Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(361,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.i (of order \(3\), degree \(2\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.961 |
Dual form | 1470.2.i.a.361.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 4.00000 | − | 6.92820i | 0.834058 | − | 1.44463i | −0.0607377 | − | 0.998154i | \(-0.519345\pi\) |
0.894795 | − | 0.446476i | \(-0.147321\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | −0.500000 | + | 0.866025i | −0.0912871 | + | 0.158114i | ||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 2.00000 | − | 3.46410i | 0.348155 | − | 0.603023i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | −2.00000 | − | 3.46410i | −0.324443 | − | 0.561951i | ||||
\(39\) | 1.00000 | + | 1.73205i | 0.160128 | + | 0.277350i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 2.00000 | − | 3.46410i | 0.301511 | − | 0.522233i | ||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 4.00000 | + | 6.92820i | 0.589768 | + | 1.02151i | ||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | 1.00000 | + | 1.73205i | 0.138675 | + | 0.240192i | ||||
\(53\) | 5.00000 | + | 8.66025i | 0.686803 | + | 1.18958i | 0.972867 | + | 0.231367i | \(0.0743197\pi\) |
−0.286064 | + | 0.958211i | \(0.592347\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 1.00000 | − | 1.73205i | 0.131306 | − | 0.227429i | ||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | −0.500000 | − | 0.866025i | −0.0645497 | − | 0.111803i | ||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 2.00000 | + | 3.46410i | 0.246183 | + | 0.426401i | ||||
\(67\) | 6.00000 | + | 10.3923i | 0.733017 | + | 1.26962i | 0.955588 | + | 0.294706i | \(0.0952216\pi\) |
−0.222571 | + | 0.974916i | \(0.571445\pi\) | |||||||
\(68\) | −1.00000 | + | 1.73205i | −0.121268 | + | 0.210042i | ||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −5.00000 | − | 8.66025i | −0.585206 | − | 1.01361i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.409644 | − | 0.912245i | \(-0.365653\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −8.00000 | + | 13.8564i | −0.900070 | + | 1.55897i | −0.0726692 | + | 0.997356i | \(0.523152\pi\) |
−0.827401 | + | 0.561611i | \(0.810182\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 2.00000 | − | 3.46410i | 0.215666 | − | 0.373544i | ||||
\(87\) | 1.00000 | + | 1.73205i | 0.107211 | + | 0.185695i | ||||
\(88\) | 2.00000 | + | 3.46410i | 0.213201 | + | 0.369274i | ||||
\(89\) | −5.00000 | + | 8.66025i | −0.529999 | + | 0.917985i | 0.469389 | + | 0.882992i | \(0.344474\pi\) |
−0.999388 | + | 0.0349934i | \(0.988859\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | − | 3.46410i | −0.205196 | − | 0.355409i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | −1.00000 | − | 1.73205i | −0.0990148 | − | 0.171499i | ||||
\(103\) | 4.00000 | − | 6.92820i | 0.394132 | − | 0.682656i | −0.598858 | − | 0.800855i | \(-0.704379\pi\) |
0.992990 | + | 0.118199i | \(0.0377120\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0000 | −0.971286 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | 2.00000 | − | 3.46410i | 0.190693 | − | 0.330289i | ||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | −2.00000 | + | 3.46410i | −0.187317 | + | 0.324443i | ||||
\(115\) | 4.00000 | + | 6.92820i | 0.373002 | + | 0.646058i | ||||
\(116\) | 1.00000 | + | 1.73205i | 0.0928477 | + | 0.160817i | ||||
\(117\) | 1.00000 | − | 1.73205i | 0.0924500 | − | 0.160128i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | −7.00000 | − | 12.1244i | −0.633750 | − | 1.09769i | ||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | + | 3.46410i | 0.176090 | + | 0.304997i | ||||
\(130\) | 1.00000 | + | 1.73205i | 0.0877058 | + | 0.151911i | ||||
\(131\) | −10.0000 | + | 17.3205i | −0.873704 | + | 1.51330i | −0.0155672 | + | 0.999879i | \(0.504955\pi\) |
−0.858137 | + | 0.513421i | \(0.828378\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −1.00000 | − | 1.73205i | −0.0857493 | − | 0.148522i | ||||
\(137\) | −5.00000 | − | 8.66025i | −0.427179 | − | 0.739895i | 0.569442 | − | 0.822031i | \(-0.307159\pi\) |
−0.996621 | + | 0.0821359i | \(0.973826\pi\) | |||||||
\(138\) | 4.00000 | − | 6.92820i | 0.340503 | − | 0.589768i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.00000 | − | 6.92820i | 0.335673 | − | 0.581402i | ||||
\(143\) | −4.00000 | − | 6.92820i | −0.334497 | − | 0.579365i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 1.00000 | − | 1.73205i | 0.0830455 | − | 0.143839i | ||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | 5.00000 | − | 8.66025i | 0.409616 | − | 0.709476i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.994847 | + | 0.101391i | \(0.0323294\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | −2.00000 | + | 3.46410i | −0.162221 | + | 0.280976i | ||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00000 | − | 1.73205i | 0.0800641 | − | 0.138675i | ||||
\(157\) | 9.00000 | + | 15.5885i | 0.718278 | + | 1.24409i | 0.961681 | + | 0.274169i | \(0.0884028\pi\) |
−0.243403 | + | 0.969925i | \(0.578264\pi\) | |||||||
\(158\) | −8.00000 | − | 13.8564i | −0.636446 | − | 1.10236i | ||||
\(159\) | 5.00000 | − | 8.66025i | 0.396526 | − | 0.686803i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −10.0000 | + | 17.3205i | −0.783260 | + | 1.35665i | 0.146772 | + | 0.989170i | \(0.453112\pi\) |
−0.930033 | + | 0.367477i | \(0.880222\pi\) | |||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | 2.00000 | + | 3.46410i | 0.155700 | + | 0.269680i | ||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −1.00000 | + | 1.73205i | −0.0766965 | + | 0.132842i | ||||
\(171\) | −2.00000 | − | 3.46410i | −0.152944 | − | 0.264906i | ||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | 9.00000 | − | 15.5885i | 0.684257 | − | 1.18517i | −0.289412 | − | 0.957205i | \(-0.593460\pi\) |
0.973670 | − | 0.227964i | \(-0.0732068\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −6.00000 | + | 10.3923i | −0.450988 | + | 0.781133i | ||||
\(178\) | −5.00000 | − | 8.66025i | −0.374766 | − | 0.649113i | ||||
\(179\) | −2.00000 | − | 3.46410i | −0.149487 | − | 0.258919i | 0.781551 | − | 0.623841i | \(-0.214429\pi\) |
−0.931038 | + | 0.364922i | \(0.881096\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0000 | 1.03491 | ||||||||
\(184\) | 4.00000 | − | 6.92820i | 0.294884 | − | 0.510754i | ||||
\(185\) | −3.00000 | − | 5.19615i | −0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | − | 6.92820i | 0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 8.00000 | − | 13.8564i | 0.578860 | − | 1.00261i | −0.416751 | − | 0.909021i | \(-0.636831\pi\) |
0.995610 | − | 0.0935936i | \(-0.0298354\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −1.00000 | − | 1.73205i | −0.0719816 | − | 0.124676i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | −1.00000 | + | 1.73205i | −0.0717958 | + | 0.124354i | ||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 2.00000 | − | 3.46410i | 0.142134 | − | 0.246183i | ||||
\(199\) | 12.0000 | + | 20.7846i | 0.850657 | + | 1.47338i | 0.880616 | + | 0.473831i | \(0.157129\pi\) |
−0.0299585 | + | 0.999551i | \(0.509538\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 6.00000 | − | 10.3923i | 0.423207 | − | 0.733017i | ||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | 4.00000 | + | 6.92820i | 0.278019 | + | 0.481543i | ||||
\(208\) | 1.00000 | − | 1.73205i | 0.0693375 | − | 0.120096i | ||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 5.00000 | − | 8.66025i | 0.343401 | − | 0.594789i | ||||
\(213\) | 4.00000 | + | 6.92820i | 0.274075 | + | 0.474713i | ||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | 2.00000 | − | 3.46410i | 0.136399 | − | 0.236250i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.0000 | 0.948200 | ||||||||
\(219\) | −5.00000 | + | 8.66025i | −0.337869 | + | 0.585206i | ||||
\(220\) | 2.00000 | + | 3.46410i | 0.134840 | + | 0.233550i | ||||
\(221\) | 2.00000 | + | 3.46410i | 0.134535 | + | 0.233021i | ||||
\(222\) | −3.00000 | + | 5.19615i | −0.201347 | + | 0.348743i | ||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −9.00000 | + | 15.5885i | −0.598671 | + | 1.03693i | ||||
\(227\) | −2.00000 | − | 3.46410i | −0.132745 | − | 0.229920i | 0.791989 | − | 0.610535i | \(-0.209046\pi\) |
−0.924734 | + | 0.380615i | \(0.875712\pi\) | |||||||
\(228\) | −2.00000 | − | 3.46410i | −0.132453 | − | 0.229416i | ||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 11.0000 | − | 19.0526i | 0.720634 | − | 1.24817i | −0.240112 | − | 0.970745i | \(-0.577184\pi\) |
0.960746 | − | 0.277429i | \(-0.0894825\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −0.500000 | + | 0.866025i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | 7.00000 | + | 12.1244i | 0.450910 | + | 0.780998i | 0.998443 | − | 0.0557856i | \(-0.0177663\pi\) |
−0.547533 | + | 0.836784i | \(0.684433\pi\) | |||||||
\(242\) | −2.50000 | − | 4.33013i | −0.160706 | − | 0.278351i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 14.0000 | 0.896258 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 4.00000 | − | 6.92820i | 0.254514 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | + | 10.3923i | 0.380235 | + | 0.658586i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.0000 | 2.01182 | ||||||||
\(254\) | 8.00000 | − | 13.8564i | 0.501965 | − | 0.869428i | ||||
\(255\) | −1.00000 | − | 1.73205i | −0.0626224 | − | 0.108465i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.00000 | − | 12.1244i | 0.436648 | − | 0.756297i | −0.560781 | − | 0.827964i | \(-0.689499\pi\) |
0.997429 | + | 0.0716680i | \(0.0228322\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 1.00000 | − | 1.73205i | 0.0618984 | − | 0.107211i | ||||
\(262\) | −10.0000 | − | 17.3205i | −0.617802 | − | 1.07006i | ||||
\(263\) | −4.00000 | − | 6.92820i | −0.246651 | − | 0.427211i | 0.715944 | − | 0.698158i | \(-0.245997\pi\) |
−0.962594 | + | 0.270947i | \(0.912663\pi\) | |||||||
\(264\) | 2.00000 | − | 3.46410i | 0.123091 | − | 0.213201i | ||||
\(265\) | −10.0000 | −0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000 | 0.611990 | ||||||||
\(268\) | 6.00000 | − | 10.3923i | 0.366508 | − | 0.634811i | ||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 4.00000 | + | 6.92820i | 0.240772 | + | 0.417029i | ||||
\(277\) | −11.0000 | − | 19.0526i | −0.660926 | − | 1.14476i | −0.980373 | − | 0.197153i | \(-0.936830\pi\) |
0.319447 | − | 0.947604i | \(-0.396503\pi\) | |||||||
\(278\) | 2.00000 | − | 3.46410i | 0.119952 | − | 0.207763i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | − | 24.2487i | −0.832214 | − | 1.44144i | −0.896279 | − | 0.443491i | \(-0.853740\pi\) |
0.0640654 | − | 0.997946i | \(-0.479593\pi\) | |||||||
\(284\) | 4.00000 | + | 6.92820i | 0.237356 | + | 0.411113i | ||||
\(285\) | −2.00000 | + | 3.46410i | −0.118470 | + | 0.205196i | ||||
\(286\) | 8.00000 | 0.473050 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 1.00000 | + | 1.73205i | 0.0587220 | + | 0.101710i | ||||
\(291\) | −1.00000 | − | 1.73205i | −0.0586210 | − | 0.101535i | ||||
\(292\) | −5.00000 | + | 8.66025i | −0.292603 | + | 0.506803i | ||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | −3.00000 | + | 5.19615i | −0.174371 | + | 0.302020i | ||||
\(297\) | 2.00000 | + | 3.46410i | 0.116052 | + | 0.201008i | ||||
\(298\) | 5.00000 | + | 8.66025i | 0.289642 | + | 0.501675i | ||||
\(299\) | −8.00000 | + | 13.8564i | −0.462652 | + | 0.801337i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | −3.00000 | + | 5.19615i | −0.172345 | + | 0.298511i | ||||
\(304\) | −2.00000 | − | 3.46410i | −0.114708 | − | 0.198680i | ||||
\(305\) | −7.00000 | − | 12.1244i | −0.400819 | − | 0.694239i | ||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | + | 6.92820i | 0.226819 | + | 0.392862i | 0.956864 | − | 0.290537i | \(-0.0938340\pi\) |
−0.730044 | + | 0.683400i | \(0.760501\pi\) | |||||||
\(312\) | 1.00000 | + | 1.73205i | 0.0566139 | + | 0.0980581i | ||||
\(313\) | 3.00000 | − | 5.19615i | 0.169570 | − | 0.293704i | −0.768699 | − | 0.639611i | \(-0.779095\pi\) |
0.938269 | + | 0.345907i | \(0.112429\pi\) | |||||||
\(314\) | −18.0000 | −1.01580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | 1.00000 | − | 1.73205i | 0.0561656 | − | 0.0972817i | −0.836576 | − | 0.547852i | \(-0.815446\pi\) |
0.892741 | + | 0.450570i | \(0.148779\pi\) | |||||||
\(318\) | 5.00000 | + | 8.66025i | 0.280386 | + | 0.485643i | ||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 1.00000 | + | 1.73205i | 0.0554700 | + | 0.0960769i | ||||
\(326\) | −10.0000 | − | 17.3205i | −0.553849 | − | 0.959294i | ||||
\(327\) | −7.00000 | + | 12.1244i | −0.387101 | + | 0.670478i | ||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.00000 | −0.220193 | ||||||||
\(331\) | −6.00000 | + | 10.3923i | −0.329790 | + | 0.571213i | −0.982470 | − | 0.186421i | \(-0.940311\pi\) |
0.652680 | + | 0.757634i | \(0.273645\pi\) | |||||||
\(332\) | 6.00000 | + | 10.3923i | 0.329293 | + | 0.570352i | ||||
\(333\) | −3.00000 | − | 5.19615i | −0.164399 | − | 0.284747i | ||||
\(334\) | 4.00000 | − | 6.92820i | 0.218870 | − | 0.379094i | ||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | −9.00000 | − | 15.5885i | −0.488813 | − | 0.846649i | ||||
\(340\) | −1.00000 | − | 1.73205i | −0.0542326 | − | 0.0939336i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 4.00000 | − | 6.92820i | 0.215353 | − | 0.373002i | ||||
\(346\) | 9.00000 | + | 15.5885i | 0.483843 | + | 0.838041i | ||||
\(347\) | 2.00000 | + | 3.46410i | 0.107366 | + | 0.185963i | 0.914702 | − | 0.404128i | \(-0.132425\pi\) |
−0.807337 | + | 0.590091i | \(0.799092\pi\) | |||||||
\(348\) | 1.00000 | − | 1.73205i | 0.0536056 | − | 0.0928477i | ||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 2.00000 | − | 3.46410i | 0.106600 | − | 0.184637i | ||||
\(353\) | 7.00000 | + | 12.1244i | 0.372572 | + | 0.645314i | 0.989960 | − | 0.141344i | \(-0.0451425\pi\) |
−0.617388 | + | 0.786659i | \(0.711809\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | 4.00000 | − | 6.92820i | 0.212298 | − | 0.367711i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000 | 0.211407 | ||||||||
\(359\) | −12.0000 | + | 20.7846i | −0.633336 | + | 1.09697i | 0.353529 | + | 0.935423i | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | −3.00000 | + | 5.19615i | −0.157676 | + | 0.273104i | ||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | −7.00000 | + | 12.1244i | −0.365896 | + | 0.633750i | ||||
\(367\) | 16.0000 | + | 27.7128i | 0.835193 | + | 1.44660i | 0.893873 | + | 0.448320i | \(0.147978\pi\) |
−0.0586798 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(368\) | 4.00000 | + | 6.92820i | 0.208514 | + | 0.361158i | ||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 4.00000 | + | 6.92820i | 0.206835 | + | 0.358249i | ||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | −2.00000 | + | 3.46410i | −0.102598 | + | 0.177705i | ||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | 8.00000 | + | 13.8564i | 0.409316 | + | 0.708955i | ||||
\(383\) | −8.00000 | + | 13.8564i | −0.408781 | + | 0.708029i | −0.994753 | − | 0.102302i | \(-0.967379\pi\) |
0.585973 | + | 0.810331i | \(0.300713\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | −1.00000 | − | 1.73205i | −0.0507673 | − | 0.0879316i | ||||
\(389\) | 13.0000 | + | 22.5167i | 0.659126 | + | 1.14164i | 0.980842 | + | 0.194804i | \(0.0624070\pi\) |
−0.321716 | + | 0.946836i | \(0.604260\pi\) | |||||||
\(390\) | 1.00000 | − | 1.73205i | 0.0506370 | − | 0.0877058i | ||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.0000 | 1.00887 | ||||||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | −8.00000 | − | 13.8564i | −0.402524 | − | 0.697191i | ||||
\(396\) | 2.00000 | + | 3.46410i | 0.100504 | + | 0.174078i | ||||
\(397\) | −15.0000 | + | 25.9808i | −0.752828 | + | 1.30394i | 0.193618 | + | 0.981077i | \(0.437978\pi\) |
−0.946447 | + | 0.322860i | \(0.895356\pi\) | |||||||
\(398\) | −24.0000 | −1.20301 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 7.00000 | − | 12.1244i | 0.349563 | − | 0.605461i | −0.636609 | − | 0.771187i | \(-0.719663\pi\) |
0.986172 | + | 0.165726i | \(0.0529966\pi\) | |||||||
\(402\) | 6.00000 | + | 10.3923i | 0.299253 | + | 0.518321i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.00000 | + | 5.19615i | −0.149256 | + | 0.258518i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | −1.00000 | + | 1.73205i | −0.0495074 | + | 0.0857493i | ||||
\(409\) | 19.0000 | + | 32.9090i | 0.939490 | + | 1.62724i | 0.766426 | + | 0.642333i | \(0.222033\pi\) |
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(410\) | 3.00000 | + | 5.19615i | 0.148159 | + | 0.256620i | ||||
\(411\) | −5.00000 | + | 8.66025i | −0.246632 | + | 0.427179i | ||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.00000 | −0.393179 | ||||||||
\(415\) | 6.00000 | − | 10.3923i | 0.294528 | − | 0.510138i | ||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | 2.00000 | + | 3.46410i | 0.0979404 | + | 0.169638i | ||||
\(418\) | 8.00000 | − | 13.8564i | 0.391293 | − | 0.677739i | ||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 6.00000 | − | 10.3923i | 0.292075 | − | 0.505889i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.00000 | + | 8.66025i | 0.242821 | + | 0.420579i | ||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | −4.00000 | + | 6.92820i | −0.193122 | + | 0.334497i | ||||
\(430\) | 2.00000 | + | 3.46410i | 0.0964486 | + | 0.167054i | ||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | 16.0000 | + | 27.7128i | 0.765384 | + | 1.32568i | ||||
\(438\) | −5.00000 | − | 8.66025i | −0.238909 | − | 0.413803i | ||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | −4.00000 | −0.190693 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | −0.190261 | ||||||||
\(443\) | 18.0000 | − | 31.1769i | 0.855206 | − | 1.48126i | −0.0212481 | − | 0.999774i | \(-0.506764\pi\) |
0.876454 | − | 0.481486i | \(-0.159903\pi\) | |||||||
\(444\) | −3.00000 | − | 5.19615i | −0.142374 | − | 0.246598i | ||||
\(445\) | −5.00000 | − | 8.66025i | −0.237023 | − | 0.410535i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | −0.500000 | + | 0.866025i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | −12.0000 | − | 20.7846i | −0.565058 | − | 0.978709i | ||||
\(452\) | −9.00000 | − | 15.5885i | −0.423324 | − | 0.733219i | ||||
\(453\) | 4.00000 | − | 6.92820i | 0.187936 | − | 0.325515i | ||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | −5.00000 | + | 8.66025i | −0.233890 | + | 0.405110i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 4.00000 | − | 6.92820i | 0.186501 | − | 0.323029i | ||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 1.00000 | − | 1.73205i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.0000 | + | 19.0526i | 0.509565 | + | 0.882593i | ||||
\(467\) | 6.00000 | − | 10.3923i | 0.277647 | − | 0.480899i | −0.693153 | − | 0.720791i | \(-0.743779\pi\) |
0.970799 | + | 0.239892i | \(0.0771121\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | − | 15.5885i | 0.414698 | − | 0.718278i | ||||
\(472\) | −6.00000 | − | 10.3923i | −0.276172 | − | 0.478345i | ||||
\(473\) | −8.00000 | − | 13.8564i | −0.367840 | − | 0.637118i | ||||
\(474\) | −8.00000 | + | 13.8564i | −0.367452 | + | 0.636446i | ||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.0000 | −0.457869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | − | 27.7128i | −0.731059 | − | 1.26623i | −0.956431 | − | 0.291958i | \(-0.905693\pi\) |
0.225372 | − | 0.974273i | \(-0.427640\pi\) | |||||||
\(480\) | −0.500000 | − | 0.866025i | −0.0228218 | − | 0.0395285i | ||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | −14.0000 | −0.637683 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 4.00000 | + | 6.92820i | 0.181257 | + | 0.313947i | 0.942309 | − | 0.334744i | \(-0.108650\pi\) |
−0.761052 | + | 0.648691i | \(0.775317\pi\) | |||||||
\(488\) | −7.00000 | + | 12.1244i | −0.316875 | + | 0.548844i | ||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 3.00000 | − | 5.19615i | 0.135250 | − | 0.234261i | ||||
\(493\) | 2.00000 | + | 3.46410i | 0.0900755 | + | 0.156015i | ||||
\(494\) | 4.00000 | + | 6.92820i | 0.179969 | + | 0.311715i | ||||
\(495\) | 2.00000 | − | 3.46410i | 0.0898933 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.0000 | −0.537733 | ||||||||
\(499\) | 6.00000 | − | 10.3923i | 0.268597 | − | 0.465223i | −0.699903 | − | 0.714238i | \(-0.746773\pi\) |
0.968500 | + | 0.249015i | \(0.0801067\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 4.00000 | + | 6.92820i | 0.178707 | + | 0.309529i | ||||
\(502\) | −6.00000 | + | 10.3923i | −0.267793 | + | 0.463831i | ||||
\(503\) | 40.0000 | 1.78351 | 0.891756 | − | 0.452517i | \(-0.149474\pi\) | ||||
0.891756 | + | 0.452517i | \(0.149474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | −16.0000 | + | 27.7128i | −0.711287 | + | 1.23198i | ||||
\(507\) | 4.50000 | + | 7.79423i | 0.199852 | + | 0.346154i | ||||
\(508\) | 8.00000 | + | 13.8564i | 0.354943 | + | 0.614779i | ||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 2.00000 | 0.0885615 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.00000 | + | 3.46410i | −0.0883022 | + | 0.152944i | ||||
\(514\) | 7.00000 | + | 12.1244i | 0.308757 | + | 0.534782i | ||||
\(515\) | 4.00000 | + | 6.92820i | 0.176261 | + | 0.305293i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | 1.00000 | − | 1.73205i | 0.0438529 | − | 0.0759555i | ||||
\(521\) | 3.00000 | + | 5.19615i | 0.131432 | + | 0.227648i | 0.924229 | − | 0.381839i | \(-0.124709\pi\) |
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(522\) | 1.00000 | + | 1.73205i | 0.0437688 | + | 0.0758098i | ||||
\(523\) | 10.0000 | − | 17.3205i | 0.437269 | − | 0.757373i | −0.560208 | − | 0.828352i | \(-0.689279\pi\) |
0.997478 | + | 0.0709788i | \(0.0226123\pi\) | |||||||
\(524\) | 20.0000 | 0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.00000 | 0.348817 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.00000 | + | 3.46410i | 0.0870388 | + | 0.150756i | ||||
\(529\) | −20.5000 | − | 35.5070i | −0.891304 | − | 1.54378i | ||||
\(530\) | 5.00000 | − | 8.66025i | 0.217186 | − | 0.376177i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | −5.00000 | + | 8.66025i | −0.216371 | + | 0.374766i | ||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | −2.00000 | + | 3.46410i | −0.0863064 | + | 0.149487i | ||||
\(538\) | −18.0000 | −0.776035 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 17.0000 | − | 29.4449i | 0.730887 | − | 1.26593i | −0.225617 | − | 0.974216i | \(-0.572440\pi\) |
0.956504 | − | 0.291718i | \(-0.0942267\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | −3.00000 | − | 5.19615i | −0.128742 | − | 0.222988i | ||||
\(544\) | −1.00000 | + | 1.73205i | −0.0428746 | + | 0.0742611i | ||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | −5.00000 | + | 8.66025i | −0.213589 | + | 0.369948i | ||||
\(549\) | −7.00000 | − | 12.1244i | −0.298753 | − | 0.517455i | ||||
\(550\) | 2.00000 | + | 3.46410i | 0.0852803 | + | 0.147710i | ||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | −8.00000 | −0.340503 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | −3.00000 | + | 5.19615i | −0.127343 | + | 0.220564i | ||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 9.00000 | + | 15.5885i | 0.381342 | + | 0.660504i | 0.991254 | − | 0.131965i | \(-0.0421286\pi\) |
−0.609912 | + | 0.792469i | \(0.708795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 3.00000 | − | 5.19615i | 0.126547 | − | 0.219186i | ||||
\(563\) | −10.0000 | − | 17.3205i | −0.421450 | − | 0.729972i | 0.574632 | − | 0.818412i | \(-0.305145\pi\) |
−0.996082 | + | 0.0884397i | \(0.971812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | + | 15.5885i | −0.378633 | + | 0.655811i | ||||
\(566\) | 28.0000 | 1.17693 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | −13.0000 | + | 22.5167i | −0.544988 | + | 0.943948i | 0.453619 | + | 0.891196i | \(0.350133\pi\) |
−0.998608 | + | 0.0527519i | \(0.983201\pi\) | |||||||
\(570\) | −2.00000 | − | 3.46410i | −0.0837708 | − | 0.145095i | ||||
\(571\) | −14.0000 | − | 24.2487i | −0.585882 | − | 1.01478i | −0.994765 | − | 0.102190i | \(-0.967415\pi\) |
0.408883 | − | 0.912587i | \(-0.365918\pi\) | |||||||
\(572\) | −4.00000 | + | 6.92820i | −0.167248 | + | 0.289683i | ||||
\(573\) | −16.0000 | −0.668410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.00000 | −0.333623 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −17.0000 | − | 29.4449i | −0.707719 | − | 1.22581i | −0.965701 | − | 0.259656i | \(-0.916391\pi\) |
0.257982 | − | 0.966150i | \(-0.416942\pi\) | |||||||
\(578\) | 6.50000 | + | 11.2583i | 0.270364 | + | 0.468285i | ||||
\(579\) | −1.00000 | + | 1.73205i | −0.0415586 | + | 0.0719816i | ||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | −20.0000 | + | 34.6410i | −0.828315 | + | 1.43468i | ||||
\(584\) | −5.00000 | − | 8.66025i | −0.206901 | − | 0.358364i | ||||
\(585\) | 1.00000 | + | 1.73205i | 0.0413449 | + | 0.0716115i | ||||
\(586\) | −3.00000 | + | 5.19615i | −0.123929 | + | 0.214651i | ||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −6.00000 | + | 10.3923i | −0.247016 | + | 0.427844i | ||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | −3.00000 | − | 5.19615i | −0.123299 | − | 0.213561i | ||||
\(593\) | 15.0000 | − | 25.9808i | 0.615976 | − | 1.06690i | −0.374236 | − | 0.927333i | \(-0.622095\pi\) |
0.990212 | − | 0.139569i | \(-0.0445716\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | 12.0000 | − | 20.7846i | 0.491127 | − | 0.850657i | ||||
\(598\) | −8.00000 | − | 13.8564i | −0.327144 | − | 0.566631i | ||||
\(599\) | 12.0000 | + | 20.7846i | 0.490307 | + | 0.849236i | 0.999938 | − | 0.0111569i | \(-0.00355143\pi\) |
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | −38.0000 | −1.55005 | −0.775026 | − | 0.631929i | \(-0.782263\pi\) | ||||
−0.775026 | + | 0.631929i | \(0.782263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | −2.50000 | − | 4.33013i | −0.101639 | − | 0.176045i | ||||
\(606\) | −3.00000 | − | 5.19615i | −0.121867 | − | 0.211079i | ||||
\(607\) | −8.00000 | + | 13.8564i | −0.324710 | + | 0.562414i | −0.981454 | − | 0.191700i | \(-0.938600\pi\) |
0.656744 | + | 0.754114i | \(0.271933\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.0000 | 0.566843 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.00000 | − | 1.73205i | −0.0404226 | − | 0.0700140i | ||||
\(613\) | −3.00000 | − | 5.19615i | −0.121169 | − | 0.209871i | 0.799060 | − | 0.601251i | \(-0.205331\pi\) |
−0.920229 | + | 0.391381i | \(0.871998\pi\) | |||||||
\(614\) | −10.0000 | + | 17.3205i | −0.403567 | + | 0.698999i | ||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0000 | −0.885687 | −0.442843 | − | 0.896599i | \(-0.646030\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(618\) | 4.00000 | − | 6.92820i | 0.160904 | − | 0.278693i | ||||
\(619\) | 2.00000 | + | 3.46410i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | − | 6.92820i | 0.160514 | − | 0.278019i | ||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 3.00000 | + | 5.19615i | 0.119904 | + | 0.207680i | ||||
\(627\) | 8.00000 | + | 13.8564i | 0.319489 | + | 0.553372i | ||||
\(628\) | 9.00000 | − | 15.5885i | 0.359139 | − | 0.622047i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | −8.00000 | + | 13.8564i | −0.318223 | + | 0.551178i | ||||
\(633\) | 6.00000 | + | 10.3923i | 0.238479 | + | 0.413057i | ||||
\(634\) | 1.00000 | + | 1.73205i | 0.0397151 | + | 0.0687885i | ||||
\(635\) | 8.00000 | − | 13.8564i | 0.317470 | − | 0.549875i | ||||
\(636\) | −10.0000 | −0.396526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.00000 | 0.316723 | ||||||||
\(639\) | 4.00000 | − | 6.92820i | 0.158238 | − | 0.274075i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | −17.0000 | − | 29.4449i | −0.671460 | − | 1.16300i | −0.977490 | − | 0.210981i | \(-0.932334\pi\) |
0.306031 | − | 0.952022i | \(-0.400999\pi\) | |||||||
\(642\) | −6.00000 | + | 10.3923i | −0.236801 | + | 0.410152i | ||||
\(643\) | −28.0000 | −1.10421 | −0.552106 | − | 0.833774i | \(-0.686176\pi\) | ||||
−0.552106 | + | 0.833774i | \(0.686176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | −4.00000 | + | 6.92820i | −0.157378 | + | 0.272587i | ||||
\(647\) | −12.0000 | − | 20.7846i | −0.471769 | − | 0.817127i | 0.527710 | − | 0.849425i | \(-0.323051\pi\) |
−0.999478 | + | 0.0322975i | \(0.989718\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 24.0000 | − | 41.5692i | 0.942082 | − | 1.63173i | ||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.0000 | 0.783260 | ||||||||
\(653\) | −7.00000 | + | 12.1244i | −0.273931 | + | 0.474463i | −0.969865 | − | 0.243643i | \(-0.921657\pi\) |
0.695934 | + | 0.718106i | \(0.254991\pi\) | |||||||
\(654\) | −7.00000 | − | 12.1244i | −0.273722 | − | 0.474100i | ||||
\(655\) | −10.0000 | − | 17.3205i | −0.390732 | − | 0.676768i | ||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 2.00000 | − | 3.46410i | 0.0778499 | − | 0.134840i | ||||
\(661\) | −19.0000 | − | 32.9090i | −0.739014 | − | 1.28001i | −0.952940 | − | 0.303160i | \(-0.901958\pi\) |
0.213925 | − | 0.976850i | \(-0.431375\pi\) | |||||||
\(662\) | −6.00000 | − | 10.3923i | −0.233197 | − | 0.403908i | ||||
\(663\) | 2.00000 | − | 3.46410i | 0.0776736 | − | 0.134535i | ||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | −8.00000 | + | 13.8564i | −0.309761 | + | 0.536522i | ||||
\(668\) | 4.00000 | + | 6.92820i | 0.154765 | + | 0.268060i | ||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | 6.00000 | − | 10.3923i | 0.231800 | − | 0.401490i | ||||
\(671\) | −56.0000 | −2.16186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0000 | −1.15642 | −0.578208 | − | 0.815890i | \(-0.696248\pi\) | ||||
−0.578208 | + | 0.815890i | \(0.696248\pi\) | |||||||
\(674\) | −9.00000 | + | 15.5885i | −0.346667 | + | 0.600445i | ||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | 13.0000 | − | 22.5167i | 0.499631 | − | 0.865386i | −0.500369 | − | 0.865812i | \(-0.666802\pi\) |
1.00000 | 0.000426509i | \(0.000135762\pi\) | ||||||||
\(678\) | 18.0000 | 0.691286 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.00000 | 0.0766965 | ||||||||
\(681\) | −2.00000 | + | 3.46410i | −0.0766402 | + | 0.132745i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | − | 10.3923i | −0.229584 | − | 0.397650i | 0.728101 | − | 0.685470i | \(-0.240403\pi\) |
−0.957685 | + | 0.287819i | \(0.907070\pi\) | |||||||
\(684\) | −2.00000 | + | 3.46410i | −0.0764719 | + | 0.132453i | ||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | −10.0000 | − | 17.3205i | −0.380970 | − | 0.659859i | ||||
\(690\) | 4.00000 | + | 6.92820i | 0.152277 | + | 0.263752i | ||||
\(691\) | −18.0000 | + | 31.1769i | −0.684752 | + | 1.18603i | 0.288762 | + | 0.957401i | \(0.406756\pi\) |
−0.973515 | + | 0.228625i | \(0.926577\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 2.00000 | − | 3.46410i | 0.0758643 | − | 0.131401i | ||||
\(696\) | 1.00000 | + | 1.73205i | 0.0379049 | + | 0.0656532i | ||||
\(697\) | 6.00000 | + | 10.3923i | 0.227266 | + | 0.393637i | ||||
\(698\) | −7.00000 | + | 12.1244i | −0.264954 | + | 0.458914i | ||||
\(699\) | −22.0000 | −0.832116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 1.00000 | − | 1.73205i | 0.0377426 | − | 0.0653720i | ||||
\(703\) | −12.0000 | − | 20.7846i | −0.452589 | − | 0.783906i | ||||
\(704\) | 2.00000 | + | 3.46410i | 0.0753778 | + | 0.130558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0000 | −0.526897 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.0000 | 0.450988 | ||||||||
\(709\) | 13.0000 | − | 22.5167i | 0.488225 | − | 0.845631i | −0.511683 | − | 0.859174i | \(-0.670978\pi\) |
0.999908 | + | 0.0135434i | \(0.00431112\pi\) | |||||||
\(710\) | 4.00000 | + | 6.92820i | 0.150117 | + | 0.260011i | ||||
\(711\) | −8.00000 | − | 13.8564i | −0.300023 | − | 0.519656i | ||||
\(712\) | −5.00000 | + | 8.66025i | −0.187383 | + | 0.324557i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | 0.299183 | ||||||||
\(716\) | −2.00000 | + | 3.46410i | −0.0747435 | + | 0.129460i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.0000 | − | 20.7846i | −0.447836 | − | 0.775675i | ||||
\(719\) | 8.00000 | − | 13.8564i | 0.298350 | − | 0.516757i | −0.677409 | − | 0.735607i | \(-0.736897\pi\) |
0.975759 | + | 0.218850i | \(0.0702305\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.00000 | −0.111648 | ||||||||
\(723\) | 7.00000 | − | 12.1244i | 0.260333 | − | 0.450910i | ||||
\(724\) | −3.00000 | − | 5.19615i | −0.111494 | − | 0.193113i | ||||
\(725\) | 1.00000 | + | 1.73205i | 0.0371391 | + | 0.0643268i | ||||
\(726\) | −2.50000 | + | 4.33013i | −0.0927837 | + | 0.160706i | ||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.00000 | + | 8.66025i | −0.185058 | + | 0.320530i | ||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | −7.00000 | − | 12.1244i | −0.258727 | − | 0.448129i | ||||
\(733\) | −23.0000 | + | 39.8372i | −0.849524 | + | 1.47142i | 0.0321090 | + | 0.999484i | \(0.489778\pi\) |
−0.881633 | + | 0.471935i | \(0.843556\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | −24.0000 | + | 41.5692i | −0.884051 | + | 1.53122i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | 14.0000 | + | 24.2487i | 0.514998 | + | 0.892003i | 0.999849 | + | 0.0174060i | \(0.00554079\pi\) |
−0.484850 | + | 0.874597i | \(0.661126\pi\) | |||||||
\(740\) | −3.00000 | + | 5.19615i | −0.110282 | + | 0.191014i | ||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | + | 8.66025i | 0.183186 | + | 0.317287i | ||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −8.00000 | + | 13.8564i | −0.291924 | + | 0.505627i | −0.974265 | − | 0.225407i | \(-0.927629\pi\) |
0.682341 | + | 0.731034i | \(0.260962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.00000 | − | 10.3923i | −0.218652 | − | 0.378717i | ||||
\(754\) | −2.00000 | + | 3.46410i | −0.0728357 | + | 0.126155i | ||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | −14.0000 | + | 24.2487i | −0.508503 | + | 0.880753i | ||||
\(759\) | −16.0000 | − | 27.7128i | −0.580763 | − | 1.00591i | ||||
\(760\) | −2.00000 | − | 3.46410i | −0.0725476 | − | 0.125656i | ||||
\(761\) | −5.00000 | + | 8.66025i | −0.181250 | + | 0.313934i | −0.942306 | − | 0.334752i | \(-0.891348\pi\) |
0.761057 | + | 0.648686i | \(0.224681\pi\) | |||||||
\(762\) | −16.0000 | −0.579619 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | −1.00000 | + | 1.73205i | −0.0361551 | + | 0.0626224i | ||||
\(766\) | −8.00000 | − | 13.8564i | −0.289052 | − | 0.500652i | ||||
\(767\) | 12.0000 | + | 20.7846i | 0.433295 | + | 0.750489i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | −1.00000 | + | 1.73205i | −0.0359908 | + | 0.0623379i | ||||
\(773\) | 13.0000 | + | 22.5167i | 0.467578 | + | 0.809868i | 0.999314 | − | 0.0370420i | \(-0.0117935\pi\) |
−0.531736 | + | 0.846910i | \(0.678460\pi\) | |||||||
\(774\) | 2.00000 | + | 3.46410i | 0.0718885 | + | 0.124515i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.0000 | −0.932145 | ||||||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 1.00000 | + | 1.73205i | 0.0358057 | + | 0.0620174i | ||||
\(781\) | −16.0000 | − | 27.7128i | −0.572525 | − | 0.991642i | ||||
\(782\) | 8.00000 | − | 13.8564i | 0.286079 | − | 0.495504i | ||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | −10.0000 | + | 17.3205i | −0.356688 | + | 0.617802i | ||||
\(787\) | −10.0000 | − | 17.3205i | −0.356462 | − | 0.617409i | 0.630905 | − | 0.775860i | \(-0.282684\pi\) |
−0.987367 | + | 0.158450i | \(0.949350\pi\) | |||||||
\(788\) | −3.00000 | − | 5.19615i | −0.106871 | − | 0.185105i | ||||
\(789\) | −4.00000 | + | 6.92820i | −0.142404 | + | 0.246651i | ||||
\(790\) | 16.0000 | 0.569254 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 14.0000 | − | 24.2487i | 0.497155 | − | 0.861097i | ||||
\(794\) | −15.0000 | − | 25.9808i | −0.532330 | − | 0.922023i | ||||
\(795\) | 5.00000 | + | 8.66025i | 0.177332 | + | 0.307148i | ||||
\(796\) | 12.0000 | − | 20.7846i | 0.425329 | − | 0.736691i | ||||
\(797\) | 30.0000 | 1.06265 | 0.531327 | − | 0.847167i | \(-0.321693\pi\) | ||||
0.531327 | + | 0.847167i | \(0.321693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −5.00000 | − | 8.66025i | −0.176666 | − | 0.305995i | ||||
\(802\) | 7.00000 | + | 12.1244i | 0.247179 | + | 0.428126i | ||||
\(803\) | 20.0000 | − | 34.6410i | 0.705785 | − | 1.22245i | ||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.00000 | − | 15.5885i | 0.316815 | − | 0.548740i | ||||
\(808\) | −3.00000 | − | 5.19615i | −0.105540 | − | 0.182800i | ||||
\(809\) | 11.0000 | + | 19.0526i | 0.386739 | + | 0.669852i | 0.992009 | − | 0.126168i | \(-0.0402680\pi\) |
−0.605269 | + | 0.796021i | \(0.706935\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0000 | 0.561144 | ||||||||
\(814\) | 12.0000 | − | 20.7846i | 0.420600 | − | 0.728500i | ||||
\(815\) | −10.0000 | − | 17.3205i | −0.350285 | − | 0.606711i | ||||
\(816\) | −1.00000 | − | 1.73205i | −0.0350070 | − | 0.0606339i | ||||
\(817\) | 8.00000 | − | 13.8564i | 0.279885 | − | 0.484774i | ||||
\(818\) | −38.0000 | −1.32864 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | −11.0000 | + | 19.0526i | −0.383903 | + | 0.664939i | −0.991616 | − | 0.129217i | \(-0.958754\pi\) |
0.607714 | + | 0.794156i | \(0.292087\pi\) | |||||||
\(822\) | −5.00000 | − | 8.66025i | −0.174395 | − | 0.302061i | ||||
\(823\) | 12.0000 | + | 20.7846i | 0.418294 | + | 0.724506i | 0.995768 | − | 0.0919029i | \(-0.0292950\pi\) |
−0.577474 | + | 0.816409i | \(0.695962\pi\) | |||||||
\(824\) | 4.00000 | − | 6.92820i | 0.139347 | − | 0.241355i | ||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 4.00000 | − | 6.92820i | 0.139010 | − | 0.240772i | ||||
\(829\) | 9.00000 | + | 15.5885i | 0.312583 | + | 0.541409i | 0.978921 | − | 0.204240i | \(-0.0654725\pi\) |
−0.666338 | + | 0.745650i | \(0.732139\pi\) | |||||||
\(830\) | 6.00000 | + | 10.3923i | 0.208263 | + | 0.360722i | ||||
\(831\) | −11.0000 | + | 19.0526i | −0.381586 | + | 0.660926i | ||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 4.00000 | − | 6.92820i | 0.138426 | − | 0.239760i | ||||
\(836\) | 8.00000 | + | 13.8564i | 0.276686 | + | 0.479234i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.0000 | + | 17.3205i | −0.345444 | + | 0.598327i | ||||
\(839\) | 8.00000 | 0.276191 | 0.138095 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138095 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 13.0000 | − | 22.5167i | 0.448010 | − | 0.775975i | ||||
\(843\) | 3.00000 | + | 5.19615i | 0.103325 | + | 0.178965i | ||||
\(844\) | 6.00000 | + | 10.3923i | 0.206529 | + | 0.357718i | ||||
\(845\) | 4.50000 | − | 7.79423i | 0.154805 | − | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.0000 | −0.343401 | ||||||||
\(849\) | −14.0000 | + | 24.2487i | −0.480479 | + | 0.832214i | ||||
\(850\) | −1.00000 | − | 1.73205i | −0.0342997 | − | 0.0594089i | ||||
\(851\) | 24.0000 | + | 41.5692i | 0.822709 | + | 1.42497i | ||||
\(852\) | 4.00000 | − | 6.92820i | 0.137038 | − | 0.237356i | ||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | 11.0000 | + | 19.0526i | 0.375753 | + | 0.650823i | 0.990439 | − | 0.137948i | \(-0.0440508\pi\) |
−0.614687 | + | 0.788771i | \(0.710717\pi\) | |||||||
\(858\) | −4.00000 | − | 6.92820i | −0.136558 | − | 0.236525i | ||||
\(859\) | 10.0000 | − | 17.3205i | 0.341196 | − | 0.590968i | −0.643459 | − | 0.765480i | \(-0.722501\pi\) |
0.984655 | + | 0.174512i | \(0.0558348\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0000 | + | 27.7128i | −0.544646 | + | 0.943355i | 0.453983 | + | 0.891010i | \(0.350003\pi\) |
−0.998629 | + | 0.0523446i | \(0.983331\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 7.00000 | − | 12.1244i | 0.237870 | − | 0.412002i | ||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −64.0000 | −2.17105 | ||||||||
\(870\) | 1.00000 | − | 1.73205i | 0.0339032 | − | 0.0587220i | ||||
\(871\) | −12.0000 | − | 20.7846i | −0.406604 | − | 0.704260i | ||||
\(872\) | −7.00000 | − | 12.1244i | −0.237050 | − | 0.410582i | ||||
\(873\) | −1.00000 | + | 1.73205i | −0.0338449 | + | 0.0586210i | ||||
\(874\) | −32.0000 | −1.08242 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.0000 | 0.337869 | ||||||||
\(877\) | −7.00000 | + | 12.1244i | −0.236373 | + | 0.409410i | −0.959671 | − | 0.281126i | \(-0.909292\pi\) |
0.723298 | + | 0.690536i | \(0.242625\pi\) | |||||||
\(878\) | 4.00000 | + | 6.92820i | 0.134993 | + | 0.233816i | ||||
\(879\) | −3.00000 | − | 5.19615i | −0.101187 | − | 0.175262i | ||||
\(880\) | 2.00000 | − | 3.46410i | 0.0674200 | − | 0.116775i | ||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 2.00000 | − | 3.46410i | 0.0672673 | − | 0.116510i | ||||
\(885\) | −6.00000 | − | 10.3923i | −0.201688 | − | 0.349334i | ||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | −4.00000 | + | 6.92820i | −0.134307 | + | 0.232626i | −0.925332 | − | 0.379157i | \(-0.876214\pi\) |
0.791026 | + | 0.611783i | \(0.209547\pi\) | |||||||
\(888\) | 6.00000 | 0.201347 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.0000 | 0.335201 | ||||||||
\(891\) | 2.00000 | − | 3.46410i | 0.0670025 | − | 0.116052i | ||||
\(892\) | 8.00000 | + | 13.8564i | 0.267860 | + | 0.463947i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.00000 | − | 8.66025i | 0.167225 | − | 0.289642i | ||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | −1.00000 | + | 1.73205i | −0.0333704 | + | 0.0577993i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 10.0000 | − | 17.3205i | 0.333148 | − | 0.577030i | ||||
\(902\) | 24.0000 | 0.799113 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | −3.00000 | + | 5.19615i | −0.0997234 | + | 0.172726i | ||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | −14.0000 | − | 24.2487i | −0.464862 | − | 0.805165i | 0.534333 | − | 0.845274i | \(-0.320563\pi\) |
−0.999195 | + | 0.0401089i | \(0.987230\pi\) | |||||||
\(908\) | −2.00000 | + | 3.46410i | −0.0663723 | + | 0.114960i | ||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0000 | 1.06021 | 0.530104 | − | 0.847933i | \(-0.322153\pi\) | ||||
0.530104 | + | 0.847933i | \(0.322153\pi\) | |||||||
\(912\) | −2.00000 | + | 3.46410i | −0.0662266 | + | 0.114708i | ||||
\(913\) | −24.0000 | − | 41.5692i | −0.794284 | − | 1.37574i | ||||
\(914\) | −5.00000 | − | 8.66025i | −0.165385 | − | 0.286456i | ||||
\(915\) | −7.00000 | + | 12.1244i | −0.231413 | + | 0.400819i | ||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.00000 | 0.0660098 | ||||||||
\(919\) | 4.00000 | − | 6.92820i | 0.131948 | − | 0.228540i | −0.792480 | − | 0.609898i | \(-0.791210\pi\) |
0.924427 | + | 0.381358i | \(0.124544\pi\) | |||||||
\(920\) | 4.00000 | + | 6.92820i | 0.131876 | + | 0.228416i | ||||
\(921\) | −10.0000 | − | 17.3205i | −0.329511 | − | 0.570730i | ||||
\(922\) | −7.00000 | + | 12.1244i | −0.230533 | + | 0.399294i | ||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00000 | + | 6.92820i | 0.131377 | + | 0.227552i | ||||
\(928\) | 1.00000 | + | 1.73205i | 0.0328266 | + | 0.0568574i | ||||
\(929\) | 7.00000 | − | 12.1244i | 0.229663 | − | 0.397787i | −0.728046 | − | 0.685529i | \(-0.759571\pi\) |
0.957708 | + | 0.287742i | \(0.0929044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −22.0000 | −0.720634 | ||||||||
\(933\) | 4.00000 | − | 6.92820i | 0.130954 | − | 0.226819i | ||||
\(934\) | 6.00000 | + | 10.3923i | 0.196326 | + | 0.340047i | ||||
\(935\) | 4.00000 | + | 6.92820i | 0.130814 | + | 0.226576i | ||||
\(936\) | 1.00000 | − | 1.73205i | 0.0326860 | − | 0.0566139i | ||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.00000 | + | 15.5885i | 0.293392 | + | 0.508169i | 0.974609 | − | 0.223912i | \(-0.0718827\pi\) |
−0.681218 | + | 0.732081i | \(0.738549\pi\) | |||||||
\(942\) | 9.00000 | + | 15.5885i | 0.293236 | + | 0.507899i | ||||
\(943\) | −24.0000 | + | 41.5692i | −0.781548 | + | 1.35368i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | 0.520205 | ||||||||
\(947\) | −26.0000 | + | 45.0333i | −0.844886 | + | 1.46339i | 0.0408333 | + | 0.999166i | \(0.486999\pi\) |
−0.885720 | + | 0.464220i | \(0.846335\pi\) | |||||||
\(948\) | −8.00000 | − | 13.8564i | −0.259828 | − | 0.450035i | ||||
\(949\) | 10.0000 | + | 17.3205i | 0.324614 | + | 0.562247i | ||||
\(950\) | −2.00000 | + | 3.46410i | −0.0648886 | + | 0.112390i | ||||
\(951\) | −2.00000 | −0.0648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.0000 | 0.842223 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(954\) | 5.00000 | − | 8.66025i | 0.161881 | − | 0.280386i | ||||
\(955\) | 8.00000 | + | 13.8564i | 0.258874 | + | 0.448383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.00000 | + | 6.92820i | −0.129302 | + | 0.223957i | ||||
\(958\) | 32.0000 | 1.03387 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 6.00000 | + | 10.3923i | 0.193448 | + | 0.335061i | ||||
\(963\) | −6.00000 | − | 10.3923i | −0.193347 | − | 0.334887i | ||||
\(964\) | 7.00000 | − | 12.1244i | 0.225455 | − | 0.390499i | ||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | −2.50000 | + | 4.33013i | −0.0803530 | + | 0.139176i | ||||
\(969\) | −4.00000 | − | 6.92820i | −0.128499 | − | 0.222566i | ||||
\(970\) | −1.00000 | − | 1.73205i | −0.0321081 | − | 0.0556128i | ||||
\(971\) | −14.0000 | + | 24.2487i | −0.449281 | + | 0.778178i | −0.998339 | − | 0.0576061i | \(-0.981653\pi\) |
0.549058 | + | 0.835784i | \(0.314987\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 1.00000 | − | 1.73205i | 0.0320256 | − | 0.0554700i | ||||
\(976\) | −7.00000 | − | 12.1244i | −0.224065 | − | 0.388091i | ||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | −10.0000 | + | 17.3205i | −0.319765 | + | 0.553849i | ||||
\(979\) | −40.0000 | −1.27841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 18.0000 | − | 31.1769i | 0.574403 | − | 0.994895i | ||||
\(983\) | 12.0000 | + | 20.7846i | 0.382741 | + | 0.662926i | 0.991453 | − | 0.130465i | \(-0.0416470\pi\) |
−0.608712 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(984\) | 3.00000 | + | 5.19615i | 0.0956365 | + | 0.165647i | ||||
\(985\) | −3.00000 | + | 5.19615i | −0.0955879 | + | 0.165563i | ||||
\(986\) | −4.00000 | −0.127386 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.00000 | −0.254514 | ||||||||
\(989\) | −16.0000 | + | 27.7128i | −0.508770 | + | 0.881216i | ||||
\(990\) | 2.00000 | + | 3.46410i | 0.0635642 | + | 0.110096i | ||||
\(991\) | 16.0000 | + | 27.7128i | 0.508257 | + | 0.880327i | 0.999954 | + | 0.00956046i | \(0.00304324\pi\) |
−0.491698 | + | 0.870766i | \(0.663623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0000 | 0.380808 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.0000 | −0.760851 | ||||||||
\(996\) | 6.00000 | − | 10.3923i | 0.190117 | − | 0.329293i | ||||
\(997\) | −11.0000 | − | 19.0526i | −0.348373 | − | 0.603401i | 0.637587 | − | 0.770378i | \(-0.279933\pi\) |
−0.985961 | + | 0.166978i | \(0.946599\pi\) | |||||||
\(998\) | 6.00000 | + | 10.3923i | 0.189927 | + | 0.328963i | ||||
\(999\) | −3.00000 | + | 5.19615i | −0.0949158 | + | 0.164399i |
(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 | 1470.2.i.a.961.1 | 2 | ||
7.2 | even | 3 | 210.2.a.e.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 1470.2.i.j.361.1 | 2 | |||
7.4 | even | 3 | inner | 1470.2.i.a.361.1 | 2 | ||
7.5 | odd | 6 | 1470.2.a.j.1.1 | 1 | |||
7.6 | odd | 2 | 1470.2.i.j.961.1 | 2 | |||
21.2 | odd | 6 | 630.2.a.a.1.1 | 1 | |||
21.5 | even | 6 | 4410.2.a.t.1.1 | 1 | |||
28.23 | odd | 6 | 1680.2.a.j.1.1 | 1 | |||
35.2 | odd | 12 | 1050.2.g.g.799.2 | 2 | |||
35.9 | even | 6 | 1050.2.a.c.1.1 | 1 | |||
35.19 | odd | 6 | 7350.2.a.w.1.1 | 1 | |||
35.23 | odd | 12 | 1050.2.g.g.799.1 | 2 | |||
56.37 | even | 6 | 6720.2.a.j.1.1 | 1 | |||
56.51 | odd | 6 | 6720.2.a.bq.1.1 | 1 | |||
84.23 | even | 6 | 5040.2.a.k.1.1 | 1 | |||
105.2 | even | 12 | 3150.2.g.q.2899.1 | 2 | |||
105.23 | even | 12 | 3150.2.g.q.2899.2 | 2 | |||
105.44 | odd | 6 | 3150.2.a.bp.1.1 | 1 | |||
140.79 | odd | 6 | 8400.2.a.ce.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.a.e.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
630.2.a.a.1.1 | 1 | 21.2 | odd | 6 | |||
1050.2.a.c.1.1 | 1 | 35.9 | even | 6 | |||
1050.2.g.g.799.1 | 2 | 35.23 | odd | 12 | |||
1050.2.g.g.799.2 | 2 | 35.2 | odd | 12 | |||
1470.2.a.j.1.1 | 1 | 7.5 | odd | 6 | |||
1470.2.i.a.361.1 | 2 | 7.4 | even | 3 | inner | ||
1470.2.i.a.961.1 | 2 | 1.1 | even | 1 | trivial | ||
1470.2.i.j.361.1 | 2 | 7.3 | odd | 6 | |||
1470.2.i.j.961.1 | 2 | 7.6 | odd | 2 | |||
1680.2.a.j.1.1 | 1 | 28.23 | odd | 6 | |||
3150.2.a.bp.1.1 | 1 | 105.44 | odd | 6 | |||
3150.2.g.q.2899.1 | 2 | 105.2 | even | 12 | |||
3150.2.g.q.2899.2 | 2 | 105.23 | even | 12 | |||
4410.2.a.t.1.1 | 1 | 21.5 | even | 6 | |||
5040.2.a.k.1.1 | 1 | 84.23 | even | 6 | |||
6720.2.a.j.1.1 | 1 | 56.37 | even | 6 | |||
6720.2.a.bq.1.1 | 1 | 56.51 | odd | 6 | |||
7350.2.a.w.1.1 | 1 | 35.19 | odd | 6 | |||
8400.2.a.ce.1.1 | 1 | 140.79 | odd | 6 |