Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, 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("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.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: | \(79.6525785077\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.o.649.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(7\) | 13.0000i | 0.701934i | 0.936388 | + | 0.350967i | \(0.114147\pi\) | ||||
−0.936388 | + | 0.350967i | \(0.885853\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.0000 | 0.822304 | 0.411152 | − | 0.911567i | \(-0.365127\pi\) | ||||
0.411152 | + | 0.911567i | \(0.365127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 61.0000i | − 1.30141i | −0.759330 | − | 0.650706i | \(-0.774473\pi\) | ||||
0.759330 | − | 0.650706i | \(-0.225527\pi\) | |||||||
\(14\) | −26.0000 | −0.496342 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 12.0000i | 0.171202i | 0.996330 | + | 0.0856008i | \(0.0272810\pi\) | ||||
−0.996330 | + | 0.0856008i | \(0.972719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 49.0000 | 0.591651 | 0.295826 | − | 0.955242i | \(-0.404405\pi\) | ||||
0.295826 | + | 0.955242i | \(0.404405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 60.0000i | 0.581456i | ||||||||
\(23\) | − 18.0000i | − 0.163185i | −0.996666 | − | 0.0815926i | \(-0.973999\pi\) | ||||
0.996666 | − | 0.0815926i | \(-0.0260006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 122.000 | 0.920237 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 52.0000i | − 0.350967i | ||||||||
\(29\) | −186.000 | −1.19101 | −0.595506 | − | 0.803351i | \(-0.703048\pi\) | ||||
−0.595506 | + | 0.803351i | \(0.703048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −160.000 | −0.926995 | −0.463498 | − | 0.886098i | \(-0.653406\pi\) | ||||
−0.463498 | + | 0.886098i | \(0.653406\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −24.0000 | −0.121058 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 91.0000i | 0.404333i | 0.979351 | + | 0.202166i | \(0.0647982\pi\) | ||||
−0.979351 | + | 0.202166i | \(0.935202\pi\) | |||||||
\(38\) | 98.0000i | 0.418361i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −378.000 | −1.43985 | −0.719923 | − | 0.694054i | \(-0.755823\pi\) | ||||
−0.719923 | + | 0.694054i | \(0.755823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 268.000i | − 0.950456i | −0.879863 | − | 0.475228i | \(-0.842366\pi\) | ||||
0.879863 | − | 0.475228i | \(-0.157634\pi\) | |||||||
\(44\) | −120.000 | −0.411152 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 36.0000 | 0.115389 | ||||||||
\(47\) | 144.000i | 0.446906i | 0.974715 | + | 0.223453i | \(0.0717328\pi\) | ||||
−0.974715 | + | 0.223453i | \(0.928267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 174.000 | 0.507289 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 244.000i | 0.650706i | ||||||||
\(53\) | − 570.000i | − 1.47727i | −0.674103 | − | 0.738637i | \(-0.735470\pi\) | ||||
0.674103 | − | 0.738637i | \(-0.264530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 104.000 | 0.248171 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 372.000i | − 0.842172i | ||||||||
\(59\) | 204.000 | 0.450145 | 0.225072 | − | 0.974342i | \(-0.427738\pi\) | ||||
0.225072 | + | 0.974342i | \(0.427738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −877.000 | −1.84079 | −0.920396 | − | 0.390987i | \(-0.872134\pi\) | ||||
−0.920396 | + | 0.390987i | \(0.872134\pi\) | |||||||
\(62\) | − 320.000i | − 0.655485i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 187.000i | 0.340980i | 0.985359 | + | 0.170490i | \(0.0545351\pi\) | ||||
−0.985359 | + | 0.170490i | \(0.945465\pi\) | |||||||
\(68\) | − 48.0000i | − 0.0856008i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 606.000 | 1.01294 | 0.506472 | − | 0.862257i | \(-0.330950\pi\) | ||||
0.506472 | + | 0.862257i | \(0.330950\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 431.000i | 0.691024i | 0.938414 | + | 0.345512i | \(0.112295\pi\) | ||||
−0.938414 | + | 0.345512i | \(0.887705\pi\) | |||||||
\(74\) | −182.000 | −0.285906 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −196.000 | −0.295826 | ||||||||
\(77\) | 390.000i | 0.577203i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1151.00 | −1.63921 | −0.819605 | − | 0.572929i | \(-0.805807\pi\) | ||||
−0.819605 | + | 0.572929i | \(0.805807\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 756.000i | − 1.01812i | ||||||||
\(83\) | − 102.000i | − 0.134891i | −0.997723 | − | 0.0674455i | \(-0.978515\pi\) | ||||
0.997723 | − | 0.0674455i | \(-0.0214849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 536.000 | 0.672074 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 240.000i | − 0.290728i | ||||||||
\(89\) | 984.000 | 1.17195 | 0.585976 | − | 0.810328i | \(-0.300711\pi\) | ||||
0.585976 | + | 0.810328i | \(0.300711\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 793.000 | 0.913505 | ||||||||
\(92\) | 72.0000i | 0.0815926i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −288.000 | −0.316010 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 265.000i | 0.277388i | 0.990335 | + | 0.138694i | \(0.0442905\pi\) | ||||
−0.990335 | + | 0.138694i | \(0.955709\pi\) | |||||||
\(98\) | 348.000i | 0.358707i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1248.00 | 1.22951 | 0.614756 | − | 0.788718i | \(-0.289255\pi\) | ||||
0.614756 | + | 0.788718i | \(0.289255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1225.00i | − 1.17187i | −0.810357 | − | 0.585936i | \(-0.800727\pi\) | ||||
0.810357 | − | 0.585936i | \(-0.199273\pi\) | |||||||
\(104\) | −488.000 | −0.460119 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1140.00 | 1.04459 | ||||||||
\(107\) | − 78.0000i | − 0.0704724i | −0.999379 | − | 0.0352362i | \(-0.988782\pi\) | ||||
0.999379 | − | 0.0352362i | \(-0.0112183\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2198.00 | −1.93147 | −0.965735 | − | 0.259530i | \(-0.916432\pi\) | ||||
−0.965735 | + | 0.259530i | \(0.916432\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 208.000i | 0.175484i | ||||||||
\(113\) | − 1986.00i | − 1.65334i | −0.562689 | − | 0.826669i | \(-0.690233\pi\) | ||||
0.562689 | − | 0.826669i | \(-0.309767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 744.000 | 0.595506 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 408.000i | 0.318300i | ||||||||
\(119\) | −156.000 | −0.120172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −431.000 | −0.323817 | ||||||||
\(122\) | − 1754.00i | − 1.30164i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 640.000 | 0.463498 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2792.00i | − 1.95079i | −0.220471 | − | 0.975393i | \(-0.570760\pi\) | ||||
0.220471 | − | 0.975393i | \(-0.429240\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 708.000 | 0.472200 | 0.236100 | − | 0.971729i | \(-0.424131\pi\) | ||||
0.236100 | + | 0.971729i | \(0.424131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 637.000i | 0.415300i | ||||||||
\(134\) | −374.000 | −0.241110 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 96.0000 | 0.0605289 | ||||||||
\(137\) | − 1686.00i | − 1.05142i | −0.850663 | − | 0.525711i | \(-0.823799\pi\) | ||||
0.850663 | − | 0.525711i | \(-0.176201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 307.000 | 0.187334 | 0.0936669 | − | 0.995604i | \(-0.470141\pi\) | ||||
0.0936669 | + | 0.995604i | \(0.470141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1212.00i | 0.716259i | ||||||||
\(143\) | − 1830.00i | − 1.07016i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −862.000 | −0.488628 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 364.000i | − 0.202166i | ||||||||
\(149\) | −1812.00 | −0.996274 | −0.498137 | − | 0.867098i | \(-0.665982\pi\) | ||||
−0.498137 | + | 0.867098i | \(0.665982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 203.000 | 0.109403 | 0.0547017 | − | 0.998503i | \(-0.482579\pi\) | ||||
0.0547017 | + | 0.998503i | \(0.482579\pi\) | |||||||
\(152\) | − 392.000i | − 0.209180i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −780.000 | −0.408144 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 214.000i | 0.108784i | 0.998520 | + | 0.0543919i | \(0.0173220\pi\) | ||||
−0.998520 | + | 0.0543919i | \(0.982678\pi\) | |||||||
\(158\) | − 2302.00i | − 1.15910i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 234.000 | 0.114545 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 673.000i | − 0.323395i | −0.986840 | − | 0.161698i | \(-0.948303\pi\) | ||||
0.986840 | − | 0.161698i | \(-0.0516969\pi\) | |||||||
\(164\) | 1512.00 | 0.719923 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 204.000 | 0.0953824 | ||||||||
\(167\) | − 3696.00i | − 1.71261i | −0.516474 | − | 0.856303i | \(-0.672756\pi\) | ||||
0.516474 | − | 0.856303i | \(-0.327244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1524.00 | −0.693673 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1072.00i | 0.475228i | ||||||||
\(173\) | − 3132.00i | − 1.37643i | −0.725509 | − | 0.688213i | \(-0.758396\pi\) | ||||
0.725509 | − | 0.688213i | \(-0.241604\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 480.000 | 0.205576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1968.00i | 0.828696i | ||||||||
\(179\) | 510.000 | 0.212956 | 0.106478 | − | 0.994315i | \(-0.466043\pi\) | ||||
0.106478 | + | 0.994315i | \(0.466043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1087.00 | −0.446387 | −0.223194 | − | 0.974774i | \(-0.571648\pi\) | ||||
−0.223194 | + | 0.974774i | \(0.571648\pi\) | |||||||
\(182\) | 1586.00i | 0.645946i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −144.000 | −0.0576947 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 360.000i | 0.140780i | ||||||||
\(188\) | − 576.000i | − 0.223453i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4056.00 | 1.53655 | 0.768277 | − | 0.640117i | \(-0.221114\pi\) | ||||
0.768277 | + | 0.640117i | \(0.221114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 473.000i | 0.176411i | 0.996102 | + | 0.0882054i | \(0.0281132\pi\) | ||||
−0.996102 | + | 0.0882054i | \(0.971887\pi\) | |||||||
\(194\) | −530.000 | −0.196143 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −696.000 | −0.253644 | ||||||||
\(197\) | 2556.00i | 0.924403i | 0.886775 | + | 0.462202i | \(0.152940\pi\) | ||||
−0.886775 | + | 0.462202i | \(0.847060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2923.00 | 1.04124 | 0.520618 | − | 0.853790i | \(-0.325702\pi\) | ||||
0.520618 | + | 0.853790i | \(0.325702\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2496.00i | 0.869396i | ||||||||
\(203\) | − 2418.00i | − 0.836011i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2450.00 | 0.828639 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 976.000i | − 0.325353i | ||||||||
\(209\) | 1470.00 | 0.486517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3175.00 | −1.03591 | −0.517953 | − | 0.855409i | \(-0.673306\pi\) | ||||
−0.517953 | + | 0.855409i | \(0.673306\pi\) | |||||||
\(212\) | 2280.00i | 0.738637i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 156.000 | 0.0498315 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2080.00i | − 0.650689i | ||||||||
\(218\) | − 4396.00i | − 1.36576i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 732.000 | 0.222804 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2176.00i | − 0.653434i | −0.945122 | − | 0.326717i | \(-0.894058\pi\) | ||||
0.945122 | − | 0.326717i | \(-0.105942\pi\) | |||||||
\(224\) | −416.000 | −0.124086 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3972.00 | 1.16909 | ||||||||
\(227\) | − 3834.00i | − 1.12102i | −0.828148 | − | 0.560510i | \(-0.810605\pi\) | ||||
0.828148 | − | 0.560510i | \(-0.189395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3202.00 | 0.923992 | 0.461996 | − | 0.886882i | \(-0.347133\pi\) | ||||
0.461996 | + | 0.886882i | \(0.347133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1488.00i | 0.421086i | ||||||||
\(233\) | − 4152.00i | − 1.16741i | −0.811966 | − | 0.583705i | \(-0.801602\pi\) | ||||
0.811966 | − | 0.583705i | \(-0.198398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −816.000 | −0.225072 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 312.000i | − 0.0849746i | ||||||||
\(239\) | −5466.00 | −1.47936 | −0.739678 | − | 0.672961i | \(-0.765022\pi\) | ||||
−0.739678 | + | 0.672961i | \(0.765022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −943.000 | −0.252050 | −0.126025 | − | 0.992027i | \(-0.540222\pi\) | ||||
−0.126025 | + | 0.992027i | \(0.540222\pi\) | |||||||
\(242\) | − 862.000i | − 0.228973i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3508.00 | 0.920396 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2989.00i | − 0.769982i | ||||||||
\(248\) | 1280.00i | 0.327742i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7290.00 | 1.83323 | 0.916615 | − | 0.399771i | \(-0.130910\pi\) | ||||
0.916615 | + | 0.399771i | \(0.130910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 540.000i | − 0.134188i | ||||||||
\(254\) | 5584.00 | 1.37941 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 312.000i | 0.0757277i | 0.999283 | + | 0.0378639i | \(0.0120553\pi\) | ||||
−0.999283 | + | 0.0378639i | \(0.987945\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1183.00 | −0.283815 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1416.00i | 0.333896i | ||||||||
\(263\) | 8004.00i | 1.87661i | 0.345812 | + | 0.938304i | \(0.387603\pi\) | ||||
−0.345812 | + | 0.938304i | \(0.612397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1274.00 | −0.293661 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 748.000i | − 0.170490i | ||||||||
\(269\) | −324.000 | −0.0734373 | −0.0367186 | − | 0.999326i | \(-0.511691\pi\) | ||||
−0.0367186 | + | 0.999326i | \(0.511691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7849.00 | −1.75938 | −0.879692 | − | 0.475545i | \(-0.842251\pi\) | ||||
−0.879692 | + | 0.475545i | \(0.842251\pi\) | |||||||
\(272\) | 192.000i | 0.0428004i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3372.00 | 0.743467 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5758.00i | 1.24897i | 0.781037 | + | 0.624485i | \(0.214691\pi\) | ||||
−0.781037 | + | 0.624485i | \(0.785309\pi\) | |||||||
\(278\) | 614.000i | 0.132465i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2688.00 | 0.570650 | 0.285325 | − | 0.958431i | \(-0.407898\pi\) | ||||
0.285325 | + | 0.958431i | \(0.407898\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3260.00i | 0.684759i | 0.939562 | + | 0.342380i | \(0.111233\pi\) | ||||
−0.939562 | + | 0.342380i | \(0.888767\pi\) | |||||||
\(284\) | −2424.00 | −0.506472 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3660.00 | 0.756714 | ||||||||
\(287\) | − 4914.00i | − 1.01068i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4769.00 | 0.970690 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 1724.00i | − 0.345512i | ||||||||
\(293\) | − 5922.00i | − 1.18077i | −0.807120 | − | 0.590387i | \(-0.798975\pi\) | ||||
0.807120 | − | 0.590387i | \(-0.201025\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 728.000 | 0.142953 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 3624.00i | − 0.704472i | ||||||||
\(299\) | −1098.00 | −0.212371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3484.00 | 0.667158 | ||||||||
\(302\) | 406.000i | 0.0773599i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 784.000 | 0.147913 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3728.00i | − 0.693056i | −0.938040 | − | 0.346528i | \(-0.887361\pi\) | ||||
0.938040 | − | 0.346528i | \(-0.112639\pi\) | |||||||
\(308\) | − 1560.00i | − 0.288601i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 732.000 | 0.133466 | 0.0667330 | − | 0.997771i | \(-0.478742\pi\) | ||||
0.0667330 | + | 0.997771i | \(0.478742\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5357.00i | 0.967398i | 0.875234 | + | 0.483699i | \(0.160707\pi\) | ||||
−0.875234 | + | 0.483699i | \(0.839293\pi\) | |||||||
\(314\) | −428.000 | −0.0769218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4604.00 | 0.819605 | ||||||||
\(317\) | − 4572.00i | − 0.810060i | −0.914303 | − | 0.405030i | \(-0.867261\pi\) | ||||
0.914303 | − | 0.405030i | \(-0.132739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5580.00 | −0.979373 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 468.000i | 0.0809957i | ||||||||
\(323\) | 588.000i | 0.101292i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1346.00 | 0.228675 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3024.00i | 0.509062i | ||||||||
\(329\) | −1872.00 | −0.313698 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 845.000 | 0.140318 | 0.0701592 | − | 0.997536i | \(-0.477649\pi\) | ||||
0.0701592 | + | 0.997536i | \(0.477649\pi\) | |||||||
\(332\) | 408.000i | 0.0674455i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7392.00 | 1.21099 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 8723.00i | − 1.41001i | −0.709204 | − | 0.705003i | \(-0.750946\pi\) | ||||
0.709204 | − | 0.705003i | \(-0.249054\pi\) | |||||||
\(338\) | − 3048.00i | − 0.490501i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4800.00 | −0.762271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6721.00i | 1.05802i | ||||||||
\(344\) | −2144.00 | −0.336037 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6264.00 | 0.973280 | ||||||||
\(347\) | 9018.00i | 1.39513i | 0.716519 | + | 0.697567i | \(0.245734\pi\) | ||||
−0.716519 | + | 0.697567i | \(0.754266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5759.00 | −0.883301 | −0.441651 | − | 0.897187i | \(-0.645607\pi\) | ||||
−0.441651 | + | 0.897187i | \(0.645607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 960.000i | 0.145364i | ||||||||
\(353\) | 5772.00i | 0.870291i | 0.900360 | + | 0.435145i | \(0.143303\pi\) | ||||
−0.900360 | + | 0.435145i | \(0.856697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3936.00 | −0.585976 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1020.00i | 0.150583i | ||||||||
\(359\) | −2046.00 | −0.300790 | −0.150395 | − | 0.988626i | \(-0.548055\pi\) | ||||
−0.150395 | + | 0.988626i | \(0.548055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4458.00 | −0.649949 | ||||||||
\(362\) | − 2174.00i | − 0.315643i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3172.00 | −0.456753 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1069.00i | 0.152047i | 0.997106 | + | 0.0760236i | \(0.0242224\pi\) | ||||
−0.997106 | + | 0.0760236i | \(0.975778\pi\) | |||||||
\(368\) | − 288.000i | − 0.0407963i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7410.00 | 1.03695 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7133.00i | 0.990168i | 0.868845 | + | 0.495084i | \(0.164863\pi\) | ||||
−0.868845 | + | 0.495084i | \(0.835137\pi\) | |||||||
\(374\) | −720.000 | −0.0995463 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1152.00 | 0.158005 | ||||||||
\(377\) | 11346.0i | 1.55000i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8557.00 | 1.15975 | 0.579873 | − | 0.814707i | \(-0.303102\pi\) | ||||
0.579873 | + | 0.814707i | \(0.303102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8112.00i | 1.08651i | ||||||||
\(383\) | − 14328.0i | − 1.91156i | −0.294086 | − | 0.955779i | \(-0.595015\pi\) | ||||
0.294086 | − | 0.955779i | \(-0.404985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −946.000 | −0.124741 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 1060.00i | − 0.138694i | ||||||||
\(389\) | 13500.0 | 1.75958 | 0.879791 | − | 0.475361i | \(-0.157683\pi\) | ||||
0.879791 | + | 0.475361i | \(0.157683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 216.000 | 0.0279376 | ||||||||
\(392\) | − 1392.00i | − 0.179354i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5112.00 | −0.653652 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1334.00i | − 0.168644i | −0.996439 | − | 0.0843218i | \(-0.973128\pi\) | ||||
0.996439 | − | 0.0843218i | \(-0.0268724\pi\) | |||||||
\(398\) | 5846.00i | 0.736265i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3474.00 | −0.432627 | −0.216313 | − | 0.976324i | \(-0.569403\pi\) | ||||
−0.216313 | + | 0.976324i | \(0.569403\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9760.00i | 1.20640i | ||||||||
\(404\) | −4992.00 | −0.614756 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4836.00 | 0.591149 | ||||||||
\(407\) | 2730.00i | 0.332484i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −569.000 | −0.0687903 | −0.0343952 | − | 0.999408i | \(-0.510950\pi\) | ||||
−0.0343952 | + | 0.999408i | \(0.510950\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4900.00i | 0.585936i | ||||||||
\(413\) | 2652.00i | 0.315972i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1952.00 | 0.230059 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2940.00i | 0.344019i | ||||||||
\(419\) | −9132.00 | −1.06474 | −0.532372 | − | 0.846511i | \(-0.678699\pi\) | ||||
−0.532372 | + | 0.846511i | \(0.678699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2971.00 | −0.343937 | −0.171969 | − | 0.985102i | \(-0.555013\pi\) | ||||
−0.171969 | + | 0.985102i | \(0.555013\pi\) | |||||||
\(422\) | − 6350.00i | − 0.732496i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4560.00 | −0.522295 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 11401.0i | − 1.29211i | ||||||||
\(428\) | 312.000i | 0.0352362i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12042.0 | −1.34581 | −0.672903 | − | 0.739730i | \(-0.734953\pi\) | ||||
−0.672903 | + | 0.739730i | \(0.734953\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 8566.00i | − 0.950706i | −0.879795 | − | 0.475353i | \(-0.842320\pi\) | ||||
0.879795 | − | 0.475353i | \(-0.157680\pi\) | |||||||
\(434\) | 4160.00 | 0.460107 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8792.00 | 0.965735 | ||||||||
\(437\) | − 882.000i | − 0.0965487i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7400.00 | −0.804516 | −0.402258 | − | 0.915526i | \(-0.631775\pi\) | ||||
−0.402258 | + | 0.915526i | \(0.631775\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1464.00i | 0.157546i | ||||||||
\(443\) | 2580.00i | 0.276703i | 0.990383 | + | 0.138352i | \(0.0441804\pi\) | ||||
−0.990383 | + | 0.138352i | \(0.955820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4352.00 | 0.462047 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 832.000i | − 0.0877418i | ||||||||
\(449\) | 13200.0 | 1.38741 | 0.693704 | − | 0.720260i | \(-0.255977\pi\) | ||||
0.693704 | + | 0.720260i | \(0.255977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11340.0 | −1.18399 | ||||||||
\(452\) | 7944.00i | 0.826669i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7668.00 | 0.792681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 18038.0i | − 1.84635i | −0.384380 | − | 0.923175i | \(-0.625585\pi\) | ||||
0.384380 | − | 0.923175i | \(-0.374415\pi\) | |||||||
\(458\) | 6404.00i | 0.653361i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5544.00 | −0.560108 | −0.280054 | − | 0.959984i | \(-0.590352\pi\) | ||||
−0.280054 | + | 0.959984i | \(0.590352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 17137.0i | − 1.72014i | −0.510178 | − | 0.860069i | \(-0.670420\pi\) | ||||
0.510178 | − | 0.860069i | \(-0.329580\pi\) | |||||||
\(464\) | −2976.00 | −0.297753 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8304.00 | 0.825484 | ||||||||
\(467\) | − 15888.0i | − 1.57432i | −0.616747 | − | 0.787162i | \(-0.711550\pi\) | ||||
0.616747 | − | 0.787162i | \(-0.288450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2431.00 | −0.239346 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 1632.00i | − 0.159150i | ||||||||
\(473\) | − 8040.00i | − 0.781564i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 624.000 | 0.0600861 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 10932.0i | − 1.04606i | ||||||||
\(479\) | 3942.00 | 0.376022 | 0.188011 | − | 0.982167i | \(-0.439796\pi\) | ||||
0.188011 | + | 0.982167i | \(0.439796\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5551.00 | 0.526203 | ||||||||
\(482\) | − 1886.00i | − 0.178226i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1724.00 | 0.161908 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1379.00i | − 0.128313i | −0.997940 | − | 0.0641565i | \(-0.979564\pi\) | ||||
0.997940 | − | 0.0641565i | \(-0.0204357\pi\) | |||||||
\(488\) | 7016.00i | 0.650818i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14214.0 | −1.30645 | −0.653227 | − | 0.757162i | \(-0.726585\pi\) | ||||
−0.653227 | + | 0.757162i | \(0.726585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2232.00i | − 0.203903i | ||||||||
\(494\) | 5978.00 | 0.544459 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2560.00 | −0.231749 | ||||||||
\(497\) | 7878.00i | 0.711019i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9992.00 | −0.896400 | −0.448200 | − | 0.893933i | \(-0.647935\pi\) | ||||
−0.448200 | + | 0.893933i | \(0.647935\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14580.0i | 1.29629i | ||||||||
\(503\) | 21258.0i | 1.88439i | 0.335067 | + | 0.942194i | \(0.391241\pi\) | ||||
−0.335067 | + | 0.942194i | \(0.608759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1080.00 | 0.0948851 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11168.0i | 0.975393i | ||||||||
\(509\) | −16614.0 | −1.44676 | −0.723382 | − | 0.690448i | \(-0.757413\pi\) | ||||
−0.723382 | + | 0.690448i | \(0.757413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5603.00 | −0.485053 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −624.000 | −0.0535476 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4320.00i | 0.367492i | ||||||||
\(518\) | − 2366.00i | − 0.200687i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11838.0 | −0.995455 | −0.497728 | − | 0.867333i | \(-0.665832\pi\) | ||||
−0.497728 | + | 0.867333i | \(0.665832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2201.00i | 0.184021i | 0.995758 | + | 0.0920105i | \(0.0293293\pi\) | ||||
−0.995758 | + | 0.0920105i | \(0.970671\pi\) | |||||||
\(524\) | −2832.00 | −0.236100 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16008.0 | −1.32696 | ||||||||
\(527\) | − 1920.00i | − 0.158703i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11843.0 | 0.973371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 2548.00i | − 0.207650i | ||||||||
\(533\) | 23058.0i | 1.87383i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1496.00 | 0.120555 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 648.000i | − 0.0519280i | ||||||||
\(539\) | 5220.00 | 0.417145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10795.0 | −0.857880 | −0.428940 | − | 0.903333i | \(-0.641113\pi\) | ||||
−0.428940 | + | 0.903333i | \(0.641113\pi\) | |||||||
\(542\) | − 15698.0i | − 1.24407i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −384.000 | −0.0302645 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14185.0i | 1.10879i | 0.832254 | + | 0.554394i | \(0.187050\pi\) | ||||
−0.832254 | + | 0.554394i | \(0.812950\pi\) | |||||||
\(548\) | 6744.00i | 0.525711i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9114.00 | −0.704663 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 14963.0i | − 1.15062i | ||||||||
\(554\) | −11516.0 | −0.883155 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1228.00 | −0.0936669 | ||||||||
\(557\) | − 3576.00i | − 0.272029i | −0.990707 | − | 0.136014i | \(-0.956571\pi\) | ||||
0.990707 | − | 0.136014i | \(-0.0434293\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16348.0 | −1.23694 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5376.00i | 0.403510i | ||||||||
\(563\) | 9132.00i | 0.683602i | 0.939772 | + | 0.341801i | \(0.111037\pi\) | ||||
−0.939772 | + | 0.341801i | \(0.888963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6520.00 | −0.484198 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 4848.00i | − 0.358130i | ||||||||
\(569\) | 25020.0 | 1.84340 | 0.921699 | − | 0.387907i | \(-0.126802\pi\) | ||||
0.921699 | + | 0.387907i | \(0.126802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15997.0 | −1.17242 | −0.586212 | − | 0.810158i | \(-0.699381\pi\) | ||||
−0.586212 | + | 0.810158i | \(0.699381\pi\) | |||||||
\(572\) | 7320.00i | 0.535078i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9828.00 | 0.714656 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5971.00i | 0.430808i | 0.976525 | + | 0.215404i | \(0.0691068\pi\) | ||||
−0.976525 | + | 0.215404i | \(0.930893\pi\) | |||||||
\(578\) | 9538.00i | 0.686381i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1326.00 | 0.0946846 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 17100.0i | − 1.21477i | ||||||||
\(584\) | 3448.00 | 0.244314 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11844.0 | 0.834934 | ||||||||
\(587\) | 19242.0i | 1.35299i | 0.736449 | + | 0.676493i | \(0.236501\pi\) | ||||
−0.736449 | + | 0.676493i | \(0.763499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7840.00 | −0.548458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1456.00i | 0.101083i | ||||||||
\(593\) | − 8118.00i | − 0.562169i | −0.959683 | − | 0.281085i | \(-0.909306\pi\) | ||||
0.959683 | − | 0.281085i | \(-0.0906941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7248.00 | 0.498137 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 2196.00i | − 0.150169i | ||||||||
\(599\) | 1902.00 | 0.129739 | 0.0648695 | − | 0.997894i | \(-0.479337\pi\) | ||||
0.0648695 | + | 0.997894i | \(0.479337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14074.0 | −0.955225 | −0.477613 | − | 0.878571i | \(-0.658498\pi\) | ||||
−0.477613 | + | 0.878571i | \(0.658498\pi\) | |||||||
\(602\) | 6968.00i | 0.471752i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −812.000 | −0.0547017 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13825.0i | 0.924447i | 0.886763 | + | 0.462224i | \(0.152948\pi\) | ||||
−0.886763 | + | 0.462224i | \(0.847052\pi\) | |||||||
\(608\) | 1568.00i | 0.104590i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8784.00 | 0.581608 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15569.0i | 1.02582i | 0.858443 | + | 0.512909i | \(0.171432\pi\) | ||||
−0.858443 | + | 0.512909i | \(0.828568\pi\) | |||||||
\(614\) | 7456.00 | 0.490065 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3120.00 | 0.204072 | ||||||||
\(617\) | 11922.0i | 0.777896i | 0.921260 | + | 0.388948i | \(0.127161\pi\) | ||||
−0.921260 | + | 0.388948i | \(0.872839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6899.00 | −0.447971 | −0.223986 | − | 0.974592i | \(-0.571907\pi\) | ||||
−0.223986 | + | 0.974592i | \(0.571907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1464.00i | 0.0943747i | ||||||||
\(623\) | 12792.0i | 0.822633i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10714.0 | −0.684054 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 856.000i | − 0.0543919i | ||||||||
\(629\) | −1092.00 | −0.0692224 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11711.0 | 0.738839 | 0.369420 | − | 0.929263i | \(-0.379557\pi\) | ||||
0.369420 | + | 0.929263i | \(0.379557\pi\) | |||||||
\(632\) | 9208.00i | 0.579548i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9144.00 | 0.572799 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 10614.0i | − 0.660192i | ||||||||
\(638\) | − 11160.0i | − 0.692521i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9240.00 | −0.569357 | −0.284679 | − | 0.958623i | \(-0.591887\pi\) | ||||
−0.284679 | + | 0.958623i | \(0.591887\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 17908.0i | − 1.09832i | −0.835716 | − | 0.549162i | \(-0.814947\pi\) | ||||
0.835716 | − | 0.549162i | \(-0.185053\pi\) | |||||||
\(644\) | −936.000 | −0.0572726 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1176.00 | −0.0716240 | ||||||||
\(647\) | 7530.00i | 0.457550i | 0.973479 | + | 0.228775i | \(0.0734720\pi\) | ||||
−0.973479 | + | 0.228775i | \(0.926528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6120.00 | 0.370156 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2692.00i | 0.161698i | ||||||||
\(653\) | 22788.0i | 1.36564i | 0.730586 | + | 0.682820i | \(0.239247\pi\) | ||||
−0.730586 | + | 0.682820i | \(0.760753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6048.00 | −0.359961 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 3744.00i | − 0.221818i | ||||||||
\(659\) | 16440.0 | 0.971793 | 0.485896 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485896 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12421.0 | −0.730894 | −0.365447 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365447 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(662\) | 1690.00i | 0.0992201i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −816.000 | −0.0476912 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3348.00i | 0.194355i | ||||||||
\(668\) | 14784.0i | 0.856303i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26310.0 | −1.51369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6461.00i | 0.370064i | 0.982732 | + | 0.185032i | \(0.0592389\pi\) | ||||
−0.982732 | + | 0.185032i | \(0.940761\pi\) | |||||||
\(674\) | 17446.0 | 0.997025 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6096.00 | 0.346837 | ||||||||
\(677\) | − 912.000i | − 0.0517740i | −0.999665 | − | 0.0258870i | \(-0.991759\pi\) | ||||
0.999665 | − | 0.0258870i | \(-0.00824101\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3445.00 | −0.194708 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 9600.00i | − 0.539007i | ||||||||
\(683\) | 14442.0i | 0.809089i | 0.914518 | + | 0.404544i | \(0.132570\pi\) | ||||
−0.914518 | + | 0.404544i | \(0.867430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13442.0 | −0.748131 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 4288.00i | − 0.237614i | ||||||||
\(689\) | −34770.0 | −1.92254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1892.00 | 0.104161 | 0.0520804 | − | 0.998643i | \(-0.483415\pi\) | ||||
0.0520804 | + | 0.998643i | \(0.483415\pi\) | |||||||
\(692\) | 12528.0i | 0.688213i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18036.0 | −0.986509 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 4536.00i | − 0.246504i | ||||||||
\(698\) | − 11518.0i | − 0.624588i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7914.00 | 0.426402 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4459.00i | 0.239224i | ||||||||
\(704\) | −1920.00 | −0.102788 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11544.0 | −0.615388 | ||||||||
\(707\) | 16224.0i | 0.863036i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1291.00 | 0.0683844 | 0.0341922 | − | 0.999415i | \(-0.489114\pi\) | ||||
0.0341922 | + | 0.999415i | \(0.489114\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 7872.00i | − 0.414348i | ||||||||
\(713\) | 2880.00i | 0.151272i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2040.00 | −0.106478 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 4092.00i | − 0.212691i | ||||||||
\(719\) | −30210.0 | −1.56696 | −0.783479 | − | 0.621418i | \(-0.786557\pi\) | ||||
−0.783479 | + | 0.621418i | \(0.786557\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15925.0 | 0.822577 | ||||||||
\(722\) | − 8916.00i | − 0.459583i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4348.00 | 0.223194 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 15680.0i | − 0.799916i | −0.916533 | − | 0.399958i | \(-0.869025\pi\) | ||||
0.916533 | − | 0.399958i | \(-0.130975\pi\) | |||||||
\(728\) | − 6344.00i | − 0.322973i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3216.00 | 0.162720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13898.0i | 0.700320i | 0.936690 | + | 0.350160i | \(0.113873\pi\) | ||||
−0.936690 | + | 0.350160i | \(0.886127\pi\) | |||||||
\(734\) | −2138.00 | −0.107514 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 576.000 | 0.0288473 | ||||||||
\(737\) | 5610.00i | 0.280389i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35300.0 | −1.75715 | −0.878573 | − | 0.477607i | \(-0.841504\pi\) | ||||
−0.878573 | + | 0.477607i | \(0.841504\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14820.0i | 0.733234i | ||||||||
\(743\) | − 28188.0i | − 1.39181i | −0.718132 | − | 0.695907i | \(-0.755003\pi\) | ||||
0.718132 | − | 0.695907i | \(-0.244997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14266.0 | −0.700155 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 1440.00i | − 0.0703899i | ||||||||
\(749\) | 1014.00 | 0.0494670 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25163.0 | 1.22265 | 0.611326 | − | 0.791379i | \(-0.290637\pi\) | ||||
0.611326 | + | 0.791379i | \(0.290637\pi\) | |||||||
\(752\) | 2304.00i | 0.111726i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22692.0 | −1.09601 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 7979.00i | − 0.383093i | −0.981484 | − | 0.191547i | \(-0.938650\pi\) | ||||
0.981484 | − | 0.191547i | \(-0.0613503\pi\) | |||||||
\(758\) | 17114.0i | 0.820064i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26622.0 | −1.26813 | −0.634065 | − | 0.773280i | \(-0.718615\pi\) | ||||
−0.634065 | + | 0.773280i | \(0.718615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 28574.0i | − 1.35576i | ||||||||
\(764\) | −16224.0 | −0.768277 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28656.0 | 1.35168 | ||||||||
\(767\) | − 12444.0i | − 0.585824i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35413.0 | 1.66063 | 0.830316 | − | 0.557293i | \(-0.188160\pi\) | ||||
0.830316 | + | 0.557293i | \(0.188160\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 1892.00i | − 0.0882054i | ||||||||
\(773\) | 33834.0i | 1.57429i | 0.616769 | + | 0.787144i | \(0.288441\pi\) | ||||
−0.616769 | + | 0.787144i | \(0.711559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2120.00 | 0.0980716 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27000.0i | 1.24421i | ||||||||
\(779\) | −18522.0 | −0.851886 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18180.0 | 0.832947 | ||||||||
\(782\) | 432.000i | 0.0197548i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2784.00 | 0.126822 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13469.0i | − 0.610061i | −0.952343 | − | 0.305030i | \(-0.901333\pi\) | ||||
0.952343 | − | 0.305030i | \(-0.0986667\pi\) | |||||||
\(788\) | − 10224.0i | − 0.462202i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25818.0 | 1.16053 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53497.0i | 2.39563i | ||||||||
\(794\) | 2668.00 | 0.119249 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11692.0 | −0.520618 | ||||||||
\(797\) | − 21168.0i | − 0.940789i | −0.882456 | − | 0.470395i | \(-0.844112\pi\) | ||||
0.882456 | − | 0.470395i | \(-0.155888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1728.00 | −0.0765109 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 6948.00i | − 0.305913i | ||||||||
\(803\) | 12930.0i | 0.568231i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19520.0 | −0.853055 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 9984.00i | − 0.434698i | ||||||||
\(809\) | 408.000 | 0.0177312 | 0.00886558 | − | 0.999961i | \(-0.497178\pi\) | ||||
0.00886558 | + | 0.999961i | \(0.497178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36916.0 | −1.59839 | −0.799196 | − | 0.601070i | \(-0.794741\pi\) | ||||
−0.799196 | + | 0.601070i | \(0.794741\pi\) | |||||||
\(812\) | 9672.00i | 0.418006i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5460.00 | −0.235102 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 13132.0i | − 0.562338i | ||||||||
\(818\) | − 1138.00i | − 0.0486421i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24636.0 | 1.04726 | 0.523631 | − | 0.851945i | \(-0.324577\pi\) | ||||
0.523631 | + | 0.851945i | \(0.324577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 18187.0i | − 0.770303i | −0.922853 | − | 0.385151i | \(-0.874149\pi\) | ||||
0.922853 | − | 0.385151i | \(-0.125851\pi\) | |||||||
\(824\) | −9800.00 | −0.414319 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5304.00 | −0.223426 | ||||||||
\(827\) | 1464.00i | 0.0615578i | 0.999526 | + | 0.0307789i | \(0.00979877\pi\) | ||||
−0.999526 | + | 0.0307789i | \(0.990201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12295.0 | 0.515106 | 0.257553 | − | 0.966264i | \(-0.417084\pi\) | ||||
0.257553 | + | 0.966264i | \(0.417084\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3904.00i | 0.162676i | ||||||||
\(833\) | 2088.00i | 0.0868486i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5880.00 | −0.243258 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 18264.0i | − 0.752887i | ||||||||
\(839\) | 46884.0 | 1.92922 | 0.964610 | − | 0.263681i | \(-0.0849367\pi\) | ||||
0.964610 | + | 0.263681i | \(0.0849367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10207.0 | 0.418508 | ||||||||
\(842\) | − 5942.00i | − 0.243201i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12700.0 | 0.517953 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 5603.00i | − 0.227298i | ||||||||
\(848\) | − 9120.00i | − 0.369318i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1638.00 | 0.0659811 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12197.0i | 0.489587i | 0.969575 | + | 0.244793i | \(0.0787201\pi\) | ||||
−0.969575 | + | 0.244793i | \(0.921280\pi\) | |||||||
\(854\) | 22802.0 | 0.913663 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −624.000 | −0.0249157 | ||||||||
\(857\) | − 28182.0i | − 1.12331i | −0.827371 | − | 0.561656i | \(-0.810164\pi\) | ||||
0.827371 | − | 0.561656i | \(-0.189836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25433.0 | −1.01020 | −0.505101 | − | 0.863060i | \(-0.668545\pi\) | ||||
−0.505101 | + | 0.863060i | \(0.668545\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 24084.0i | − 0.951629i | ||||||||
\(863\) | 16968.0i | 0.669290i | 0.942344 | + | 0.334645i | \(0.108616\pi\) | ||||
−0.942344 | + | 0.334645i | \(0.891384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17132.0 | 0.672251 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8320.00i | 0.325345i | ||||||||
\(869\) | −34530.0 | −1.34793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11407.0 | 0.443756 | ||||||||
\(872\) | 17584.0i | 0.682878i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1764.00 | 0.0682702 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22423.0i | 0.863365i | 0.902026 | + | 0.431682i | \(0.142080\pi\) | ||||
−0.902026 | + | 0.431682i | \(0.857920\pi\) | |||||||
\(878\) | − 14800.0i | − 0.568879i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8442.00 | −0.322836 | −0.161418 | − | 0.986886i | \(-0.551607\pi\) | ||||
−0.161418 | + | 0.986886i | \(0.551607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41207.0i | 1.57047i | 0.619197 | + | 0.785236i | \(0.287458\pi\) | ||||
−0.619197 | + | 0.785236i | \(0.712542\pi\) | |||||||
\(884\) | −2928.00 | −0.111402 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5160.00 | −0.195659 | ||||||||
\(887\) | 8472.00i | 0.320701i | 0.987060 | + | 0.160351i | \(0.0512625\pi\) | ||||
−0.987060 | + | 0.160351i | \(0.948738\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36296.0 | 1.36932 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8704.00i | 0.326717i | ||||||||
\(893\) | 7056.00i | 0.264412i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1664.00 | 0.0620428 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26400.0i | 0.981046i | ||||||||
\(899\) | 29760.0 | 1.10406 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6840.00 | 0.252912 | ||||||||
\(902\) | − 22680.0i | − 0.837208i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15888.0 | −0.584543 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21799.0i | 0.798042i | 0.916942 | + | 0.399021i | \(0.130650\pi\) | ||||
−0.916942 | + | 0.399021i | \(0.869350\pi\) | |||||||
\(908\) | 15336.0i | 0.560510i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23544.0 | −0.856254 | −0.428127 | − | 0.903719i | \(-0.640826\pi\) | ||||
−0.428127 | + | 0.903719i | \(0.640826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 3060.00i | − 0.110921i | ||||||||
\(914\) | 36076.0 | 1.30557 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12808.0 | −0.461996 | ||||||||
\(917\) | 9204.00i | 0.331453i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11072.0 | −0.397423 | −0.198711 | − | 0.980058i | \(-0.563676\pi\) | ||||
−0.198711 | + | 0.980058i | \(0.563676\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 11088.0i | − 0.396056i | ||||||||
\(923\) | − 36966.0i | − 1.31826i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34274.0 | 1.21632 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 5952.00i | − 0.210543i | ||||||||
\(929\) | −21654.0 | −0.764741 | −0.382371 | − | 0.924009i | \(-0.624892\pi\) | ||||
−0.382371 | + | 0.924009i | \(0.624892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8526.00 | 0.300138 | ||||||||
\(932\) | 16608.0i | 0.583705i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31776.0 | 1.11321 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42835.0i | 1.49345i | 0.665135 | + | 0.746723i | \(0.268374\pi\) | ||||
−0.665135 | + | 0.746723i | \(0.731626\pi\) | |||||||
\(938\) | − 4862.00i | − 0.169243i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48534.0 | 1.68136 | 0.840682 | − | 0.541529i | \(-0.182155\pi\) | ||||
0.840682 | + | 0.541529i | \(0.182155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6804.00i | 0.234962i | ||||||||
\(944\) | 3264.00 | 0.112536 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16080.0 | 0.552649 | ||||||||
\(947\) | 14676.0i | 0.503597i | 0.967780 | + | 0.251798i | \(0.0810219\pi\) | ||||
−0.967780 | + | 0.251798i | \(0.918978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26291.0 | 0.899307 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1248.00i | 0.0424873i | ||||||||
\(953\) | − 27372.0i | − 0.930395i | −0.885207 | − | 0.465197i | \(-0.845983\pi\) | ||||
0.885207 | − | 0.465197i | \(-0.154017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21864.0 | 0.739678 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7884.00i | 0.265888i | ||||||||
\(959\) | 21918.0 | 0.738028 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4191.00 | −0.140680 | ||||||||
\(962\) | 11102.0i | 0.372082i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3772.00 | 0.126025 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3581.00i | − 0.119087i | −0.998226 | − | 0.0595435i | \(-0.981035\pi\) | ||||
0.998226 | − | 0.0595435i | \(-0.0189645\pi\) | |||||||
\(968\) | 3448.00i | 0.114486i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1824.00 | 0.0602832 | 0.0301416 | − | 0.999546i | \(-0.490404\pi\) | ||||
0.0301416 | + | 0.999546i | \(0.490404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3991.00i | 0.131496i | ||||||||
\(974\) | 2758.00 | 0.0907310 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14032.0 | −0.460198 | ||||||||
\(977\) | − 29778.0i | − 0.975110i | −0.873092 | − | 0.487555i | \(-0.837889\pi\) | ||||
0.873092 | − | 0.487555i | \(-0.162111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29520.0 | 0.963701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 28428.0i | − 0.923802i | ||||||||
\(983\) | − 9402.00i | − 0.305063i | −0.988299 | − | 0.152532i | \(-0.951257\pi\) | ||||
0.988299 | − | 0.152532i | \(-0.0487426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4464.00 | 0.144181 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11956.0i | 0.384991i | ||||||||
\(989\) | −4824.00 | −0.155100 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24907.0 | −0.798382 | −0.399191 | − | 0.916868i | \(-0.630709\pi\) | ||||
−0.399191 | + | 0.916868i | \(0.630709\pi\) | |||||||
\(992\) | − 5120.00i | − 0.163871i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15756.0 | −0.502767 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 27830.0i | − 0.884037i | −0.897006 | − | 0.442019i | \(-0.854263\pi\) | ||||
0.897006 | − | 0.442019i | \(-0.145737\pi\) | |||||||
\(998\) | − 19984.0i | − 0.633850i | ||||||||
\(999\) | 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 | 1350.4.c.o.649.2 | 2 | ||
3.2 | odd | 2 | 1350.4.c.f.649.1 | 2 | |||
5.2 | odd | 4 | 270.4.a.d.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 1350.4.a.w.1.1 | 1 | |||
5.4 | even | 2 | inner | 1350.4.c.o.649.1 | 2 | ||
15.2 | even | 4 | 270.4.a.h.1.1 | yes | 1 | ||
15.8 | even | 4 | 1350.4.a.i.1.1 | 1 | |||
15.14 | odd | 2 | 1350.4.c.f.649.2 | 2 | |||
20.7 | even | 4 | 2160.4.a.q.1.1 | 1 | |||
45.2 | even | 12 | 810.4.e.j.271.1 | 2 | |||
45.7 | odd | 12 | 810.4.e.r.271.1 | 2 | |||
45.22 | odd | 12 | 810.4.e.r.541.1 | 2 | |||
45.32 | even | 12 | 810.4.e.j.541.1 | 2 | |||
60.47 | odd | 4 | 2160.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.d.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
270.4.a.h.1.1 | yes | 1 | 15.2 | even | 4 | ||
810.4.e.j.271.1 | 2 | 45.2 | even | 12 | |||
810.4.e.j.541.1 | 2 | 45.32 | even | 12 | |||
810.4.e.r.271.1 | 2 | 45.7 | odd | 12 | |||
810.4.e.r.541.1 | 2 | 45.22 | odd | 12 | |||
1350.4.a.i.1.1 | 1 | 15.8 | even | 4 | |||
1350.4.a.w.1.1 | 1 | 5.3 | odd | 4 | |||
1350.4.c.f.649.1 | 2 | 3.2 | odd | 2 | |||
1350.4.c.f.649.2 | 2 | 15.14 | odd | 2 | |||
1350.4.c.o.649.1 | 2 | 5.4 | even | 2 | inner | ||
1350.4.c.o.649.2 | 2 | 1.1 | even | 1 | trivial | ||
2160.4.a.g.1.1 | 1 | 60.47 | odd | 4 | |||
2160.4.a.q.1.1 | 1 | 20.7 | even | 4 |