Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(61,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, 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("390.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.i (of order \(3\), degree \(2\), 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: | \(3.11416567883\) |
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 | 61.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.61 |
Dual form | 390.2.i.a.211.1 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −1.00000 | − | 1.73205i | −0.377964 | − | 0.654654i | 0.612801 | − | 0.790237i | \(-0.290043\pi\) |
−0.990766 | + | 0.135583i | \(0.956709\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | −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 | \(0.911312\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.50000 | + | 0.866025i | 0.686406 | + | 0.169842i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | + | 1.73205i | −0.188982 | + | 0.327327i | ||||
\(29\) | 0.500000 | − | 0.866025i | 0.0928477 | − | 0.160817i | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.500000 | + | 0.866025i | 0.0870388 | + | 0.150756i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 1.00000 | + | 1.73205i | 0.169031 | + | 0.292770i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 2.50000 | − | 4.33013i | 0.410997 | − | 0.711868i | −0.584002 | − | 0.811752i | \(-0.698514\pi\) |
0.994999 | + | 0.0998840i | \(0.0318472\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | −3.50000 | − | 0.866025i | −0.560449 | − | 0.138675i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.00000 | + | 8.66025i | −0.780869 | + | 1.35250i | 0.150567 | + | 0.988600i | \(0.451890\pi\) |
−0.931436 | + | 0.363905i | \(0.881443\pi\) | |||||||
\(42\) | 1.00000 | − | 1.73205i | 0.154303 | − | 0.267261i | ||||
\(43\) | −2.50000 | − | 4.33013i | −0.381246 | − | 0.660338i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −2.50000 | + | 2.59808i | −0.346688 | + | 0.360288i | ||||
\(53\) | 14.0000 | 1.92305 | 0.961524 | − | 0.274721i | \(-0.0885855\pi\) | ||||
0.961524 | + | 0.274721i | \(0.0885855\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0.500000 | − | 0.866025i | 0.0674200 | − | 0.116775i | ||||
\(56\) | −1.00000 | − | 1.73205i | −0.133631 | − | 0.231455i | ||||
\(57\) | −6.00000 | −0.794719 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | 2.50000 | + | 4.33013i | 0.325472 | + | 0.563735i | 0.981608 | − | 0.190909i | \(-0.0611434\pi\) |
−0.656136 | + | 0.754643i | \(0.727810\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 1.50000 | − | 2.59808i | 0.190500 | − | 0.329956i | ||||
\(63\) | −1.00000 | + | 1.73205i | −0.125988 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | + | 3.46410i | 0.124035 | + | 0.429669i | ||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(68\) | −1.00000 | + | 1.73205i | −0.121268 | + | 0.210042i | ||||
\(69\) | −1.50000 | − | 2.59808i | −0.180579 | − | 0.312772i | ||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | −2.00000 | − | 3.46410i | −0.237356 | − | 0.411113i | 0.722599 | − | 0.691268i | \(-0.242948\pi\) |
−0.959955 | + | 0.280155i | \(0.909614\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 2.50000 | + | 4.33013i | 0.290619 | + | 0.503367i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | −3.00000 | + | 5.19615i | −0.344124 | + | 0.596040i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 2.50000 | − | 2.59808i | 0.283069 | − | 0.294174i | ||||
\(79\) | 5.00000 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(80\) | 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 | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 1.00000 | + | 1.73205i | 0.109109 | + | 0.188982i | ||||
\(85\) | 1.00000 | + | 1.73205i | 0.108465 | + | 0.187867i | ||||
\(86\) | 5.00000 | 0.539164 | ||||||||
\(87\) | −0.500000 | − | 0.866025i | −0.0536056 | − | 0.0928477i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −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 | ||||||||
\(91\) | −5.00000 | + | 5.19615i | −0.524142 | + | 0.544705i | ||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | −1.50000 | + | 2.59808i | −0.155543 | + | 0.269408i | ||||
\(94\) | −1.50000 | + | 2.59808i | −0.154713 | + | 0.267971i | ||||
\(95\) | 3.00000 | + | 5.19615i | 0.307794 | + | 0.533114i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.00000 | + | 8.66025i | 0.507673 | + | 0.879316i | 0.999961 | + | 0.00888289i | \(0.00282755\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | 1.50000 | + | 2.59808i | 0.151523 | + | 0.262445i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −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 | \(0.921395\pi\) | |||||||
\(102\) | 1.00000 | − | 1.73205i | 0.0990148 | − | 0.171499i | ||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | −1.00000 | − | 3.46410i | −0.0980581 | − | 0.339683i | ||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | −7.00000 | + | 12.1244i | −0.679900 | + | 1.17762i | ||||
\(107\) | 3.00000 | − | 5.19615i | 0.290021 | − | 0.502331i | −0.683793 | − | 0.729676i | \(-0.739671\pi\) |
0.973814 | + | 0.227345i | \(0.0730044\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −6.00000 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | 0.500000 | + | 0.866025i | 0.0476731 | + | 0.0825723i | ||||
\(111\) | −2.50000 | − | 4.33013i | −0.237289 | − | 0.410997i | ||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | −8.50000 | − | 14.7224i | −0.799613 | − | 1.38497i | −0.919868 | − | 0.392227i | \(-0.871705\pi\) |
0.120256 | − | 0.992743i | \(-0.461629\pi\) | |||||||
\(114\) | 3.00000 | − | 5.19615i | 0.280976 | − | 0.486664i | ||||
\(115\) | −1.50000 | + | 2.59808i | −0.139876 | + | 0.242272i | ||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −2.50000 | + | 2.59808i | −0.231125 | + | 0.240192i | ||||
\(118\) | −5.00000 | −0.460287 | ||||||||
\(119\) | −2.00000 | + | 3.46410i | −0.183340 | + | 0.317554i | ||||
\(120\) | −0.500000 | + | 0.866025i | −0.0456435 | + | 0.0790569i | ||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 5.00000 | + | 8.66025i | 0.450835 | + | 0.780869i | ||||
\(124\) | 1.50000 | + | 2.59808i | 0.134704 | + | 0.233314i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.00000 | − | 1.73205i | −0.0890871 | − | 0.154303i | ||||
\(127\) | 7.00000 | − | 12.1244i | 0.621150 | − | 1.07586i | −0.368122 | − | 0.929777i | \(-0.619999\pi\) |
0.989272 | − | 0.146085i | \(-0.0466674\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −5.00000 | −0.440225 | ||||||||
\(130\) | −3.50000 | − | 0.866025i | −0.306970 | − | 0.0759555i | ||||
\(131\) | 13.0000 | 1.13582 | 0.567908 | − | 0.823092i | \(-0.307753\pi\) | ||||
0.567908 | + | 0.823092i | \(0.307753\pi\) | |||||||
\(132\) | 0.500000 | − | 0.866025i | 0.0435194 | − | 0.0753778i | ||||
\(133\) | −6.00000 | + | 10.3923i | −0.520266 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −1.00000 | − | 1.73205i | −0.0857493 | − | 0.148522i | ||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | 3.00000 | 0.255377 | ||||||||
\(139\) | −5.00000 | − | 8.66025i | −0.424094 | − | 0.734553i | 0.572241 | − | 0.820086i | \(-0.306074\pi\) |
−0.996335 | + | 0.0855324i | \(0.972741\pi\) | |||||||
\(140\) | 1.00000 | − | 1.73205i | 0.0845154 | − | 0.146385i | ||||
\(141\) | 1.50000 | − | 2.59808i | 0.126323 | − | 0.218797i | ||||
\(142\) | 4.00000 | 0.335673 | ||||||||
\(143\) | 3.50000 | + | 0.866025i | 0.292685 | + | 0.0724207i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.500000 | + | 0.866025i | −0.0415227 | + | 0.0719195i | ||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | −1.50000 | − | 2.59808i | −0.123718 | − | 0.214286i | ||||
\(148\) | −5.00000 | −0.410997 | ||||||||
\(149\) | −5.50000 | − | 9.52628i | −0.450578 | − | 0.780423i | 0.547844 | − | 0.836580i | \(-0.315449\pi\) |
−0.998422 | + | 0.0561570i | \(0.982115\pi\) | |||||||
\(150\) | 0.500000 | + | 0.866025i | 0.0408248 | + | 0.0707107i | ||||
\(151\) | 24.0000 | 1.95309 | 0.976546 | − | 0.215308i | \(-0.0690756\pi\) | ||||
0.976546 | + | 0.215308i | \(0.0690756\pi\) | |||||||
\(152\) | −3.00000 | − | 5.19615i | −0.243332 | − | 0.421464i | ||||
\(153\) | −1.00000 | + | 1.73205i | −0.0808452 | + | 0.140028i | ||||
\(154\) | −1.00000 | + | 1.73205i | −0.0805823 | + | 0.139573i | ||||
\(155\) | 3.00000 | 0.240966 | ||||||||
\(156\) | 1.00000 | + | 3.46410i | 0.0800641 | + | 0.277350i | ||||
\(157\) | 25.0000 | 1.99522 | 0.997609 | − | 0.0691164i | \(-0.0220180\pi\) | ||||
0.997609 | + | 0.0691164i | \(0.0220180\pi\) | |||||||
\(158\) | −2.50000 | + | 4.33013i | −0.198889 | + | 0.344486i | ||||
\(159\) | 7.00000 | − | 12.1244i | 0.555136 | − | 0.961524i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −8.50000 | − | 14.7224i | −0.665771 | − | 1.15315i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.313304 | − | 0.949653i | \(-0.398564\pi\) | |||||||
\(164\) | 10.0000 | 0.780869 | ||||||||
\(165\) | −0.500000 | − | 0.866025i | −0.0389249 | − | 0.0674200i | ||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | 3.50000 | − | 6.06218i | 0.270838 | − | 0.469105i | −0.698239 | − | 0.715865i | \(-0.746033\pi\) |
0.969077 | + | 0.246760i | \(0.0793659\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | −3.00000 | + | 5.19615i | −0.229416 | + | 0.397360i | ||||
\(172\) | −2.50000 | + | 4.33013i | −0.190623 | + | 0.330169i | ||||
\(173\) | −2.00000 | − | 3.46410i | −0.152057 | − | 0.263371i | 0.779926 | − | 0.625871i | \(-0.215256\pi\) |
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | −0.500000 | − | 0.866025i | −0.0376889 | − | 0.0652791i | ||||
\(177\) | 5.00000 | 0.375823 | ||||||||
\(178\) | −5.00000 | − | 8.66025i | −0.374766 | − | 0.649113i | ||||
\(179\) | 3.50000 | − | 6.06218i | 0.261602 | − | 0.453108i | −0.705066 | − | 0.709142i | \(-0.749082\pi\) |
0.966668 | + | 0.256034i | \(0.0824158\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | −2.00000 | − | 6.92820i | −0.148250 | − | 0.513553i | ||||
\(183\) | 10.0000 | 0.739221 | ||||||||
\(184\) | 1.50000 | − | 2.59808i | 0.110581 | − | 0.191533i | ||||
\(185\) | −2.50000 | + | 4.33013i | −0.183804 | + | 0.318357i | ||||
\(186\) | −1.50000 | − | 2.59808i | −0.109985 | − | 0.190500i | ||||
\(187\) | 2.00000 | 0.146254 | ||||||||
\(188\) | −1.50000 | − | 2.59808i | −0.109399 | − | 0.189484i | ||||
\(189\) | 1.00000 | + | 1.73205i | 0.0727393 | + | 0.125988i | ||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | −12.0000 | − | 20.7846i | −0.868290 | − | 1.50392i | −0.863743 | − | 0.503932i | \(-0.831886\pi\) |
−0.00454614 | − | 0.999990i | \(-0.501447\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.00000 | − | 3.46410i | 0.143963 | − | 0.249351i | −0.785022 | − | 0.619467i | \(-0.787349\pi\) |
0.928986 | + | 0.370116i | \(0.120682\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 3.50000 | + | 0.866025i | 0.250640 | + | 0.0620174i | ||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 6.00000 | − | 10.3923i | 0.427482 | − | 0.740421i | −0.569166 | − | 0.822222i | \(-0.692734\pi\) |
0.996649 | + | 0.0818013i | \(0.0260673\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.00000 | − | 12.1244i | −0.492518 | − | 0.853067i | ||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 1.00000 | + | 1.73205i | 0.0700140 | + | 0.121268i | ||||
\(205\) | 5.00000 | − | 8.66025i | 0.349215 | − | 0.604858i | ||||
\(206\) | 3.00000 | − | 5.19615i | 0.209020 | − | 0.362033i | ||||
\(207\) | −3.00000 | −0.208514 | ||||||||
\(208\) | 3.50000 | + | 0.866025i | 0.242681 | + | 0.0600481i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | −1.00000 | + | 1.73205i | −0.0690066 | + | 0.119523i | ||||
\(211\) | 4.00000 | − | 6.92820i | 0.275371 | − | 0.476957i | −0.694857 | − | 0.719148i | \(-0.744533\pi\) |
0.970229 | + | 0.242190i | \(0.0778659\pi\) | |||||||
\(212\) | −7.00000 | − | 12.1244i | −0.480762 | − | 0.832704i | ||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | 2.50000 | + | 4.33013i | 0.170499 | + | 0.295312i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.00000 | + | 5.19615i | 0.203653 | + | 0.352738i | ||||
\(218\) | 3.00000 | − | 5.19615i | 0.203186 | − | 0.351928i | ||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −5.00000 | + | 5.19615i | −0.336336 | + | 0.349531i | ||||
\(222\) | 5.00000 | 0.335578 | ||||||||
\(223\) | −5.00000 | + | 8.66025i | −0.334825 | + | 0.579934i | −0.983451 | − | 0.181173i | \(-0.942010\pi\) |
0.648626 | + | 0.761107i | \(0.275344\pi\) | |||||||
\(224\) | −1.00000 | + | 1.73205i | −0.0668153 | + | 0.115728i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 17.0000 | 1.13082 | ||||||||
\(227\) | −10.0000 | − | 17.3205i | −0.663723 | − | 1.14960i | −0.979630 | − | 0.200812i | \(-0.935642\pi\) |
0.315906 | − | 0.948790i | \(-0.397691\pi\) | |||||||
\(228\) | 3.00000 | + | 5.19615i | 0.198680 | + | 0.344124i | ||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | −1.50000 | − | 2.59808i | −0.0989071 | − | 0.171312i | ||||
\(231\) | 1.00000 | − | 1.73205i | 0.0657952 | − | 0.113961i | ||||
\(232\) | 0.500000 | − | 0.866025i | 0.0328266 | − | 0.0568574i | ||||
\(233\) | 3.00000 | 0.196537 | 0.0982683 | − | 0.995160i | \(-0.468670\pi\) | ||||
0.0982683 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(234\) | −1.00000 | − | 3.46410i | −0.0653720 | − | 0.226455i | ||||
\(235\) | −3.00000 | −0.195698 | ||||||||
\(236\) | 2.50000 | − | 4.33013i | 0.162736 | − | 0.281867i | ||||
\(237\) | 2.50000 | − | 4.33013i | 0.162392 | − | 0.281272i | ||||
\(238\) | −2.00000 | − | 3.46410i | −0.129641 | − | 0.224544i | ||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | −0.500000 | − | 0.866025i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | 3.50000 | + | 6.06218i | 0.225455 | + | 0.390499i | 0.956456 | − | 0.291877i | \(-0.0942799\pi\) |
−0.731001 | + | 0.682376i | \(0.760947\pi\) | |||||||
\(242\) | −10.0000 | −0.642824 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 5.00000 | − | 8.66025i | 0.320092 | − | 0.554416i | ||||
\(245\) | −1.50000 | + | 2.59808i | −0.0958315 | + | 0.165985i | ||||
\(246\) | −10.0000 | −0.637577 | ||||||||
\(247\) | −15.0000 | + | 15.5885i | −0.954427 | + | 0.991870i | ||||
\(248\) | −3.00000 | −0.190500 | ||||||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −1.50000 | − | 2.59808i | −0.0946792 | − | 0.163989i | 0.814795 | − | 0.579748i | \(-0.196849\pi\) |
−0.909475 | + | 0.415759i | \(0.863516\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 1.50000 | + | 2.59808i | 0.0943042 | + | 0.163340i | ||||
\(254\) | 7.00000 | + | 12.1244i | 0.439219 | + | 0.760750i | ||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.5000 | + | 18.1865i | −0.654972 | + | 1.13444i | 0.326929 | + | 0.945049i | \(0.393986\pi\) |
−0.981901 | + | 0.189396i | \(0.939347\pi\) | |||||||
\(258\) | 2.50000 | − | 4.33013i | 0.155643 | − | 0.269582i | ||||
\(259\) | −10.0000 | −0.621370 | ||||||||
\(260\) | 2.50000 | − | 2.59808i | 0.155043 | − | 0.161126i | ||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −6.50000 | + | 11.2583i | −0.401571 | + | 0.695542i | ||||
\(263\) | −11.5000 | + | 19.9186i | −0.709120 | + | 1.22823i | 0.256063 | + | 0.966660i | \(0.417574\pi\) |
−0.965184 | + | 0.261573i | \(0.915759\pi\) | |||||||
\(264\) | 0.500000 | + | 0.866025i | 0.0307729 | + | 0.0533002i | ||||
\(265\) | −14.0000 | −0.860013 | ||||||||
\(266\) | −6.00000 | − | 10.3923i | −0.367884 | − | 0.637193i | ||||
\(267\) | 5.00000 | + | 8.66025i | 0.305995 | + | 0.529999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | 14.5000 | − | 25.1147i | 0.880812 | − | 1.52561i | 0.0303728 | − | 0.999539i | \(-0.490331\pi\) |
0.850439 | − | 0.526073i | \(-0.176336\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 2.00000 | + | 6.92820i | 0.121046 | + | 0.419314i | ||||
\(274\) | −9.00000 | −0.543710 | ||||||||
\(275\) | −0.500000 | + | 0.866025i | −0.0301511 | + | 0.0522233i | ||||
\(276\) | −1.50000 | + | 2.59808i | −0.0902894 | + | 0.156386i | ||||
\(277\) | 9.50000 | + | 16.4545i | 0.570800 | + | 0.988654i | 0.996484 | + | 0.0837823i | \(0.0267000\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(278\) | 10.0000 | 0.599760 | ||||||||
\(279\) | 1.50000 | + | 2.59808i | 0.0898027 | + | 0.155543i | ||||
\(280\) | 1.00000 | + | 1.73205i | 0.0597614 | + | 0.103510i | ||||
\(281\) | −30.0000 | −1.78965 | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 1.50000 | + | 2.59808i | 0.0893237 | + | 0.154713i | ||||
\(283\) | 6.50000 | − | 11.2583i | 0.386385 | − | 0.669238i | −0.605575 | − | 0.795788i | \(-0.707057\pi\) |
0.991960 | + | 0.126550i | \(0.0403903\pi\) | |||||||
\(284\) | −2.00000 | + | 3.46410i | −0.118678 | + | 0.205557i | ||||
\(285\) | 6.00000 | 0.355409 | ||||||||
\(286\) | −2.50000 | + | 2.59808i | −0.147828 | + | 0.153627i | ||||
\(287\) | 20.0000 | 1.18056 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | −0.500000 | − | 0.866025i | −0.0293610 | − | 0.0508548i | ||||
\(291\) | 10.0000 | 0.586210 | ||||||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | 7.00000 | + | 12.1244i | 0.408944 | + | 0.708312i | 0.994772 | − | 0.102123i | \(-0.0325637\pi\) |
−0.585827 | + | 0.810436i | \(0.699230\pi\) | |||||||
\(294\) | 3.00000 | 0.174964 | ||||||||
\(295\) | −2.50000 | − | 4.33013i | −0.145556 | − | 0.252110i | ||||
\(296\) | 2.50000 | − | 4.33013i | 0.145310 | − | 0.251684i | ||||
\(297\) | 0.500000 | − | 0.866025i | 0.0290129 | − | 0.0502519i | ||||
\(298\) | 11.0000 | 0.637213 | ||||||||
\(299\) | −10.5000 | − | 2.59808i | −0.607231 | − | 0.150251i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −5.00000 | + | 8.66025i | −0.288195 | + | 0.499169i | ||||
\(302\) | −12.0000 | + | 20.7846i | −0.690522 | + | 1.19602i | ||||
\(303\) | 7.00000 | + | 12.1244i | 0.402139 | + | 0.696526i | ||||
\(304\) | 6.00000 | 0.344124 | ||||||||
\(305\) | −5.00000 | − | 8.66025i | −0.286299 | − | 0.495885i | ||||
\(306\) | −1.00000 | − | 1.73205i | −0.0571662 | − | 0.0990148i | ||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −1.00000 | − | 1.73205i | −0.0569803 | − | 0.0986928i | ||||
\(309\) | −3.00000 | + | 5.19615i | −0.170664 | + | 0.295599i | ||||
\(310\) | −1.50000 | + | 2.59808i | −0.0851943 | + | 0.147561i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | −3.50000 | − | 0.866025i | −0.198148 | − | 0.0490290i | ||||
\(313\) | −12.0000 | −0.678280 | −0.339140 | − | 0.940736i | \(-0.610136\pi\) | ||||
−0.339140 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(314\) | −12.5000 | + | 21.6506i | −0.705416 | + | 1.22182i | ||||
\(315\) | 1.00000 | − | 1.73205i | 0.0563436 | − | 0.0975900i | ||||
\(316\) | −2.50000 | − | 4.33013i | −0.140636 | − | 0.243589i | ||||
\(317\) | 12.0000 | 0.673987 | 0.336994 | − | 0.941507i | \(-0.390590\pi\) | ||||
0.336994 | + | 0.941507i | \(0.390590\pi\) | |||||||
\(318\) | 7.00000 | + | 12.1244i | 0.392541 | + | 0.679900i | ||||
\(319\) | 0.500000 | + | 0.866025i | 0.0279946 | + | 0.0484881i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.00000 | − | 5.19615i | −0.167444 | − | 0.290021i | ||||
\(322\) | 3.00000 | − | 5.19615i | 0.167183 | − | 0.289570i | ||||
\(323\) | −6.00000 | + | 10.3923i | −0.333849 | + | 0.578243i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.00000 | − | 3.46410i | −0.0554700 | − | 0.192154i | ||||
\(326\) | 17.0000 | 0.941543 | ||||||||
\(327\) | −3.00000 | + | 5.19615i | −0.165900 | + | 0.287348i | ||||
\(328\) | −5.00000 | + | 8.66025i | −0.276079 | + | 0.478183i | ||||
\(329\) | −3.00000 | − | 5.19615i | −0.165395 | − | 0.286473i | ||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 3.00000 | + | 5.19615i | 0.164646 | + | 0.285176i | ||||
\(333\) | −5.00000 | −0.273998 | ||||||||
\(334\) | 3.50000 | + | 6.06218i | 0.191511 | + | 0.331708i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.00000 | − | 1.73205i | 0.0545545 | − | 0.0944911i | ||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | −0.500000 | − | 12.9904i | −0.0271964 | − | 0.706584i | ||||
\(339\) | −17.0000 | −0.923313 | ||||||||
\(340\) | 1.00000 | − | 1.73205i | 0.0542326 | − | 0.0939336i | ||||
\(341\) | 1.50000 | − | 2.59808i | 0.0812296 | − | 0.140694i | ||||
\(342\) | −3.00000 | − | 5.19615i | −0.162221 | − | 0.280976i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −2.50000 | − | 4.33013i | −0.134791 | − | 0.233465i | ||||
\(345\) | 1.50000 | + | 2.59808i | 0.0807573 | + | 0.139876i | ||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | 9.00000 | + | 15.5885i | 0.483145 | + | 0.836832i | 0.999813 | − | 0.0193540i | \(-0.00616095\pi\) |
−0.516667 | + | 0.856186i | \(0.672828\pi\) | |||||||
\(348\) | −0.500000 | + | 0.866025i | −0.0268028 | + | 0.0464238i | ||||
\(349\) | −4.00000 | + | 6.92820i | −0.214115 | + | 0.370858i | −0.952998 | − | 0.302975i | \(-0.902020\pi\) |
0.738883 | + | 0.673833i | \(0.235353\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 1.00000 | + | 3.46410i | 0.0533761 | + | 0.184900i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 7.00000 | − | 12.1244i | 0.372572 | − | 0.645314i | −0.617388 | − | 0.786659i | \(-0.711809\pi\) |
0.989960 | + | 0.141344i | \(0.0451425\pi\) | |||||||
\(354\) | −2.50000 | + | 4.33013i | −0.132874 | + | 0.230144i | ||||
\(355\) | 2.00000 | + | 3.46410i | 0.106149 | + | 0.183855i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 2.00000 | + | 3.46410i | 0.105851 | + | 0.183340i | ||||
\(358\) | 3.50000 | + | 6.06218i | 0.184981 | + | 0.320396i | ||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −8.00000 | + | 13.8564i | −0.420471 | + | 0.728277i | ||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | 7.00000 | + | 1.73205i | 0.366900 | + | 0.0907841i | ||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | −5.00000 | + | 8.66025i | −0.261354 | + | 0.452679i | ||||
\(367\) | −18.0000 | + | 31.1769i | −0.939592 | + | 1.62742i | −0.173360 | + | 0.984859i | \(0.555462\pi\) |
−0.766233 | + | 0.642563i | \(0.777871\pi\) | |||||||
\(368\) | 1.50000 | + | 2.59808i | 0.0781929 | + | 0.135434i | ||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | −2.50000 | − | 4.33013i | −0.129969 | − | 0.225113i | ||||
\(371\) | −14.0000 | − | 24.2487i | −0.726844 | − | 1.25893i | ||||
\(372\) | 3.00000 | 0.155543 | ||||||||
\(373\) | −18.5000 | − | 32.0429i | −0.957894 | − | 1.65912i | −0.727603 | − | 0.685999i | \(-0.759366\pi\) |
−0.230291 | − | 0.973122i | \(-0.573968\pi\) | |||||||
\(374\) | −1.00000 | + | 1.73205i | −0.0517088 | + | 0.0895622i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | −3.50000 | − | 0.866025i | −0.180259 | − | 0.0446026i | ||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 15.0000 | − | 25.9808i | 0.770498 | − | 1.33454i | −0.166792 | − | 0.985992i | \(-0.553341\pi\) |
0.937290 | − | 0.348550i | \(-0.113326\pi\) | |||||||
\(380\) | 3.00000 | − | 5.19615i | 0.153897 | − | 0.266557i | ||||
\(381\) | −7.00000 | − | 12.1244i | −0.358621 | − | 0.621150i | ||||
\(382\) | 24.0000 | 1.22795 | ||||||||
\(383\) | 13.5000 | + | 23.3827i | 0.689818 | + | 1.19480i | 0.971897 | + | 0.235408i | \(0.0756427\pi\) |
−0.282079 | + | 0.959391i | \(0.591024\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −2.00000 | −0.101929 | ||||||||
\(386\) | 2.00000 | + | 3.46410i | 0.101797 | + | 0.176318i | ||||
\(387\) | −2.50000 | + | 4.33013i | −0.127082 | + | 0.220113i | ||||
\(388\) | 5.00000 | − | 8.66025i | 0.253837 | − | 0.439658i | ||||
\(389\) | −1.00000 | −0.0507020 | −0.0253510 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253510 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(390\) | −2.50000 | + | 2.59808i | −0.126592 | + | 0.131559i | ||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | 1.50000 | − | 2.59808i | 0.0757614 | − | 0.131223i | ||||
\(393\) | 6.50000 | − | 11.2583i | 0.327882 | − | 0.567908i | ||||
\(394\) | 6.00000 | + | 10.3923i | 0.302276 | + | 0.523557i | ||||
\(395\) | −5.00000 | −0.251577 | ||||||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 6.50000 | + | 11.2583i | 0.326226 | + | 0.565039i | 0.981760 | − | 0.190126i | \(-0.0608897\pi\) |
−0.655534 | + | 0.755166i | \(0.727556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.00000 | + | 10.3923i | 0.300376 | + | 0.520266i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00000 | + | 10.3923i | 0.149441 | + | 0.517678i | ||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 1.00000 | − | 1.73205i | 0.0496292 | − | 0.0859602i | ||||
\(407\) | 2.50000 | + | 4.33013i | 0.123920 | + | 0.214636i | ||||
\(408\) | −2.00000 | −0.0990148 | ||||||||
\(409\) | 13.0000 | + | 22.5167i | 0.642809 | + | 1.11338i | 0.984803 | + | 0.173675i | \(0.0555643\pi\) |
−0.341994 | + | 0.939702i | \(0.611102\pi\) | |||||||
\(410\) | 5.00000 | + | 8.66025i | 0.246932 | + | 0.427699i | ||||
\(411\) | 9.00000 | 0.443937 | ||||||||
\(412\) | 3.00000 | + | 5.19615i | 0.147799 | + | 0.255996i | ||||
\(413\) | 5.00000 | − | 8.66025i | 0.246034 | − | 0.426143i | ||||
\(414\) | 1.50000 | − | 2.59808i | 0.0737210 | − | 0.127688i | ||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | −10.0000 | −0.489702 | ||||||||
\(418\) | −3.00000 | + | 5.19615i | −0.146735 | + | 0.254152i | ||||
\(419\) | −2.00000 | + | 3.46410i | −0.0977064 | + | 0.169232i | −0.910735 | − | 0.412991i | \(-0.864484\pi\) |
0.813029 | + | 0.582224i | \(0.197817\pi\) | |||||||
\(420\) | −1.00000 | − | 1.73205i | −0.0487950 | − | 0.0845154i | ||||
\(421\) | 28.0000 | 1.36464 | 0.682318 | − | 0.731055i | \(-0.260972\pi\) | ||||
0.682318 | + | 0.731055i | \(0.260972\pi\) | |||||||
\(422\) | 4.00000 | + | 6.92820i | 0.194717 | + | 0.337260i | ||||
\(423\) | −1.50000 | − | 2.59808i | −0.0729325 | − | 0.126323i | ||||
\(424\) | 14.0000 | 0.679900 | ||||||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | 2.00000 | − | 3.46410i | 0.0969003 | − | 0.167836i | ||||
\(427\) | 10.0000 | − | 17.3205i | 0.483934 | − | 0.838198i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 2.50000 | − | 2.59808i | 0.120701 | − | 0.125436i | ||||
\(430\) | −5.00000 | −0.241121 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −8.00000 | − | 13.8564i | −0.384455 | − | 0.665896i | 0.607238 | − | 0.794520i | \(-0.292277\pi\) |
−0.991693 | + | 0.128624i | \(0.958944\pi\) | |||||||
\(434\) | −6.00000 | −0.288009 | ||||||||
\(435\) | 0.500000 | + | 0.866025i | 0.0239732 | + | 0.0415227i | ||||
\(436\) | 3.00000 | + | 5.19615i | 0.143674 | + | 0.248851i | ||||
\(437\) | −18.0000 | −0.861057 | ||||||||
\(438\) | −1.00000 | − | 1.73205i | −0.0477818 | − | 0.0827606i | ||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0.500000 | − | 0.866025i | 0.0238366 | − | 0.0412861i | ||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −2.00000 | − | 6.92820i | −0.0951303 | − | 0.329541i | ||||
\(443\) | 16.0000 | 0.760183 | 0.380091 | − | 0.924949i | \(-0.375893\pi\) | ||||
0.380091 | + | 0.924949i | \(0.375893\pi\) | |||||||
\(444\) | −2.50000 | + | 4.33013i | −0.118645 | + | 0.205499i | ||||
\(445\) | 5.00000 | − | 8.66025i | 0.237023 | − | 0.410535i | ||||
\(446\) | −5.00000 | − | 8.66025i | −0.236757 | − | 0.410075i | ||||
\(447\) | −11.0000 | −0.520282 | ||||||||
\(448\) | −1.00000 | − | 1.73205i | −0.0472456 | − | 0.0818317i | ||||
\(449\) | 18.0000 | + | 31.1769i | 0.849473 | + | 1.47133i | 0.881680 | + | 0.471848i | \(0.156413\pi\) |
−0.0322072 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −5.00000 | − | 8.66025i | −0.235441 | − | 0.407795i | ||||
\(452\) | −8.50000 | + | 14.7224i | −0.399806 | + | 0.692485i | ||||
\(453\) | 12.0000 | − | 20.7846i | 0.563809 | − | 0.976546i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 5.00000 | − | 5.19615i | 0.234404 | − | 0.243599i | ||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | −7.00000 | + | 12.1244i | −0.327446 | + | 0.567153i | −0.982004 | − | 0.188858i | \(-0.939521\pi\) |
0.654558 | + | 0.756012i | \(0.272855\pi\) | |||||||
\(458\) | −11.0000 | + | 19.0526i | −0.513996 | + | 0.890268i | ||||
\(459\) | 1.00000 | + | 1.73205i | 0.0466760 | + | 0.0808452i | ||||
\(460\) | 3.00000 | 0.139876 | ||||||||
\(461\) | −13.5000 | − | 23.3827i | −0.628758 | − | 1.08904i | −0.987801 | − | 0.155719i | \(-0.950230\pi\) |
0.359044 | − | 0.933321i | \(-0.383103\pi\) | |||||||
\(462\) | 1.00000 | + | 1.73205i | 0.0465242 | + | 0.0805823i | ||||
\(463\) | 10.0000 | 0.464739 | 0.232370 | − | 0.972628i | \(-0.425352\pi\) | ||||
0.232370 | + | 0.972628i | \(0.425352\pi\) | |||||||
\(464\) | 0.500000 | + | 0.866025i | 0.0232119 | + | 0.0402042i | ||||
\(465\) | 1.50000 | − | 2.59808i | 0.0695608 | − | 0.120483i | ||||
\(466\) | −1.50000 | + | 2.59808i | −0.0694862 | + | 0.120354i | ||||
\(467\) | −2.00000 | −0.0925490 | −0.0462745 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462745 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(468\) | 3.50000 | + | 0.866025i | 0.161788 | + | 0.0400320i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.50000 | − | 2.59808i | 0.0691898 | − | 0.119840i | ||||
\(471\) | 12.5000 | − | 21.6506i | 0.575970 | − | 0.997609i | ||||
\(472\) | 2.50000 | + | 4.33013i | 0.115072 | + | 0.199310i | ||||
\(473\) | 5.00000 | 0.229900 | ||||||||
\(474\) | 2.50000 | + | 4.33013i | 0.114829 | + | 0.198889i | ||||
\(475\) | −3.00000 | − | 5.19615i | −0.137649 | − | 0.238416i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | −7.00000 | − | 12.1244i | −0.320508 | − | 0.555136i | ||||
\(478\) | 4.00000 | − | 6.92820i | 0.182956 | − | 0.316889i | ||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −17.5000 | − | 4.33013i | −0.797931 | − | 0.197437i | ||||
\(482\) | −7.00000 | −0.318841 | ||||||||
\(483\) | −3.00000 | + | 5.19615i | −0.136505 | + | 0.236433i | ||||
\(484\) | 5.00000 | − | 8.66025i | 0.227273 | − | 0.393648i | ||||
\(485\) | −5.00000 | − | 8.66025i | −0.227038 | − | 0.393242i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −1.00000 | − | 1.73205i | −0.0453143 | − | 0.0784867i | 0.842479 | − | 0.538730i | \(-0.181096\pi\) |
−0.887793 | + | 0.460243i | \(0.847762\pi\) | |||||||
\(488\) | 5.00000 | + | 8.66025i | 0.226339 | + | 0.392031i | ||||
\(489\) | −17.0000 | −0.768767 | ||||||||
\(490\) | −1.50000 | − | 2.59808i | −0.0677631 | − | 0.117369i | ||||
\(491\) | −12.0000 | + | 20.7846i | −0.541552 | + | 0.937996i | 0.457263 | + | 0.889332i | \(0.348830\pi\) |
−0.998815 | + | 0.0486647i | \(0.984503\pi\) | |||||||
\(492\) | 5.00000 | − | 8.66025i | 0.225417 | − | 0.390434i | ||||
\(493\) | −2.00000 | −0.0900755 | ||||||||
\(494\) | −6.00000 | − | 20.7846i | −0.269953 | − | 0.935144i | ||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 1.50000 | − | 2.59808i | 0.0673520 | − | 0.116657i | ||||
\(497\) | −4.00000 | + | 6.92820i | −0.179425 | + | 0.310772i | ||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | −40.0000 | −1.79065 | −0.895323 | − | 0.445418i | \(-0.853055\pi\) | ||||
−0.895323 | + | 0.445418i | \(0.853055\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −3.50000 | − | 6.06218i | −0.156368 | − | 0.270838i | ||||
\(502\) | 3.00000 | 0.133897 | ||||||||
\(503\) | −20.0000 | − | 34.6410i | −0.891756 | − | 1.54457i | −0.837769 | − | 0.546025i | \(-0.816140\pi\) |
−0.0539870 | − | 0.998542i | \(-0.517193\pi\) | |||||||
\(504\) | −1.00000 | + | 1.73205i | −0.0445435 | + | 0.0771517i | ||||
\(505\) | 7.00000 | − | 12.1244i | 0.311496 | − | 0.539527i | ||||
\(506\) | −3.00000 | −0.133366 | ||||||||
\(507\) | 0.500000 | + | 12.9904i | 0.0222058 | + | 0.576923i | ||||
\(508\) | −14.0000 | −0.621150 | ||||||||
\(509\) | 4.50000 | − | 7.79423i | 0.199459 | − | 0.345473i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317217i | \(0.102748\pi\) | |||||||
\(510\) | −1.00000 | + | 1.73205i | −0.0442807 | + | 0.0766965i | ||||
\(511\) | 2.00000 | + | 3.46410i | 0.0884748 | + | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.00000 | + | 5.19615i | 0.132453 | + | 0.229416i | ||||
\(514\) | −10.5000 | − | 18.1865i | −0.463135 | − | 0.802174i | ||||
\(515\) | 6.00000 | 0.264392 | ||||||||
\(516\) | 2.50000 | + | 4.33013i | 0.110056 | + | 0.190623i | ||||
\(517\) | −1.50000 | + | 2.59808i | −0.0659699 | + | 0.114263i | ||||
\(518\) | 5.00000 | − | 8.66025i | 0.219687 | − | 0.380510i | ||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | 1.00000 | + | 3.46410i | 0.0438529 | + | 0.151911i | ||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 0.500000 | − | 0.866025i | 0.0218844 | − | 0.0379049i | ||||
\(523\) | −16.5000 | + | 28.5788i | −0.721495 | + | 1.24967i | 0.238906 | + | 0.971043i | \(0.423211\pi\) |
−0.960401 | + | 0.278623i | \(0.910122\pi\) | |||||||
\(524\) | −6.50000 | − | 11.2583i | −0.283954 | − | 0.491822i | ||||
\(525\) | −2.00000 | −0.0872872 | ||||||||
\(526\) | −11.5000 | − | 19.9186i | −0.501424 | − | 0.868492i | ||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 7.00000 | − | 12.1244i | 0.304061 | − | 0.526648i | ||||
\(531\) | 2.50000 | − | 4.33013i | 0.108491 | − | 0.187912i | ||||
\(532\) | 12.0000 | 0.520266 | ||||||||
\(533\) | 35.0000 | + | 8.66025i | 1.51602 | + | 0.375117i | ||||
\(534\) | −10.0000 | −0.432742 | ||||||||
\(535\) | −3.00000 | + | 5.19615i | −0.129701 | + | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50000 | − | 6.06218i | −0.151036 | − | 0.261602i | ||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | 1.50000 | + | 2.59808i | 0.0646096 | + | 0.111907i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | 14.5000 | + | 25.1147i | 0.622828 | + | 1.07877i | ||||
\(543\) | 8.00000 | − | 13.8564i | 0.343313 | − | 0.594635i | ||||
\(544\) | −1.00000 | + | 1.73205i | −0.0428746 | + | 0.0742611i | ||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | −7.00000 | − | 1.73205i | −0.299572 | − | 0.0741249i | ||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 4.50000 | − | 7.79423i | 0.192230 | − | 0.332953i | ||||
\(549\) | 5.00000 | − | 8.66025i | 0.213395 | − | 0.369611i | ||||
\(550\) | −0.500000 | − | 0.866025i | −0.0213201 | − | 0.0369274i | ||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | −1.50000 | − | 2.59808i | −0.0638442 | − | 0.110581i | ||||
\(553\) | −5.00000 | − | 8.66025i | −0.212622 | − | 0.368271i | ||||
\(554\) | −19.0000 | −0.807233 | ||||||||
\(555\) | 2.50000 | + | 4.33013i | 0.106119 | + | 0.183804i | ||||
\(556\) | −5.00000 | + | 8.66025i | −0.212047 | + | 0.367277i | ||||
\(557\) | 17.0000 | − | 29.4449i | 0.720313 | − | 1.24762i | −0.240561 | − | 0.970634i | \(-0.577331\pi\) |
0.960874 | − | 0.276985i | \(-0.0893352\pi\) | |||||||
\(558\) | −3.00000 | −0.127000 | ||||||||
\(559\) | −12.5000 | + | 12.9904i | −0.528694 | + | 0.549435i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 1.00000 | − | 1.73205i | 0.0422200 | − | 0.0731272i | ||||
\(562\) | 15.0000 | − | 25.9808i | 0.632737 | − | 1.09593i | ||||
\(563\) | 12.0000 | + | 20.7846i | 0.505740 | + | 0.875967i | 0.999978 | + | 0.00664037i | \(0.00211371\pi\) |
−0.494238 | + | 0.869326i | \(0.664553\pi\) | |||||||
\(564\) | −3.00000 | −0.126323 | ||||||||
\(565\) | 8.50000 | + | 14.7224i | 0.357598 | + | 0.619377i | ||||
\(566\) | 6.50000 | + | 11.2583i | 0.273215 | + | 0.473223i | ||||
\(567\) | 2.00000 | 0.0839921 | ||||||||
\(568\) | −2.00000 | − | 3.46410i | −0.0839181 | − | 0.145350i | ||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | −3.00000 | + | 5.19615i | −0.125656 | + | 0.217643i | ||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | −1.00000 | − | 3.46410i | −0.0418121 | − | 0.144841i | ||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | −10.0000 | + | 17.3205i | −0.417392 | + | 0.722944i | ||||
\(575\) | 1.50000 | − | 2.59808i | 0.0625543 | − | 0.108347i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 6.50000 | + | 11.2583i | 0.270364 | + | 0.468285i | ||||
\(579\) | −2.00000 | − | 3.46410i | −0.0831172 | − | 0.143963i | ||||
\(580\) | 1.00000 | 0.0415227 | ||||||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | −5.00000 | + | 8.66025i | −0.207257 | + | 0.358979i | ||||
\(583\) | −7.00000 | + | 12.1244i | −0.289910 | + | 0.502140i | ||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 2.50000 | − | 2.59808i | 0.103362 | − | 0.107417i | ||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | 9.00000 | − | 15.5885i | 0.371470 | − | 0.643404i | −0.618322 | − | 0.785925i | \(-0.712187\pi\) |
0.989792 | + | 0.142520i | \(0.0455206\pi\) | |||||||
\(588\) | −1.50000 | + | 2.59808i | −0.0618590 | + | 0.107143i | ||||
\(589\) | 9.00000 | + | 15.5885i | 0.370839 | + | 0.642311i | ||||
\(590\) | 5.00000 | 0.205847 | ||||||||
\(591\) | −6.00000 | − | 10.3923i | −0.246807 | − | 0.427482i | ||||
\(592\) | 2.50000 | + | 4.33013i | 0.102749 | + | 0.177967i | ||||
\(593\) | −35.0000 | −1.43728 | −0.718639 | − | 0.695383i | \(-0.755235\pi\) | ||||
−0.718639 | + | 0.695383i | \(0.755235\pi\) | |||||||
\(594\) | 0.500000 | + | 0.866025i | 0.0205152 | + | 0.0355335i | ||||
\(595\) | 2.00000 | − | 3.46410i | 0.0819920 | − | 0.142014i | ||||
\(596\) | −5.50000 | + | 9.52628i | −0.225289 | + | 0.390212i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.50000 | − | 7.79423i | 0.306698 | − | 0.318730i | ||||
\(599\) | 30.0000 | 1.22577 | 0.612883 | − | 0.790173i | \(-0.290010\pi\) | ||||
0.612883 | + | 0.790173i | \(0.290010\pi\) | |||||||
\(600\) | 0.500000 | − | 0.866025i | 0.0204124 | − | 0.0353553i | ||||
\(601\) | 5.50000 | − | 9.52628i | 0.224350 | − | 0.388585i | −0.731774 | − | 0.681547i | \(-0.761308\pi\) |
0.956124 | + | 0.292962i | \(0.0946409\pi\) | |||||||
\(602\) | −5.00000 | − | 8.66025i | −0.203785 | − | 0.352966i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.0000 | − | 20.7846i | −0.488273 | − | 0.845714i | ||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | −14.0000 | −0.568711 | ||||||||
\(607\) | 5.00000 | + | 8.66025i | 0.202944 | + | 0.351509i | 0.949476 | − | 0.313841i | \(-0.101616\pi\) |
−0.746532 | + | 0.665350i | \(0.768282\pi\) | |||||||
\(608\) | −3.00000 | + | 5.19615i | −0.121666 | + | 0.210732i | ||||
\(609\) | −1.00000 | + | 1.73205i | −0.0405220 | + | 0.0701862i | ||||
\(610\) | 10.0000 | 0.404888 | ||||||||
\(611\) | −3.00000 | − | 10.3923i | −0.121367 | − | 0.420428i | ||||
\(612\) | 2.00000 | 0.0808452 | ||||||||
\(613\) | 18.5000 | − | 32.0429i | 0.747208 | − | 1.29420i | −0.201948 | − | 0.979396i | \(-0.564727\pi\) |
0.949156 | − | 0.314806i | \(-0.101939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.00000 | − | 8.66025i | −0.201619 | − | 0.349215i | ||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −1.50000 | − | 2.59808i | −0.0603877 | − | 0.104595i | 0.834251 | − | 0.551385i | \(-0.185900\pi\) |
−0.894639 | + | 0.446790i | \(0.852567\pi\) | |||||||
\(618\) | −3.00000 | − | 5.19615i | −0.120678 | − | 0.209020i | ||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | −1.50000 | − | 2.59808i | −0.0602414 | − | 0.104341i | ||||
\(621\) | −1.50000 | + | 2.59808i | −0.0601929 | + | 0.104257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.0000 | 0.801283 | ||||||||
\(624\) | 2.50000 | − | 2.59808i | 0.100080 | − | 0.104006i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.00000 | − | 10.3923i | 0.239808 | − | 0.415360i | ||||
\(627\) | 3.00000 | − | 5.19615i | 0.119808 | − | 0.207514i | ||||
\(628\) | −12.5000 | − | 21.6506i | −0.498804 | − | 0.863954i | ||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 1.00000 | + | 1.73205i | 0.0398410 | + | 0.0690066i | ||||
\(631\) | −24.0000 | − | 41.5692i | −0.955425 | − | 1.65484i | −0.733393 | − | 0.679805i | \(-0.762064\pi\) |
−0.222032 | − | 0.975039i | \(-0.571269\pi\) | |||||||
\(632\) | 5.00000 | 0.198889 | ||||||||
\(633\) | −4.00000 | − | 6.92820i | −0.158986 | − | 0.275371i | ||||
\(634\) | −6.00000 | + | 10.3923i | −0.238290 | + | 0.412731i | ||||
\(635\) | −7.00000 | + | 12.1244i | −0.277787 | + | 0.481140i | ||||
\(636\) | −14.0000 | −0.555136 | ||||||||
\(637\) | −10.5000 | − | 2.59808i | −0.416025 | − | 0.102940i | ||||
\(638\) | −1.00000 | −0.0395904 | ||||||||
\(639\) | −2.00000 | + | 3.46410i | −0.0791188 | + | 0.137038i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | 6.00000 | 0.236801 | ||||||||
\(643\) | 20.0000 | + | 34.6410i | 0.788723 | + | 1.36611i | 0.926750 | + | 0.375680i | \(0.122591\pi\) |
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 3.00000 | + | 5.19615i | 0.118217 | + | 0.204757i | ||||
\(645\) | 5.00000 | 0.196875 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −5.00000 | −0.196267 | ||||||||
\(650\) | 3.50000 | + | 0.866025i | 0.137281 | + | 0.0339683i | ||||
\(651\) | 6.00000 | 0.235159 | ||||||||
\(652\) | −8.50000 | + | 14.7224i | −0.332886 | + | 0.576575i | ||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | −3.00000 | − | 5.19615i | −0.117309 | − | 0.203186i | ||||
\(655\) | −13.0000 | −0.507952 | ||||||||
\(656\) | −5.00000 | − | 8.66025i | −0.195217 | − | 0.338126i | ||||
\(657\) | 1.00000 | + | 1.73205i | 0.0390137 | + | 0.0675737i | ||||
\(658\) | 6.00000 | 0.233904 | ||||||||
\(659\) | 6.50000 | + | 11.2583i | 0.253204 | + | 0.438562i | 0.964406 | − | 0.264425i | \(-0.0851823\pi\) |
−0.711202 | + | 0.702988i | \(0.751849\pi\) | |||||||
\(660\) | −0.500000 | + | 0.866025i | −0.0194625 | + | 0.0337100i | ||||
\(661\) | 6.00000 | − | 10.3923i | 0.233373 | − | 0.404214i | −0.725426 | − | 0.688301i | \(-0.758357\pi\) |
0.958799 | + | 0.284087i | \(0.0916904\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 2.00000 | + | 6.92820i | 0.0776736 | + | 0.269069i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 6.00000 | − | 10.3923i | 0.232670 | − | 0.402996i | ||||
\(666\) | 2.50000 | − | 4.33013i | 0.0968730 | − | 0.167789i | ||||
\(667\) | −1.50000 | − | 2.59808i | −0.0580802 | − | 0.100598i | ||||
\(668\) | −7.00000 | −0.270838 | ||||||||
\(669\) | 5.00000 | + | 8.66025i | 0.193311 | + | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0000 | −0.386046 | ||||||||
\(672\) | 1.00000 | + | 1.73205i | 0.0385758 | + | 0.0668153i | ||||
\(673\) | 8.00000 | − | 13.8564i | 0.308377 | − | 0.534125i | −0.669630 | − | 0.742695i | \(-0.733547\pi\) |
0.978008 | + | 0.208569i | \(0.0668807\pi\) | |||||||
\(674\) | 11.0000 | − | 19.0526i | 0.423704 | − | 0.733877i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 11.5000 | + | 6.06218i | 0.442308 | + | 0.233161i | ||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 8.50000 | − | 14.7224i | 0.326441 | − | 0.565412i | ||||
\(679\) | 10.0000 | − | 17.3205i | 0.383765 | − | 0.664700i | ||||
\(680\) | 1.00000 | + | 1.73205i | 0.0383482 | + | 0.0664211i | ||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 1.50000 | + | 2.59808i | 0.0574380 | + | 0.0994855i | ||||
\(683\) | 22.0000 | + | 38.1051i | 0.841807 | + | 1.45805i | 0.888366 | + | 0.459136i | \(0.151841\pi\) |
−0.0465592 | + | 0.998916i | \(0.514826\pi\) | |||||||
\(684\) | 6.00000 | 0.229416 | ||||||||
\(685\) | −4.50000 | − | 7.79423i | −0.171936 | − | 0.297802i | ||||
\(686\) | 10.0000 | − | 17.3205i | 0.381802 | − | 0.661300i | ||||
\(687\) | 11.0000 | − | 19.0526i | 0.419676 | − | 0.726900i | ||||
\(688\) | 5.00000 | 0.190623 | ||||||||
\(689\) | −14.0000 | − | 48.4974i | −0.533358 | − | 1.84760i | ||||
\(690\) | −3.00000 | −0.114208 | ||||||||
\(691\) | 7.00000 | − | 12.1244i | 0.266293 | − | 0.461232i | −0.701609 | − | 0.712562i | \(-0.747535\pi\) |
0.967901 | + | 0.251330i | \(0.0808679\pi\) | |||||||
\(692\) | −2.00000 | + | 3.46410i | −0.0760286 | + | 0.131685i | ||||
\(693\) | −1.00000 | − | 1.73205i | −0.0379869 | − | 0.0657952i | ||||
\(694\) | −18.0000 | −0.683271 | ||||||||
\(695\) | 5.00000 | + | 8.66025i | 0.189661 | + | 0.328502i | ||||
\(696\) | −0.500000 | − | 0.866025i | −0.0189525 | − | 0.0328266i | ||||
\(697\) | 20.0000 | 0.757554 | ||||||||
\(698\) | −4.00000 | − | 6.92820i | −0.151402 | − | 0.262236i | ||||
\(699\) | 1.50000 | − | 2.59808i | 0.0567352 | − | 0.0982683i | ||||
\(700\) | −1.00000 | + | 1.73205i | −0.0377964 | + | 0.0654654i | ||||
\(701\) | 23.0000 | 0.868698 | 0.434349 | − | 0.900745i | \(-0.356978\pi\) | ||||
0.434349 | + | 0.900745i | \(0.356978\pi\) | |||||||
\(702\) | −3.50000 | − | 0.866025i | −0.132099 | − | 0.0326860i | ||||
\(703\) | −30.0000 | −1.13147 | ||||||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | −1.50000 | + | 2.59808i | −0.0564933 | + | 0.0978492i | ||||
\(706\) | 7.00000 | + | 12.1244i | 0.263448 | + | 0.456306i | ||||
\(707\) | 28.0000 | 1.05305 | ||||||||
\(708\) | −2.50000 | − | 4.33013i | −0.0939558 | − | 0.162736i | ||||
\(709\) | 8.00000 | + | 13.8564i | 0.300446 | + | 0.520388i | 0.976237 | − | 0.216705i | \(-0.0695310\pi\) |
−0.675791 | + | 0.737093i | \(0.736198\pi\) | |||||||
\(710\) | −4.00000 | −0.150117 | ||||||||
\(711\) | −2.50000 | − | 4.33013i | −0.0937573 | − | 0.162392i | ||||
\(712\) | −5.00000 | + | 8.66025i | −0.187383 | + | 0.324557i | ||||
\(713\) | −4.50000 | + | 7.79423i | −0.168526 | + | 0.291896i | ||||
\(714\) | −4.00000 | −0.149696 | ||||||||
\(715\) | −3.50000 | − | 0.866025i | −0.130893 | − | 0.0323875i | ||||
\(716\) | −7.00000 | −0.261602 | ||||||||
\(717\) | −4.00000 | + | 6.92820i | −0.149383 | + | 0.258738i | ||||
\(718\) | −6.00000 | + | 10.3923i | −0.223918 | + | 0.387837i | ||||
\(719\) | 24.0000 | + | 41.5692i | 0.895049 | + | 1.55027i | 0.833744 | + | 0.552151i | \(0.186193\pi\) |
0.0613050 | + | 0.998119i | \(0.480474\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 6.00000 | + | 10.3923i | 0.223452 | + | 0.387030i | ||||
\(722\) | −8.50000 | − | 14.7224i | −0.316337 | − | 0.547912i | ||||
\(723\) | 7.00000 | 0.260333 | ||||||||
\(724\) | −8.00000 | − | 13.8564i | −0.297318 | − | 0.514969i | ||||
\(725\) | 0.500000 | − | 0.866025i | 0.0185695 | − | 0.0321634i | ||||
\(726\) | −5.00000 | + | 8.66025i | −0.185567 | + | 0.321412i | ||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | −5.00000 | + | 5.19615i | −0.185312 | + | 0.192582i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | + | 1.73205i | −0.0370117 | + | 0.0641061i | ||||
\(731\) | −5.00000 | + | 8.66025i | −0.184932 | + | 0.320311i | ||||
\(732\) | −5.00000 | − | 8.66025i | −0.184805 | − | 0.320092i | ||||
\(733\) | 14.0000 | 0.517102 | 0.258551 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | −18.0000 | − | 31.1769i | −0.664392 | − | 1.15076i | ||||
\(735\) | 1.50000 | + | 2.59808i | 0.0553283 | + | 0.0958315i | ||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.00000 | + | 8.66025i | −0.184053 | + | 0.318788i | ||||
\(739\) | −12.0000 | + | 20.7846i | −0.441427 | + | 0.764574i | −0.997796 | − | 0.0663614i | \(-0.978861\pi\) |
0.556369 | + | 0.830936i | \(0.312194\pi\) | |||||||
\(740\) | 5.00000 | 0.183804 | ||||||||
\(741\) | 6.00000 | + | 20.7846i | 0.220416 | + | 0.763542i | ||||
\(742\) | 28.0000 | 1.02791 | ||||||||
\(743\) | 7.50000 | − | 12.9904i | 0.275148 | − | 0.476571i | −0.695024 | − | 0.718986i | \(-0.744606\pi\) |
0.970173 | + | 0.242415i | \(0.0779397\pi\) | |||||||
\(744\) | −1.50000 | + | 2.59808i | −0.0549927 | + | 0.0952501i | ||||
\(745\) | 5.50000 | + | 9.52628i | 0.201504 | + | 0.349016i | ||||
\(746\) | 37.0000 | 1.35467 | ||||||||
\(747\) | 3.00000 | + | 5.19615i | 0.109764 | + | 0.190117i | ||||
\(748\) | −1.00000 | − | 1.73205i | −0.0365636 | − | 0.0633300i | ||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | −0.500000 | − | 0.866025i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | −20.5000 | + | 35.5070i | −0.748056 | + | 1.29567i | 0.200698 | + | 0.979653i | \(0.435679\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | −1.50000 | + | 2.59808i | −0.0546994 | + | 0.0947421i | ||||
\(753\) | −3.00000 | −0.109326 | ||||||||
\(754\) | 2.50000 | − | 2.59808i | 0.0910446 | − | 0.0946164i | ||||
\(755\) | −24.0000 | −0.873449 | ||||||||
\(756\) | 1.00000 | − | 1.73205i | 0.0363696 | − | 0.0629941i | ||||
\(757\) | 27.0000 | − | 46.7654i | 0.981332 | − | 1.69972i | 0.324109 | − | 0.946020i | \(-0.394935\pi\) |
0.657222 | − | 0.753697i | \(-0.271731\pi\) | |||||||
\(758\) | 15.0000 | + | 25.9808i | 0.544825 | + | 0.943664i | ||||
\(759\) | 3.00000 | 0.108893 | ||||||||
\(760\) | 3.00000 | + | 5.19615i | 0.108821 | + | 0.188484i | ||||
\(761\) | 10.0000 | + | 17.3205i | 0.362500 | + | 0.627868i | 0.988372 | − | 0.152058i | \(-0.0485900\pi\) |
−0.625872 | + | 0.779926i | \(0.715257\pi\) | |||||||
\(762\) | 14.0000 | 0.507166 | ||||||||
\(763\) | 6.00000 | + | 10.3923i | 0.217215 | + | 0.376227i | ||||
\(764\) | −12.0000 | + | 20.7846i | −0.434145 | + | 0.751961i | ||||
\(765\) | 1.00000 | − | 1.73205i | 0.0361551 | − | 0.0626224i | ||||
\(766\) | −27.0000 | −0.975550 | ||||||||
\(767\) | 12.5000 | − | 12.9904i | 0.451349 | − | 0.469055i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 14.5000 | − | 25.1147i | 0.522883 | − | 0.905661i | −0.476762 | − | 0.879032i | \(-0.658190\pi\) |
0.999645 | − | 0.0266282i | \(-0.00847701\pi\) | |||||||
\(770\) | 1.00000 | − | 1.73205i | 0.0360375 | − | 0.0624188i | ||||
\(771\) | 10.5000 | + | 18.1865i | 0.378148 | + | 0.654972i | ||||
\(772\) | −4.00000 | −0.143963 | ||||||||
\(773\) | 8.00000 | + | 13.8564i | 0.287740 | + | 0.498380i | 0.973270 | − | 0.229664i | \(-0.0737628\pi\) |
−0.685530 | + | 0.728044i | \(0.740429\pi\) | |||||||
\(774\) | −2.50000 | − | 4.33013i | −0.0898606 | − | 0.155643i | ||||
\(775\) | −3.00000 | −0.107763 | ||||||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | −5.00000 | + | 8.66025i | −0.179374 | + | 0.310685i | ||||
\(778\) | 0.500000 | − | 0.866025i | 0.0179259 | − | 0.0310485i | ||||
\(779\) | 60.0000 | 2.14972 | ||||||||
\(780\) | −1.00000 | − | 3.46410i | −0.0358057 | − | 0.124035i | ||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 3.00000 | − | 5.19615i | 0.107280 | − | 0.185814i | ||||
\(783\) | −0.500000 | + | 0.866025i | −0.0178685 | + | 0.0309492i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | −25.0000 | −0.892288 | ||||||||
\(786\) | 6.50000 | + | 11.2583i | 0.231847 | + | 0.401571i | ||||
\(787\) | −12.5000 | − | 21.6506i | −0.445577 | − | 0.771762i | 0.552515 | − | 0.833503i | \(-0.313668\pi\) |
−0.998092 | + | 0.0617409i | \(0.980335\pi\) | |||||||
\(788\) | −12.0000 | −0.427482 | ||||||||
\(789\) | 11.5000 | + | 19.9186i | 0.409411 | + | 0.709120i | ||||
\(790\) | 2.50000 | − | 4.33013i | 0.0889460 | − | 0.154059i | ||||
\(791\) | −17.0000 | + | 29.4449i | −0.604450 | + | 1.04694i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 25.0000 | − | 25.9808i | 0.887776 | − | 0.922604i | ||||
\(794\) | −13.0000 | −0.461353 | ||||||||
\(795\) | −7.00000 | + | 12.1244i | −0.248264 | + | 0.430007i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.0000 | + | 45.0333i | 0.920967 | + | 1.59516i | 0.797922 | + | 0.602761i | \(0.205933\pi\) |
0.123045 | + | 0.992401i | \(0.460734\pi\) | |||||||
\(798\) | −12.0000 | −0.424795 | ||||||||
\(799\) | −3.00000 | − | 5.19615i | −0.106132 | − | 0.183827i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | 6.00000 | + | 10.3923i | 0.211867 | + | 0.366965i | ||||
\(803\) | 1.00000 | − | 1.73205i | 0.0352892 | − | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.00000 | 0.211472 | ||||||||
\(806\) | −10.5000 | − | 2.59808i | −0.369847 | − | 0.0915133i | ||||
\(807\) | −18.0000 | −0.633630 | ||||||||
\(808\) | −7.00000 | + | 12.1244i | −0.246259 | + | 0.426533i | ||||
\(809\) | −1.00000 | + | 1.73205i | −0.0351581 | + | 0.0608957i | −0.883069 | − | 0.469243i | \(-0.844527\pi\) |
0.847911 | + | 0.530139i | \(0.177860\pi\) | |||||||
\(810\) | 0.500000 | + | 0.866025i | 0.0175682 | + | 0.0304290i | ||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 1.00000 | + | 1.73205i | 0.0350931 | + | 0.0607831i | ||||
\(813\) | −14.5000 | − | 25.1147i | −0.508537 | − | 0.880812i | ||||
\(814\) | −5.00000 | −0.175250 | ||||||||
\(815\) | 8.50000 | + | 14.7224i | 0.297742 | + | 0.515704i | ||||
\(816\) | 1.00000 | − | 1.73205i | 0.0350070 | − | 0.0606339i | ||||
\(817\) | −15.0000 | + | 25.9808i | −0.524784 | + | 0.908952i | ||||
\(818\) | −26.0000 | −0.909069 | ||||||||
\(819\) | 7.00000 | + | 1.73205i | 0.244600 | + | 0.0605228i | ||||
\(820\) | −10.0000 | −0.349215 | ||||||||
\(821\) | −11.5000 | + | 19.9186i | −0.401353 | + | 0.695163i | −0.993889 | − | 0.110380i | \(-0.964793\pi\) |
0.592537 | + | 0.805543i | \(0.298127\pi\) | |||||||
\(822\) | −4.50000 | + | 7.79423i | −0.156956 | + | 0.271855i | ||||
\(823\) | 11.0000 | + | 19.0526i | 0.383436 | + | 0.664130i | 0.991551 | − | 0.129719i | \(-0.0414074\pi\) |
−0.608115 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | 0.500000 | + | 0.866025i | 0.0174078 | + | 0.0301511i | ||||
\(826\) | 5.00000 | + | 8.66025i | 0.173972 | + | 0.301329i | ||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | 1.50000 | + | 2.59808i | 0.0521286 | + | 0.0902894i | ||||
\(829\) | −13.0000 | + | 22.5167i | −0.451509 | + | 0.782036i | −0.998480 | − | 0.0551154i | \(-0.982447\pi\) |
0.546971 | + | 0.837151i | \(0.315781\pi\) | |||||||
\(830\) | −3.00000 | + | 5.19615i | −0.104132 | + | 0.180361i | ||||
\(831\) | 19.0000 | 0.659103 | ||||||||
\(832\) | −1.00000 | − | 3.46410i | −0.0346688 | − | 0.120096i | ||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | 5.00000 | − | 8.66025i | 0.173136 | − | 0.299880i | ||||
\(835\) | −3.50000 | + | 6.06218i | −0.121122 | + | 0.209790i | ||||
\(836\) | −3.00000 | − | 5.19615i | −0.103757 | − | 0.179713i | ||||
\(837\) | 3.00000 | 0.103695 | ||||||||
\(838\) | −2.00000 | − | 3.46410i | −0.0690889 | − | 0.119665i | ||||
\(839\) | −19.0000 | − | 32.9090i | −0.655953 | − | 1.13614i | −0.981654 | − | 0.190671i | \(-0.938934\pi\) |
0.325701 | − | 0.945473i | \(-0.394400\pi\) | |||||||
\(840\) | 2.00000 | 0.0690066 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | −14.0000 | + | 24.2487i | −0.482472 | + | 0.835666i | ||||
\(843\) | −15.0000 | + | 25.9808i | −0.516627 | + | 0.894825i | ||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 11.0000 | − | 6.92820i | 0.378412 | − | 0.238337i | ||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | 10.0000 | − | 17.3205i | 0.343604 | − | 0.595140i | ||||
\(848\) | −7.00000 | + | 12.1244i | −0.240381 | + | 0.416352i | ||||
\(849\) | −6.50000 | − | 11.2583i | −0.223079 | − | 0.386385i | ||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | −7.50000 | − | 12.9904i | −0.257097 | − | 0.445305i | ||||
\(852\) | 2.00000 | + | 3.46410i | 0.0685189 | + | 0.118678i | ||||
\(853\) | 7.00000 | 0.239675 | 0.119838 | − | 0.992793i | \(-0.461763\pi\) | ||||
0.119838 | + | 0.992793i | \(0.461763\pi\) | |||||||
\(854\) | 10.0000 | + | 17.3205i | 0.342193 | + | 0.592696i | ||||
\(855\) | 3.00000 | − | 5.19615i | 0.102598 | − | 0.177705i | ||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | −35.0000 | −1.19558 | −0.597789 | − | 0.801654i | \(-0.703954\pi\) | ||||
−0.597789 | + | 0.801654i | \(0.703954\pi\) | |||||||
\(858\) | 1.00000 | + | 3.46410i | 0.0341394 | + | 0.118262i | ||||
\(859\) | 18.0000 | 0.614152 | 0.307076 | − | 0.951685i | \(-0.400649\pi\) | ||||
0.307076 | + | 0.951685i | \(0.400649\pi\) | |||||||
\(860\) | 2.50000 | − | 4.33013i | 0.0852493 | − | 0.147656i | ||||
\(861\) | 10.0000 | − | 17.3205i | 0.340799 | − | 0.590281i | ||||
\(862\) | −6.00000 | − | 10.3923i | −0.204361 | − | 0.353963i | ||||
\(863\) | −51.0000 | −1.73606 | −0.868030 | − | 0.496512i | \(-0.834614\pi\) | ||||
−0.868030 | + | 0.496512i | \(0.834614\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 2.00000 | + | 3.46410i | 0.0680020 | + | 0.117783i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | −6.50000 | − | 11.2583i | −0.220752 | − | 0.382353i | ||||
\(868\) | 3.00000 | − | 5.19615i | 0.101827 | − | 0.176369i | ||||
\(869\) | −2.50000 | + | 4.33013i | −0.0848067 | + | 0.146889i | ||||
\(870\) | −1.00000 | −0.0339032 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | 5.00000 | − | 8.66025i | 0.169224 | − | 0.293105i | ||||
\(874\) | 9.00000 | − | 15.5885i | 0.304430 | − | 0.527287i | ||||
\(875\) | 1.00000 | + | 1.73205i | 0.0338062 | + | 0.0585540i | ||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −6.50000 | − | 11.2583i | −0.219489 | − | 0.380167i | 0.735163 | − | 0.677891i | \(-0.237106\pi\) |
−0.954652 | + | 0.297724i | \(0.903772\pi\) | |||||||
\(878\) | −14.0000 | − | 24.2487i | −0.472477 | − | 0.818354i | ||||
\(879\) | 14.0000 | 0.472208 | ||||||||
\(880\) | 0.500000 | + | 0.866025i | 0.0168550 | + | 0.0291937i | ||||
\(881\) | −27.0000 | + | 46.7654i | −0.909653 | + | 1.57557i | −0.0951067 | + | 0.995467i | \(0.530319\pi\) |
−0.814546 | + | 0.580098i | \(0.803014\pi\) | |||||||
\(882\) | 1.50000 | − | 2.59808i | 0.0505076 | − | 0.0874818i | ||||
\(883\) | −1.00000 | −0.0336527 | −0.0168263 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168263 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(884\) | 7.00000 | + | 1.73205i | 0.235435 | + | 0.0582552i | ||||
\(885\) | −5.00000 | −0.168073 | ||||||||
\(886\) | −8.00000 | + | 13.8564i | −0.268765 | + | 0.465515i | ||||
\(887\) | −0.500000 | + | 0.866025i | −0.0167884 | + | 0.0290783i | −0.874298 | − | 0.485390i | \(-0.838677\pi\) |
0.857509 | + | 0.514469i | \(0.172011\pi\) | |||||||
\(888\) | −2.50000 | − | 4.33013i | −0.0838945 | − | 0.145310i | ||||
\(889\) | −28.0000 | −0.939090 | ||||||||
\(890\) | 5.00000 | + | 8.66025i | 0.167600 | + | 0.290292i | ||||
\(891\) | −0.500000 | − | 0.866025i | −0.0167506 | − | 0.0290129i | ||||
\(892\) | 10.0000 | 0.334825 | ||||||||
\(893\) | −9.00000 | − | 15.5885i | −0.301174 | − | 0.521648i | ||||
\(894\) | 5.50000 | − | 9.52628i | 0.183948 | − | 0.318606i | ||||
\(895\) | −3.50000 | + | 6.06218i | −0.116992 | + | 0.202636i | ||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | −7.50000 | + | 7.79423i | −0.250418 | + | 0.260242i | ||||
\(898\) | −36.0000 | −1.20134 | ||||||||
\(899\) | −1.50000 | + | 2.59808i | −0.0500278 | + | 0.0866507i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −14.0000 | − | 24.2487i | −0.466408 | − | 0.807842i | ||||
\(902\) | 10.0000 | 0.332964 | ||||||||
\(903\) | 5.00000 | + | 8.66025i | 0.166390 | + | 0.288195i | ||||
\(904\) | −8.50000 | − | 14.7224i | −0.282706 | − | 0.489661i | ||||
\(905\) | −16.0000 | −0.531858 | ||||||||
\(906\) | 12.0000 | + | 20.7846i | 0.398673 | + | 0.690522i | ||||
\(907\) | 26.5000 | − | 45.8993i | 0.879918 | − | 1.52406i | 0.0284883 | − | 0.999594i | \(-0.490931\pi\) |
0.851430 | − | 0.524469i | \(-0.175736\pi\) | |||||||
\(908\) | −10.0000 | + | 17.3205i | −0.331862 | + | 0.574801i | ||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | 2.00000 | + | 6.92820i | 0.0662994 | + | 0.229668i | ||||
\(911\) | 34.0000 | 1.12647 | 0.563235 | − | 0.826297i | \(-0.309557\pi\) | ||||
0.563235 | + | 0.826297i | \(0.309557\pi\) | |||||||
\(912\) | 3.00000 | − | 5.19615i | 0.0993399 | − | 0.172062i | ||||
\(913\) | 3.00000 | − | 5.19615i | 0.0992855 | − | 0.171968i | ||||
\(914\) | −7.00000 | − | 12.1244i | −0.231539 | − | 0.401038i | ||||
\(915\) | −10.0000 | −0.330590 | ||||||||
\(916\) | −11.0000 | − | 19.0526i | −0.363450 | − | 0.629514i | ||||
\(917\) | −13.0000 | − | 22.5167i | −0.429298 | − | 0.743566i | ||||
\(918\) | −2.00000 | −0.0660098 | ||||||||
\(919\) | 28.0000 | + | 48.4974i | 0.923635 | + | 1.59978i | 0.793742 | + | 0.608254i | \(0.208130\pi\) |
0.129893 | + | 0.991528i | \(0.458537\pi\) | |||||||
\(920\) | −1.50000 | + | 2.59808i | −0.0494535 | + | 0.0856560i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.0000 | 0.889198 | ||||||||
\(923\) | −10.0000 | + | 10.3923i | −0.329154 | + | 0.342067i | ||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 2.50000 | − | 4.33013i | 0.0821995 | − | 0.142374i | ||||
\(926\) | −5.00000 | + | 8.66025i | −0.164310 | + | 0.284594i | ||||
\(927\) | 3.00000 | + | 5.19615i | 0.0985329 | + | 0.170664i | ||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −12.0000 | − | 20.7846i | −0.393707 | − | 0.681921i | 0.599228 | − | 0.800578i | \(-0.295474\pi\) |
−0.992935 | + | 0.118657i | \(0.962141\pi\) | |||||||
\(930\) | 1.50000 | + | 2.59808i | 0.0491869 | + | 0.0851943i | ||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | −1.50000 | − | 2.59808i | −0.0491341 | − | 0.0851028i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.00000 | − | 1.73205i | 0.0327210 | − | 0.0566744i | ||||
\(935\) | −2.00000 | −0.0654070 | ||||||||
\(936\) | −2.50000 | + | 2.59808i | −0.0817151 | + | 0.0849208i | ||||
\(937\) | −18.0000 | −0.588034 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00000 | + | 10.3923i | −0.195803 | + | 0.339140i | ||||
\(940\) | 1.50000 | + | 2.59808i | 0.0489246 | + | 0.0847399i | ||||
\(941\) | 26.0000 | 0.847576 | 0.423788 | − | 0.905761i | \(-0.360700\pi\) | ||||
0.423788 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(942\) | 12.5000 | + | 21.6506i | 0.407272 | + | 0.705416i | ||||
\(943\) | 15.0000 | + | 25.9808i | 0.488467 | + | 0.846050i | ||||
\(944\) | −5.00000 | −0.162736 | ||||||||
\(945\) | −1.00000 | − | 1.73205i | −0.0325300 | − | 0.0563436i | ||||
\(946\) | −2.50000 | + | 4.33013i | −0.0812820 | + | 0.140785i | ||||
\(947\) | −26.0000 | + | 45.0333i | −0.844886 | + | 1.46339i | 0.0408333 | + | 0.999166i | \(0.486999\pi\) |
−0.885720 | + | 0.464220i | \(0.846335\pi\) | |||||||
\(948\) | −5.00000 | −0.162392 | ||||||||
\(949\) | 2.00000 | + | 6.92820i | 0.0649227 | + | 0.224899i | ||||
\(950\) | 6.00000 | 0.194666 | ||||||||
\(951\) | 6.00000 | − | 10.3923i | 0.194563 | − | 0.336994i | ||||
\(952\) | −2.00000 | + | 3.46410i | −0.0648204 | + | 0.112272i | ||||
\(953\) | −7.50000 | − | 12.9904i | −0.242949 | − | 0.420800i | 0.718604 | − | 0.695419i | \(-0.244781\pi\) |
−0.961553 | + | 0.274620i | \(0.911448\pi\) | |||||||
\(954\) | 14.0000 | 0.453267 | ||||||||
\(955\) | 12.0000 | + | 20.7846i | 0.388311 | + | 0.672574i | ||||
\(956\) | 4.00000 | + | 6.92820i | 0.129369 | + | 0.224074i | ||||
\(957\) | 1.00000 | 0.0323254 | ||||||||
\(958\) | 2.00000 | + | 3.46410i | 0.0646171 | + | 0.111920i | ||||
\(959\) | 9.00000 | − | 15.5885i | 0.290625 | − | 0.503378i | ||||
\(960\) | −0.500000 | + | 0.866025i | −0.0161374 | + | 0.0279508i | ||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 12.5000 | − | 12.9904i | 0.403016 | − | 0.418827i | ||||
\(963\) | −6.00000 | −0.193347 | ||||||||
\(964\) | 3.50000 | − | 6.06218i | 0.112727 | − | 0.195250i | ||||
\(965\) | −2.00000 | + | 3.46410i | −0.0643823 | + | 0.111513i | ||||
\(966\) | −3.00000 | − | 5.19615i | −0.0965234 | − | 0.167183i | ||||
\(967\) | 16.0000 | 0.514525 | 0.257263 | − | 0.966342i | \(-0.417179\pi\) | ||||
0.257263 | + | 0.966342i | \(0.417179\pi\) | |||||||
\(968\) | 5.00000 | + | 8.66025i | 0.160706 | + | 0.278351i | ||||
\(969\) | 6.00000 | + | 10.3923i | 0.192748 | + | 0.333849i | ||||
\(970\) | 10.0000 | 0.321081 | ||||||||
\(971\) | 20.0000 | + | 34.6410i | 0.641831 | + | 1.11168i | 0.985024 | + | 0.172418i | \(0.0551581\pi\) |
−0.343193 | + | 0.939265i | \(0.611509\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −10.0000 | + | 17.3205i | −0.320585 | + | 0.555270i | ||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | −3.50000 | − | 0.866025i | −0.112090 | − | 0.0277350i | ||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | 19.5000 | − | 33.7750i | 0.623860 | − | 1.08056i | −0.364900 | − | 0.931047i | \(-0.618897\pi\) |
0.988760 | − | 0.149511i | \(-0.0477699\pi\) | |||||||
\(978\) | 8.50000 | − | 14.7224i | 0.271800 | − | 0.470771i | ||||
\(979\) | −5.00000 | − | 8.66025i | −0.159801 | − | 0.276783i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 3.00000 | + | 5.19615i | 0.0957826 | + | 0.165900i | ||||
\(982\) | −12.0000 | − | 20.7846i | −0.382935 | − | 0.663264i | ||||
\(983\) | −25.0000 | −0.797376 | −0.398688 | − | 0.917087i | \(-0.630534\pi\) | ||||
−0.398688 | + | 0.917087i | \(0.630534\pi\) | |||||||
\(984\) | 5.00000 | + | 8.66025i | 0.159394 | + | 0.276079i | ||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | 1.00000 | − | 1.73205i | 0.0318465 | − | 0.0551597i | ||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 21.0000 | + | 5.19615i | 0.668099 | + | 0.165312i | ||||
\(989\) | −15.0000 | −0.476972 | ||||||||
\(990\) | 0.500000 | − | 0.866025i | 0.0158910 | − | 0.0275241i | ||||
\(991\) | −19.5000 | + | 33.7750i | −0.619438 | + | 1.07290i | 0.370151 | + | 0.928972i | \(0.379306\pi\) |
−0.989588 | + | 0.143926i | \(0.954027\pi\) | |||||||
\(992\) | 1.50000 | + | 2.59808i | 0.0476250 | + | 0.0824890i | ||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | −4.00000 | − | 6.92820i | −0.126872 | − | 0.219749i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | 1.00000 | + | 1.73205i | 0.0316703 | + | 0.0548546i | 0.881426 | − | 0.472322i | \(-0.156584\pi\) |
−0.849756 | + | 0.527176i | \(0.823251\pi\) | |||||||
\(998\) | 20.0000 | − | 34.6410i | 0.633089 | − | 1.09654i | ||||
\(999\) | −2.50000 | + | 4.33013i | −0.0790965 | + | 0.136999i |
(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 | 390.2.i.a.61.1 | ✓ | 2 | |
3.2 | odd | 2 | 1170.2.i.k.451.1 | 2 | |||
5.2 | odd | 4 | 1950.2.z.h.1699.1 | 4 | |||
5.3 | odd | 4 | 1950.2.z.h.1699.2 | 4 | |||
5.4 | even | 2 | 1950.2.i.s.451.1 | 2 | |||
13.3 | even | 3 | inner | 390.2.i.a.211.1 | yes | 2 | |
13.4 | even | 6 | 5070.2.a.f.1.1 | 1 | |||
13.6 | odd | 12 | 5070.2.b.g.1351.1 | 2 | |||
13.7 | odd | 12 | 5070.2.b.g.1351.2 | 2 | |||
13.9 | even | 3 | 5070.2.a.o.1.1 | 1 | |||
39.29 | odd | 6 | 1170.2.i.k.991.1 | 2 | |||
65.3 | odd | 12 | 1950.2.z.h.1849.1 | 4 | |||
65.29 | even | 6 | 1950.2.i.s.601.1 | 2 | |||
65.42 | odd | 12 | 1950.2.z.h.1849.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.a.61.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
390.2.i.a.211.1 | yes | 2 | 13.3 | even | 3 | inner | |
1170.2.i.k.451.1 | 2 | 3.2 | odd | 2 | |||
1170.2.i.k.991.1 | 2 | 39.29 | odd | 6 | |||
1950.2.i.s.451.1 | 2 | 5.4 | even | 2 | |||
1950.2.i.s.601.1 | 2 | 65.29 | even | 6 | |||
1950.2.z.h.1699.1 | 4 | 5.2 | odd | 4 | |||
1950.2.z.h.1699.2 | 4 | 5.3 | odd | 4 | |||
1950.2.z.h.1849.1 | 4 | 65.3 | odd | 12 | |||
1950.2.z.h.1849.2 | 4 | 65.42 | odd | 12 | |||
5070.2.a.f.1.1 | 1 | 13.4 | even | 6 | |||
5070.2.a.o.1.1 | 1 | 13.9 | even | 3 | |||
5070.2.b.g.1351.1 | 2 | 13.6 | odd | 12 | |||
5070.2.b.g.1351.2 | 2 | 13.7 | odd | 12 |