Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(32,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.e (of order \(4\), degree \(2\), 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: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 32.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.32 |
Dual form | 75.4.e.b.68.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.67423 | − | 3.67423i | 1.29904 | − | 1.29904i | 0.370011 | − | 0.929028i | \(-0.379354\pi\) |
0.929028 | − | 0.370011i | \(-0.120646\pi\) | |||||||
\(3\) | 3.67423 | + | 3.67423i | 0.707107 | + | 0.707107i | ||||
\(4\) | − | 19.0000i | − | 2.37500i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 27.0000 | 1.83712 | ||||||||
\(7\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | −40.4166 | − | 40.4166i | −1.78618 | − | 1.78618i | ||||
\(9\) | 27.0000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 69.8105 | − | 69.8105i | 1.67938 | − | 1.67938i | ||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −145.000 | −2.26562 | ||||||||
\(17\) | −14.6969 | + | 14.6969i | −0.209678 | + | 0.209678i | −0.804131 | − | 0.594452i | \(-0.797369\pi\) |
0.594452 | + | 0.804131i | \(0.297369\pi\) | |||||||
\(18\) | 99.2043 | + | 99.2043i | 1.29904 | + | 1.29904i | ||||
\(19\) | 164.000i | 1.98022i | 0.140293 | + | 0.990110i | \(0.455195\pi\) | ||||
−0.140293 | + | 0.990110i | \(0.544805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −139.621 | − | 139.621i | −1.26578 | − | 1.26578i | −0.948247 | − | 0.317535i | \(-0.897145\pi\) |
−0.317535 | − | 0.948247i | \(-0.602855\pi\) | |||||||
\(24\) | − | 297.000i | − | 2.52604i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −99.2043 | + | 99.2043i | −0.707107 | + | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 232.000 | 1.34414 | 0.672071 | − | 0.740486i | \(-0.265405\pi\) | ||||
0.672071 | + | 0.740486i | \(0.265405\pi\) | |||||||
\(32\) | −209.431 | + | 209.431i | −1.15696 | + | 1.15696i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 108.000i | 0.544760i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 513.000 | 2.37500 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 602.574 | + | 602.574i | 2.57238 | + | 2.57238i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1026.00 | −3.28860 | ||||||||
\(47\) | 242.499 | − | 242.499i | 0.752600 | − | 0.752600i | −0.222364 | − | 0.974964i | \(-0.571377\pi\) |
0.974964 | + | 0.222364i | \(0.0713773\pi\) | |||||||
\(48\) | −532.764 | − | 532.764i | −1.60204 | − | 1.60204i | ||||
\(49\) | − | 343.000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −108.000 | −0.296530 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −323.333 | − | 323.333i | −0.837984 | − | 0.837984i | 0.150609 | − | 0.988593i | \(-0.451876\pi\) |
−0.988593 | + | 0.150609i | \(0.951876\pi\) | |||||||
\(54\) | 729.000i | 1.83712i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −602.574 | + | 602.574i | −1.40023 | + | 1.40023i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −358.000 | −0.751430 | −0.375715 | − | 0.926735i | \(-0.622603\pi\) | ||||
−0.375715 | + | 0.926735i | \(0.622603\pi\) | |||||||
\(62\) | 852.422 | − | 852.422i | 1.74609 | − | 1.74609i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 379.000i | 0.740234i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 279.242 | + | 279.242i | 0.497986 | + | 0.497986i | ||||
\(69\) | − | 1026.00i | − | 1.79009i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 1091.25 | − | 1091.25i | 1.78618 | − | 1.78618i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3116.00 | 4.70302 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 304.000i | 0.432945i | 0.976289 | + | 0.216473i | \(0.0694552\pi\) | ||||
−0.976289 | + | 0.216473i | \(0.930545\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −729.000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −580.529 | − | 580.529i | −0.767727 | − | 0.767727i | 0.209979 | − | 0.977706i | \(-0.432660\pi\) |
−0.977706 | + | 0.209979i | \(0.932660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2652.80 | + | 2652.80i | −3.00623 | + | 3.00623i | ||||
\(93\) | 852.422 | + | 852.422i | 0.950453 | + | 0.950453i | ||||
\(94\) | − | 1782.00i | − | 1.95531i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1539.00 | −1.63618 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | −1260.26 | − | 1260.26i | −1.29904 | − | 1.29904i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | −396.817 | + | 396.817i | −0.385204 | + | 0.385204i | ||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2376.00 | −2.17715 | ||||||||
\(107\) | 1565.22 | − | 1565.22i | 1.41417 | − | 1.41417i | 0.701370 | − | 0.712798i | \(-0.252572\pi\) |
0.712798 | − | 0.701370i | \(-0.247428\pi\) | |||||||
\(108\) | 1884.88 | + | 1884.88i | 1.67938 | + | 1.67938i | ||||
\(109\) | 1834.00i | 1.61161i | 0.592182 | + | 0.805804i | \(0.298267\pi\) | ||||
−0.592182 | + | 0.805804i | \(0.701733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1366.82 | + | 1366.82i | 1.13787 | + | 1.13787i | 0.988832 | + | 0.149037i | \(0.0476174\pi\) |
0.149037 | + | 0.988832i | \(0.452383\pi\) | |||||||
\(114\) | 4428.00i | 3.63790i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1331.00 | 1.00000 | ||||||||
\(122\) | −1315.38 | + | 1315.38i | −0.976136 | + | 0.976136i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4408.00i | − | 3.19234i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −282.916 | − | 282.916i | −0.195363 | − | 0.195363i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1188.00 | 0.749045 | ||||||||
\(137\) | −1778.33 | + | 1778.33i | −1.10900 | + | 1.10900i | −0.115717 | + | 0.993282i | \(0.536917\pi\) |
−0.993282 | + | 0.115717i | \(0.963083\pi\) | |||||||
\(138\) | −3769.76 | − | 3769.76i | −2.32539 | − | 2.32539i | ||||
\(139\) | 1604.00i | 0.978773i | 0.872067 | + | 0.489387i | \(0.162779\pi\) | ||||
−0.872067 | + | 0.489387i | \(0.837221\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1782.00 | 1.06434 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 3915.00i | − | 2.26562i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1260.26 | − | 1260.26i | 0.707107 | − | 0.707107i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3112.00 | 1.67716 | 0.838579 | − | 0.544779i | \(-0.183387\pi\) | ||||
0.838579 | + | 0.544779i | \(0.183387\pi\) | |||||||
\(152\) | 6628.32 | − | 6628.32i | 3.53702 | − | 3.53702i | ||||
\(153\) | −396.817 | − | 396.817i | −0.209678 | − | 0.209678i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 1116.97 | + | 1116.97i | 0.562412 | + | 0.562412i | ||||
\(159\) | − | 2376.00i | − | 1.18509i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2678.52 | + | 2678.52i | −1.29904 | + | 1.29904i | ||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4266.00 | −1.99461 | ||||||||
\(167\) | 1491.74 | − | 1491.74i | 0.691223 | − | 0.691223i | −0.271278 | − | 0.962501i | \(-0.587446\pi\) |
0.962501 | + | 0.271278i | \(0.0874463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4428.00 | −1.98022 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3203.93 | + | 3203.93i | 1.40804 | + | 1.40804i | 0.770031 | + | 0.638007i | \(0.220241\pi\) |
0.638007 | + | 0.770031i | \(0.279759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1298.00 | −0.533036 | −0.266518 | − | 0.963830i | \(-0.585873\pi\) | ||||
−0.266518 | + | 0.963830i | \(0.585873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1315.38 | − | 1315.38i | −0.531341 | − | 0.531341i | ||||
\(184\) | 11286.0i | 4.52182i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6264.00 | 2.46935 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4607.49 | − | 4607.49i | −1.78742 | − | 1.78742i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | −1392.53 | + | 1392.53i | −0.523425 | + | 0.523425i | ||||
\(193\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6517.00 | −2.37500 | ||||||||
\(197\) | −3468.48 | + | 3468.48i | −1.25441 | + | 1.25441i | −0.300687 | + | 0.953723i | \(0.597216\pi\) |
−0.953723 | + | 0.300687i | \(0.902784\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5456.00i | − | 1.94355i | −0.235919 | − | 0.971773i | \(-0.575810\pi\) | ||
0.235919 | − | 0.971773i | \(-0.424190\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2052.00i | 0.704259i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3769.76 | − | 3769.76i | 1.26578 | − | 1.26578i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4228.00 | −1.37947 | −0.689733 | − | 0.724063i | \(-0.742272\pi\) | ||||
−0.689733 | + | 0.724063i | \(0.742272\pi\) | |||||||
\(212\) | −6143.32 | + | 6143.32i | −1.99021 | + | 1.99021i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 11502.0i | − | 3.67411i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8019.00 | 2.52604 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6738.55 | + | 6738.55i | 2.09354 | + | 2.09354i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10044.0 | 2.95627 | ||||||||
\(227\) | −1594.62 | + | 1594.62i | −0.466249 | + | 0.466249i | −0.900697 | − | 0.434448i | \(-0.856943\pi\) |
0.434448 | + | 0.900697i | \(0.356943\pi\) | |||||||
\(228\) | 11448.9 | + | 11448.9i | 3.32554 | + | 3.32554i | ||||
\(229\) | − | 286.000i | − | 0.0825302i | −0.999148 | − | 0.0412651i | \(-0.986861\pi\) | ||
0.999148 | − | 0.0412651i | \(-0.0131388\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3924.08 | − | 3924.08i | −1.10333 | − | 1.10333i | −0.994007 | − | 0.109320i | \(-0.965133\pi\) |
−0.109320 | − | 0.994007i | \(-0.534867\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1116.97 | + | 1116.97i | −0.306138 | + | 0.306138i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1438.00 | −0.384356 | −0.192178 | − | 0.981360i | \(-0.561555\pi\) | ||||
−0.192178 | + | 0.981360i | \(0.561555\pi\) | |||||||
\(242\) | 4890.41 | − | 4890.41i | 1.29904 | − | 1.29904i | ||||
\(243\) | −2678.52 | − | 2678.52i | −0.707107 | − | 0.707107i | ||||
\(244\) | 6802.00i | 1.78465i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9376.65 | − | 9376.65i | −2.40088 | − | 2.40088i | ||||
\(249\) | − | 4266.00i | − | 1.08573i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5111.00 | −1.24780 | ||||||||
\(257\) | −3541.96 | + | 3541.96i | −0.859695 | + | 0.859695i | −0.991302 | − | 0.131607i | \(-0.957986\pi\) |
0.131607 | + | 0.991302i | \(0.457986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4034.31 | − | 4034.31i | −0.945879 | − | 0.945879i | 0.0527298 | − | 0.998609i | \(-0.483208\pi\) |
−0.998609 | + | 0.0527298i | \(0.983208\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6752.00 | 1.51349 | 0.756743 | − | 0.653712i | \(-0.226789\pi\) | ||||
0.756743 | + | 0.653712i | \(0.226789\pi\) | |||||||
\(272\) | 2131.06 | − | 2131.06i | 0.475052 | − | 0.475052i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13068.0i | 2.88127i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −19494.0 | −4.25145 | ||||||||
\(277\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(278\) | 5893.47 | + | 5893.47i | 1.27146 | + | 1.27146i | ||||
\(279\) | 6264.00i | 1.34414i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 6547.49 | − | 6547.49i | 1.38261 | − | 1.38261i | ||||
\(283\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5654.65 | − | 5654.65i | −1.15696 | − | 1.15696i | ||||
\(289\) | 4481.00i | 0.912070i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6731.20 | + | 6731.20i | 1.34212 | + | 1.34212i | 0.893948 | + | 0.448171i | \(0.147924\pi\) |
0.448171 | + | 0.893948i | \(0.352076\pi\) | |||||||
\(294\) | − | 9261.00i | − | 1.83712i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11434.2 | − | 11434.2i | 2.17869 | − | 2.17869i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 23780.0i | − | 4.48644i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2916.00 | −0.544760 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5776.00 | 1.02824 | ||||||||
\(317\) | 3586.05 | − | 3586.05i | 0.635372 | − | 0.635372i | −0.314039 | − | 0.949410i | \(-0.601682\pi\) |
0.949410 | + | 0.314039i | \(0.101682\pi\) | |||||||
\(318\) | −8729.98 | − | 8729.98i | −1.53947 | − | 1.53947i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11502.0 | 1.99993 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2410.30 | − | 2410.30i | −0.415209 | − | 0.415209i | ||||
\(324\) | 13851.0i | 2.37500i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6738.55 | + | 6738.55i | −1.13958 | + | 1.13958i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5852.00 | 0.971767 | 0.485884 | − | 0.874023i | \(-0.338498\pi\) | ||||
0.485884 | + | 0.874023i | \(0.338498\pi\) | |||||||
\(332\) | −11030.1 | + | 11030.1i | −1.82335 | + | 1.82335i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 10962.0i | − | 1.79585i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(338\) | 8072.29 | + | 8072.29i | 1.29904 | + | 1.29904i | ||||
\(339\) | 10044.0i | 1.60919i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −16269.5 | + | 16269.5i | −2.57238 | + | 2.57238i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23544.0 | 3.65819 | ||||||||
\(347\) | 6856.12 | − | 6856.12i | 1.06068 | − | 1.06068i | 0.0626439 | − | 0.998036i | \(-0.480047\pi\) |
0.998036 | − | 0.0626439i | \(-0.0199532\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3706.00i | − | 0.568417i | −0.958762 | − | 0.284209i | \(-0.908269\pi\) | ||
0.958762 | − | 0.284209i | \(-0.0917308\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9214.98 | − | 9214.98i | −1.38942 | − | 1.38942i | −0.826544 | − | 0.562872i | \(-0.809696\pi\) |
−0.562872 | − | 0.826544i | \(-0.690304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −20037.0 | −2.92127 | ||||||||
\(362\) | −4769.16 | + | 4769.16i | −0.692435 | + | 0.692435i | ||||
\(363\) | 4890.41 | + | 4890.41i | 0.707107 | + | 0.707107i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9666.00 | −1.38046 | ||||||||
\(367\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | 20245.0 | + | 20245.0i | 2.86779 | + | 2.86779i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 16196.0 | − | 16196.0i | 2.25732 | − | 2.25732i | ||||
\(373\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19602.0 | −2.68855 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4484.00i | 0.607725i | 0.952716 | + | 0.303862i | \(0.0982763\pi\) | ||||
−0.952716 | + | 0.303862i | \(0.901724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8164.15 | + | 8164.15i | 1.08921 | + | 1.08921i | 0.995610 | + | 0.0936033i | \(0.0298385\pi\) |
0.0936033 | + | 0.995610i | \(0.470161\pi\) | |||||||
\(384\) | − | 2079.00i | − | 0.276285i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4104.00 | 0.530814 | ||||||||
\(392\) | −13862.9 | + | 13862.9i | −1.78618 | + | 1.78618i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25488.0i | 3.25905i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | −20046.6 | − | 20046.6i | −2.52474 | − | 2.52474i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4364.99 | + | 4364.99i | 0.529655 | + | 0.529655i | ||||
\(409\) | − | 14326.0i | − | 1.73197i | −0.500071 | − | 0.865984i | \(-0.666693\pi\) | ||
0.500071 | − | 0.865984i | \(-0.333307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13068.0 | −1.56836 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 27702.0i | − | 3.28860i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5893.47 | + | 5893.47i | −0.692097 | + | 0.692097i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6878.00 | −0.796231 | −0.398115 | − | 0.917335i | \(-0.630336\pi\) | ||||
−0.398115 | + | 0.917335i | \(0.630336\pi\) | |||||||
\(422\) | −15534.7 | + | 15534.7i | −1.79198 | + | 1.79198i | ||||
\(423\) | 6547.49 | + | 6547.49i | 0.752600 | + | 0.752600i | ||||
\(424\) | 26136.0i | 2.99358i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −29739.3 | − | 29739.3i | −3.35865 | − | 3.35865i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 14384.6 | − | 14384.6i | 1.60204 | − | 1.60204i | ||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 34846.0 | 3.82757 | ||||||||
\(437\) | 22897.8 | − | 22897.8i | 2.50653 | − | 2.50653i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16976.0i | − | 1.84560i | −0.385274 | − | 0.922802i | \(-0.625893\pi\) | ||
0.385274 | − | 0.922802i | \(-0.374107\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9261.00 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3314.16 | + | 3314.16i | 0.355441 | + | 0.355441i | 0.862129 | − | 0.506688i | \(-0.169130\pi\) |
−0.506688 | + | 0.862129i | \(0.669130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 25969.5 | − | 25969.5i | 2.70244 | − | 2.70244i | ||||
\(453\) | 11434.2 | + | 11434.2i | 1.18593 | + | 1.18593i | ||||
\(454\) | 11718.0i | 1.21135i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 48708.0 | 5.00211 | ||||||||
\(457\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(458\) | −1050.83 | − | 1050.83i | −0.107210 | − | 0.107210i | ||||
\(459\) | − | 2916.00i | − | 0.296530i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28836.0 | −2.86653 | ||||||||
\(467\) | −13940.0 | + | 13940.0i | −1.38130 | + | 1.38130i | −0.538992 | + | 0.842311i | \(0.681195\pi\) |
−0.842311 | + | 0.538992i | \(0.818805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8208.00i | 0.795371i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8729.98 | − | 8729.98i | 0.837984 | − | 0.837984i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5283.55 | + | 5283.55i | −0.499293 | + | 0.499293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 25289.0i | − | 2.37500i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19683.0 | −1.83712 | ||||||||
\(487\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | 14469.1 | + | 14469.1i | 1.34219 | + | 1.34219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33640.0 | −3.04532 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15674.3 | − | 15674.3i | −1.41040 | − | 1.41040i | ||||
\(499\) | − | 19316.0i | − | 1.73287i | −0.499289 | − | 0.866436i | \(-0.666405\pi\) | ||
0.499289 | − | 0.866436i | \(-0.333595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10962.0 | 0.977537 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3666.89 | − | 3666.89i | −0.325046 | − | 0.325046i | 0.525653 | − | 0.850699i | \(-0.323821\pi\) |
−0.850699 | + | 0.525653i | \(0.823821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8072.29 | + | 8072.29i | −0.707107 | + | 0.707107i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16515.7 | + | 16515.7i | −1.42558 | + | 1.42558i | ||||
\(513\) | −16269.5 | − | 16269.5i | −1.40023 | − | 1.40023i | ||||
\(514\) | 26028.0i | 2.23355i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23544.0i | 1.99127i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29646.0 | −2.45747 | ||||||||
\(527\) | −3409.69 | + | 3409.69i | −0.281838 | + | 0.281838i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26821.0i | 2.20441i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3238.00 | −0.257324 | −0.128662 | − | 0.991688i | \(-0.541068\pi\) | ||||
−0.128662 | + | 0.991688i | \(0.541068\pi\) | |||||||
\(542\) | 24808.4 | − | 24808.4i | 1.96608 | − | 1.96608i | ||||
\(543\) | −4769.16 | − | 4769.16i | −0.376914 | − | 0.376914i | ||||
\(544\) | − | 6156.00i | − | 0.485177i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | 33788.3 | + | 33788.3i | 2.63387 | + | 2.63387i | ||||
\(549\) | − | 9666.00i | − | 0.751430i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −41467.4 | + | 41467.4i | −3.19741 | + | 3.19741i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30476.0 | 2.32459 | ||||||||
\(557\) | 1675.45 | − | 1675.45i | 0.127453 | − | 0.127453i | −0.640503 | − | 0.767956i | \(-0.721274\pi\) |
0.767956 | + | 0.640503i | \(0.221274\pi\) | |||||||
\(558\) | 23015.4 | + | 23015.4i | 1.74609 | + | 1.74609i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15806.6 | + | 15806.6i | 1.18325 | + | 1.18325i | 0.978899 | + | 0.204346i | \(0.0655069\pi\) |
0.204346 | + | 0.978899i | \(0.434493\pi\) | |||||||
\(564\) | − | 33858.0i | − | 2.52780i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26012.0 | 1.90642 | 0.953212 | − | 0.302302i | \(-0.0977551\pi\) | ||||
0.953212 | + | 0.302302i | \(0.0977551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10233.0 | −0.740234 | ||||||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | 16464.2 | + | 16464.2i | 1.18481 | + | 1.18481i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 49464.0 | 3.48693 | ||||||||
\(587\) | −8502.18 | + | 8502.18i | −0.597824 | + | 0.597824i | −0.939733 | − | 0.341909i | \(-0.888926\pi\) |
0.341909 | + | 0.939733i | \(0.388926\pi\) | |||||||
\(588\) | −23945.0 | − | 23945.0i | −1.67938 | − | 1.67938i | ||||
\(589\) | 38048.0i | 2.66170i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25488.0 | −1.77400 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19649.8 | − | 19649.8i | −1.36074 | − | 1.36074i | −0.872971 | − | 0.487773i | \(-0.837809\pi\) |
−0.487773 | − | 0.872971i | \(-0.662191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20046.6 | − | 20046.6i | 1.37429 | − | 1.37429i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13642.0 | 0.925905 | 0.462952 | − | 0.886383i | \(-0.346790\pi\) | ||||
0.462952 | + | 0.886383i | \(0.346790\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 59128.0i | − | 3.98325i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | −34346.7 | − | 34346.7i | −2.29103 | − | 2.29103i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7539.53 | + | 7539.53i | −0.497986 | + | 0.497986i | ||||
\(613\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8832.86 | + | 8832.86i | −0.576333 | + | 0.576333i | −0.933891 | − | 0.357558i | \(-0.883609\pi\) |
0.357558 | + | 0.933891i | \(0.383609\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3476.00i | − | 0.225706i | −0.993612 | − | 0.112853i | \(-0.964001\pi\) | ||
0.993612 | − | 0.112853i | \(-0.0359990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27702.0 | 1.79009 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27808.0 | −1.75439 | −0.877194 | − | 0.480136i | \(-0.840587\pi\) | ||||
−0.877194 | + | 0.480136i | \(0.840587\pi\) | |||||||
\(632\) | 12286.6 | − | 12286.6i | 0.773317 | − | 0.773317i | ||||
\(633\) | −15534.7 | − | 15534.7i | −0.975430 | − | 0.975430i | ||||
\(634\) | − | 26352.0i | − | 1.65074i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −45144.0 | −2.81458 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 42261.0 | − | 42261.0i | 2.59799 | − | 2.59799i | ||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17712.0 | −1.07875 | ||||||||
\(647\) | −23199.1 | + | 23199.1i | −1.40966 | + | 1.40966i | −0.648146 | + | 0.761516i | \(0.724456\pi\) |
−0.761516 | + | 0.648146i | \(0.775544\pi\) | |||||||
\(648\) | 29463.7 | + | 29463.7i | 1.78618 | + | 1.78618i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17313.0 | + | 17313.0i | 1.03753 | + | 1.03753i | 0.999268 | + | 0.0382666i | \(0.0121836\pi\) |
0.0382666 | + | 0.999268i | \(0.487816\pi\) | |||||||
\(654\) | 49518.0i | 2.96071i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32978.0 | −1.94054 | −0.970269 | − | 0.242029i | \(-0.922187\pi\) | ||||
−0.970269 | + | 0.242029i | \(0.922187\pi\) | |||||||
\(662\) | 21501.6 | − | 21501.6i | 1.26236 | − | 1.26236i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 46926.0i | 2.74259i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −28343.0 | − | 28343.0i | −1.64165 | − | 1.64165i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 41743.0 | 2.37500 | ||||||||
\(677\) | −8906.34 | + | 8906.34i | −0.505611 | + | 0.505611i | −0.913176 | − | 0.407565i | \(-0.866378\pi\) |
0.407565 | + | 0.913176i | \(0.366378\pi\) | |||||||
\(678\) | 36904.0 | + | 36904.0i | 2.09040 | + | 2.09040i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11718.0 | −0.659376 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16085.8 | − | 16085.8i | −0.901180 | − | 0.901180i | 0.0943582 | − | 0.995538i | \(-0.469920\pi\) |
−0.995538 | + | 0.0943582i | \(0.969920\pi\) | |||||||
\(684\) | 84132.0i | 4.70302i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1050.83 | − | 1050.83i | 0.0583577 | − | 0.0583577i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32812.0 | 1.80641 | 0.903204 | − | 0.429212i | \(-0.141209\pi\) | ||||
0.903204 | + | 0.429212i | \(0.141209\pi\) | |||||||
\(692\) | 60874.7 | − | 60874.7i | 3.34409 | − | 3.34409i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 50382.0i | − | 2.75573i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −13616.7 | − | 13616.7i | −0.738396 | − | 0.738396i | ||||
\(699\) | − | 28836.0i | − | 1.56034i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −67716.0 | −3.60981 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 37726.0i | − | 1.99835i | −0.0406201 | − | 0.999175i | \(-0.512933\pi\) | ||
0.0406201 | − | 0.999175i | \(-0.487067\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8208.00 | −0.432945 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32392.1 | − | 32392.1i | −1.70139 | − | 1.70139i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −73620.6 | + | 73620.6i | −3.79484 | + | 3.79484i | ||||
\(723\) | −5283.55 | − | 5283.55i | −0.271781 | − | 0.271781i | ||||
\(724\) | 24662.0i | 1.26596i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 35937.0 | 1.83712 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 19683.0i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −24992.1 | + | 24992.1i | −1.26193 | + | 1.26193i | ||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 58482.0 | 2.92891 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8804.00i | 0.438241i | 0.975698 | + | 0.219121i | \(0.0703188\pi\) | ||||
−0.975698 | + | 0.219121i | \(0.929681\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27711.1 | + | 27711.1i | 1.36826 | + | 1.36826i | 0.862914 | + | 0.505351i | \(0.168637\pi\) |
0.505351 | + | 0.862914i | \(0.331363\pi\) | |||||||
\(744\) | − | 68904.0i | − | 3.39535i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15674.3 | − | 15674.3i | 0.767727 | − | 0.767727i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17512.0 | 0.850895 | 0.425447 | − | 0.904983i | \(-0.360117\pi\) | ||||
0.425447 | + | 0.904983i | \(0.360117\pi\) | |||||||
\(752\) | −35162.4 | + | 35162.4i | −1.70511 | + | 1.70511i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | 16475.3 | + | 16475.3i | 0.789457 | + | 0.789457i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 59994.0 | 2.82986 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −18779.0 | − | 18779.0i | −0.882330 | − | 0.882330i | ||||
\(769\) | − | 8786.00i | − | 0.412004i | −0.978552 | − | 0.206002i | \(-0.933955\pi\) | ||
0.978552 | − | 0.206002i | \(-0.0660454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26028.0 | −1.21579 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29511.5 | + | 29511.5i | 1.37316 | + | 1.37316i | 0.855718 | + | 0.517443i | \(0.173116\pi\) |
0.517443 | + | 0.855718i | \(0.326884\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 15079.1 | − | 15079.1i | 0.689547 | − | 0.689547i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 49735.0i | 2.26562i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(788\) | 65901.1 | + | 65901.1i | 2.97922 | + | 2.97922i | ||||
\(789\) | − | 29646.0i | − | 1.33767i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −103664. | −4.61592 | ||||||||
\(797\) | 31804.2 | − | 31804.2i | 1.41350 | − | 1.41350i | 0.684335 | − | 0.729168i | \(-0.260093\pi\) |
0.729168 | − | 0.684335i | \(-0.239907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7128.00i | 0.315608i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14092.0 | 0.610157 | 0.305078 | − | 0.952327i | \(-0.401317\pi\) | ||||
0.305078 | + | 0.952327i | \(0.401317\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24808.4 | + | 24808.4i | 1.07020 | + | 1.07020i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15660.0 | 0.671826 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −52637.1 | − | 52637.1i | −2.24989 | − | 2.24989i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | −48014.9 | + | 48014.9i | −2.03736 | + | 2.03736i | ||||
\(823\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14425.0 | − | 14425.0i | 0.606539 | − | 0.606539i | −0.335501 | − | 0.942040i | \(-0.608905\pi\) |
0.942040 | + | 0.335501i | \(0.108905\pi\) | |||||||
\(828\) | −71625.5 | − | 71625.5i | −3.00623 | − | 3.00623i | ||||
\(829\) | 45254.0i | 1.89594i | 0.318356 | + | 0.947971i | \(0.396869\pi\) | ||||
−0.318356 | + | 0.947971i | \(0.603131\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5041.05 | + | 5041.05i | 0.209678 | + | 0.209678i | ||||
\(834\) | 43308.0i | 1.79812i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23015.4 | + | 23015.4i | −0.950453 | + | 0.950453i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24389.0 | −1.00000 | ||||||||
\(842\) | −25271.4 | + | 25271.4i | −1.03433 | + | 1.03433i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 80332.0i | 3.27623i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 48114.0 | 1.95531 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 46883.2 | + | 46883.2i | 1.89856 | + | 1.89856i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −126522. | −5.05191 | ||||||||
\(857\) | −12360.1 | + | 12360.1i | −0.492665 | + | 0.492665i | −0.909145 | − | 0.416480i | \(-0.863264\pi\) |
0.416480 | + | 0.909145i | \(0.363264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28204.0i | 1.12027i | 0.828403 | + | 0.560133i | \(0.189250\pi\) | ||||
−0.828403 | + | 0.560133i | \(0.810750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30635.8 | − | 30635.8i | −1.20841 | − | 1.20841i | −0.971543 | − | 0.236862i | \(-0.923881\pi\) |
−0.236862 | − | 0.971543i | \(-0.576119\pi\) | |||||||
\(864\) | − | 41553.0i | − | 1.63618i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16464.2 | + | 16464.2i | −0.644931 | + | 0.644931i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 74124.0 | − | 74124.0i | 2.87862 | − | 2.87862i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 168264.i | − | 6.51214i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | −62373.8 | − | 62373.8i | −2.39751 | − | 2.39751i | ||||
\(879\) | 49464.0i | 1.89804i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 34027.1 | − | 34027.1i | 1.29904 | − | 1.29904i | ||||
\(883\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24354.0 | 0.923463 | ||||||||
\(887\) | 33604.5 | − | 33604.5i | 1.27207 | − | 1.27207i | 0.327077 | − | 0.944998i | \(-0.393936\pi\) |
0.944998 | − | 0.327077i | \(-0.106064\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39769.9 | + | 39769.9i | 1.49031 | + | 1.49031i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9504.00 | 0.351414 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 110484.i | − | 4.06487i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 84024.0 | 3.08114 | ||||||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | 30297.7 | + | 30297.7i | 1.10734 | + | 1.10734i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 87373.3 | − | 87373.3i | 3.17239 | − | 3.17239i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5434.00 | −0.196009 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −10714.1 | − | 10714.1i | −0.385204 | − | 0.385204i | ||||
\(919\) | 21224.0i | 0.761823i | 0.924612 | + | 0.380911i | \(0.124390\pi\) | ||||
−0.924612 | + | 0.380911i | \(0.875610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 56252.0 | 1.98022 | ||||||||
\(932\) | −74557.6 | + | 74557.6i | −2.62040 | + | 2.62040i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 102438.i | 3.58873i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26109.1 | − | 26109.1i | 0.895916 | − | 0.895916i | −0.0991562 | − | 0.995072i | \(-0.531614\pi\) |
0.995072 | + | 0.0991562i | \(0.0316144\pi\) | |||||||
\(948\) | 21222.4 | + | 21222.4i | 0.727079 | + | 0.727079i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26352.0 | 0.898551 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35669.5 | − | 35669.5i | −1.21243 | − | 1.21243i | −0.970225 | − | 0.242207i | \(-0.922129\pi\) |
−0.242207 | − | 0.970225i | \(-0.577871\pi\) | |||||||
\(954\) | − | 64152.0i | − | 2.17715i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24033.0 | 0.806720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42261.0 | + | 42261.0i | 1.41417 | + | 1.41417i | ||||
\(964\) | 27322.0i | 0.912845i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | −53794.5 | − | 53794.5i | −1.78618 | − | 1.78618i | ||||
\(969\) | − | 17712.0i | − | 0.587194i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | −50891.8 | + | 50891.8i | −1.67938 | + | 1.67938i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 51910.0 | 1.70246 | ||||||||
\(977\) | −42194.9 | + | 42194.9i | −1.38171 | + | 1.38171i | −0.540137 | + | 0.841577i | \(0.681628\pi\) |
−0.841577 | + | 0.540137i | \(0.818372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −49518.0 | −1.61161 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7194.15 | − | 7194.15i | −0.233426 | − | 0.233426i | 0.580695 | − | 0.814121i | \(-0.302781\pi\) |
−0.814121 | + | 0.580695i | \(0.802781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62368.0 | −1.99918 | −0.999589 | − | 0.0286779i | \(-0.990870\pi\) | ||||
−0.999589 | + | 0.0286779i | \(0.990870\pi\) | |||||||
\(992\) | −48588.1 | + | 48588.1i | −1.55511 | + | 1.55511i | ||||
\(993\) | 21501.6 | + | 21501.6i | 0.687143 | + | 0.687143i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −81054.0 | −2.57861 | ||||||||
\(997\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(998\) | −70971.5 | − | 70971.5i | −2.25107 | − | 2.25107i | ||||
\(999\) | 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 | 75.4.e.b.32.2 | yes | 4 | |
3.2 | odd | 2 | inner | 75.4.e.b.32.1 | ✓ | 4 | |
5.2 | odd | 4 | inner | 75.4.e.b.68.2 | yes | 4 | |
5.3 | odd | 4 | inner | 75.4.e.b.68.1 | yes | 4 | |
5.4 | even | 2 | inner | 75.4.e.b.32.1 | ✓ | 4 | |
15.2 | even | 4 | inner | 75.4.e.b.68.1 | yes | 4 | |
15.8 | even | 4 | inner | 75.4.e.b.68.2 | yes | 4 | |
15.14 | odd | 2 | CM | 75.4.e.b.32.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.e.b.32.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
75.4.e.b.32.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
75.4.e.b.32.2 | yes | 4 | 1.1 | even | 1 | trivial | |
75.4.e.b.32.2 | yes | 4 | 15.14 | odd | 2 | CM | |
75.4.e.b.68.1 | yes | 4 | 5.3 | odd | 4 | inner | |
75.4.e.b.68.1 | yes | 4 | 15.2 | even | 4 | inner | |
75.4.e.b.68.2 | yes | 4 | 5.2 | odd | 4 | inner | |
75.4.e.b.68.2 | yes | 4 | 15.8 | even | 4 | inner |