Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2872,1,Mod(717,2872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2872, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2872.717");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2872 = 2^{3} \cdot 359 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2872.b (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: | \(1.43331471628\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\Q(\zeta_{38})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{38}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{38} - \cdots)\) |
Embedding invariants
Embedding label | 717.7 | ||
Root | \(0.677282 + 0.735724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2872.717 |
Dual form | 2872.1.b.e.717.8 |
$q$-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 \(\left(\mathbb{Z}/2872\mathbb{Z}\right)^\times\).
\(n\) | \(719\) | \(1437\) | \(2161\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.245485 | − | 0.969400i | −0.245485 | − | 0.969400i | ||||
\(3\) | − | 0.649399i | − | 0.649399i | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||
0.945817 | − | 0.324699i | \(-0.105263\pi\) | |||||||
\(4\) | −0.879474 | + | 0.475947i | −0.879474 | + | 0.475947i | ||||
\(5\) | − | 1.83155i | − | 1.83155i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||
0.401695 | − | 0.915773i | \(-0.368421\pi\) | |||||||
\(6\) | −0.629528 | + | 0.159418i | −0.629528 | + | 0.159418i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0.677282 | + | 0.735724i | 0.677282 | + | 0.735724i | ||||
\(9\) | 0.578281 | 0.578281 | ||||||||
\(10\) | −1.77550 | + | 0.449618i | −1.77550 | + | 0.449618i | ||||
\(11\) | 0.329189i | 0.329189i | 0.986361 | + | 0.164595i | \(0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(12\) | 0.309080 | + | 0.571129i | 0.309080 | + | 0.571129i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.18940 | −1.18940 | ||||||||
\(16\) | 0.546948 | − | 0.837166i | 0.546948 | − | 0.837166i | ||||
\(17\) | −1.09390 | −1.09390 | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(18\) | −0.141960 | − | 0.560586i | −0.141960 | − | 0.560586i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0.871720 | + | 1.61080i | 0.871720 | + | 1.61080i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.319116 | − | 0.0808112i | 0.319116 | − | 0.0808112i | ||||
\(23\) | −1.75895 | −1.75895 | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(24\) | 0.477778 | − | 0.439826i | 0.477778 | − | 0.439826i | ||||
\(25\) | −2.35456 | −2.35456 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.02493i | − | 1.02493i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0.291982 | + | 1.15301i | 0.291982 | + | 1.15301i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −0.945817 | − | 0.324699i | −0.945817 | − | 0.324699i | ||||
\(33\) | 0.213775 | 0.213775 | ||||||||
\(34\) | 0.268536 | + | 1.06042i | 0.268536 | + | 1.06042i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.508583 | + | 0.275231i | −0.508583 | + | 0.275231i | ||||
\(37\) | − | 1.99317i | − | 1.99317i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||
0.0825793 | − | 0.996584i | \(-0.473684\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.34751 | − | 1.24047i | 1.34751 | − | 1.24047i | ||||
\(41\) | −0.165159 | −0.165159 | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −0.156677 | − | 0.289513i | −0.156677 | − | 0.289513i | ||||
\(45\) | − | 1.05915i | − | 1.05915i | ||||||
\(46\) | 0.431796 | + | 1.70512i | 0.431796 | + | 1.70512i | ||||
\(47\) | −1.57828 | −1.57828 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(48\) | −0.543655 | − | 0.355188i | −0.543655 | − | 0.355188i | ||||
\(49\) | 1.00000 | 1.00000 | ||||||||
\(50\) | 0.578011 | + | 2.28251i | 0.578011 | + | 2.28251i | ||||
\(51\) | 0.710375i | 0.710375i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −0.993571 | + | 0.251606i | −0.993571 | + | 0.251606i | ||||
\(55\) | 0.602925 | 0.602925 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 1.04605 | − | 0.566094i | 1.04605 | − | 0.566094i | ||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.0825793 | + | 0.996584i | −0.0825793 | + | 0.996584i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0524787 | − | 0.207234i | −0.0524787 | − | 0.207234i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0.962053 | − | 0.520637i | 0.962053 | − | 0.520637i | ||||
\(69\) | 1.14226i | 1.14226i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0.391659 | + | 0.425455i | 0.391659 | + | 0.425455i | ||||
\(73\) | 0.490971 | 0.490971 | 0.245485 | − | 0.969400i | \(-0.421053\pi\) | ||||
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(74\) | −1.93218 | + | 0.489294i | −1.93218 | + | 0.489294i | ||||
\(75\) | 1.52905i | 1.52905i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.803391 | 0.803391 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(80\) | −1.53331 | − | 1.00176i | −1.53331 | − | 1.00176i | ||||
\(81\) | −0.0873100 | −0.0873100 | ||||||||
\(82\) | 0.0405441 | + | 0.160105i | 0.0405441 | + | 0.160105i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00352i | 2.00352i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.242192 | + | 0.222954i | −0.242192 | + | 0.222954i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −1.02674 | + | 0.260006i | −1.02674 | + | 0.260006i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.54695 | − | 0.837166i | 1.54695 | − | 0.837166i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.387445 | + | 1.52999i | 0.387445 | + | 1.52999i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.210859 | + | 0.614213i | −0.210859 | + | 0.614213i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | −0.245485 | − | 0.969400i | −0.245485 | − | 0.969400i | ||||
\(99\) | 0.190364i | 0.190364i | ||||||||
\(100\) | 2.07078 | − | 1.12065i | 2.07078 | − | 1.12065i | ||||
\(101\) | − | 1.47145i | − | 1.47145i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||
0.677282 | − | 0.735724i | \(-0.263158\pi\) | |||||||
\(102\) | 0.688638 | − | 0.174387i | 0.688638 | − | 0.174387i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.99317i | 1.99317i | 0.0825793 | + | 0.996584i | \(0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(108\) | 0.487815 | + | 0.901403i | 0.487815 | + | 0.901403i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | −0.148009 | − | 0.584476i | −0.148009 | − | 0.584476i | ||||
\(111\) | −1.29436 | −1.29436 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.22159i | 3.22159i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.805562 | − | 0.875073i | −0.805562 | − | 0.875073i | ||||
\(121\) | 0.891634 | 0.891634 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.107254i | 0.107254i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.48095i | 2.48095i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.57828 | 1.57828 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(128\) | 0.986361 | − | 0.164595i | 0.986361 | − | 0.164595i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.47145i | − | 1.47145i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||
0.677282 | − | 0.735724i | \(-0.263158\pi\) | |||||||
\(132\) | −0.188010 | + | 0.101746i | −0.188010 | + | 0.101746i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.87721 | −1.87721 | ||||||||
\(136\) | −0.740876 | − | 0.804806i | −0.740876 | − | 0.804806i | ||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 1.10731 | − | 0.280408i | 1.10731 | − | 0.280408i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.02493i | 1.02493i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.316290 | − | 0.484117i | 0.316290 | − | 0.484117i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.120526 | − | 0.475947i | −0.120526 | − | 0.475947i | ||||
\(147\) | − | 0.649399i | − | 0.649399i | ||||||
\(148\) | 0.948644 | + | 1.75294i | 0.948644 | + | 1.75294i | ||||
\(149\) | − | 0.951895i | − | 0.951895i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||
0.879474 | − | 0.475947i | \(-0.157895\pi\) | |||||||
\(150\) | 1.48226 | − | 0.375360i | 1.48226 | − | 0.375360i | ||||
\(151\) | 1.97272 | 1.97272 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.632579 | −0.632579 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | −0.197221 | − | 0.778807i | −0.197221 | − | 0.778807i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.594702 | + | 1.73231i | −0.594702 | + | 1.73231i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.0214333 | + | 0.0846384i | 0.0214333 | + | 0.0846384i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0.145253 | − | 0.0786068i | 0.145253 | − | 0.0786068i | ||||
\(165\) | − | 0.391539i | − | 0.391539i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −1.00000 | ||||||||
\(170\) | 1.94221 | − | 0.491836i | 1.94221 | − | 0.491836i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.22843i | 1.22843i | 0.789141 | + | 0.614213i | \(0.210526\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.275586 | + | 0.180049i | 0.275586 | + | 0.180049i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0.504099 | + | 0.931493i | 0.504099 | + | 0.931493i | ||||
\(181\) | − | 1.93880i | − | 1.93880i | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||
0.245485 | − | 0.969400i | \(-0.421053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.19130 | − | 1.29410i | −1.19130 | − | 1.29410i | ||||
\(185\) | −3.65058 | −3.65058 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.360099i | − | 0.360099i | ||||||
\(188\) | 1.38806 | − | 0.751179i | 1.38806 | − | 0.751179i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.09390 | 1.09390 | 0.546948 | − | 0.837166i | \(-0.315789\pi\) | ||||
0.546948 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(192\) | 0.647181 | + | 0.0536269i | 0.647181 | + | 0.0536269i | ||||
\(193\) | −1.97272 | −1.97272 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.879474 | + | 0.475947i | −0.879474 | + | 0.475947i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0.184539 | − | 0.0467316i | 0.184539 | − | 0.0467316i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −1.59470 | − | 1.73231i | −1.59470 | − | 1.73231i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.42642 | + | 0.361219i | −1.42642 | + | 0.361219i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.338101 | − | 0.624756i | −0.338101 | − | 0.624756i | ||||
\(205\) | 0.302496i | 0.302496i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.01717 | −1.01717 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.93218 | − | 0.489294i | 1.93218 | − | 0.489294i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.754068 | − | 0.694169i | 0.754068 | − | 0.694169i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 0.318836i | − | 0.318836i | ||||||
\(220\) | −0.530257 | + | 0.286961i | −0.530257 | + | 0.286961i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.317747 | + | 1.25475i | 0.317747 | + | 1.25475i | ||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.36160 | −1.36160 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.22843i | − | 1.22843i | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(230\) | 3.12301 | − | 0.790855i | 3.12301 | − | 0.790855i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.35456 | 1.35456 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.89070i | 2.89070i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.521721i | − | 0.521721i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −0.650543 | + | 0.995730i | −0.650543 | + | 0.995730i | ||||
\(241\) | 1.75895 | 1.75895 | 0.879474 | − | 0.475947i | \(-0.157895\pi\) | ||||
0.879474 | + | 0.475947i | \(0.157895\pi\) | |||||||
\(242\) | −0.218883 | − | 0.864351i | −0.218883 | − | 0.864351i | ||||
\(243\) | − | 0.968235i | − | 0.968235i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.83155i | − | 1.83155i | ||||||
\(246\) | 0.103972 | − | 0.0263293i | 0.103972 | − | 0.0263293i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.40503 | − | 0.609036i | 2.40503 | − | 0.609036i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.579026i | − | 0.579026i | ||||||
\(254\) | −0.387445 | − | 1.52999i | −0.387445 | − | 1.52999i | ||||
\(255\) | 1.30109 | 1.30109 | ||||||||
\(256\) | −0.401695 | − | 0.915773i | −0.401695 | − | 0.915773i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.42642 | + | 0.361219i | −1.42642 | + | 0.361219i | ||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0.144786 | + | 0.157279i | 0.144786 | + | 0.157279i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0.460829 | + | 1.81977i | 0.460829 | + | 1.81977i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −0.598305 | + | 0.915773i | −0.598305 | + | 0.915773i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.775097i | − | 0.775097i | ||||||
\(276\) | −0.543655 | − | 1.00459i | −0.543655 | − | 1.00459i | ||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.89163 | 1.89163 | 0.945817 | − | 0.324699i | \(-0.105263\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(282\) | 0.993571 | − | 0.251606i | 0.993571 | − | 0.251606i | ||||
\(283\) | − | 1.47145i | − | 1.47145i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||
0.677282 | − | 0.735724i | \(-0.263158\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.546948 | − | 0.187768i | −0.546948 | − | 0.187768i | ||||
\(289\) | 0.196609 | 0.196609 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.431796 | + | 0.233676i | −0.431796 | + | 0.233676i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −0.629528 | + | 0.159418i | −0.629528 | + | 0.159418i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.46642 | − | 1.34994i | 1.46642 | − | 1.34994i | ||||
\(297\) | 0.337397 | 0.337397 | ||||||||
\(298\) | −0.922767 | + | 0.233676i | −0.922767 | + | 0.233676i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.727748 | − | 1.34476i | −0.727748 | − | 1.34476i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.484275 | − | 1.91236i | −0.484275 | − | 1.91236i | ||||
\(303\) | −0.955557 | −0.955557 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.155289 | + | 0.613223i | 0.155289 | + | 0.613223i | ||||
\(307\) | 0.951895i | 0.951895i | 0.879474 | + | 0.475947i | \(0.157895\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.706561 | + | 0.382372i | −0.706561 | + | 0.382372i | ||||
\(317\) | − | 0.329189i | − | 0.329189i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||
0.986361 | − | 0.164595i | \(-0.0526316\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.82529 | + | 0.151248i | 1.82529 | + | 0.151248i | ||||
\(321\) | 1.29436 | 1.29436 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.0767869 | − | 0.0415550i | 0.0767869 | − | 0.0415550i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.111859 | − | 0.121511i | −0.111859 | − | 0.121511i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.379558 | + | 0.0961172i | −0.379558 | + | 0.0961172i | ||||
\(331\) | 1.83155i | 1.83155i | 0.401695 | + | 0.915773i | \(0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.15261i | − | 1.15261i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0.245485 | + | 0.969400i | 0.245485 | + | 0.969400i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.953571 | − | 1.76205i | −0.953571 | − | 1.76205i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.09210 | 2.09210 | ||||||||
\(346\) | 1.19084 | − | 0.301561i | 1.19084 | − | 0.301561i | ||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.106888 | − | 0.311353i | 0.106888 | − | 0.311353i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.00000 | −1.00000 | ||||||||
\(360\) | 0.779241 | − | 0.717342i | 0.779241 | − | 0.717342i | ||||
\(361\) | −1.00000 | −1.00000 | ||||||||
\(362\) | −1.87947 | + | 0.475947i | −1.87947 | + | 0.475947i | ||||
\(363\) | − | 0.579026i | − | 0.579026i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.899236i | − | 0.899236i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.97272 | 1.97272 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(368\) | −0.962053 | + | 1.47253i | −0.962053 | + | 1.47253i | ||||
\(369\) | −0.0955081 | −0.0955081 | ||||||||
\(370\) | 0.896165 | + | 3.53888i | 0.896165 | + | 3.53888i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | −0.349080 | + | 0.0883990i | −0.349080 | + | 0.0883990i | ||||
\(375\) | 1.61112 | 1.61112 | ||||||||
\(376\) | −1.06894 | − | 1.16118i | −1.06894 | − | 1.16118i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.67433i | 1.67433i | 0.546948 | + | 0.837166i | \(0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 1.02493i | − | 1.02493i | ||||||
\(382\) | −0.268536 | − | 1.06042i | −0.268536 | − | 1.06042i | ||||
\(383\) | 1.35456 | 1.35456 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(384\) | −0.106888 | − | 0.640542i | −0.106888 | − | 0.640542i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.484275 | + | 1.91236i | 0.484275 | + | 1.91236i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.99317i | 1.99317i | 0.0825793 | + | 0.996584i | \(0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.92411 | 1.92411 | ||||||||
\(392\) | 0.677282 | + | 0.735724i | 0.677282 | + | 0.735724i | ||||
\(393\) | −0.955557 | −0.955557 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.47145i | − | 1.47145i | ||||||
\(396\) | −0.0906032 | − | 0.167420i | −0.0906032 | − | 0.167420i | ||||
\(397\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.28782 | + | 1.97116i | −1.28782 | + | 1.97116i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.700332 | + | 1.29410i | 0.700332 | + | 1.29410i | ||||
\(405\) | 0.159912i | 0.159912i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.656130 | 0.656130 | ||||||||
\(408\) | −0.522640 | + | 0.481124i | −0.522640 | + | 0.481124i | ||||
\(409\) | 0.165159 | 0.165159 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
0.0825793 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(410\) | 0.293240 | − | 0.0742583i | 0.293240 | − | 0.0742583i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.249699 | + | 0.986041i | 0.249699 | + | 0.986041i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.93880i | − | 1.93880i | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||
0.245485 | − | 0.969400i | \(-0.421053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.912690 | −0.912690 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.57565 | 2.57565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.948644 | − | 1.75294i | −0.948644 | − | 1.75294i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.09390 | −1.09390 | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(432\) | −0.858040 | − | 0.560586i | −0.858040 | − | 0.560586i | ||||
\(433\) | 0.803391 | 0.803391 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.309080 | + | 0.0782696i | −0.309080 | + | 0.0782696i | ||||
\(439\) | −1.35456 | −1.35456 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(440\) | 0.408350 | + | 0.443587i | 0.408350 | + | 0.443587i | ||||
\(441\) | 0.578281 | 0.578281 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 1.13836 | − | 0.616048i | 1.13836 | − | 0.616048i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.618159 | −0.618159 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.490971 | −0.490971 | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(450\) | 0.334253 | + | 1.31993i | 0.334253 | + | 1.31993i | ||||
\(451\) | − | 0.0543685i | − | 0.0543685i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.28108i | − | 1.28108i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.09390 | −1.09390 | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(458\) | −1.19084 | + | 0.301561i | −1.19084 | + | 0.301561i | ||||
\(459\) | 1.12117i | 1.12117i | ||||||||
\(460\) | −1.53331 | − | 2.83331i | −1.53331 | − | 2.83331i | ||||
\(461\) | − | 0.649399i | − | 0.649399i | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||
0.945817 | − | 0.324699i | \(-0.105263\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.332526 | − | 1.31311i | −0.332526 | − | 1.31311i | ||||
\(467\) | − | 1.22843i | − | 1.22843i | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.80224 | − | 0.709624i | 2.80224 | − | 0.709624i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.505757 | + | 0.128075i | −0.505757 | + | 0.128075i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(480\) | 1.12496 | + | 0.386199i | 1.12496 | + | 0.386199i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.431796 | − | 1.70512i | −0.431796 | − | 1.70512i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.784169 | + | 0.424371i | −0.784169 | + | 0.424371i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.938607 | + | 0.237688i | −0.938607 | + | 0.237688i | ||||
\(487\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.77550 | + | 0.449618i | −1.77550 | + | 0.449618i | ||||
\(491\) | − | 1.99317i | − | 1.99317i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||
0.0825793 | − | 0.996584i | \(-0.473684\pi\) | |||||||
\(492\) | −0.0510472 | − | 0.0943270i | −0.0510472 | − | 0.0943270i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.348660 | 0.348660 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −1.18080 | − | 2.18193i | −1.18080 | − | 2.18193i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.69503 | −2.69503 | ||||||||
\(506\) | −0.561308 | + | 0.142143i | −0.561308 | + | 0.142143i | ||||
\(507\) | 0.649399i | 0.649399i | ||||||||
\(508\) | −1.38806 | + | 0.751179i | −1.38806 | + | 0.751179i | ||||
\(509\) | 1.93880i | 1.93880i | 0.245485 | + | 0.969400i | \(0.421053\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(510\) | −0.319398 | − | 1.26127i | −0.319398 | − | 1.26127i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.789141 | + | 0.614213i | −0.789141 | + | 0.614213i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.519553i | − | 0.519553i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.797738 | 0.797738 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.97272 | 1.97272 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.329189i | − | 0.329189i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||
0.986361 | − | 0.164595i | \(-0.0526316\pi\) | |||||||
\(524\) | 0.700332 | + | 1.29410i | 0.700332 | + | 1.29410i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.116924 | − | 0.178965i | 0.116924 | − | 0.178965i | ||||
\(529\) | 2.09390 | 2.09390 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.65058 | 3.65058 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.329189i | 0.329189i | ||||||||
\(540\) | 1.65096 | − | 0.893455i | 1.65096 | − | 0.893455i | ||||
\(541\) | − | 1.93880i | − | 1.93880i | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||
0.245485 | − | 0.969400i | \(-0.421053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.25906 | −1.25906 | ||||||||
\(544\) | 1.03463 | + | 0.355188i | 1.03463 | + | 0.355188i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.67433i | − | 1.67433i | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||
0.546948 | − | 0.837166i | \(-0.315789\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.751379 | + | 0.190275i | −0.751379 | + | 0.190275i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.840387 | + | 0.773631i | −0.840387 | + | 0.773631i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.37068i | 2.37068i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.93880i | 1.93880i | 0.245485 | + | 0.969400i | \(0.421053\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.233848 | −0.233848 | ||||||||
\(562\) | −0.464369 | − | 1.83375i | −0.464369 | − | 1.83375i | ||||
\(563\) | − | 0.951895i | − | 0.951895i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||
0.879474 | − | 0.475947i | \(-0.157895\pi\) | |||||||
\(564\) | −0.487815 | − | 0.901403i | −0.487815 | − | 0.901403i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.42642 | + | 0.361219i | −1.42642 | + | 0.361219i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.710375i | − | 0.710375i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.14155 | 4.14155 | ||||||||
\(576\) | −0.0477541 | + | 0.576306i | −0.0477541 | + | 0.576306i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −0.0482647 | − | 0.190593i | −0.0482647 | − | 0.190593i | ||||
\(579\) | 1.28108i | 1.28108i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.332526 | + | 0.361219i | 0.332526 | + | 0.361219i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0.309080 | + | 0.571129i | 0.309080 | + | 0.571129i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.66861 | − | 1.09016i | −1.66861 | − | 1.09016i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −0.0828261 | − | 0.327073i | −0.0828261 | − | 0.327073i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.453052 | + | 0.837166i | 0.453052 | + | 0.837166i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(600\) | −1.12496 | + | 1.03560i | −1.12496 | + | 1.03560i | ||||
\(601\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.73496 | + | 0.938912i | −1.73496 | + | 0.938912i | ||||
\(605\) | − | 1.63307i | − | 1.63307i | ||||||
\(606\) | 0.234575 | + | 0.926317i | 0.234575 | + | 0.926317i | ||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.556337 | − | 0.301075i | 0.556337 | − | 0.301075i | ||||
\(613\) | 1.47145i | 1.47145i | 0.677282 | + | 0.735724i | \(0.263158\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(614\) | 0.922767 | − | 0.233676i | 0.922767 | − | 0.233676i | ||||
\(615\) | 0.196440 | 0.196440 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.80281i | 1.80281i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.18940 | 2.18940 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.18032i | 2.18032i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.35456 | −1.35456 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(632\) | 0.544122 | + | 0.591074i | 0.544122 | + | 0.591074i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.319116 | + | 0.0808112i | −0.319116 | + | 0.0808112i | ||||
\(635\) | − | 2.89070i | − | 2.89070i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.301463 | − | 1.80657i | −0.301463 | − | 1.80657i | ||||
\(641\) | 1.57828 | 1.57828 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(642\) | −0.317747 | − | 1.25475i | −0.317747 | − | 1.25475i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.803391 | 0.803391 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(648\) | −0.0591335 | − | 0.0642361i | −0.0591335 | − | 0.0642361i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 0.649399i | − | 0.649399i | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||
0.945817 | − | 0.324699i | \(-0.105263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.69503 | −2.69503 | ||||||||
\(656\) | −0.0903332 | + | 0.138265i | −0.0903332 | + | 0.138265i | ||||
\(657\) | 0.283919 | 0.283919 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.83155i | 1.83155i | 0.401695 | + | 0.915773i | \(0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(660\) | 0.186352 | + | 0.344348i | 0.186352 | + | 0.344348i | ||||
\(661\) | − | 1.67433i | − | 1.67433i | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||
0.546948 | − | 0.837166i | \(-0.315789\pi\) | |||||||
\(662\) | 1.77550 | − | 0.449618i | 1.77550 | − | 0.449618i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.11734 | + | 0.282949i | −1.11734 | + | 0.282949i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.41327i | 2.41327i | ||||||||
\(676\) | 0.879474 | − | 0.475947i | 0.879474 | − | 0.475947i | ||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.47404 | + | 1.35695i | −1.47404 | + | 1.35695i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.797738 | −0.797738 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.513580 | − | 2.02808i | −0.513580 | − | 2.02808i | ||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | −0.584666 | − | 1.08037i | −0.584666 | − | 1.08037i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.180666 | 0.180666 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 0.879652i | − | 0.879652i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.328065 | − | 0.0271842i | −0.328065 | − | 0.0271842i | ||||
\(705\) | 1.87721 | 1.87721 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.464586 | 0.464586 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.245485 | + | 0.969400i | 0.245485 | + | 0.969400i | ||||
\(719\) | −0.165159 | −0.165159 | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(720\) | −0.886684 | − | 0.579299i | −0.886684 | − | 0.579299i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.245485 | + | 0.969400i | 0.245485 | + | 0.969400i | ||||
\(723\) | − | 1.14226i | − | 1.14226i | ||||||
\(724\) | 0.922767 | + | 1.70512i | 0.922767 | + | 1.70512i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.561308 | + | 0.142143i | −0.561308 | + | 0.142143i | ||||
\(727\) | −1.97272 | −1.97272 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.716081 | −0.716081 | ||||||||
\(730\) | −0.871720 | + | 0.220749i | −0.871720 | + | 0.220749i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.67433i | 1.67433i | 0.546948 | + | 0.837166i | \(0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(734\) | −0.484275 | − | 1.91236i | −0.484275 | − | 1.91236i | ||||
\(735\) | −1.18940 | −1.18940 | ||||||||
\(736\) | 1.66364 | + | 0.571129i | 1.66364 | + | 0.571129i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.0234459 | + | 0.0925856i | 0.0234459 | + | 0.0925856i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 3.21059 | − | 1.73748i | 3.21059 | − | 1.73748i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.803391 | −0.803391 | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.74344 | −1.74344 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.171388 | + | 0.316697i | 0.171388 | + | 0.316697i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.395507 | − | 1.56182i | −0.395507 | − | 1.56182i | ||||
\(751\) | −1.57828 | −1.57828 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(752\) | −0.863238 | + | 1.32128i | −0.863238 | + | 1.32128i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.61313i | − | 3.61313i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(758\) | 1.62310 | − | 0.411024i | 1.62310 | − | 0.411024i | ||||
\(759\) | −0.376019 | −0.376019 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | −0.993571 | + | 0.251606i | −0.993571 | + | 0.251606i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.962053 | + | 0.520637i | −0.962053 | + | 0.520637i | ||||
\(765\) | 1.15860i | 1.15860i | ||||||||
\(766\) | −0.332526 | − | 1.31311i | −0.332526 | − | 1.31311i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.594702 | + | 0.260861i | −0.594702 | + | 0.260861i | ||||
\(769\) | 1.97272 | 1.97272 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.73496 | − | 0.938912i | 1.73496 | − | 0.938912i | ||||
\(773\) | − | 1.99317i | − | 1.99317i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||
0.0825793 | − | 0.996584i | \(-0.473684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.93218 | − | 0.489294i | 1.93218 | − | 0.489294i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.472340 | − | 1.86523i | −0.472340 | − | 1.86523i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.546948 | − | 0.837166i | 0.546948 | − | 0.837166i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.234575 | + | 0.926317i | 0.234575 | + | 0.926317i | ||||
\(787\) | − | 1.22843i | − | 1.22843i | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.42642 | + | 0.361219i | −1.42642 | + | 0.361219i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.140055 | + | 0.128930i | −0.140055 | + | 0.128930i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.67433i | 1.67433i | 0.546948 | + | 0.837166i | \(0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.72648 | 1.72648 | ||||||||
\(800\) | 2.22699 | + | 0.764525i | 2.22699 | + | 0.764525i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.161622i | 0.161622i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.08258 | − | 0.996584i | 1.08258 | − | 0.996584i | ||||
\(809\) | 1.75895 | 1.75895 | 0.879474 | − | 0.475947i | \(-0.157895\pi\) | ||||
0.879474 | + | 0.475947i | \(0.157895\pi\) | |||||||
\(810\) | 0.155019 | − | 0.0392562i | 0.155019 | − | 0.0392562i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.161070 | − | 0.636052i | −0.161070 | − | 0.636052i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.594702 | + | 0.388538i | 0.594702 | + | 0.388538i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.0405441 | − | 0.160105i | −0.0405441 | − | 0.160105i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.143972 | − | 0.266037i | −0.143972 | − | 0.266037i | ||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.503347 | −0.503347 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0.894571 | − | 0.484117i | 0.894571 | − | 0.484117i | ||||
\(829\) | 0.329189i | 0.329189i | 0.986361 | + | 0.164595i | \(0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.09390 | −1.09390 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.87947 | + | 0.475947i | −1.87947 | + | 0.475947i | ||||
\(839\) | 0.490971 | 0.490971 | 0.245485 | − | 0.969400i | \(-0.421053\pi\) | ||||
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.22843i | − | 1.22843i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.83155i | 1.83155i | ||||||||
\(846\) | 0.224052 | + | 0.884762i | 0.224052 | + | 0.884762i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.955557 | −0.955557 | ||||||||
\(850\) | −0.632284 | − | 2.49683i | −0.632284 | − | 2.49683i | ||||
\(851\) | 3.50588i | 3.50588i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.22843i | 1.22843i | 0.789141 | + | 0.614213i | \(0.210526\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.46642 | + | 1.34994i | −1.46642 | + | 1.34994i | ||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.99317i | 1.99317i | 0.0825793 | + | 0.996584i | \(0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.268536 | + | 1.06042i | 0.268536 | + | 1.06042i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −0.332796 | + | 0.969400i | −0.332796 | + | 0.969400i | ||||
\(865\) | 2.24992 | 2.24992 | ||||||||
\(866\) | −0.197221 | − | 0.778807i | −0.197221 | − | 0.778807i | ||||
\(867\) | − | 0.127678i | − | 0.127678i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.264468i | 0.264468i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.151749 | + | 0.280408i | 0.151749 | + | 0.280408i | ||||
\(877\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(878\) | 0.332526 | + | 1.31311i | 0.332526 | + | 1.31311i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.329769 | − | 0.504749i | 0.329769 | − | 0.504749i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −0.141960 | − | 0.560586i | −0.141960 | − | 0.560586i | ||||
\(883\) | 0.329189i | 0.329189i | 0.986361 | + | 0.164595i | \(0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.89163 | 1.89163 | 0.945817 | − | 0.324699i | \(-0.105263\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(888\) | −0.876647 | − | 0.952293i | −0.876647 | − | 0.952293i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 0.0287415i | − | 0.0287415i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.151749 | + | 0.599244i | 0.151749 | + | 0.599244i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.120526 | + | 0.475947i | 0.120526 | + | 0.475947i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.19749 | − | 0.648050i | 1.19749 | − | 0.648050i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.0527048 | + | 0.0133467i | −0.0527048 | + | 0.0133467i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.55100 | −3.55100 | ||||||||
\(906\) | −1.24188 | + | 0.314488i | −1.24188 | + | 0.314488i | ||||
\(907\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 0.850910i | − | 0.850910i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.35456 | 1.35456 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.268536 | + | 1.06042i | 0.268536 | + | 1.06042i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.584666 | + | 1.08037i | 0.584666 | + | 1.08037i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.08686 | − | 0.275231i | 1.08686 | − | 0.275231i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | −2.37020 | + | 2.18193i | −2.37020 | + | 2.18193i | ||||
\(921\) | 0.618159 | 0.618159 | ||||||||
\(922\) | −0.629528 | + | 0.159418i | −0.629528 | + | 0.159418i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.69304i | 4.69304i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.19130 | + | 0.644701i | −1.19130 | + | 0.644701i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.19084 | + | 0.301561i | −1.19084 | + | 0.301561i | ||||
\(935\) | −0.659538 | −0.659538 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.803391 | 0.803391 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.37582 | − | 2.54229i | −1.37582 | − | 2.54229i | ||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.290505 | 0.290505 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.47145i | 1.47145i | 0.677282 | + | 0.735724i | \(0.263158\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(948\) | 0.248312 | + | 0.458840i | 0.248312 | + | 0.458840i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.213775 | −0.213775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.89163 | 1.89163 | 0.945817 | − | 0.324699i | \(-0.105263\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.00352i | − | 2.00352i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.464369 | + | 1.83375i | 0.464369 | + | 1.83375i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0982202 | − | 1.18534i | 0.0982202 | − | 1.18534i | ||||
\(961\) | 1.00000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.15261i | 1.15261i | ||||||||
\(964\) | −1.54695 | + | 0.837166i | −1.54695 | + | 0.837166i | ||||
\(965\) | 3.61313i | 3.61313i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0.603888 | + | 0.655997i | 0.603888 | + | 0.655997i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.951895i | 0.951895i | 0.879474 | + | 0.475947i | \(0.157895\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(972\) | 0.460829 | + | 0.851537i | 0.460829 | + | 0.851537i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.464369 | + | 1.83375i | 0.464369 | + | 1.83375i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.871720 | + | 1.61080i | 0.871720 | + | 1.61080i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.93218 | + | 0.489294i | −1.93218 | + | 0.489294i | ||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | −0.0789092 | + | 0.0726411i | −0.0789092 | + | 0.0726411i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −0.0855910 | − | 0.337991i | −0.0855910 | − | 0.337991i | ||||
\(991\) | −0.490971 | −0.490971 | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.18940 | 1.18940 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.04287 | −2.04287 |
(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 | 2872.1.b.e.717.7 | ✓ | 18 | |
8.5 | even | 2 | inner | 2872.1.b.e.717.8 | yes | 18 | |
359.358 | odd | 2 | CM | 2872.1.b.e.717.7 | ✓ | 18 | |
2872.717 | odd | 2 | inner | 2872.1.b.e.717.8 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2872.1.b.e.717.7 | ✓ | 18 | 1.1 | even | 1 | trivial | |
2872.1.b.e.717.7 | ✓ | 18 | 359.358 | odd | 2 | CM | |
2872.1.b.e.717.8 | yes | 18 | 8.5 | even | 2 | inner | |
2872.1.b.e.717.8 | yes | 18 | 2872.717 | odd | 2 | inner |