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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.361 |
Dual form | 1470.2.i.r.961.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(11\) | −3.00000 | + | 5.19615i | −0.904534 | + | 1.56670i | −0.0829925 | + | 0.996550i | \(0.526448\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −3.00000 | − | 5.19615i | −0.588348 | − | 1.01905i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 2.00000 | − | 3.46410i | 0.324443 | − | 0.561951i | ||||
\(39\) | −3.00000 | + | 5.19615i | −0.480384 | + | 0.832050i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | 10.0000 | 1.56174 | 0.780869 | − | 0.624695i | \(-0.214777\pi\) | ||||
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | −3.00000 | − | 5.19615i | −0.452267 | − | 0.783349i | ||||
\(45\) | 0.500000 | − | 0.866025i | 0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.00000 | − | 5.19615i | 0.416025 | − | 0.720577i | ||||
\(53\) | −5.00000 | + | 8.66025i | −0.686803 | + | 1.18958i | 0.286064 | + | 0.958211i | \(0.407653\pi\) |
−0.972867 | + | 0.231367i | \(0.925680\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | −4.00000 | − | 6.92820i | −0.525226 | − | 0.909718i | ||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | −0.500000 | + | 0.866025i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 7.00000 | + | 12.1244i | 0.896258 | + | 1.55236i | 0.832240 | + | 0.554416i | \(0.187058\pi\) |
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | −3.00000 | + | 5.19615i | −0.369274 | + | 0.639602i | ||||
\(67\) | −7.00000 | + | 12.1244i | −0.855186 | + | 1.48123i | 0.0212861 | + | 0.999773i | \(0.493224\pi\) |
−0.876472 | + | 0.481452i | \(0.840109\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 3.00000 | − | 5.19615i | 0.351123 | − | 0.608164i | −0.635323 | − | 0.772246i | \(-0.719133\pi\) |
0.986447 | + | 0.164083i | \(0.0524664\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.00000 | + | 8.66025i | 0.552158 | + | 0.956365i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.00000 | − | 5.19615i | −0.323498 | − | 0.560316i | ||||
\(87\) | −4.00000 | + | 6.92820i | −0.428845 | + | 0.742781i | ||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | −9.00000 | − | 15.5885i | −0.953998 | − | 1.65237i | −0.736644 | − | 0.676280i | \(-0.763591\pi\) |
−0.217354 | − | 0.976093i | \(-0.569742\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | − | 1.73205i | −0.103695 | − | 0.179605i | ||||
\(94\) | 1.00000 | − | 1.73205i | 0.103142 | − | 0.178647i | ||||
\(95\) | 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 | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −7.00000 | + | 12.1244i | −0.696526 | + | 1.20642i | 0.273138 | + | 0.961975i | \(0.411939\pi\) |
−0.969664 | + | 0.244443i | \(0.921395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | − | 10.3923i | −0.591198 | − | 1.02398i | −0.994071 | − | 0.108729i | \(-0.965322\pi\) |
0.402874 | − | 0.915255i | \(-0.368011\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0000 | −0.971286 | ||||||||
\(107\) | −2.00000 | − | 3.46410i | −0.193347 | − | 0.334887i | 0.753010 | − | 0.658009i | \(-0.228601\pi\) |
−0.946357 | + | 0.323122i | \(0.895268\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −3.00000 | + | 5.19615i | −0.287348 | + | 0.497701i | −0.973176 | − | 0.230063i | \(-0.926107\pi\) |
0.685828 | + | 0.727764i | \(0.259440\pi\) | |||||||
\(110\) | −3.00000 | − | 5.19615i | −0.286039 | − | 0.495434i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | −2.00000 | − | 3.46410i | −0.187317 | − | 0.324443i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.00000 | − | 6.92820i | 0.371391 | − | 0.643268i | ||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | −7.00000 | + | 12.1244i | −0.633750 | + | 1.09769i | ||||
\(123\) | 5.00000 | − | 8.66025i | 0.450835 | − | 0.780869i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −3.00000 | + | 5.19615i | −0.264135 | + | 0.457496i | ||||
\(130\) | 3.00000 | − | 5.19615i | 0.263117 | − | 0.455733i | ||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.0000 | −1.20942 | ||||||||
\(135\) | −0.500000 | − | 0.866025i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | + | 8.66025i | −0.427179 | + | 0.739895i | −0.996621 | − | 0.0821359i | \(-0.973826\pi\) |
0.569442 | + | 0.822031i | \(0.307159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 4.00000 | + | 6.92820i | 0.335673 | + | 0.581402i | ||||
\(143\) | 18.0000 | − | 31.1769i | 1.50524 | − | 2.60714i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −4.00000 | − | 6.92820i | −0.332182 | − | 0.575356i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 2.00000 | + | 3.46410i | 0.162221 | + | 0.280976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | −3.00000 | − | 5.19615i | −0.240192 | − | 0.416025i | ||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | −4.00000 | + | 6.92820i | −0.318223 | + | 0.551178i | ||||
\(159\) | 5.00000 | + | 8.66025i | 0.396526 | + | 0.686803i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −1.00000 | − | 1.73205i | −0.0783260 | − | 0.135665i | 0.824202 | − | 0.566296i | \(-0.191624\pi\) |
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(164\) | −5.00000 | + | 8.66025i | −0.390434 | + | 0.676252i | ||||
\(165\) | −3.00000 | + | 5.19615i | −0.233550 | + | 0.404520i | ||||
\(166\) | 4.00000 | + | 6.92820i | 0.310460 | + | 0.537733i | ||||
\(167\) | 18.0000 | 1.39288 | 0.696441 | − | 0.717614i | \(-0.254766\pi\) | ||||
0.696441 | + | 0.717614i | \(0.254766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | 3.00000 | − | 5.19615i | 0.228748 | − | 0.396203i | ||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | −8.00000 | −0.606478 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | 9.00000 | − | 15.5885i | 0.674579 | − | 1.16840i | ||||
\(179\) | −1.00000 | + | 1.73205i | −0.0747435 | + | 0.129460i | −0.900975 | − | 0.433872i | \(-0.857147\pi\) |
0.826231 | + | 0.563331i | \(0.190480\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0000 | 1.03491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 10.0000 | + | 17.3205i | 0.723575 | + | 1.25327i | 0.959558 | + | 0.281511i | \(0.0908356\pi\) |
−0.235983 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −11.0000 | + | 19.0526i | −0.791797 | + | 1.37143i | 0.133056 | + | 0.991109i | \(0.457521\pi\) |
−0.924853 | + | 0.380325i | \(0.875812\pi\) | |||||||
\(194\) | −1.00000 | − | 1.73205i | −0.0717958 | − | 0.124354i | ||||
\(195\) | −6.00000 | −0.429669 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 3.00000 | + | 5.19615i | 0.213201 | + | 0.369274i | ||||
\(199\) | −9.00000 | + | 15.5885i | −0.637993 | + | 1.10504i | 0.347879 | + | 0.937539i | \(0.386902\pi\) |
−0.985873 | + | 0.167497i | \(0.946431\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 7.00000 | + | 12.1244i | 0.493742 | + | 0.855186i | ||||
\(202\) | −14.0000 | −0.985037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00000 | + | 8.66025i | 0.349215 | + | 0.604858i | ||||
\(206\) | 6.00000 | − | 10.3923i | 0.418040 | − | 0.724066i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.00000 | + | 5.19615i | 0.208013 | + | 0.360288i | ||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | −5.00000 | − | 8.66025i | −0.343401 | − | 0.594789i | ||||
\(213\) | 4.00000 | − | 6.92820i | 0.274075 | − | 0.474713i | ||||
\(214\) | 2.00000 | − | 3.46410i | 0.136717 | − | 0.236801i | ||||
\(215\) | −3.00000 | − | 5.19615i | −0.204598 | − | 0.354375i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | −3.00000 | − | 5.19615i | −0.202721 | − | 0.351123i | ||||
\(220\) | 3.00000 | − | 5.19615i | 0.202260 | − | 0.350325i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.00000 | − | 3.46410i | −0.134231 | − | 0.232495i | ||||
\(223\) | −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 | ||||||||
\(226\) | 3.00000 | + | 5.19615i | 0.199557 | + | 0.345643i | ||||
\(227\) | 10.0000 | − | 17.3205i | 0.663723 | − | 1.14960i | −0.315906 | − | 0.948790i | \(-0.602309\pi\) |
0.979630 | − | 0.200812i | \(-0.0643581\pi\) | |||||||
\(228\) | 2.00000 | − | 3.46410i | 0.132453 | − | 0.229416i | ||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | 5.00000 | + | 8.66025i | 0.327561 | + | 0.567352i | 0.982027 | − | 0.188739i | \(-0.0604400\pi\) |
−0.654466 | + | 0.756091i | \(0.727107\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | 1.00000 | − | 1.73205i | 0.0652328 | − | 0.112987i | ||||
\(236\) | −2.00000 | − | 3.46410i | −0.130189 | − | 0.225494i | ||||
\(237\) | 8.00000 | 0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | −0.500000 | − | 0.866025i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | −14.0000 | + | 24.2487i | −0.901819 | + | 1.56200i | −0.0766885 | + | 0.997055i | \(0.524435\pi\) |
−0.825131 | + | 0.564942i | \(0.808899\pi\) | |||||||
\(242\) | 12.5000 | − | 21.6506i | 0.803530 | − | 1.39176i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −14.0000 | −0.896258 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | 12.0000 | + | 20.7846i | 0.763542 | + | 1.32249i | ||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | 4.00000 | − | 6.92820i | 0.253490 | − | 0.439057i | ||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.00000 | + | 3.46410i | 0.125491 | + | 0.217357i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.00000 | − | 6.92820i | −0.249513 | − | 0.432169i | 0.713878 | − | 0.700270i | \(-0.246937\pi\) |
−0.963391 | + | 0.268101i | \(0.913604\pi\) | |||||||
\(258\) | −6.00000 | −0.373544 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 4.00000 | + | 6.92820i | 0.247594 | + | 0.428845i | ||||
\(262\) | −6.00000 | + | 10.3923i | −0.370681 | + | 0.642039i | ||||
\(263\) | 16.0000 | − | 27.7128i | 0.986602 | − | 1.70885i | 0.352014 | − | 0.935995i | \(-0.385497\pi\) |
0.634588 | − | 0.772851i | \(-0.281170\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | −10.0000 | −0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | −7.00000 | − | 12.1244i | −0.427593 | − | 0.740613i | ||||
\(269\) | 11.0000 | − | 19.0526i | 0.670682 | − | 1.16166i | −0.307029 | − | 0.951700i | \(-0.599335\pi\) |
0.977711 | − | 0.209955i | \(-0.0673317\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | −9.00000 | − | 15.5885i | −0.546711 | − | 0.946931i | −0.998497 | − | 0.0548050i | \(-0.982546\pi\) |
0.451786 | − | 0.892126i | \(-0.350787\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | −3.00000 | − | 5.19615i | −0.180907 | − | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | − | 6.92820i | 0.240337 | − | 0.416275i | −0.720473 | − | 0.693482i | \(-0.756075\pi\) |
0.960810 | + | 0.277207i | \(0.0894088\pi\) | |||||||
\(278\) | −4.00000 | − | 6.92820i | −0.239904 | − | 0.415526i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | −1.00000 | − | 1.73205i | −0.0595491 | − | 0.103142i | ||||
\(283\) | 14.0000 | − | 24.2487i | 0.832214 | − | 1.44144i | −0.0640654 | − | 0.997946i | \(-0.520407\pi\) |
0.896279 | − | 0.443491i | \(-0.146260\pi\) | |||||||
\(284\) | −4.00000 | + | 6.92820i | −0.237356 | + | 0.411113i | ||||
\(285\) | −2.00000 | − | 3.46410i | −0.118470 | − | 0.205196i | ||||
\(286\) | 36.0000 | 2.12872 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 4.00000 | − | 6.92820i | 0.234888 | − | 0.406838i | ||||
\(291\) | −1.00000 | + | 1.73205i | −0.0586210 | + | 0.101535i | ||||
\(292\) | 3.00000 | + | 5.19615i | 0.175562 | + | 0.304082i | ||||
\(293\) | −22.0000 | −1.28525 | −0.642627 | − | 0.766179i | \(-0.722155\pi\) | ||||
−0.642627 | + | 0.766179i | \(0.722155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 2.00000 | + | 3.46410i | 0.116248 | + | 0.201347i | ||||
\(297\) | 3.00000 | − | 5.19615i | 0.174078 | − | 0.301511i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | 7.00000 | + | 12.1244i | 0.402139 | + | 0.696526i | ||||
\(304\) | −2.00000 | + | 3.46410i | −0.114708 | + | 0.198680i | ||||
\(305\) | −7.00000 | + | 12.1244i | −0.400819 | + | 0.694239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | −0.682656 | ||||||||
\(310\) | 1.00000 | + | 1.73205i | 0.0567962 | + | 0.0983739i | ||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | 3.00000 | − | 5.19615i | 0.169842 | − | 0.294174i | ||||
\(313\) | 13.0000 | + | 22.5167i | 0.734803 | + | 1.27272i | 0.954810 | + | 0.297218i | \(0.0960589\pi\) |
−0.220006 | + | 0.975499i | \(0.570608\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −5.00000 | − | 8.66025i | −0.280828 | − | 0.486408i | 0.690761 | − | 0.723083i | \(-0.257276\pi\) |
−0.971589 | + | 0.236675i | \(0.923942\pi\) | |||||||
\(318\) | −5.00000 | + | 8.66025i | −0.280386 | + | 0.485643i | ||||
\(319\) | 24.0000 | − | 41.5692i | 1.34374 | − | 2.32743i | ||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 3.00000 | − | 5.19615i | 0.166410 | − | 0.288231i | ||||
\(326\) | 1.00000 | − | 1.73205i | 0.0553849 | − | 0.0959294i | ||||
\(327\) | 3.00000 | + | 5.19615i | 0.165900 | + | 0.287348i | ||||
\(328\) | −10.0000 | −0.552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.00000 | −0.330289 | ||||||||
\(331\) | 10.0000 | + | 17.3205i | 0.549650 | + | 0.952021i | 0.998298 | + | 0.0583130i | \(0.0185721\pi\) |
−0.448649 | + | 0.893708i | \(0.648095\pi\) | |||||||
\(332\) | −4.00000 | + | 6.92820i | −0.219529 | + | 0.380235i | ||||
\(333\) | −2.00000 | + | 3.46410i | −0.109599 | + | 0.189832i | ||||
\(334\) | 9.00000 | + | 15.5885i | 0.492458 | + | 0.852962i | ||||
\(335\) | −14.0000 | −0.764902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0000 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(338\) | 11.5000 | + | 19.9186i | 0.625518 | + | 1.08343i | ||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.00000 | 0.323498 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | 14.0000 | − | 24.2487i | 0.751559 | − | 1.30174i | −0.195507 | − | 0.980702i | \(-0.562635\pi\) |
0.947067 | − | 0.321037i | \(-0.104031\pi\) | |||||||
\(348\) | −4.00000 | − | 6.92820i | −0.214423 | − | 0.371391i | ||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | 3.00000 | + | 5.19615i | 0.159901 | + | 0.276956i | ||||
\(353\) | 2.00000 | − | 3.46410i | 0.106449 | − | 0.184376i | −0.807880 | − | 0.589347i | \(-0.799385\pi\) |
0.914329 | + | 0.404971i | \(0.132718\pi\) | |||||||
\(354\) | −2.00000 | + | 3.46410i | −0.106299 | + | 0.184115i | ||||
\(355\) | 4.00000 | + | 6.92820i | 0.212298 | + | 0.367711i | ||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | −0.105703 | ||||||||
\(359\) | 12.0000 | + | 20.7846i | 0.633336 | + | 1.09697i | 0.986865 | + | 0.161546i | \(0.0516481\pi\) |
−0.353529 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(360\) | −0.500000 | + | 0.866025i | −0.0263523 | + | 0.0456435i | ||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | −5.00000 | − | 8.66025i | −0.262794 | − | 0.455173i | ||||
\(363\) | −25.0000 | −1.31216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 7.00000 | + | 12.1244i | 0.365896 | + | 0.633750i | ||||
\(367\) | −2.00000 | + | 3.46410i | −0.104399 | + | 0.180825i | −0.913493 | − | 0.406855i | \(-0.866625\pi\) |
0.809093 | + | 0.587680i | \(0.199959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.00000 | − | 8.66025i | −0.260290 | − | 0.450835i | ||||
\(370\) | 4.00000 | 0.207950 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 4.00000 | + | 6.92820i | 0.207112 | + | 0.358729i | 0.950804 | − | 0.309794i | \(-0.100260\pi\) |
−0.743691 | + | 0.668523i | \(0.766927\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 1.00000 | + | 1.73205i | 0.0515711 | + | 0.0893237i | ||||
\(377\) | 48.0000 | 2.47213 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 2.00000 | + | 3.46410i | 0.102598 | + | 0.177705i | ||||
\(381\) | 2.00000 | − | 3.46410i | 0.102463 | − | 0.177471i | ||||
\(382\) | −10.0000 | + | 17.3205i | −0.511645 | + | 0.886194i | ||||
\(383\) | −7.00000 | − | 12.1244i | −0.357683 | − | 0.619526i | 0.629890 | − | 0.776684i | \(-0.283100\pi\) |
−0.987573 | + | 0.157159i | \(0.949767\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | 3.00000 | + | 5.19615i | 0.152499 | + | 0.264135i | ||||
\(388\) | 1.00000 | − | 1.73205i | 0.0507673 | − | 0.0879316i | ||||
\(389\) | −12.0000 | + | 20.7846i | −0.608424 | + | 1.05382i | 0.383076 | + | 0.923717i | \(0.374865\pi\) |
−0.991500 | + | 0.130105i | \(0.958469\pi\) | |||||||
\(390\) | −3.00000 | − | 5.19615i | −0.151911 | − | 0.263117i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 3.00000 | + | 5.19615i | 0.151138 | + | 0.261778i | ||||
\(395\) | −4.00000 | + | 6.92820i | −0.201262 | + | 0.348596i | ||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | −7.00000 | − | 12.1244i | −0.351320 | − | 0.608504i | 0.635161 | − | 0.772380i | \(-0.280934\pi\) |
−0.986481 | + | 0.163876i | \(0.947600\pi\) | |||||||
\(398\) | −18.0000 | −0.902258 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | − | 1.73205i | −0.0499376 | − | 0.0864945i | 0.839976 | − | 0.542623i | \(-0.182569\pi\) |
−0.889914 | + | 0.456129i | \(0.849236\pi\) | |||||||
\(402\) | −7.00000 | + | 12.1244i | −0.349128 | + | 0.604708i | ||||
\(403\) | −6.00000 | + | 10.3923i | −0.298881 | + | 0.517678i | ||||
\(404\) | −7.00000 | − | 12.1244i | −0.348263 | − | 0.603209i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.00000 | + | 13.8564i | −0.395575 | + | 0.685155i | −0.993174 | − | 0.116639i | \(-0.962788\pi\) |
0.597600 | + | 0.801795i | \(0.296121\pi\) | |||||||
\(410\) | −5.00000 | + | 8.66025i | −0.246932 | + | 0.427699i | ||||
\(411\) | 5.00000 | + | 8.66025i | 0.246632 | + | 0.427179i | ||||
\(412\) | 12.0000 | 0.591198 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | + | 6.92820i | 0.196352 | + | 0.340092i | ||||
\(416\) | −3.00000 | + | 5.19615i | −0.147087 | + | 0.254762i | ||||
\(417\) | −4.00000 | + | 6.92820i | −0.195881 | + | 0.339276i | ||||
\(418\) | 12.0000 | + | 20.7846i | 0.586939 | + | 1.01661i | ||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 6.00000 | + | 10.3923i | 0.292075 | + | 0.505889i | ||||
\(423\) | −1.00000 | + | 1.73205i | −0.0486217 | + | 0.0842152i | ||||
\(424\) | 5.00000 | − | 8.66025i | 0.242821 | − | 0.420579i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | −18.0000 | − | 31.1769i | −0.869048 | − | 1.50524i | ||||
\(430\) | 3.00000 | − | 5.19615i | 0.144673 | − | 0.250581i | ||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −18.0000 | −0.865025 | −0.432512 | − | 0.901628i | \(-0.642373\pi\) | ||||
−0.432512 | + | 0.901628i | \(0.642373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | −3.00000 | − | 5.19615i | −0.143674 | − | 0.248851i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.00000 | − | 5.19615i | 0.143346 | − | 0.248282i | ||||
\(439\) | 5.00000 | + | 8.66025i | 0.238637 | + | 0.413331i | 0.960323 | − | 0.278889i | \(-0.0899661\pi\) |
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(440\) | 6.00000 | 0.286039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | + | 10.3923i | 0.285069 | + | 0.493753i | 0.972626 | − | 0.232377i | \(-0.0746503\pi\) |
−0.687557 | + | 0.726130i | \(0.741317\pi\) | |||||||
\(444\) | 2.00000 | − | 3.46410i | 0.0949158 | − | 0.164399i | ||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | −8.00000 | − | 13.8564i | −0.378811 | − | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0.500000 | + | 0.866025i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | −30.0000 | + | 51.9615i | −1.41264 | + | 2.44677i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | −4.00000 | − | 6.92820i | −0.187936 | − | 0.325515i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | −19.0000 | − | 32.9090i | −0.888783 | − | 1.53942i | −0.841316 | − | 0.540544i | \(-0.818219\pi\) |
−0.0474665 | − | 0.998873i | \(-0.515115\pi\) | |||||||
\(458\) | 7.00000 | − | 12.1244i | 0.327089 | − | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 4.00000 | + | 6.92820i | 0.185695 | + | 0.321634i | ||||
\(465\) | 1.00000 | − | 1.73205i | 0.0463739 | − | 0.0803219i | ||||
\(466\) | −5.00000 | + | 8.66025i | −0.231621 | + | 0.401179i | ||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.00000 | 0.0922531 | ||||||||
\(471\) | 7.00000 | + | 12.1244i | 0.322543 | + | 0.558661i | ||||
\(472\) | 2.00000 | − | 3.46410i | 0.0920575 | − | 0.159448i | ||||
\(473\) | 18.0000 | − | 31.1769i | 0.827641 | − | 1.43352i | ||||
\(474\) | 4.00000 | + | 6.92820i | 0.183726 | + | 0.318223i | ||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0000 | 0.457869 | ||||||||
\(478\) | −2.00000 | − | 3.46410i | −0.0914779 | − | 0.158444i | ||||
\(479\) | −18.0000 | + | 31.1769i | −0.822441 | + | 1.42451i | 0.0814184 | + | 0.996680i | \(0.474055\pi\) |
−0.903859 | + | 0.427830i | \(0.859278\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | −28.0000 | −1.27537 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.0000 | 1.13636 | ||||||||
\(485\) | −1.00000 | − | 1.73205i | −0.0454077 | − | 0.0786484i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −6.00000 | + | 10.3923i | −0.271886 | + | 0.470920i | −0.969345 | − | 0.245705i | \(-0.920981\pi\) |
0.697459 | + | 0.716625i | \(0.254314\pi\) | |||||||
\(488\) | −7.00000 | − | 12.1244i | −0.316875 | − | 0.548844i | ||||
\(489\) | −2.00000 | −0.0904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0000 | −0.992846 | −0.496423 | − | 0.868081i | \(-0.665354\pi\) | ||||
−0.496423 | + | 0.868081i | \(0.665354\pi\) | |||||||
\(492\) | 5.00000 | + | 8.66025i | 0.225417 | + | 0.390434i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −12.0000 | + | 20.7846i | −0.539906 | + | 0.935144i | ||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.00000 | 0.358489 | ||||||||
\(499\) | 16.0000 | + | 27.7128i | 0.716258 | + | 1.24060i | 0.962472 | + | 0.271380i | \(0.0874801\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 9.00000 | − | 15.5885i | 0.402090 | − | 0.696441i | ||||
\(502\) | 10.0000 | + | 17.3205i | 0.446322 | + | 0.773052i | ||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0000 | −0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.5000 | − | 19.9186i | 0.510733 | − | 0.884615i | ||||
\(508\) | −2.00000 | + | 3.46410i | −0.0887357 | + | 0.153695i | ||||
\(509\) | 17.0000 | + | 29.4449i | 0.753512 | + | 1.30512i | 0.946111 | + | 0.323843i | \(0.104975\pi\) |
−0.192599 | + | 0.981278i | \(0.561692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.00000 | + | 3.46410i | 0.0883022 | + | 0.152944i | ||||
\(514\) | 4.00000 | − | 6.92820i | 0.176432 | − | 0.305590i | ||||
\(515\) | 6.00000 | − | 10.3923i | 0.264392 | − | 0.457940i | ||||
\(516\) | −3.00000 | − | 5.19615i | −0.132068 | − | 0.228748i | ||||
\(517\) | 12.0000 | 0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 3.00000 | + | 5.19615i | 0.131559 | + | 0.227866i | ||||
\(521\) | −1.00000 | + | 1.73205i | −0.0438108 | + | 0.0758825i | −0.887099 | − | 0.461579i | \(-0.847283\pi\) |
0.843288 | + | 0.537461i | \(0.180617\pi\) | |||||||
\(522\) | −4.00000 | + | 6.92820i | −0.175075 | + | 0.303239i | ||||
\(523\) | −22.0000 | − | 38.1051i | −0.961993 | − | 1.66622i | −0.717486 | − | 0.696573i | \(-0.754707\pi\) |
−0.244507 | − | 0.969648i | \(-0.578626\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.0000 | 1.39527 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.00000 | − | 5.19615i | 0.130558 | − | 0.226134i | ||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | −5.00000 | − | 8.66025i | −0.217186 | − | 0.376177i | ||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.0000 | −2.59889 | ||||||||
\(534\) | −9.00000 | − | 15.5885i | −0.389468 | − | 0.674579i | ||||
\(535\) | 2.00000 | − | 3.46410i | 0.0864675 | − | 0.149766i | ||||
\(536\) | 7.00000 | − | 12.1244i | 0.302354 | − | 0.523692i | ||||
\(537\) | 1.00000 | + | 1.73205i | 0.0431532 | + | 0.0747435i | ||||
\(538\) | 22.0000 | 0.948487 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −9.00000 | − | 15.5885i | −0.386940 | − | 0.670200i | 0.605096 | − | 0.796152i | \(-0.293135\pi\) |
−0.992036 | + | 0.125952i | \(0.959801\pi\) | |||||||
\(542\) | 9.00000 | − | 15.5885i | 0.386583 | − | 0.669582i | ||||
\(543\) | −5.00000 | + | 8.66025i | −0.214571 | + | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0000 | 1.28271 | 0.641354 | − | 0.767245i | \(-0.278373\pi\) | ||||
0.641354 | + | 0.767245i | \(0.278373\pi\) | |||||||
\(548\) | −5.00000 | − | 8.66025i | −0.213589 | − | 0.369948i | ||||
\(549\) | 7.00000 | − | 12.1244i | 0.298753 | − | 0.517455i | ||||
\(550\) | 3.00000 | − | 5.19615i | 0.127920 | − | 0.221565i | ||||
\(551\) | 16.0000 | + | 27.7128i | 0.681623 | + | 1.18061i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.00000 | 0.339887 | ||||||||
\(555\) | −2.00000 | − | 3.46410i | −0.0848953 | − | 0.147043i | ||||
\(556\) | 4.00000 | − | 6.92820i | 0.169638 | − | 0.293821i | ||||
\(557\) | −1.00000 | + | 1.73205i | −0.0423714 | + | 0.0733893i | −0.886433 | − | 0.462856i | \(-0.846825\pi\) |
0.844062 | + | 0.536246i | \(0.180158\pi\) | |||||||
\(558\) | −1.00000 | − | 1.73205i | −0.0423334 | − | 0.0733236i | ||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | 12.0000 | − | 20.7846i | 0.505740 | − | 0.875967i | −0.494238 | − | 0.869326i | \(-0.664553\pi\) |
0.999978 | − | 0.00664037i | \(-0.00211371\pi\) | |||||||
\(564\) | 1.00000 | − | 1.73205i | 0.0421076 | − | 0.0729325i | ||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 28.0000 | 1.17693 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | −13.0000 | − | 22.5167i | −0.544988 | − | 0.943948i | −0.998608 | − | 0.0527519i | \(-0.983201\pi\) |
0.453619 | − | 0.891196i | \(-0.350133\pi\) | |||||||
\(570\) | 2.00000 | − | 3.46410i | 0.0837708 | − | 0.145095i | ||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 18.0000 | + | 31.1769i | 0.752618 | + | 1.30357i | ||||
\(573\) | 20.0000 | 0.835512 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −7.00000 | + | 12.1244i | −0.291414 | + | 0.504744i | −0.974144 | − | 0.225927i | \(-0.927459\pi\) |
0.682730 | + | 0.730670i | \(0.260792\pi\) | |||||||
\(578\) | −8.50000 | + | 14.7224i | −0.353553 | + | 0.612372i | ||||
\(579\) | 11.0000 | + | 19.0526i | 0.457144 | + | 0.791797i | ||||
\(580\) | 8.00000 | 0.332182 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.00000 | −0.0829027 | ||||||||
\(583\) | −30.0000 | − | 51.9615i | −1.24247 | − | 2.15203i | ||||
\(584\) | −3.00000 | + | 5.19615i | −0.124141 | + | 0.215018i | ||||
\(585\) | −3.00000 | + | 5.19615i | −0.124035 | + | 0.214834i | ||||
\(586\) | −11.0000 | − | 19.0526i | −0.454406 | − | 0.787054i | ||||
\(587\) | −32.0000 | −1.32078 | −0.660391 | − | 0.750922i | \(-0.729609\pi\) | ||||
−0.660391 | + | 0.750922i | \(0.729609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | −2.00000 | − | 3.46410i | −0.0823387 | − | 0.142615i | ||||
\(591\) | 3.00000 | − | 5.19615i | 0.123404 | − | 0.213741i | ||||
\(592\) | −2.00000 | + | 3.46410i | −0.0821995 | + | 0.142374i | ||||
\(593\) | −8.00000 | − | 13.8564i | −0.328521 | − | 0.569014i | 0.653698 | − | 0.756756i | \(-0.273217\pi\) |
−0.982219 | + | 0.187741i | \(0.939883\pi\) | |||||||
\(594\) | 6.00000 | 0.246183 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.00000 | + | 15.5885i | 0.368345 | + | 0.637993i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.0000 | + | 38.1051i | −0.898896 | + | 1.55693i | −0.0699877 | + | 0.997548i | \(0.522296\pi\) |
−0.828908 | + | 0.559385i | \(0.811037\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | −12.0000 | −0.489490 | −0.244745 | − | 0.969587i | \(-0.578704\pi\) | ||||
−0.244745 | + | 0.969587i | \(0.578704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0000 | 0.570124 | ||||||||
\(604\) | 4.00000 | + | 6.92820i | 0.162758 | + | 0.281905i | ||||
\(605\) | 12.5000 | − | 21.6506i | 0.508197 | − | 0.880223i | ||||
\(606\) | −7.00000 | + | 12.1244i | −0.284356 | + | 0.492518i | ||||
\(607\) | −20.0000 | − | 34.6410i | −0.811775 | − | 1.40604i | −0.911621 | − | 0.411033i | \(-0.865168\pi\) |
0.0998457 | − | 0.995003i | \(-0.468165\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.0000 | −0.566843 | ||||||||
\(611\) | 6.00000 | + | 10.3923i | 0.242734 | + | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.0000 | + | 31.1769i | −0.727013 | + | 1.25922i | 0.231127 | + | 0.972924i | \(0.425759\pi\) |
−0.958140 | + | 0.286300i | \(0.907575\pi\) | |||||||
\(614\) | 10.0000 | + | 17.3205i | 0.403567 | + | 0.698999i | ||||
\(615\) | 10.0000 | 0.403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | −6.00000 | − | 10.3923i | −0.241355 | − | 0.418040i | ||||
\(619\) | 10.0000 | − | 17.3205i | 0.401934 | − | 0.696170i | −0.592025 | − | 0.805919i | \(-0.701671\pi\) |
0.993959 | + | 0.109749i | \(0.0350048\pi\) | |||||||
\(620\) | −1.00000 | + | 1.73205i | −0.0401610 | + | 0.0695608i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −13.0000 | + | 22.5167i | −0.519584 | + | 0.899947i | ||||
\(627\) | 12.0000 | − | 20.7846i | 0.479234 | − | 0.830057i | ||||
\(628\) | −7.00000 | − | 12.1244i | −0.279330 | − | 0.483814i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | 6.00000 | − | 10.3923i | 0.238479 | − | 0.413057i | ||||
\(634\) | 5.00000 | − | 8.66025i | 0.198575 | − | 0.343943i | ||||
\(635\) | 2.00000 | + | 3.46410i | 0.0793676 | + | 0.137469i | ||||
\(636\) | −10.0000 | −0.396526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 48.0000 | 1.90034 | ||||||||
\(639\) | −4.00000 | − | 6.92820i | −0.158238 | − | 0.274075i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | −2.00000 | − | 3.46410i | −0.0789337 | − | 0.136717i | ||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.0000 | + | 39.8372i | −0.904223 | + | 1.56616i | −0.0822669 | + | 0.996610i | \(0.526216\pi\) |
−0.821956 | + | 0.569550i | \(0.807117\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −12.0000 | − | 20.7846i | −0.471041 | − | 0.815867i | ||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | −7.00000 | − | 12.1244i | −0.273931 | − | 0.474463i | 0.695934 | − | 0.718106i | \(-0.254991\pi\) |
−0.969865 | + | 0.243643i | \(0.921657\pi\) | |||||||
\(654\) | −3.00000 | + | 5.19615i | −0.117309 | + | 0.203186i | ||||
\(655\) | −6.00000 | + | 10.3923i | −0.234439 | + | 0.406061i | ||||
\(656\) | −5.00000 | − | 8.66025i | −0.195217 | − | 0.338126i | ||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | −3.00000 | − | 5.19615i | −0.116775 | − | 0.202260i | ||||
\(661\) | −9.00000 | + | 15.5885i | −0.350059 | + | 0.606321i | −0.986260 | − | 0.165203i | \(-0.947172\pi\) |
0.636200 | + | 0.771524i | \(0.280505\pi\) | |||||||
\(662\) | −10.0000 | + | 17.3205i | −0.388661 | + | 0.673181i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −9.00000 | + | 15.5885i | −0.348220 | + | 0.603136i | ||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | −7.00000 | − | 12.1244i | −0.270434 | − | 0.468405i | ||||
\(671\) | −84.0000 | −3.24278 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | −13.0000 | − | 22.5167i | −0.500741 | − | 0.867309i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | −11.0000 | − | 19.0526i | −0.422764 | − | 0.732249i | 0.573444 | − | 0.819244i | \(-0.305607\pi\) |
−0.996209 | + | 0.0869952i | \(0.972274\pi\) | |||||||
\(678\) | 6.00000 | 0.230429 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0000 | − | 17.3205i | −0.383201 | − | 0.663723i | ||||
\(682\) | −6.00000 | + | 10.3923i | −0.229752 | + | 0.397942i | ||||
\(683\) | 12.0000 | − | 20.7846i | 0.459167 | − | 0.795301i | −0.539750 | − | 0.841825i | \(-0.681481\pi\) |
0.998917 | + | 0.0465244i | \(0.0148145\pi\) | |||||||
\(684\) | −2.00000 | − | 3.46410i | −0.0764719 | − | 0.132453i | ||||
\(685\) | −10.0000 | −0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | 3.00000 | + | 5.19615i | 0.114374 | + | 0.198101i | ||||
\(689\) | 30.0000 | − | 51.9615i | 1.14291 | − | 1.97958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | + | 34.6410i | 0.760836 | + | 1.31781i | 0.942420 | + | 0.334431i | \(0.108544\pi\) |
−0.181584 | + | 0.983375i | \(0.558123\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | −4.00000 | − | 6.92820i | −0.151729 | − | 0.262802i | ||||
\(696\) | 4.00000 | − | 6.92820i | 0.151620 | − | 0.262613i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.00000 | − | 1.73205i | −0.0378506 | − | 0.0655591i | ||||
\(699\) | 10.0000 | 0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.0000 | 0.906467 | 0.453234 | − | 0.891392i | \(-0.350270\pi\) | ||||
0.453234 | + | 0.891392i | \(0.350270\pi\) | |||||||
\(702\) | 3.00000 | + | 5.19615i | 0.113228 | + | 0.196116i | ||||
\(703\) | −8.00000 | + | 13.8564i | −0.301726 | + | 0.522604i | ||||
\(704\) | −3.00000 | + | 5.19615i | −0.113067 | + | 0.195837i | ||||
\(705\) | −1.00000 | − | 1.73205i | −0.0376622 | − | 0.0652328i | ||||
\(706\) | 4.00000 | 0.150542 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | −1.00000 | − | 1.73205i | −0.0375558 | − | 0.0650485i | 0.846637 | − | 0.532172i | \(-0.178624\pi\) |
−0.884192 | + | 0.467123i | \(0.845291\pi\) | |||||||
\(710\) | −4.00000 | + | 6.92820i | −0.150117 | + | 0.260011i | ||||
\(711\) | 4.00000 | − | 6.92820i | 0.150012 | − | 0.259828i | ||||
\(712\) | 9.00000 | + | 15.5885i | 0.337289 | + | 0.584202i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | 1.34632 | ||||||||
\(716\) | −1.00000 | − | 1.73205i | −0.0373718 | − | 0.0647298i | ||||
\(717\) | −2.00000 | + | 3.46410i | −0.0746914 | + | 0.129369i | ||||
\(718\) | −12.0000 | + | 20.7846i | −0.447836 | + | 0.775675i | ||||
\(719\) | −8.00000 | − | 13.8564i | −0.298350 | − | 0.516757i | 0.677409 | − | 0.735607i | \(-0.263103\pi\) |
−0.975759 | + | 0.218850i | \(0.929769\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 14.0000 | + | 24.2487i | 0.520666 | + | 0.901819i | ||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | 4.00000 | − | 6.92820i | 0.148556 | − | 0.257307i | ||||
\(726\) | −12.5000 | − | 21.6506i | −0.463919 | − | 0.803530i | ||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.00000 | + | 5.19615i | 0.111035 | + | 0.192318i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −7.00000 | + | 12.1244i | −0.258727 | + | 0.448129i | ||||
\(733\) | −23.0000 | − | 39.8372i | −0.849524 | − | 1.47142i | −0.881633 | − | 0.471935i | \(-0.843556\pi\) |
0.0321090 | − | 0.999484i | \(-0.489778\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.0000 | − | 72.7461i | −1.54709 | − | 2.67964i | ||||
\(738\) | 5.00000 | − | 8.66025i | 0.184053 | − | 0.318788i | ||||
\(739\) | 20.0000 | − | 34.6410i | 0.735712 | − | 1.27429i | −0.218698 | − | 0.975793i | \(-0.570181\pi\) |
0.954410 | − | 0.298498i | \(-0.0964856\pi\) | |||||||
\(740\) | 2.00000 | + | 3.46410i | 0.0735215 | + | 0.127343i | ||||
\(741\) | 24.0000 | 0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 1.00000 | + | 1.73205i | 0.0366618 | + | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.00000 | + | 6.92820i | −0.146450 | + | 0.253660i | ||||
\(747\) | −4.00000 | − | 6.92820i | −0.146352 | − | 0.253490i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −20.0000 | − | 34.6410i | −0.729810 | − | 1.26407i | −0.956963 | − | 0.290209i | \(-0.906275\pi\) |
0.227153 | − | 0.973859i | \(-0.427058\pi\) | |||||||
\(752\) | −1.00000 | + | 1.73205i | −0.0364662 | + | 0.0631614i | ||||
\(753\) | 10.0000 | − | 17.3205i | 0.364420 | − | 0.631194i | ||||
\(754\) | 24.0000 | + | 41.5692i | 0.874028 | + | 1.51386i | ||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.0000 | −1.45382 | −0.726912 | − | 0.686730i | \(-0.759045\pi\) | ||||
−0.726912 | + | 0.686730i | \(0.759045\pi\) | |||||||
\(758\) | 8.00000 | + | 13.8564i | 0.290573 | + | 0.503287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.00000 | + | 3.46410i | −0.0725476 | + | 0.125656i | ||||
\(761\) | −3.00000 | − | 5.19615i | −0.108750 | − | 0.188360i | 0.806514 | − | 0.591215i | \(-0.201351\pi\) |
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(762\) | 4.00000 | 0.144905 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.0000 | −0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | − | 12.1244i | 0.252920 | − | 0.438071i | ||||
\(767\) | 12.0000 | − | 20.7846i | 0.433295 | − | 0.750489i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −40.0000 | −1.44244 | −0.721218 | − | 0.692708i | \(-0.756418\pi\) | ||||
−0.721218 | + | 0.692708i | \(0.756418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.00000 | −0.288113 | ||||||||
\(772\) | −11.0000 | − | 19.0526i | −0.395899 | − | 0.685717i | ||||
\(773\) | −13.0000 | + | 22.5167i | −0.467578 | + | 0.809868i | −0.999314 | − | 0.0370420i | \(-0.988206\pi\) |
0.531736 | + | 0.846910i | \(0.321540\pi\) | |||||||
\(774\) | −3.00000 | + | 5.19615i | −0.107833 | + | 0.186772i | ||||
\(775\) | 1.00000 | + | 1.73205i | 0.0359211 | + | 0.0622171i | ||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | −20.0000 | − | 34.6410i | −0.716574 | − | 1.24114i | ||||
\(780\) | 3.00000 | − | 5.19615i | 0.107417 | − | 0.186052i | ||||
\(781\) | −24.0000 | + | 41.5692i | −0.858788 | + | 1.48746i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | 6.00000 | + | 10.3923i | 0.214013 | + | 0.370681i | ||||
\(787\) | 10.0000 | − | 17.3205i | 0.356462 | − | 0.617409i | −0.630905 | − | 0.775860i | \(-0.717316\pi\) |
0.987367 | + | 0.158450i | \(0.0506498\pi\) | |||||||
\(788\) | −3.00000 | + | 5.19615i | −0.106871 | + | 0.185105i | ||||
\(789\) | −16.0000 | − | 27.7128i | −0.569615 | − | 0.986602i | ||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.00000 | −0.213201 | ||||||||
\(793\) | −42.0000 | − | 72.7461i | −1.49146 | − | 2.58329i | ||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | −5.00000 | + | 8.66025i | −0.177332 | + | 0.307148i | ||||
\(796\) | −9.00000 | − | 15.5885i | −0.318997 | − | 0.552518i | ||||
\(797\) | −18.0000 | −0.637593 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −9.00000 | + | 15.5885i | −0.317999 | + | 0.550791i | ||||
\(802\) | 1.00000 | − | 1.73205i | 0.0353112 | − | 0.0611608i | ||||
\(803\) | 18.0000 | + | 31.1769i | 0.635206 | + | 1.10021i | ||||
\(804\) | −14.0000 | −0.493742 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | −0.422682 | ||||||||
\(807\) | −11.0000 | − | 19.0526i | −0.387218 | − | 0.670682i | ||||
\(808\) | 7.00000 | − | 12.1244i | 0.246259 | − | 0.426533i | ||||
\(809\) | 9.00000 | − | 15.5885i | 0.316423 | − | 0.548061i | −0.663316 | − | 0.748340i | \(-0.730851\pi\) |
0.979739 | + | 0.200279i | \(0.0641847\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0000 | −0.631288 | ||||||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 1.00000 | − | 1.73205i | 0.0350285 | − | 0.0606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | + | 20.7846i | 0.419827 | + | 0.727161i | ||||
\(818\) | −16.0000 | −0.559427 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.0000 | −0.349215 | ||||||||
\(821\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | −5.00000 | + | 8.66025i | −0.174395 | + | 0.302061i | ||||
\(823\) | 12.0000 | − | 20.7846i | 0.418294 | − | 0.724506i | −0.577474 | − | 0.816409i | \(-0.695962\pi\) |
0.995768 | + | 0.0919029i | \(0.0292950\pi\) | |||||||
\(824\) | 6.00000 | + | 10.3923i | 0.209020 | + | 0.362033i | ||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.0000 | −0.834562 | −0.417281 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0000 | − | 19.0526i | 0.382046 | − | 0.661723i | −0.609309 | − | 0.792933i | \(-0.708553\pi\) |
0.991355 | + | 0.131210i | \(0.0418863\pi\) | |||||||
\(830\) | −4.00000 | + | 6.92820i | −0.138842 | + | 0.240481i | ||||
\(831\) | −4.00000 | − | 6.92820i | −0.138758 | − | 0.240337i | ||||
\(832\) | −6.00000 | −0.208013 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.00000 | −0.277017 | ||||||||
\(835\) | 9.00000 | + | 15.5885i | 0.311458 | + | 0.539461i | ||||
\(836\) | −12.0000 | + | 20.7846i | −0.415029 | + | 0.718851i | ||||
\(837\) | −1.00000 | + | 1.73205i | −0.0345651 | + | 0.0598684i | ||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | 44.0000 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | −17.0000 | − | 29.4449i | −0.585859 | − | 1.01474i | ||||
\(843\) | 3.00000 | − | 5.19615i | 0.103325 | − | 0.178965i | ||||
\(844\) | −6.00000 | + | 10.3923i | −0.206529 | + | 0.357718i | ||||
\(845\) | 11.5000 | + | 19.9186i | 0.395612 | + | 0.685220i | ||||
\(846\) | −2.00000 | −0.0687614 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.0000 | 0.343401 | ||||||||
\(849\) | −14.0000 | − | 24.2487i | −0.480479 | − | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 4.00000 | + | 6.92820i | 0.137038 | + | 0.237356i | ||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 2.00000 | + | 3.46410i | 0.0683586 | + | 0.118401i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 18.0000 | − | 31.1769i | 0.614510 | − | 1.06436i | ||||
\(859\) | 8.00000 | + | 13.8564i | 0.272956 | + | 0.472774i | 0.969618 | − | 0.244626i | \(-0.0786652\pi\) |
−0.696661 | + | 0.717400i | \(0.745332\pi\) | |||||||
\(860\) | 6.00000 | 0.204598 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.0000 | + | 27.7128i | 0.544646 | + | 0.943355i | 0.998629 | + | 0.0523446i | \(0.0166694\pi\) |
−0.453983 | + | 0.891010i | \(0.649997\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 3.00000 | − | 5.19615i | 0.102003 | − | 0.176674i | ||||
\(866\) | −9.00000 | − | 15.5885i | −0.305832 | − | 0.529717i | ||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.0000 | −1.62829 | ||||||||
\(870\) | −4.00000 | − | 6.92820i | −0.135613 | − | 0.234888i | ||||
\(871\) | 42.0000 | − | 72.7461i | 1.42312 | − | 2.46491i | ||||
\(872\) | 3.00000 | − | 5.19615i | 0.101593 | − | 0.175964i | ||||
\(873\) | 1.00000 | + | 1.73205i | 0.0338449 | + | 0.0586210i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | 16.0000 | + | 27.7128i | 0.540282 | + | 0.935795i | 0.998888 | + | 0.0471555i | \(0.0150156\pi\) |
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(878\) | −5.00000 | + | 8.66025i | −0.168742 | + | 0.292269i | ||||
\(879\) | −11.0000 | + | 19.0526i | −0.371021 | + | 0.642627i | ||||
\(880\) | 3.00000 | + | 5.19615i | 0.101130 | + | 0.175162i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.0000 | 0.471138 | 0.235569 | − | 0.971858i | \(-0.424305\pi\) | ||||
0.235569 | + | 0.971858i | \(0.424305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.00000 | + | 3.46410i | −0.0672293 | + | 0.116445i | ||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 13.0000 | + | 22.5167i | 0.436497 | + | 0.756035i | 0.997417 | − | 0.0718351i | \(-0.0228855\pi\) |
−0.560919 | + | 0.827871i | \(0.689552\pi\) | |||||||
\(888\) | 4.00000 | 0.134231 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | −3.00000 | − | 5.19615i | −0.100504 | − | 0.174078i | ||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | −4.00000 | + | 6.92820i | −0.133855 | + | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.00000 | −0.0668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.00000 | − | 8.66025i | −0.166852 | − | 0.288996i | ||||
\(899\) | −8.00000 | + | 13.8564i | −0.266815 | + | 0.462137i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −60.0000 | −1.99778 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −5.00000 | − | 8.66025i | −0.166206 | − | 0.287877i | ||||
\(906\) | 4.00000 | − | 6.92820i | 0.132891 | − | 0.230174i | ||||
\(907\) | 5.00000 | − | 8.66025i | 0.166022 | − | 0.287559i | −0.770996 | − | 0.636841i | \(-0.780241\pi\) |
0.937018 | + | 0.349281i | \(0.113574\pi\) | |||||||
\(908\) | 10.0000 | + | 17.3205i | 0.331862 | + | 0.574801i | ||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 2.00000 | + | 3.46410i | 0.0662266 | + | 0.114708i | ||||
\(913\) | −24.0000 | + | 41.5692i | −0.794284 | + | 1.37574i | ||||
\(914\) | 19.0000 | − | 32.9090i | 0.628464 | − | 1.08853i | ||||
\(915\) | 7.00000 | + | 12.1244i | 0.231413 | + | 0.400819i | ||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | + | 6.92820i | 0.131948 | + | 0.228540i | 0.924427 | − | 0.381358i | \(-0.124544\pi\) |
−0.792480 | + | 0.609898i | \(0.791210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | − | 17.3205i | 0.329511 | − | 0.570730i | ||||
\(922\) | 1.00000 | + | 1.73205i | 0.0329332 | + | 0.0570421i | ||||
\(923\) | −48.0000 | −1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 4.00000 | + | 6.92820i | 0.131448 | + | 0.227675i | ||||
\(927\) | −6.00000 | + | 10.3923i | −0.197066 | + | 0.341328i | ||||
\(928\) | −4.00000 | + | 6.92820i | −0.131306 | + | 0.227429i | ||||
\(929\) | 21.0000 | + | 36.3731i | 0.688988 | + | 1.19336i | 0.972166 | + | 0.234294i | \(0.0752779\pi\) |
−0.283178 | + | 0.959067i | \(0.591389\pi\) | |||||||
\(930\) | 2.00000 | 0.0655826 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.0000 | −0.327561 | ||||||||
\(933\) | 6.00000 | + | 10.3923i | 0.196431 | + | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.00000 | − | 5.19615i | −0.0980581 | − | 0.169842i | ||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.0000 | 0.848478 | ||||||||
\(940\) | 1.00000 | + | 1.73205i | 0.0326164 | + | 0.0564933i | ||||
\(941\) | 1.00000 | − | 1.73205i | 0.0325991 | − | 0.0564632i | −0.849266 | − | 0.527966i | \(-0.822955\pi\) |
0.881865 | + | 0.471503i | \(0.156288\pi\) | |||||||
\(942\) | −7.00000 | + | 12.1244i | −0.228072 | + | 0.395033i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.0000 | 1.17046 | ||||||||
\(947\) | 24.0000 | + | 41.5692i | 0.779895 | + | 1.35082i | 0.932002 | + | 0.362454i | \(0.118061\pi\) |
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(948\) | −4.00000 | + | 6.92820i | −0.129914 | + | 0.225018i | ||||
\(949\) | −18.0000 | + | 31.1769i | −0.584305 | + | 1.01205i | ||||
\(950\) | 2.00000 | + | 3.46410i | 0.0648886 | + | 0.112390i | ||||
\(951\) | −10.0000 | −0.324272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 5.00000 | + | 8.66025i | 0.161881 | + | 0.280386i | ||||
\(955\) | −10.0000 | + | 17.3205i | −0.323592 | + | 0.560478i | ||||
\(956\) | 2.00000 | − | 3.46410i | 0.0646846 | − | 0.112037i | ||||
\(957\) | −24.0000 | − | 41.5692i | −0.775810 | − | 1.34374i | ||||
\(958\) | −36.0000 | −1.16311 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −12.0000 | + | 20.7846i | −0.386896 | + | 0.670123i | ||||
\(963\) | −2.00000 | + | 3.46410i | −0.0644491 | + | 0.111629i | ||||
\(964\) | −14.0000 | − | 24.2487i | −0.450910 | − | 0.780998i | ||||
\(965\) | −22.0000 | −0.708205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.0000 | −1.54358 | −0.771788 | − | 0.635880i | \(-0.780637\pi\) | ||||
−0.771788 | + | 0.635880i | \(0.780637\pi\) | |||||||
\(968\) | 12.5000 | + | 21.6506i | 0.401765 | + | 0.695878i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.00000 | − | 1.73205i | 0.0321081 | − | 0.0556128i | ||||
\(971\) | −2.00000 | − | 3.46410i | −0.0641831 | − | 0.111168i | 0.832148 | − | 0.554553i | \(-0.187111\pi\) |
−0.896331 | + | 0.443385i | \(0.853777\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12.0000 | −0.384505 | ||||||||
\(975\) | −3.00000 | − | 5.19615i | −0.0960769 | − | 0.166410i | ||||
\(976\) | 7.00000 | − | 12.1244i | 0.224065 | − | 0.388091i | ||||
\(977\) | −27.0000 | + | 46.7654i | −0.863807 | + | 1.49616i | 0.00442082 | + | 0.999990i | \(0.498593\pi\) |
−0.868227 | + | 0.496167i | \(0.834741\pi\) | |||||||
\(978\) | −1.00000 | − | 1.73205i | −0.0319765 | − | 0.0553849i | ||||
\(979\) | 108.000 | 3.45169 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | −11.0000 | − | 19.0526i | −0.351024 | − | 0.607992i | ||||
\(983\) | −21.0000 | + | 36.3731i | −0.669796 | + | 1.16012i | 0.308165 | + | 0.951333i | \(0.400285\pi\) |
−0.977961 | + | 0.208788i | \(0.933048\pi\) | |||||||
\(984\) | −5.00000 | + | 8.66025i | −0.159394 | + | 0.276079i | ||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.0000 | −0.763542 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −3.00000 | + | 5.19615i | −0.0953463 | + | 0.165145i | ||||
\(991\) | −4.00000 | + | 6.92820i | −0.127064 | + | 0.220082i | −0.922538 | − | 0.385906i | \(-0.873889\pi\) |
0.795474 | + | 0.605988i | \(0.207222\pi\) | |||||||
\(992\) | −1.00000 | − | 1.73205i | −0.0317500 | − | 0.0549927i | ||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.0000 | −0.570638 | ||||||||
\(996\) | 4.00000 | + | 6.92820i | 0.126745 | + | 0.219529i | ||||
\(997\) | 21.0000 | − | 36.3731i | 0.665077 | − | 1.15195i | −0.314188 | − | 0.949361i | \(-0.601732\pi\) |
0.979265 | − | 0.202586i | \(-0.0649345\pi\) | |||||||
\(998\) | −16.0000 | + | 27.7128i | −0.506471 | + | 0.877234i | ||||
\(999\) | 2.00000 | + | 3.46410i | 0.0632772 | + | 0.109599i |
(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.r.361.1 | 2 | ||
7.2 | even | 3 | inner | 1470.2.i.r.961.1 | 2 | ||
7.3 | odd | 6 | 1470.2.a.i.1.1 | yes | 1 | ||
7.4 | even | 3 | 1470.2.a.c.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 1470.2.i.k.961.1 | 2 | |||
7.6 | odd | 2 | 1470.2.i.k.361.1 | 2 | |||
21.11 | odd | 6 | 4410.2.a.be.1.1 | 1 | |||
21.17 | even | 6 | 4410.2.a.v.1.1 | 1 | |||
35.4 | even | 6 | 7350.2.a.da.1.1 | 1 | |||
35.24 | odd | 6 | 7350.2.a.cf.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.a.c.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
1470.2.a.i.1.1 | yes | 1 | 7.3 | odd | 6 | ||
1470.2.i.k.361.1 | 2 | 7.6 | odd | 2 | |||
1470.2.i.k.961.1 | 2 | 7.5 | odd | 6 | |||
1470.2.i.r.361.1 | 2 | 1.1 | even | 1 | trivial | ||
1470.2.i.r.961.1 | 2 | 7.2 | even | 3 | inner | ||
4410.2.a.v.1.1 | 1 | 21.17 | even | 6 | |||
4410.2.a.be.1.1 | 1 | 21.11 | odd | 6 | |||
7350.2.a.cf.1.1 | 1 | 35.24 | odd | 6 | |||
7350.2.a.da.1.1 | 1 | 35.4 | even | 6 |