Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.109 |
Dual form | 324.4.e.b.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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −4.50000 | + | 7.79423i | −0.402492 | + | 0.697137i | −0.994026 | − | 0.109143i | \(-0.965189\pi\) |
0.591534 | + | 0.806280i | \(0.298523\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.0269975 | + | 0.0467610i | 0.879208 | − | 0.476437i | \(-0.158072\pi\) |
−0.852211 | + | 0.523198i | \(0.824739\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −31.5000 | − | 54.5596i | −0.863419 | − | 1.49549i | −0.868609 | − | 0.495499i | \(-0.834985\pi\) |
0.00518978 | − | 0.999987i | \(-0.498348\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.0000 | − | 24.2487i | 0.298685 | − | 0.517337i | −0.677151 | − | 0.735844i | \(-0.736785\pi\) |
0.975835 | + | 0.218507i | \(0.0701188\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 72.0000 | 1.02721 | 0.513605 | − | 0.858027i | \(-0.328310\pi\) | ||||
0.513605 | + | 0.858027i | \(0.328310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 98.0000 | 1.18330 | 0.591651 | − | 0.806194i | \(-0.298476\pi\) | ||||
0.591651 | + | 0.806194i | \(0.298476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −63.0000 | + | 109.119i | −0.571148 | + | 0.989258i | 0.425300 | + | 0.905052i | \(0.360169\pi\) |
−0.996448 | + | 0.0842053i | \(0.973165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.0000 | + | 38.1051i | 0.176000 | + | 0.304841i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 63.0000 | + | 109.119i | 0.403407 | + | 0.698722i | 0.994135 | − | 0.108149i | \(-0.0344925\pi\) |
−0.590728 | + | 0.806871i | \(0.701159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 129.500 | − | 224.301i | 0.750287 | − | 1.29953i | −0.197397 | − | 0.980324i | \(-0.563249\pi\) |
0.947684 | − | 0.319211i | \(-0.103418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.00000 | −0.0434651 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 386.000 | 1.71508 | 0.857541 | − | 0.514416i | \(-0.171991\pi\) | ||||
0.857541 | + | 0.514416i | \(0.171991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 225.000 | − | 389.711i | 0.857051 | − | 1.48446i | −0.0176779 | − | 0.999844i | \(-0.505627\pi\) |
0.874729 | − | 0.484612i | \(-0.161039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.0000 | + | 29.4449i | 0.0602901 | + | 0.104426i | 0.894595 | − | 0.446878i | \(-0.147464\pi\) |
−0.834305 | + | 0.551303i | \(0.814131\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 27.0000 | + | 46.7654i | 0.0837948 | + | 0.145137i | 0.904877 | − | 0.425673i | \(-0.139963\pi\) |
−0.821082 | + | 0.570810i | \(0.806629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 171.000 | − | 296.181i | 0.498542 | − | 0.863501i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −693.000 | −1.79605 | −0.898027 | − | 0.439940i | \(-0.855000\pi\) | ||||
−0.898027 | + | 0.439940i | \(0.855000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 567.000 | 1.39008 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −90.0000 | + | 155.885i | −0.198593 | + | 0.343974i | −0.948073 | − | 0.318054i | \(-0.896971\pi\) |
0.749479 | + | 0.662028i | \(0.230304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 140.000 | + | 242.487i | 0.293855 | + | 0.508972i | 0.974718 | − | 0.223439i | \(-0.0717283\pi\) |
−0.680863 | + | 0.732411i | \(0.738395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 126.000 | + | 218.238i | 0.240437 | + | 0.416448i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 293.000 | − | 507.491i | 0.534263 | − | 0.925371i | −0.464935 | − | 0.885345i | \(-0.653922\pi\) |
0.999199 | − | 0.0400266i | \(-0.0127443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 504.000 | 0.842448 | 0.421224 | − | 0.906957i | \(-0.361601\pi\) | ||||
0.421224 | + | 0.906957i | \(0.361601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 161.000 | 0.258132 | 0.129066 | − | 0.991636i | \(-0.458802\pi\) | ||||
0.129066 | + | 0.991636i | \(0.458802\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31.5000 | − | 54.5596i | 0.0466202 | − | 0.0807486i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −220.000 | − | 381.051i | −0.313316 | − | 0.542679i | 0.665762 | − | 0.746164i | \(-0.268106\pi\) |
−0.979078 | + | 0.203485i | \(0.934773\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −499.500 | − | 865.159i | −0.660569 | − | 1.14414i | −0.980466 | − | 0.196687i | \(-0.936982\pi\) |
0.319897 | − | 0.947452i | \(-0.396352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −324.000 | + | 561.184i | −0.413444 | + | 0.716106i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 882.000 | 1.05047 | 0.525235 | − | 0.850957i | \(-0.323977\pi\) | ||||
0.525235 | + | 0.850957i | \(0.323977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28.0000 | 0.0322549 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −441.000 | + | 763.834i | −0.476270 | + | 0.824924i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 360.500 | + | 624.404i | 0.377353 | + | 0.653594i | 0.990676 | − | 0.136238i | \(-0.0435011\pi\) |
−0.613323 | + | 0.789832i | \(0.710168\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 220.500 | + | 381.917i | 0.217233 | + | 0.376259i | 0.953961 | − | 0.299930i | \(-0.0969634\pi\) |
−0.736728 | + | 0.676189i | \(0.763630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 266.000 | − | 460.726i | 0.254464 | − | 0.440744i | −0.710286 | − | 0.703913i | \(-0.751434\pi\) |
0.964750 | + | 0.263169i | \(0.0847677\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 819.000 | 0.739960 | 0.369980 | − | 0.929040i | \(-0.379365\pi\) | ||||
0.369980 | + | 0.929040i | \(0.379365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1294.00 | −1.13709 | −0.568545 | − | 0.822652i | \(-0.692493\pi\) | ||||
−0.568545 | + | 0.822652i | \(0.692493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −567.000 | + | 982.073i | −0.472025 | + | 0.817572i | −0.999488 | − | 0.0320065i | \(-0.989810\pi\) |
0.527462 | + | 0.849578i | \(0.323144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −567.000 | − | 982.073i | −0.459765 | − | 0.796337i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 36.0000 | + | 62.3538i | 0.0277321 | + | 0.0480333i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1319.00 | + | 2284.58i | −0.990984 | + | 1.71644i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1807.00 | −1.26256 | −0.631281 | − | 0.775554i | \(-0.717470\pi\) | ||||
−0.631281 | + | 0.775554i | \(0.717470\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1102.50 | − | 1909.59i | 0.735312 | − | 1.27360i | −0.219274 | − | 0.975663i | \(-0.570369\pi\) |
0.954586 | − | 0.297934i | \(-0.0962977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 49.0000 | + | 84.8705i | 0.0319462 | + | 0.0553324i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −693.000 | − | 1200.31i | −0.432168 | − | 0.748537i | 0.564892 | − | 0.825165i | \(-0.308918\pi\) |
−0.997060 | + | 0.0766283i | \(0.975585\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −238.000 | + | 412.228i | −0.145229 | + | 0.251545i | −0.929459 | − | 0.368927i | \(-0.879725\pi\) |
0.784229 | + | 0.620471i | \(0.213059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1764.00 | −1.03156 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1134.00 | −0.649473 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 787.500 | − | 1363.99i | 0.432983 | − | 0.749949i | −0.564145 | − | 0.825676i | \(-0.690794\pi\) |
0.997129 | + | 0.0757264i | \(0.0241276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −224.500 | − | 388.845i | −0.120990 | − | 0.209562i | 0.799168 | − | 0.601108i | \(-0.205274\pi\) |
−0.920159 | + | 0.391546i | \(0.871940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1165.50 | + | 2018.71i | 0.603969 | + | 1.04611i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −910.000 | + | 1576.17i | −0.462585 | + | 0.801221i | −0.999089 | − | 0.0426767i | \(-0.986411\pi\) |
0.536504 | + | 0.843898i | \(0.319745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −126.000 | −0.0616782 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1828.00 | −0.878405 | −0.439202 | − | 0.898388i | \(-0.644739\pi\) | ||||
−0.439202 | + | 0.898388i | \(0.644739\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 405.000 | − | 701.481i | 0.187664 | − | 0.325043i | −0.756807 | − | 0.653638i | \(-0.773242\pi\) |
0.944471 | + | 0.328595i | \(0.106575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 706.500 | + | 1223.69i | 0.321575 | + | 0.556984i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 661.500 | + | 1145.75i | 0.290710 | + | 0.503525i | 0.973978 | − | 0.226643i | \(-0.0727750\pi\) |
−0.683267 | + | 0.730168i | \(0.739442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.0000 | + | 38.1051i | −0.00950311 | + | 0.0164599i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −315.000 | −0.131532 | −0.0657659 | − | 0.997835i | \(-0.520949\pi\) | ||||
−0.0657659 | + | 0.997835i | \(0.520949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2800.00 | −1.14985 | −0.574924 | − | 0.818207i | \(-0.694968\pi\) | ||||
−0.574924 | + | 0.818207i | \(0.694968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1737.00 | + | 3008.57i | −0.690307 | + | 1.19565i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2268.00 | − | 3928.29i | −0.886912 | − | 1.53618i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1638.00 | + | 2837.10i | 0.620532 | + | 1.07479i | 0.989387 | + | 0.145305i | \(0.0464164\pi\) |
−0.368855 | + | 0.929487i | \(0.620250\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1610.50 | + | 2789.47i | −0.600655 | + | 1.04036i | 0.392068 | + | 0.919936i | \(0.371760\pi\) |
−0.992722 | + | 0.120428i | \(0.961573\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3339.00 | 1.20758 | 0.603792 | − | 0.797142i | \(-0.293656\pi\) | ||||
0.603792 | + | 0.797142i | \(0.293656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3689.00 | 1.31410 | 0.657051 | − | 0.753846i | \(-0.271804\pi\) | ||||
0.657051 | + | 0.753846i | \(0.271804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −63.0000 | + | 109.119i | −0.0217819 | + | 0.0377274i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2025.00 | + | 3507.40i | 0.689913 | + | 1.19496i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3087.00 | − | 5346.84i | −1.02169 | − | 1.76961i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3011.00 | − | 5215.20i | 0.982397 | − | 1.70156i | 0.329421 | − | 0.944183i | \(-0.393146\pi\) |
0.652976 | − | 0.757379i | \(-0.273520\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −306.000 | −0.0970652 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 259.000 | 0.0810233 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1008.00 | − | 1745.91i | 0.306812 | − | 0.531414i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 476.000 | + | 824.456i | 0.142939 | + | 0.247577i | 0.928602 | − | 0.371077i | \(-0.121012\pi\) |
−0.785663 | + | 0.618654i | \(0.787678\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2646.00 | − | 4583.01i | −0.773662 | − | 1.34002i | −0.935544 | − | 0.353211i | \(-0.885090\pi\) |
0.161882 | − | 0.986810i | \(-0.448244\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1099.00 | + | 1903.52i | −0.317135 | + | 0.549294i | −0.979889 | − | 0.199543i | \(-0.936054\pi\) |
0.662754 | + | 0.748837i | \(0.269388\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5166.00 | 1.45251 | 0.726257 | − | 0.687423i | \(-0.241258\pi\) | ||||
0.726257 | + | 0.687423i | \(0.241258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −486.000 | −0.134907 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1701.00 | + | 2946.22i | −0.460370 | + | 0.797385i | −0.998979 | − | 0.0451709i | \(-0.985617\pi\) |
0.538609 | + | 0.842556i | \(0.318950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −931.000 | − | 1612.54i | −0.248842 | − | 0.431007i | 0.714363 | − | 0.699776i | \(-0.246717\pi\) |
−0.963205 | + | 0.268768i | \(0.913383\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1539.00 | + | 2665.63i | 0.401319 | + | 0.695105i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1372.00 | − | 2376.37i | 0.353434 | − | 0.612166i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5472.00 | −1.37605 | −0.688027 | − | 0.725685i | \(-0.741523\pi\) | ||||
−0.688027 | + | 0.725685i | \(0.741523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7938.00 | 1.97256 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2646.00 | + | 4583.01i | −0.642229 | + | 1.11237i | 0.342705 | + | 0.939443i | \(0.388657\pi\) |
−0.984934 | + | 0.172931i | \(0.944676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 193.000 | + | 334.286i | 0.0463028 | + | 0.0801989i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −819.000 | − | 1418.55i | −0.192022 | − | 0.332591i | 0.753898 | − | 0.656991i | \(-0.228171\pi\) |
−0.945920 | + | 0.324400i | \(0.894838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3118.50 | − | 5401.40i | 0.722898 | − | 1.25210i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1206.00 | −0.273350 | −0.136675 | − | 0.990616i | \(-0.543642\pi\) | ||||
−0.136675 | + | 0.990616i | \(0.543642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4319.00 | 0.968120 | 0.484060 | − | 0.875035i | \(-0.339162\pi\) | ||||
0.484060 | + | 0.875035i | \(0.339162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1386.00 | − | 2400.62i | 0.303923 | − | 0.526411i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1124.00 | + | 1946.83i | 0.243807 | + | 0.422287i | 0.961796 | − | 0.273769i | \(-0.0882702\pi\) |
−0.717988 | + | 0.696055i | \(0.754937\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1008.00 | + | 1745.91i | 0.213994 | + | 0.370648i | 0.952961 | − | 0.303094i | \(-0.0980195\pi\) |
−0.738967 | + | 0.673742i | \(0.764686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1169.00 | − | 2024.77i | 0.245547 | − | 0.425300i | −0.716738 | − | 0.697342i | \(-0.754366\pi\) |
0.962285 | + | 0.272042i | \(0.0876991\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 450.000 | 0.0925528 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 271.000 | 0.0551598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4257.00 | − | 7373.34i | 0.848794 | − | 1.47015i | −0.0334915 | − | 0.999439i | \(-0.510663\pi\) |
0.882285 | − | 0.470715i | \(-0.156004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −810.000 | − | 1402.96i | −0.159864 | − | 0.276893i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1764.00 | + | 3055.34i | 0.341186 | + | 0.590952i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0000 | + | 29.4449i | −0.00325536 | + | 0.00563845i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2520.00 | −0.473098 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6104.00 | 1.13477 | 0.567384 | − | 0.823453i | \(-0.307956\pi\) | ||||
0.567384 | + | 0.823453i | \(0.307956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2169.00 | − | 3756.82i | 0.395475 | − | 0.684983i | −0.597687 | − | 0.801730i | \(-0.703913\pi\) |
0.993162 | + | 0.116747i | \(0.0372467\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4077.50 | + | 7062.44i | 0.736338 | + | 1.27538i | 0.954134 | + | 0.299381i | \(0.0967802\pi\) |
−0.217795 | + | 0.975994i | \(0.569886\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2488.50 | + | 4310.21i | 0.440909 | + | 0.763676i | 0.997757 | − | 0.0669378i | \(-0.0213229\pi\) |
−0.556848 | + | 0.830614i | \(0.687990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3969.00 | − | 6874.51i | 0.696619 | − | 1.20658i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7056.00 | 1.21550 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1232.00 | 0.210274 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.0000 | + | 46.7654i | −0.00452449 | + | 0.00783665i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2839.00 | − | 4917.29i | −0.471437 | − | 0.816552i | 0.528029 | − | 0.849226i | \(-0.322931\pi\) |
−0.999466 | + | 0.0326738i | \(0.989598\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2637.00 | + | 4567.42i | 0.430074 | + | 0.744910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1453.00 | + | 2516.67i | −0.234866 | + | 0.406800i | −0.959234 | − | 0.282614i | \(-0.908799\pi\) |
0.724367 | + | 0.689414i | \(0.242132\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16317.0 | −2.59125 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 685.000 | 0.107832 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3496.50 | + | 6056.12i | −0.540928 | + | 0.936914i | 0.457923 | + | 0.888992i | \(0.348593\pi\) |
−0.998851 | + | 0.0479227i | \(0.984740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3955.00 | − | 6850.26i | −0.606608 | − | 1.05068i | −0.991795 | − | 0.127838i | \(-0.959196\pi\) |
0.385187 | − | 0.922839i | \(-0.374137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1233.00 | − | 2135.62i | −0.185909 | − | 0.322004i | 0.757973 | − | 0.652286i | \(-0.226190\pi\) |
−0.943883 | + | 0.330281i | \(0.892856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2268.00 | + | 3928.29i | −0.339079 | + | 0.587302i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7182.00 | 1.05585 | 0.527927 | − | 0.849290i | \(-0.322970\pi\) | ||||
0.527927 | + | 0.849290i | \(0.322970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2745.00 | 0.400204 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −724.500 | + | 1254.87i | −0.103896 | + | 0.179953i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5715.50 | + | 9899.54i | 0.812934 | + | 1.40804i | 0.910802 | + | 0.412843i | \(0.135464\pi\) |
−0.0978684 | + | 0.995199i | \(0.531202\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −346.500 | − | 600.156i | −0.0484889 | − | 0.0839852i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3308.00 | − | 5729.62i | 0.459200 | − | 0.795358i | −0.539718 | − | 0.841846i | \(-0.681469\pi\) |
0.998919 | + | 0.0464871i | \(0.0148027\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3528.00 | 0.481966 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9820.00 | −1.33092 | −0.665461 | − | 0.746433i | \(-0.731765\pi\) | ||||
−0.665461 | + | 0.746433i | \(0.731765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −720.000 | + | 1247.08i | −0.0960582 | + | 0.166378i | −0.910050 | − | 0.414499i | \(-0.863957\pi\) |
0.813992 | + | 0.580877i | \(0.197290\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 283.500 | + | 491.036i | 0.0375286 | + | 0.0650014i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2992.50 | − | 5183.16i | −0.390041 | − | 0.675570i | 0.602414 | − | 0.798184i | \(-0.294206\pi\) |
−0.992454 | + | 0.122614i | \(0.960872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4536.00 | + | 7856.58i | −0.586689 | + | 1.01618i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3960.00 | 0.504428 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11284.0 | −1.42652 | −0.713259 | − | 0.700900i | \(-0.752782\pi\) | ||||
−0.713259 | + | 0.700900i | \(0.752782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3654.00 | − | 6328.91i | 0.455043 | − | 0.788157i | −0.543648 | − | 0.839313i | \(-0.682957\pi\) |
0.998691 | + | 0.0511565i | \(0.0162907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3626.00 | − | 6280.42i | −0.448198 | − | 0.776302i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12159.0 | − | 21060.0i | −1.48083 | − | 2.56488i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3167.50 | + | 5486.27i | −0.382941 | + | 0.663273i | −0.991481 | − | 0.130250i | \(-0.958422\pi\) |
0.608540 | + | 0.793523i | \(0.291755\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −180.000 | −0.0214461 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8991.00 | 1.06350 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3186.00 | + | 5518.31i | −0.371471 | + | 0.643406i | −0.989792 | − | 0.142519i | \(-0.954480\pi\) |
0.618321 | + | 0.785926i | \(0.287813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1660.00 | − | 2875.20i | −0.192170 | − | 0.332848i | 0.753799 | − | 0.657105i | \(-0.228219\pi\) |
−0.945969 | + | 0.324257i | \(0.894886\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1584.00 | + | 2743.57i | 0.180789 | + | 0.313136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −140.000 | + | 242.487i | −0.0158667 | + | 0.0274819i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2898.00 | −0.323879 | −0.161939 | − | 0.986801i | \(-0.551775\pi\) | ||||
−0.161939 | + | 0.986801i | \(0.551775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4291.00 | −0.476241 | −0.238120 | − | 0.971236i | \(-0.576531\pi\) | ||||
−0.238120 | + | 0.971236i | \(0.576531\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6174.00 | + | 10693.7i | −0.675841 | + | 1.17059i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4161.50 | + | 7207.93i | 0.452432 | + | 0.783635i | 0.998536 | − | 0.0540821i | \(-0.0172233\pi\) |
−0.546105 | + | 0.837717i | \(0.683890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1890.00 | + | 3273.58i | 0.202701 | + | 0.351089i | 0.949398 | − | 0.314076i | \(-0.101695\pi\) |
−0.746697 | + | 0.665165i | \(0.768361\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3969.00 | + | 6874.51i | −0.422806 | + | 0.732321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12474.0 | 1.31110 | 0.655551 | − | 0.755151i | \(-0.272437\pi\) | ||||
0.655551 | + | 0.755151i | \(0.272437\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28350.0 | −2.95998 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −126.000 | + | 218.238i | −0.0129824 | + | 0.0224861i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8339.50 | − | 14444.4i | −0.853622 | − | 1.47852i | −0.877917 | − | 0.478812i | \(-0.841067\pi\) |
0.0242951 | − | 0.999705i | \(-0.492266\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8635.50 | + | 14957.1i | 0.872441 | + | 1.51111i | 0.859464 | + | 0.511196i | \(0.170798\pi\) |
0.0129772 | + | 0.999916i | \(0.495869\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8693.50 | + | 15057.6i | −0.872616 | + | 1.51142i | −0.0133352 | + | 0.999911i | \(0.504245\pi\) |
−0.859281 | + | 0.511504i | \(0.829088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3087.00 | 0.305887 | 0.152944 | − | 0.988235i | \(-0.451125\pi\) | ||||
0.152944 | + | 0.988235i | \(0.451125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 586.000 | 0.0576950 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1071.00 | − | 1855.03i | 0.104111 | − | 0.180326i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2156.00 | + | 3734.30i | 0.208261 | + | 0.360719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2619.00 | + | 4536.24i | 0.249823 | + | 0.432706i | 0.963477 | − | 0.267793i | \(-0.0862943\pi\) |
−0.713654 | + | 0.700499i | \(0.752961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5404.00 | − | 9360.00i | 0.512269 | − | 0.887275i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6489.00 | −0.607526 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4384.00 | −0.407922 | −0.203961 | − | 0.978979i | \(-0.565382\pi\) | ||||
−0.203961 | + | 0.978979i | \(0.565382\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1921.50 | − | 3328.14i | 0.176611 | − | 0.305900i | −0.764107 | − | 0.645090i | \(-0.776820\pi\) |
0.940718 | + | 0.339191i | \(0.110153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4536.00 | + | 7856.58i | 0.414384 | + | 0.717734i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 252.000 | + | 436.477i | 0.0227440 | + | 0.0393937i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6283.00 | + | 10882.5i | −0.563659 | + | 0.976286i | 0.433514 | + | 0.901147i | \(0.357273\pi\) |
−0.997173 | + | 0.0751389i | \(0.976060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5238.00 | −0.464316 | −0.232158 | − | 0.972678i | \(-0.574579\pi\) | ||||
−0.232158 | + | 0.972678i | \(0.574579\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3969.00 | −0.349739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3154.50 | − | 5463.75i | 0.274697 | − | 0.475789i | −0.695362 | − | 0.718660i | \(-0.744756\pi\) |
0.970059 | + | 0.242871i | \(0.0780891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 80.5000 | + | 139.430i | 0.00696890 | + | 0.0120705i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2394.00 | + | 4146.53i | 0.204839 | + | 0.354792i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1701.00 | − | 2946.22i | 0.144700 | − | 0.250628i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5868.00 | −0.493439 | −0.246720 | − | 0.969087i | \(-0.579353\pi\) | ||||
−0.246720 | + | 0.969087i | \(0.579353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6776.00 | 0.566527 | 0.283264 | − | 0.959042i | \(-0.408583\pi\) | ||||
0.283264 | + | 0.959042i | \(0.408583\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9324.00 | − | 16149.6i | 0.770702 | − | 1.33489i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1854.50 | − | 3212.09i | −0.152420 | − | 0.264000i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6300.00 | − | 10911.9i | −0.511976 | − | 0.886769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3685.50 | + | 6383.47i | −0.297828 | + | 0.515853i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21546.0 | −1.72180 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9388.00 | −0.746066 | −0.373033 | − | 0.927818i | \(-0.621682\pi\) | ||||
−0.373033 | + | 0.927818i | \(0.621682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5823.00 | − | 10085.7i | 0.457670 | − | 0.792707i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7528.00 | − | 13038.9i | −0.588435 | − | 1.01920i | −0.994438 | − | 0.105328i | \(-0.966411\pi\) |
0.406002 | − | 0.913872i | \(-0.366922\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6174.00 | + | 10693.7i | 0.477353 | + | 0.826799i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 220.000 | − | 381.051i | 0.0169175 | − | 0.0293019i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16569.0 | 1.26041 | 0.630207 | − | 0.776427i | \(-0.282970\pi\) | ||||
0.630207 | + | 0.776427i | \(0.282970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 952.000 | 0.0720310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7276.50 | + | 12603.3i | −0.544703 | + | 0.943454i | 0.453922 | + | 0.891041i | \(0.350024\pi\) |
−0.998626 | + | 0.0524124i | \(0.983309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5103.00 | − | 8838.66i | −0.379973 | − | 0.658133i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2142.00 | − | 3710.05i | −0.157816 | − | 0.273345i | 0.776265 | − | 0.630407i | \(-0.217112\pi\) |
−0.934081 | + | 0.357062i | \(0.883779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −346.000 | + | 599.290i | −0.0253584 | + | 0.0439220i | −0.878426 | − | 0.477878i | \(-0.841406\pi\) |
0.853068 | + | 0.521800i | \(0.174739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5544.00 | −0.402088 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4886.00 | 0.352525 | 0.176262 | − | 0.984343i | \(-0.443599\pi\) | ||||
0.176262 | + | 0.984343i | \(0.443599\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 499.500 | − | 865.159i | 0.0356674 | − | 0.0617777i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21829.5 | + | 37809.8i | 1.55075 | + | 2.68597i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5512.50 | + | 9547.93i | 0.387607 | + | 0.671355i | 0.992127 | − | 0.125235i | \(-0.0399685\pi\) |
−0.604520 | + | 0.796590i | \(0.706635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12691.0 | − | 21981.5i | 0.887816 | − | 1.53774i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14562.0 | −1.00841 | −0.504207 | − | 0.863583i | \(-0.668215\pi\) | ||||
−0.504207 | + | 0.863583i | \(0.668215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −648.000 | −0.0446477 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5733.00 | + | 9929.85i | −0.391058 | + | 0.677333i | −0.992589 | − | 0.121516i | \(-0.961224\pi\) |
0.601531 | + | 0.798849i | \(0.294558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5477.50 | − | 9487.31i | −0.371767 | − | 0.643919i | 0.618071 | − | 0.786123i | \(-0.287915\pi\) |
−0.989837 | + | 0.142204i | \(0.954581\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11871.0 | − | 20561.2i | −0.797727 | − | 1.38170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −616.000 | + | 1066.94i | −0.0411906 | + | 0.0713441i | −0.885886 | − | 0.463904i | \(-0.846448\pi\) |
0.844695 | + | 0.535248i | \(0.179782\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1512.00 | 0.100113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25622.0 | 1.68819 | 0.844097 | − | 0.536191i | \(-0.180137\pi\) | ||||
0.844097 | + | 0.536191i | \(0.180137\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10521.0 | + | 18222.9i | −0.686482 | + | 1.18902i | 0.286486 | + | 0.958084i | \(0.407513\pi\) |
−0.972969 | + | 0.230938i | \(0.925821\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3262.00 | − | 5649.95i | −0.211811 | − | 0.366867i | 0.740471 | − | 0.672089i | \(-0.234603\pi\) |
−0.952281 | + | 0.305222i | \(0.901269\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 441.000 | + | 763.834i | 0.0283600 | + | 0.0491210i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4094.50 | − | 7091.88i | 0.262048 | − | 0.453880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27792.0 | 1.76175 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20663.0 | 1.30361 | 0.651807 | − | 0.758384i | \(-0.274011\pi\) | ||||
0.651807 | + | 0.758384i | \(0.274011\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8131.50 | − | 14084.2i | 0.508171 | − | 0.880178i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4788.00 | − | 8293.06i | −0.297814 | − | 0.515829i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 441.000 | + | 763.834i | 0.0271739 | + | 0.0470665i | 0.879293 | − | 0.476282i | \(-0.158016\pi\) |
−0.852119 | + | 0.523349i | \(0.824683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3626.00 | − | 6280.42i | 0.222388 | − | 0.385187i | −0.733145 | − | 0.680073i | \(-0.761948\pi\) |
0.955533 | + | 0.294885i | \(0.0952815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21168.0 | 1.28624 | 0.643122 | − | 0.765764i | \(-0.277639\pi\) | ||||
0.643122 | + | 0.765764i | \(0.277639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11340.0 | 0.685877 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7150.50 | + | 12385.0i | −0.428516 | + | 0.742211i | −0.996742 | − | 0.0806618i | \(-0.974297\pi\) |
0.568226 | + | 0.822873i | \(0.307630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9922.50 | + | 17186.3i | 0.591915 | + | 1.02523i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7528.50 | − | 13039.7i | −0.445021 | − | 0.770799i | 0.553033 | − | 0.833159i | \(-0.313470\pi\) |
−0.998054 | + | 0.0623608i | \(0.980137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2345.00 | − | 4061.66i | 0.137988 | − | 0.239002i | −0.788747 | − | 0.614718i | \(-0.789270\pi\) |
0.926735 | + | 0.375716i | \(0.122603\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −882.000 | −0.0514323 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15876.0 | −0.921621 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8820.00 | − | 15276.7i | 0.507440 | − | 0.878912i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2601.50 | + | 4505.93i | 0.149005 | + | 0.258084i | 0.930860 | − | 0.365376i | \(-0.119060\pi\) |
−0.781855 | + | 0.623460i | \(0.785726\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3087.00 | − | 5346.84i | −0.175248 | − | 0.303539i | 0.764999 | − | 0.644032i | \(-0.222739\pi\) |
−0.940247 | + | 0.340493i | \(0.889406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −360.500 | + | 624.404i | −0.0203751 | + | 0.0352908i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 756.000 | 0.0423536 | 0.0211768 | − | 0.999776i | \(-0.493259\pi\) | ||||
0.0211768 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12474.0 | 0.695777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9702.00 | + | 16804.4i | −0.536454 | + | 0.929165i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8974.00 | − | 15543.4i | −0.494048 | − | 0.855716i | 0.505929 | − | 0.862575i | \(-0.331150\pi\) |
−0.999976 | + | 0.00685939i | \(0.997817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2142.00 | − | 3710.05i | −0.116907 | − | 0.202490i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16200.0 | − | 28059.2i | 0.880371 | − | 1.52485i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34083.0 | 1.83637 | 0.918186 | − | 0.396149i | \(-0.129654\pi\) | ||||
0.918186 | + | 0.396149i | \(0.129654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37828.0 | 2.02946 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −220.500 | + | 381.917i | −0.0117295 | + | 0.0203161i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2642.00 | + | 4576.08i | 0.139947 | + | 0.242395i | 0.927476 | − | 0.373882i | \(-0.121973\pi\) |
−0.787529 | + | 0.616277i | \(0.788640\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16317.0 | + | 28261.9i | 0.857050 | + | 1.48445i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7938.00 | − | 13749.0i | 0.415195 | − | 0.719139i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24516.0 | −1.27162 | −0.635808 | − | 0.771847i | \(-0.719333\pi\) | ||||
−0.635808 | + | 0.771847i | \(0.719333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 532.000 | 0.0274795 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2772.00 | + | 4801.24i | −0.141999 | + | 0.245950i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6240.50 | + | 10808.9i | 0.318359 | + | 0.551415i | 0.980146 | − | 0.198278i | \(-0.0635348\pi\) |
−0.661786 | + | 0.749692i | \(0.730201\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1224.00 | + | 2120.03i | 0.0619306 | + | 0.107267i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1547.00 | − | 2679.48i | 0.0779533 | − | 0.135019i | −0.824413 | − | 0.565988i | \(-0.808495\pi\) |
0.902367 | + | 0.430969i | \(0.141828\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36918.0 | −1.84517 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −376.000 | −0.0187164 | −0.00935818 | − | 0.999956i | \(-0.502979\pi\) | ||||
−0.00935818 | + | 0.999956i | \(0.502979\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14742.0 | + | 25533.9i | −0.727902 | + | 1.26076i | 0.229866 | + | 0.973222i | \(0.426171\pi\) |
−0.957768 | + | 0.287542i | \(0.907162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7087.50 | + | 12275.9i | 0.348545 | + | 0.603697i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 409.500 | + | 709.275i | 0.0199770 | + | 0.0346013i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5840.50 | + | 10116.0i | −0.283785 | + | 0.491531i | −0.972314 | − | 0.233678i | \(-0.924924\pi\) |
0.688528 | + | 0.725209i | \(0.258257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4041.00 | 0.194791 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 890.000 | 0.0427313 | 0.0213657 | − | 0.999772i | \(-0.493199\pi\) | ||||
0.0213657 | + | 0.999772i | \(0.493199\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16416.0 | − | 28433.3i | 0.781970 | − | 1.35441i | −0.148822 | − | 0.988864i | \(-0.547548\pi\) |
0.930792 | − | 0.365549i | \(-0.119119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −647.000 | − | 1120.64i | −0.0306985 | − | 0.0531714i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2520.00 | + | 4364.77i | 0.118634 | + | 0.205479i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1592.50 | + | 2758.29i | −0.0746775 | + | 0.129345i | −0.900946 | − | 0.433931i | \(-0.857126\pi\) |
0.826268 | + | 0.563277i | \(0.190459\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21222.0 | −0.987454 | −0.493727 | − | 0.869617i | \(-0.664366\pi\) | ||||
−0.493727 | + | 0.869617i | \(0.664366\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11396.0 | 0.528202 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22050.0 | − | 38191.7i | 1.01415 | − | 1.75656i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15876.0 | − | 27498.0i | −0.727385 | − | 1.25987i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8190.00 | − | 14185.5i | −0.372374 | − | 0.644971i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6160.00 | + | 10669.4i | −0.279009 | + | 0.483258i | −0.971139 | − | 0.238515i | \(-0.923339\pi\) |
0.692130 | + | 0.721773i | \(0.256673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1134.00 | −0.0509740 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7840.00 | 0.351080 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5953.50 | − | 10311.8i | 0.264597 | − | 0.458295i | −0.702861 | − | 0.711327i | \(-0.748094\pi\) |
0.967458 | + | 0.253032i | \(0.0814277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1944.00 | + | 3367.11i | 0.0860748 | + | 0.149086i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5071.50 | − | 8784.10i | −0.222876 | − | 0.386032i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 567.000 | − | 982.073i | 0.0248250 | − | 0.0429982i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14994.0 | −0.651620 | −0.325810 | − | 0.945435i | \(-0.605637\pi\) | ||||
−0.325810 | + | 0.945435i | \(0.605637\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38878.0 | −1.68334 | −0.841672 | − | 0.539990i | \(-0.818428\pi\) | ||||
−0.841672 | + | 0.539990i | \(0.818428\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8226.00 | − | 14247.8i | 0.353551 | − | 0.612369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1666.00 | + | 2885.60i | 0.0713414 | + | 0.123567i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1953.00 | − | 3382.70i | −0.0830209 | − | 0.143796i | 0.821525 | − | 0.570172i | \(-0.193123\pi\) |
−0.904546 | + | 0.426376i | \(0.859790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5103.50 | − | 8839.52i | 0.216157 | − | 0.374394i | −0.737473 | − | 0.675376i | \(-0.763981\pi\) |
0.953630 | + | 0.300982i | \(0.0973145\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8064.00 | 0.339072 | 0.169536 | − | 0.985524i | \(-0.445773\pi\) | ||||
0.169536 | + | 0.985524i | \(0.445773\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10486.0 | −0.439317 | −0.219659 | − | 0.975577i | \(-0.570494\pi\) | ||||
−0.219659 | + | 0.975577i | \(0.570494\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12312.0 | − | 21325.0i | 0.512107 | − | 0.886996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3645.00 | + | 6313.33i | 0.151066 | + | 0.261655i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16848.0 | + | 29181.6i | 0.693275 | + | 1.20079i | 0.970759 | + | 0.240057i | \(0.0771661\pi\) |
−0.277484 | + | 0.960730i | \(0.589501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4256.50 | − | 7372.47i | 0.174525 | − | 0.302287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12717.0 | −0.517726 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2638.00 | −0.107016 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24318.0 | + | 42120.0i | −0.979566 | + | 1.69666i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7889.00 | + | 13664.1i | 0.316664 | + | 0.548478i | 0.979790 | − | 0.200030i | \(-0.0641040\pi\) |
−0.663126 | + | 0.748508i | \(0.730771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13068.0 | + | 22634.4i | 0.520880 | + | 0.902191i | 0.999705 | + | 0.0242807i | \(0.00772953\pi\) |
−0.478825 | + | 0.877910i | \(0.658937\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11956.0 | + | 20708.4i | −0.474893 | + | 0.822540i | −0.999587 | − | 0.0287519i | \(-0.990847\pi\) |
0.524693 | + | 0.851291i | \(0.324180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17892.0 | 0.705737 | 0.352868 | − | 0.935673i | \(-0.385206\pi\) | ||||
0.352868 | + | 0.935673i | \(0.385206\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11907.0 | −0.468035 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13860.0 | + | 24006.2i | −0.541045 | + | 0.937118i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8204.00 | − | 14209.7i | −0.319153 | − | 0.552789i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −760.500 | − | 1317.22i | −0.0293824 | − | 0.0508918i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22081.0 | + | 38245.4i | −0.850197 | + | 1.47258i | 0.0308341 | + | 0.999525i | \(0.490184\pi\) |
−0.881031 | + | 0.473059i | \(0.843150\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8820.00 | −0.337291 | −0.168645 | − | 0.985677i | \(-0.553939\pi\) | ||||
−0.168645 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4654.00 | −0.177372 | −0.0886861 | − | 0.996060i | \(-0.528267\pi\) | ||||
−0.0886861 | + | 0.996060i | \(0.528267\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16542.0 | + | 28651.6i | −0.626185 | + | 1.08458i | 0.362126 | + | 0.932129i | \(0.382051\pi\) |
−0.988310 | + | 0.152455i | \(0.951282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −903.500 | − | 1564.91i | −0.0340860 | − | 0.0590386i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2646.00 | + | 4583.01i | 0.0991546 | + | 0.171741i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1417.50 | − | 2455.18i | 0.0529406 | − | 0.0916957i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32634.0 | 1.21068 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49896.0 | −1.84492 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12600.0 | − | 21823.8i | 0.462805 | − | 0.801601i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23629.0 | − | 40926.6i | −0.865036 | − | 1.49829i | −0.867011 | − | 0.498289i | \(-0.833962\pi\) |
0.00197452 | − | 0.999998i | \(-0.499371\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18333.0 | − | 31753.7i | −0.666739 | − | 1.15483i | −0.978811 | − | 0.204767i | \(-0.934356\pi\) |
0.312071 | − | 0.950059i | \(-0.398977\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31468.5 | + | 54505.0i | −1.14070 | + | 1.97574i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2205.00 | 0.0794062 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2995.00 | −0.107504 | −0.0537519 | − | 0.998554i | \(-0.517118\pi\) | ||||
−0.0537519 | + | 0.998554i | \(0.517118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7056.00 | − | 12221.4i | 0.251626 | − | 0.435830i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8492.00 | + | 14708.6i | 0.301854 | + | 0.522827i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6642.00 | + | 11504.3i | 0.234572 | + | 0.406290i | 0.959148 | − | 0.282905i | \(-0.0912980\pi\) |
−0.724577 | + | 0.689194i | \(0.757965\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16758.0 | − | 29025.7i | 0.589926 | − | 1.02178i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40824.0 | 1.42790 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2989.00 | −0.104212 | −0.0521059 | − | 0.998642i | \(-0.516593\pi\) | ||||
−0.0521059 | + | 0.998642i | \(0.516593\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23242.5 | + | 40257.2i | −0.805190 | + | 1.39463i | 0.110973 | + | 0.993823i | \(0.464603\pi\) |
−0.916163 | + | 0.400807i | \(0.868730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28350.0 | + | 49103.6i | 0.979006 | + | 1.69569i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5764.50 | − | 9984.41i | −0.197805 | − | 0.342608i | 0.750012 | − | 0.661425i | \(-0.230048\pi\) |
−0.947816 | + | 0.318817i | \(0.896715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2254.00 | − | 3904.04i | 0.0771000 | − | 0.133541i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37044.0 | 1.25915 | 0.629577 | − | 0.776938i | \(-0.283228\pi\) | ||||
0.629577 | + | 0.776938i | \(0.283228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29484.0 | −0.999036 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 693.000 | − | 1200.31i | 0.0233349 | − | 0.0404172i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18645.0 | − | 32294.1i | −0.625860 | − | 1.08402i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14494.5 | − | 25105.2i | −0.483518 | − | 0.837477i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6227.50 | + | 10786.3i | −0.207097 | + | 0.358703i | −0.950799 | − | 0.309809i | \(-0.899735\pi\) |
0.743702 | + | 0.668512i | \(0.233068\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20169.0 | −0.666585 | −0.333292 | − | 0.942823i | \(-0.608160\pi\) | ||||
−0.333292 | + | 0.942823i | \(0.608160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −476.000 | −0.0156833 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19971.0 | − | 34590.8i | 0.653970 | − | 1.13271i | −0.328181 | − | 0.944615i | \(-0.606435\pi\) |
0.982151 | − | 0.188095i | \(-0.0602312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27783.0 | − | 48121.6i | −0.906995 | − | 1.57096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27117.0 | − | 46968.0i | −0.879856 | − | 1.52395i | −0.851499 | − | 0.524357i | \(-0.824306\pi\) |
−0.0283568 | − | 0.999598i | \(-0.509027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15025.5 | + | 26024.9i | −0.486043 | + | 0.841851i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4284.00 | −0.137738 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26137.0 | −0.837809 | −0.418905 | − | 0.908030i | \(-0.637586\pi\) | ||||
−0.418905 | + | 0.908030i | \(0.637586\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16600.5 | + | 28752.9i | −0.528916 | + | 0.916109i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16730.0 | + | 28977.2i | 0.531439 | + | 0.920479i | 0.999327 | + | 0.0366911i | \(0.0116818\pi\) |
−0.467888 | + | 0.883788i | \(0.654985\pi\) | |||||||
\(998\) | 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 | 324.4.e.b.109.1 | 2 | ||
3.2 | odd | 2 | 324.4.e.g.109.1 | 2 | |||
9.2 | odd | 6 | 324.4.e.g.217.1 | 2 | |||
9.4 | even | 3 | 108.4.a.d.1.1 | yes | 1 | ||
9.5 | odd | 6 | 108.4.a.a.1.1 | ✓ | 1 | ||
9.7 | even | 3 | inner | 324.4.e.b.217.1 | 2 | ||
36.23 | even | 6 | 432.4.a.c.1.1 | 1 | |||
36.31 | odd | 6 | 432.4.a.l.1.1 | 1 | |||
72.5 | odd | 6 | 1728.4.a.y.1.1 | 1 | |||
72.13 | even | 6 | 1728.4.a.g.1.1 | 1 | |||
72.59 | even | 6 | 1728.4.a.z.1.1 | 1 | |||
72.67 | odd | 6 | 1728.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.a.a.1.1 | ✓ | 1 | 9.5 | odd | 6 | ||
108.4.a.d.1.1 | yes | 1 | 9.4 | even | 3 | ||
324.4.e.b.109.1 | 2 | 1.1 | even | 1 | trivial | ||
324.4.e.b.217.1 | 2 | 9.7 | even | 3 | inner | ||
324.4.e.g.109.1 | 2 | 3.2 | odd | 2 | |||
324.4.e.g.217.1 | 2 | 9.2 | odd | 6 | |||
432.4.a.c.1.1 | 1 | 36.23 | even | 6 | |||
432.4.a.l.1.1 | 1 | 36.31 | odd | 6 | |||
1728.4.a.g.1.1 | 1 | 72.13 | even | 6 | |||
1728.4.a.h.1.1 | 1 | 72.67 | odd | 6 | |||
1728.4.a.y.1.1 | 1 | 72.5 | odd | 6 | |||
1728.4.a.z.1.1 | 1 | 72.59 | even | 6 |