Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(7.71354883526\) |
Analytic rank: | \(1\) |
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 | 415.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.415 |
Dual form | 966.2.i.b.277.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 2.00000 | + | 1.73205i | 0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | + | 0.866025i | −0.545545 | + | 0.188982i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | ||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 3.00000 | − | 5.19615i | 0.588348 | − | 1.01905i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.50000 | + | 0.866025i | −0.472456 | + | 0.163663i | ||||
\(29\) | 9.00000 | 1.67126 | 0.835629 | − | 0.549294i | \(-0.185103\pi\) | ||||
0.835629 | + | 0.549294i | \(0.185103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | + | 5.19615i | 0.538816 | + | 0.933257i | 0.998968 | + | 0.0454165i | \(0.0144615\pi\) |
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | −3.00000 | − | 5.19615i | −0.486664 | − | 0.842927i | ||||
\(39\) | 3.00000 | + | 5.19615i | 0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0.500000 | − | 2.59808i | 0.0771517 | − | 0.400892i | ||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | −5.50000 | + | 9.52628i | −0.802257 | + | 1.38955i | 0.115870 | + | 0.993264i | \(0.463035\pi\) |
−0.918127 | + | 0.396286i | \(0.870299\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | −2.50000 | + | 4.33013i | −0.350070 | + | 0.606339i | ||||
\(52\) | 3.00000 | + | 5.19615i | 0.416025 | + | 0.720577i | ||||
\(53\) | −7.00000 | − | 12.1244i | −0.961524 | − | 1.66541i | −0.718677 | − | 0.695344i | \(-0.755252\pi\) |
−0.242846 | − | 0.970065i | \(-0.578081\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | − | 2.59808i | 0.0668153 | − | 0.347183i | ||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | −4.50000 | + | 7.79423i | −0.590879 | + | 1.02343i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 2.00000 | + | 1.73205i | 0.251976 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | −5.00000 | − | 8.66025i | −0.610847 | − | 1.05802i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.380251 | − | 0.924883i | \(-0.375838\pi\) | |||||||
\(68\) | −2.50000 | + | 4.33013i | −0.303170 | + | 0.525105i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | \(-0.0721453\pi\) |
−0.681822 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | 2.50000 | − | 4.33013i | 0.288675 | − | 0.500000i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | −2.50000 | + | 0.866025i | −0.284901 | + | 0.0986928i | ||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | −2.50000 | + | 4.33013i | −0.281272 | + | 0.487177i | −0.971698 | − | 0.236225i | \(-0.924090\pi\) |
0.690426 | + | 0.723403i | \(0.257423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 2.00000 | + | 1.73205i | 0.218218 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.00000 | − | 5.19615i | 0.323498 | − | 0.560316i | ||||
\(87\) | −4.50000 | − | 7.79423i | −0.482451 | − | 0.835629i | ||||
\(88\) | −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 | \(0.988859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 15.5885i | −0.314485 | + | 1.63411i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 3.00000 | − | 5.19615i | 0.311086 | − | 0.538816i | ||||
\(94\) | −5.50000 | − | 9.52628i | −0.567282 | − | 0.982561i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −4.00000 | −0.406138 | −0.203069 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203069 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(98\) | 5.50000 | − | 4.33013i | 0.555584 | − | 0.437409i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 2.50000 | − | 4.33013i | 0.250000 | − | 0.433013i | ||||
\(101\) | −3.50000 | − | 6.06218i | −0.348263 | − | 0.603209i | 0.637678 | − | 0.770303i | \(-0.279895\pi\) |
−0.985941 | + | 0.167094i | \(0.946562\pi\) | |||||||
\(102\) | −2.50000 | − | 4.33013i | −0.247537 | − | 0.428746i | ||||
\(103\) | −5.50000 | + | 9.52628i | −0.541931 | + | 0.938652i | 0.456862 | + | 0.889538i | \(0.348973\pi\) |
−0.998793 | + | 0.0491146i | \(0.984360\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.0000 | 1.35980 | ||||||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 1.50000 | + | 2.59808i | 0.143674 | + | 0.248851i | 0.928877 | − | 0.370387i | \(-0.120775\pi\) |
−0.785203 | + | 0.619238i | \(0.787442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | −3.00000 | + | 5.19615i | −0.280976 | + | 0.486664i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.50000 | − | 7.79423i | −0.417815 | − | 0.723676i | ||||
\(117\) | 3.00000 | − | 5.19615i | 0.277350 | − | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.5000 | + | 4.33013i | −1.14587 | + | 0.396942i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 1.00000 | + | 1.73205i | 0.0905357 | + | 0.156813i | ||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | 3.00000 | − | 5.19615i | 0.269408 | − | 0.466628i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.50000 | + | 0.866025i | −0.222718 | + | 0.0771517i | ||||
\(127\) | −14.0000 | −1.24230 | −0.621150 | − | 0.783692i | \(-0.713334\pi\) | ||||
−0.621150 | + | 0.783692i | \(0.713334\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 3.00000 | + | 5.19615i | 0.264135 | + | 0.457496i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 12.0000 | + | 10.3923i | 1.04053 | + | 0.901127i | ||||
\(134\) | 10.0000 | 0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | −1.50000 | − | 2.59808i | −0.128154 | − | 0.221969i | 0.794808 | − | 0.606861i | \(-0.207572\pi\) |
−0.922961 | + | 0.384893i | \(0.874238\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.0425628 | + | 0.0737210i | ||||
\(139\) | 15.0000 | 1.27228 | 0.636142 | − | 0.771572i | \(-0.280529\pi\) | ||||
0.636142 | + | 0.771572i | \(0.280529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0000 | 0.926367 | ||||||||
\(142\) | 1.50000 | − | 2.59808i | 0.125877 | − | 0.218026i | ||||
\(143\) | 3.00000 | + | 5.19615i | 0.250873 | + | 0.434524i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.00000 | −0.413803 | ||||||||
\(147\) | 1.00000 | + | 6.92820i | 0.0824786 | + | 0.571429i | ||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | 4.00000 | − | 6.92820i | 0.327693 | − | 0.567581i | −0.654361 | − | 0.756182i | \(-0.727062\pi\) |
0.982054 | + | 0.188602i | \(0.0603956\pi\) | |||||||
\(150\) | 2.50000 | + | 4.33013i | 0.204124 | + | 0.353553i | ||||
\(151\) | −6.00000 | − | 10.3923i | −0.488273 | − | 0.845714i | 0.511636 | − | 0.859202i | \(-0.329040\pi\) |
−0.999909 | + | 0.0134886i | \(0.995706\pi\) | |||||||
\(152\) | −3.00000 | + | 5.19615i | −0.243332 | + | 0.421464i | ||||
\(153\) | 5.00000 | 0.404226 | ||||||||
\(154\) | 0.500000 | − | 2.59808i | 0.0402911 | − | 0.209359i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | −6.50000 | − | 11.2583i | −0.518756 | − | 0.898513i | −0.999762 | − | 0.0217953i | \(-0.993062\pi\) |
0.481006 | − | 0.876717i | \(-0.340272\pi\) | |||||||
\(158\) | −2.50000 | − | 4.33013i | −0.198889 | − | 0.344486i | ||||
\(159\) | −7.00000 | + | 12.1244i | −0.555136 | + | 0.961524i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | + | 1.73205i | 0.157622 | + | 0.136505i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −9.50000 | + | 16.4545i | −0.744097 | + | 1.28881i | 0.206518 | + | 0.978443i | \(0.433787\pi\) |
−0.950615 | + | 0.310372i | \(0.899546\pi\) | |||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | − | 6.92820i | 0.310460 | − | 0.537733i | ||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | −2.50000 | + | 0.866025i | −0.192879 | + | 0.0668153i | ||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | 3.00000 | + | 5.19615i | 0.228748 | + | 0.396203i | ||||
\(173\) | 10.5000 | − | 18.1865i | 0.798300 | − | 1.38270i | −0.122422 | − | 0.992478i | \(-0.539066\pi\) |
0.920722 | − | 0.390218i | \(-0.127601\pi\) | |||||||
\(174\) | 9.00000 | 0.682288 | ||||||||
\(175\) | 12.5000 | − | 4.33013i | 0.944911 | − | 0.327327i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.00000 | − | 8.66025i | −0.374766 | − | 0.649113i | ||||
\(179\) | −11.0000 | − | 19.0526i | −0.822179 | − | 1.42406i | −0.904057 | − | 0.427413i | \(-0.859425\pi\) |
0.0818780 | − | 0.996642i | \(-0.473908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0000 | −1.70958 | −0.854788 | − | 0.518977i | \(-0.826313\pi\) | ||||
−0.854788 | + | 0.518977i | \(0.826313\pi\) | |||||||
\(182\) | −12.0000 | − | 10.3923i | −0.889499 | − | 0.770329i | ||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.00000 | + | 5.19615i | 0.219971 | + | 0.381000i | ||||
\(187\) | −2.50000 | + | 4.33013i | −0.182818 | + | 0.316650i | ||||
\(188\) | 11.0000 | 0.802257 | ||||||||
\(189\) | 0.500000 | − | 2.59808i | 0.0363696 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 13.0000 | + | 22.5167i | 0.935760 | + | 1.62078i | 0.773272 | + | 0.634074i | \(0.218619\pi\) |
0.162488 | + | 0.986710i | \(0.448048\pi\) | |||||||
\(194\) | 2.00000 | − | 3.46410i | 0.143592 | − | 0.248708i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 13.0000 | 0.926212 | 0.463106 | − | 0.886303i | \(-0.346735\pi\) | ||||
0.463106 | + | 0.886303i | \(0.346735\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | −3.50000 | − | 6.06218i | −0.248108 | − | 0.429736i | 0.714893 | − | 0.699234i | \(-0.246476\pi\) |
−0.963001 | + | 0.269498i | \(0.913142\pi\) | |||||||
\(200\) | 2.50000 | + | 4.33013i | 0.176777 | + | 0.306186i | ||||
\(201\) | −5.00000 | + | 8.66025i | −0.352673 | + | 0.610847i | ||||
\(202\) | 7.00000 | 0.492518 | ||||||||
\(203\) | 4.50000 | − | 23.3827i | 0.315838 | − | 1.64114i | ||||
\(204\) | 5.00000 | 0.350070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.50000 | − | 9.52628i | −0.383203 | − | 0.663727i | ||||
\(207\) | −0.500000 | − | 0.866025i | −0.0347524 | − | 0.0601929i | ||||
\(208\) | 3.00000 | − | 5.19615i | 0.208013 | − | 0.360288i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | 0.619586 | 0.309793 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309793 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(212\) | −7.00000 | + | 12.1244i | −0.480762 | + | 0.832704i | ||||
\(213\) | 1.50000 | + | 2.59808i | 0.102778 | + | 0.178017i | ||||
\(214\) | 2.00000 | + | 3.46410i | 0.136717 | + | 0.236801i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 15.0000 | − | 5.19615i | 1.01827 | − | 0.352738i | ||||
\(218\) | −3.00000 | −0.203186 | ||||||||
\(219\) | 2.50000 | − | 4.33013i | 0.168934 | − | 0.292603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0000 | + | 25.9808i | 1.00901 | + | 1.74766i | ||||
\(222\) | −3.00000 | + | 5.19615i | −0.201347 | + | 0.348743i | ||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | −2.50000 | + | 0.866025i | −0.167038 | + | 0.0578638i | ||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | −9.00000 | + | 15.5885i | −0.598671 | + | 1.03693i | ||||
\(227\) | −8.50000 | − | 14.7224i | −0.564165 | − | 0.977162i | −0.997127 | − | 0.0757500i | \(-0.975865\pi\) |
0.432962 | − | 0.901412i | \(-0.357468\pi\) | |||||||
\(228\) | −3.00000 | − | 5.19615i | −0.198680 | − | 0.344124i | ||||
\(229\) | −10.5000 | + | 18.1865i | −0.693860 | + | 1.20180i | 0.276704 | + | 0.960955i | \(0.410758\pi\) |
−0.970564 | + | 0.240845i | \(0.922576\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | + | 1.73205i | 0.131590 | + | 0.113961i | ||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | −4.00000 | + | 6.92820i | −0.262049 | + | 0.453882i | −0.966786 | − | 0.255586i | \(-0.917731\pi\) |
0.704737 | + | 0.709468i | \(0.251065\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.00000 | 0.324785 | ||||||||
\(238\) | 2.50000 | − | 12.9904i | 0.162051 | − | 0.842041i | ||||
\(239\) | 9.00000 | 0.582162 | 0.291081 | − | 0.956698i | \(-0.405985\pi\) | ||||
0.291081 | + | 0.956698i | \(0.405985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | + | 12.1244i | 0.450910 | + | 0.780998i | 0.998443 | − | 0.0557856i | \(-0.0177663\pi\) |
−0.547533 | + | 0.836784i | \(0.684433\pi\) | |||||||
\(242\) | 5.00000 | + | 8.66025i | 0.321412 | + | 0.556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 18.0000 | − | 31.1769i | 1.14531 | − | 1.98374i | ||||
\(248\) | 3.00000 | + | 5.19615i | 0.190500 | + | 0.329956i | ||||
\(249\) | 4.00000 | + | 6.92820i | 0.253490 | + | 0.439057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.0000 | −1.07303 | −0.536515 | − | 0.843891i | \(-0.680260\pi\) | ||||
−0.536515 | + | 0.843891i | \(0.680260\pi\) | |||||||
\(252\) | 0.500000 | − | 2.59808i | 0.0314970 | − | 0.163663i | ||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | 7.00000 | − | 12.1244i | 0.439219 | − | 0.760750i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.00000 | − | 12.1244i | 0.436648 | − | 0.756297i | −0.560781 | − | 0.827964i | \(-0.689499\pi\) |
0.997429 | + | 0.0716680i | \(0.0228322\pi\) | |||||||
\(258\) | −6.00000 | −0.373544 | ||||||||
\(259\) | 12.0000 | + | 10.3923i | 0.745644 | + | 0.645746i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.50000 | + | 7.79423i | −0.278543 | + | 0.482451i | ||||
\(262\) | 6.00000 | + | 10.3923i | 0.370681 | + | 0.642039i | ||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.0000 | + | 5.19615i | −0.919709 | + | 0.318597i | ||||
\(267\) | 10.0000 | 0.611990 | ||||||||
\(268\) | −5.00000 | + | 8.66025i | −0.305424 | + | 0.529009i | ||||
\(269\) | 1.50000 | + | 2.59808i | 0.0914566 | + | 0.158408i | 0.908124 | − | 0.418701i | \(-0.137514\pi\) |
−0.816668 | + | 0.577108i | \(0.804181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0000 | − | 19.0526i | 0.668202 | − | 1.15736i | −0.310204 | − | 0.950670i | \(-0.600397\pi\) |
0.978406 | − | 0.206691i | \(-0.0662693\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | 15.0000 | − | 5.19615i | 0.907841 | − | 0.314485i | ||||
\(274\) | 3.00000 | 0.181237 | ||||||||
\(275\) | 2.50000 | − | 4.33013i | 0.150756 | − | 0.261116i | ||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | −16.0000 | − | 27.7128i | −0.961347 | − | 1.66510i | −0.719125 | − | 0.694881i | \(-0.755457\pi\) |
−0.242222 | − | 0.970221i | \(-0.577876\pi\) | |||||||
\(278\) | −7.50000 | + | 12.9904i | −0.449820 | + | 0.779111i | ||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.00000 | 0.298275 | 0.149137 | − | 0.988816i | \(-0.452350\pi\) | ||||
0.149137 | + | 0.988816i | \(0.452350\pi\) | |||||||
\(282\) | −5.50000 | + | 9.52628i | −0.327520 | + | 0.567282i | ||||
\(283\) | 6.00000 | + | 10.3923i | 0.356663 | + | 0.617758i | 0.987401 | − | 0.158237i | \(-0.0505811\pi\) |
−0.630738 | + | 0.775996i | \(0.717248\pi\) | |||||||
\(284\) | 1.50000 | + | 2.59808i | 0.0890086 | + | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | −3.00000 | + | 15.5885i | −0.177084 | + | 0.920158i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | + | 3.46410i | 0.117242 | + | 0.203069i | ||||
\(292\) | 2.50000 | − | 4.33013i | 0.146301 | − | 0.253402i | ||||
\(293\) | −12.0000 | −0.701047 | −0.350524 | − | 0.936554i | \(-0.613996\pi\) | ||||
−0.350524 | + | 0.936554i | \(0.613996\pi\) | |||||||
\(294\) | −6.50000 | − | 2.59808i | −0.379088 | − | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.00000 | + | 5.19615i | −0.174371 | + | 0.302020i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | 4.00000 | + | 6.92820i | 0.231714 | + | 0.401340i | ||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | −3.00000 | + | 15.5885i | −0.172917 | + | 0.898504i | ||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −3.50000 | + | 6.06218i | −0.201070 | + | 0.348263i | ||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.50000 | + | 4.33013i | −0.142915 | + | 0.247537i | ||||
\(307\) | −33.0000 | −1.88341 | −0.941705 | − | 0.336440i | \(-0.890777\pi\) | ||||
−0.941705 | + | 0.336440i | \(0.890777\pi\) | |||||||
\(308\) | 2.00000 | + | 1.73205i | 0.113961 | + | 0.0986928i | ||||
\(309\) | 11.0000 | 0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.50000 | + | 11.2583i | 0.368581 | + | 0.638401i | 0.989344 | − | 0.145597i | \(-0.0465103\pi\) |
−0.620763 | + | 0.783998i | \(0.713177\pi\) | |||||||
\(312\) | 3.00000 | + | 5.19615i | 0.169842 | + | 0.294174i | ||||
\(313\) | 10.0000 | − | 17.3205i | 0.565233 | − | 0.979013i | −0.431795 | − | 0.901972i | \(-0.642119\pi\) |
0.997028 | − | 0.0770410i | \(-0.0245472\pi\) | |||||||
\(314\) | 13.0000 | 0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | −1.00000 | + | 1.73205i | −0.0561656 | + | 0.0972817i | −0.892741 | − | 0.450570i | \(-0.851221\pi\) |
0.836576 | + | 0.547852i | \(0.184554\pi\) | |||||||
\(318\) | −7.00000 | − | 12.1244i | −0.392541 | − | 0.679900i | ||||
\(319\) | −4.50000 | − | 7.79423i | −0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | −2.50000 | + | 0.866025i | −0.139320 | + | 0.0482617i | ||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −15.0000 | − | 25.9808i | −0.832050 | − | 1.44115i | ||||
\(326\) | −9.50000 | − | 16.4545i | −0.526156 | − | 0.911330i | ||||
\(327\) | 1.50000 | − | 2.59808i | 0.0829502 | − | 0.143674i | ||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 22.0000 | + | 19.0526i | 1.21290 | + | 1.05040i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | + | 27.7128i | −0.879440 | + | 1.52323i | −0.0274825 | + | 0.999622i | \(0.508749\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 4.00000 | + | 6.92820i | 0.219529 | + | 0.380235i | ||||
\(333\) | −3.00000 | − | 5.19615i | −0.164399 | − | 0.284747i | ||||
\(334\) | 4.00000 | − | 6.92820i | 0.218870 | − | 0.379094i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.500000 | − | 2.59808i | 0.0272772 | − | 0.141737i | ||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | −11.5000 | + | 19.9186i | −0.625518 | + | 1.08343i | ||||
\(339\) | −9.00000 | − | 15.5885i | −0.488813 | − | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | 6.00000 | 0.324443 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −6.00000 | −0.323498 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5000 | + | 18.1865i | 0.564483 | + | 0.977714i | ||||
\(347\) | 11.0000 | + | 19.0526i | 0.590511 | + | 1.02279i | 0.994164 | + | 0.107883i | \(0.0344071\pi\) |
−0.403653 | + | 0.914912i | \(0.632260\pi\) | |||||||
\(348\) | −4.50000 | + | 7.79423i | −0.241225 | + | 0.417815i | ||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | −2.50000 | + | 12.9904i | −0.133631 | + | 0.694365i | ||||
\(351\) | −6.00000 | −0.320256 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 7.00000 | + | 12.1244i | 0.372572 | + | 0.645314i | 0.989960 | − | 0.141344i | \(-0.0451425\pi\) |
−0.617388 | + | 0.786659i | \(0.711809\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 10.0000 | + | 8.66025i | 0.529256 | + | 0.458349i | ||||
\(358\) | 22.0000 | 1.16274 | ||||||||
\(359\) | 8.00000 | − | 13.8564i | 0.422224 | − | 0.731313i | −0.573933 | − | 0.818902i | \(-0.694583\pi\) |
0.996157 | + | 0.0875892i | \(0.0279163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 11.5000 | − | 19.9186i | 0.604427 | − | 1.04690i | ||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 15.0000 | − | 5.19615i | 0.786214 | − | 0.272352i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.00000 | − | 1.73205i | 0.0522708 | − | 0.0905357i | ||||
\(367\) | −8.00000 | − | 13.8564i | −0.417597 | − | 0.723299i | 0.578101 | − | 0.815966i | \(-0.303794\pi\) |
−0.995697 | + | 0.0926670i | \(0.970461\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.0260643 | − | 0.0451447i | ||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.0000 | + | 12.1244i | −1.81711 | + | 0.629465i | ||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 11.5000 | − | 19.9186i | 0.595447 | − | 1.03135i | −0.398036 | − | 0.917370i | \(-0.630308\pi\) |
0.993484 | − | 0.113975i | \(-0.0363585\pi\) | |||||||
\(374\) | −2.50000 | − | 4.33013i | −0.129272 | − | 0.223906i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.50000 | + | 9.52628i | −0.283641 | + | 0.491280i | ||||
\(377\) | −54.0000 | −2.78114 | ||||||||
\(378\) | 2.00000 | + | 1.73205i | 0.102869 | + | 0.0890871i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.00000 | + | 12.1244i | 0.358621 | + | 0.621150i | ||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | 9.00000 | − | 15.5885i | 0.459879 | − | 0.796533i | −0.539076 | − | 0.842257i | \(-0.681226\pi\) |
0.998954 | + | 0.0457244i | \(0.0145596\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.0000 | −1.32337 | ||||||||
\(387\) | 3.00000 | − | 5.19615i | 0.152499 | − | 0.264135i | ||||
\(388\) | 2.00000 | + | 3.46410i | 0.101535 | + | 0.175863i | ||||
\(389\) | 6.00000 | + | 10.3923i | 0.304212 | + | 0.526911i | 0.977086 | − | 0.212847i | \(-0.0682735\pi\) |
−0.672874 | + | 0.739758i | \(0.734940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.00000 | 0.252861 | ||||||||
\(392\) | −6.50000 | − | 2.59808i | −0.328300 | − | 0.131223i | ||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | −6.50000 | + | 11.2583i | −0.327465 | + | 0.567186i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 19.0000 | − | 32.9090i | 0.953583 | − | 1.65165i | 0.216004 | − | 0.976392i | \(-0.430698\pi\) |
0.737579 | − | 0.675261i | \(-0.235969\pi\) | |||||||
\(398\) | 7.00000 | 0.350878 | ||||||||
\(399\) | 3.00000 | − | 15.5885i | 0.150188 | − | 0.780399i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 15.5000 | − | 26.8468i | 0.774033 | − | 1.34066i | −0.161303 | − | 0.986905i | \(-0.551570\pi\) |
0.935336 | − | 0.353760i | \(-0.115097\pi\) | |||||||
\(402\) | −5.00000 | − | 8.66025i | −0.249377 | − | 0.431934i | ||||
\(403\) | −18.0000 | − | 31.1769i | −0.896644 | − | 1.55303i | ||||
\(404\) | −3.50000 | + | 6.06218i | −0.174132 | + | 0.301605i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.0000 | + | 15.5885i | 0.893325 | + | 0.773642i | ||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | −2.50000 | + | 4.33013i | −0.123768 | + | 0.214373i | ||||
\(409\) | −6.50000 | − | 11.2583i | −0.321404 | − | 0.556689i | 0.659374 | − | 0.751815i | \(-0.270822\pi\) |
−0.980778 | + | 0.195127i | \(0.937488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50000 | + | 2.59808i | −0.0739895 | + | 0.128154i | ||||
\(412\) | 11.0000 | 0.541931 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | −7.50000 | − | 12.9904i | −0.367277 | − | 0.636142i | ||||
\(418\) | −3.00000 | + | 5.19615i | −0.146735 | + | 0.254152i | ||||
\(419\) | −25.0000 | −1.22133 | −0.610665 | − | 0.791889i | \(-0.709098\pi\) | ||||
−0.610665 | + | 0.791889i | \(0.709098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.0000 | −1.02348 | −0.511739 | − | 0.859141i | \(-0.670998\pi\) | ||||
−0.511739 | + | 0.859141i | \(0.670998\pi\) | |||||||
\(422\) | −4.50000 | + | 7.79423i | −0.219057 | + | 0.379417i | ||||
\(423\) | −5.50000 | − | 9.52628i | −0.267419 | − | 0.463184i | ||||
\(424\) | −7.00000 | − | 12.1244i | −0.339950 | − | 0.588811i | ||||
\(425\) | 12.5000 | − | 21.6506i | 0.606339 | − | 1.05021i | ||||
\(426\) | −3.00000 | −0.145350 | ||||||||
\(427\) | −4.00000 | − | 3.46410i | −0.193574 | − | 0.167640i | ||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 3.00000 | − | 5.19615i | 0.144841 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | −3.00000 | + | 15.5885i | −0.144005 | + | 0.748270i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.50000 | − | 2.59808i | 0.0718370 | − | 0.124425i | ||||
\(437\) | −3.00000 | − | 5.19615i | −0.143509 | − | 0.248566i | ||||
\(438\) | 2.50000 | + | 4.33013i | 0.119455 | + | 0.206901i | ||||
\(439\) | −10.0000 | + | 17.3205i | −0.477274 | + | 0.826663i | −0.999661 | − | 0.0260459i | \(-0.991708\pi\) |
0.522387 | + | 0.852709i | \(0.325042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | −30.0000 | −1.42695 | ||||||||
\(443\) | 10.0000 | − | 17.3205i | 0.475114 | − | 0.822922i | −0.524479 | − | 0.851423i | \(-0.675740\pi\) |
0.999594 | + | 0.0285009i | \(0.00907336\pi\) | |||||||
\(444\) | −3.00000 | − | 5.19615i | −0.142374 | − | 0.246598i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.00000 | + | 8.66025i | −0.236757 | + | 0.410075i | ||||
\(447\) | −8.00000 | −0.378387 | ||||||||
\(448\) | 0.500000 | − | 2.59808i | 0.0236228 | − | 0.122748i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 2.50000 | − | 4.33013i | 0.117851 | − | 0.204124i | ||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | −9.00000 | − | 15.5885i | −0.423324 | − | 0.733219i | ||||
\(453\) | −6.00000 | + | 10.3923i | −0.281905 | + | 0.488273i | ||||
\(454\) | 17.0000 | 0.797850 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | −6.00000 | + | 10.3923i | −0.280668 | + | 0.486132i | −0.971549 | − | 0.236837i | \(-0.923889\pi\) |
0.690881 | + | 0.722968i | \(0.257223\pi\) | |||||||
\(458\) | −10.5000 | − | 18.1865i | −0.490633 | − | 0.849801i | ||||
\(459\) | −2.50000 | − | 4.33013i | −0.116690 | − | 0.202113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | −2.50000 | + | 0.866025i | −0.116311 | + | 0.0402911i | ||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | −4.50000 | + | 7.79423i | −0.208907 | + | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00000 | − | 6.92820i | −0.185296 | − | 0.320943i | ||||
\(467\) | −15.5000 | + | 26.8468i | −0.717254 | + | 1.24232i | 0.244829 | + | 0.969566i | \(0.421268\pi\) |
−0.962084 | + | 0.272755i | \(0.912065\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | −25.0000 | + | 8.66025i | −1.15439 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.50000 | + | 11.2583i | −0.299504 | + | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | + | 5.19615i | 0.137940 | + | 0.238919i | ||||
\(474\) | −2.50000 | + | 4.33013i | −0.114829 | + | 0.198889i | ||||
\(475\) | −30.0000 | −1.37649 | ||||||||
\(476\) | 10.0000 | + | 8.66025i | 0.458349 | + | 0.396942i | ||||
\(477\) | 14.0000 | 0.641016 | ||||||||
\(478\) | −4.50000 | + | 7.79423i | −0.205825 | + | 0.356500i | ||||
\(479\) | −15.0000 | − | 25.9808i | −0.685367 | − | 1.18709i | −0.973321 | − | 0.229447i | \(-0.926308\pi\) |
0.287954 | − | 0.957644i | \(-0.407025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | − | 31.1769i | 0.820729 | − | 1.42154i | ||||
\(482\) | −14.0000 | −0.637683 | ||||||||
\(483\) | 0.500000 | − | 2.59808i | 0.0227508 | − | 0.118217i | ||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 7.00000 | + | 12.1244i | 0.317200 | + | 0.549407i | 0.979903 | − | 0.199476i | \(-0.0639239\pi\) |
−0.662702 | + | 0.748883i | \(0.730591\pi\) | |||||||
\(488\) | 1.00000 | − | 1.73205i | 0.0452679 | − | 0.0784063i | ||||
\(489\) | 19.0000 | 0.859210 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 3.00000 | − | 5.19615i | 0.135250 | − | 0.234261i | ||||
\(493\) | −22.5000 | − | 38.9711i | −1.01335 | − | 1.75517i | ||||
\(494\) | 18.0000 | + | 31.1769i | 0.809858 | + | 1.40272i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | −1.50000 | + | 7.79423i | −0.0672842 | + | 0.349619i | ||||
\(498\) | −8.00000 | −0.358489 | ||||||||
\(499\) | −3.50000 | + | 6.06218i | −0.156682 | + | 0.271380i | −0.933670 | − | 0.358134i | \(-0.883413\pi\) |
0.776989 | + | 0.629515i | \(0.216746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.00000 | + | 6.92820i | 0.178707 | + | 0.309529i | ||||
\(502\) | 8.50000 | − | 14.7224i | 0.379374 | − | 0.657094i | ||||
\(503\) | 18.0000 | 0.802580 | 0.401290 | − | 0.915951i | \(-0.368562\pi\) | ||||
0.401290 | + | 0.915951i | \(0.368562\pi\) | |||||||
\(504\) | 2.00000 | + | 1.73205i | 0.0890871 | + | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.500000 | + | 0.866025i | −0.0222277 | + | 0.0384995i | ||||
\(507\) | −11.5000 | − | 19.9186i | −0.510733 | − | 0.884615i | ||||
\(508\) | 7.00000 | + | 12.1244i | 0.310575 | + | 0.537931i | ||||
\(509\) | −20.5000 | + | 35.5070i | −0.908647 | + | 1.57382i | −0.0927004 | + | 0.995694i | \(0.529550\pi\) |
−0.815946 | + | 0.578128i | \(0.803783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5000 | − | 4.33013i | 0.552967 | − | 0.191554i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.00000 | + | 5.19615i | −0.132453 | + | 0.229416i | ||||
\(514\) | 7.00000 | + | 12.1244i | 0.308757 | + | 0.534782i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.00000 | − | 5.19615i | 0.132068 | − | 0.228748i | ||||
\(517\) | 11.0000 | 0.483779 | ||||||||
\(518\) | −15.0000 | + | 5.19615i | −0.659062 | + | 0.228306i | ||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | + | 15.5885i | 0.394297 | + | 0.682943i | 0.993011 | − | 0.118020i | \(-0.0376547\pi\) |
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(522\) | −4.50000 | − | 7.79423i | −0.196960 | − | 0.341144i | ||||
\(523\) | −9.00000 | + | 15.5885i | −0.393543 | + | 0.681636i | −0.992914 | − | 0.118835i | \(-0.962084\pi\) |
0.599371 | + | 0.800471i | \(0.295417\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | −10.0000 | − | 8.66025i | −0.436436 | − | 0.377964i | ||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | 15.0000 | − | 25.9808i | 0.653410 | − | 1.13174i | ||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.00000 | − | 15.5885i | 0.130066 | − | 0.675845i | ||||
\(533\) | 36.0000 | 1.55933 | ||||||||
\(534\) | −5.00000 | + | 8.66025i | −0.216371 | + | 0.374766i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.00000 | − | 8.66025i | −0.215967 | − | 0.374066i | ||||
\(537\) | −11.0000 | + | 19.0526i | −0.474685 | + | 0.822179i | ||||
\(538\) | −3.00000 | −0.129339 | ||||||||
\(539\) | 1.00000 | + | 6.92820i | 0.0430730 | + | 0.298419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | 11.0000 | + | 19.0526i | 0.472490 | + | 0.818377i | ||||
\(543\) | 11.5000 | + | 19.9186i | 0.493512 | + | 0.854788i | ||||
\(544\) | −2.50000 | + | 4.33013i | −0.107187 | + | 0.185653i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.00000 | + | 15.5885i | −0.128388 | + | 0.667124i | ||||
\(547\) | 13.0000 | 0.555840 | 0.277920 | − | 0.960604i | \(-0.410355\pi\) | ||||
0.277920 | + | 0.960604i | \(0.410355\pi\) | |||||||
\(548\) | −1.50000 | + | 2.59808i | −0.0640768 | + | 0.110984i | ||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | 2.50000 | + | 4.33013i | 0.106600 | + | 0.184637i | ||||
\(551\) | −27.0000 | + | 46.7654i | −1.15024 | + | 1.99227i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 10.0000 | + | 8.66025i | 0.425243 | + | 0.368271i | ||||
\(554\) | 32.0000 | 1.35955 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.50000 | − | 12.9904i | −0.318071 | − | 0.550915i | ||||
\(557\) | −15.0000 | − | 25.9808i | −0.635570 | − | 1.10084i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.350824 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(558\) | 3.00000 | − | 5.19615i | 0.127000 | − | 0.219971i | ||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.00000 | 0.211100 | ||||||||
\(562\) | −2.50000 | + | 4.33013i | −0.105456 | + | 0.182655i | ||||
\(563\) | 10.5000 | + | 18.1865i | 0.442522 | + | 0.766471i | 0.997876 | − | 0.0651433i | \(-0.0207504\pi\) |
−0.555354 | + | 0.831614i | \(0.687417\pi\) | |||||||
\(564\) | −5.50000 | − | 9.52628i | −0.231592 | − | 0.401129i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | −1.00000 | + | 1.73205i | −0.0419222 | + | 0.0726113i | −0.886225 | − | 0.463255i | \(-0.846681\pi\) |
0.844303 | + | 0.535866i | \(0.180015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | + | 27.7128i | 0.669579 | + | 1.15975i | 0.978022 | + | 0.208502i | \(0.0668588\pi\) |
−0.308443 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(572\) | 3.00000 | − | 5.19615i | 0.125436 | − | 0.217262i | ||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | −12.0000 | − | 10.3923i | −0.500870 | − | 0.433766i | ||||
\(575\) | −5.00000 | −0.208514 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −16.5000 | − | 28.5788i | −0.686904 | − | 1.18975i | −0.972834 | − | 0.231502i | \(-0.925636\pi\) |
0.285930 | − | 0.958250i | \(-0.407697\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 13.0000 | − | 22.5167i | 0.540262 | − | 0.935760i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | + | 20.7846i | −0.165948 | + | 0.862291i | ||||
\(582\) | −4.00000 | −0.165805 | ||||||||
\(583\) | −7.00000 | + | 12.1244i | −0.289910 | + | 0.502140i | ||||
\(584\) | 2.50000 | + | 4.33013i | 0.103451 | + | 0.179182i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | − | 10.3923i | 0.247858 | − | 0.429302i | ||||
\(587\) | −24.0000 | −0.990586 | −0.495293 | − | 0.868726i | \(-0.664939\pi\) | ||||
−0.495293 | + | 0.868726i | \(0.664939\pi\) | |||||||
\(588\) | 5.50000 | − | 4.33013i | 0.226816 | − | 0.178571i | ||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.50000 | − | 11.2583i | −0.267374 | − | 0.463106i | ||||
\(592\) | −3.00000 | − | 5.19615i | −0.123299 | − | 0.213561i | ||||
\(593\) | 11.0000 | − | 19.0526i | 0.451716 | − | 0.782395i | −0.546777 | − | 0.837278i | \(-0.684145\pi\) |
0.998493 | + | 0.0548835i | \(0.0174787\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.00000 | −0.327693 | ||||||||
\(597\) | −3.50000 | + | 6.06218i | −0.143245 | + | 0.248108i | ||||
\(598\) | 3.00000 | + | 5.19615i | 0.122679 | + | 0.212486i | ||||
\(599\) | 3.50000 | + | 6.06218i | 0.143006 | + | 0.247694i | 0.928627 | − | 0.371014i | \(-0.120990\pi\) |
−0.785621 | + | 0.618708i | \(0.787656\pi\) | |||||||
\(600\) | 2.50000 | − | 4.33013i | 0.102062 | − | 0.176777i | ||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | −12.0000 | − | 10.3923i | −0.489083 | − | 0.423559i | ||||
\(603\) | 10.0000 | 0.407231 | ||||||||
\(604\) | −6.00000 | + | 10.3923i | −0.244137 | + | 0.422857i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.50000 | − | 6.06218i | −0.142178 | − | 0.246259i | ||||
\(607\) | −3.00000 | + | 5.19615i | −0.121766 | + | 0.210905i | −0.920464 | − | 0.390827i | \(-0.872189\pi\) |
0.798698 | + | 0.601732i | \(0.205522\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | −22.5000 | + | 7.79423i | −0.911746 | + | 0.315838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.0000 | − | 57.1577i | 1.33504 | − | 2.31235i | ||||
\(612\) | −2.50000 | − | 4.33013i | −0.101057 | − | 0.175035i | ||||
\(613\) | −3.50000 | − | 6.06218i | −0.141364 | − | 0.244849i | 0.786647 | − | 0.617403i | \(-0.211815\pi\) |
−0.928010 | + | 0.372554i | \(0.878482\pi\) | |||||||
\(614\) | 16.5000 | − | 28.5788i | 0.665886 | − | 1.15335i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.50000 | + | 0.866025i | −0.100728 | + | 0.0348932i | ||||
\(617\) | 33.0000 | 1.32853 | 0.664265 | − | 0.747497i | \(-0.268745\pi\) | ||||
0.664265 | + | 0.747497i | \(0.268745\pi\) | |||||||
\(618\) | −5.50000 | + | 9.52628i | −0.221242 | + | 0.383203i | ||||
\(619\) | −4.00000 | − | 6.92820i | −0.160774 | − | 0.278468i | 0.774373 | − | 0.632730i | \(-0.218066\pi\) |
−0.935146 | + | 0.354262i | \(0.884732\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | −13.0000 | −0.521253 | ||||||||
\(623\) | 20.0000 | + | 17.3205i | 0.801283 | + | 0.693932i | ||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 10.0000 | + | 17.3205i | 0.399680 | + | 0.692267i | ||||
\(627\) | −3.00000 | − | 5.19615i | −0.119808 | − | 0.207514i | ||||
\(628\) | −6.50000 | + | 11.2583i | −0.259378 | + | 0.449256i | ||||
\(629\) | 30.0000 | 1.19618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.0000 | −1.63218 | −0.816092 | − | 0.577922i | \(-0.803864\pi\) | ||||
−0.816092 | + | 0.577922i | \(0.803864\pi\) | |||||||
\(632\) | −2.50000 | + | 4.33013i | −0.0994447 | + | 0.172243i | ||||
\(633\) | −4.50000 | − | 7.79423i | −0.178859 | − | 0.309793i | ||||
\(634\) | −1.00000 | − | 1.73205i | −0.0397151 | − | 0.0687885i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.0000 | 0.555136 | ||||||||
\(637\) | 39.0000 | + | 15.5885i | 1.54524 | + | 0.617637i | ||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | 1.50000 | − | 2.59808i | 0.0593391 | − | 0.102778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | 2.00000 | − | 3.46410i | 0.0789337 | − | 0.136717i | ||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | 0.500000 | − | 2.59808i | 0.0197028 | − | 0.102379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.0000 | + | 25.9808i | −0.590167 | + | 1.02220i | ||||
\(647\) | −7.50000 | − | 12.9904i | −0.294855 | − | 0.510705i | 0.680096 | − | 0.733123i | \(-0.261938\pi\) |
−0.974951 | + | 0.222419i | \(0.928605\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 30.0000 | 1.17670 | ||||||||
\(651\) | −12.0000 | − | 10.3923i | −0.470317 | − | 0.407307i | ||||
\(652\) | 19.0000 | 0.744097 | ||||||||
\(653\) | −24.5000 | + | 42.4352i | −0.958759 | + | 1.66062i | −0.233238 | + | 0.972420i | \(0.574932\pi\) |
−0.725521 | + | 0.688200i | \(0.758401\pi\) | |||||||
\(654\) | 1.50000 | + | 2.59808i | 0.0586546 | + | 0.101593i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | −5.00000 | −0.195069 | ||||||||
\(658\) | −27.5000 | + | 9.52628i | −1.07206 | + | 0.371373i | ||||
\(659\) | −33.0000 | −1.28550 | −0.642749 | − | 0.766077i | \(-0.722206\pi\) | ||||
−0.642749 | + | 0.766077i | \(0.722206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.50000 | − | 6.06218i | −0.136134 | − | 0.235791i | 0.789896 | − | 0.613241i | \(-0.210135\pi\) |
−0.926030 | + | 0.377450i | \(0.876801\pi\) | |||||||
\(662\) | −16.0000 | − | 27.7128i | −0.621858 | − | 1.07709i | ||||
\(663\) | 15.0000 | − | 25.9808i | 0.582552 | − | 1.00901i | ||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | −4.50000 | + | 7.79423i | −0.174241 | + | 0.301794i | ||||
\(668\) | 4.00000 | + | 6.92820i | 0.154765 | + | 0.268060i | ||||
\(669\) | −5.00000 | − | 8.66025i | −0.193311 | − | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 2.00000 | + | 1.73205i | 0.0771517 | + | 0.0668153i | ||||
\(673\) | −35.0000 | −1.34915 | −0.674575 | − | 0.738206i | \(-0.735673\pi\) | ||||
−0.674575 | + | 0.738206i | \(0.735673\pi\) | |||||||
\(674\) | 9.00000 | − | 15.5885i | 0.346667 | − | 0.600445i | ||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | −11.5000 | − | 19.9186i | −0.442308 | − | 0.766099i | ||||
\(677\) | 7.00000 | − | 12.1244i | 0.269032 | − | 0.465977i | −0.699580 | − | 0.714554i | \(-0.746630\pi\) |
0.968612 | + | 0.248577i | \(0.0799630\pi\) | |||||||
\(678\) | 18.0000 | 0.691286 | ||||||||
\(679\) | −2.00000 | + | 10.3923i | −0.0767530 | + | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.50000 | + | 14.7224i | −0.325721 | + | 0.564165i | ||||
\(682\) | 3.00000 | + | 5.19615i | 0.114876 | + | 0.198971i | ||||
\(683\) | 20.0000 | + | 34.6410i | 0.765279 | + | 1.32550i | 0.940099 | + | 0.340901i | \(0.110732\pi\) |
−0.174820 | + | 0.984600i | \(0.555934\pi\) | |||||||
\(684\) | −3.00000 | + | 5.19615i | −0.114708 | + | 0.198680i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 21.0000 | 0.801200 | ||||||||
\(688\) | 3.00000 | − | 5.19615i | 0.114374 | − | 0.198101i | ||||
\(689\) | 42.0000 | + | 72.7461i | 1.60007 | + | 2.77141i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.50000 | + | 11.2583i | −0.247272 | + | 0.428287i | −0.962768 | − | 0.270330i | \(-0.912867\pi\) |
0.715496 | + | 0.698617i | \(0.246201\pi\) | |||||||
\(692\) | −21.0000 | −0.798300 | ||||||||
\(693\) | 0.500000 | − | 2.59808i | 0.0189934 | − | 0.0986928i | ||||
\(694\) | −22.0000 | −0.835109 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.50000 | − | 7.79423i | −0.170572 | − | 0.295439i | ||||
\(697\) | 15.0000 | + | 25.9808i | 0.568166 | + | 0.984092i | ||||
\(698\) | −5.00000 | + | 8.66025i | −0.189253 | + | 0.327795i | ||||
\(699\) | 8.00000 | 0.302588 | ||||||||
\(700\) | −10.0000 | − | 8.66025i | −0.377964 | − | 0.327327i | ||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 3.00000 | − | 5.19615i | 0.113228 | − | 0.196116i | ||||
\(703\) | −18.0000 | − | 31.1769i | −0.678883 | − | 1.17586i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0000 | −0.526897 | ||||||||
\(707\) | −17.5000 | + | 6.06218i | −0.658155 | + | 0.227992i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5000 | − | 32.0429i | 0.694782 | − | 1.20340i | −0.275472 | − | 0.961309i | \(-0.588834\pi\) |
0.970254 | − | 0.242089i | \(-0.0778325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | − | 4.33013i | −0.0937573 | − | 0.162392i | ||||
\(712\) | −5.00000 | + | 8.66025i | −0.187383 | + | 0.324557i | ||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | −12.5000 | + | 4.33013i | −0.467801 | + | 0.162051i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.0000 | + | 19.0526i | −0.411089 | + | 0.712028i | ||||
\(717\) | −4.50000 | − | 7.79423i | −0.168056 | − | 0.291081i | ||||
\(718\) | 8.00000 | + | 13.8564i | 0.298557 | + | 0.517116i | ||||
\(719\) | 20.0000 | − | 34.6410i | 0.745874 | − | 1.29189i | −0.203911 | − | 0.978989i | \(-0.565365\pi\) |
0.949785 | − | 0.312903i | \(-0.101301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0000 | + | 19.0526i | 0.819323 | + | 0.709554i | ||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 7.00000 | − | 12.1244i | 0.260333 | − | 0.450910i | ||||
\(724\) | 11.5000 | + | 19.9186i | 0.427394 | + | 0.740268i | ||||
\(725\) | 22.5000 | + | 38.9711i | 0.835629 | + | 1.44735i | ||||
\(726\) | 5.00000 | − | 8.66025i | 0.185567 | − | 0.321412i | ||||
\(727\) | 25.0000 | 0.927199 | 0.463599 | − | 0.886045i | \(-0.346558\pi\) | ||||
0.463599 | + | 0.886045i | \(0.346558\pi\) | |||||||
\(728\) | −3.00000 | + | 15.5885i | −0.111187 | + | 0.577747i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0000 | + | 25.9808i | 0.554795 | + | 0.960933i | ||||
\(732\) | 1.00000 | + | 1.73205i | 0.0369611 | + | 0.0640184i | ||||
\(733\) | 6.50000 | − | 11.2583i | 0.240083 | − | 0.415836i | −0.720655 | − | 0.693294i | \(-0.756159\pi\) |
0.960738 | + | 0.277458i | \(0.0894920\pi\) | |||||||
\(734\) | 16.0000 | 0.590571 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −5.00000 | + | 8.66025i | −0.184177 | + | 0.319005i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | 18.5000 | + | 32.0429i | 0.680534 | + | 1.17872i | 0.974818 | + | 0.223001i | \(0.0715853\pi\) |
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.0000 | −1.32249 | ||||||||
\(742\) | 7.00000 | − | 36.3731i | 0.256978 | − | 1.33530i | ||||
\(743\) | −20.0000 | −0.733729 | −0.366864 | − | 0.930274i | \(-0.619569\pi\) | ||||
−0.366864 | + | 0.930274i | \(0.619569\pi\) | |||||||
\(744\) | 3.00000 | − | 5.19615i | 0.109985 | − | 0.190500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.5000 | + | 19.9186i | 0.421045 | + | 0.729271i | ||||
\(747\) | 4.00000 | − | 6.92820i | 0.146352 | − | 0.253490i | ||||
\(748\) | 5.00000 | 0.182818 | ||||||||
\(749\) | −8.00000 | − | 6.92820i | −0.292314 | − | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | − | 34.6410i | 0.729810 | − | 1.26407i | −0.227153 | − | 0.973859i | \(-0.572942\pi\) |
0.956963 | − | 0.290209i | \(-0.0937250\pi\) | |||||||
\(752\) | −5.50000 | − | 9.52628i | −0.200564 | − | 0.347388i | ||||
\(753\) | 8.50000 | + | 14.7224i | 0.309757 | + | 0.536515i | ||||
\(754\) | 27.0000 | − | 46.7654i | 0.983282 | − | 1.70309i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.50000 | + | 0.866025i | −0.0909241 | + | 0.0314970i | ||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | −10.0000 | + | 17.3205i | −0.363216 | + | 0.629109i | ||||
\(759\) | −0.500000 | − | 0.866025i | −0.0181489 | − | 0.0314347i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | + | 10.3923i | −0.217500 | + | 0.376721i | −0.954043 | − | 0.299670i | \(-0.903123\pi\) |
0.736543 | + | 0.676391i | \(0.236457\pi\) | |||||||
\(762\) | −14.0000 | −0.507166 | ||||||||
\(763\) | 7.50000 | − | 2.59808i | 0.271518 | − | 0.0940567i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.00000 | + | 15.5885i | 0.325183 | + | 0.563234i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 26.0000 | 0.937584 | 0.468792 | − | 0.883309i | \(-0.344689\pi\) | ||||
0.468792 | + | 0.883309i | \(0.344689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 13.0000 | − | 22.5167i | 0.467880 | − | 0.810392i | ||||
\(773\) | −20.0000 | − | 34.6410i | −0.719350 | − | 1.24595i | −0.961258 | − | 0.275651i | \(-0.911106\pi\) |
0.241908 | − | 0.970299i | \(-0.422227\pi\) | |||||||
\(774\) | 3.00000 | + | 5.19615i | 0.107833 | + | 0.186772i | ||||
\(775\) | −15.0000 | + | 25.9808i | −0.538816 | + | 0.933257i | ||||
\(776\) | −4.00000 | −0.143592 | ||||||||
\(777\) | 3.00000 | − | 15.5885i | 0.107624 | − | 0.559233i | ||||
\(778\) | −12.0000 | −0.430221 | ||||||||
\(779\) | 18.0000 | − | 31.1769i | 0.644917 | − | 1.11703i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.50000 | + | 2.59808i | 0.0536742 | + | 0.0929665i | ||||
\(782\) | −2.50000 | + | 4.33013i | −0.0893998 | + | 0.154845i | ||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.00000 | − | 10.3923i | 0.214013 | − | 0.370681i | ||||
\(787\) | 14.0000 | + | 24.2487i | 0.499046 | + | 0.864373i | 0.999999 | − | 0.00110111i | \(-0.000350496\pi\) |
−0.500953 | + | 0.865474i | \(0.667017\pi\) | |||||||
\(788\) | −6.50000 | − | 11.2583i | −0.231553 | − | 0.401061i | ||||
\(789\) | 6.00000 | − | 10.3923i | 0.213606 | − | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.00000 | − | 46.7654i | 0.320003 | − | 1.66279i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −6.00000 | + | 10.3923i | −0.213066 | + | 0.369042i | ||||
\(794\) | 19.0000 | + | 32.9090i | 0.674285 | + | 1.16790i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.50000 | + | 6.06218i | −0.124054 | + | 0.214868i | ||||
\(797\) | 2.00000 | 0.0708436 | 0.0354218 | − | 0.999372i | \(-0.488723\pi\) | ||||
0.0354218 | + | 0.999372i | \(0.488723\pi\) | |||||||
\(798\) | 12.0000 | + | 10.3923i | 0.424795 | + | 0.367884i | ||||
\(799\) | 55.0000 | 1.94576 | ||||||||
\(800\) | 2.50000 | − | 4.33013i | 0.0883883 | − | 0.153093i | ||||
\(801\) | −5.00000 | − | 8.66025i | −0.176666 | − | 0.305995i | ||||
\(802\) | 15.5000 | + | 26.8468i | 0.547324 | + | 0.947993i | ||||
\(803\) | 2.50000 | − | 4.33013i | 0.0882231 | − | 0.152807i | ||||
\(804\) | 10.0000 | 0.352673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 36.0000 | 1.26805 | ||||||||
\(807\) | 1.50000 | − | 2.59808i | 0.0528025 | − | 0.0914566i | ||||
\(808\) | −3.50000 | − | 6.06218i | −0.123130 | − | 0.213267i | ||||
\(809\) | 17.0000 | + | 29.4449i | 0.597688 | + | 1.03523i | 0.993161 | + | 0.116749i | \(0.0372472\pi\) |
−0.395473 | + | 0.918477i | \(0.629419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0000 | −0.948098 | −0.474049 | − | 0.880498i | \(-0.657208\pi\) | ||||
−0.474049 | + | 0.880498i | \(0.657208\pi\) | |||||||
\(812\) | −22.5000 | + | 7.79423i | −0.789595 | + | 0.273524i | ||||
\(813\) | −22.0000 | −0.771574 | ||||||||
\(814\) | −3.00000 | + | 5.19615i | −0.105150 | + | 0.182125i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.50000 | − | 4.33013i | −0.0875175 | − | 0.151585i | ||||
\(817\) | 18.0000 | − | 31.1769i | 0.629740 | − | 1.09074i | ||||
\(818\) | 13.0000 | 0.454534 | ||||||||
\(819\) | −12.0000 | − | 10.3923i | −0.419314 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.50000 | + | 2.59808i | −0.0523504 | + | 0.0906735i | −0.891013 | − | 0.453978i | \(-0.850005\pi\) |
0.838663 | + | 0.544651i | \(0.183338\pi\) | |||||||
\(822\) | −1.50000 | − | 2.59808i | −0.0523185 | − | 0.0906183i | ||||
\(823\) | 19.0000 | + | 32.9090i | 0.662298 | + | 1.14713i | 0.980010 | + | 0.198947i | \(0.0637522\pi\) |
−0.317712 | + | 0.948187i | \(0.602914\pi\) | |||||||
\(824\) | −5.50000 | + | 9.52628i | −0.191602 | + | 0.331864i | ||||
\(825\) | −5.00000 | −0.174078 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.00000 | −0.312961 | −0.156480 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156480 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(828\) | −0.500000 | + | 0.866025i | −0.0173762 | + | 0.0300965i | ||||
\(829\) | −1.00000 | − | 1.73205i | −0.0347314 | − | 0.0601566i | 0.848137 | − | 0.529777i | \(-0.177724\pi\) |
−0.882869 | + | 0.469620i | \(0.844391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0000 | + | 27.7128i | −0.555034 | + | 0.961347i | ||||
\(832\) | −6.00000 | −0.208013 | ||||||||
\(833\) | 5.00000 | + | 34.6410i | 0.173240 | + | 1.20024i | ||||
\(834\) | 15.0000 | 0.519408 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.00000 | − | 5.19615i | −0.103757 | − | 0.179713i | ||||
\(837\) | 3.00000 | + | 5.19615i | 0.103695 | + | 0.179605i | ||||
\(838\) | 12.5000 | − | 21.6506i | 0.431805 | − | 0.747909i | ||||
\(839\) | −48.0000 | −1.65714 | −0.828572 | − | 0.559883i | \(-0.810846\pi\) | ||||
−0.828572 | + | 0.559883i | \(0.810846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 10.5000 | − | 18.1865i | 0.361854 | − | 0.626749i | ||||
\(843\) | −2.50000 | − | 4.33013i | −0.0861046 | − | 0.149137i | ||||
\(844\) | −4.50000 | − | 7.79423i | −0.154896 | − | 0.268288i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.0000 | 0.378188 | ||||||||
\(847\) | −20.0000 | − | 17.3205i | −0.687208 | − | 0.595140i | ||||
\(848\) | 14.0000 | 0.480762 | ||||||||
\(849\) | 6.00000 | − | 10.3923i | 0.205919 | − | 0.356663i | ||||
\(850\) | 12.5000 | + | 21.6506i | 0.428746 | + | 0.742611i | ||||
\(851\) | −3.00000 | − | 5.19615i | −0.102839 | − | 0.178122i | ||||
\(852\) | 1.50000 | − | 2.59808i | 0.0513892 | − | 0.0890086i | ||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 5.00000 | − | 1.73205i | 0.171096 | − | 0.0592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.00000 | − | 3.46410i | 0.0683586 | − | 0.118401i | ||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 3.00000 | + | 5.19615i | 0.102418 | + | 0.177394i | ||||
\(859\) | 8.50000 | − | 14.7224i | 0.290016 | − | 0.502323i | −0.683797 | − | 0.729672i | \(-0.739673\pi\) |
0.973813 | + | 0.227349i | \(0.0730059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.0000 | − | 5.19615i | 0.511199 | − | 0.177084i | ||||
\(862\) | 6.00000 | 0.204361 | ||||||||
\(863\) | −18.5000 | + | 32.0429i | −0.629747 | + | 1.09075i | 0.357855 | + | 0.933777i | \(0.383508\pi\) |
−0.987602 | + | 0.156977i | \(0.949825\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.00000 | + | 1.73205i | −0.0339814 | + | 0.0588575i | ||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | −12.0000 | − | 10.3923i | −0.407307 | − | 0.352738i | ||||
\(869\) | 5.00000 | 0.169613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.0000 | + | 51.9615i | 1.01651 | + | 1.76065i | ||||
\(872\) | 1.50000 | + | 2.59808i | 0.0507964 | + | 0.0879820i | ||||
\(873\) | 2.00000 | − | 3.46410i | 0.0676897 | − | 0.117242i | ||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.00000 | −0.168934 | ||||||||
\(877\) | 12.0000 | − | 20.7846i | 0.405211 | − | 0.701846i | −0.589135 | − | 0.808035i | \(-0.700531\pi\) |
0.994346 | + | 0.106188i | \(0.0338646\pi\) | |||||||
\(878\) | −10.0000 | − | 17.3205i | −0.337484 | − | 0.584539i | ||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.0000 | −1.31394 | −0.656972 | − | 0.753915i | \(-0.728163\pi\) | ||||
−0.656972 | + | 0.753915i | \(0.728163\pi\) | |||||||
\(882\) | 1.00000 | + | 6.92820i | 0.0336718 | + | 0.233285i | ||||
\(883\) | −36.0000 | −1.21150 | −0.605748 | − | 0.795656i | \(-0.707126\pi\) | ||||
−0.605748 | + | 0.795656i | \(0.707126\pi\) | |||||||
\(884\) | 15.0000 | − | 25.9808i | 0.504505 | − | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.0000 | + | 17.3205i | 0.335957 | + | 0.581894i | ||||
\(887\) | 1.50000 | − | 2.59808i | 0.0503651 | − | 0.0872349i | −0.839744 | − | 0.542983i | \(-0.817295\pi\) |
0.890109 | + | 0.455748i | \(0.150628\pi\) | |||||||
\(888\) | 6.00000 | 0.201347 | ||||||||
\(889\) | −7.00000 | + | 36.3731i | −0.234772 | + | 1.21991i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | −5.00000 | − | 8.66025i | −0.167412 | − | 0.289967i | ||||
\(893\) | −33.0000 | − | 57.1577i | −1.10430 | − | 1.91271i | ||||
\(894\) | 4.00000 | − | 6.92820i | 0.133780 | − | 0.231714i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | + | 1.73205i | 0.0668153 | + | 0.0578638i | ||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.0000 | + | 46.7654i | 0.900500 | + | 1.55971i | ||||
\(900\) | 2.50000 | + | 4.33013i | 0.0833333 | + | 0.144338i | ||||
\(901\) | −35.0000 | + | 60.6218i | −1.16602 | + | 2.01960i | ||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | 15.0000 | − | 5.19615i | 0.499169 | − | 0.172917i | ||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.00000 | − | 10.3923i | −0.199337 | − | 0.345261i | ||||
\(907\) | −2.00000 | − | 3.46410i | −0.0664089 | − | 0.115024i | 0.830909 | − | 0.556408i | \(-0.187821\pi\) |
−0.897318 | + | 0.441384i | \(0.854488\pi\) | |||||||
\(908\) | −8.50000 | + | 14.7224i | −0.282082 | + | 0.488581i | ||||
\(909\) | 7.00000 | 0.232175 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | −3.00000 | + | 5.19615i | −0.0993399 | + | 0.172062i | ||||
\(913\) | 4.00000 | + | 6.92820i | 0.132381 | + | 0.229290i | ||||
\(914\) | −6.00000 | − | 10.3923i | −0.198462 | − | 0.343747i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.0000 | 0.693860 | ||||||||
\(917\) | −24.0000 | − | 20.7846i | −0.792550 | − | 0.686368i | ||||
\(918\) | 5.00000 | 0.165025 | ||||||||
\(919\) | −25.5000 | + | 44.1673i | −0.841167 | + | 1.45694i | 0.0477411 | + | 0.998860i | \(0.484798\pi\) |
−0.888908 | + | 0.458085i | \(0.848536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.5000 | + | 28.5788i | 0.543693 | + | 0.941705i | ||||
\(922\) | −7.00000 | + | 12.1244i | −0.230533 | + | 0.399294i | ||||
\(923\) | 18.0000 | 0.592477 | ||||||||
\(924\) | 0.500000 | − | 2.59808i | 0.0164488 | − | 0.0854704i | ||||
\(925\) | −30.0000 | −0.986394 | ||||||||
\(926\) | 10.0000 | − | 17.3205i | 0.328620 | − | 0.569187i | ||||
\(927\) | −5.50000 | − | 9.52628i | −0.180644 | − | 0.312884i | ||||
\(928\) | −4.50000 | − | 7.79423i | −0.147720 | − | 0.255858i | ||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.0000 | − | 25.9808i | 1.08153 | − | 0.851485i | ||||
\(932\) | 8.00000 | 0.262049 | ||||||||
\(933\) | 6.50000 | − | 11.2583i | 0.212800 | − | 0.368581i | ||||
\(934\) | −15.5000 | − | 26.8468i | −0.507175 | − | 0.878454i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.00000 | − | 5.19615i | 0.0980581 | − | 0.169842i | ||||
\(937\) | 34.0000 | 1.11073 | 0.555366 | − | 0.831606i | \(-0.312578\pi\) | ||||
0.555366 | + | 0.831606i | \(0.312578\pi\) | |||||||
\(938\) | 5.00000 | − | 25.9808i | 0.163256 | − | 0.848302i | ||||
\(939\) | −20.0000 | −0.652675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | + | 5.19615i | 0.0977972 | + | 0.169390i | 0.910773 | − | 0.412908i | \(-0.135487\pi\) |
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(942\) | −6.50000 | − | 11.2583i | −0.211781 | − | 0.366816i | ||||
\(943\) | 3.00000 | − | 5.19615i | 0.0976934 | − | 0.169210i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | 5.00000 | − | 8.66025i | 0.162478 | − | 0.281420i | −0.773279 | − | 0.634066i | \(-0.781385\pi\) |
0.935757 | + | 0.352646i | \(0.114718\pi\) | |||||||
\(948\) | −2.50000 | − | 4.33013i | −0.0811962 | − | 0.140636i | ||||
\(949\) | −15.0000 | − | 25.9808i | −0.486921 | − | 0.843371i | ||||
\(950\) | 15.0000 | − | 25.9808i | 0.486664 | − | 0.842927i | ||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | −12.5000 | + | 4.33013i | −0.405127 | + | 0.140340i | ||||
\(953\) | 1.00000 | 0.0323932 | 0.0161966 | − | 0.999869i | \(-0.494844\pi\) | ||||
0.0161966 | + | 0.999869i | \(0.494844\pi\) | |||||||
\(954\) | −7.00000 | + | 12.1244i | −0.226633 | + | 0.392541i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.50000 | − | 7.79423i | −0.145540 | − | 0.252083i | ||||
\(957\) | −4.50000 | + | 7.79423i | −0.145464 | + | 0.251952i | ||||
\(958\) | 30.0000 | 0.969256 | ||||||||
\(959\) | −7.50000 | + | 2.59808i | −0.242188 | + | 0.0838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 18.0000 | + | 31.1769i | 0.580343 | + | 1.00518i | ||||
\(963\) | 2.00000 | + | 3.46410i | 0.0644491 | + | 0.111629i | ||||
\(964\) | 7.00000 | − | 12.1244i | 0.225455 | − | 0.390499i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.00000 | + | 1.73205i | 0.0643489 | + | 0.0557278i | ||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | 5.00000 | − | 8.66025i | 0.160706 | − | 0.278351i | ||||
\(969\) | −15.0000 | − | 25.9808i | −0.481869 | − | 0.834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | − | 12.9904i | 0.240686 | − | 0.416881i | −0.720224 | − | 0.693742i | \(-0.755961\pi\) |
0.960910 | + | 0.276861i | \(0.0892941\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 7.50000 | − | 38.9711i | 0.240439 | − | 1.24936i | ||||
\(974\) | −14.0000 | −0.448589 | ||||||||
\(975\) | −15.0000 | + | 25.9808i | −0.480384 | + | 0.832050i | ||||
\(976\) | 1.00000 | + | 1.73205i | 0.0320092 | + | 0.0554416i | ||||
\(977\) | −17.0000 | − | 29.4449i | −0.543878 | − | 0.942025i | −0.998677 | − | 0.0514302i | \(-0.983622\pi\) |
0.454798 | − | 0.890594i | \(-0.349711\pi\) | |||||||
\(978\) | −9.50000 | + | 16.4545i | −0.303777 | + | 0.526156i | ||||
\(979\) | 10.0000 | 0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | −0.0957826 | ||||||||
\(982\) | 12.0000 | − | 20.7846i | 0.382935 | − | 0.663264i | ||||
\(983\) | −3.00000 | − | 5.19615i | −0.0956851 | − | 0.165732i | 0.814209 | − | 0.580572i | \(-0.197171\pi\) |
−0.909894 | + | 0.414840i | \(0.863838\pi\) | |||||||
\(984\) | 3.00000 | + | 5.19615i | 0.0956365 | + | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 45.0000 | 1.43309 | ||||||||
\(987\) | 5.50000 | − | 28.5788i | 0.175067 | − | 0.909674i | ||||
\(988\) | −36.0000 | −1.14531 | ||||||||
\(989\) | 3.00000 | − | 5.19615i | 0.0953945 | − | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0000 | − | 20.7846i | −0.381193 | − | 0.660245i | 0.610040 | − | 0.792370i | \(-0.291153\pi\) |
−0.991233 | + | 0.132125i | \(0.957820\pi\) | |||||||
\(992\) | 3.00000 | − | 5.19615i | 0.0952501 | − | 0.164978i | ||||
\(993\) | 32.0000 | 1.01549 | ||||||||
\(994\) | −6.00000 | − | 5.19615i | −0.190308 | − | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.00000 | − | 6.92820i | 0.126745 | − | 0.219529i | ||||
\(997\) | −16.0000 | − | 27.7128i | −0.506725 | − | 0.877674i | −0.999970 | − | 0.00778294i | \(-0.997523\pi\) |
0.493245 | − | 0.869891i | \(-0.335811\pi\) | |||||||
\(998\) | −3.50000 | − | 6.06218i | −0.110791 | − | 0.191895i | ||||
\(999\) | −3.00000 | + | 5.19615i | −0.0949158 | + | 0.164399i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 966.2.i.b.415.1 | yes | 2 | |
7.2 | even | 3 | 6762.2.a.bk.1.1 | 1 | |||
7.4 | even | 3 | inner | 966.2.i.b.277.1 | ✓ | 2 | |
7.5 | odd | 6 | 6762.2.a.ba.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.b.277.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
966.2.i.b.415.1 | yes | 2 | 1.1 | even | 1 | trivial | |
6762.2.a.ba.1.1 | 1 | 7.5 | odd | 6 | |||
6762.2.a.bk.1.1 | 1 | 7.2 | even | 3 |