Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,3,Mod(321,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1840.321");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.k (of order \(2\), degree \(1\), not 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: | \(50.1363686423\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 64 x^{14} - 16 x^{13} + 2252 x^{12} + 648 x^{11} - 30106 x^{10} + 12360 x^{9} + \cdots + 1535848276 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 460) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 321.1 | ||
Root | \(5.89296 - 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.321 |
Dual form | 1840.3.k.c.321.2 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −5.89296 | −1.96432 | −0.982159 | − | 0.188050i | \(-0.939783\pi\) | ||||
−0.982159 | + | 0.188050i | \(0.939783\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.21480i | 0.173543i | 0.996228 | + | 0.0867716i | \(0.0276550\pi\) | ||||
−0.996228 | + | 0.0867716i | \(0.972345\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 25.7269 | 2.85855 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.1790i | 1.74355i | 0.489908 | + | 0.871774i | \(0.337030\pi\) | ||||
−0.489908 | + | 0.871774i | \(0.662970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.79358 | −0.522583 | −0.261291 | − | 0.965260i | \(-0.584148\pi\) | ||||
−0.261291 | + | 0.965260i | \(0.584148\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.1771i | 0.878470i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.3706i | 1.25709i | 0.777772 | + | 0.628546i | \(0.216350\pi\) | ||||
−0.777772 | + | 0.628546i | \(0.783650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.5552i | 1.08185i | 0.841070 | + | 0.540927i | \(0.181926\pi\) | ||||
−0.841070 | + | 0.540927i | \(0.818074\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 7.15878i | − | 0.340894i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.0815 | − | 18.9176i | 0.568760 | − | 0.822503i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −98.5711 | −3.65078 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.1176 | 0.521296 | 0.260648 | − | 0.965434i | \(-0.416064\pi\) | ||||
0.260648 | + | 0.965434i | \(0.416064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.27990 | −0.234836 | −0.117418 | − | 0.993083i | \(-0.537462\pi\) | ||||
−0.117418 | + | 0.993083i | \(0.537462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 113.021i | − | 3.42488i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.71638 | 0.0776109 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51.4644i | 1.39093i | 0.718560 | + | 0.695465i | \(0.244801\pi\) | ||||
−0.718560 | + | 0.695465i | \(0.755199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 40.0343 | 1.02652 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.1873 | 0.346032 | 0.173016 | − | 0.984919i | \(-0.444649\pi\) | ||||
0.173016 | + | 0.984919i | \(0.444649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 37.4927i | − | 0.871924i | −0.899965 | − | 0.435962i | \(-0.856408\pi\) | ||
0.899965 | − | 0.435962i | \(-0.143592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 57.5272i | − | 1.27838i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.7126 | 1.24920 | 0.624602 | − | 0.780943i | \(-0.285261\pi\) | ||||
0.624602 | + | 0.780943i | \(0.285261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.5243 | 0.969883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 125.936i | − | 2.46933i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 24.6357i | − | 0.464824i | −0.972617 | − | 0.232412i | \(-0.925338\pi\) | ||
0.972617 | − | 0.232412i | \(-0.0746618\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 42.8856 | 0.779739 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 121.131i | − | 2.12511i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 68.9831 | 1.16920 | 0.584602 | − | 0.811320i | \(-0.301251\pi\) | ||||
0.584602 | + | 0.811320i | \(0.301251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 98.9407i | 1.62198i | 0.585061 | + | 0.810989i | \(0.301070\pi\) | ||||
−0.585061 | + | 0.810989i | \(0.698930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31.2532i | 0.496082i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.1909i | 0.233706i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 52.1637i | − | 0.778563i | −0.921119 | − | 0.389281i | \(-0.872723\pi\) | ||
0.921119 | − | 0.389281i | \(-0.127277\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −77.0886 | + | 111.480i | −1.11723 | + | 1.61566i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −82.9700 | −1.16859 | −0.584296 | − | 0.811541i | \(-0.698629\pi\) | ||||
−0.584296 | + | 0.811541i | \(0.698629\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −68.0710 | −0.932480 | −0.466240 | − | 0.884658i | \(-0.654392\pi\) | ||||
−0.466240 | + | 0.884658i | \(0.654392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 29.4648 | 0.392864 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23.2987 | −0.302581 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.71508i | 0.0470264i | 0.999724 | + | 0.0235132i | \(0.00748517\pi\) | ||||
−0.999724 | + | 0.0235132i | \(0.992515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 349.333 | 4.31275 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 90.1400i | 1.08602i | 0.839725 | + | 0.543012i | \(0.182716\pi\) | ||||
−0.839725 | + | 0.543012i | \(0.817284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 47.7860 | 0.562189 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −89.0872 | −1.02399 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 103.447i | − | 1.16233i | −0.813786 | − | 0.581164i | \(-0.802597\pi\) | ||
0.813786 | − | 0.581164i | \(-0.197403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.25286i | − | 0.0906907i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 42.9001 | 0.461292 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 45.9629 | 0.483820 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 73.2599i | − | 0.755257i | −0.925957 | − | 0.377629i | \(-0.876740\pi\) | ||
0.925957 | − | 0.377629i | \(-0.123260\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 493.418i | 4.98402i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7274 | −0.126014 | −0.0630069 | − | 0.998013i | \(-0.520069\pi\) | ||||
−0.0630069 | + | 0.998013i | \(0.520069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 99.7786i | 0.968725i | 0.874867 | + | 0.484362i | \(0.160948\pi\) | ||||
−0.874867 | + | 0.484362i | \(0.839052\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.0075 | −0.152453 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 185.420i | − | 1.73290i | −0.499263 | − | 0.866450i | \(-0.666396\pi\) | ||
0.499263 | − | 0.866450i | \(-0.333604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 47.7532i | 0.438102i | 0.975713 | + | 0.219051i | \(0.0702962\pi\) | ||||
−0.975713 | + | 0.219051i | \(0.929704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 303.277i | − | 2.73223i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 60.3411i | 0.533992i | 0.963698 | + | 0.266996i | \(0.0860310\pi\) | ||||
−0.963698 | + | 0.266996i | \(0.913969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −42.3010 | − | 29.2511i | −0.367835 | − | 0.254357i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −174.778 | −1.49383 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.9610 | −0.218160 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −246.835 | −2.03996 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −83.6052 | −0.679717 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 91.1969 | 0.718086 | 0.359043 | − | 0.933321i | \(-0.383103\pi\) | ||||
0.359043 | + | 0.933321i | \(0.383103\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 220.943i | 1.71274i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −227.631 | −1.73764 | −0.868822 | − | 0.495125i | \(-0.835122\pi\) | ||||
−0.868822 | + | 0.495125i | \(0.835122\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.9705 | −0.187748 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 220.412i | 1.63268i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 60.9616i | − | 0.444975i | −0.974936 | − | 0.222488i | \(-0.928582\pi\) | ||
0.974936 | − | 0.222488i | \(-0.0714177\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 153.735 | 1.10601 | 0.553003 | − | 0.833180i | \(-0.313482\pi\) | ||||
0.553003 | + | 0.833180i | \(0.313482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −345.991 | −2.45383 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 130.294i | − | 0.911148i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 33.8039i | − | 0.233130i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −280.058 | −1.90516 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 126.021i | 0.845776i | 0.906182 | + | 0.422888i | \(0.138984\pi\) | ||||
−0.906182 | + | 0.422888i | \(0.861016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 243.700 | 1.61391 | 0.806955 | − | 0.590613i | \(-0.201114\pi\) | ||||
0.806955 | + | 0.590613i | \(0.201114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 549.799i | 3.59346i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.2784i | 0.105022i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 158.005i | 1.00640i | 0.864170 | + | 0.503200i | \(0.167844\pi\) | ||||
−0.864170 | + | 0.503200i | \(0.832156\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 145.177i | 0.913063i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.9811 | + | 15.8914i | 0.142740 | + | 0.0987045i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −67.8522 | −0.416271 | −0.208136 | − | 0.978100i | \(-0.566740\pi\) | ||||
−0.208136 | + | 0.978100i | \(0.566740\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −252.723 | −1.53166 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −163.592 | −0.979591 | −0.489795 | − | 0.871837i | \(-0.662929\pi\) | ||||
−0.489795 | + | 0.871837i | \(0.662929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −122.847 | −0.726907 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 528.823i | 3.09253i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −252.094 | −1.45719 | −0.728597 | − | 0.684943i | \(-0.759827\pi\) | ||||
−0.728597 | + | 0.684943i | \(0.759827\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.07401i | − | 0.0347086i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −406.514 | −2.29669 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −106.081 | −0.592630 | −0.296315 | − | 0.955090i | \(-0.595758\pi\) | ||||
−0.296315 | + | 0.955090i | \(0.595758\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 63.8813i | 0.352936i | 0.984306 | + | 0.176468i | \(0.0564671\pi\) | ||||
−0.984306 | + | 0.176468i | \(0.943533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 583.053i | − | 3.18608i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 115.078 | 0.622042 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −409.867 | −2.19180 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 119.744i | − | 0.633569i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 247.573i | 1.29619i | 0.761559 | + | 0.648096i | \(0.224434\pi\) | ||||
−0.761559 | + | 0.648096i | \(0.775566\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −108.671 | −0.563063 | −0.281531 | − | 0.959552i | \(-0.590842\pi\) | ||||
−0.281531 | + | 0.959552i | \(0.590842\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 89.5193i | − | 0.459073i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −127.968 | −0.649586 | −0.324793 | − | 0.945785i | \(-0.605295\pi\) | ||||
−0.324793 | + | 0.945785i | \(0.605295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 187.445i | 0.941937i | 0.882150 | + | 0.470968i | \(0.156095\pi\) | ||||
−0.882150 | + | 0.470968i | \(0.843905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 307.398i | 1.52935i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.3649i | 0.0904673i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 31.7238i | − | 0.154750i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 336.547 | − | 486.691i | 1.62583 | − | 2.35117i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −394.229 | −1.88626 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 204.271 | 0.968111 | 0.484055 | − | 0.875037i | \(-0.339163\pi\) | ||||
0.484055 | + | 0.875037i | \(0.339163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 488.938 | 2.29549 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −83.8363 | −0.389936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.84364i | − | 0.0407541i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 401.140 | 1.83169 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 145.183i | − | 0.656935i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 225.207 | 1.00990 | 0.504948 | − | 0.863150i | \(-0.331512\pi\) | ||||
0.504948 | + | 0.863150i | \(0.331512\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −128.635 | −0.571710 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 148.291i | 0.653264i | 0.945152 | + | 0.326632i | \(0.105914\pi\) | ||||
−0.945152 | + | 0.326632i | \(0.894086\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 69.3950i | 0.303035i | 0.988455 | + | 0.151518i | \(0.0484160\pi\) | ||||
−0.988455 | + | 0.151518i | \(0.951584\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 137.298 | 0.594366 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 134.731 | 0.578244 | 0.289122 | − | 0.957292i | \(-0.406637\pi\) | ||||
0.289122 | + | 0.957292i | \(0.406637\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 131.285i | − | 0.558661i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 21.8928i | − | 0.0923748i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 156.166 | 0.653413 | 0.326707 | − | 0.945126i | \(-0.394061\pi\) | ||||
0.326707 | + | 0.945126i | \(0.394061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.20765i | − | 0.0133097i | −0.999978 | − | 0.00665487i | \(-0.997882\pi\) | ||
0.999978 | − | 0.00665487i | \(-0.00211833\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1171.46 | −4.82084 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 106.267i | − | 0.433745i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 139.644i | − | 0.565358i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 531.191i | − | 2.13330i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 172.125i | 0.685758i | 0.939380 | + | 0.342879i | \(0.111402\pi\) | ||||
−0.939380 | + | 0.342879i | \(0.888598\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 362.821 | + | 250.890i | 1.43407 | + | 0.991661i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −281.601 | −1.10432 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 184.115 | 0.716402 | 0.358201 | − | 0.933644i | \(-0.383390\pi\) | ||||
0.358201 | + | 0.933644i | \(0.383390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −62.5191 | −0.241386 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 388.929 | 1.49015 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 344.445i | 1.30968i | 0.755768 | + | 0.654839i | \(0.227264\pi\) | ||||
−0.755768 | + | 0.654839i | \(0.772736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −55.0871 | −0.207876 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 609.610i | 2.28318i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 367.014 | 1.36437 | 0.682183 | − | 0.731181i | \(-0.261031\pi\) | ||||
0.682183 | + | 0.731181i | \(0.261031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −314.590 | −1.16085 | −0.580425 | − | 0.814314i | \(-0.697114\pi\) | ||||
−0.580425 | + | 0.814314i | \(0.697114\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 48.6337i | 0.178145i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 95.8952i | − | 0.348710i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.5629 | −0.0958951 | −0.0479476 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479476 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −187.290 | −0.671289 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 63.1722i | − | 0.224812i | −0.993662 | − | 0.112406i | \(-0.964144\pi\) | ||
0.993662 | − | 0.112406i | \(-0.0358557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 215.448i | − | 0.761302i | −0.924719 | − | 0.380651i | \(-0.875700\pi\) | ||
0.924719 | − | 0.380651i | \(-0.124300\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −270.857 | −0.950376 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.2348i | 0.0600515i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −167.701 | −0.580280 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 431.718i | 1.48357i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 293.367i | 1.00125i | 0.865663 | + | 0.500626i | \(0.166897\pi\) | ||||
−0.865663 | + | 0.500626i | \(0.833103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 154.251i | − | 0.522884i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1890.50i | − | 6.36532i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −88.8701 | + | 128.518i | −0.297224 | + | 0.429826i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 45.5462 | 0.151316 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 75.0020 | 0.247531 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 221.238 | 0.725371 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 50.1619 | 0.163394 | 0.0816970 | − | 0.996657i | \(-0.473966\pi\) | ||||
0.0816970 | + | 0.996657i | \(0.473966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 587.991i | − | 1.90288i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −547.613 | −1.76081 | −0.880407 | − | 0.474219i | \(-0.842731\pi\) | ||||
−0.880407 | + | 0.474219i | \(0.842731\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.7281i | 0.0598342i | 0.999552 | + | 0.0299171i | \(0.00952433\pi\) | ||||
−0.999552 | + | 0.0299171i | \(0.990476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 69.8842 | 0.221855 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 73.9497 | 0.233280 | 0.116640 | − | 0.993174i | \(-0.462788\pi\) | ||||
0.116640 | + | 0.993174i | \(0.462788\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 289.940i | 0.908904i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1092.67i | 3.40397i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −439.277 | −1.35999 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.9679 | 0.104517 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 281.407i | − | 0.860573i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 71.3242i | 0.216791i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −332.772 | −1.00535 | −0.502677 | − | 0.864474i | \(-0.667651\pi\) | ||||
−0.502677 | + | 0.864474i | \(0.667651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1324.02i | 3.97604i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −116.642 | −0.348184 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 316.494i | 0.939152i | 0.882892 | + | 0.469576i | \(0.155593\pi\) | ||||
−0.882892 | + | 0.469576i | \(0.844407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 355.587i | − | 1.04893i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 139.621i | − | 0.409447i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117.258i | 0.341860i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 249.278 | + | 172.375i | 0.722545 | + | 0.499639i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 176.028 | 0.507286 | 0.253643 | − | 0.967298i | \(-0.418371\pi\) | ||||
0.253643 | + | 0.967298i | \(0.418371\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −458.207 | −1.31291 | −0.656457 | − | 0.754363i | \(-0.727946\pi\) | ||||
−0.656457 | + | 0.754363i | \(0.727946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 669.651 | 1.90784 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 62.0444 | 0.175763 | 0.0878816 | − | 0.996131i | \(-0.471990\pi\) | ||||
0.0878816 | + | 0.996131i | \(0.471990\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 185.526i | 0.522610i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 152.987 | 0.428535 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 190.457i | 0.530520i | 0.964177 | + | 0.265260i | \(0.0854578\pi\) | ||||
−0.964177 | + | 0.265260i | \(0.914542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −61.5173 | −0.170408 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1454.59 | 4.00713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 152.211i | 0.417018i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 491.688i | − | 1.33975i | −0.742474 | − | 0.669875i | \(-0.766348\pi\) | ||
0.742474 | − | 0.669875i | \(-0.233652\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 364.996 | 0.989149 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.9275 | 0.0806671 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 726.490i | − | 1.94769i | −0.227204 | − | 0.973847i | \(-0.572958\pi\) | ||
0.227204 | − | 0.973847i | \(-0.427042\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 65.8853i | − | 0.175694i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −102.702 | −0.272420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 165.365i | − | 0.436320i | −0.975913 | − | 0.218160i | \(-0.929995\pi\) | ||
0.975913 | − | 0.218160i | \(-0.0700055\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −537.420 | −1.41055 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 654.544i | 1.70899i | 0.519457 | + | 0.854497i | \(0.326134\pi\) | ||||
−0.519457 | + | 0.854497i | \(0.673866\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 52.0976i | 0.135318i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 964.573i | − | 2.49244i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 660.920i | − | 1.69902i | −0.527570 | − | 0.849512i | \(-0.676897\pi\) | ||
0.527570 | − | 0.849512i | \(-0.323103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 404.279 | + | 279.559i | 1.03396 | + | 0.714984i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1341.42 | 3.41329 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.30718 | 0.0210308 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −255.774 | −0.644267 | −0.322133 | − | 0.946694i | \(-0.604400\pi\) | ||||
−0.322133 | + | 0.946694i | \(0.604400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 147.150 | 0.368798 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 607.765i | 1.51562i | 0.652474 | + | 0.757811i | \(0.273731\pi\) | ||||
−0.652474 | + | 0.757811i | \(0.726269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.4566 | 0.122721 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 781.132i | − | 1.92872i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −987.037 | −2.42515 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −49.7513 | −0.121641 | −0.0608207 | − | 0.998149i | \(-0.519372\pi\) | ||||
−0.0608207 | + | 0.998149i | \(0.519372\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 359.244i | 0.874073i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 83.8008i | 0.202908i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 201.559 | 0.485685 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −905.952 | −2.17255 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 613.574i | 1.46438i | 0.681102 | + | 0.732188i | \(0.261501\pi\) | ||||
−0.681102 | + | 0.732188i | \(0.738499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 780.040i | − | 1.85283i | −0.376507 | − | 0.926414i | \(-0.622875\pi\) | ||
0.376507 | − | 0.926414i | \(-0.377125\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1510.49 | 3.57091 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 106.853i | − | 0.251418i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −120.193 | −0.281483 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 767.818i | 1.78979i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 421.761i | − | 0.978565i | −0.872125 | − | 0.489282i | \(-0.837259\pi\) | ||
0.872125 | − | 0.489282i | \(-0.162741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 198.107i | − | 0.457521i | −0.973483 | − | 0.228761i | \(-0.926533\pi\) | ||
0.973483 | − | 0.228761i | \(-0.0734673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 199.205i | 0.457943i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 388.855 | + | 268.893i | 0.889829 | + | 0.615315i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −382.455 | −0.871195 | −0.435598 | − | 0.900141i | \(-0.643463\pi\) | ||||
−0.435598 | + | 0.900141i | \(0.643463\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1222.65 | 2.77246 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −589.236 | −1.33010 | −0.665052 | − | 0.746797i | \(-0.731591\pi\) | ||||
−0.665052 | + | 0.746797i | \(0.731591\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −231.315 | −0.519809 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 742.634i | − | 1.66137i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 417.233 | 0.929249 | 0.464624 | − | 0.885508i | \(-0.346189\pi\) | ||||
0.464624 | + | 0.885508i | \(0.346189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 272.099i | 0.603324i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1436.12 | −3.17023 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.4539 | −0.0405581 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 304.457i | − | 0.666207i | −0.942890 | − | 0.333104i | \(-0.891904\pi\) | ||
0.942890 | − | 0.333104i | \(-0.108096\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 2106.52i | − | 4.58937i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −398.642 | −0.864734 | −0.432367 | − | 0.901698i | \(-0.642322\pi\) | ||||
−0.432367 | + | 0.901698i | \(0.642322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 254.794 | 0.550310 | 0.275155 | − | 0.961400i | \(-0.411271\pi\) | ||||
0.275155 | + | 0.961400i | \(0.411271\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 95.9276i | − | 0.206296i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 170.860i | − | 0.365868i | −0.983125 | − | 0.182934i | \(-0.941441\pi\) | ||
0.983125 | − | 0.182934i | \(-0.0585594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 63.3686 | 0.135114 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 931.115i | − | 1.97689i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 719.074 | 1.52024 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 102.776i | − | 0.216371i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 633.801i | − | 1.32872i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 254.888i | − | 0.532126i | −0.963956 | − | 0.266063i | \(-0.914277\pi\) | ||
0.963956 | − | 0.266063i | \(-0.0857229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 349.627i | − | 0.726876i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −135.427 | − | 93.6475i | −0.280387 | − | 0.193887i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −163.814 | −0.337761 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −280.911 | −0.576819 | −0.288410 | − | 0.957507i | \(-0.593126\pi\) | ||||
−0.288410 | + | 0.957507i | \(0.593126\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 399.850 | 0.817690 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 365.779 | 0.744966 | 0.372483 | − | 0.928039i | \(-0.378506\pi\) | ||||
0.372483 | + | 0.928039i | \(0.378506\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 323.071i | 0.655317i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1103.32 | 2.22892 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 100.792i | − | 0.202801i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −301.893 | −0.604996 | −0.302498 | − | 0.953150i | \(-0.597821\pi\) | ||||
−0.302498 | + | 0.953150i | \(0.597821\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 964.039 | 1.92423 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 881.655i | 1.75279i | 0.481590 | + | 0.876397i | \(0.340060\pi\) | ||||
−0.481590 | + | 0.876397i | \(0.659940\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.4593i | 0.0563551i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 723.934 | 1.42788 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 639.641 | 1.25666 | 0.628331 | − | 0.777946i | \(-0.283738\pi\) | ||||
0.628331 | + | 0.777946i | \(0.283738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 82.6929i | − | 0.161826i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2026.15i | − | 3.94961i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 223.112 | 0.433227 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1126.05i | 2.17805i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1485.58 | 2.86239 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 45.5463i | 0.0874209i | 0.999044 | + | 0.0437104i | \(0.0139179\pi\) | ||||
−0.999044 | + | 0.0437104i | \(0.986082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 100.120i | 0.191434i | 0.995409 | + | 0.0957172i | \(0.0305144\pi\) | ||||
−0.995409 | + | 0.0957172i | \(0.969486\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 35.7939i | 0.0681788i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 155.576i | − | 0.295210i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −186.749 | − | 494.940i | −0.353024 | − | 0.935614i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1774.72 | 3.34223 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −96.3826 | −0.180830 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −414.613 | −0.774977 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 625.130 | 1.16411 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 911.469i | 1.69104i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −89.5038 | −0.165441 | −0.0827207 | − | 0.996573i | \(-0.526361\pi\) | ||||
−0.0827207 | + | 0.996573i | \(0.526361\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 376.450i | − | 0.693278i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 106.779 | 0.195925 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −536.646 | −0.981071 | −0.490535 | − | 0.871421i | \(-0.663199\pi\) | ||||
−0.490535 | + | 0.871421i | \(0.663199\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2545.44i | 4.63650i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 310.745i | 0.563966i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.51309 | −0.00816111 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −678.149 | −1.22189 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 600.369i | 1.07786i | 0.842350 | + | 0.538931i | \(0.181172\pi\) | ||||
−0.842350 | + | 0.538931i | \(0.818828\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 254.710i | 0.455652i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2415.33 | 4.30540 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 723.749i | 1.28552i | 0.766067 | + | 0.642761i | \(0.222211\pi\) | ||||
−0.766067 | + | 0.642761i | \(0.777789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 134.927 | 0.238808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 424.371i | 0.748449i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 707.638i | − | 1.24365i | −0.783156 | − | 0.621826i | \(-0.786391\pi\) | ||
0.783156 | − | 0.621826i | \(-0.213609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1007.22i | − | 1.76396i | −0.471287 | − | 0.881980i | \(-0.656210\pi\) | ||
0.471287 | − | 0.881980i | \(-0.343790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1458.93i | − | 2.54613i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −65.4074 | + | 94.5879i | −0.113752 | + | 0.164501i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 280.046 | 0.485349 | 0.242674 | − | 0.970108i | \(-0.421975\pi\) | ||||
0.242674 | + | 0.970108i | \(0.421975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 640.394 | 1.10603 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −109.502 | −0.188472 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 472.489 | 0.810443 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 390.815i | 0.668060i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1165.03 | −1.98473 | −0.992363 | − | 0.123352i | \(-0.960635\pi\) | ||||
−0.992363 | + | 0.123352i | \(0.960635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 149.640i | − | 0.254058i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 754.112 | 1.27599 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −982.609 | −1.65701 | −0.828507 | − | 0.559979i | \(-0.810809\pi\) | ||||
−0.828507 | + | 0.559979i | \(0.810809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 58.0506i | 0.0975640i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1104.61i | − | 1.85026i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.9515 | 0.0383163 | 0.0191581 | − | 0.999816i | \(-0.493901\pi\) | ||||
0.0191581 | + | 0.999816i | \(0.493901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 475.853 | 0.791769 | 0.395885 | − | 0.918300i | \(-0.370438\pi\) | ||||
0.395885 | + | 0.918300i | \(0.370438\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1342.01i | − | 2.22556i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 551.940i | 0.912298i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −754.060 | −1.24227 | −0.621137 | − | 0.783702i | \(-0.713329\pi\) | ||||
−0.621137 | + | 0.783702i | \(0.713329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 108.223i | − | 0.177707i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −398.868 | −0.652812 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 559.933i | − | 0.913431i | −0.889613 | − | 0.456715i | \(-0.849026\pi\) | ||
0.889613 | − | 0.456715i | \(-0.150974\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 186.947i | 0.303979i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 657.899i | − | 1.06629i | −0.846025 | − | 0.533144i | \(-0.821011\pi\) | ||
0.846025 | − | 0.533144i | \(-0.178989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 648.359i | − | 1.04743i | −0.851893 | − | 0.523715i | \(-0.824546\pi\) | ||
0.851893 | − | 0.523715i | \(-0.175454\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1289.46 | + | 1864.73i | −2.07642 | + | 3.00278i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 125.668 | 0.201714 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2323.18 | 3.70523 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1099.82 | −1.74853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 426.772i | 0.676342i | 0.941085 | + | 0.338171i | \(0.109808\pi\) | ||||
−0.941085 | + | 0.338171i | \(0.890192\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1203.76 | −1.90168 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 203.923i | − | 0.321138i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −322.860 | −0.506844 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2134.56 | −3.34047 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 933.107i | 1.45570i | 0.685734 | + | 0.727852i | \(0.259481\pi\) | ||||
−0.685734 | + | 0.727852i | \(0.740519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 887.579i | − | 1.38037i | −0.723632 | − | 0.690186i | \(-0.757529\pi\) | ||
0.723632 | − | 0.690186i | \(-0.242471\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 494.043 | 0.765959 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 733.964 | 1.13441 | 0.567206 | − | 0.823576i | \(-0.308024\pi\) | ||||
0.567206 | + | 0.823576i | \(0.308024\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1323.03i | 2.03856i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 52.1152i | 0.0800541i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1156.08 | −1.77041 | −0.885207 | − | 0.465198i | \(-0.845983\pi\) | ||||
−0.885207 | + | 0.465198i | \(0.845983\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 508.999i | 0.777098i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1751.26 | −2.66554 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5959i | 0.0327707i | 0.999866 | + | 0.0163853i | \(0.00521585\pi\) | ||||
−0.999866 | + | 0.0163853i | \(0.994784\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 529.666i | 0.801310i | 0.916229 | + | 0.400655i | \(0.131217\pi\) | ||||
−0.916229 | + | 0.400655i | \(0.868783\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 855.555i | 1.29043i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.8358i | 0.0839636i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 197.760 | − | 285.988i | 0.296492 | − | 0.428767i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1327.13 | −1.98376 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1897.59 | −2.82800 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −551.811 | −0.819927 | −0.409964 | − | 0.912102i | \(-0.634459\pi\) | ||||
−0.409964 | + | 0.912102i | \(0.634459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 492.856 | 0.730156 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 732.982i | − | 1.08269i | −0.840800 | − | 0.541346i | \(-0.817915\pi\) | ||
0.840800 | − | 0.541346i | \(-0.182085\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 88.9964 | 0.131070 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 873.872i | − | 1.28322i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −444.506 | −0.650814 | −0.325407 | − | 0.945574i | \(-0.605501\pi\) | ||||
−0.325407 | + | 0.945574i | \(0.605501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −136.314 | −0.198999 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 408.942i | − | 0.595258i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 167.364i | 0.242909i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 613.573 | 0.887950 | 0.443975 | − | 0.896039i | \(-0.353568\pi\) | ||||
0.443975 | + | 0.896039i | \(0.353568\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −599.405 | −0.864943 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 343.761i | − | 0.494621i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 303.191i | 0.434994i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −793.963 | −1.13586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 539.961i | − | 0.770272i | −0.922860 | − | 0.385136i | \(-0.874155\pi\) | ||
0.922860 | − | 0.385136i | \(-0.125845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1057.86 | −1.50478 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 773.659i | 1.09739i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 15.4613i | − | 0.0218689i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.68407i | − | 0.00378571i | −0.999998 | − | 0.00189286i | \(-0.999397\pi\) | ||
0.999998 | − | 0.00189286i | \(-0.000602515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 95.5777i | 0.134427i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −95.2319 | + | 137.718i | −0.133565 | + | 0.193153i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −291.347 | −0.407478 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −920.278 | −1.28351 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.2700 | −0.0393185 | −0.0196592 | − | 0.999807i | \(-0.506258\pi\) | ||||
−0.0196592 | + | 0.999807i | \(0.506258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −121.211 | −0.168116 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.9025i | 0.0261446i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −75.5879 | −0.104259 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 305.976i | 0.420875i | 0.977607 | + | 0.210437i | \(0.0674888\pi\) | ||||
−0.977607 | + | 0.210437i | \(0.932511\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3759.39 | 5.15691 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 801.240 | 1.09609 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 635.448i | 0.866914i | 0.901174 | + | 0.433457i | \(0.142706\pi\) | ||||
−0.901174 | + | 0.433457i | \(0.857294\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 626.230i | 0.852013i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1000.45 | 1.35746 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1273.79 | 1.72367 | 0.861834 | − | 0.507191i | \(-0.169316\pi\) | ||||
0.861834 | + | 0.507191i | \(0.169316\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 822.913i | 1.11054i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 680.588i | 0.916000i | 0.888952 | + | 0.458000i | \(0.151434\pi\) | ||||
−0.888952 | + | 0.458000i | \(0.848566\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 281.791 | 0.378242 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2319.03i | 3.10445i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 225.249 | 0.300733 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 391.564i | 0.521390i | 0.965421 | + | 0.260695i | \(0.0839517\pi\) | ||||
−0.965421 | + | 0.260695i | \(0.916048\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1014.33i | − | 1.34705i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 544.931i | − | 0.721763i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1212.06i | 1.60114i | 0.599238 | + | 0.800571i | \(0.295470\pi\) | ||||
−0.599238 | + | 0.800571i | \(0.704530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2138.09 | − | 1478.49i | −2.81698 | − | 1.94794i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1190.50 | −1.56439 | −0.782196 | − | 0.623032i | \(-0.785901\pi\) | ||||
−0.782196 | + | 0.623032i | \(0.785901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −58.0107 | −0.0760297 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1229.39 | 1.60704 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −468.642 | −0.611006 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 228.068i | − | 0.296577i | −0.988944 | − | 0.148289i | \(-0.952624\pi\) | ||
0.988944 | − | 0.148289i | \(-0.0473765\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1084.98 | −1.40724 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 245.060i | − | 0.317025i | −0.987357 | − | 0.158513i | \(-0.949330\pi\) | ||
0.987357 | − | 0.158513i | \(-0.0506698\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.3995 | 0.0469671 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 368.422 | 0.474160 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 291.623i | 0.374356i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1591.28i | − | 2.03750i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1490.16 | −1.90314 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 353.309 | 0.450075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 749.447i | − | 0.952283i | −0.879369 | − | 0.476141i | \(-0.842035\pi\) | ||
0.879369 | − | 0.476141i | \(-0.157965\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 2029.80i | − | 2.57263i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −73.3025 | −0.0926707 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 672.161i | − | 0.847618i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 324.626 | 0.408334 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 223.282i | 0.280152i | 0.990141 | + | 0.140076i | \(0.0447348\pi\) | ||||
−0.990141 | + | 0.140076i | \(0.955265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1254.72i | 1.57036i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2661.38i | − | 3.32257i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1305.54i | − | 1.62582i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.5343 | − | 51.3874i | 0.0441420 | − | 0.0638352i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2162.80 | −2.68005 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1224.34 | −1.51340 | −0.756699 | − | 0.653763i | \(-0.773189\pi\) | ||||
−0.756699 | + | 0.653763i | \(0.773189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 895.177 | 1.10379 | 0.551897 | − | 0.833912i | \(-0.313904\pi\) | ||||
0.551897 | + | 0.833912i | \(0.313904\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1853.87 | 2.28028 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 151.722i | 0.186162i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 770.671 | 0.943294 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 212.321i | − | 0.259244i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −55.9736 | −0.0681773 | −0.0340886 | − | 0.999419i | \(-0.510853\pi\) | ||||
−0.0340886 | + | 0.999419i | \(0.510853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 785.724 | 0.954707 | 0.477354 | − | 0.878711i | \(-0.341596\pi\) | ||||
0.477354 | + | 0.878711i | \(0.341596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 565.106i | 0.684977i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 130.624i | − | 0.157949i | −0.996877 | − | 0.0789745i | \(-0.974835\pi\) | ||
0.996877 | − | 0.0789745i | \(-0.0251646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 166.204 | 0.200487 | 0.100243 | − | 0.994963i | \(-0.468038\pi\) | ||||
0.100243 | + | 0.994963i | \(0.468038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 156.534 | 0.188369 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1015.62i | 1.21923i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 365.802i | 0.438086i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 717.588 | 0.857333 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1048.75i | − | 1.25000i | −0.780624 | − | 0.625001i | \(-0.785098\pi\) | ||
0.780624 | − | 0.625001i | \(-0.214902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −612.459 | −0.728251 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 372.271i | 0.441602i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 274.695i | 0.325083i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 299.856i | − | 0.354021i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1269.63i | 1.49544i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 973.581 | + | 673.230i | 1.14404 | + | 0.791105i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1171.23 | 1.37307 | 0.686533 | − | 0.727099i | \(-0.259132\pi\) | ||||
0.686533 | + | 0.727099i | \(0.259132\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1182.48 | 1.38302 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.578597 | −0.000675142 | −0.000337571 | − | 1.00000i | \(-0.500107\pi\) | ||||
−0.000337571 | 1.00000i | \(0.500107\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1095.88 | −1.27576 | −0.637878 | − | 0.770137i | \(-0.720188\pi\) | ||||
−0.637878 | + | 0.770137i | \(0.720188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 101.564i | − | 0.117960i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −494.808 | −0.573358 | −0.286679 | − | 0.958027i | \(-0.592551\pi\) | ||||
−0.286679 | + | 0.958027i | \(0.592551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 563.700i | 0.651677i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 988.255 | 1.13986 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −71.2517 | −0.0819928 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 354.378i | 0.406864i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1884.75i | − | 2.15894i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.5819 | −0.0155222 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 86.7161 | 0.0988781 | 0.0494390 | − | 0.998777i | \(-0.484257\pi\) | ||||
0.0494390 | + | 0.998777i | \(0.484257\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1728.80i | − | 1.96678i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 497.562i | − | 0.564770i | −0.959301 | − | 0.282385i | \(-0.908874\pi\) | ||
0.959301 | − | 0.282385i | \(-0.0911255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 70.9475 | 0.0803483 | 0.0401741 | − | 0.999193i | \(-0.487209\pi\) | ||||
0.0401741 | + | 0.999193i | \(0.487209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 908.994i | 1.02711i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −265.641 | −0.299482 | −0.149741 | − | 0.988725i | \(-0.547844\pi\) | ||||
−0.149741 | + | 0.988725i | \(0.547844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 110.786i | 0.124619i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6699.87i | 7.51949i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1206.85i | 1.35146i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 237.204i | 0.265032i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 523.708 | − | 757.351i | 0.583843 | − | 0.844316i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −110.054 | −0.122419 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 526.478 | 0.584327 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −268.402 | −0.297234 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 142.843 | 0.157838 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 845.489i | − | 0.932182i | −0.884737 | − | 0.466091i | \(-0.845662\pi\) | ||
0.884737 | − | 0.466091i | \(-0.154338\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −327.437 | −0.360217 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1170.60i | − | 1.28496i | −0.766303 | − | 0.642479i | \(-0.777906\pi\) | ||
0.766303 | − | 0.642479i | \(-0.222094\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1728.80 | −1.89354 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1303.75 | −1.42486 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 276.527i | − | 0.301556i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 318.340i | 0.346399i | 0.984887 | + | 0.173199i | \(0.0554105\pi\) | ||||
−0.984887 | + | 0.173199i | \(0.944590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −295.602 | −0.320958 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 563.663 | 0.610686 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 257.322i | − | 0.278186i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2567.00i | 2.76915i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −539.462 | −0.580691 | −0.290346 | − | 0.956922i | \(-0.593770\pi\) | ||||
−0.290346 | + | 0.956922i | \(0.593770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 976.872i | 1.04927i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3227.06 | 3.45880 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 916.490i | 0.980203i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.93311i | 0.00419755i | 0.999998 | + | 0.00209878i | \(0.000668062\pi\) | ||||
−0.999998 | + | 0.00209878i | \(0.999332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 110.364i | − | 0.117533i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 805.991i | 0.856526i | 0.903654 | + | 0.428263i | \(0.140874\pi\) | ||||
−0.903654 | + | 0.428263i | \(0.859126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 185.591 | − | 268.390i | 0.196809 | − | 0.284613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −267.757 | −0.283340 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −184.198 | −0.194506 | −0.0972532 | − | 0.995260i | \(-0.531006\pi\) | ||||
−0.0972532 | + | 0.995260i | \(0.531006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 462.446 | 0.487298 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −435.782 | −0.458236 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 15.5674i | − | 0.0163351i | −0.999967 | − | 0.00816757i | \(-0.997400\pi\) | ||
0.999967 | − | 0.00816757i | \(-0.00259985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 553.589 | 0.579675 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1708.61i | − | 1.78538i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 74.0563 | 0.0772225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −908.003 | −0.944852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 4770.30i | − | 4.95358i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 242.996i | 0.251809i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1777.81 | 1.83848 | 0.919238 | − | 0.393702i | \(-0.128806\pi\) | ||||
0.919238 | + | 0.393702i | \(0.128806\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2588.64 | 2.67145 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 111.995i | − | 0.115340i | −0.998336 | − | 0.0576702i | \(-0.981633\pi\) | ||
0.998336 | − | 0.0576702i | \(-0.0183672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 186.757i | 0.191940i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −200.171 | −0.205304 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1090.61i | 1.11629i | 0.829744 | + | 0.558144i | \(0.188486\pi\) | ||||
−0.829744 | + | 0.558144i | \(0.811514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1984.02 | 2.02658 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1228.54i | 1.25234i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1464.77i | 1.49010i | 0.667009 | + | 0.745049i | \(0.267574\pi\) | ||||
−0.667009 | + | 0.745049i | \(0.732426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 286.146i | 0.290504i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 420.310i | − | 0.425846i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −709.271 | − | 490.460i | −0.717160 | − | 0.495915i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.4257 | −0.0579473 | −0.0289736 | − | 0.999580i | \(-0.509224\pi\) | ||||
−0.0289736 | + | 0.999580i | \(0.509224\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1961.01 | 1.97484 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 419.141 | 0.421247 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 859.060 | 0.861644 | 0.430822 | − | 0.902437i | \(-0.358224\pi\) | ||||
0.430822 | + | 0.902437i | \(0.358224\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 5072.90i | − | 5.07798i |
(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 | 1840.3.k.c.321.1 | 16 | ||
4.3 | odd | 2 | 460.3.f.a.321.15 | ✓ | 16 | ||
12.11 | even | 2 | 4140.3.d.a.2161.12 | 16 | |||
20.3 | even | 4 | 2300.3.d.b.1149.12 | 32 | |||
20.7 | even | 4 | 2300.3.d.b.1149.21 | 32 | |||
20.19 | odd | 2 | 2300.3.f.e.1701.2 | 16 | |||
23.22 | odd | 2 | inner | 1840.3.k.c.321.2 | 16 | ||
92.91 | even | 2 | 460.3.f.a.321.16 | yes | 16 | ||
276.275 | odd | 2 | 4140.3.d.a.2161.5 | 16 | |||
460.183 | odd | 4 | 2300.3.d.b.1149.22 | 32 | |||
460.367 | odd | 4 | 2300.3.d.b.1149.11 | 32 | |||
460.459 | even | 2 | 2300.3.f.e.1701.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.3.f.a.321.15 | ✓ | 16 | 4.3 | odd | 2 | ||
460.3.f.a.321.16 | yes | 16 | 92.91 | even | 2 | ||
1840.3.k.c.321.1 | 16 | 1.1 | even | 1 | trivial | ||
1840.3.k.c.321.2 | 16 | 23.22 | odd | 2 | inner | ||
2300.3.d.b.1149.11 | 32 | 460.367 | odd | 4 | |||
2300.3.d.b.1149.12 | 32 | 20.3 | even | 4 | |||
2300.3.d.b.1149.21 | 32 | 20.7 | even | 4 | |||
2300.3.d.b.1149.22 | 32 | 460.183 | odd | 4 | |||
2300.3.f.e.1701.1 | 16 | 460.459 | even | 2 | |||
2300.3.f.e.1701.2 | 16 | 20.19 | odd | 2 | |||
4140.3.d.a.2161.5 | 16 | 276.275 | odd | 2 | |||
4140.3.d.a.2161.12 | 16 | 12.11 | even | 2 |