Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(521,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.521");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.t (of order \(6\), 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: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 42x^{12} + 1139x^{8} + 26250x^{4} + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{16} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.2 | ||
Root | \(1.75687 + 1.38326i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.521 |
Dual form | 1764.4.t.a.1097.2 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | −7.66648 | − | 13.2787i | −0.685711 | − | 1.18769i | −0.973213 | − | 0.229907i | \(-0.926158\pi\) |
0.287501 | − | 0.957780i | \(-0.407175\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.6210 | + | 10.1735i | 0.482994 | + | 0.278857i | 0.721663 | − | 0.692244i | \(-0.243378\pi\) |
−0.238669 | + | 0.971101i | \(0.576711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 30.5385i | − | 0.651528i | −0.945451 | − | 0.325764i | \(-0.894379\pi\) | ||
0.945451 | − | 0.325764i | \(-0.105621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.72504 | − | 2.98786i | 0.0246108 | − | 0.0426272i | −0.853458 | − | 0.521162i | \(-0.825499\pi\) |
0.878069 | + | 0.478535i | \(0.158832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 127.619 | − | 73.6807i | 1.54093 | − | 0.889659i | 0.542154 | − | 0.840279i | \(-0.317609\pi\) |
0.998780 | − | 0.0493798i | \(-0.0157245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −110.150 | + | 63.5954i | −0.998607 | + | 0.576546i | −0.907836 | − | 0.419326i | \(-0.862266\pi\) |
−0.0907711 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −55.0500 | + | 95.3494i | −0.440400 | + | 0.762795i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 216.198i | − | 1.38438i | −0.721717 | − | 0.692188i | \(-0.756647\pi\) | ||
0.721717 | − | 0.692188i | \(-0.243353\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −89.6694 | − | 51.7707i | −0.519519 | − | 0.299945i | 0.217219 | − | 0.976123i | \(-0.430302\pi\) |
−0.736738 | + | 0.676178i | \(0.763635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −118.325 | − | 204.945i | −0.525743 | − | 0.910614i | −0.999550 | − | 0.0299855i | \(-0.990454\pi\) |
0.473807 | − | 0.880629i | \(-0.342879\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 480.305 | 1.82954 | 0.914768 | − | 0.403979i | \(-0.132373\pi\) | ||||
0.914768 | + | 0.403979i | \(0.132373\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 147.875 | 0.524435 | 0.262218 | − | 0.965009i | \(-0.415546\pi\) | ||||
0.262218 | + | 0.965009i | \(0.415546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 227.503 | + | 394.047i | 0.706059 | + | 1.22293i | 0.966308 | + | 0.257388i | \(0.0828618\pi\) |
−0.260250 | + | 0.965541i | \(0.583805\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 173.883 | + | 100.391i | 0.450654 | + | 0.260185i | 0.708106 | − | 0.706106i | \(-0.249550\pi\) |
−0.257452 | + | 0.966291i | \(0.582883\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 311.980i | − | 0.764861i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −80.1149 | + | 138.763i | −0.176781 | + | 0.306194i | −0.940776 | − | 0.339028i | \(-0.889902\pi\) |
0.763995 | + | 0.645222i | \(0.223235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 712.818 | − | 411.546i | 1.49618 | − | 0.863820i | 0.496190 | − | 0.868214i | \(-0.334732\pi\) |
0.999990 | + | 0.00439331i | \(0.00139844\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −405.513 | + | 234.123i | −0.773811 | + | 0.446760i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 203.550 | − | 352.559i | 0.371158 | − | 0.642865i | −0.618586 | − | 0.785717i | \(-0.712294\pi\) |
0.989744 | + | 0.142853i | \(0.0456275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 513.872i | 0.858949i | 0.903079 | + | 0.429475i | \(0.141301\pi\) | ||||
−0.903079 | + | 0.429475i | \(0.858699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −410.478 | − | 236.989i | −0.658120 | − | 0.379966i | 0.133440 | − | 0.991057i | \(-0.457398\pi\) |
−0.791560 | + | 0.611091i | \(0.790731\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 60.6499 | + | 105.049i | 0.0863753 | + | 0.149606i | 0.905976 | − | 0.423328i | \(-0.139138\pi\) |
−0.819601 | + | 0.572935i | \(0.805805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −536.269 | −0.709195 | −0.354597 | − | 0.935019i | \(-0.615382\pi\) | ||||
−0.354597 | + | 0.935019i | \(0.615382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −52.9000 | −0.0675037 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −115.956 | − | 200.842i | −0.138105 | − | 0.239204i | 0.788675 | − | 0.614811i | \(-0.210768\pi\) |
−0.926779 | + | 0.375607i | \(0.877434\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1956.77 | − | 1129.74i | −2.11327 | − | 1.22010i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 734.188i | − | 0.768510i | −0.923227 | − | 0.384255i | \(-0.874458\pi\) | ||
0.923227 | − | 0.384255i | \(-0.125542\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 363.775 | − | 630.077i | 0.358386 | − | 0.620742i | −0.629306 | − | 0.777158i | \(-0.716661\pi\) |
0.987691 | + | 0.156416i | \(0.0499940\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −703.585 | + | 406.215i | −0.673070 | + | 0.388597i | −0.797239 | − | 0.603664i | \(-0.793707\pi\) |
0.124169 | + | 0.992261i | \(0.460374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 766.093 | − | 442.304i | 0.692159 | − | 0.399618i | −0.112262 | − | 0.993679i | \(-0.535809\pi\) |
0.804420 | + | 0.594061i | \(0.202476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 800.525 | − | 1386.55i | 0.703453 | − | 1.21842i | −0.263794 | − | 0.964579i | \(-0.584974\pi\) |
0.967247 | − | 0.253837i | \(-0.0816928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 740.553i | 0.616508i | 0.951304 | + | 0.308254i | \(0.0997446\pi\) | ||||
−0.951304 | + | 0.308254i | \(0.900255\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1688.93 | + | 975.106i | 1.36951 | + | 0.790688i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −458.500 | − | 794.145i | −0.344478 | − | 0.596653i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −228.462 | −0.163474 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2428.70 | −1.69695 | −0.848473 | − | 0.529238i | \(-0.822478\pi\) | ||||
−0.848473 | + | 0.529238i | \(0.822478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 254.334 | + | 440.520i | 0.169628 | + | 0.293805i | 0.938289 | − | 0.345852i | \(-0.112410\pi\) |
−0.768661 | + | 0.639656i | \(0.779077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1748.26 | − | 1009.36i | −1.09025 | − | 0.629456i | −0.156606 | − | 0.987661i | \(-0.550055\pi\) |
−0.933643 | + | 0.358206i | \(0.883389\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3146.55i | 1.92005i | 0.279920 | + | 0.960023i | \(0.409692\pi\) | ||||
−0.279920 | + | 0.960023i | \(0.590308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 310.683 | − | 538.119i | 0.181683 | − | 0.314684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2870.83 | + | 1657.48i | −1.64421 | + | 0.949283i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2647.01 | + | 1528.25i | −1.45538 | + | 0.840264i | −0.998779 | − | 0.0494081i | \(-0.984267\pi\) |
−0.456601 | + | 0.889672i | \(0.650933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 900.513 | − | 1559.73i | 0.485316 | − | 0.840591i | −0.514542 | − | 0.857465i | \(-0.672038\pi\) |
0.999858 | + | 0.0168738i | \(0.00537134\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1587.60i | 0.822702i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1165.70 | − | 673.019i | −0.592568 | − | 0.342119i | 0.173544 | − | 0.984826i | \(-0.444478\pi\) |
−0.766112 | + | 0.642707i | \(0.777811\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 373.250 | + | 646.487i | 0.179357 | + | 0.310655i | 0.941660 | − | 0.336564i | \(-0.109265\pi\) |
−0.762304 | + | 0.647220i | \(0.775932\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2625.39 | −1.21652 | −0.608259 | − | 0.793738i | \(-0.708132\pi\) | ||||
−0.608259 | + | 0.793738i | \(0.708132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1264.40 | 0.575512 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1838.42 | − | 3184.24i | −0.807934 | − | 1.39938i | −0.914293 | − | 0.405054i | \(-0.867253\pi\) |
0.106359 | − | 0.994328i | \(-0.466081\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3447.70 | − | 1990.53i | −1.43963 | − | 0.831170i | −0.441804 | − | 0.897111i | \(-0.645661\pi\) |
−0.997823 | + | 0.0659418i | \(0.978995\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1230.75i | − | 0.505421i | −0.967542 | − | 0.252711i | \(-0.918678\pi\) | ||
0.967542 | − | 0.252711i | \(-0.0813221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1814.27 | + | 3142.41i | −0.721016 | + | 1.24884i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 60.7940 | − | 35.0994i | 0.0237738 | − | 0.0137258i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2746.14 | + | 1585.48i | −1.04033 | + | 0.600636i | −0.919928 | − | 0.392088i | \(-0.871753\pi\) |
−0.120405 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 120.100 | − | 208.020i | 0.0447928 | − | 0.0775834i | −0.842760 | − | 0.538290i | \(-0.819071\pi\) |
0.887553 | + | 0.460706i | \(0.152404\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2565.35i | − | 0.927784i | −0.885892 | − | 0.463892i | \(-0.846453\pi\) | ||
0.885892 | − | 0.463892i | \(-0.153547\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1129.94 | + | 652.372i | 0.402510 | + | 0.232389i | 0.687566 | − | 0.726122i | \(-0.258679\pi\) |
−0.285057 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3682.25 | − | 6377.84i | −1.25453 | − | 2.17292i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2998.36 | 0.992349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1773.22 | 0.578549 | 0.289274 | − | 0.957246i | \(-0.406586\pi\) | ||||
0.289274 | + | 0.957246i | \(0.406586\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1133.68 | − | 1963.59i | −0.359611 | − | 0.622865i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −91.2448 | − | 52.6802i | −0.0277728 | − | 0.0160346i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3314.68i | 0.995369i | 0.867358 | + | 0.497684i | \(0.165816\pi\) | ||||
−0.867358 | + | 0.497684i | \(0.834184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −658.933 | + | 1141.31i | −0.192665 | + | 0.333705i | −0.946132 | − | 0.323780i | \(-0.895046\pi\) |
0.753468 | + | 0.657485i | \(0.228380\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1826.72 | − | 1054.66i | 0.527131 | − | 0.304339i | −0.212716 | − | 0.977114i | \(-0.568231\pi\) |
0.739848 | + | 0.672775i | \(0.234898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5715.21 | + | 3299.68i | −1.60694 | + | 0.927764i | −0.616884 | + | 0.787054i | \(0.711605\pi\) |
−0.990051 | + | 0.140711i | \(0.955061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3488.30 | − | 6041.91i | 0.968305 | − | 1.67715i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 300.361i | 0.0812919i | 0.999174 | + | 0.0406459i | \(0.0129416\pi\) | ||||
−0.999174 | + | 0.0406459i | \(0.987058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3960.64 | − | 2286.68i | −1.05862 | − | 0.611194i | −0.133569 | − | 0.991040i | \(-0.542644\pi\) |
−0.925050 | + | 0.379846i | \(0.875977\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2250.10 | − | 3897.29i | −0.579637 | − | 1.00396i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −165.982 | −0.0417399 | −0.0208699 | − | 0.999782i | \(-0.506644\pi\) | ||||
−0.0208699 | + | 0.999782i | \(0.506644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2587.95 | −0.643095 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3308.66 | + | 5730.77i | 0.803069 | + | 1.39096i | 0.917587 | + | 0.397535i | \(0.130134\pi\) |
−0.114518 | + | 0.993421i | \(0.536532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3956.13 | − | 2284.07i | −0.927548 | − | 0.535520i | −0.0415128 | − | 0.999138i | \(-0.513218\pi\) |
−0.886035 | + | 0.463618i | \(0.846551\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3078.60i | − | 0.713648i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3839.76 | − | 6650.66i | 0.870314 | − | 1.50743i | 0.00864111 | − | 0.999963i | \(-0.497249\pi\) |
0.861673 | − | 0.507465i | \(-0.169417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2481.49 | − | 1432.69i | 0.556236 | − | 0.321143i | −0.195397 | − | 0.980724i | \(-0.562600\pi\) |
0.751633 | + | 0.659581i | \(0.229266\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1940.07 | + | 1120.10i | −0.425421 | + | 0.245617i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −84.3492 | + | 146.097i | −0.0182962 | + | 0.0316900i | −0.875029 | − | 0.484071i | \(-0.839158\pi\) |
0.856732 | + | 0.515761i | \(0.172491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5412.27i | 1.14900i | 0.818505 | + | 0.574499i | \(0.194803\pi\) | ||||
−0.818505 | + | 0.574499i | \(0.805197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2834.46 | + | 1636.48i | 0.595375 | + | 0.343740i | 0.767220 | − | 0.641384i | \(-0.221639\pi\) |
−0.171845 | + | 0.985124i | \(0.554973\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2450.55 | + | 4244.47i | 0.498789 | + | 0.863927i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7800.65 | 1.55535 | 0.777677 | − | 0.628664i | \(-0.216398\pi\) | ||||
0.777677 | + | 0.628664i | \(0.216398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2456.80 | 0.484883 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1942.11 | + | 3363.83i | 0.375636 | + | 0.650620i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10929.6 | − | 6310.22i | −2.05190 | − | 1.18466i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7079.58i | − | 1.31613i | −0.752960 | − | 0.658066i | \(-0.771375\pi\) | ||
0.752960 | − | 0.658066i | \(-0.228625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2905.22 | + | 5031.98i | −0.529710 | + | 0.917484i | 0.469690 | + | 0.882832i | \(0.344366\pi\) |
−0.999399 | + | 0.0346525i | \(0.988968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4042.49 | − | 2333.93i | 0.730016 | − | 0.421475i | −0.0884122 | − | 0.996084i | \(-0.528179\pi\) |
0.818428 | + | 0.574609i | \(0.194846\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4416.52 | + | 2549.88i | −0.782513 | + | 0.451784i | −0.837320 | − | 0.546713i | \(-0.815879\pi\) |
0.0548072 | + | 0.998497i | \(0.482546\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2199.49 | − | 3809.62i | 0.386043 | − | 0.668646i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 508.409i | − | 0.0875810i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2911.83 | + | 1681.14i | 0.496982 | + | 0.286933i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2036.04 | − | 3526.52i | −0.338099 | − | 0.585604i | 0.645976 | − | 0.763357i | \(-0.276450\pi\) |
−0.984075 | + | 0.177753i | \(0.943117\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6242.05 | −1.01803 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8456.90 | −1.36699 | −0.683496 | − | 0.729954i | \(-0.739542\pi\) | ||||
−0.683496 | + | 0.729954i | \(0.739542\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1053.38 | − | 1824.50i | −0.167283 | − | 0.289743i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6815.08 | − | 3934.69i | −1.05433 | − | 0.608718i | −0.130472 | − | 0.991452i | \(-0.541649\pi\) |
−0.923858 | + | 0.382734i | \(0.874982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3417.23i | − | 0.524127i | −0.965051 | − | 0.262063i | \(-0.915597\pi\) | ||
0.965051 | − | 0.262063i | \(-0.0844030\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3998.64 | − | 6925.85i | 0.602907 | − | 1.04427i | −0.389472 | − | 0.921039i | \(-0.627342\pi\) |
0.992379 | − | 0.123227i | \(-0.0393243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6823.57 | − | 3939.59i | 1.02016 | − | 0.588991i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4233.62 | − | 2444.28i | 0.622401 | − | 0.359343i | −0.155402 | − | 0.987851i | \(-0.549667\pi\) |
0.777803 | + | 0.628508i | \(0.216334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7428.20 | − | 12866.0i | 1.08299 | − | 1.87579i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7267.50i | 1.04219i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9088.63 | − | 5247.32i | −1.29271 | − | 0.746344i | −0.313572 | − | 0.949564i | \(-0.601526\pi\) |
−0.979133 | + | 0.203221i | \(0.934859\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2698.30 | − | 4673.59i | −0.374565 | − | 0.648765i | 0.615697 | − | 0.787983i | \(-0.288875\pi\) |
−0.990262 | + | 0.139218i | \(0.955541\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6602.36 | −0.901960 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10159.5 | −1.37693 | −0.688466 | − | 0.725269i | \(-0.741715\pi\) | ||||
−0.688466 | + | 0.725269i | \(0.741715\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3503.40 | + | 6068.06i | 0.467403 | + | 0.809565i | 0.999306 | − | 0.0372396i | \(-0.0118565\pi\) |
−0.531904 | + | 0.846805i | \(0.678523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7529.03 | − | 4346.88i | −0.981328 | − | 0.566570i | −0.0786575 | − | 0.996902i | \(-0.525063\pi\) |
−0.902671 | + | 0.430331i | \(0.858397\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 438.819i | 0.0567571i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 929.944 | − | 1610.71i | 0.118457 | − | 0.205174i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6502.69 | + | 3754.33i | −0.822067 | + | 0.474620i | −0.851129 | − | 0.524957i | \(-0.824081\pi\) |
0.0290620 | + | 0.999578i | \(0.490748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1927.81 | − | 1113.02i | 0.240075 | − | 0.138607i | −0.375136 | − | 0.926970i | \(-0.622404\pi\) |
0.615211 | + | 0.788362i | \(0.289071\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1581.00 | + | 2738.37i | −0.195422 | + | 0.338481i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4815.11i | − | 0.586428i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3966.88 | + | 2290.28i | 0.479584 | + | 0.276888i | 0.720243 | − | 0.693722i | \(-0.244030\pi\) |
−0.240659 | + | 0.970610i | \(0.577364\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4111.30 | + | 7120.98i | 0.486303 | + | 0.842301i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9723.41 | 1.13370 | 0.566849 | − | 0.823821i | \(-0.308162\pi\) | ||||
0.566849 | + | 0.823821i | \(0.308162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6827.70 | 0.790408 | 0.395204 | − | 0.918593i | \(-0.370674\pi\) | ||||
0.395204 | + | 0.918593i | \(0.370674\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 189.927 | + | 328.963i | 0.0216772 | + | 0.0375460i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4019.87 | + | 2320.87i | 0.449258 | + | 0.259379i | 0.707517 | − | 0.706696i | \(-0.249815\pi\) |
−0.258259 | + | 0.966076i | \(0.583149\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3332.86i | 0.369900i | 0.982748 | + | 0.184950i | \(0.0592124\pi\) | ||||
−0.982748 | + | 0.184950i | \(0.940788\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9371.51 | + | 16231.9i | −1.02586 | + | 1.77684i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13274.2 | + | 7663.84i | −1.44315 | + | 0.833201i | −0.998058 | − | 0.0622858i | \(-0.980161\pi\) |
−0.445088 | + | 0.895487i | \(0.646828\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4878.42 | + | 2816.55i | −0.523207 | + | 0.302073i | −0.738246 | − | 0.674532i | \(-0.764345\pi\) |
0.215039 | + | 0.976605i | \(0.431012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1777.95 | + | 3079.50i | −0.189400 | + | 0.328050i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17327.5i | 1.82124i | 0.413248 | + | 0.910619i | \(0.364394\pi\) | ||||
−0.413248 | + | 0.910619i | \(0.635606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8463.46 | + | 4886.38i | 0.883655 | + | 0.510179i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2456.00 | − | 4253.92i | −0.251394 | − | 0.435426i | 0.712516 | − | 0.701656i | \(-0.247555\pi\) |
−0.963910 | + | 0.266229i | \(0.914222\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6760.33 | −0.682993 | −0.341497 | − | 0.939883i | \(-0.610934\pi\) | ||||
−0.341497 | + | 0.939883i | \(0.610934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16397.3 | 1.64589 | 0.822945 | − | 0.568121i | \(-0.192330\pi\) | ||||
0.822945 | + | 0.568121i | \(0.192330\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6290.15 | − | 10894.9i | −0.623284 | − | 1.07956i | −0.988870 | − | 0.148781i | \(-0.952465\pi\) |
0.365587 | − | 0.930777i | \(-0.380868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2605.71 | + | 1504.41i | 0.253299 | + | 0.146242i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16224.5i | 1.56722i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6373.15 | − | 11038.6i | 0.607927 | − | 1.05296i | −0.383655 | − | 0.923477i | \(-0.625335\pi\) |
0.991582 | − | 0.129483i | \(-0.0413319\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6258.71 | + | 3613.47i | −0.593290 | + | 0.342536i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9749.09 | + | 5628.64i | −0.912749 | + | 0.526976i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −786.712 | + | 1362.63i | −0.0732019 | + | 0.126789i | −0.900303 | − | 0.435264i | \(-0.856655\pi\) |
0.827101 | + | 0.562053i | \(0.189988\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17035.7i | − | 1.56581i | −0.622142 | − | 0.782904i | \(-0.713737\pi\) | ||
0.622142 | − | 0.782904i | \(-0.286263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −645.969 | − | 372.950i | −0.0590121 | − | 0.0340707i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.6112 | − | 35.6996i | −0.00184907 | − | 0.00320268i | 0.865099 | − | 0.501600i | \(-0.167255\pi\) |
−0.866948 | + | 0.498398i | \(0.833922\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6871.06 | 0.609076 | 0.304538 | − | 0.952500i | \(-0.401498\pi\) | ||||
0.304538 | + | 0.952500i | \(0.401498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11155.5 | −0.982996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1102.82 | − | 1910.14i | −0.0960349 | − | 0.166337i | 0.814005 | − | 0.580858i | \(-0.197283\pi\) |
−0.910040 | + | 0.414520i | \(0.863949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10788.0 | + | 6228.48i | 0.923064 | + | 0.532931i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9258.01i | 0.787557i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3862.18 | − | 6689.50i | 0.324770 | − | 0.562519i | −0.656696 | − | 0.754156i | \(-0.728046\pi\) |
0.981466 | + | 0.191637i | \(0.0613797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1917.64 | − | 1107.15i | 0.160330 | − | 0.0925667i | −0.417688 | − | 0.908590i | \(-0.637160\pi\) |
0.578018 | + | 0.816024i | \(0.303826\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −309.367 | + | 178.613i | −0.0255716 | + | 0.0147638i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2005.25 | − | 3473.19i | 0.164810 | − | 0.285460i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 14667.8i | − | 1.19199i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11746.5 | − | 6781.83i | −0.949242 | − | 0.548045i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6535.15 | − | 11319.2i | −0.519349 | − | 0.899539i | −0.999747 | − | 0.0224886i | \(-0.992841\pi\) |
0.480398 | − | 0.877051i | \(-0.340492\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24548.8 | −1.92946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19391.3 | 1.51574 | 0.757872 | − | 0.652403i | \(-0.226239\pi\) | ||||
0.757872 | + | 0.652403i | \(0.226239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15929.6 | − | 27590.9i | −1.23162 | − | 2.13323i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20477.8 | + | 11822.9i | 1.55776 | + | 0.899374i | 0.997471 | + | 0.0710781i | \(0.0226439\pi\) |
0.560291 | + | 0.828296i | \(0.310689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4515.88i | − | 0.341684i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11635.2 | + | 20152.8i | −0.870988 | + | 1.50859i | −0.0100112 | + | 0.999950i | \(0.503187\pi\) |
−0.860976 | + | 0.508645i | \(0.830147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9833.61 | − | 5677.44i | 0.732218 | − | 0.422746i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11785.6 | − | 6804.42i | 0.868326 | − | 0.501329i | 0.00153471 | − | 0.999999i | \(-0.499511\pi\) |
0.866792 | + | 0.498670i | \(0.166178\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10558.1 | + | 18287.2i | −0.773809 | + | 1.34028i | 0.161653 | + | 0.986848i | \(0.448317\pi\) |
−0.935462 | + | 0.353428i | \(0.885016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14003.7i | − | 1.01564i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8887.46 | + | 5131.18i | 0.641230 | + | 0.370215i | 0.785088 | − | 0.619384i | \(-0.212617\pi\) |
−0.143858 | + | 0.989598i | \(0.545951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2042.66 | + | 3538.00i | 0.145109 | + | 0.251336i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13227.4 | 0.930072 | 0.465036 | − | 0.885292i | \(-0.346041\pi\) | ||||
0.465036 | + | 0.885292i | \(0.346041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15258.0 | −1.06739 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4129.36 | − | 7152.26i | −0.285957 | − | 0.495292i | 0.686884 | − | 0.726767i | \(-0.258978\pi\) |
−0.972841 | + | 0.231475i | \(0.925645\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3549.97 | − | 2049.57i | −0.242150 | − | 0.139805i | 0.374015 | − | 0.927423i | \(-0.377981\pi\) |
−0.616164 | + | 0.787618i | \(0.711314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 480.297i | 0.0325985i | 0.999867 | + | 0.0162993i | \(0.00518844\pi\) | ||||
−0.999867 | + | 0.0162993i | \(0.994812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7030.17 | + | 12176.6i | −0.472425 | + | 0.818264i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10878.6 | + | 6280.76i | −0.727428 | + | 0.419981i | −0.817481 | − | 0.575956i | \(-0.804630\pi\) |
0.0900524 | + | 0.995937i | \(0.471297\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12033.6 | − | 6947.61i | 0.796772 | − | 0.460017i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15062.7 | + | 26089.4i | −0.992458 | + | 1.71899i | −0.390065 | + | 0.920787i | \(0.627548\pi\) |
−0.602392 | + | 0.798200i | \(0.705786\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13044.4i | 0.851132i | 0.904927 | + | 0.425566i | \(0.139925\pi\) | ||||
−0.904927 | + | 0.425566i | \(0.860075\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7878.85 | + | 4548.85i | 0.511595 | + | 0.295370i | 0.733489 | − | 0.679701i | \(-0.237890\pi\) |
−0.221894 | + | 0.975071i | \(0.571224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8632.75 | + | 14952.4i | 0.552496 | + | 0.956951i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −816.462 | −0.0517559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1769.90 | 0.111662 | 0.0558310 | − | 0.998440i | \(-0.482219\pi\) | ||||
0.0558310 | + | 0.998440i | \(0.482219\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18619.6 | + | 32250.1i | 1.16362 | + | 2.01544i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7935.19 | + | 4581.38i | 0.488956 | + | 0.282299i | 0.724141 | − | 0.689652i | \(-0.242236\pi\) |
−0.235185 | + | 0.971951i | \(0.575570\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24337.4i | − | 1.49265i | −0.665581 | − | 0.746326i | \(-0.731816\pi\) | ||
0.665581 | − | 0.746326i | \(-0.268184\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15143.6 | − | 26229.5i | 0.920180 | − | 1.59380i | 0.121044 | − | 0.992647i | \(-0.461376\pi\) |
0.799135 | − | 0.601151i | \(-0.205291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2823.41 | + | 1630.10i | −0.170768 | + | 0.0985931i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14499.5 | + | 8371.28i | −0.868925 | + | 0.501674i | −0.866991 | − | 0.498324i | \(-0.833949\pi\) |
−0.00193444 | + | 0.999998i | \(0.500616\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3899.70 | − | 6754.48i | 0.232632 | − | 0.402930i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9709.90i | 0.573966i | 0.957936 | + | 0.286983i | \(0.0926524\pi\) | ||||
−0.957936 | + | 0.286983i | \(0.907348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10470.1 | − | 6044.90i | −0.616095 | − | 0.355703i | 0.159252 | − | 0.987238i | \(-0.449092\pi\) |
−0.775347 | + | 0.631535i | \(0.782425\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13749.2 | + | 23814.3i | 0.798157 | + | 1.38245i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16747.4 | 0.963529 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1800.90 | 0.103150 | 0.0515748 | − | 0.998669i | \(-0.483576\pi\) | ||||
0.0515748 | + | 0.998669i | \(0.483576\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14153.9 | + | 24515.2i | 0.803512 | + | 1.39172i | 0.917291 | + | 0.398218i | \(0.130371\pi\) |
−0.113779 | + | 0.993506i | \(0.536295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10251.0 | + | 5918.41i | 0.574294 | + | 0.331569i | 0.758863 | − | 0.651251i | \(-0.225755\pi\) |
−0.184569 | + | 0.982820i | \(0.559089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30953.0i | 1.72650i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3065.80 | − | 5310.13i | 0.169518 | − | 0.293614i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16366.4 | − | 9449.13i | 0.901022 | − | 0.520205i | 0.0234902 | − | 0.999724i | \(-0.492522\pi\) |
0.877532 | + | 0.479519i | \(0.159189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41782.2 | − | 24122.9i | 2.28041 | − | 1.31660i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 828.546 | − | 1435.08i | 0.0450264 | − | 0.0779881i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3733.84i | − | 0.201177i | −0.994928 | − | 0.100589i | \(-0.967927\pi\) | ||
0.994928 | − | 0.100589i | \(-0.0320726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30201.0 | − | 17436.5i | −1.62027 | − | 0.935464i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1672.07 | + | 2896.12i | 0.0885699 | + | 0.153408i | 0.906907 | − | 0.421331i | \(-0.138437\pi\) |
−0.818337 | + | 0.574739i | \(0.805104\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13169.5 | 0.691728 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9527.40 | −0.498328 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7627.74 | + | 13211.6i | 0.395642 | + | 0.685273i | 0.993183 | − | 0.116566i | \(-0.0371887\pi\) |
−0.597541 | + | 0.801839i | \(0.703855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20614.3 | + | 11901.7i | 1.05600 | + | 0.609679i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31743.3i | − | 1.61939i | −0.586854 | − | 0.809693i | \(-0.699634\pi\) | ||
0.586854 | − | 0.809693i | \(-0.300366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 255.091 | − | 441.830i | 0.0129068 | − | 0.0223552i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9653.79 | − | 5573.62i | 0.486454 | − | 0.280854i | −0.236648 | − | 0.971595i | \(-0.576049\pi\) |
0.723102 | + | 0.690741i | \(0.242716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7173.51 | − | 4141.63i | 0.358534 | − | 0.207000i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1875.05 | − | 3247.68i | 0.0933352 | − | 0.161661i | −0.815577 | − | 0.578648i | \(-0.803581\pi\) |
0.908913 | + | 0.416987i | \(0.136914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12014.8i | − | 0.593245i | −0.954995 | − | 0.296623i | \(-0.904140\pi\) | ||
0.954995 | − | 0.296623i | \(-0.0958603\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40586.5 | + | 23432.6i | 1.99594 | + | 1.15236i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11928.6 | + | 20661.0i | 0.579603 | + | 1.00390i | 0.995525 | + | 0.0945019i | \(0.0301259\pi\) |
−0.415921 | + | 0.909401i | \(0.636541\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27615.1 | −1.33115 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18603.5 | 0.893206 | 0.446603 | − | 0.894732i | \(-0.352634\pi\) | ||||
0.446603 | + | 0.894732i | \(0.352634\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1982.35 | + | 3433.53i | 0.0944286 | + | 0.163555i | 0.909370 | − | 0.415988i | \(-0.136564\pi\) |
−0.814941 | + | 0.579543i | \(0.803231\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4237.62 | + | 2446.59i | 0.199494 | + | 0.115178i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 20811.6i | − | 0.975925i | −0.872865 | − | 0.487962i | \(-0.837740\pi\) | ||
0.872865 | − | 0.487962i | \(-0.162260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2025.85 | + | 3508.87i | −0.0942621 | + | 0.163267i | −0.909300 | − | 0.416140i | \(-0.863383\pi\) |
0.815038 | + | 0.579407i | \(0.196716\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9872.60 | − | 5699.95i | 0.457592 | − | 0.264191i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 61295.9 | − | 35389.2i | 2.81920 | − | 1.62766i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5227.87 | + | 9054.94i | −0.239524 | + | 0.414867i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20638.7i | 0.938380i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6765.77 | + | 3906.22i | 0.306447 | + | 0.176927i | 0.645335 | − | 0.763899i | \(-0.276718\pi\) |
−0.338889 | + | 0.940826i | \(0.610051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12568.0 | − | 21768.4i | −0.562803 | − | 0.974803i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20518.5 | 0.911925 | 0.455962 | − | 0.889999i | \(-0.349295\pi\) | ||||
0.455962 | + | 0.889999i | \(0.349295\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1569.81 | 0.0695068 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4822.02 | − | 8351.98i | −0.211912 | − | 0.367042i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5160.47 | + | 2979.40i | 0.224267 | + | 0.129481i | 0.607925 | − | 0.793995i | \(-0.292002\pi\) |
−0.383657 | + | 0.923476i | \(0.625336\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35305.0i | − | 1.52864i | −0.644838 | − | 0.764319i | \(-0.723075\pi\) | ||
0.644838 | − | 0.764319i | \(-0.276925\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5723.03 | − | 9912.57i | 0.245974 | − | 0.426040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18871.6 | − | 10895.5i | 0.808120 | − | 0.466568i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23053.5 | + | 13310.0i | −0.979992 | + | 0.565799i | −0.902268 | − | 0.431176i | \(-0.858099\pi\) |
−0.0777242 | + | 0.996975i | \(0.524765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13046.9 | + | 22598.0i | −0.552598 | + | 0.957128i | 0.445488 | + | 0.895288i | \(0.353030\pi\) |
−0.998086 | + | 0.0618398i | \(0.980303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 264.904i | − | 0.0111386i | −0.999984 | − | 0.00556930i | \(-0.998227\pi\) | ||
0.999984 | − | 0.00556930i | \(-0.00177277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19446.4 | − | 11227.4i | −0.814718 | − | 0.470377i | 0.0338739 | − | 0.999426i | \(-0.489216\pi\) |
−0.848591 | + | 0.529049i | \(0.822549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20127.5 | + | 34861.8i | 0.834181 | + | 1.44484i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31288.8 | −1.28750 | −0.643748 | − | 0.765238i | \(-0.722621\pi\) | ||||
−0.643748 | + | 0.765238i | \(0.722621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22352.5 | −0.916499 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9693.50 | − | 16789.6i | −0.394635 | − | 0.683528i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26067.1 | + | 15049.8i | 1.05002 | + | 0.606230i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4559.95i | 0.183036i | 0.995803 | + | 0.0915180i | \(0.0291719\pi\) | ||||
−0.995803 | + | 0.0915180i | \(0.970828\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8935.12 | − | 15476.1i | 0.356147 | − | 0.616865i | −0.631167 | − | 0.775647i | \(-0.717424\pi\) |
0.987314 | + | 0.158783i | \(0.0507569\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6639.43 | − | 3833.28i | 0.263719 | − | 0.152258i | −0.362311 | − | 0.932057i | \(-0.618012\pi\) |
0.626030 | + | 0.779799i | \(0.284679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4683.45 | − | 2703.99i | 0.184735 | − | 0.106657i | −0.404780 | − | 0.914414i | \(-0.632652\pi\) |
0.589515 | + | 0.807757i | \(0.299319\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28188.4 | + | 48823.8i | −1.10802 | + | 1.91914i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2468.09i | 0.0963454i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10766.6 | − | 6216.11i | −0.418844 | − | 0.241820i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2847.40 | − | 4931.84i | −0.109635 | − | 0.189893i | 0.805987 | − | 0.591933i | \(-0.201635\pi\) |
−0.915622 | + | 0.402039i | \(0.868302\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17761.3 | 0.679221 | 0.339611 | − | 0.940566i | \(-0.389705\pi\) | ||||
0.339611 | + | 0.940566i | \(0.389705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27753.8 | 1.05774 | 0.528872 | − | 0.848701i | \(-0.322615\pi\) | ||||
0.528872 | + | 0.848701i | \(0.322615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11406.0 | − | 19755.8i | −0.431766 | − | 0.747841i | 0.565259 | − | 0.824913i | \(-0.308776\pi\) |
−0.997025 | + | 0.0770725i | \(0.975443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 58067.3 | + | 33525.2i | 2.17598 | + | 1.25630i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 61041.5i | 2.27977i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11192.7 | + | 19386.3i | −0.415236 | + | 0.719211i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 599.911 | − | 346.359i | 0.0221820 | − | 0.0128068i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16342.9 | + | 9435.56i | −0.600282 | + | 0.346573i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12499.0 | − | 21648.8i | 0.457576 | − | 0.792544i | −0.541257 | − | 0.840857i | \(-0.682051\pi\) |
0.998832 | + | 0.0483132i | \(0.0153846\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 49221.0i | − | 1.79008i | −0.445985 | − | 0.895040i | \(-0.647147\pi\) | ||
0.445985 | − | 0.895040i | \(-0.352853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9449.60 | − | 5455.73i | −0.342537 | − | 0.197764i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11943.1 | + | 20686.0i | 0.428690 | + | 0.742513i | 0.996757 | − | 0.0804694i | \(-0.0256419\pi\) |
−0.568067 | + | 0.822982i | \(0.692309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15692.9 | 0.559629 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26055.1 | 0.926149 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10399.8 | + | 18013.0i | 0.367283 | + | 0.636153i | 0.989140 | − | 0.146978i | \(-0.0469547\pi\) |
−0.621857 | + | 0.783131i | \(0.713621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −932.152 | − | 538.178i | −0.0326039 | − | 0.0188239i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29654.7i | 1.03391i | 0.856011 | + | 0.516957i | \(0.172935\pi\) | ||||
−0.856011 | + | 0.516957i | \(0.827065\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7850.46 | + | 13597.4i | −0.271963 | + | 0.471054i | −0.969365 | − | 0.245627i | \(-0.921006\pi\) |
0.697401 | + | 0.716681i | \(0.254340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52905.8 | + | 30545.2i | −1.82699 | + | 1.05481i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19293.1 | − | 11138.9i | 0.662030 | − | 0.382223i | −0.131020 | − | 0.991380i | \(-0.541825\pi\) |
0.793050 | + | 0.609157i | \(0.208492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7237.30 | + | 12535.4i | −0.247558 | + | 0.428783i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26599.9i | − | 0.904149i | −0.891980 | − | 0.452074i | \(-0.850684\pi\) | ||
0.891980 | − | 0.452074i | \(-0.149316\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42106.4 | + | 24310.2i | 1.42674 | + | 0.823726i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9535.10 | − | 16515.3i | −0.320066 | − | 0.554371i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3682.99 | −0.122860 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −482.698 | −0.0160523 | −0.00802613 | − | 0.999968i | \(-0.502555\pi\) | ||||
−0.00802613 | + | 0.999968i | \(0.502555\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12535.9 | + | 21712.8i | 0.414310 | + | 0.717607i | 0.995356 | − | 0.0962646i | \(-0.0306895\pi\) |
−0.581045 | + | 0.813871i | \(0.697356\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29435.3 | + | 16994.5i | 0.963887 | + | 0.556500i | 0.897367 | − | 0.441285i | \(-0.145477\pi\) |
0.0665199 | + | 0.997785i | \(0.478810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4718.71i | − | 0.154046i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2763.57 | + | 4786.64i | −0.0896685 | + | 0.155310i | −0.907371 | − | 0.420331i | \(-0.861914\pi\) |
0.817703 | + | 0.575641i | \(0.195247\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34064.6 | + | 19667.2i | −1.10192 | + | 0.636192i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16288.5 | + | 9404.17i | −0.523705 | + | 0.302361i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16600.4 | + | 28752.8i | −0.532119 | + | 0.921658i | 0.467178 | + | 0.884163i | \(0.345271\pi\) |
−0.999297 | + | 0.0374940i | \(0.988062\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 20005.6i | − | 0.637407i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20369.1 | − | 11760.1i | −0.647037 | − | 0.373567i | 0.140283 | − | 0.990111i | \(-0.455199\pi\) |
−0.787320 | + | 0.616545i | \(0.788532\pi\) | |||||||
\(998\) | 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 | 1764.4.t.a.521.2 | 16 | ||
3.2 | odd | 2 | inner | 1764.4.t.a.521.7 | 16 | ||
7.2 | even | 3 | inner | 1764.4.t.a.1097.1 | 16 | ||
7.3 | odd | 6 | 252.4.f.a.125.2 | yes | 8 | ||
7.4 | even | 3 | 252.4.f.a.125.7 | yes | 8 | ||
7.5 | odd | 6 | inner | 1764.4.t.a.1097.7 | 16 | ||
7.6 | odd | 2 | inner | 1764.4.t.a.521.8 | 16 | ||
21.2 | odd | 6 | inner | 1764.4.t.a.1097.8 | 16 | ||
21.5 | even | 6 | inner | 1764.4.t.a.1097.2 | 16 | ||
21.11 | odd | 6 | 252.4.f.a.125.1 | ✓ | 8 | ||
21.17 | even | 6 | 252.4.f.a.125.8 | yes | 8 | ||
21.20 | even | 2 | inner | 1764.4.t.a.521.1 | 16 | ||
28.3 | even | 6 | 1008.4.k.d.881.1 | 8 | |||
28.11 | odd | 6 | 1008.4.k.d.881.8 | 8 | |||
84.11 | even | 6 | 1008.4.k.d.881.2 | 8 | |||
84.59 | odd | 6 | 1008.4.k.d.881.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.f.a.125.1 | ✓ | 8 | 21.11 | odd | 6 | ||
252.4.f.a.125.2 | yes | 8 | 7.3 | odd | 6 | ||
252.4.f.a.125.7 | yes | 8 | 7.4 | even | 3 | ||
252.4.f.a.125.8 | yes | 8 | 21.17 | even | 6 | ||
1008.4.k.d.881.1 | 8 | 28.3 | even | 6 | |||
1008.4.k.d.881.2 | 8 | 84.11 | even | 6 | |||
1008.4.k.d.881.7 | 8 | 84.59 | odd | 6 | |||
1008.4.k.d.881.8 | 8 | 28.11 | odd | 6 | |||
1764.4.t.a.521.1 | 16 | 21.20 | even | 2 | inner | ||
1764.4.t.a.521.2 | 16 | 1.1 | even | 1 | trivial | ||
1764.4.t.a.521.7 | 16 | 3.2 | odd | 2 | inner | ||
1764.4.t.a.521.8 | 16 | 7.6 | odd | 2 | inner | ||
1764.4.t.a.1097.1 | 16 | 7.2 | even | 3 | inner | ||
1764.4.t.a.1097.2 | 16 | 21.5 | even | 6 | inner | ||
1764.4.t.a.1097.7 | 16 | 7.5 | odd | 6 | inner | ||
1764.4.t.a.1097.8 | 16 | 21.2 | odd | 6 | inner |