Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,4,Mod(199,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.c (of order \(2\), degree \(1\), 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: | \(26.5508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.199 |
Dual form | 450.4.c.k.199.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 32.0000i | − 1.72784i | −0.503631 | − | 0.863919i | \(-0.668003\pi\) | ||||
0.503631 | − | 0.863919i | \(-0.331997\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.0000 | 1.64461 | 0.822304 | − | 0.569049i | \(-0.192689\pi\) | ||||
0.822304 | + | 0.569049i | \(0.192689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 34.0000i | − 0.725377i | −0.931910 | − | 0.362689i | \(-0.881859\pi\) | ||||
0.931910 | − | 0.362689i | \(-0.118141\pi\) | |||||||
\(14\) | −64.0000 | −1.22177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 42.0000i | 0.599206i | 0.954064 | + | 0.299603i | \(0.0968542\pi\) | ||||
−0.954064 | + | 0.299603i | \(0.903146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76.0000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 120.000i | − 1.16291i | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −68.0000 | −0.512919 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 128.000i | 0.863919i | ||||||||
\(29\) | 6.00000 | 0.0384197 | 0.0192099 | − | 0.999815i | \(-0.493885\pi\) | ||||
0.0192099 | + | 0.999815i | \(0.493885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −232.000 | −1.34414 | −0.672071 | − | 0.740486i | \(-0.734595\pi\) | ||||
−0.672071 | + | 0.740486i | \(0.734595\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 84.0000 | 0.423702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 134.000i | − 0.595391i | −0.954661 | − | 0.297695i | \(-0.903782\pi\) | ||||
0.954661 | − | 0.297695i | \(-0.0962180\pi\) | |||||||
\(38\) | − 152.000i | − 0.648886i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −234.000 | −0.891333 | −0.445667 | − | 0.895199i | \(-0.647033\pi\) | ||||
−0.445667 | + | 0.895199i | \(0.647033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 412.000i | − 1.46115i | −0.682833 | − | 0.730575i | \(-0.739252\pi\) | ||||
0.682833 | − | 0.730575i | \(-0.260748\pi\) | |||||||
\(44\) | −240.000 | −0.822304 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 360.000i | − 1.11726i | −0.829416 | − | 0.558632i | \(-0.811326\pi\) | ||||
0.829416 | − | 0.558632i | \(-0.188674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −681.000 | −1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 136.000i | 0.362689i | ||||||||
\(53\) | − 222.000i | − 0.575359i | −0.957727 | − | 0.287680i | \(-0.907116\pi\) | ||||
0.957727 | − | 0.287680i | \(-0.0928838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 256.000 | 0.610883 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 12.0000i | − 0.0271668i | ||||||||
\(59\) | 660.000 | 1.45635 | 0.728175 | − | 0.685391i | \(-0.240369\pi\) | ||||
0.728175 | + | 0.685391i | \(0.240369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −490.000 | −1.02849 | −0.514246 | − | 0.857642i | \(-0.671928\pi\) | ||||
−0.514246 | + | 0.857642i | \(0.671928\pi\) | |||||||
\(62\) | 464.000i | 0.950453i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 812.000i | − 1.48062i | −0.672265 | − | 0.740310i | \(-0.734679\pi\) | ||||
0.672265 | − | 0.740310i | \(-0.265321\pi\) | |||||||
\(68\) | − 168.000i | − 0.299603i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.000 | −0.200583 | −0.100291 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 746.000i | 1.19606i | 0.801472 | + | 0.598032i | \(0.204051\pi\) | ||||
−0.801472 | + | 0.598032i | \(0.795949\pi\) | |||||||
\(74\) | −268.000 | −0.421005 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −304.000 | −0.458831 | ||||||||
\(77\) | − 1920.00i | − 2.84161i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −152.000 | −0.216473 | −0.108236 | − | 0.994125i | \(-0.534520\pi\) | ||||
−0.108236 | + | 0.994125i | \(0.534520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 468.000i | 0.630268i | ||||||||
\(83\) | 804.000i | 1.06326i | 0.846977 | + | 0.531629i | \(0.178420\pi\) | ||||
−0.846977 | + | 0.531629i | \(0.821580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −824.000 | −1.03319 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 480.000i | 0.581456i | ||||||||
\(89\) | −678.000 | −0.807504 | −0.403752 | − | 0.914868i | \(-0.632294\pi\) | ||||
−0.403752 | + | 0.914868i | \(0.632294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1088.00 | −1.25333 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −720.000 | −0.790025 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 194.000i | − 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | 1362.00i | 1.40391i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −798.000 | −0.786178 | −0.393089 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393089 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1088.00i | 1.04081i | 0.853918 | + | 0.520407i | \(0.174220\pi\) | ||||
−0.853918 | + | 0.520407i | \(0.825780\pi\) | |||||||
\(104\) | 272.000 | 0.256460 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −444.000 | −0.406840 | ||||||||
\(107\) | 1716.00i | 1.55039i | 0.631721 | + | 0.775196i | \(0.282349\pi\) | ||||
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 970.000 | 0.852378 | 0.426189 | − | 0.904634i | \(-0.359856\pi\) | ||||
0.426189 | + | 0.904634i | \(0.359856\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 512.000i | − 0.431959i | ||||||||
\(113\) | − 426.000i | − 0.354643i | −0.984153 | − | 0.177322i | \(-0.943257\pi\) | ||||
0.984153 | − | 0.177322i | \(-0.0567433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −24.0000 | −0.0192099 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 1320.00i | − 1.02980i | ||||||||
\(119\) | 1344.00 | 1.03533 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 980.000i | 0.727254i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 928.000 | 0.672071 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 200.000i | − 0.139741i | −0.997556 | − | 0.0698706i | \(-0.977741\pi\) | ||||
0.997556 | − | 0.0698706i | \(-0.0222586\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −60.0000 | −0.0400170 | −0.0200085 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200085 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2432.00i | − 1.58557i | ||||||||
\(134\) | −1624.00 | −1.04696 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −336.000 | −0.211851 | ||||||||
\(137\) | 642.000i | 0.400363i | 0.979759 | + | 0.200182i | \(0.0641532\pi\) | ||||
−0.979759 | + | 0.200182i | \(0.935847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2836.00 | 1.73055 | 0.865275 | − | 0.501298i | \(-0.167144\pi\) | ||||
0.865275 | + | 0.501298i | \(0.167144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 240.000i | 0.141833i | ||||||||
\(143\) | − 2040.00i | − 1.19296i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1492.00 | 0.845745 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 536.000i | 0.297695i | ||||||||
\(149\) | −1554.00 | −0.854420 | −0.427210 | − | 0.904152i | \(-0.640504\pi\) | ||||
−0.427210 | + | 0.904152i | \(0.640504\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2272.00 | −1.22446 | −0.612228 | − | 0.790682i | \(-0.709726\pi\) | ||||
−0.612228 | + | 0.790682i | \(0.709726\pi\) | |||||||
\(152\) | 608.000i | 0.324443i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3840.00 | −2.00932 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1694.00i | − 0.861120i | −0.902562 | − | 0.430560i | \(-0.858316\pi\) | ||||
0.902562 | − | 0.430560i | \(-0.141684\pi\) | |||||||
\(158\) | 304.000i | 0.153069i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 52.0000i | − 0.0249874i | −0.999922 | − | 0.0124937i | \(-0.996023\pi\) | ||||
0.999922 | − | 0.0124937i | \(-0.00397698\pi\) | |||||||
\(164\) | 936.000 | 0.445667 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1608.00 | 0.751837 | ||||||||
\(167\) | − 1200.00i | − 0.556041i | −0.960575 | − | 0.278020i | \(-0.910322\pi\) | ||||
0.960575 | − | 0.278020i | \(-0.0896783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1041.00 | 0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1648.00i | 0.730575i | ||||||||
\(173\) | − 54.0000i | − 0.0237315i | −0.999930 | − | 0.0118657i | \(-0.996223\pi\) | ||||
0.999930 | − | 0.0118657i | \(-0.00377707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 960.000 | 0.411152 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1356.00i | 0.570992i | ||||||||
\(179\) | 876.000 | 0.365784 | 0.182892 | − | 0.983133i | \(-0.441454\pi\) | ||||
0.182892 | + | 0.983133i | \(0.441454\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3854.00 | 1.58268 | 0.791341 | − | 0.611375i | \(-0.209383\pi\) | ||||
0.791341 | + | 0.611375i | \(0.209383\pi\) | |||||||
\(182\) | 2176.00i | 0.886241i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2520.00i | 0.985458i | ||||||||
\(188\) | 1440.00i | 0.558632i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2784.00 | 1.05468 | 0.527338 | − | 0.849656i | \(-0.323190\pi\) | ||||
0.527338 | + | 0.849656i | \(0.323190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 914.000i | 0.340887i | 0.985367 | + | 0.170443i | \(0.0545200\pi\) | ||||
−0.985367 | + | 0.170443i | \(0.945480\pi\) | |||||||
\(194\) | −388.000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2724.00 | 0.992711 | ||||||||
\(197\) | − 5202.00i | − 1.88136i | −0.339300 | − | 0.940678i | \(-0.610190\pi\) | ||||
0.339300 | − | 0.940678i | \(-0.389810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3152.00 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1596.00i | 0.555912i | ||||||||
\(203\) | − 192.000i | − 0.0663830i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2176.00 | 0.735967 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 544.000i | − 0.181344i | ||||||||
\(209\) | 4560.00 | 1.50920 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 740.000 | 0.241439 | 0.120720 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120720 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(212\) | 888.000i | 0.287680i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3432.00 | 1.09629 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7424.00i | 2.32246i | ||||||||
\(218\) | − 1940.00i | − 0.602722i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1428.00 | 0.434650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 520.000i | − 0.156151i | −0.996947 | − | 0.0780757i | \(-0.975122\pi\) | ||||
0.996947 | − | 0.0780757i | \(-0.0248776\pi\) | |||||||
\(224\) | −1024.00 | −0.305441 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −852.000 | −0.250771 | ||||||||
\(227\) | 396.000i | 0.115786i | 0.998323 | + | 0.0578930i | \(0.0184382\pi\) | ||||
−0.998323 | + | 0.0578930i | \(0.981562\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1330.00 | 0.383794 | 0.191897 | − | 0.981415i | \(-0.438536\pi\) | ||||
0.191897 | + | 0.981415i | \(0.438536\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 48.0000i | 0.0135834i | ||||||||
\(233\) | − 4866.00i | − 1.36816i | −0.729405 | − | 0.684082i | \(-0.760203\pi\) | ||||
0.729405 | − | 0.684082i | \(-0.239797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2640.00 | −0.728175 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 2688.00i | − 0.732089i | ||||||||
\(239\) | −1824.00 | −0.493660 | −0.246830 | − | 0.969059i | \(-0.579389\pi\) | ||||
−0.246830 | + | 0.969059i | \(0.579389\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6482.00 | 1.73254 | 0.866270 | − | 0.499575i | \(-0.166511\pi\) | ||||
0.866270 | + | 0.499575i | \(0.166511\pi\) | |||||||
\(242\) | − 4538.00i | − 1.20543i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1960.00 | 0.514246 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2584.00i | − 0.665652i | ||||||||
\(248\) | − 1856.00i | − 0.475226i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1476.00 | −0.371172 | −0.185586 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185586 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −400.000 | −0.0988119 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4314.00i | 1.04708i | 0.852001 | + | 0.523541i | \(0.175389\pi\) | ||||
−0.852001 | + | 0.523541i | \(0.824611\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4288.00 | −1.02874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 120.000i | 0.0282963i | ||||||||
\(263\) | 5280.00i | 1.23794i | 0.785414 | + | 0.618971i | \(0.212450\pi\) | ||||
−0.785414 | + | 0.618971i | \(0.787550\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4864.00 | −1.12117 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3248.00i | 0.740310i | ||||||||
\(269\) | 5526.00 | 1.25251 | 0.626257 | − | 0.779617i | \(-0.284586\pi\) | ||||
0.626257 | + | 0.779617i | \(0.284586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2024.00 | 0.453687 | 0.226844 | − | 0.973931i | \(-0.427159\pi\) | ||||
0.226844 | + | 0.973931i | \(0.427159\pi\) | |||||||
\(272\) | 672.000i | 0.149801i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1284.00 | 0.283100 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2054.00i | − 0.445534i | −0.974872 | − | 0.222767i | \(-0.928491\pi\) | ||||
0.974872 | − | 0.222767i | \(-0.0715089\pi\) | |||||||
\(278\) | − 5672.00i | − 1.22368i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7302.00 | 1.55018 | 0.775090 | − | 0.631850i | \(-0.217704\pi\) | ||||
0.775090 | + | 0.631850i | \(0.217704\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3724.00i | − 0.782222i | −0.920344 | − | 0.391111i | \(-0.872091\pi\) | ||||
0.920344 | − | 0.391111i | \(-0.127909\pi\) | |||||||
\(284\) | 480.000 | 0.100291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4080.00 | −0.843551 | ||||||||
\(287\) | 7488.00i | 1.54008i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3149.00 | 0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 2984.00i | − 0.598032i | ||||||||
\(293\) | 7218.00i | 1.43918i | 0.694399 | + | 0.719591i | \(0.255670\pi\) | ||||
−0.694399 | + | 0.719591i | \(0.744330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1072.00 | 0.210502 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3108.00i | 0.604166i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13184.0 | −2.52463 | ||||||||
\(302\) | 4544.00i | 0.865821i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1216.00 | 0.229416 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2540.00i | − 0.472200i | −0.971729 | − | 0.236100i | \(-0.924131\pi\) | ||||
0.971729 | − | 0.236100i | \(-0.0758693\pi\) | |||||||
\(308\) | 7680.00i | 1.42081i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1560.00 | −0.284436 | −0.142218 | − | 0.989835i | \(-0.545423\pi\) | ||||
−0.142218 | + | 0.989835i | \(0.545423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 934.000i | − 0.168667i | −0.996438 | − | 0.0843335i | \(-0.973124\pi\) | ||||
0.996438 | − | 0.0843335i | \(-0.0268761\pi\) | |||||||
\(314\) | −3388.00 | −0.608904 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 608.000 | 0.108236 | ||||||||
\(317\) | − 1674.00i | − 0.296597i | −0.988943 | − | 0.148298i | \(-0.952620\pi\) | ||||
0.988943 | − | 0.148298i | \(-0.0473796\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 360.000 | 0.0631854 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3192.00i | 0.549869i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −104.000 | −0.0176688 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 1872.00i | − 0.315134i | ||||||||
\(329\) | −11520.0 | −1.93045 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3988.00 | −0.662237 | −0.331118 | − | 0.943589i | \(-0.607426\pi\) | ||||
−0.331118 | + | 0.943589i | \(0.607426\pi\) | |||||||
\(332\) | − 3216.00i | − 0.531629i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2400.00 | −0.393180 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.00000i | 0 0.000323285i | −1.00000 | 0.000161642i | \(-0.999949\pi\) | |||||
1.00000 | 0.000161642i | \(-5.14524e-5\pi\) | ||||||||
\(338\) | − 2082.00i | − 0.335047i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13920.0 | −2.21059 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10816.0i | 1.70265i | ||||||||
\(344\) | 3296.00 | 0.516594 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −108.000 | −0.0167807 | ||||||||
\(347\) | 1764.00i | 0.272901i | 0.990647 | + | 0.136450i | \(0.0435694\pi\) | ||||
−0.990647 | + | 0.136450i | \(0.956431\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4310.00 | −0.661057 | −0.330529 | − | 0.943796i | \(-0.607227\pi\) | ||||
−0.330529 | + | 0.943796i | \(0.607227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 1920.00i | − 0.290728i | ||||||||
\(353\) | − 138.000i | − 0.0208074i | −0.999946 | − | 0.0104037i | \(-0.996688\pi\) | ||||
0.999946 | − | 0.0104037i | \(-0.00331165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2712.00 | 0.403752 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 1752.00i | − 0.258648i | ||||||||
\(359\) | −11976.0 | −1.76064 | −0.880319 | − | 0.474382i | \(-0.842672\pi\) | ||||
−0.880319 | + | 0.474382i | \(0.842672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1083.00 | −0.157895 | ||||||||
\(362\) | − 7708.00i | − 1.11913i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4352.00 | 0.626667 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 9704.00i | − 1.38023i | −0.723699 | − | 0.690115i | \(-0.757560\pi\) | ||||
0.723699 | − | 0.690115i | \(-0.242440\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7104.00 | −0.994128 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8122.00i | − 1.12746i | −0.825960 | − | 0.563728i | \(-0.809367\pi\) | ||||
0.825960 | − | 0.563728i | \(-0.190633\pi\) | |||||||
\(374\) | 5040.00 | 0.696824 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2880.00 | 0.395012 | ||||||||
\(377\) | − 204.000i | − 0.0278688i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3404.00 | −0.461350 | −0.230675 | − | 0.973031i | \(-0.574093\pi\) | ||||
−0.230675 | + | 0.973031i | \(0.574093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 5568.00i | − 0.745769i | ||||||||
\(383\) | 2520.00i | 0.336204i | 0.985770 | + | 0.168102i | \(0.0537637\pi\) | ||||
−0.985770 | + | 0.168102i | \(0.946236\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1828.00 | 0.241043 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 776.000i | 0.101535i | ||||||||
\(389\) | 1566.00 | 0.204111 | 0.102056 | − | 0.994779i | \(-0.467458\pi\) | ||||
0.102056 | + | 0.994779i | \(0.467458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − 5448.00i | − 0.701953i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10404.0 | −1.33032 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4354.00i | 0.550431i | 0.961383 | + | 0.275215i | \(0.0887492\pi\) | ||||
−0.961383 | + | 0.275215i | \(0.911251\pi\) | |||||||
\(398\) | 6304.00i | 0.793947i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8046.00 | 1.00199 | 0.500995 | − | 0.865450i | \(-0.332967\pi\) | ||||
0.500995 | + | 0.865450i | \(0.332967\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7888.00i | 0.975011i | ||||||||
\(404\) | 3192.00 | 0.393089 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −384.000 | −0.0469399 | ||||||||
\(407\) | − 8040.00i | − 0.979184i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2806.00 | 0.339237 | 0.169618 | − | 0.985510i | \(-0.445747\pi\) | ||||
0.169618 | + | 0.985510i | \(0.445747\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 4352.00i | − 0.520407i | ||||||||
\(413\) | − 21120.0i | − 2.51634i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1088.00 | −0.128230 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 9120.00i | − 1.06716i | ||||||||
\(419\) | 11580.0 | 1.35017 | 0.675084 | − | 0.737741i | \(-0.264108\pi\) | ||||
0.675084 | + | 0.737741i | \(0.264108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −370.000 | −0.0428330 | −0.0214165 | − | 0.999771i | \(-0.506818\pi\) | ||||
−0.0214165 | + | 0.999771i | \(0.506818\pi\) | |||||||
\(422\) | − 1480.00i | − 0.170723i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1776.00 | 0.203420 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15680.0i | 1.77707i | ||||||||
\(428\) | − 6864.00i | − 0.775196i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5040.00 | −0.563267 | −0.281634 | − | 0.959522i | \(-0.590876\pi\) | ||||
−0.281634 | + | 0.959522i | \(0.590876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 3742.00i | − 0.415310i | −0.978202 | − | 0.207655i | \(-0.933417\pi\) | ||||
0.978202 | − | 0.207655i | \(-0.0665831\pi\) | |||||||
\(434\) | 14848.0 | 1.64223 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3880.00 | −0.426189 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6208.00 | 0.674924 | 0.337462 | − | 0.941339i | \(-0.390432\pi\) | ||||
0.337462 | + | 0.941339i | \(0.390432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 2856.00i | − 0.307344i | ||||||||
\(443\) | 15564.0i | 1.66923i | 0.550835 | + | 0.834614i | \(0.314309\pi\) | ||||
−0.550835 | + | 0.834614i | \(0.685691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1040.00 | −0.110416 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2048.00i | 0.215980i | ||||||||
\(449\) | −15774.0 | −1.65795 | −0.828977 | − | 0.559283i | \(-0.811076\pi\) | ||||
−0.828977 | + | 0.559283i | \(0.811076\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14040.0 | −1.46589 | ||||||||
\(452\) | 1704.00i | 0.177322i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 792.000 | 0.0818731 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 9722.00i | − 0.995133i | −0.867426 | − | 0.497567i | \(-0.834227\pi\) | ||||
0.867426 | − | 0.497567i | \(-0.165773\pi\) | |||||||
\(458\) | − 2660.00i | − 0.271383i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10890.0 | 1.10021 | 0.550106 | − | 0.835095i | \(-0.314587\pi\) | ||||
0.550106 | + | 0.835095i | \(0.314587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15128.0i | 1.51848i | 0.650809 | + | 0.759242i | \(0.274430\pi\) | ||||
−0.650809 | + | 0.759242i | \(0.725570\pi\) | |||||||
\(464\) | 96.0000 | 0.00960493 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9732.00 | −0.967438 | ||||||||
\(467\) | 10668.0i | 1.05708i | 0.848909 | + | 0.528540i | \(0.177260\pi\) | ||||
−0.848909 | + | 0.528540i | \(0.822740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25984.0 | −2.55827 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5280.00i | 0.514898i | ||||||||
\(473\) | − 24720.0i | − 2.40302i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5376.00 | −0.517665 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3648.00i | 0.349070i | ||||||||
\(479\) | 15264.0 | 1.45601 | 0.728006 | − | 0.685571i | \(-0.240447\pi\) | ||||
0.728006 | + | 0.685571i | \(0.240447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4556.00 | −0.431883 | ||||||||
\(482\) | − 12964.0i | − 1.22509i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9076.00 | −0.852367 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5776.00i | 0.537445i | 0.963218 | + | 0.268722i | \(0.0866014\pi\) | ||||
−0.963218 | + | 0.268722i | \(0.913399\pi\) | |||||||
\(488\) | − 3920.00i | − 0.363627i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14244.0 | −1.30921 | −0.654606 | − | 0.755971i | \(-0.727165\pi\) | ||||
−0.654606 | + | 0.755971i | \(0.727165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 252.000i | 0.0230213i | ||||||||
\(494\) | −5168.00 | −0.470687 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3712.00 | −0.336036 | ||||||||
\(497\) | 3840.00i | 0.346575i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17116.0 | 1.53551 | 0.767753 | − | 0.640746i | \(-0.221375\pi\) | ||||
0.767753 | + | 0.640746i | \(0.221375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2952.00i | 0.262459i | ||||||||
\(503\) | 16848.0i | 1.49347i | 0.665122 | + | 0.746735i | \(0.268380\pi\) | ||||
−0.665122 | + | 0.746735i | \(0.731620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 800.000i | 0.0698706i | ||||||||
\(509\) | −3834.00 | −0.333868 | −0.166934 | − | 0.985968i | \(-0.553387\pi\) | ||||
−0.166934 | + | 0.985968i | \(0.553387\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23872.0 | 2.06660 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8628.00 | 0.740398 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 21600.0i | − 1.83746i | ||||||||
\(518\) | 8576.00i | 0.727428i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18822.0 | 1.58274 | 0.791369 | − | 0.611338i | \(-0.209369\pi\) | ||||
0.791369 | + | 0.611338i | \(0.209369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 15340.0i | − 1.28255i | −0.767313 | − | 0.641273i | \(-0.778407\pi\) | ||||
0.767313 | − | 0.641273i | \(-0.221593\pi\) | |||||||
\(524\) | 240.000 | 0.0200085 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10560.0 | 0.875357 | ||||||||
\(527\) | − 9744.00i | − 0.805418i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12167.0 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9728.00i | 0.792786i | ||||||||
\(533\) | 7956.00i | 0.646553i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6496.00 | 0.523478 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 11052.0i | − 0.885661i | ||||||||
\(539\) | −40860.0 | −3.26524 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18950.0 | 1.50596 | 0.752980 | − | 0.658044i | \(-0.228616\pi\) | ||||
0.752980 | + | 0.658044i | \(0.228616\pi\) | |||||||
\(542\) | − 4048.00i | − 0.320805i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1344.00 | 0.105926 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10036.0i | 0.784476i | 0.919864 | + | 0.392238i | \(0.128299\pi\) | ||||
−0.919864 | + | 0.392238i | \(0.871701\pi\) | |||||||
\(548\) | − 2568.00i | − 0.200182i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 456.000 | 0.0352564 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4864.00i | 0.374030i | ||||||||
\(554\) | −4108.00 | −0.315040 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11344.0 | −0.865275 | ||||||||
\(557\) | 10326.0i | 0.785506i | 0.919644 | + | 0.392753i | \(0.128477\pi\) | ||||
−0.919644 | + | 0.392753i | \(0.871523\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14008.0 | −1.05988 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 14604.0i | − 1.09614i | ||||||||
\(563\) | − 4524.00i | − 0.338657i | −0.985560 | − | 0.169328i | \(-0.945840\pi\) | ||||
0.985560 | − | 0.169328i | \(-0.0541599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7448.00 | −0.553114 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 960.000i | − 0.0709167i | ||||||||
\(569\) | 16362.0 | 1.20550 | 0.602751 | − | 0.797929i | \(-0.294071\pi\) | ||||
0.602751 | + | 0.797929i | \(0.294071\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6620.00 | 0.485181 | 0.242591 | − | 0.970129i | \(-0.422003\pi\) | ||||
0.242591 | + | 0.970129i | \(0.422003\pi\) | |||||||
\(572\) | 8160.00i | 0.596480i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14976.0 | 1.08900 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 8834.00i | − 0.637373i | −0.947860 | − | 0.318687i | \(-0.896758\pi\) | ||||
0.947860 | − | 0.318687i | \(-0.103242\pi\) | |||||||
\(578\) | − 6298.00i | − 0.453222i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25728.0 | 1.83714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 13320.0i | − 0.946240i | ||||||||
\(584\) | −5968.00 | −0.422873 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14436.0 | 1.01765 | ||||||||
\(587\) | 3636.00i | 0.255662i | 0.991796 | + | 0.127831i | \(0.0408016\pi\) | ||||
−0.991796 | + | 0.127831i | \(0.959198\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17632.0 | −1.23347 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 2144.00i | − 0.148848i | ||||||||
\(593\) | − 6570.00i | − 0.454971i | −0.973782 | − | 0.227485i | \(-0.926950\pi\) | ||||
0.973782 | − | 0.227485i | \(-0.0730504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6216.00 | 0.427210 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16584.0 | 1.13123 | 0.565613 | − | 0.824671i | \(-0.308640\pi\) | ||||
0.565613 | + | 0.824671i | \(0.308640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −502.000 | −0.0340716 | −0.0170358 | − | 0.999855i | \(-0.505423\pi\) | ||||
−0.0170358 | + | 0.999855i | \(0.505423\pi\) | |||||||
\(602\) | 26368.0i | 1.78518i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9088.00 | 0.612228 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18568.0i | 1.24160i | 0.783969 | + | 0.620801i | \(0.213192\pi\) | ||||
−0.783969 | + | 0.620801i | \(0.786808\pi\) | |||||||
\(608\) | − 2432.00i | − 0.162221i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12240.0 | −0.810438 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13114.0i | − 0.864061i | −0.901859 | − | 0.432031i | \(-0.857797\pi\) | ||||
0.901859 | − | 0.432031i | \(-0.142203\pi\) | |||||||
\(614\) | −5080.00 | −0.333896 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15360.0 | 1.00466 | ||||||||
\(617\) | 5250.00i | 0.342556i | 0.985223 | + | 0.171278i | \(0.0547896\pi\) | ||||
−0.985223 | + | 0.171278i | \(0.945210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10804.0 | 0.701534 | 0.350767 | − | 0.936463i | \(-0.385921\pi\) | ||||
0.350767 | + | 0.936463i | \(0.385921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3120.00i | 0.201126i | ||||||||
\(623\) | 21696.0i | 1.39524i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1868.00 | −0.119266 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6776.00i | 0.430560i | ||||||||
\(629\) | 5628.00 | 0.356762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27088.0 | −1.70896 | −0.854482 | − | 0.519481i | \(-0.826125\pi\) | ||||
−0.854482 | + | 0.519481i | \(0.826125\pi\) | |||||||
\(632\) | − 1216.00i | − 0.0765346i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3348.00 | −0.209726 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23154.0i | 1.44018i | ||||||||
\(638\) | − 720.000i | − 0.0446788i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18930.0 | −1.16644 | −0.583222 | − | 0.812313i | \(-0.698208\pi\) | ||||
−0.583222 | + | 0.812313i | \(0.698208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20108.0i | 1.23325i | 0.787256 | + | 0.616627i | \(0.211501\pi\) | ||||
−0.787256 | + | 0.616627i | \(0.788499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6384.00 | 0.388816 | ||||||||
\(647\) | − 7152.00i | − 0.434581i | −0.976107 | − | 0.217291i | \(-0.930278\pi\) | ||||
0.976107 | − | 0.217291i | \(-0.0697219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39600.0 | 2.39512 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 208.000i | 0.0124937i | ||||||||
\(653\) | 31626.0i | 1.89528i | 0.319333 | + | 0.947642i | \(0.396541\pi\) | ||||
−0.319333 | + | 0.947642i | \(0.603459\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3744.00 | −0.222833 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23040.0i | 1.36503i | ||||||||
\(659\) | 28092.0 | 1.66056 | 0.830280 | − | 0.557347i | \(-0.188181\pi\) | ||||
0.830280 | + | 0.557347i | \(0.188181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13186.0 | −0.775909 | −0.387955 | − | 0.921678i | \(-0.626818\pi\) | ||||
−0.387955 | + | 0.921678i | \(0.626818\pi\) | |||||||
\(662\) | 7976.00i | 0.468272i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6432.00 | −0.375919 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 4800.00i | 0.278020i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29400.0 | −1.69147 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5138.00i | 0.294287i | 0.989115 | + | 0.147144i | \(0.0470080\pi\) | ||||
−0.989115 | + | 0.147144i | \(0.952992\pi\) | |||||||
\(674\) | −4.00000 | −0.000228597 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4164.00 | −0.236914 | ||||||||
\(677\) | 6078.00i | 0.345047i | 0.985005 | + | 0.172523i | \(0.0551920\pi\) | ||||
−0.985005 | + | 0.172523i | \(0.944808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6208.00 | −0.350871 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27840.0i | 1.56312i | ||||||||
\(683\) | − 32244.0i | − 1.80642i | −0.429203 | − | 0.903208i | \(-0.641205\pi\) | ||||
0.429203 | − | 0.903208i | \(-0.358795\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 21632.0 | 1.20396 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 6592.00i | − 0.365287i | ||||||||
\(689\) | −7548.00 | −0.417353 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4484.00 | 0.246859 | 0.123429 | − | 0.992353i | \(-0.460611\pi\) | ||||
0.123429 | + | 0.992353i | \(0.460611\pi\) | |||||||
\(692\) | 216.000i | 0.0118657i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3528.00 | 0.192970 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 9828.00i | − 0.534092i | ||||||||
\(698\) | 8620.00i | 0.467438i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30426.0 | 1.63934 | 0.819668 | − | 0.572839i | \(-0.194158\pi\) | ||||
0.819668 | + | 0.572839i | \(0.194158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 10184.0i | − 0.546368i | ||||||||
\(704\) | −3840.00 | −0.205576 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −276.000 | −0.0147130 | ||||||||
\(707\) | 25536.0i | 1.35839i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13262.0 | −0.702489 | −0.351245 | − | 0.936284i | \(-0.614241\pi\) | ||||
−0.351245 | + | 0.936284i | \(0.614241\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 5424.00i | − 0.285496i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3504.00 | −0.182892 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23952.0i | 1.24496i | ||||||||
\(719\) | 13920.0 | 0.722014 | 0.361007 | − | 0.932563i | \(-0.382433\pi\) | ||||
0.361007 | + | 0.932563i | \(0.382433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34816.0 | 1.79836 | ||||||||
\(722\) | 2166.00i | 0.111648i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15416.0 | −0.791341 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9376.00i | 0.478317i | 0.970981 | + | 0.239159i | \(0.0768716\pi\) | ||||
−0.970981 | + | 0.239159i | \(0.923128\pi\) | |||||||
\(728\) | − 8704.00i | − 0.443120i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17304.0 | 0.875529 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6014.00i | 0.303045i | 0.988454 | + | 0.151523i | \(0.0484176\pi\) | ||||
−0.988454 | + | 0.151523i | \(0.951582\pi\) | |||||||
\(734\) | −19408.0 | −0.975971 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 48720.0i | − 2.43504i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7468.00 | 0.371739 | 0.185869 | − | 0.982574i | \(-0.440490\pi\) | ||||
0.185869 | + | 0.982574i | \(0.440490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14208.0i | 0.702954i | ||||||||
\(743\) | − 31248.0i | − 1.54290i | −0.636287 | − | 0.771452i | \(-0.719531\pi\) | ||||
0.636287 | − | 0.771452i | \(-0.280469\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16244.0 | −0.797232 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 10080.0i | − 0.492729i | ||||||||
\(749\) | 54912.0 | 2.67883 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32840.0 | 1.59567 | 0.797835 | − | 0.602875i | \(-0.205978\pi\) | ||||
0.797835 | + | 0.602875i | \(0.205978\pi\) | |||||||
\(752\) | − 5760.00i | − 0.279316i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −408.000 | −0.0197062 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19066.0i | 0.915410i | 0.889104 | + | 0.457705i | \(0.151328\pi\) | ||||
−0.889104 | + | 0.457705i | \(0.848672\pi\) | |||||||
\(758\) | 6808.00i | 0.326224i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6858.00 | −0.326678 | −0.163339 | − | 0.986570i | \(-0.552227\pi\) | ||||
−0.163339 | + | 0.986570i | \(0.552227\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 31040.0i | − 1.47277i | ||||||||
\(764\) | −11136.0 | −0.527338 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5040.00 | 0.237732 | ||||||||
\(767\) | − 22440.0i | − 1.05640i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22178.0 | −1.04000 | −0.519999 | − | 0.854167i | \(-0.674068\pi\) | ||||
−0.519999 | + | 0.854167i | \(0.674068\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 3656.00i | − 0.170443i | ||||||||
\(773\) | − 14286.0i | − 0.664724i | −0.943152 | − | 0.332362i | \(-0.892154\pi\) | ||||
0.943152 | − | 0.332362i | \(-0.107846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1552.00 | 0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 3132.00i | − 0.144329i | ||||||||
\(779\) | −17784.0 | −0.817943 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7200.00 | −0.329880 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10896.0 | −0.496356 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18868.0i | 0.854602i | 0.904109 | + | 0.427301i | \(0.140535\pi\) | ||||
−0.904109 | + | 0.427301i | \(0.859465\pi\) | |||||||
\(788\) | 20808.0i | 0.940678i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13632.0 | −0.612766 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16660.0i | 0.746045i | ||||||||
\(794\) | 8708.00 | 0.389213 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12608.0 | 0.561405 | ||||||||
\(797\) | − 21690.0i | − 0.963989i | −0.876174 | − | 0.481994i | \(-0.839913\pi\) | ||||
0.876174 | − | 0.481994i | \(-0.160087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15120.0 | 0.669471 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 16092.0i | − 0.708514i | ||||||||
\(803\) | 44760.0i | 1.96706i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15776.0 | 0.689437 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 6384.00i | − 0.277956i | ||||||||
\(809\) | −24726.0 | −1.07456 | −0.537281 | − | 0.843404i | \(-0.680548\pi\) | ||||
−0.537281 | + | 0.843404i | \(0.680548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2644.00 | −0.114480 | −0.0572401 | − | 0.998360i | \(-0.518230\pi\) | ||||
−0.0572401 | + | 0.998360i | \(0.518230\pi\) | |||||||
\(812\) | 768.000i | 0.0331915i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16080.0 | −0.692388 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 31312.0i | − 1.34084i | ||||||||
\(818\) | − 5612.00i | − 0.239877i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37842.0 | 1.60864 | 0.804321 | − | 0.594195i | \(-0.202529\pi\) | ||||
0.804321 | + | 0.594195i | \(0.202529\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 880.000i | − 0.0372720i | −0.999826 | − | 0.0186360i | \(-0.994068\pi\) | ||||
0.999826 | − | 0.0186360i | \(-0.00593237\pi\) | |||||||
\(824\) | −8704.00 | −0.367983 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42240.0 | −1.77932 | ||||||||
\(827\) | − 12876.0i | − 0.541406i | −0.962663 | − | 0.270703i | \(-0.912744\pi\) | ||||
0.962663 | − | 0.270703i | \(-0.0872561\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25498.0 | 1.06825 | 0.534127 | − | 0.845404i | \(-0.320641\pi\) | ||||
0.534127 | + | 0.845404i | \(0.320641\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2176.00i | 0.0906721i | ||||||||
\(833\) | − 28602.0i | − 1.18968i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18240.0 | −0.754598 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 23160.0i | − 0.954712i | ||||||||
\(839\) | −40584.0 | −1.66998 | −0.834991 | − | 0.550263i | \(-0.814527\pi\) | ||||
−0.834991 | + | 0.550263i | \(0.814527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 740.000i | 0.0302875i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2960.00 | −0.120720 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 72608.0i | − 2.94550i | ||||||||
\(848\) | − 3552.00i | − 0.143840i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 25738.0i | − 1.03312i | −0.856251 | − | 0.516561i | \(-0.827212\pi\) | ||||
0.856251 | − | 0.516561i | \(-0.172788\pi\) | |||||||
\(854\) | 31360.0 | 1.25658 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13728.0 | −0.548146 | ||||||||
\(857\) | 13314.0i | 0.530686i | 0.964154 | + | 0.265343i | \(0.0854851\pi\) | ||||
−0.964154 | + | 0.265343i | \(0.914515\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24524.0 | −0.974096 | −0.487048 | − | 0.873375i | \(-0.661926\pi\) | ||||
−0.487048 | + | 0.873375i | \(0.661926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10080.0i | 0.398290i | ||||||||
\(863\) | − 5592.00i | − 0.220572i | −0.993900 | − | 0.110286i | \(-0.964823\pi\) | ||||
0.993900 | − | 0.110286i | \(-0.0351767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7484.00 | −0.293668 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 29696.0i | − 1.16123i | ||||||||
\(869\) | −9120.00 | −0.356012 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27608.0 | −1.07401 | ||||||||
\(872\) | 7760.00i | 0.301361i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14386.0i | 0.553912i | 0.960883 | + | 0.276956i | \(0.0893256\pi\) | ||||
−0.960883 | + | 0.276956i | \(0.910674\pi\) | |||||||
\(878\) | − 12416.0i | − 0.477243i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47106.0 | −1.80141 | −0.900705 | − | 0.434432i | \(-0.856949\pi\) | ||||
−0.900705 | + | 0.434432i | \(0.856949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51548.0i | 1.96458i | 0.187354 | + | 0.982292i | \(0.440009\pi\) | ||||
−0.187354 | + | 0.982292i | \(0.559991\pi\) | |||||||
\(884\) | −5712.00 | −0.217325 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31128.0 | 1.18032 | ||||||||
\(887\) | 34080.0i | 1.29007i | 0.764152 | + | 0.645036i | \(0.223158\pi\) | ||||
−0.764152 | + | 0.645036i | \(0.776842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6400.00 | −0.241450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2080.00i | 0.0780757i | ||||||||
\(893\) | − 27360.0i | − 1.02527i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4096.00 | 0.152721 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31548.0i | 1.17235i | ||||||||
\(899\) | −1392.00 | −0.0516416 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9324.00 | 0.344759 | ||||||||
\(902\) | 28080.0i | 1.03654i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3408.00 | 0.125385 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 25748.0i | − 0.942611i | −0.881970 | − | 0.471306i | \(-0.843783\pi\) | ||||
0.881970 | − | 0.471306i | \(-0.156217\pi\) | |||||||
\(908\) | − 1584.00i | − 0.0578930i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24768.0 | 0.900769 | 0.450384 | − | 0.892835i | \(-0.351287\pi\) | ||||
0.450384 | + | 0.892835i | \(0.351287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48240.0i | 1.74864i | ||||||||
\(914\) | −19444.0 | −0.703666 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5320.00 | −0.191897 | ||||||||
\(917\) | 1920.00i | 0.0691428i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31264.0 | 1.12220 | 0.561101 | − | 0.827747i | \(-0.310378\pi\) | ||||
0.561101 | + | 0.827747i | \(0.310378\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 21780.0i | − 0.777968i | ||||||||
\(923\) | 4080.00i | 0.145498i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30256.0 | 1.07373 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 192.000i | − 0.00679171i | ||||||||
\(929\) | −6174.00 | −0.218043 | −0.109022 | − | 0.994039i | \(-0.534772\pi\) | ||||
−0.109022 | + | 0.994039i | \(0.534772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51756.0 | −1.82195 | ||||||||
\(932\) | 19464.0i | 0.684082i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21336.0 | 0.747468 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 28922.0i | − 1.00837i | −0.863596 | − | 0.504184i | \(-0.831793\pi\) | ||||
0.863596 | − | 0.504184i | \(-0.168207\pi\) | |||||||
\(938\) | 51968.0i | 1.80897i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29238.0 | −1.01289 | −0.506446 | − | 0.862272i | \(-0.669041\pi\) | ||||
−0.506446 | + | 0.862272i | \(0.669041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 10560.0 | 0.364088 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −49440.0 | −1.69919 | ||||||||
\(947\) | − 2868.00i | − 0.0984134i | −0.998789 | − | 0.0492067i | \(-0.984331\pi\) | ||||
0.998789 | − | 0.0492067i | \(-0.0156693\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25364.0 | 0.867598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10752.0i | 0.366044i | ||||||||
\(953\) | − 24018.0i | − 0.816390i | −0.912895 | − | 0.408195i | \(-0.866158\pi\) | ||||
0.912895 | − | 0.408195i | \(-0.133842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7296.00 | 0.246830 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 30528.0i | − 1.02956i | ||||||||
\(959\) | 20544.0 | 0.691763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24033.0 | 0.806720 | ||||||||
\(962\) | 9112.00i | 0.305387i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25928.0 | −0.866270 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 25712.0i | − 0.855059i | −0.904001 | − | 0.427530i | \(-0.859384\pi\) | ||||
0.904001 | − | 0.427530i | \(-0.140616\pi\) | |||||||
\(968\) | 18152.0i | 0.602714i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12396.0 | 0.409688 | 0.204844 | − | 0.978795i | \(-0.434331\pi\) | ||||
0.204844 | + | 0.978795i | \(0.434331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 90752.0i | − 2.99011i | ||||||||
\(974\) | 11552.0 | 0.380031 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7840.00 | −0.257123 | ||||||||
\(977\) | − 46614.0i | − 1.52642i | −0.646150 | − | 0.763211i | \(-0.723622\pi\) | ||||
0.646150 | − | 0.763211i | \(-0.276378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40680.0 | −1.32803 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28488.0i | 0.925752i | ||||||||
\(983\) | 672.000i | 0.0218041i | 0.999941 | + | 0.0109021i | \(0.00347031\pi\) | ||||
−0.999941 | + | 0.0109021i | \(0.996530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 504.000 | 0.0162785 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10336.0i | 0.332826i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38776.0 | −1.24295 | −0.621473 | − | 0.783435i | \(-0.713466\pi\) | ||||
−0.621473 | + | 0.783435i | \(0.713466\pi\) | |||||||
\(992\) | 7424.00i | 0.237613i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7680.00 | 0.245065 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 30422.0i | − 0.966374i | −0.875517 | − | 0.483187i | \(-0.839479\pi\) | ||||
0.875517 | − | 0.483187i | \(-0.160521\pi\) | |||||||
\(998\) | − 34232.0i | − 1.08577i | ||||||||
\(999\) | 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 | 450.4.c.k.199.1 | 2 | ||
3.2 | odd | 2 | 150.4.c.a.49.2 | 2 | |||
5.2 | odd | 4 | 90.4.a.d.1.1 | 1 | |||
5.3 | odd | 4 | 450.4.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 450.4.c.k.199.2 | 2 | ||
12.11 | even | 2 | 1200.4.f.u.49.1 | 2 | |||
15.2 | even | 4 | 30.4.a.a.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 150.4.a.e.1.1 | 1 | |||
15.14 | odd | 2 | 150.4.c.a.49.1 | 2 | |||
20.7 | even | 4 | 720.4.a.b.1.1 | 1 | |||
45.2 | even | 12 | 810.4.e.m.271.1 | 2 | |||
45.7 | odd | 12 | 810.4.e.e.271.1 | 2 | |||
45.22 | odd | 12 | 810.4.e.e.541.1 | 2 | |||
45.32 | even | 12 | 810.4.e.m.541.1 | 2 | |||
60.23 | odd | 4 | 1200.4.a.bk.1.1 | 1 | |||
60.47 | odd | 4 | 240.4.a.c.1.1 | 1 | |||
60.59 | even | 2 | 1200.4.f.u.49.2 | 2 | |||
105.62 | odd | 4 | 1470.4.a.a.1.1 | 1 | |||
120.77 | even | 4 | 960.4.a.j.1.1 | 1 | |||
120.107 | odd | 4 | 960.4.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.4.a.a.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
90.4.a.d.1.1 | 1 | 5.2 | odd | 4 | |||
150.4.a.e.1.1 | 1 | 15.8 | even | 4 | |||
150.4.c.a.49.1 | 2 | 15.14 | odd | 2 | |||
150.4.c.a.49.2 | 2 | 3.2 | odd | 2 | |||
240.4.a.c.1.1 | 1 | 60.47 | odd | 4 | |||
450.4.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
450.4.c.k.199.1 | 2 | 1.1 | even | 1 | trivial | ||
450.4.c.k.199.2 | 2 | 5.4 | even | 2 | inner | ||
720.4.a.b.1.1 | 1 | 20.7 | even | 4 | |||
810.4.e.e.271.1 | 2 | 45.7 | odd | 12 | |||
810.4.e.e.541.1 | 2 | 45.22 | odd | 12 | |||
810.4.e.m.271.1 | 2 | 45.2 | even | 12 | |||
810.4.e.m.541.1 | 2 | 45.32 | even | 12 | |||
960.4.a.j.1.1 | 1 | 120.77 | even | 4 | |||
960.4.a.s.1.1 | 1 | 120.107 | odd | 4 | |||
1200.4.a.bk.1.1 | 1 | 60.23 | odd | 4 | |||
1200.4.f.u.49.1 | 2 | 12.11 | even | 2 | |||
1200.4.f.u.49.2 | 2 | 60.59 | even | 2 | |||
1470.4.a.a.1.1 | 1 | 105.62 | odd | 4 |