Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.897122304.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 51x^{4} - 104x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(1.30421 - 0.752986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.433 |
Dual form | 648.4.i.v.217.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.26031 | + | 9.11112i | −0.470496 | + | 0.814923i | −0.999431 | − | 0.0337394i | \(-0.989258\pi\) |
0.528935 | + | 0.848663i | \(0.322592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.177444 | + | 0.307342i | 0.00958108 | + | 0.0165949i | 0.870776 | − | 0.491680i | \(-0.163617\pi\) |
−0.861195 | + | 0.508275i | \(0.830284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.30734 | + | 7.46054i | 0.118065 | + | 0.204494i | 0.919001 | − | 0.394256i | \(-0.128998\pi\) |
−0.800936 | + | 0.598750i | \(0.795664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.3942 | − | 30.1277i | 0.371099 | − | 0.642762i | −0.618636 | − | 0.785678i | \(-0.712314\pi\) |
0.989735 | + | 0.142916i | \(0.0456477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −72.5080 | −1.03446 | −0.517228 | − | 0.855847i | \(-0.673036\pi\) | ||||
−0.517228 | + | 0.855847i | \(0.673036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −78.3905 | −0.946527 | −0.473263 | − | 0.880921i | \(-0.656924\pi\) | ||||
−0.473263 | + | 0.880921i | \(0.656924\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.6122 | + | 42.6295i | −0.223130 | + | 0.386473i | −0.955757 | − | 0.294158i | \(-0.904961\pi\) |
0.732627 | + | 0.680631i | \(0.238294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.15835 | + | 12.3986i | 0.0572668 | + | 0.0991890i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 69.4036 | + | 120.211i | 0.444411 | + | 0.769743i | 0.998011 | − | 0.0630400i | \(-0.0200796\pi\) |
−0.553600 | + | 0.832783i | \(0.686746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.2143 | − | 54.0648i | 0.180847 | − | 0.313236i | −0.761322 | − | 0.648374i | \(-0.775449\pi\) |
0.942169 | + | 0.335137i | \(0.108783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.73364 | −0.0180314 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.0226 | 0.160056 | 0.0800281 | − | 0.996793i | \(-0.474499\pi\) | ||||
0.0800281 | + | 0.996793i | \(0.474499\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 95.4936 | − | 165.400i | 0.363746 | − | 0.630027i | −0.624828 | − | 0.780763i | \(-0.714831\pi\) |
0.988574 | + | 0.150736i | \(0.0481642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −266.190 | − | 461.054i | −0.944035 | − | 1.63512i | −0.757671 | − | 0.652636i | \(-0.773663\pi\) |
−0.186364 | − | 0.982481i | \(-0.559670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −35.3418 | − | 61.2138i | −0.109684 | − | 0.189978i | 0.805958 | − | 0.591972i | \(-0.201650\pi\) |
−0.915642 | + | 0.401994i | \(0.868317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 171.437 | − | 296.938i | 0.499816 | − | 0.865707i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −245.898 | −0.637296 | −0.318648 | − | 0.947873i | \(-0.603229\pi\) | ||||
−0.318648 | + | 0.947873i | \(0.603229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −90.6318 | −0.222196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 417.859 | − | 723.752i | 0.922043 | − | 1.59703i | 0.125794 | − | 0.992056i | \(-0.459852\pi\) |
0.796249 | − | 0.604969i | \(-0.206815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −240.379 | − | 416.348i | −0.504547 | − | 0.873900i | −0.999986 | − | 0.00525798i | \(-0.998326\pi\) |
0.495440 | − | 0.868642i | \(-0.335007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 182.998 | + | 316.961i | 0.349201 | + | 0.604834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −55.2706 | + | 95.7315i | −0.100782 | + | 0.174559i | −0.912007 | − | 0.410175i | \(-0.865468\pi\) |
0.811225 | + | 0.584734i | \(0.198801\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58.4968 | 0.0977787 | 0.0488894 | − | 0.998804i | \(-0.484432\pi\) | ||||
0.0488894 | + | 0.998804i | \(0.484432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −313.784 | −0.503090 | −0.251545 | − | 0.967846i | \(-0.580939\pi\) | ||||
−0.251545 | + | 0.967846i | \(0.580939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.52863 | + | 2.64766i | −0.00226238 | + | 0.00391855i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −497.611 | − | 861.887i | −0.708679 | − | 1.22747i | −0.965347 | − | 0.260968i | \(-0.915958\pi\) |
0.256669 | − | 0.966499i | \(-0.417375\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 366.646 | + | 635.049i | 0.484875 | + | 0.839828i | 0.999849 | − | 0.0173777i | \(-0.00553178\pi\) |
−0.514974 | + | 0.857206i | \(0.672198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 381.414 | − | 660.629i | 0.486708 | − | 0.843003i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −994.244 | −1.18415 | −0.592077 | − | 0.805881i | \(-0.701692\pi\) | ||||
−0.592077 | + | 0.805881i | \(0.701692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.3460 | 0.0142221 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 412.358 | − | 714.225i | 0.445337 | − | 0.771347i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −529.088 | − | 916.408i | −0.553823 | − | 0.959249i | −0.997994 | − | 0.0633070i | \(-0.979835\pi\) |
0.444172 | − | 0.895942i | \(-0.353498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 304.465 | + | 527.349i | 0.299955 | + | 0.519537i | 0.976125 | − | 0.217208i | \(-0.0696951\pi\) |
−0.676171 | + | 0.736745i | \(0.736362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 906.306 | − | 1569.77i | 0.867000 | − | 1.50169i | 0.00195270 | − | 0.999998i | \(-0.499378\pi\) |
0.865047 | − | 0.501690i | \(-0.167288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −707.990 | −0.639664 | −0.319832 | − | 0.947474i | \(-0.603626\pi\) | ||||
−0.319832 | + | 0.947474i | \(0.603626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2101.35 | −1.84654 | −0.923270 | − | 0.384153i | \(-0.874494\pi\) | ||||
−0.923270 | + | 0.384153i | \(0.874494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −682.328 | + | 1181.83i | −0.568035 | + | 0.983866i | 0.428725 | + | 0.903435i | \(0.358963\pi\) |
−0.996760 | + | 0.0804308i | \(0.974370\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −258.935 | − | 448.489i | −0.209964 | − | 0.363668i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.8661 | − | 22.2848i | −0.00991122 | − | 0.0171667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 628.394 | − | 1088.41i | 0.472121 | − | 0.817738i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1465.70 | −1.04877 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1473.64 | 1.02964 | 0.514819 | − | 0.857299i | \(-0.327859\pi\) | ||||
0.514819 | + | 0.857299i | \(0.327859\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 861.853 | − | 1492.77i | 0.574813 | − | 0.995605i | −0.421249 | − | 0.906945i | \(-0.638408\pi\) |
0.996062 | − | 0.0886598i | \(-0.0282584\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.9099 | − | 24.0927i | −0.00906875 | − | 0.0157075i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 666.021 | + | 1153.58i | 0.415343 | + | 0.719395i | 0.995464 | − | 0.0951350i | \(-0.0303283\pi\) |
−0.580122 | + | 0.814530i | \(0.696995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1046.34 | + | 1812.32i | −0.638488 | + | 1.10589i | 0.347277 | + | 0.937763i | \(0.387106\pi\) |
−0.985765 | + | 0.168131i | \(0.946227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 299.691 | 0.175255 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1460.34 | −0.836375 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −708.617 | + | 1227.36i | −0.389612 | + | 0.674828i | −0.992397 | − | 0.123076i | \(-0.960724\pi\) |
0.602785 | + | 0.797903i | \(0.294058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1265.42 | − | 2191.77i | −0.681976 | − | 1.18122i | −0.974377 | − | 0.224921i | \(-0.927788\pi\) |
0.292401 | − | 0.956296i | \(-0.405546\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 328.394 | + | 568.795i | 0.170176 | + | 0.294753i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 804.996 | − | 1394.29i | 0.409208 | − | 0.708769i | −0.585593 | − | 0.810605i | \(-0.699138\pi\) |
0.994801 | + | 0.101836i | \(0.0324717\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.4691 | −0.00855131 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −162.622 | −0.0781445 | −0.0390722 | − | 0.999236i | \(-0.512440\pi\) | ||||
−0.0390722 | + | 0.999236i | \(0.512440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1879.83 | − | 3255.97i | 0.871053 | − | 1.50871i | 0.0101438 | − | 0.999949i | \(-0.496771\pi\) |
0.860909 | − | 0.508759i | \(-0.169896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 493.383 | + | 854.564i | 0.224571 | + | 0.388969i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −119.704 | − | 207.334i | −0.0526067 | − | 0.0911174i | 0.838523 | − | 0.544866i | \(-0.183420\pi\) |
−0.891130 | + | 0.453749i | \(0.850086\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.54041 | + | 4.40012i | −0.00109736 | + | 0.00190068i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2212.57 | 0.923885 | 0.461943 | − | 0.886910i | \(-0.347153\pi\) | ||||
0.461943 | + | 0.886910i | \(0.347153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1754.76 | 0.720608 | 0.360304 | − | 0.932835i | \(-0.382673\pi\) | ||||
0.360304 | + | 0.932835i | \(0.382673\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −189.490 | + | 328.206i | −0.0753058 | + | 0.130433i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −312.317 | − | 540.948i | −0.122133 | − | 0.211540i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2000.98 | − | 3465.80i | −0.758040 | − | 1.31296i | −0.943849 | − | 0.330378i | \(-0.892824\pi\) |
0.185808 | − | 0.982586i | \(-0.440510\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −317.205 | + | 549.415i | −0.118305 | + | 0.204911i | −0.919096 | − | 0.394033i | \(-0.871079\pi\) |
0.800791 | + | 0.598944i | \(0.204413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −889.895 | −0.321839 | −0.160920 | − | 0.986967i | \(-0.551446\pi\) | ||||
−0.160920 | + | 0.986967i | \(0.551446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1653.18 | 0.588900 | 0.294450 | − | 0.955667i | \(-0.404864\pi\) | ||||
0.294450 | + | 0.955667i | \(0.404864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.6305 | + | 42.6613i | −0.00851588 | + | 0.0147499i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1004.65 | + | 1740.11i | 0.342282 | + | 0.592851i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −337.655 | − | 584.835i | −0.111751 | − | 0.193559i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1685.31 | + | 2919.05i | −0.549866 | + | 0.952396i | 0.448417 | + | 0.893824i | \(0.351988\pi\) |
−0.998283 | + | 0.0585714i | \(0.981345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5600.95 | 1.77666 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.1552 | 0.00693084 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1261.22 | + | 2184.50i | −0.383886 | + | 0.664910i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 655.080 | + | 1134.63i | 0.196715 | + | 0.340720i | 0.947461 | − | 0.319870i | \(-0.103639\pi\) |
−0.750747 | + | 0.660590i | \(0.770306\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 356.934 | + | 618.228i | 0.104364 | + | 0.180763i | 0.913478 | − | 0.406888i | \(-0.133386\pi\) |
−0.809114 | + | 0.587651i | \(0.800053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −671.809 | + | 1163.61i | −0.193862 | + | 0.335779i | −0.946527 | − | 0.322625i | \(-0.895435\pi\) |
0.752665 | + | 0.658404i | \(0.228768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3886.80 | −1.09284 | −0.546422 | − | 0.837510i | \(-0.684011\pi\) | ||||
−0.546422 | + | 0.837510i | \(0.684011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 743.635 | 0.206423 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −484.583 | + | 839.323i | −0.131151 | + | 0.227160i | −0.924121 | − | 0.382101i | \(-0.875201\pi\) |
0.792970 | + | 0.609261i | \(0.208534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2985.89 | + | 5171.72i | 0.798084 | + | 1.38232i | 0.920862 | + | 0.389888i | \(0.127486\pi\) |
−0.122779 | + | 0.992434i | \(0.539181\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1803.62 | + | 3123.97i | 0.470323 | + | 0.814624i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1363.54 | + | 2361.72i | −0.351255 | + | 0.608392i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 605.752 | 0.152330 | 0.0761648 | − | 0.997095i | \(-0.475732\pi\) | ||||
0.0761648 | + | 0.997095i | \(0.475732\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −424.052 | −0.105375 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2988.71 | + | 5176.60i | −0.725411 | + | 1.25645i | 0.233393 | + | 0.972382i | \(0.425017\pi\) |
−0.958805 | + | 0.284067i | \(0.908316\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.39200 | + | 11.0713i | 0.00153351 | + | 0.00265612i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3429.70 | − | 5940.42i | −0.804124 | − | 1.39278i | −0.916881 | − | 0.399160i | \(-0.869302\pi\) |
0.112758 | − | 0.993623i | \(-0.464032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1293.50 | − | 2240.41i | 0.299845 | − | 0.519347i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1166.26 | 0.264342 | 0.132171 | − | 0.991227i | \(-0.457805\pi\) | ||||
0.132171 | + | 0.991227i | \(0.457805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1286.99 | −0.288483 | −0.144241 | − | 0.989543i | \(-0.546074\pi\) | ||||
−0.144241 | + | 0.989543i | \(0.546074\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −61.6669 | + | 106.810i | −0.0135224 | + | 0.0234214i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3816.32 | + | 6610.06i | 0.827800 | + | 1.43379i | 0.899761 | + | 0.436384i | \(0.143741\pi\) |
−0.0719611 | + | 0.997407i | \(0.522926\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1532.19 | − | 2653.83i | −0.325277 | − | 0.563397i | 0.656291 | − | 0.754508i | \(-0.272124\pi\) |
−0.981568 | + | 0.191111i | \(0.938791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2119.31 | + | 3670.76i | −0.445159 | + | 0.771039i | −0.998063 | − | 0.0622063i | \(-0.980186\pi\) |
0.552904 | + | 0.833245i | \(0.313520\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 67.7791 | 0.0139403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 344.406 | 0.0701011 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2780.18 | + | 4815.41i | −0.554333 | + | 0.960133i | 0.443622 | + | 0.896214i | \(0.353693\pi\) |
−0.997955 | + | 0.0639191i | \(0.979640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4396.13 | + | 7614.32i | 0.867635 | + | 1.50279i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 856.219 | + | 1483.01i | 0.165607 | + | 0.286839i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 94.4675 | − | 163.623i | 0.0180898 | − | 0.0313324i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5057.86 | 0.949549 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6287.70 | 1.16892 | 0.584459 | − | 0.811423i | \(-0.301307\pi\) | ||||
0.584459 | + | 0.811423i | \(0.301307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1228.74 | + | 2128.25i | −0.224038 | + | 0.388045i | −0.956030 | − | 0.293268i | \(-0.905257\pi\) |
0.731993 | + | 0.681313i | \(0.238591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 803.340 | + | 1391.42i | 0.145072 | + | 0.251272i | 0.929400 | − | 0.369075i | \(-0.120325\pi\) |
−0.784328 | + | 0.620346i | \(0.786992\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2298.89 | − | 3981.80i | −0.407314 | − | 0.705489i | 0.587274 | − | 0.809389i | \(-0.300201\pi\) |
−0.994588 | + | 0.103900i | \(0.966868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −597.890 | + | 1035.58i | −0.104939 | + | 0.181759i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5683.93 | 0.979141 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 498.055 | 0.0850065 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.5424 | − | 21.7241i | 0.00210178 | − | 0.00364039i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −474.670 | − | 822.152i | −0.0788224 | − | 0.136524i | 0.823920 | − | 0.566707i | \(-0.191783\pi\) |
−0.902742 | + | 0.430182i | \(0.858449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −581.481 | − | 1007.15i | −0.0948349 | − | 0.164259i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3750.27 | + | 6495.65i | −0.606202 | + | 1.04997i | 0.385658 | + | 0.922642i | \(0.373974\pi\) |
−0.991860 | + | 0.127331i | \(0.959359\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 537.803 | 0.0854067 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 243.409 | 0.0383173 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1134.36 | + | 1964.78i | −0.175493 | + | 0.303962i | −0.940332 | − | 0.340259i | \(-0.889485\pi\) |
0.764839 | + | 0.644221i | \(0.222818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1871.54 | − | 3241.60i | −0.287052 | − | 0.497189i | 0.686053 | − | 0.727552i | \(-0.259342\pi\) |
−0.973105 | + | 0.230363i | \(0.926009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1165.52 | + | 2018.74i | 0.175735 | + | 0.304381i | 0.940415 | − | 0.340028i | \(-0.110437\pi\) |
−0.764681 | + | 0.644409i | \(0.777103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −307.711 | + | 532.971i | −0.0460045 | + | 0.0796821i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7364.86 | −1.08274 | −0.541368 | − | 0.840785i | \(-0.682094\pi\) | ||||
−0.541368 | + | 0.840785i | \(0.682094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −713.935 | −0.104087 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1650.60 | − | 2858.92i | 0.236702 | − | 0.409980i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3191.08 | + | 5527.11i | 0.453877 | + | 0.786138i | 0.998623 | − | 0.0524634i | \(-0.0167073\pi\) |
−0.544746 | + | 0.838601i | \(0.683374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −43.6331 | − | 75.5748i | −0.00610598 | − | 0.0105759i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4399.77 | + | 7620.62i | −0.610754 | + | 1.05786i | 0.380359 | + | 0.924839i | \(0.375800\pi\) |
−0.991114 | + | 0.133019i | \(0.957533\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4828.88 | 0.659682 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8742.11 | 1.18483 | 0.592417 | − | 0.805631i | \(-0.298174\pi\) | ||||
0.592417 | + | 0.805631i | \(0.298174\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7199.35 | − | 12469.6i | 0.960495 | − | 1.66363i | 0.239234 | − | 0.970962i | \(-0.423104\pi\) |
0.721261 | − | 0.692664i | \(-0.243563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0821 | − | 27.8550i | −0.00212888 | − | 0.00368733i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5122.02 | − | 8871.59i | −0.667600 | − | 1.15632i | −0.978573 | − | 0.205899i | \(-0.933988\pi\) |
0.310973 | − | 0.950419i | \(-0.399345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1784.58 | − | 3090.98i | 0.230819 | − | 0.399789i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10470.3 | 1.33372 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3791.18 | −0.479279 | −0.239639 | − | 0.970862i | \(-0.577029\pi\) | ||||
−0.239639 | + | 0.970862i | \(0.577029\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 684.394 | − | 1185.41i | 0.0852295 | − | 0.147622i | −0.820260 | − | 0.571992i | \(-0.806171\pi\) |
0.905489 | + | 0.424370i | \(0.139504\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1085.90 | − | 1880.83i | −0.134224 | − | 0.232483i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 155.162 | + | 268.748i | 0.0188970 | + | 0.0327306i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 677.589 | − | 1173.62i | 0.0819184 | − | 0.141887i | −0.822156 | − | 0.569263i | \(-0.807229\pi\) |
0.904074 | + | 0.427376i | \(0.140562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 296.586 | 0.0353367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7714.68 | −0.912527 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7056.01 | + | 12221.4i | −0.822694 | + | 1.42495i | 0.0809752 | + | 0.996716i | \(0.474197\pi\) |
−0.903669 | + | 0.428231i | \(0.859137\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 121.566 | + | 210.559i | 0.0140731 | + | 0.0243753i | 0.872976 | − | 0.487763i | \(-0.162187\pi\) |
−0.858903 | + | 0.512138i | \(0.828854\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −519.037 | − | 898.999i | −0.0592400 | − | 0.102607i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 85.3076 | − | 147.757i | 0.00966821 | − | 0.0167458i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6214.92 | −0.694575 | −0.347288 | − | 0.937759i | \(-0.612897\pi\) | ||||
−0.347288 | + | 0.937759i | \(0.612897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7922.06 | 0.879238 | 0.439619 | − | 0.898184i | \(-0.355114\pi\) | ||||
0.439619 | + | 0.898184i | \(0.355114\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1929.36 | − | 3341.75i | 0.211199 | − | 0.365807i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.05559 | − | 8.75654i | −0.000549636 | − | 0.000951997i | 0.865750 | − | 0.500476i | \(-0.166842\pi\) |
−0.866300 | + | 0.499524i | \(0.833508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4314.13 | + | 7472.29i | 0.462687 | + | 0.801398i | 0.999094 | − | 0.0425616i | \(-0.0135519\pi\) |
−0.536406 | + | 0.843960i | \(0.680219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5230.03 | − | 9058.68i | 0.557140 | − | 0.964995i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3543.11 | −0.372405 | −0.186202 | − | 0.982511i | \(-0.559618\pi\) | ||||
−0.186202 | + | 0.982511i | \(0.559618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1645.29 | 0.171782 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −64.9438 | + | 112.486i | −0.00669145 | + | 0.0115899i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7333.85 | − | 12702.6i | −0.750685 | − | 1.30022i | −0.947491 | − | 0.319782i | \(-0.896390\pi\) |
0.196806 | − | 0.980442i | \(-0.436943\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7288.07 | + | 12623.3i | 0.736311 | + | 1.27533i | 0.954146 | + | 0.299342i | \(0.0967672\pi\) |
−0.217835 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2538.59 | − | 4396.97i | 0.254813 | − | 0.441349i | −0.710032 | − | 0.704170i | \(-0.751319\pi\) |
0.964845 | + | 0.262821i | \(0.0846527\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12469.1 | −1.23555 | −0.617774 | − | 0.786356i | \(-0.711965\pi\) | ||||
−0.617774 | + | 0.786356i | \(0.711965\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.2298 | −0.00386240 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2293.14 | − | 3971.83i | 0.222915 | − | 0.386099i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −561.146 | − | 971.934i | −0.0542045 | − | 0.0938850i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1965.53 | − | 3404.39i | −0.187489 | − | 0.324740i | 0.756923 | − | 0.653504i | \(-0.226702\pi\) |
−0.944412 | + | 0.328763i | \(0.893368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 626.584 | − | 1085.28i | 0.0593967 | − | 0.102878i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11132.7 | 1.04229 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20710.1 | −1.92703 | −0.963516 | − | 0.267652i | \(-0.913752\pi\) | ||||
−0.963516 | + | 0.267652i | \(0.913752\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6248.38 | + | 10822.5i | −0.574308 | + | 0.994731i | 0.421808 | + | 0.906685i | \(0.361396\pi\) |
−0.996116 | + | 0.0880459i | \(0.971938\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5032.32 | − | 8716.23i | −0.459724 | − | 0.796266i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3799 | + | 17.9785i | 0.000936826 | + | 0.00162263i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5077.47 | − | 8794.44i | 0.455509 | − | 0.788965i | −0.543208 | − | 0.839598i | \(-0.682791\pi\) |
0.998717 | + | 0.0506334i | \(0.0161240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20309.2 | −1.80029 | −0.900143 | − | 0.435594i | \(-0.856538\pi\) | ||||
−0.900143 | + | 0.435594i | \(0.856538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6406.32 | −0.564510 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7097.29 | − | 12292.9i | 0.618039 | − | 1.07047i | −0.371805 | − | 0.928311i | \(-0.621261\pi\) |
0.989843 | − | 0.142163i | \(-0.0454058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −55.6790 | − | 96.4389i | −0.00482015 | − | 0.00834874i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9534.90 | + | 16514.9i | 0.815840 | + | 1.41308i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 304.459 | − | 527.338i | 0.0258996 | − | 0.0448594i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10644.1 | −0.895057 | −0.447528 | − | 0.894270i | \(-0.647696\pi\) | ||||
−0.447528 | + | 0.894270i | \(0.647696\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2761.82 | −0.230910 | −0.115455 | − | 0.993313i | \(-0.536833\pi\) | ||||
−0.115455 | + | 0.993313i | \(0.536833\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2263.29 | + | 3920.13i | −0.187079 | + | 0.324029i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4871.98 | + | 8438.52i | 0.400426 | + | 0.693558i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3322.07 | − | 5754.00i | −0.269972 | − | 0.467605i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3724.25 | − | 6450.58i | 0.300959 | − | 0.521277i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2953.75 | 0.236043 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13261.6 | 1.05390 | 0.526952 | − | 0.849895i | \(-0.323335\pi\) | ||||
0.526952 | + | 0.849895i | \(0.323335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11053.7 | − | 19145.6i | 0.868790 | − | 1.50479i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10223.8 | − | 17708.1i | −0.799155 | − | 1.38418i | −0.920167 | − | 0.391526i | \(-0.871947\pi\) |
0.121012 | − | 0.992651i | \(-0.461386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5440.58 | − | 9423.36i | −0.420647 | − | 0.728582i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 176.596 | − | 305.874i | 0.0135798 | − | 0.0235209i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13888.2 | −1.05649 | −0.528243 | − | 0.849093i | \(-0.677149\pi\) | ||||
−0.528243 | + | 0.849093i | \(0.677149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18520.6 | −1.40132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8439.11 | + | 14617.0i | −0.631734 | + | 1.09419i | 0.355464 | + | 0.934690i | \(0.384323\pi\) |
−0.987197 | + | 0.159505i | \(0.949010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7178.51 | − | 12433.5i | −0.534517 | − | 0.925810i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5926.87 | + | 10265.6i | 0.436674 | + | 0.756341i | 0.997431 | − | 0.0716394i | \(-0.0228231\pi\) |
−0.560757 | + | 0.827981i | \(0.689490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7006.38 | − | 12135.4i | 0.513499 | − | 0.889406i | −0.486378 | − | 0.873748i | \(-0.661682\pi\) |
0.999877 | − | 0.0156581i | \(-0.00498433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −704.730 | −0.0511118 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2886.05 | 0.208228 | 0.104114 | − | 0.994565i | \(-0.466799\pi\) | ||||
0.104114 | + | 0.994565i | \(0.466799\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −130.118 | + | 225.372i | −0.00929125 | + | 0.0160929i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1059.17 | − | 1834.53i | −0.0752422 | − | 0.130323i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7020.02 | + | 12159.0i | 0.493607 | + | 0.854952i | 0.999973 | − | 0.00736684i | \(-0.00234496\pi\) |
−0.506366 | + | 0.862318i | \(0.669012\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2446.91 | + | 4238.17i | −0.171177 | + | 0.296487i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18394.8 | 1.27383 | 0.636917 | − | 0.770932i | \(-0.280209\pi\) | ||||
0.636917 | + | 0.770932i | \(0.280209\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 270.719 | 0.0186528 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14098.8 | − | 24419.8i | 0.961704 | − | 1.66572i | 0.243485 | − | 0.969905i | \(-0.421709\pi\) |
0.718220 | − | 0.695816i | \(-0.244957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13271.1 | − | 22986.2i | −0.900731 | − | 1.56011i | −0.826547 | − | 0.562868i | \(-0.809698\pi\) |
−0.0741848 | − | 0.997245i | \(-0.523635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6611.09 | + | 11450.7i | 0.444263 | + | 0.769485i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5446.04 | − | 9432.82i | 0.364165 | − | 0.630752i | −0.624477 | − | 0.781043i | \(-0.714688\pi\) |
0.988642 | + | 0.150291i | \(0.0480212\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2458.97 | −0.162814 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6843.92 | 0.450935 | 0.225467 | − | 0.974251i | \(-0.427609\pi\) | ||||
0.225467 | + | 0.974251i | \(0.427609\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8209.71 | − | 14219.6i | 0.535673 | − | 0.927813i | −0.463457 | − | 0.886119i | \(-0.653391\pi\) |
0.999130 | − | 0.0416941i | \(-0.0132755\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7033.72 | − | 12182.8i | −0.456719 | − | 0.791061i | 0.542066 | − | 0.840336i | \(-0.317642\pi\) |
−0.998785 | + | 0.0492751i | \(0.984309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −176.423 | − | 305.573i | −0.0113455 | − | 0.0196509i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6815.22 | − | 11804.3i | 0.436174 | − | 0.755476i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2611.92 | −0.165571 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 91.1166 | 0.00574848 | 0.00287424 | − | 0.999996i | \(-0.499085\pi\) | ||||
0.00287424 | + | 0.999996i | \(0.499085\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7751.78 | + | 13426.5i | −0.484441 | + | 0.839077i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5964.02 | − | 10330.0i | −0.370963 | − | 0.642526i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12314.9 | − | 21330.1i | −0.758831 | − | 1.31433i | −0.943447 | − | 0.331524i | \(-0.892437\pi\) |
0.184616 | − | 0.982811i | \(-0.440896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3033.79 | + | 5254.67i | −0.186067 | + | 0.322277i | −0.943935 | − | 0.330130i | \(-0.892907\pi\) |
0.757869 | + | 0.652407i | \(0.226241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 890.884 | 0.0541334 | 0.0270667 | − | 0.999634i | \(-0.491383\pi\) | ||||
0.0270667 | + | 0.999634i | \(0.491383\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7199.44 | 0.435443 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13850.5 | − | 23989.9i | 0.830036 | − | 1.43767i | −0.0679720 | − | 0.997687i | \(-0.521653\pi\) |
0.898008 | − | 0.439978i | \(-0.145014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9067.22 | + | 15704.9i | 0.540894 | + | 0.936856i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9789.10 | + | 16955.2i | 0.578648 | + | 1.00225i | 0.995635 | + | 0.0933353i | \(0.0297529\pi\) |
−0.416987 | + | 0.908913i | \(0.636914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5504.14 | + | 9533.45i | −0.323882 | + | 0.560981i | −0.981286 | − | 0.192558i | \(-0.938321\pi\) |
0.657403 | + | 0.753539i | \(0.271655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 292.682 | 0.0170672 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6832.70 | −0.396646 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2070.79 | − | 3586.71i | 0.119138 | − | 0.206354i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2246.03 | − | 3890.24i | −0.128645 | − | 0.222820i | 0.794507 | − | 0.607255i | \(-0.207729\pi\) |
−0.923152 | + | 0.384435i | \(0.874396\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3036.02 | − | 5258.54i | −0.172354 | − | 0.298526i | 0.766888 | − | 0.641781i | \(-0.221804\pi\) |
−0.939242 | + | 0.343254i | \(0.888471\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 187.767 | − | 325.222i | 0.0106124 | − | 0.0183813i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20709.0 | −1.16018 | −0.580092 | − | 0.814551i | \(-0.696984\pi\) | ||||
−0.580092 | + | 0.814551i | \(0.696984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14013.9 | −0.781669 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4277.20 | + | 7408.33i | −0.236500 | + | 0.409630i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3558.80 | − | 6164.03i | −0.195924 | − | 0.339350i | 0.751279 | − | 0.659984i | \(-0.229437\pi\) |
−0.947203 | + | 0.320635i | \(0.896104\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11008.2 | − | 19066.7i | −0.600812 | − | 1.04064i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6924.05 | + | 11992.8i | −0.376280 | + | 0.651736i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26295.0 | 1.41676 | 0.708379 | − | 0.705833i | \(-0.249427\pi\) | ||||
0.708379 | + | 0.705833i | \(0.249427\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2823.83 | −0.151497 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −108.051 | + | 187.150i | −0.00574778 | + | 0.00995545i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4364.83 | + | 7560.11i | 0.231206 | + | 0.400460i | 0.958163 | − | 0.286223i | \(-0.0923997\pi\) |
−0.726958 | + | 0.686682i | \(0.759066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1536.51 | + | 2661.31i | 0.0807049 | + | 0.139785i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1576.47 | + | 2730.52i | −0.0824567 | + | 0.142819i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32340.7 | −1.67747 | −0.838736 | − | 0.544538i | \(-0.816705\pi\) | ||||
−0.838736 | + | 0.544538i | \(0.816705\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 643.275 | 0.0332272 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −993.630 | + | 1721.02i | −0.0509000 | + | 0.0881614i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13152.9 | + | 22781.5i | 0.670997 | + | 1.16220i | 0.977622 | + | 0.210371i | \(0.0674671\pi\) |
−0.306624 | + | 0.951831i | \(0.599200\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19300.9 | + | 33430.1i | 0.976564 | + | 1.69146i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8186.73 | − | 14179.8i | 0.412529 | − | 0.714521i | −0.582636 | − | 0.812733i | \(-0.697979\pi\) |
0.995166 | + | 0.0982115i | \(0.0313122\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −952.278 | −0.0475951 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17567.9 | 0.874486 | 0.437243 | − | 0.899343i | \(-0.355955\pi\) | ||||
0.437243 | + | 0.899343i | \(0.355955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11410.7 | + | 19763.9i | −0.563416 | + | 0.975865i | 0.433779 | + | 0.901019i | \(0.357180\pi\) |
−0.997195 | + | 0.0748455i | \(0.976154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7455.09 | − | 12912.6i | −0.366622 | − | 0.635008i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −125.629 | − | 217.595i | −0.00612867 | − | 0.0106152i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17748.5 | − | 30741.4i | 0.862388 | − | 1.49370i | −0.00722941 | − | 0.999974i | \(-0.502301\pi\) |
0.869617 | − | 0.493726i | \(-0.164365\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26626.0 | 1.28347 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2676.83 | −0.128522 | −0.0642609 | − | 0.997933i | \(-0.520469\pi\) | ||||
−0.0642609 | + | 0.997933i | \(0.520469\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1523.77 | + | 2639.24i | −0.0725841 | + | 0.125719i | −0.900033 | − | 0.435821i | \(-0.856458\pi\) |
0.827449 | + | 0.561541i | \(0.189791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −372.872 | − | 645.833i | −0.0176918 | − | 0.0306432i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14536.6 | − | 25178.2i | −0.684338 | − | 1.18531i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10296.2 | + | 17833.5i | −0.482823 | + | 0.836273i | −0.999805 | − | 0.0197225i | \(-0.993722\pi\) |
0.516983 | + | 0.855996i | \(0.327055\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3252.88 | −0.151356 | −0.0756779 | − | 0.997132i | \(-0.524112\pi\) | ||||
−0.0756779 | + | 0.997132i | \(0.524112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 893.772 | 0.0414261 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7485.79 | + | 12965.8i | −0.344296 | + | 0.596337i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 251.966 | + | 436.417i | 0.0115442 | + | 0.0199952i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8469.05 | + | 14668.8i | 0.385062 | + | 0.666946i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19168.1 | + | 33200.2i | −0.868196 | + | 1.50376i | −0.00435673 | + | 0.999991i | \(0.501387\pi\) |
−0.863839 | + | 0.503768i | \(0.831947\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −484.300 | −0.0217696 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16724.8 | −0.748947 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12578.9 | + | 21787.3i | −0.559056 | + | 0.968313i | 0.438520 | + | 0.898721i | \(0.355503\pi\) |
−0.997576 | + | 0.0695913i | \(0.977830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2562.56 | + | 4438.49i | 0.113463 | + | 0.196524i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1351.57 | − | 2340.99i | −0.0593972 | − | 0.102879i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 91.8931 | − | 159.163i | 0.00402336 | − | 0.00696866i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 159.016 | 0.00691064 | 0.00345532 | − | 0.999994i | \(-0.498900\pi\) | ||||
0.00345532 | + | 0.999994i | \(0.498900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16146.0 | 0.699093 | 0.349547 | − | 0.936919i | \(-0.386336\pi\) | ||||
0.349547 | + | 0.936919i | \(0.386336\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 855.443 | − | 1481.67i | 0.0367667 | − | 0.0636818i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20866.7 | + | 36142.2i | 0.893555 | + | 1.54768i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16363.8 | − | 28343.0i | −0.695616 | − | 1.20484i | −0.969972 | − | 0.243215i | \(-0.921798\pi\) |
0.274356 | − | 0.961628i | \(-0.411535\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16419.2 | − | 28438.9i | 0.695428 | − | 1.20452i | −0.274608 | − | 0.961556i | \(-0.588548\pi\) |
0.970036 | − | 0.242960i | \(-0.0781185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4725.60 | 0.198700 | 0.0993502 | − | 0.995053i | \(-0.468324\pi\) | ||||
0.0993502 | + | 0.995053i | \(0.468324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2080.19 | 0.0871510 | 0.0435755 | − | 0.999050i | \(-0.486125\pi\) | ||||
0.0435755 | + | 0.999050i | \(0.486125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12430.6 | + | 21530.3i | −0.517039 | + | 0.895537i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19777.0 | + | 34254.8i | 0.819654 | + | 1.41968i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 164.372 | + | 284.701i | 0.00676371 | + | 0.0117151i | 0.869387 | − | 0.494131i | \(-0.164514\pi\) |
−0.862624 | + | 0.505846i | \(0.831180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2560.78 | − | 4435.39i | 0.104997 | − | 0.181860i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10381.4 | −0.422640 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 446.019 | 0.0180937 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −886.594 | + | 1535.63i | −0.0357133 | + | 0.0618573i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15356.3 | + | 26597.9i | 0.616400 | + | 1.06764i | 0.990137 | + | 0.140101i | \(0.0447428\pi\) |
−0.373738 | + | 0.927535i | \(0.621924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5484.54 | − | 9499.51i | −0.218610 | − | 0.378643i | 0.735774 | − | 0.677228i | \(-0.236819\pi\) |
−0.954383 | + | 0.298585i | \(0.903485\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19632.9 | + | 34005.2i | −0.779821 | + | 1.35069i | 0.152224 | + | 0.988346i | \(0.451356\pi\) |
−0.932045 | + | 0.362343i | \(0.881977\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23715.3 | 0.935433 | 0.467716 | − | 0.883879i | \(-0.345077\pi\) | ||||
0.467716 | + | 0.883879i | \(0.345077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2518.73 | 0.0990050 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4286.76 | − | 7424.89i | 0.167340 | − | 0.289841i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1922.78 | + | 3330.35i | 0.0748000 | + | 0.129557i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −260.079 | − | 450.471i | −0.0100483 | − | 0.0174042i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14343.5 | + | 24843.6i | −0.552275 | + | 0.956568i | 0.445835 | + | 0.895115i | \(0.352907\pi\) |
−0.998110 | + | 0.0614526i | \(0.980427\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27975.8 | 1.06984 | 0.534920 | − | 0.844903i | \(-0.320342\pi\) | ||||
0.534920 | + | 0.844903i | \(0.320342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4610.87 | 0.175728 | 0.0878642 | − | 0.996132i | \(-0.471996\pi\) | ||||
0.0878642 | + | 0.996132i | \(0.471996\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12831.9 | − | 22225.5i | 0.485741 | − | 0.841329i | −0.514124 | − | 0.857716i | \(-0.671883\pi\) |
0.999866 | + | 0.0163868i | \(0.00521632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 261.488 | + | 452.911i | 0.00986506 | + | 0.0170868i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2770.46 | + | 4798.58i | 0.103819 | + | 0.179819i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11638.8 | + | 20159.0i | −0.434685 | + | 0.752896i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8665.55 | 0.321482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17829.6 | 0.659255 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9230.55 | + | 15987.8i | −0.339043 | + | 0.587240i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4666.86 | − | 8083.24i | −0.170850 | − | 0.295920i | 0.767868 | − | 0.640609i | \(-0.221318\pi\) |
−0.938717 | + | 0.344688i | \(0.887985\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24069.0 | − | 41688.8i | −0.875348 | − | 1.51615i | −0.856392 | − | 0.516327i | \(-0.827299\pi\) |
−0.0189566 | − | 0.999820i | \(-0.506034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3158.54 | + | 5470.75i | −0.114493 | + | 0.198308i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 611.723 | 0.0220293 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32300.1 | −1.15939 | −0.579696 | − | 0.814833i | \(-0.696829\pi\) | ||||
−0.579696 | + | 0.814833i | \(0.696829\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1017.51 | − | 1762.37i | 0.0362856 | − | 0.0628485i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 257.862 | + | 446.630i | 0.00916590 | + | 0.0158758i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4506.77 | − | 7805.96i | −0.159163 | − | 0.275678i | 0.775404 | − | 0.631465i | \(-0.217546\pi\) |
−0.934567 | + | 0.355787i | \(0.884213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13439.0 | + | 23277.1i | −0.473090 | + | 0.819415i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6571.53 | 0.229852 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47418.3 | 1.65324 | 0.826622 | − | 0.562758i | \(-0.190260\pi\) | ||||
0.826622 | + | 0.562758i | \(0.190260\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10946.8 | + | 18960.4i | −0.379229 | + | 0.656844i | −0.990950 | − | 0.134229i | \(-0.957144\pi\) |
0.611721 | + | 0.791073i | \(0.290477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4700.61 | + | 8141.70i | 0.162326 | + | 0.281156i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22034.7 | + | 38165.3i | 0.756107 | + | 1.30962i | 0.944822 | + | 0.327583i | \(0.106234\pi\) |
−0.188716 | + | 0.982032i | \(0.560432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5458.02 | + | 9453.56i | −0.186696 | + | 0.323367i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22429.1 | −0.762382 | −0.381191 | − | 0.924496i | \(-0.624486\pi\) | ||||
−0.381191 | + | 0.924496i | \(0.624486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42103.0 | 1.42662 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −236.363 | + | 409.393i | −0.00795887 | + | 0.0137852i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12946.8 | + | 22424.6i | 0.434589 | + | 0.752730i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3337.19 | − | 5780.18i | −0.111324 | − | 0.192819i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2638.70 | − | 4570.36i | 0.0877507 | − | 0.151989i | −0.818809 | − | 0.574066i | \(-0.805365\pi\) |
0.906560 | + | 0.422077i | \(0.138699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53211.8 | 1.75865 | 0.879325 | − | 0.476223i | \(-0.157995\pi\) | ||||
0.879325 | + | 0.476223i | \(0.157995\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −742.671 | −0.0244696 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20046.8 | − | 34722.1i | 0.656453 | − | 1.13701i | −0.325074 | − | 0.945689i | \(-0.605389\pi\) |
0.981527 | − | 0.191322i | \(-0.0612775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4282.55 | − | 7417.60i | −0.139807 | − | 0.242153i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25123.7 | − | 43515.6i | −0.815180 | − | 1.41193i | −0.909198 | − | 0.416363i | \(-0.863304\pi\) |
0.0940181 | − | 0.995570i | \(-0.470029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4681.12 | − | 8107.94i | 0.151424 | − | 0.262274i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26206.0 | 0.842571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32333.6 | 1.03644 | 0.518219 | − | 0.855248i | \(-0.326595\pi\) | ||||
0.518219 | + | 0.855248i | \(0.326595\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8696.26 | + | 15062.4i | −0.277075 | + | 0.479909i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10619.5 | + | 18393.6i | 0.337336 | + | 0.584283i | 0.983931 | − | 0.178551i | \(-0.0571408\pi\) |
−0.646595 | + | 0.762834i | \(0.723808\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 648.4.i.v.433.1 | 8 | ||
3.2 | odd | 2 | 648.4.i.u.433.4 | 8 | |||
9.2 | odd | 6 | 648.4.i.u.217.4 | 8 | |||
9.4 | even | 3 | 648.4.a.g.1.4 | ✓ | 4 | ||
9.5 | odd | 6 | 648.4.a.j.1.1 | yes | 4 | ||
9.7 | even | 3 | inner | 648.4.i.v.217.1 | 8 | ||
36.23 | even | 6 | 1296.4.a.bb.1.1 | 4 | |||
36.31 | odd | 6 | 1296.4.a.x.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.g.1.4 | ✓ | 4 | 9.4 | even | 3 | ||
648.4.a.j.1.1 | yes | 4 | 9.5 | odd | 6 | ||
648.4.i.u.217.4 | 8 | 9.2 | odd | 6 | |||
648.4.i.u.433.4 | 8 | 3.2 | odd | 2 | |||
648.4.i.v.217.1 | 8 | 9.7 | even | 3 | inner | ||
648.4.i.v.433.1 | 8 | 1.1 | even | 1 | trivial | ||
1296.4.a.x.1.4 | 4 | 36.31 | odd | 6 | |||
1296.4.a.bb.1.1 | 4 | 36.23 | even | 6 |