Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.c (of order \(2\), degree \(1\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.j.451.2 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 10.3923i | − | 1.48461i | −0.670059 | − | 0.742307i | \(-0.733731\pi\) | ||
0.670059 | − | 0.742307i | \(-0.266269\pi\) | |||||||
\(8\) | −8.00000 | −1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.3923i | − | 0.944755i | −0.881396 | − | 0.472377i | \(-0.843396\pi\) | ||
0.881396 | − | 0.472377i | \(-0.156604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.0000 | −1.38462 | −0.692308 | − | 0.721602i | \(-0.743406\pi\) | ||||
−0.692308 | + | 0.721602i | \(0.743406\pi\) | |||||||
\(14\) | −18.0000 | − | 10.3923i | −1.28571 | − | 0.742307i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | 10.0000 | 0.588235 | 0.294118 | − | 0.955769i | \(-0.404974\pi\) | ||||
0.294118 | + | 0.955769i | \(0.404974\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.8564i | 0.729285i | 0.931148 | + | 0.364642i | \(0.118809\pi\) | ||||
−0.931148 | + | 0.364642i | \(0.881191\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −18.0000 | − | 10.3923i | −0.818182 | − | 0.472377i | ||||
\(23\) | 6.92820i | 0.301226i | 0.988593 | + | 0.150613i | \(0.0481248\pi\) | ||||
−0.988593 | + | 0.150613i | \(0.951875\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −18.0000 | + | 31.1769i | −0.692308 | + | 1.19911i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −36.0000 | + | 20.7846i | −1.28571 | + | 0.742307i | ||||
\(29\) | 36.0000 | 1.24138 | 0.620690 | − | 0.784056i | \(-0.286853\pi\) | ||||
0.620690 | + | 0.784056i | \(0.286853\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.92820i | − | 0.223490i | −0.993737 | − | 0.111745i | \(-0.964356\pi\) | ||
0.993737 | − | 0.111745i | \(-0.0356441\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.500000 | + | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0000 | − | 17.3205i | 0.294118 | − | 0.509427i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −54.0000 | −1.45946 | −0.729730 | − | 0.683736i | \(-0.760354\pi\) | ||||
−0.729730 | + | 0.683736i | \(0.760354\pi\) | |||||||
\(38\) | 24.0000 | + | 13.8564i | 0.631579 | + | 0.364642i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.0000 | −0.439024 | −0.219512 | − | 0.975610i | \(-0.570447\pi\) | ||||
−0.219512 | + | 0.975610i | \(0.570447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 20.7846i | − | 0.483363i | −0.970356 | − | 0.241682i | \(-0.922301\pi\) | ||
0.970356 | − | 0.241682i | \(-0.0776989\pi\) | |||||||
\(44\) | −36.0000 | + | 20.7846i | −0.818182 | + | 0.472377i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.0000 | + | 6.92820i | 0.260870 | + | 0.150613i | ||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −59.0000 | −1.20408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 36.0000 | + | 62.3538i | 0.692308 | + | 1.19911i | ||||
\(53\) | −26.0000 | −0.490566 | −0.245283 | − | 0.969452i | \(-0.578881\pi\) | ||||
−0.245283 | + | 0.969452i | \(0.578881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 83.1384i | 1.48461i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 36.0000 | − | 62.3538i | 0.620690 | − | 1.07507i | ||||
\(59\) | 31.1769i | 0.528422i | 0.964465 | + | 0.264211i | \(0.0851116\pi\) | ||||
−0.964465 | + | 0.264211i | \(0.914888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −74.0000 | −1.21311 | −0.606557 | − | 0.795040i | \(-0.707450\pi\) | ||||
−0.606557 | + | 0.795040i | \(0.707450\pi\) | |||||||
\(62\) | −12.0000 | − | 6.92820i | −0.193548 | − | 0.111745i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 41.5692i | − | 0.620436i | −0.950665 | − | 0.310218i | \(-0.899598\pi\) | ||
0.950665 | − | 0.310218i | \(-0.100402\pi\) | |||||||
\(68\) | −20.0000 | − | 34.6410i | −0.294118 | − | 0.509427i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 103.923i | 1.46370i | 0.681463 | + | 0.731852i | \(0.261344\pi\) | ||||
−0.681463 | + | 0.731852i | \(0.738656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −36.0000 | −0.493151 | −0.246575 | − | 0.969124i | \(-0.579305\pi\) | ||||
−0.246575 | + | 0.969124i | \(0.579305\pi\) | |||||||
\(74\) | −54.0000 | + | 93.5307i | −0.729730 | + | 1.26393i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 48.0000 | − | 27.7128i | 0.631579 | − | 0.364642i | ||||
\(77\) | −108.000 | −1.40260 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 90.0666i | 1.14008i | 0.821616 | + | 0.570042i | \(0.193073\pi\) | ||||
−0.821616 | + | 0.570042i | \(0.806927\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.0000 | + | 31.1769i | −0.219512 | + | 0.380206i | ||||
\(83\) | − | 90.0666i | − | 1.08514i | −0.840011 | − | 0.542570i | \(-0.817451\pi\) | ||
0.840011 | − | 0.542570i | \(-0.182549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −36.0000 | − | 20.7846i | −0.418605 | − | 0.241682i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 83.1384i | 0.944755i | ||||||||
\(89\) | 18.0000 | 0.202247 | 0.101124 | − | 0.994874i | \(-0.467756\pi\) | ||||
0.101124 | + | 0.994874i | \(0.467756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 187.061i | 2.05562i | ||||||||
\(92\) | 24.0000 | − | 13.8564i | 0.260870 | − | 0.150613i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 72.0000 | 0.742268 | 0.371134 | − | 0.928579i | \(-0.378969\pi\) | ||||
0.371134 | + | 0.928579i | \(0.378969\pi\) | |||||||
\(98\) | −59.0000 | + | 102.191i | −0.602041 | + | 1.04277i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −36.0000 | −0.356436 | −0.178218 | − | 0.983991i | \(-0.557033\pi\) | ||||
−0.178218 | + | 0.983991i | \(0.557033\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.3923i | − | 0.100896i | −0.998727 | − | 0.0504481i | \(-0.983935\pi\) | ||
0.998727 | − | 0.0504481i | \(-0.0160649\pi\) | |||||||
\(104\) | 144.000 | 1.38462 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.0000 | + | 45.0333i | −0.245283 | + | 0.424843i | ||||
\(107\) | − | 187.061i | − | 1.74824i | −0.485712 | − | 0.874119i | \(-0.661439\pi\) | ||
0.485712 | − | 0.874119i | \(-0.338561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −26.0000 | −0.238532 | −0.119266 | − | 0.992862i | \(-0.538054\pi\) | ||||
−0.119266 | + | 0.992862i | \(0.538054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 144.000 | + | 83.1384i | 1.28571 | + | 0.742307i | ||||
\(113\) | −10.0000 | −0.0884956 | −0.0442478 | − | 0.999021i | \(-0.514089\pi\) | ||||
−0.0442478 | + | 0.999021i | \(0.514089\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −72.0000 | − | 124.708i | −0.620690 | − | 1.07507i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 54.0000 | + | 31.1769i | 0.457627 | + | 0.264211i | ||||
\(119\) | − | 103.923i | − | 0.873303i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 0.107438 | ||||||||
\(122\) | −74.0000 | + | 128.172i | −0.606557 | + | 1.05059i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −24.0000 | + | 13.8564i | −0.193548 | + | 0.111745i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 218.238i | − | 1.71841i | −0.511629 | − | 0.859206i | \(-0.670958\pi\) | ||
0.511629 | − | 0.859206i | \(-0.329042\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 135.100i | 1.03130i | 0.856800 | + | 0.515649i | \(0.172449\pi\) | ||||
−0.856800 | + | 0.515649i | \(0.827551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 144.000 | 1.08271 | ||||||||
\(134\) | −72.0000 | − | 41.5692i | −0.537313 | − | 0.310218i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −80.0000 | −0.588235 | ||||||||
\(137\) | 110.000 | 0.802920 | 0.401460 | − | 0.915877i | \(-0.368503\pi\) | ||||
0.401460 | + | 0.915877i | \(0.368503\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 187.061i | − | 1.34577i | −0.739749 | − | 0.672883i | \(-0.765056\pi\) | ||
0.739749 | − | 0.672883i | \(-0.234944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 180.000 | + | 103.923i | 1.26761 | + | 0.731852i | ||||
\(143\) | 187.061i | 1.30812i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −36.0000 | + | 62.3538i | −0.246575 | + | 0.427081i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 108.000 | + | 187.061i | 0.729730 | + | 1.26393i | ||||
\(149\) | −288.000 | −1.93289 | −0.966443 | − | 0.256881i | \(-0.917305\pi\) | ||||
−0.966443 | + | 0.256881i | \(0.917305\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 187.061i | − | 1.23882i | −0.785069 | − | 0.619409i | \(-0.787372\pi\) | ||
0.785069 | − | 0.619409i | \(-0.212628\pi\) | |||||||
\(152\) | − | 110.851i | − | 0.729285i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −108.000 | + | 187.061i | −0.701299 | + | 1.21468i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −234.000 | −1.49045 | −0.745223 | − | 0.666815i | \(-0.767657\pi\) | ||||
−0.745223 | + | 0.666815i | \(0.767657\pi\) | |||||||
\(158\) | 156.000 | + | 90.0666i | 0.987342 | + | 0.570042i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 72.0000 | 0.447205 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 124.708i | − | 0.765078i | −0.923939 | − | 0.382539i | \(-0.875050\pi\) | ||
0.923939 | − | 0.382539i | \(-0.124950\pi\) | |||||||
\(164\) | 36.0000 | + | 62.3538i | 0.219512 | + | 0.380206i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −156.000 | − | 90.0666i | −0.939759 | − | 0.542570i | ||||
\(167\) | 131.636i | 0.788239i | 0.919059 | + | 0.394119i | \(0.128950\pi\) | ||||
−0.919059 | + | 0.394119i | \(0.871050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 155.000 | 0.917160 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −72.0000 | + | 41.5692i | −0.418605 | + | 0.241682i | ||||
\(173\) | 146.000 | 0.843931 | 0.421965 | − | 0.906612i | \(-0.361340\pi\) | ||||
0.421965 | + | 0.906612i | \(0.361340\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 144.000 | + | 83.1384i | 0.818182 | + | 0.472377i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.0000 | − | 31.1769i | 0.101124 | − | 0.175151i | ||||
\(179\) | 72.7461i | 0.406403i | 0.979137 | + | 0.203201i | \(0.0651346\pi\) | ||||
−0.979137 | + | 0.203201i | \(0.934865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 262.000 | 1.44751 | 0.723757 | − | 0.690055i | \(-0.242414\pi\) | ||||
0.723757 | + | 0.690055i | \(0.242414\pi\) | |||||||
\(182\) | 324.000 | + | 187.061i | 1.78022 | + | 1.02781i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 55.4256i | − | 0.301226i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 103.923i | − | 0.555738i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 187.061i | − | 0.979380i | −0.871897 | − | 0.489690i | \(-0.837110\pi\) | ||
0.871897 | − | 0.489690i | \(-0.162890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −180.000 | −0.932642 | −0.466321 | − | 0.884615i | \(-0.654421\pi\) | ||||
−0.466321 | + | 0.884615i | \(0.654421\pi\) | |||||||
\(194\) | 72.0000 | − | 124.708i | 0.371134 | − | 0.642823i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 118.000 | + | 204.382i | 0.602041 | + | 1.04277i | ||||
\(197\) | −154.000 | −0.781726 | −0.390863 | − | 0.920449i | \(-0.627823\pi\) | ||||
−0.390863 | + | 0.920449i | \(0.627823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 187.061i | − | 0.940007i | −0.882664 | − | 0.470004i | \(-0.844253\pi\) | ||
0.882664 | − | 0.470004i | \(-0.155747\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −36.0000 | + | 62.3538i | −0.178218 | + | 0.308682i | ||||
\(203\) | − | 374.123i | − | 1.84297i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −18.0000 | − | 10.3923i | −0.0873786 | − | 0.0504481i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 144.000 | − | 249.415i | 0.692308 | − | 1.19911i | ||||
\(209\) | 144.000 | 0.688995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 242.487i | − | 1.14923i | −0.818425 | − | 0.574614i | \(-0.805152\pi\) | ||
0.818425 | − | 0.574614i | \(-0.194848\pi\) | |||||||
\(212\) | 52.0000 | + | 90.0666i | 0.245283 | + | 0.424843i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −324.000 | − | 187.061i | −1.51402 | − | 0.874119i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −72.0000 | −0.331797 | ||||||||
\(218\) | −26.0000 | + | 45.0333i | −0.119266 | + | 0.206575i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −180.000 | −0.814480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 93.5307i | − | 0.419420i | −0.977764 | − | 0.209710i | \(-0.932748\pi\) | ||
0.977764 | − | 0.209710i | \(-0.0672521\pi\) | |||||||
\(224\) | 288.000 | − | 166.277i | 1.28571 | − | 0.742307i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0000 | + | 17.3205i | −0.0442478 | + | 0.0766394i | ||||
\(227\) | − | 214.774i | − | 0.946142i | −0.881024 | − | 0.473071i | \(-0.843145\pi\) | ||
0.881024 | − | 0.473071i | \(-0.156855\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 338.000 | 1.47598 | 0.737991 | − | 0.674810i | \(-0.235775\pi\) | ||||
0.737991 | + | 0.674810i | \(0.235775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −288.000 | −1.24138 | ||||||||
\(233\) | −182.000 | −0.781116 | −0.390558 | − | 0.920578i | \(-0.627718\pi\) | ||||
−0.390558 | + | 0.920578i | \(0.627718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 108.000 | − | 62.3538i | 0.457627 | − | 0.264211i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −180.000 | − | 103.923i | −0.756303 | − | 0.436651i | ||||
\(239\) | 353.338i | 1.47840i | 0.673484 | + | 0.739202i | \(0.264797\pi\) | ||||
−0.673484 | + | 0.739202i | \(0.735203\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −106.000 | −0.439834 | −0.219917 | − | 0.975519i | \(-0.570579\pi\) | ||||
−0.219917 | + | 0.975519i | \(0.570579\pi\) | |||||||
\(242\) | 13.0000 | − | 22.5167i | 0.0537190 | − | 0.0930441i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 148.000 | + | 256.344i | 0.606557 | + | 1.05059i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 249.415i | − | 1.00978i | ||||||
\(248\) | 55.4256i | 0.223490i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 322.161i | − | 1.28351i | −0.766909 | − | 0.641756i | \(-0.778206\pi\) | ||
0.766909 | − | 0.641756i | \(-0.221794\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 72.0000 | 0.284585 | ||||||||
\(254\) | −378.000 | − | 218.238i | −1.48819 | − | 0.859206i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | 14.0000 | 0.0544747 | 0.0272374 | − | 0.999629i | \(-0.491329\pi\) | ||||
0.0272374 | + | 0.999629i | \(0.491329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 561.184i | 2.16674i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 234.000 | + | 135.100i | 0.893130 | + | 0.515649i | ||||
\(263\) | 187.061i | 0.711260i | 0.934627 | + | 0.355630i | \(0.115734\pi\) | ||||
−0.934627 | + | 0.355630i | \(0.884266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 144.000 | − | 249.415i | 0.541353 | − | 0.937652i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −144.000 | + | 83.1384i | −0.537313 | + | 0.310218i | ||||
\(269\) | 108.000 | 0.401487 | 0.200743 | − | 0.979644i | \(-0.435664\pi\) | ||||
0.200743 | + | 0.979644i | \(0.435664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 325.626i | 1.20157i | 0.799411 | + | 0.600785i | \(0.205145\pi\) | ||||
−0.799411 | + | 0.600785i | \(0.794855\pi\) | |||||||
\(272\) | −80.0000 | + | 138.564i | −0.294118 | + | 0.509427i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 110.000 | − | 190.526i | 0.401460 | − | 0.695349i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −270.000 | −0.974729 | −0.487365 | − | 0.873199i | \(-0.662042\pi\) | ||||
−0.487365 | + | 0.873199i | \(0.662042\pi\) | |||||||
\(278\) | −324.000 | − | 187.061i | −1.16547 | − | 0.672883i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 234.000 | 0.832740 | 0.416370 | − | 0.909195i | \(-0.363302\pi\) | ||||
0.416370 | + | 0.909195i | \(0.363302\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 83.1384i | 0.293775i | 0.989153 | + | 0.146888i | \(0.0469256\pi\) | ||||
−0.989153 | + | 0.146888i | \(0.953074\pi\) | |||||||
\(284\) | 360.000 | − | 207.846i | 1.26761 | − | 0.731852i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 324.000 | + | 187.061i | 1.13287 | + | 0.654061i | ||||
\(287\) | 187.061i | 0.651782i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −189.000 | −0.653979 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 72.0000 | + | 124.708i | 0.246575 | + | 0.427081i | ||||
\(293\) | −58.0000 | −0.197952 | −0.0989761 | − | 0.995090i | \(-0.531557\pi\) | ||||
−0.0989761 | + | 0.995090i | \(0.531557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 432.000 | 1.45946 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −288.000 | + | 498.831i | −0.966443 | + | 1.67393i | ||||
\(299\) | − | 124.708i | − | 0.417082i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −216.000 | −0.717608 | ||||||||
\(302\) | −324.000 | − | 187.061i | −1.07285 | − | 0.619409i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −192.000 | − | 110.851i | −0.631579 | − | 0.364642i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 270.200i | 0.880130i | 0.897966 | + | 0.440065i | \(0.145045\pi\) | ||||
−0.897966 | + | 0.440065i | \(0.854955\pi\) | |||||||
\(308\) | 216.000 | + | 374.123i | 0.701299 | + | 1.21468i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 270.200i | − | 0.868810i | −0.900718 | − | 0.434405i | \(-0.856959\pi\) | ||
0.900718 | − | 0.434405i | \(-0.143041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −468.000 | −1.49521 | −0.747604 | − | 0.664145i | \(-0.768796\pi\) | ||||
−0.747604 | + | 0.664145i | \(0.768796\pi\) | |||||||
\(314\) | −234.000 | + | 405.300i | −0.745223 | + | 1.29076i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 312.000 | − | 180.133i | 0.987342 | − | 0.570042i | ||||
\(317\) | 250.000 | 0.788644 | 0.394322 | − | 0.918972i | \(-0.370980\pi\) | ||||
0.394322 | + | 0.918972i | \(0.370980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 374.123i | − | 1.17280i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 72.0000 | − | 124.708i | 0.223602 | − | 0.387291i | ||||
\(323\) | 138.564i | 0.428991i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −216.000 | − | 124.708i | −0.662577 | − | 0.382539i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 144.000 | 0.439024 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 374.123i | − | 1.13028i | −0.824995 | − | 0.565140i | \(-0.808822\pi\) | ||
0.824995 | − | 0.565140i | \(-0.191178\pi\) | |||||||
\(332\) | −312.000 | + | 180.133i | −0.939759 | + | 0.542570i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 228.000 | + | 131.636i | 0.682635 | + | 0.394119i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 468.000 | 1.38872 | 0.694362 | − | 0.719626i | \(-0.255687\pi\) | ||||
0.694362 | + | 0.719626i | \(0.255687\pi\) | |||||||
\(338\) | 155.000 | − | 268.468i | 0.458580 | − | 0.794284i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −72.0000 | −0.211144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 103.923i | 0.302983i | ||||||||
\(344\) | 166.277i | 0.483363i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 146.000 | − | 252.879i | 0.421965 | − | 0.730865i | ||||
\(347\) | − | 561.184i | − | 1.61725i | −0.588327 | − | 0.808623i | \(-0.700213\pi\) | ||
0.588327 | − | 0.808623i | \(-0.299787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −434.000 | −1.24355 | −0.621777 | − | 0.783195i | \(-0.713589\pi\) | ||||
−0.621777 | + | 0.783195i | \(0.713589\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 288.000 | − | 166.277i | 0.818182 | − | 0.472377i | ||||
\(353\) | −158.000 | −0.447592 | −0.223796 | − | 0.974636i | \(-0.571845\pi\) | ||||
−0.223796 | + | 0.974636i | \(0.571845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −36.0000 | − | 62.3538i | −0.101124 | − | 0.175151i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 126.000 | + | 72.7461i | 0.351955 | + | 0.203201i | ||||
\(359\) | − | 457.261i | − | 1.27371i | −0.770984 | − | 0.636854i | \(-0.780235\pi\) | ||
0.770984 | − | 0.636854i | \(-0.219765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 169.000 | 0.468144 | ||||||||
\(362\) | 262.000 | − | 453.797i | 0.723757 | − | 1.25358i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 648.000 | − | 374.123i | 1.78022 | − | 1.02781i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 218.238i | − | 0.594655i | −0.954776 | − | 0.297328i | \(-0.903905\pi\) | ||
0.954776 | − | 0.297328i | \(-0.0960953\pi\) | |||||||
\(368\) | −96.0000 | − | 55.4256i | −0.260870 | − | 0.150613i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 270.200i | 0.728302i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 270.000 | 0.723861 | 0.361930 | − | 0.932205i | \(-0.382118\pi\) | ||||
0.361930 | + | 0.932205i | \(0.382118\pi\) | |||||||
\(374\) | −180.000 | − | 103.923i | −0.481283 | − | 0.277869i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −648.000 | −1.71883 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 325.626i | − | 0.859170i | −0.903026 | − | 0.429585i | \(-0.858660\pi\) | ||
0.903026 | − | 0.429585i | \(-0.141340\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −324.000 | − | 187.061i | −0.848168 | − | 0.489690i | ||||
\(383\) | − | 55.4256i | − | 0.144714i | −0.997379 | − | 0.0723572i | \(-0.976948\pi\) | ||
0.997379 | − | 0.0723572i | \(-0.0230522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −180.000 | + | 311.769i | −0.466321 | + | 0.807692i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −144.000 | − | 249.415i | −0.371134 | − | 0.642823i | ||||
\(389\) | 288.000 | 0.740360 | 0.370180 | − | 0.928960i | \(-0.379296\pi\) | ||||
0.370180 | + | 0.928960i | \(0.379296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 69.2820i | 0.177192i | ||||||||
\(392\) | 472.000 | 1.20408 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −154.000 | + | 266.736i | −0.390863 | + | 0.676994i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 306.000 | 0.770781 | 0.385390 | − | 0.922754i | \(-0.374067\pi\) | ||||
0.385390 | + | 0.922754i | \(0.374067\pi\) | |||||||
\(398\) | −324.000 | − | 187.061i | −0.814070 | − | 0.470004i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 450.000 | 1.12219 | 0.561097 | − | 0.827750i | \(-0.310379\pi\) | ||||
0.561097 | + | 0.827750i | \(0.310379\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 124.708i | 0.309448i | ||||||||
\(404\) | 72.0000 | + | 124.708i | 0.178218 | + | 0.308682i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −648.000 | − | 374.123i | −1.59606 | − | 0.921485i | ||||
\(407\) | 561.184i | 1.37883i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −50.0000 | −0.122249 | −0.0611247 | − | 0.998130i | \(-0.519469\pi\) | ||||
−0.0611247 | + | 0.998130i | \(0.519469\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −36.0000 | + | 20.7846i | −0.0873786 | + | 0.0504481i | ||||
\(413\) | 324.000 | 0.784504 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −288.000 | − | 498.831i | −0.692308 | − | 1.19911i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 144.000 | − | 249.415i | 0.344498 | − | 0.596687i | ||||
\(419\) | − | 737.854i | − | 1.76099i | −0.474058 | − | 0.880494i | \(-0.657211\pi\) | ||
0.474058 | − | 0.880494i | \(-0.342789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −286.000 | −0.679335 | −0.339667 | − | 0.940546i | \(-0.610315\pi\) | ||||
−0.339667 | + | 0.940546i | \(0.610315\pi\) | |||||||
\(422\) | −420.000 | − | 242.487i | −0.995261 | − | 0.574614i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 208.000 | 0.490566 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 769.031i | 1.80101i | ||||||||
\(428\) | −648.000 | + | 374.123i | −1.51402 | + | 0.874119i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 124.708i | 0.289345i | 0.989480 | + | 0.144672i | \(0.0462128\pi\) | ||||
−0.989480 | + | 0.144672i | \(0.953787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.0000 | 0.0831409 | 0.0415704 | − | 0.999136i | \(-0.486764\pi\) | ||||
0.0415704 | + | 0.999136i | \(0.486764\pi\) | |||||||
\(434\) | −72.0000 | + | 124.708i | −0.165899 | + | 0.287345i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 52.0000 | + | 90.0666i | 0.119266 | + | 0.206575i | ||||
\(437\) | −96.0000 | −0.219680 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 782.887i | 1.78334i | 0.452684 | + | 0.891671i | \(0.350466\pi\) | ||||
−0.452684 | + | 0.891671i | \(0.649534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −180.000 | + | 311.769i | −0.407240 | + | 0.705360i | ||||
\(443\) | − | 214.774i | − | 0.484818i | −0.970174 | − | 0.242409i | \(-0.922062\pi\) | ||
0.970174 | − | 0.242409i | \(-0.0779376\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −162.000 | − | 93.5307i | −0.363229 | − | 0.209710i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 665.108i | − | 1.48461i | ||||||
\(449\) | −54.0000 | −0.120267 | −0.0601336 | − | 0.998190i | \(-0.519153\pi\) | ||||
−0.0601336 | + | 0.998190i | \(0.519153\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 187.061i | 0.414770i | ||||||||
\(452\) | 20.0000 | + | 34.6410i | 0.0442478 | + | 0.0766394i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −372.000 | − | 214.774i | −0.819383 | − | 0.473071i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −288.000 | −0.630197 | −0.315098 | − | 0.949059i | \(-0.602038\pi\) | ||||
−0.315098 | + | 0.949059i | \(0.602038\pi\) | |||||||
\(458\) | 338.000 | − | 585.433i | 0.737991 | − | 1.27824i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 288.000 | 0.624729 | 0.312364 | − | 0.949962i | \(-0.398879\pi\) | ||||
0.312364 | + | 0.949962i | \(0.398879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 405.300i | − | 0.875378i | −0.899126 | − | 0.437689i | \(-0.855797\pi\) | ||
0.899126 | − | 0.437689i | \(-0.144203\pi\) | |||||||
\(464\) | −288.000 | + | 498.831i | −0.620690 | + | 1.07507i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −182.000 | + | 315.233i | −0.390558 | + | 0.676466i | ||||
\(467\) | 575.041i | 1.23135i | 0.788000 | + | 0.615675i | \(0.211117\pi\) | ||||
−0.788000 | + | 0.615675i | \(0.788883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −432.000 | −0.921109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 249.415i | − | 0.528422i | ||||||
\(473\) | −216.000 | −0.456660 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −360.000 | + | 207.846i | −0.756303 | + | 0.436651i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 612.000 | + | 353.338i | 1.28033 | + | 0.739202i | ||||
\(479\) | 145.492i | 0.303742i | 0.988400 | + | 0.151871i | \(0.0485298\pi\) | ||||
−0.988400 | + | 0.151871i | \(0.951470\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 972.000 | 2.02079 | ||||||||
\(482\) | −106.000 | + | 183.597i | −0.219917 | + | 0.380907i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.0000 | − | 45.0333i | −0.0537190 | − | 0.0930441i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 259.808i | 0.533486i | 0.963768 | + | 0.266743i | \(0.0859475\pi\) | ||||
−0.963768 | + | 0.266743i | \(0.914053\pi\) | |||||||
\(488\) | 592.000 | 1.21311 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 72.7461i | − | 0.148159i | −0.997252 | − | 0.0740796i | \(-0.976398\pi\) | ||
0.997252 | − | 0.0740796i | \(-0.0236019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 360.000 | 0.730223 | ||||||||
\(494\) | −432.000 | − | 249.415i | −0.874494 | − | 0.504889i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 96.0000 | + | 55.4256i | 0.193548 | + | 0.111745i | ||||
\(497\) | 1080.00 | 2.17304 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 443.405i | − | 0.888587i | −0.895881 | − | 0.444294i | \(-0.853455\pi\) | ||
0.895881 | − | 0.444294i | \(-0.146545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −558.000 | − | 322.161i | −1.11155 | − | 0.641756i | ||||
\(503\) | 110.851i | 0.220380i | 0.993911 | + | 0.110190i | \(0.0351460\pi\) | ||||
−0.993911 | + | 0.110190i | \(0.964854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 72.0000 | − | 124.708i | 0.142292 | − | 0.246458i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −756.000 | + | 436.477i | −1.48819 | + | 0.859206i | ||||
\(509\) | 252.000 | 0.495088 | 0.247544 | − | 0.968877i | \(-0.420376\pi\) | ||||
0.247544 | + | 0.968877i | \(0.420376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 374.123i | 0.732139i | ||||||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.0000 | − | 24.2487i | 0.0272374 | − | 0.0471765i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 972.000 | + | 561.184i | 1.87645 | + | 1.08337i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −54.0000 | −0.103647 | −0.0518234 | − | 0.998656i | \(-0.516503\pi\) | ||||
−0.0518234 | + | 0.998656i | \(0.516503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 623.538i | 1.19223i | 0.802898 | + | 0.596117i | \(0.203291\pi\) | ||||
−0.802898 | + | 0.596117i | \(0.796709\pi\) | |||||||
\(524\) | 468.000 | − | 270.200i | 0.893130 | − | 0.515649i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 324.000 | + | 187.061i | 0.615970 | + | 0.355630i | ||||
\(527\) | − | 69.2820i | − | 0.131465i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 481.000 | 0.909263 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −288.000 | − | 498.831i | −0.541353 | − | 0.937652i | ||||
\(533\) | 324.000 | 0.607880 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 332.554i | 0.620436i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 108.000 | − | 187.061i | 0.200743 | − | 0.347698i | ||||
\(539\) | 613.146i | 1.13756i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −650.000 | −1.20148 | −0.600739 | − | 0.799445i | \(-0.705127\pi\) | ||||
−0.600739 | + | 0.799445i | \(0.705127\pi\) | |||||||
\(542\) | 564.000 | + | 325.626i | 1.04059 | + | 0.600785i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 160.000 | + | 277.128i | 0.294118 | + | 0.509427i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 685.892i | 1.25392i | 0.779053 | + | 0.626958i | \(0.215700\pi\) | ||||
−0.779053 | + | 0.626958i | \(0.784300\pi\) | |||||||
\(548\) | −220.000 | − | 381.051i | −0.401460 | − | 0.695349i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 498.831i | 0.905319i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 936.000 | 1.69259 | ||||||||
\(554\) | −270.000 | + | 467.654i | −0.487365 | + | 0.844140i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −648.000 | + | 374.123i | −1.16547 | + | 0.672883i | ||||
\(557\) | 574.000 | 1.03052 | 0.515260 | − | 0.857034i | \(-0.327695\pi\) | ||||
0.515260 | + | 0.857034i | \(0.327695\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 374.123i | 0.669272i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 234.000 | − | 405.300i | 0.416370 | − | 0.721174i | ||||
\(563\) | 561.184i | 0.996775i | 0.866954 | + | 0.498388i | \(0.166074\pi\) | ||||
−0.866954 | + | 0.498388i | \(0.833926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 144.000 | + | 83.1384i | 0.254417 | + | 0.146888i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 831.384i | − | 1.46370i | ||||||
\(569\) | −198.000 | −0.347979 | −0.173989 | − | 0.984748i | \(-0.555666\pi\) | ||||
−0.173989 | + | 0.984748i | \(0.555666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 180.133i | 0.315470i | 0.987481 | + | 0.157735i | \(0.0504192\pi\) | ||||
−0.987481 | + | 0.157735i | \(0.949581\pi\) | |||||||
\(572\) | 648.000 | − | 374.123i | 1.13287 | − | 0.654061i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 324.000 | + | 187.061i | 0.564460 | + | 0.325891i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 504.000 | 0.873484 | 0.436742 | − | 0.899587i | \(-0.356132\pi\) | ||||
0.436742 | + | 0.899587i | \(0.356132\pi\) | |||||||
\(578\) | −189.000 | + | 327.358i | −0.326990 | + | 0.566363i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −936.000 | −1.61102 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 270.200i | 0.463465i | ||||||||
\(584\) | 288.000 | 0.493151 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −58.0000 | + | 100.459i | −0.0989761 | + | 0.171432i | ||||
\(587\) | − | 408.764i | − | 0.696361i | −0.937427 | − | 0.348181i | \(-0.886800\pi\) | ||
0.937427 | − | 0.348181i | \(-0.113200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 96.0000 | 0.162988 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 432.000 | − | 748.246i | 0.729730 | − | 1.26393i | ||||
\(593\) | 998.000 | 1.68297 | 0.841484 | − | 0.540282i | \(-0.181682\pi\) | ||||
0.841484 | + | 0.540282i | \(0.181682\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 576.000 | + | 997.661i | 0.966443 | + | 1.67393i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −216.000 | − | 124.708i | −0.361204 | − | 0.208541i | ||||
\(599\) | 540.400i | 0.902170i | 0.892481 | + | 0.451085i | \(0.148963\pi\) | ||||
−0.892481 | + | 0.451085i | \(0.851037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −614.000 | −1.02163 | −0.510815 | − | 0.859690i | \(-0.670656\pi\) | ||||
−0.510815 | + | 0.859690i | \(0.670656\pi\) | |||||||
\(602\) | −216.000 | + | 374.123i | −0.358804 | + | 0.621467i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −648.000 | + | 374.123i | −1.07285 | + | 0.619409i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 654.715i | − | 1.07861i | −0.842111 | − | 0.539304i | \(-0.818687\pi\) | ||
0.842111 | − | 0.539304i | \(-0.181313\pi\) | |||||||
\(608\) | −384.000 | + | 221.703i | −0.631579 | + | 0.364642i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −414.000 | −0.675367 | −0.337684 | − | 0.941260i | \(-0.609643\pi\) | ||||
−0.337684 | + | 0.941260i | \(0.609643\pi\) | |||||||
\(614\) | 468.000 | + | 270.200i | 0.762215 | + | 0.440065i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 864.000 | 1.40260 | ||||||||
\(617\) | 58.0000 | 0.0940032 | 0.0470016 | − | 0.998895i | \(-0.485033\pi\) | ||||
0.0470016 | + | 0.998895i | \(0.485033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 187.061i | 0.302199i | 0.988519 | + | 0.151100i | \(0.0482815\pi\) | ||||
−0.988519 | + | 0.151100i | \(0.951719\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −468.000 | − | 270.200i | −0.752412 | − | 0.434405i | ||||
\(623\) | − | 187.061i | − | 0.300259i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −468.000 | + | 810.600i | −0.747604 | + | 1.29489i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 468.000 | + | 810.600i | 0.745223 | + | 1.29076i | ||||
\(629\) | −540.000 | −0.858506 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 824.456i | − | 1.30659i | −0.757105 | − | 0.653293i | \(-0.773387\pi\) | ||
0.757105 | − | 0.653293i | \(-0.226613\pi\) | |||||||
\(632\) | − | 720.533i | − | 1.14008i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 250.000 | − | 433.013i | 0.394322 | − | 0.682985i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1062.00 | 1.66719 | ||||||||
\(638\) | −648.000 | − | 374.123i | −1.01567 | − | 0.586400i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −810.000 | −1.26365 | −0.631825 | − | 0.775111i | \(-0.717694\pi\) | ||||
−0.631825 | + | 0.775111i | \(0.717694\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 415.692i | 0.646489i | 0.946316 | + | 0.323244i | \(0.104774\pi\) | ||||
−0.946316 | + | 0.323244i | \(0.895226\pi\) | |||||||
\(644\) | −144.000 | − | 249.415i | −0.223602 | − | 0.387291i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 240.000 | + | 138.564i | 0.371517 | + | 0.214495i | ||||
\(647\) | 983.805i | 1.52056i | 0.649593 | + | 0.760282i | \(0.274939\pi\) | ||||
−0.649593 | + | 0.760282i | \(0.725061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 324.000 | 0.499230 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −432.000 | + | 249.415i | −0.662577 | + | 0.382539i | ||||
\(653\) | −950.000 | −1.45482 | −0.727412 | − | 0.686201i | \(-0.759277\pi\) | ||||
−0.727412 | + | 0.686201i | \(0.759277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 144.000 | − | 249.415i | 0.219512 | − | 0.380206i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1132.76i | 1.71891i | 0.511212 | + | 0.859455i | \(0.329197\pi\) | ||||
−0.511212 | + | 0.859455i | \(0.670803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −242.000 | −0.366112 | −0.183056 | − | 0.983102i | \(-0.558599\pi\) | ||||
−0.183056 | + | 0.983102i | \(0.558599\pi\) | |||||||
\(662\) | −648.000 | − | 374.123i | −0.978852 | − | 0.565140i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 720.533i | 1.08514i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 249.415i | 0.373936i | ||||||||
\(668\) | 456.000 | − | 263.272i | 0.682635 | − | 0.394119i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 769.031i | 1.14610i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −324.000 | −0.481426 | −0.240713 | − | 0.970596i | \(-0.577381\pi\) | ||||
−0.240713 | + | 0.970596i | \(0.577381\pi\) | |||||||
\(674\) | 468.000 | − | 810.600i | 0.694362 | − | 1.20267i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −310.000 | − | 536.936i | −0.458580 | − | 0.794284i | ||||
\(677\) | −806.000 | −1.19055 | −0.595273 | − | 0.803523i | \(-0.702956\pi\) | ||||
−0.595273 | + | 0.803523i | \(0.702956\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 748.246i | − | 1.10198i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −72.0000 | + | 124.708i | −0.105572 | + | 0.182856i | ||||
\(683\) | 575.041i | 0.841934i | 0.907076 | + | 0.420967i | \(0.138309\pi\) | ||||
−0.907076 | + | 0.420967i | \(0.861691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 180.000 | + | 103.923i | 0.262391 | + | 0.151491i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 288.000 | + | 166.277i | 0.418605 | + | 0.241682i | ||||
\(689\) | 468.000 | 0.679245 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 775.959i | 1.12295i | 0.827494 | + | 0.561475i | \(0.189766\pi\) | ||||
−0.827494 | + | 0.561475i | \(0.810234\pi\) | |||||||
\(692\) | −292.000 | − | 505.759i | −0.421965 | − | 0.730865i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −972.000 | − | 561.184i | −1.40058 | − | 0.808623i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −180.000 | −0.258250 | ||||||||
\(698\) | −434.000 | + | 751.710i | −0.621777 | + | 1.07695i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −756.000 | −1.07846 | −0.539230 | − | 0.842159i | \(-0.681285\pi\) | ||||
−0.539230 | + | 0.842159i | \(0.681285\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 748.246i | − | 1.06436i | ||||||
\(704\) | − | 665.108i | − | 0.944755i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −158.000 | + | 273.664i | −0.223796 | + | 0.387626i | ||||
\(707\) | 374.123i | 0.529170i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −310.000 | −0.437236 | −0.218618 | − | 0.975811i | \(-0.570155\pi\) | ||||
−0.218618 | + | 0.975811i | \(0.570155\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −144.000 | −0.202247 | ||||||||
\(713\) | 48.0000 | 0.0673212 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 252.000 | − | 145.492i | 0.351955 | − | 0.203201i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −792.000 | − | 457.261i | −1.10306 | − | 0.636854i | ||||
\(719\) | − | 83.1384i | − | 0.115631i | −0.998327 | − | 0.0578153i | \(-0.981587\pi\) | ||
0.998327 | − | 0.0578153i | \(-0.0184135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −108.000 | −0.149792 | ||||||||
\(722\) | 169.000 | − | 292.717i | 0.234072 | − | 0.405425i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −524.000 | − | 907.595i | −0.723757 | − | 1.25358i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1091.19i | 1.50095i | 0.660898 | + | 0.750476i | \(0.270176\pi\) | ||||
−0.660898 | + | 0.750476i | \(0.729824\pi\) | |||||||
\(728\) | − | 1496.49i | − | 2.05562i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 207.846i | − | 0.284331i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1206.00 | −1.64529 | −0.822647 | − | 0.568553i | \(-0.807503\pi\) | ||||
−0.822647 | + | 0.568553i | \(0.807503\pi\) | |||||||
\(734\) | −378.000 | − | 218.238i | −0.514986 | − | 0.297328i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −192.000 | + | 110.851i | −0.260870 | + | 0.150613i | ||||
\(737\) | −432.000 | −0.586160 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 484.974i | 0.656257i | 0.944633 | + | 0.328129i | \(0.106418\pi\) | ||||
−0.944633 | + | 0.328129i | \(0.893582\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 468.000 | + | 270.200i | 0.630728 | + | 0.364151i | ||||
\(743\) | − | 1122.37i | − | 1.51059i | −0.655385 | − | 0.755295i | \(-0.727493\pi\) | ||
0.655385 | − | 0.755295i | \(-0.272507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 270.000 | − | 467.654i | 0.361930 | − | 0.626882i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −360.000 | + | 207.846i | −0.481283 | + | 0.277869i | ||||
\(749\) | −1944.00 | −2.59546 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 242.487i | − | 0.322886i | −0.986882 | − | 0.161443i | \(-0.948385\pi\) | ||
0.986882 | − | 0.161443i | \(-0.0516147\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −648.000 | + | 1122.37i | −0.859416 | + | 1.48855i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −846.000 | −1.11757 | −0.558785 | − | 0.829313i | \(-0.688732\pi\) | ||||
−0.558785 | + | 0.829313i | \(0.688732\pi\) | |||||||
\(758\) | −564.000 | − | 325.626i | −0.744063 | − | 0.429585i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1458.00 | 1.91590 | 0.957950 | − | 0.286935i | \(-0.0926364\pi\) | ||||
0.957950 | + | 0.286935i | \(0.0926364\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 270.200i | 0.354128i | ||||||||
\(764\) | −648.000 | + | 374.123i | −0.848168 | + | 0.489690i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −96.0000 | − | 55.4256i | −0.125326 | − | 0.0723572i | ||||
\(767\) | − | 561.184i | − | 0.731662i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1282.00 | 1.66710 | 0.833550 | − | 0.552444i | \(-0.186305\pi\) | ||||
0.833550 | + | 0.552444i | \(0.186305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 360.000 | + | 623.538i | 0.466321 | + | 0.807692i | ||||
\(773\) | −422.000 | −0.545925 | −0.272962 | − | 0.962025i | \(-0.588003\pi\) | ||||
−0.272962 | + | 0.962025i | \(0.588003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −576.000 | −0.742268 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 288.000 | − | 498.831i | 0.370180 | − | 0.641170i | ||||
\(779\) | − | 249.415i | − | 0.320174i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1080.00 | 1.38284 | ||||||||
\(782\) | 120.000 | + | 69.2820i | 0.153453 | + | 0.0885959i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 472.000 | − | 817.528i | 0.602041 | − | 1.04277i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1205.51i | 1.53178i | 0.642974 | + | 0.765888i | \(0.277700\pi\) | ||||
−0.642974 | + | 0.765888i | \(0.722300\pi\) | |||||||
\(788\) | 308.000 | + | 533.472i | 0.390863 | + | 0.676994i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 103.923i | 0.131382i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1332.00 | 1.67970 | ||||||||
\(794\) | 306.000 | − | 530.008i | 0.385390 | − | 0.667516i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −648.000 | + | 374.123i | −0.814070 | + | 0.470004i | ||||
\(797\) | −94.0000 | −0.117942 | −0.0589711 | − | 0.998260i | \(-0.518782\pi\) | ||||
−0.0589711 | + | 0.998260i | \(0.518782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 450.000 | − | 779.423i | 0.561097 | − | 0.971849i | ||||
\(803\) | 374.123i | 0.465907i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 216.000 | + | 124.708i | 0.267990 | + | 0.154724i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 288.000 | 0.356436 | ||||||||
\(809\) | 270.000 | 0.333745 | 0.166873 | − | 0.985978i | \(-0.446633\pi\) | ||||
0.166873 | + | 0.985978i | \(0.446633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 187.061i | − | 0.230655i | −0.993328 | − | 0.115328i | \(-0.963208\pi\) | ||
0.993328 | − | 0.115328i | \(-0.0367918\pi\) | |||||||
\(812\) | −1296.00 | + | 748.246i | −1.59606 | + | 0.921485i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 972.000 | + | 561.184i | 1.19410 | + | 0.689416i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 288.000 | 0.352509 | ||||||||
\(818\) | −50.0000 | + | 86.6025i | −0.0611247 | + | 0.105871i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1188.00 | −1.44702 | −0.723508 | − | 0.690316i | \(-0.757471\pi\) | ||||
−0.723508 | + | 0.690316i | \(0.757471\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 384.515i | 0.467212i | 0.972331 | + | 0.233606i | \(0.0750525\pi\) | ||||
−0.972331 | + | 0.233606i | \(0.924947\pi\) | |||||||
\(824\) | 83.1384i | 0.100896i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 324.000 | − | 561.184i | 0.392252 | − | 0.679400i | ||||
\(827\) | − | 450.333i | − | 0.544538i | −0.962221 | − | 0.272269i | \(-0.912226\pi\) | ||
0.962221 | − | 0.272269i | \(-0.0877741\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 718.000 | 0.866104 | 0.433052 | − | 0.901369i | \(-0.357437\pi\) | ||||
0.433052 | + | 0.901369i | \(0.357437\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1152.00 | −1.38462 | ||||||||
\(833\) | −590.000 | −0.708283 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −288.000 | − | 498.831i | −0.344498 | − | 0.596687i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1278.00 | − | 737.854i | −1.52506 | − | 0.880494i | ||||
\(839\) | − | 914.523i | − | 1.09002i | −0.838431 | − | 0.545008i | \(-0.816527\pi\) | ||
0.838431 | − | 0.545008i | \(-0.183473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 455.000 | 0.541023 | ||||||||
\(842\) | −286.000 | + | 495.367i | −0.339667 | + | 0.588321i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −840.000 | + | 484.974i | −0.995261 | + | 0.574614i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 135.100i | − | 0.159504i | ||||||
\(848\) | 208.000 | − | 360.267i | 0.245283 | − | 0.424843i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 374.123i | − | 0.439627i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 666.000 | 0.780774 | 0.390387 | − | 0.920651i | \(-0.372341\pi\) | ||||
0.390387 | + | 0.920651i | \(0.372341\pi\) | |||||||
\(854\) | 1332.00 | + | 769.031i | 1.55972 | + | 0.900504i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1496.49i | 1.74824i | ||||||||
\(857\) | −182.000 | −0.212369 | −0.106184 | − | 0.994346i | \(-0.533863\pi\) | ||||
−0.106184 | + | 0.994346i | \(0.533863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 990.733i | − | 1.15336i | −0.816971 | − | 0.576678i | \(-0.804349\pi\) | ||
0.816971 | − | 0.576678i | \(-0.195651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 216.000 | + | 124.708i | 0.250580 | + | 0.144672i | ||||
\(863\) | 1170.87i | 1.35674i | 0.734721 | + | 0.678370i | \(0.237313\pi\) | ||||
−0.734721 | + | 0.678370i | \(0.762687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.0000 | − | 62.3538i | 0.0415704 | − | 0.0720021i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 144.000 | + | 249.415i | 0.165899 | + | 0.287345i | ||||
\(869\) | 936.000 | 1.07710 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 748.246i | 0.859065i | ||||||||
\(872\) | 208.000 | 0.238532 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −96.0000 | + | 166.277i | −0.109840 | + | 0.190248i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 774.000 | 0.882554 | 0.441277 | − | 0.897371i | \(-0.354526\pi\) | ||||
0.441277 | + | 0.897371i | \(0.354526\pi\) | |||||||
\(878\) | 1356.00 | + | 782.887i | 1.54442 | + | 0.891671i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1602.00 | 1.81839 | 0.909194 | − | 0.416373i | \(-0.136699\pi\) | ||||
0.909194 | + | 0.416373i | \(0.136699\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 415.692i | − | 0.470773i | −0.971902 | − | 0.235386i | \(-0.924364\pi\) | ||
0.971902 | − | 0.235386i | \(-0.0756355\pi\) | |||||||
\(884\) | 360.000 | + | 623.538i | 0.407240 | + | 0.705360i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −372.000 | − | 214.774i | −0.419865 | − | 0.242409i | ||||
\(887\) | − | 367.195i | − | 0.413974i | −0.978344 | − | 0.206987i | \(-0.933634\pi\) | ||
0.978344 | − | 0.206987i | \(-0.0663658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2268.00 | −2.55118 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −324.000 | + | 187.061i | −0.363229 | + | 0.209710i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1152.00 | − | 665.108i | −1.28571 | − | 0.742307i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −54.0000 | + | 93.5307i | −0.0601336 | + | 0.104155i | ||||
\(899\) | − | 249.415i | − | 0.277436i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −260.000 | −0.288568 | ||||||||
\(902\) | 324.000 | + | 187.061i | 0.359202 | + | 0.207385i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 80.0000 | 0.0884956 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1434.14i | − | 1.58119i | −0.612340 | − | 0.790594i | \(-0.709772\pi\) | ||
0.612340 | − | 0.790594i | \(-0.290228\pi\) | |||||||
\(908\) | −744.000 | + | 429.549i | −0.819383 | + | 0.473071i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1080.80i | − | 1.18639i | −0.805059 | − | 0.593194i | \(-0.797867\pi\) | ||
0.805059 | − | 0.593194i | \(-0.202133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −936.000 | −1.02519 | ||||||||
\(914\) | −288.000 | + | 498.831i | −0.315098 | + | 0.545767i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −676.000 | − | 1170.87i | −0.737991 | − | 1.27824i | ||||
\(917\) | 1404.00 | 1.53108 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 187.061i | − | 0.203549i | −0.994807 | − | 0.101774i | \(-0.967548\pi\) | ||
0.994807 | − | 0.101774i | \(-0.0324520\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 288.000 | − | 498.831i | 0.312364 | − | 0.541031i | ||||
\(923\) | − | 1870.61i | − | 2.02667i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −702.000 | − | 405.300i | −0.758099 | − | 0.437689i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 576.000 | + | 997.661i | 0.620690 | + | 1.07507i | ||||
\(929\) | −54.0000 | −0.0581270 | −0.0290635 | − | 0.999578i | \(-0.509253\pi\) | ||||
−0.0290635 | + | 0.999578i | \(0.509253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 817.528i | − | 0.878118i | ||||||
\(932\) | 364.000 | + | 630.466i | 0.390558 | + | 0.676466i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 996.000 | + | 575.041i | 1.06638 | + | 0.615675i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −936.000 | −0.998933 | −0.499466 | − | 0.866333i | \(-0.666471\pi\) | ||||
−0.499466 | + | 0.866333i | \(0.666471\pi\) | |||||||
\(938\) | −432.000 | + | 748.246i | −0.460554 | + | 0.797704i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 124.708i | − | 0.132246i | ||||||
\(944\) | −432.000 | − | 249.415i | −0.457627 | − | 0.264211i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −216.000 | + | 374.123i | −0.228330 | + | 0.395479i | ||||
\(947\) | 1032.30i | 1.09008i | 0.838411 | + | 0.545038i | \(0.183485\pi\) | ||||
−0.838411 | + | 0.545038i | \(0.816515\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 648.000 | 0.682824 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 831.384i | 0.873303i | ||||||||
\(953\) | 1550.00 | 1.62644 | 0.813221 | − | 0.581954i | \(-0.197712\pi\) | ||||
0.813221 | + | 0.581954i | \(0.197712\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1224.00 | − | 706.677i | 1.28033 | − | 0.739202i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 252.000 | + | 145.492i | 0.263048 | + | 0.151871i | ||||
\(959\) | − | 1143.15i | − | 1.19203i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 913.000 | 0.950052 | ||||||||
\(962\) | 972.000 | − | 1683.55i | 1.01040 | − | 1.75006i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 212.000 | + | 367.195i | 0.219917 | + | 0.380907i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1215.90i | − | 1.25739i | −0.777650 | − | 0.628697i | \(-0.783589\pi\) | ||
0.777650 | − | 0.628697i | \(-0.216411\pi\) | |||||||
\(968\) | −104.000 | −0.107438 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1839.44i | 1.89437i | 0.320681 | + | 0.947187i | \(0.396088\pi\) | ||||
−0.320681 | + | 0.947187i | \(0.603912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1944.00 | −1.99794 | ||||||||
\(974\) | 450.000 | + | 259.808i | 0.462012 | + | 0.266743i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 592.000 | − | 1025.37i | 0.606557 | − | 1.05059i | ||||
\(977\) | −206.000 | −0.210850 | −0.105425 | − | 0.994427i | \(-0.533620\pi\) | ||||
−0.105425 | + | 0.994427i | \(0.533620\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 187.061i | − | 0.191074i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −126.000 | − | 72.7461i | −0.128310 | − | 0.0740796i | ||||
\(983\) | − | 720.533i | − | 0.732994i | −0.930419 | − | 0.366497i | \(-0.880557\pi\) | ||
0.930419 | − | 0.366497i | \(-0.119443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 360.000 | − | 623.538i | 0.365112 | − | 0.632392i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −864.000 | + | 498.831i | −0.874494 | + | 0.504889i | ||||
\(989\) | 144.000 | 0.145602 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1323.29i | − | 1.33530i | −0.744473 | − | 0.667652i | \(-0.767299\pi\) | ||
0.744473 | − | 0.667652i | \(-0.232701\pi\) | |||||||
\(992\) | 192.000 | − | 110.851i | 0.193548 | − | 0.111745i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1080.00 | − | 1870.61i | 1.08652 | − | 1.88191i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 198.000 | 0.198596 | 0.0992979 | − | 0.995058i | \(-0.468340\pi\) | ||||
0.0992979 | + | 0.995058i | \(0.468340\pi\) | |||||||
\(998\) | −768.000 | − | 443.405i | −0.769539 | − | 0.444294i | ||||
\(999\) | 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 | 900.3.c.j.451.1 | 2 | ||
3.2 | odd | 2 | 300.3.c.a.151.2 | 2 | |||
4.3 | odd | 2 | inner | 900.3.c.j.451.2 | 2 | ||
5.2 | odd | 4 | 180.3.f.e.19.4 | 4 | |||
5.3 | odd | 4 | 180.3.f.e.19.1 | 4 | |||
5.4 | even | 2 | 900.3.c.f.451.2 | 2 | |||
12.11 | even | 2 | 300.3.c.a.151.1 | 2 | |||
15.2 | even | 4 | 60.3.f.a.19.1 | ✓ | 4 | ||
15.8 | even | 4 | 60.3.f.a.19.4 | yes | 4 | ||
15.14 | odd | 2 | 300.3.c.c.151.1 | 2 | |||
20.3 | even | 4 | 180.3.f.e.19.3 | 4 | |||
20.7 | even | 4 | 180.3.f.e.19.2 | 4 | |||
20.19 | odd | 2 | 900.3.c.f.451.1 | 2 | |||
60.23 | odd | 4 | 60.3.f.a.19.2 | yes | 4 | ||
60.47 | odd | 4 | 60.3.f.a.19.3 | yes | 4 | ||
60.59 | even | 2 | 300.3.c.c.151.2 | 2 | |||
120.53 | even | 4 | 960.3.j.b.319.2 | 4 | |||
120.77 | even | 4 | 960.3.j.b.319.3 | 4 | |||
120.83 | odd | 4 | 960.3.j.b.319.4 | 4 | |||
120.107 | odd | 4 | 960.3.j.b.319.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.f.a.19.1 | ✓ | 4 | 15.2 | even | 4 | ||
60.3.f.a.19.2 | yes | 4 | 60.23 | odd | 4 | ||
60.3.f.a.19.3 | yes | 4 | 60.47 | odd | 4 | ||
60.3.f.a.19.4 | yes | 4 | 15.8 | even | 4 | ||
180.3.f.e.19.1 | 4 | 5.3 | odd | 4 | |||
180.3.f.e.19.2 | 4 | 20.7 | even | 4 | |||
180.3.f.e.19.3 | 4 | 20.3 | even | 4 | |||
180.3.f.e.19.4 | 4 | 5.2 | odd | 4 | |||
300.3.c.a.151.1 | 2 | 12.11 | even | 2 | |||
300.3.c.a.151.2 | 2 | 3.2 | odd | 2 | |||
300.3.c.c.151.1 | 2 | 15.14 | odd | 2 | |||
300.3.c.c.151.2 | 2 | 60.59 | even | 2 | |||
900.3.c.f.451.1 | 2 | 20.19 | odd | 2 | |||
900.3.c.f.451.2 | 2 | 5.4 | even | 2 | |||
900.3.c.j.451.1 | 2 | 1.1 | even | 1 | trivial | ||
900.3.c.j.451.2 | 2 | 4.3 | odd | 2 | inner | ||
960.3.j.b.319.1 | 4 | 120.107 | odd | 4 | |||
960.3.j.b.319.2 | 4 | 120.53 | even | 4 | |||
960.3.j.b.319.3 | 4 | 120.77 | even | 4 | |||
960.3.j.b.319.4 | 4 | 120.83 | odd | 4 |