i | − | 0.340165i | −0.985430 | − | 0.170083i | \(-0.945597\pi\) | ||
0.985430 | − | 0.170083i | \(-0.0544034\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 66.6176i | 0.331431i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 341.454i | 1.68204i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 333.948i | 1.61328i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 113.859i | 0.544778i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 415.648 | 1.96990 | 0.984949 | − | 0.172847i | \(-0.0552965\pi\) | ||||
0.984949 | + | 0.172847i | \(0.0552965\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.48384i | 0.0163560i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 102.346 | − | 260.211i | 0.471639 | − | 1.19913i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −53.1379 | −0.242639 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.15703 | 0.0142852 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.69524i | − | 0.0389921i | −0.999810 | − | 0.0194961i | \(-0.993794\pi\) | ||
0.999810 | − | 0.0194961i | \(-0.00620618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 352.159 | 1.55136 | 0.775680 | − | 0.631126i | \(-0.217407\pi\) | ||||
0.775680 | + | 0.631126i | \(0.217407\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 74.0055i | 0.323168i | 0.986859 | + | 0.161584i | \(0.0516603\pi\) | ||||
−0.986859 | + | 0.161584i | \(0.948340\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 45.7852 | 0.198204 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 268.408 | 1.15197 | 0.575983 | − | 0.817461i | \(-0.304619\pi\) | ||||
0.575983 | + | 0.817461i | \(0.304619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −34.9400 | −0.147426 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 157.032i | − | 0.657036i | −0.944498 | − | 0.328518i | \(-0.893451\pi\) | ||
0.944498 | − | 0.328518i | \(-0.106549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6119i | 0.0440327i | 0.999758 | + | 0.0220164i | \(0.00700859\pi\) | ||||
−0.999758 | + | 0.0220164i | \(0.992991\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 156.592i | 0.644411i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.7377i | − | 0.0758609i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −78.6673 | −0.315933 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 404.851i | − | 1.61295i | −0.591265 | − | 0.806477i | \(-0.701371\pi\) | ||
0.591265 | − | 0.806477i | \(-0.298629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 287.081 | 1.13471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −271.328 | −1.05575 | −0.527875 | − | 0.849322i | \(-0.677011\pi\) | ||||
−0.527875 | + | 0.849322i | \(0.677011\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 655.869i | 2.53231i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 322.519i | 1.23570i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 120.787i | 0.459267i | 0.973277 | + | 0.229633i | \(0.0737527\pi\) | ||||
−0.973277 | + | 0.229633i | \(0.926247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 100.614 | 0.376833 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 280.569i | 1.04301i | 0.853249 | + | 0.521503i | \(0.174629\pi\) | ||||
−0.853249 | + | 0.521503i | \(0.825371\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 244.579i | 0.902504i | 0.892397 | + | 0.451252i | \(0.149022\pi\) | ||||
−0.892397 | + | 0.451252i | \(0.850978\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.53485 | −0.0276002 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 98.5407i | − | 0.355743i | −0.984054 | − | 0.177871i | \(-0.943079\pi\) | ||
0.984054 | − | 0.177871i | \(-0.0569211\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 96.6703 | − | 245.781i | 0.346488 | − | 0.880937i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 206.677 | 0.735504 | 0.367752 | − | 0.929924i | \(-0.380128\pi\) | ||||
0.367752 | + | 0.929924i | \(0.380128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 389.808 | 1.37741 | 0.688706 | − | 0.725041i | \(-0.258179\pi\) | ||||
0.688706 | + | 0.725041i | \(0.258179\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −492.954 | −1.71761 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 282.139 | 0.976261 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0466i | 0.0413973i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −103.473 | −0.353150 | −0.176575 | − | 0.984287i | \(-0.556502\pi\) | ||||
−0.176575 | + | 0.984287i | \(0.556502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 88.9308 | 0.299430 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −47.2448 | −0.158009 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 485.605i | 1.61331i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 85.6622i | 0.282714i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −230.191 | −0.749807 | −0.374903 | − | 0.927064i | \(-0.622324\pi\) | ||||
−0.374903 | + | 0.927064i | \(0.622324\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 23.7631i | − | 0.0769033i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −209.481 | −0.673572 | −0.336786 | − | 0.941581i | \(-0.609340\pi\) | ||||
−0.336786 | + | 0.941581i | \(0.609340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 296.621i | 0.947671i | 0.880613 | + | 0.473835i | \(0.157131\pi\) | ||||
−0.880613 | + | 0.473835i | \(0.842869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −59.4210 | −0.187448 | −0.0937239 | − | 0.995598i | \(-0.529877\pi\) | ||||
−0.0937239 | + | 0.995598i | \(0.529877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 277.256 | 0.869141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 84.7852i | − | 0.264128i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.7194i | 0.126066i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 134.213i | − | 0.410437i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −45.8621 | −0.139398 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 286.896i | 0.866757i | 0.901212 | + | 0.433378i | \(0.142679\pi\) | ||||
−0.901212 | + | 0.433378i | \(0.857321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 619.499i | 1.86036i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 496.446i | − | 1.47313i | −0.676364 | − | 0.736567i | \(-0.736445\pi\) | ||
0.676364 | − | 0.736567i | \(-0.263555\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 131.216i | 0.387068i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −211.288 | − | 83.1034i | −0.619613 | − | 0.243705i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −150.114 | −0.437650 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.3455i | 0.0903329i | 0.998979 | + | 0.0451664i | \(0.0143818\pi\) | ||||
−0.998979 | + | 0.0451664i | \(0.985618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 364.479 | 1.04435 | 0.522176 | − | 0.852838i | \(-0.325120\pi\) | ||||
0.522176 | + | 0.852838i | \(0.325120\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.6353 | −0.0416960 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 537.862i | 1.52369i | 0.647760 | + | 0.761845i | \(0.275706\pi\) | ||||
−0.647760 | + | 0.761845i | \(0.724294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.3742 | 0.0458661 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −530.782 | −1.47850 | −0.739251 | − | 0.673430i | \(-0.764820\pi\) | ||||
−0.739251 | + | 0.673430i | \(0.764820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −119.322 | −0.330531 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 46.6850i | 0.128609i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 515.419i | 1.40441i | 0.711974 | + | 0.702206i | \(0.247801\pi\) | ||||
−0.711974 | + | 0.702206i | \(0.752199\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −465.618 | −1.26184 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 307.425i | − | 0.828640i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 434.313 | 1.16438 | 0.582189 | − | 0.813053i | \(-0.302196\pi\) | ||||
0.582189 | + | 0.813053i | \(0.302196\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −45.6278 | −0.121029 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 485.580 | 1.28121 | 0.640607 | − | 0.767869i | \(-0.278683\pi\) | ||||
0.640607 | + | 0.767869i | \(0.278683\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 132.370 | 0.347428 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 465.117i | 1.21440i | 0.794548 | + | 0.607202i | \(0.207708\pi\) | ||||
−0.794548 | + | 0.607202i | \(0.792292\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 458.677i | 1.18521i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 400.345i | − | 1.02917i | −0.857441 | − | 0.514583i | \(-0.827947\pi\) | ||
0.857441 | − | 0.514583i | \(-0.172053\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 102.669 | 0.262581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 42.4352i | 0.107978i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.7892 | 0.0901490 | 0.0450745 | − | 0.998984i | \(-0.485647\pi\) | ||||
0.0450745 | + | 0.998984i | \(0.485647\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 97.1845i | − | 0.243570i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 369.186i | − | 0.920664i | −0.887747 | − | 0.460332i | \(-0.847730\pi\) | ||
0.887747 | − | 0.460332i | \(-0.152270\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.7715 | + | 13.6763i | 0.0862817 | + | 0.0339362i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 532.557 | 1.30849 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 687.009i | − | 1.67973i | −0.542796 | − | 0.839864i | \(-0.682634\pi\) | ||
0.542796 | − | 0.839864i | \(-0.317366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 45.9680 | 0.111844 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 207.477 | 0.502366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 56.2036 | 0.134781 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −123.910 | −0.295729 | −0.147864 | − | 0.989008i | \(-0.547240\pi\) | ||||
−0.147864 | + | 0.989008i | \(0.547240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 69.4701 | 0.165012 | 0.0825060 | − | 0.996591i | \(-0.473708\pi\) | ||||
0.0825060 | + | 0.996591i | \(0.473708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −43.3189 | −0.102409 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4607i | 0.0315239i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.11820i | 0.0142615i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −92.6617 | −0.214992 | −0.107496 | − | 0.994205i | \(-0.534283\pi\) | ||||
−0.107496 | + | 0.994205i | \(0.534283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 226.729i | − | 0.523622i | −0.965119 | − | 0.261811i | \(-0.915680\pi\) | ||
0.965119 | − | 0.261811i | \(-0.0843198\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 609.363i | − | 1.39442i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −699.079 | −1.59244 | −0.796218 | − | 0.605010i | \(-0.793169\pi\) | ||||
−0.796218 | + | 0.605010i | \(0.793169\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 275.673 | 0.625109 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 165.572 | 0.373751 | 0.186876 | − | 0.982384i | \(-0.440164\pi\) | ||||
0.186876 | + | 0.982384i | \(0.440164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 80.1205i | 0.179240i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 199.826i | − | 0.445046i | −0.974927 | − | 0.222523i | \(-0.928571\pi\) | ||
0.974927 | − | 0.222523i | \(-0.0714293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 400.272i | 0.887522i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −140.723 | −0.310646 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 91.6074i | 0.200454i | 0.994965 | + | 0.100227i | \(0.0319569\pi\) | ||||
−0.994965 | + | 0.100227i | \(0.968043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.8044 | 0.0692906 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 510.100i | − | 1.10651i | −0.833013 | − | 0.553254i | \(-0.813386\pi\) | ||
0.833013 | − | 0.553254i | \(-0.186614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.1149i | − | 0.0758422i | −0.999281 | − | 0.0379211i | \(-0.987926\pi\) | ||
0.999281 | − | 0.0379211i | \(-0.0120736\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −584.719 | −1.25207 | −0.626037 | − | 0.779793i | \(-0.715324\pi\) | ||||
−0.626037 | + | 0.779793i | \(0.715324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 866.978 | 1.84857 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 100.200i | − | 0.212738i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 394.305 | 0.833626 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 290.377i | − | 0.608758i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −354.617 | −0.740327 | −0.370163 | − | 0.928967i | \(-0.620698\pi\) | ||||
−0.370163 | + | 0.928967i | \(0.620698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −87.6426 | −0.182209 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −245.039 | −0.507327 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 100.571i | 0.206511i | 0.994655 | + | 0.103255i | \(0.0329259\pi\) | ||||
−0.994655 | + | 0.103255i | \(0.967074\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.1609i | 0.0698587i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 751.241i | 1.53002i | 0.644017 | + | 0.765011i | \(0.277266\pi\) | ||||
−0.644017 | + | 0.765011i | \(0.722734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 99.1553 | 0.201126 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 45.3395 | 0.0912263 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 47.1472i | 0.0944833i | 0.998883 | + | 0.0472416i | \(0.0150431\pi\) | ||||
−0.998883 | + | 0.0472416i | \(0.984957\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 156.045 | 0.311467 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −254.863 | −0.506686 | −0.253343 | − | 0.967377i | \(-0.581530\pi\) | ||||
−0.253343 | + | 0.967377i | \(0.581530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 116.123i | 0.229039i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 126.136i | − | 0.247811i | −0.992294 | − | 0.123905i | \(-0.960458\pi\) | ||
0.992294 | − | 0.123905i | \(-0.0395419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 691.549i | 1.35333i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 188.766i | − | 0.367965i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.2394i | 0.0720298i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 57.6239i | − | 0.111029i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −814.952 | −1.56421 | −0.782103 | − | 0.623149i | \(-0.785853\pi\) | ||||
−0.782103 | + | 0.623149i | \(0.785853\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.1549i | − | 0.0461853i | −0.999733 | − | 0.0230926i | \(-0.992649\pi\) | ||
0.999733 | − | 0.0230926i | \(-0.00735127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −75.5630 | − | 29.7203i | −0.143383 | − | 0.0563953i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1007.44 | −1.90442 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 195.972 | 0.369062 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 65.8726i | − | 0.123588i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −153.796 | −0.286398 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 236.985i | − | 0.439675i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 241.017 | 0.445503 | 0.222752 | − | 0.974875i | \(-0.428496\pi\) | ||||
0.222752 | + | 0.974875i | \(0.428496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −214.980 | −0.395912 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 640.236 | 1.17045 | 0.585225 | − | 0.810871i | \(-0.301006\pi\) | ||||
0.585225 | + | 0.810871i | \(0.301006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.7143i | 0.0231589i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 588.508i | − | 1.06807i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 454.718i | 0.822274i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 290.241i | − | 0.521079i | −0.965463 | − | 0.260539i | \(-0.916100\pi\) | ||
0.965463 | − | 0.260539i | \(-0.0839004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −64.8906 | −0.116083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 13.2956i | − | 0.0236999i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −546.321 | −0.970375 | −0.485187 | − | 0.874410i | \(-0.661249\pi\) | ||||
−0.485187 | + | 0.874410i | \(0.661249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 615.705 | 1.08590 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 799.608i | − | 1.40529i | −0.711543 | − | 0.702643i | \(-0.752003\pi\) | ||
0.711543 | − | 0.702643i | \(-0.247997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 343.911i | − | 0.602296i | −0.953577 | − | 0.301148i | \(-0.902630\pi\) | ||
0.953577 | − | 0.301148i | \(-0.0973697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 71.1612i | − | 0.124191i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −388.763 | −0.673767 | −0.336883 | − | 0.941546i | \(-0.609373\pi\) | ||||
−0.336883 | + | 0.941546i | \(0.609373\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 160.145i | − | 0.276589i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1023.79i | 1.76213i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −249.625 | −0.428174 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 501.375i | 0.854131i | 0.904221 | + | 0.427065i | \(0.140453\pi\) | ||||
−0.904221 | + | 0.427065i | \(0.859547\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −176.397 | + | 448.483i | −0.299485 | + | 0.761431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.9380 | 0.0794213 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −914.823 | −1.54270 | −0.771352 | − | 0.636409i | \(-0.780419\pi\) | ||||
−0.771352 | + | 0.636409i | \(0.780419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46.9162 | 0.0785865 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 891.875 | 1.48894 | 0.744470 | − | 0.667656i | \(-0.232702\pi\) | ||||
0.744470 | + | 0.667656i | \(0.232702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 532.088i | − | 0.885338i | −0.896685 | − | 0.442669i | \(-0.854032\pi\) | ||
0.896685 | − | 0.442669i | \(-0.145968\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 818.901 | 1.35804 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 777.101 | 1.28023 | 0.640116 | − | 0.768278i | \(-0.278886\pi\) | ||||
0.640116 | + | 0.768278i | \(0.278886\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −236.653 | −0.388592 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6.12847i | − | 0.0100302i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 253.403i | − | 0.413381i | −0.978406 | − | 0.206691i | \(-0.933731\pi\) | ||
0.978406 | − | 0.206691i | \(-0.0662693\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −590.743 | −0.957444 | −0.478722 | − | 0.877966i | \(-0.658900\pi\) | ||||
−0.478722 | + | 0.877966i | \(0.658900\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 905.297i | 1.46252i | 0.682101 | + | 0.731258i | \(0.261066\pi\) | ||||
−0.682101 | + | 0.731258i | \(0.738934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −475.951 | −0.766427 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1309.42i | − | 2.10180i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −78.9125 | −0.125857 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 190.459 | 0.302796 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 384.376i | 0.609154i | 0.952488 | + | 0.304577i | \(0.0985151\pi\) | ||||
−0.952488 | + | 0.304577i | \(0.901485\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 288.075i | 0.455095i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.0004i | 0.0612251i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 42.8252 | 0.0670191 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1141.36i | − | 1.78059i | −0.455379 | − | 0.890297i | \(-0.650496\pi\) | ||
0.455379 | − | 0.890297i | \(-0.349504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1011.71i | − | 1.57342i | −0.617324 | − | 0.786709i | \(-0.711783\pi\) | ||
0.617324 | − | 0.786709i | \(-0.288217\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 230.511i | 0.356276i | 0.984005 | + | 0.178138i | \(0.0570074\pi\) | ||||
−0.984005 | + | 0.178138i | \(0.942993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 168.469i | − | 0.259582i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 180.345 | + | 70.9332i | 0.277028 | + | 0.108960i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −462.269 | −0.707916 | −0.353958 | − | 0.935261i | \(-0.615164\pi\) | ||||
−0.353958 | + | 0.935261i | \(0.615164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 653.200i | 0.994217i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 911.200 | 1.38270 | 0.691350 | − | 0.722520i | \(-0.257016\pi\) | ||||
0.691350 | + | 0.722520i | \(0.257016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 122.411 | 0.185191 | 0.0925954 | − | 0.995704i | \(-0.470484\pi\) | ||||
0.0925954 | + | 0.995704i | \(0.470484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.18805i | 0.00330023i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1483.85 | −2.22467 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.02645 | 0.00900814 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.9299 | 0.0162890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 381.492i | 0.566853i | 0.958994 | + | 0.283427i | \(0.0914712\pi\) | ||||
−0.958994 | + | 0.283427i | \(0.908529\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 882.565i | − | 1.30364i | −0.758373 | − | 0.651821i | \(-0.774005\pi\) | ||
0.758373 | − | 0.651821i | \(-0.225995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 156.777 | 0.230895 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 244.072i | 0.358403i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1084.00 | 1.58712 | 0.793561 | − | 0.608490i | \(-0.208225\pi\) | ||||
0.793561 | + | 0.608490i | \(0.208225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −51.2913 | −0.0746599 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.0807 | 0.0596236 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.47645 | −0.00937258 | −0.00468629 | − | 0.999989i | \(-0.501492\pi\) | ||||
−0.00468629 | + | 0.999989i | \(0.501492\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 562.817i | − | 0.812146i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 143.150i | 0.205380i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 186.027i | 0.266133i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 780.180 | 1.11295 | 0.556476 | − | 0.830864i | \(-0.312153\pi\) | ||||
0.556476 | + | 0.830864i | \(0.312153\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1130.41i | − | 1.60799i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1114.83 | 1.57684 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1369.94i | 1.93221i | 0.258149 | + | 0.966105i | \(0.416887\pi\) | ||||
−0.258149 | + | 0.966105i | \(0.583113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 429.502i | 0.604081i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1130.80 | + | 444.763i | 1.58597 | + | 0.623791i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 108.835 | 0.151792 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1101.50i | 1.53198i | 0.642851 | + | 0.765992i | \(0.277752\pi\) | ||||
−0.642851 | + | 0.765992i | \(0.722248\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −309.259 | −0.428931 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.35482 | −0.0101726 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 556.384 | 0.765314 | 0.382657 | − | 0.923890i | \(-0.375009\pi\) | ||||
0.382657 | + | 0.923890i | \(0.375009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 505.821 | 0.693857 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 141.016 | 0.192908 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −482.566 | −0.658343 | −0.329172 | − | 0.944270i | \(-0.606769\pi\) | ||||
−0.329172 | + | 0.944270i | \(0.606769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 703.974i | − | 0.955189i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 386.972i | 0.523643i | 0.965116 | + | 0.261822i | \(0.0843232\pi\) | ||||
−0.965116 | + | 0.261822i | \(0.915677\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.9866 | 0.0175257 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 230.629i | 0.310402i | 0.987883 | + | 0.155201i | \(0.0496026\pi\) | ||||
−0.987883 | + | 0.155201i | \(0.950397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 967.022i | 1.29454i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1103.42 | −1.47318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 736.091 | 0.980148 | 0.490074 | − | 0.871681i | \(-0.336970\pi\) | ||||
0.490074 | + | 0.871681i | \(0.336970\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 280.592 | 0.372632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 151.962i | 0.200743i | 0.994950 | + | 0.100371i | \(0.0320031\pi\) | ||||
−0.994950 | + | 0.100371i | \(0.967997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 198.969i | 0.262146i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 400.905i | − | 0.526813i | −0.964685 | − | 0.263407i | \(-0.915154\pi\) | ||
0.964685 | − | 0.263407i | \(-0.0848461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1746.68 | −2.28923 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.7248i | 0.0361470i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −806.936 | −1.04933 | −0.524666 | − | 0.851308i | \(-0.675810\pi\) | ||||
−0.524666 | + | 0.851308i | \(0.675810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 188.050i | − | 0.243904i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 478.951i | − | 0.619601i | −0.950802 | − | 0.309800i | \(-0.899738\pi\) | ||
0.950802 | − | 0.309800i | \(-0.100262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −454.566 | −0.585027 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 849.624 | 1.09066 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 36.8150i | − | 0.0471383i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −459.662 | −0.587052 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 85.3203i | − | 0.108412i | −0.998530 | − | 0.0542060i | \(-0.982737\pi\) | ||
0.998530 | − | 0.0542060i | \(-0.0172628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −83.7144 | −0.106102 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1707.68 | 2.15889 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.79873 | −0.00226826 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 176.296i | − | 0.221200i | −0.993865 | − | 0.110600i | \(-0.964723\pi\) | ||
0.993865 | − | 0.110600i | \(-0.0352772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.3180i | 0.0166683i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1236.81i | − | 1.54408i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 561.529 | 0.699289 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −194.455 | −0.240960 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 708.863i | − | 0.876222i | −0.898921 | − | 0.438111i | \(-0.855648\pi\) | ||
0.898921 | − | 0.438111i | \(-0.144352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −361.574 | −0.445837 | −0.222919 | − | 0.974837i | \(-0.571558\pi\) | ||||
−0.222919 | + | 0.974837i | \(0.571558\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −169.511 | −0.208501 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 836.959i | − | 1.02443i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 92.6225i | 0.113092i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1155.39i | − | 1.40730i | −0.710547 | − | 0.703650i | \(-0.751552\pi\) | ||
0.710547 | − | 0.703650i | \(-0.248448\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 578.491i | − | 0.702905i | −0.936206 | − | 0.351453i | \(-0.885688\pi\) | ||
0.936206 | − | 0.351453i | \(-0.114312\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 824.460i | − | 0.996929i | −0.866910 | − | 0.498465i | \(-0.833897\pi\) | ||
0.866910 | − | 0.498465i | \(-0.166103\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 745.335i | − | 0.899077i | −0.893261 | − | 0.449538i | \(-0.851588\pi\) | ||
0.893261 | − | 0.449538i | \(-0.148412\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 68.2960 | 0.0821853 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 84.7530i | − | 0.101744i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 350.294 | + | 137.777i | 0.418511 | + | 0.164608i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1102.25 | −1.31377 | −0.656884 | − | 0.753991i | \(-0.728126\pi\) | ||||
−0.656884 | + | 0.753991i | \(0.728126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −592.069 | −0.704006 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 143.242i | 0.169920i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 607.569 | 0.717319 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 270.165i | 0.318216i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2850.21 | −3.34924 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −733.709 | −0.860151 | −0.430075 | − | 0.902793i | \(-0.641513\pi\) | ||||
−0.430075 | + | 0.902793i | \(0.641513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1050.67 | 1.22599 | 0.612995 | − | 0.790087i | \(-0.289964\pi\) | ||||
0.612995 | + | 0.790087i | \(0.289964\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1488.78i | 1.73316i | 0.499040 | + | 0.866579i | \(0.333686\pi\) | ||||
−0.499040 | + | 0.866579i | \(0.666314\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 341.654i | − | 0.396810i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 268.208i | − | 0.310786i | −0.987853 | − | 0.155393i | \(-0.950336\pi\) | ||
0.987853 | − | 0.155393i | \(-0.0496644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 195.543i | 0.225540i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 369.225 | 0.424885 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 115.853i | 0.133011i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 148.084 | 0.169626 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1595.55 | −1.81933 | −0.909664 | − | 0.415344i | \(-0.863661\pi\) | ||||
−0.909664 | + | 0.415344i | \(0.863661\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 71.7144i | − | 0.0815864i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 134.904i | − | 0.153126i | −0.997065 | − | 0.0765630i | \(-0.975605\pi\) | ||
0.997065 | − | 0.0765630i | \(-0.0243946\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 721.579i | 0.817191i | 0.912716 | + | 0.408595i | \(0.133981\pi\) | ||||
−0.912716 | + | 0.408595i | \(0.866019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −357.058 | −0.402545 | −0.201273 | − | 0.979535i | \(-0.564508\pi\) | ||||
−0.201273 | + | 0.979535i | \(0.564508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1722.70i | − | 1.93779i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 499.944i | − | 0.561105i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 79.0450 | 0.0885162 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 32.7441i | − | 0.0365041i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1092.10 | + | 429.541i | 1.21479 | + | 0.477799i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −89.2737 | −0.0990829 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −336.561 | −0.372714 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −695.351 | −0.766650 | −0.383325 | − | 0.923614i | \(-0.625221\pi\) | ||||
−0.383325 | + | 0.923614i | \(0.625221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1053.01 | 1.15842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 700.661i | 0.769112i | 0.923102 | + | 0.384556i | \(0.125645\pi\) | ||||
−0.923102 | + | 0.384556i | \(0.874355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 831.308 | 0.910523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 552.261 | 0.602248 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1217.24 | 1.32452 | 0.662261 | − | 0.749273i | \(-0.269597\pi\) | ||||
0.662261 | + | 0.749273i | \(0.269597\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 159.539i | − | 0.173224i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.05863i | 0.00656406i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −292.110 | −0.315113 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1412.58i | − | 1.52054i | −0.649610 | − | 0.760268i | \(-0.725068\pi\) | ||
0.649610 | − | 0.760268i | \(-0.274932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −503.027 | −0.540309 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 145.186i | − | 0.155612i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 768.384 | 0.820047 | 0.410023 | − | 0.912075i | \(-0.365521\pi\) | ||||
0.410023 | + | 0.912075i | \(0.365521\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −205.580 | −0.218935 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1009.58i | 1.07289i | 0.843937 | + | 0.536443i | \(0.180232\pi\) | ||||
−0.843937 | + | 0.536443i | \(0.819768\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2142.23i | − | 2.27172i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 759.057i | 0.801539i | 0.916179 | + | 0.400769i | \(0.131257\pi\) | ||||
−0.916179 | + | 0.400769i | \(0.868743\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −92.4105 | −0.0973767 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 41.1831i | − | 0.0433051i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 122.027i | − | 0.128045i | −0.997948 | − | 0.0640227i | \(-0.979607\pi\) | ||
0.997948 | − | 0.0640227i | \(-0.0203930\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 192.159i | 0.200793i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 598.239i | − | 0.623815i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −703.503 | − | 654.679i | −0.732053 | − | 0.681248i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1042.23 | −1.08227 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 294.473i | 0.304523i | 0.988340 | + | 0.152261i | \(0.0486555\pi\) | ||||
−0.988340 | + | 0.152261i | \(0.951344\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.2215 | −0.0291244 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.5432 | 0.0283658 | 0.0141829 | − | 0.999899i | \(-0.495485\pi\) | ||||
0.0141829 | + | 0.999899i | \(0.495485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 731.447i | − | 0.751744i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −353.842 | −0.362172 | −0.181086 | − | 0.983467i | \(-0.557961\pi\) | ||||
−0.181086 | + | 0.983467i | \(0.557961\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1063.23 | −1.08604 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1649.82 | −1.68177 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 514.232i | 0.523125i | 0.965186 | + | 0.261563i | \(0.0842378\pi\) | ||||
−0.965186 | + | 0.261563i | \(0.915762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 31.7858i | − | 0.0322045i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2110.29 | −2.13376 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1484.21i | − | 1.49769i | −0.662746 | − | 0.748845i | \(-0.730609\pi\) | ||
0.662746 | − | 0.748845i | \(-0.269391\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −198.840 | −0.200242 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −876.530 | −0.879168 | −0.439584 | − | 0.898202i | \(-0.644874\pi\) | ||||
−0.439584 | + | 0.898202i | \(0.644874\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −882.925 | −0.883808 |
(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 | 3100.3.d.e.1301.11 | 20 | ||
5.2 | odd | 4 | 3100.3.f.c.1549.21 | 40 | |||
5.3 | odd | 4 | 3100.3.f.c.1549.20 | 40 | |||
5.4 | even | 2 | 620.3.d.a.61.10 | ✓ | 20 | ||
31.30 | odd | 2 | inner | 3100.3.d.e.1301.10 | 20 | ||
155.92 | even | 4 | 3100.3.f.c.1549.19 | 40 | |||
155.123 | even | 4 | 3100.3.f.c.1549.22 | 40 | |||
155.154 | odd | 2 | 620.3.d.a.61.11 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
620.3.d.a.61.10 | ✓ | 20 | 5.4 | even | 2 | ||
620.3.d.a.61.11 | yes | 20 | 155.154 | odd | 2 | ||
3100.3.d.e.1301.10 | 20 | 31.30 | odd | 2 | inner | ||
3100.3.d.e.1301.11 | 20 | 1.1 | even | 1 | trivial | ||
3100.3.f.c.1549.19 | 40 | 155.92 | even | 4 | |||
3100.3.f.c.1549.20 | 40 | 5.3 | odd | 4 | |||
3100.3.f.c.1549.21 | 40 | 5.2 | odd | 4 | |||
3100.3.f.c.1549.22 | 40 | 155.123 | even | 4 |