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 | 717.15 | ||
Root | \(0.0825793 - 0.996584i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2872.717 |
Dual form | 2872.1.b.e.717.16 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.879474 | − | 0.475947i | 0.879474 | − | 0.475947i | ||||
\(3\) | − | 1.22843i | − | 1.22843i | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(4\) | 0.546948 | − | 0.837166i | 0.546948 | − | 0.837166i | ||||
\(5\) | 1.47145i | 1.47145i | 0.677282 | + | 0.735724i | \(0.263158\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(6\) | −0.584666 | − | 1.08037i | −0.584666 | − | 1.08037i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0.0825793 | − | 0.996584i | 0.0825793 | − | 0.996584i | ||||
\(9\) | −0.509029 | −0.509029 | ||||||||
\(10\) | 0.700332 | + | 1.29410i | 0.700332 | + | 1.29410i | ||||
\(11\) | − | 0.649399i | − | 0.649399i | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||
0.945817 | − | 0.324699i | \(-0.105263\pi\) | |||||||
\(12\) | −1.02840 | − | 0.671885i | −1.02840 | − | 0.671885i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.80756 | 1.80756 | ||||||||
\(16\) | −0.401695 | − | 0.915773i | −0.401695 | − | 0.915773i | ||||
\(17\) | 0.803391 | 0.803391 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(18\) | −0.447678 | + | 0.242271i | −0.447678 | + | 0.242271i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 1.23185 | + | 0.804806i | 1.23185 | + | 0.804806i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.309080 | − | 0.571129i | −0.309080 | − | 0.571129i | ||||
\(23\) | 1.09390 | 1.09390 | 0.546948 | − | 0.837166i | \(-0.315789\pi\) | ||||
0.546948 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(24\) | −1.22423 | − | 0.101443i | −1.22423 | − | 0.101443i | ||||
\(25\) | −1.16516 | −1.16516 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.603121i | − | 0.603121i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 1.58971 | − | 0.860305i | 1.58971 | − | 0.860305i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −0.789141 | − | 0.614213i | −0.789141 | − | 0.614213i | ||||
\(33\) | −0.797738 | −0.797738 | ||||||||
\(34\) | 0.706561 | − | 0.382372i | 0.706561 | − | 0.382372i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.278412 | + | 0.426142i | −0.278412 | + | 0.426142i | ||||
\(37\) | 0.329189i | 0.329189i | 0.986361 | + | 0.164595i | \(0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.46642 | + | 0.121511i | 1.46642 | + | 0.121511i | ||||
\(41\) | −1.97272 | −1.97272 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −0.543655 | − | 0.355188i | −0.543655 | − | 0.355188i | ||||
\(45\) | − | 0.749010i | − | 0.749010i | ||||||
\(46\) | 0.962053 | − | 0.520637i | 0.962053 | − | 0.520637i | ||||
\(47\) | −0.490971 | −0.490971 | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(48\) | −1.12496 | + | 0.493453i | −1.12496 | + | 0.493453i | ||||
\(49\) | 1.00000 | 1.00000 | ||||||||
\(50\) | −1.02473 | + | 0.554554i | −1.02473 | + | 0.554554i | ||||
\(51\) | − | 0.986906i | − | 0.986906i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −0.287054 | − | 0.530429i | −0.287054 | − | 0.530429i | ||||
\(55\) | 0.955557 | 0.955557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0.988644 | − | 1.51323i | 0.988644 | − | 1.51323i | ||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.986361 | − | 0.164595i | −0.986361 | − | 0.164595i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.701590 | + | 0.379681i | −0.701590 | + | 0.379681i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0.439413 | − | 0.672572i | 0.439413 | − | 0.672572i | ||||
\(69\) | − | 1.34377i | − | 1.34377i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −0.0420353 | + | 0.507290i | −0.0420353 | + | 0.507290i | ||||
\(73\) | −1.75895 | −1.75895 | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(74\) | 0.156677 | + | 0.289513i | 0.156677 | + | 0.289513i | ||||
\(75\) | 1.43131i | 1.43131i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.35456 | 1.35456 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(80\) | 1.34751 | − | 0.591074i | 1.34751 | − | 0.591074i | ||||
\(81\) | −1.24992 | −1.24992 | ||||||||
\(82\) | −1.73496 | + | 0.938912i | −1.73496 | + | 0.938912i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18215i | 1.18215i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.647181 | − | 0.0536269i | −0.647181 | − | 0.0536269i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −0.356489 | − | 0.658734i | −0.356489 | − | 0.658734i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.598305 | − | 0.915773i | 0.598305 | − | 0.915773i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.431796 | + | 0.233676i | −0.431796 | + | 0.233676i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.754515 | + | 0.969400i | −0.754515 | + | 0.969400i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0.879474 | − | 0.475947i | 0.879474 | − | 0.475947i | ||||
\(99\) | 0.330563i | 0.330563i | ||||||||
\(100\) | −0.637281 | + | 0.975432i | −0.637281 | + | 0.975432i | ||||
\(101\) | 1.99317i | 1.99317i | 0.0825793 | + | 0.996584i | \(0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(102\) | −0.469715 | − | 0.867958i | −0.469715 | − | 0.867958i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.329189i | − | 0.329189i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||
0.986361 | − | 0.164595i | \(-0.0526316\pi\) | |||||||
\(108\) | −0.504913 | − | 0.329876i | −0.504913 | − | 0.329876i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0.840387 | − | 0.454795i | 0.840387 | − | 0.454795i | ||||
\(111\) | 0.404384 | 0.404384 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.60961i | 1.60961i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.149267 | − | 1.80139i | 0.149267 | − | 1.80139i | ||||
\(121\) | 0.578281 | 0.578281 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.42334i | 2.42334i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 0.243022i | − | 0.243022i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.490971 | 0.490971 | 0.245485 | − | 0.969400i | \(-0.421053\pi\) | ||||
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(128\) | −0.945817 | + | 0.324699i | −0.945817 | + | 0.324699i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.99317i | 1.99317i | 0.0825793 | + | 0.996584i | \(0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(132\) | −0.436321 | + | 0.667840i | −0.436321 | + | 0.667840i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.887461 | 0.887461 | ||||||||
\(136\) | 0.0663435 | − | 0.800647i | 0.0663435 | − | 0.800647i | ||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | −0.639564 | − | 1.18181i | −0.639564 | − | 1.18181i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.603121i | 0.603121i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.204475 | + | 0.466155i | 0.204475 | + | 0.466155i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.54695 | + | 0.837166i | −1.54695 | + | 0.837166i | ||||
\(147\) | − | 1.22843i | − | 1.22843i | ||||||
\(148\) | 0.275586 | + | 0.180049i | 0.275586 | + | 0.180049i | ||||
\(149\) | 1.67433i | 1.67433i | 0.546948 | + | 0.837166i | \(0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(150\) | 0.681229 | + | 1.25880i | 0.681229 | + | 1.25880i | ||||
\(151\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.408949 | −0.408949 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | 1.19130 | − | 0.644701i | 1.19130 | − | 0.644701i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.903782 | − | 1.16118i | 0.903782 | − | 1.16118i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.09927 | + | 0.594895i | −1.09927 | + | 0.594895i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | −1.07898 | + | 1.65150i | −1.07898 | + | 1.65150i | ||||
\(165\) | − | 1.17383i | − | 1.17383i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −1.00000 | ||||||||
\(170\) | 0.562640 | + | 1.03967i | 0.562640 | + | 1.03967i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.93880i | 1.93880i | 0.245485 | + | 0.969400i | \(0.421053\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.594702 | + | 0.260861i | −0.594702 | + | 0.260861i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −0.627046 | − | 0.409669i | −0.627046 | − | 0.409669i | ||||
\(181\) | − | 0.951895i | − | 0.951895i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||
0.879474 | − | 0.475947i | \(-0.157895\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0903332 | − | 1.09016i | 0.0903332 | − | 1.09016i | ||||
\(185\) | −0.484385 | −0.484385 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.521721i | − | 0.521721i | ||||||
\(188\) | −0.268536 | + | 0.411024i | −0.268536 | + | 0.411024i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.803391 | −0.803391 | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(192\) | −0.202192 | + | 1.21167i | −0.202192 | + | 1.21167i | ||||
\(193\) | 1.89163 | 1.89163 | 0.945817 | − | 0.324699i | \(-0.105263\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.546948 | − | 0.837166i | 0.546948 | − | 0.837166i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0.157331 | + | 0.290721i | 0.157331 | + | 0.290721i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −0.0962180 | + | 1.16118i | −0.0962180 | + | 1.16118i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.948644 | + | 1.75294i | 0.948644 | + | 1.75294i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.826204 | − | 0.539786i | −0.826204 | − | 0.539786i | ||||
\(205\) | − | 2.90276i | − | 2.90276i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.556825 | −0.556825 | ||||||||
\(208\) | 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 | ||||||||
\(214\) | −0.156677 | − | 0.289513i | −0.156677 | − | 0.289513i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.601061 | − | 0.0498054i | −0.601061 | − | 0.0498054i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.16074i | 2.16074i | ||||||||
\(220\) | 0.522640 | − | 0.799960i | 0.522640 | − | 0.799960i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.355645 | − | 0.192466i | 0.355645 | − | 0.192466i | ||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.593100 | 0.593100 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.93880i | − | 1.93880i | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||
0.245485 | − | 0.969400i | \(-0.421053\pi\) | |||||||
\(230\) | 0.766090 | + | 1.41561i | 0.766090 | + | 1.41561i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.165159 | 0.165159 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
0.0825793 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 0.722438i | − | 0.722438i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.66398i | − | 1.66398i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −0.726090 | − | 1.65532i | −0.726090 | − | 1.65532i | ||||
\(241\) | −1.09390 | −1.09390 | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(242\) | 0.508583 | − | 0.275231i | 0.508583 | − | 0.275231i | ||||
\(243\) | 0.932310i | 0.932310i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.47145i | 1.47145i | ||||||||
\(246\) | 1.15338 | + | 2.13127i | 1.15338 | + | 2.13127i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.115666 | − | 0.213732i | −0.115666 | − | 0.213732i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.710375i | − | 0.710375i | ||||||
\(254\) | 0.431796 | − | 0.233676i | 0.431796 | − | 0.233676i | ||||
\(255\) | 1.45218 | 1.45218 | ||||||||
\(256\) | −0.677282 | + | 0.735724i | −0.677282 | + | 0.735724i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.948644 | + | 1.75294i | 0.948644 | + | 1.75294i | ||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | −0.0658767 | + | 0.795013i | −0.0658767 | + | 0.795013i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0.780499 | − | 0.422385i | 0.780499 | − | 0.422385i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −0.322718 | − | 0.735724i | −0.322718 | − | 0.735724i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.756653i | 0.756653i | ||||||||
\(276\) | −1.12496 | − | 0.734973i | −1.12496 | − | 0.734973i | ||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.57828 | 1.57828 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(282\) | 0.287054 | + | 0.530429i | 0.287054 | + | 0.530429i | ||||
\(283\) | 1.99317i | 1.99317i | 0.0825793 | + | 0.996584i | \(0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.401695 | + | 0.312652i | 0.401695 | + | 0.312652i | ||||
\(289\) | −0.354563 | −0.354563 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.962053 | + | 1.47253i | −0.962053 | + | 1.47253i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −0.584666 | − | 1.08037i | −0.584666 | − | 1.08037i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.328065 | + | 0.0271842i | 0.328065 | + | 0.0271842i | ||||
\(297\) | −0.391666 | −0.391666 | ||||||||
\(298\) | 0.796894 | + | 1.47253i | 0.796894 | + | 1.47253i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.19825 | + | 0.782853i | 1.19825 | + | 0.782853i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.66364 | + | 0.900319i | −1.66364 | + | 0.900319i | ||||
\(303\) | 2.44846 | 2.44846 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.359660 | + | 0.194638i | −0.359660 | + | 0.194638i | ||||
\(307\) | − | 1.67433i | − | 1.67433i | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||
0.546948 | − | 0.837166i | \(-0.315789\pi\) | |||||||
\(308\) | 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 | ||||||||
\(316\) | 0.740876 | − | 1.13399i | 0.740876 | − | 1.13399i | ||||
\(317\) | 0.649399i | 0.649399i | 0.945817 | + | 0.324699i | \(0.105263\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.242192 | − | 1.45138i | 0.242192 | − | 1.45138i | ||||
\(321\) | −0.404384 | −0.404384 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.683641 | + | 1.04639i | −0.683641 | + | 1.04639i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.162906 | + | 1.96598i | −0.162906 | + | 1.96598i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.558681 | − | 1.03235i | −0.558681 | − | 1.03235i | ||||
\(331\) | − | 1.47145i | − | 1.47145i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||
0.677282 | − | 0.735724i | \(-0.263158\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.167567i | − | 0.167567i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | −0.879474 | + | 0.475947i | −0.879474 | + | 0.475947i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.989654 | + | 0.646574i | 0.989654 | + | 0.646574i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.97729 | 1.97729 | ||||||||
\(346\) | 0.922767 | + | 1.70512i | 0.922767 | + | 1.70512i | ||||
\(347\) | 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 | ||||||||
\(352\) | −0.398869 | + | 0.512467i | −0.398869 | + | 0.512467i | ||||
\(353\) | 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 | ||||||||
\(360\) | −0.746451 | − | 0.0618527i | −0.746451 | − | 0.0618527i | ||||
\(361\) | −1.00000 | −1.00000 | ||||||||
\(362\) | −0.453052 | − | 0.837166i | −0.453052 | − | 0.837166i | ||||
\(363\) | − | 0.710375i | − | 0.710375i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.58820i | − | 2.58820i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(368\) | −0.439413 | − | 1.00176i | −0.439413 | − | 1.00176i | ||||
\(369\) | 1.00417 | 1.00417 | ||||||||
\(370\) | −0.426004 | + | 0.230542i | −0.426004 | + | 0.230542i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | −0.248312 | − | 0.458840i | −0.248312 | − | 0.458840i | ||||
\(375\) | −0.298535 | −0.298535 | ||||||||
\(376\) | −0.0405441 | + | 0.489294i | −0.0405441 | + | 0.489294i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.83155i | 1.83155i | 0.401695 | + | 0.915773i | \(0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 0.603121i | − | 0.603121i | ||||||
\(382\) | −0.706561 | + | 0.382372i | −0.706561 | + | 0.382372i | ||||
\(383\) | 0.165159 | 0.165159 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
0.0825793 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(384\) | 0.398869 | + | 1.16187i | 0.398869 | + | 1.16187i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.66364 | − | 0.900319i | 1.66364 | − | 0.900319i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 0.329189i | − | 0.329189i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||
0.986361 | − | 0.164595i | \(-0.0526316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.878826 | 0.878826 | ||||||||
\(392\) | 0.0825793 | − | 0.996584i | 0.0825793 | − | 0.996584i | ||||
\(393\) | 2.44846 | 2.44846 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.99317i | 1.99317i | ||||||||
\(396\) | 0.276736 | + | 0.180801i | 0.276736 | + | 0.180801i | ||||
\(397\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.468039 | + | 1.06702i | 0.468039 | + | 1.06702i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.66861 | + | 1.09016i | 1.66861 | + | 1.09016i | ||||
\(405\) | − | 1.83919i | − | 1.83919i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.213775 | 0.213775 | ||||||||
\(408\) | −0.983535 | − | 0.0814980i | −0.983535 | − | 0.0814980i | ||||
\(409\) | 1.97272 | 1.97272 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(410\) | −1.38156 | − | 2.55290i | −1.38156 | − | 2.55290i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.489713 | + | 0.265019i | −0.489713 | + | 0.265019i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 0.951895i | − | 0.951895i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||
0.879474 | − | 0.475947i | \(-0.157895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.249918 | 0.249918 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.936078 | −0.936078 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.275586 | − | 0.180049i | −0.275586 | − | 0.180049i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.803391 | 0.803391 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(432\) | −0.552322 | + | 0.242271i | −0.552322 | + | 0.242271i | ||||
\(433\) | 1.35456 | 1.35456 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.02840 | + | 1.90031i | 1.02840 | + | 1.90031i | ||||
\(439\) | −0.165159 | −0.165159 | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(440\) | 0.0789092 | − | 0.952293i | 0.0789092 | − | 0.952293i | ||||
\(441\) | −0.509029 | −0.509029 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0.221177 | − | 0.338537i | 0.221177 | − | 0.338537i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.05679 | 2.05679 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.75895 | 1.75895 | 0.879474 | − | 0.475947i | \(-0.157895\pi\) | ||||
0.879474 | + | 0.475947i | \(0.157895\pi\) | |||||||
\(450\) | 0.521616 | − | 0.282284i | 0.521616 | − | 0.282284i | ||||
\(451\) | 1.28108i | 1.28108i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.32373i | 2.32373i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.803391 | 0.803391 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(458\) | −0.922767 | − | 1.70512i | −0.922767 | − | 1.70512i | ||||
\(459\) | − | 0.484542i | − | 0.484542i | ||||||
\(460\) | 1.34751 | + | 0.880374i | 1.34751 | + | 0.880374i | ||||
\(461\) | − | 1.22843i | − | 1.22843i | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.145253 | − | 0.0786068i | 0.145253 | − | 0.0786068i | ||||
\(467\) | − | 1.93880i | − | 1.93880i | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||
0.245485 | − | 0.969400i | \(-0.421053\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.343843 | − | 0.635365i | −0.343843 | − | 0.635365i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.791967 | − | 1.46343i | −0.791967 | − | 1.46343i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.57828 | −1.57828 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(480\) | −1.42642 | − | 1.11023i | −1.42642 | − | 1.11023i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.962053 | + | 0.520637i | −0.962053 | + | 0.520637i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.316290 | − | 0.484117i | 0.316290 | − | 0.484117i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.443731 | + | 0.819943i | 0.443731 | + | 0.819943i | ||||
\(487\) | −1.57828 | −1.57828 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.700332 | + | 1.29410i | 0.700332 | + | 1.29410i | ||||
\(491\) | 0.329189i | 0.329189i | 0.986361 | + | 0.164595i | \(0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(492\) | 2.02874 | + | 1.32544i | 2.02874 | + | 1.32544i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.486406 | −0.486406 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −0.203450 | − | 0.132921i | −0.203450 | − | 0.132921i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.93284 | −2.93284 | ||||||||
\(506\) | −0.338101 | − | 0.624756i | −0.338101 | − | 0.624756i | ||||
\(507\) | 1.22843i | 1.22843i | ||||||||
\(508\) | 0.268536 | − | 0.411024i | 0.268536 | − | 0.411024i | ||||
\(509\) | 0.951895i | 0.951895i | 0.879474 | + | 0.475947i | \(0.157895\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(510\) | 1.27715 | − | 0.691161i | 1.27715 | − | 0.691161i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.245485 | + | 0.969400i | −0.245485 | + | 0.969400i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.318836i | 0.318836i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.38167 | 2.38167 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.649399i | 0.649399i | 0.945817 | + | 0.324699i | \(0.105263\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(524\) | 1.66861 | + | 1.09016i | 1.66861 | + | 1.09016i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.320448 | + | 0.730547i | 0.320448 | + | 0.730547i | ||||
\(529\) | 0.196609 | 0.196609 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.484385 | 0.484385 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.649399i | − | 0.649399i | ||||||
\(540\) | 0.485395 | − | 0.742953i | 0.485395 | − | 0.742953i | ||||
\(541\) | − | 0.951895i | − | 0.951895i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||
0.879474 | − | 0.475947i | \(-0.157895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.16933 | −1.16933 | ||||||||
\(544\) | −0.633988 | − | 0.493453i | −0.633988 | − | 0.493453i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.83155i | − | 1.83155i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||
0.401695 | − | 0.915773i | \(-0.368421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.360127 | + | 0.665456i | 0.360127 | + | 0.665456i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.33918 | − | 0.110968i | −1.33918 | − | 0.110968i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.595030i | 0.595030i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.951895i | 0.951895i | 0.879474 | + | 0.475947i | \(0.157895\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.640896 | −0.640896 | ||||||||
\(562\) | 1.38806 | − | 0.751179i | 1.38806 | − | 0.751179i | ||||
\(563\) | 1.67433i | 1.67433i | 0.546948 | + | 0.837166i | \(0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(564\) | 0.504913 | + | 0.329876i | 0.504913 | + | 0.329876i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.948644 | + | 1.75294i | 0.948644 | + | 1.75294i | ||||
\(567\) | 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 | ||||||||
\(573\) | 0.986906i | 0.986906i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.27456 | −1.27456 | ||||||||
\(576\) | 0.502087 | + | 0.0837834i | 0.502087 | + | 0.0837834i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −0.311829 | + | 0.168753i | −0.311829 | + | 0.168753i | ||||
\(579\) | − | 2.32373i | − | 2.32373i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.145253 | + | 1.75294i | −0.145253 | + | 1.75294i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −1.02840 | − | 0.671885i | −1.02840 | − | 0.671885i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.301463 | − | 0.132234i | 0.301463 | − | 0.132234i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −0.344460 | + | 0.186413i | −0.344460 | + | 0.186413i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.40170 | + | 0.915773i | 1.40170 | + | 0.915773i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.57828 | −1.57828 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(600\) | 1.42642 | + | 0.118197i | 1.42642 | + | 0.118197i | ||||
\(601\) | −1.57828 | −1.57828 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.03463 | + | 1.58361i | −1.03463 | + | 1.58361i | ||||
\(605\) | 0.850910i | 0.850910i | ||||||||
\(606\) | 2.15336 | − | 1.16534i | 2.15336 | − | 1.16534i | ||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.223674 | + | 0.342359i | −0.223674 | + | 0.342359i | ||||
\(613\) | − | 1.99317i | − | 1.99317i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||
0.0825793 | − | 0.996584i | \(-0.473684\pi\) | |||||||
\(614\) | −0.796894 | − | 1.47253i | −0.796894 | − | 1.47253i | ||||
\(615\) | −3.56582 | −3.56582 | ||||||||
\(616\) | 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 | ||||||||
\(621\) | − | 0.659752i | − | 0.659752i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.807564 | −0.807564 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.264468i | 0.264468i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.165159 | −0.165159 | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(632\) | 0.111859 | − | 1.34994i | 0.111859 | − | 1.34994i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.309080 | + | 0.571129i | 0.309080 | + | 0.571129i | ||||
\(635\) | 0.722438i | 0.722438i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.477778 | − | 1.39172i | −0.477778 | − | 1.39172i | ||||
\(641\) | 0.490971 | 0.490971 | 0.245485 | − | 0.969400i | \(-0.421053\pi\) | ||||
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(642\) | −0.355645 | + | 0.192466i | −0.355645 | + | 0.192466i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.35456 | 1.35456 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(648\) | −0.103217 | + | 1.24565i | −0.103217 | + | 1.24565i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.22843i | − | 1.22843i | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.93284 | −2.93284 | ||||||||
\(656\) | 0.792434 | + | 1.80657i | 0.792434 | + | 1.80657i | ||||
\(657\) | 0.895355 | 0.895355 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.47145i | − | 1.47145i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||
0.677282 | − | 0.735724i | \(-0.263158\pi\) | |||||||
\(660\) | −0.982691 | − | 0.642024i | −0.982691 | − | 0.642024i | ||||
\(661\) | − | 1.83155i | − | 1.83155i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||
0.401695 | − | 0.915773i | \(-0.368421\pi\) | |||||||
\(662\) | −0.700332 | − | 1.29410i | −0.700332 | − | 1.29410i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0797530 | − | 0.147371i | −0.0797530 | − | 0.147371i | ||||
\(667\) | 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 | ||||||||
\(675\) | 0.702732i | 0.702732i | ||||||||
\(676\) | −0.546948 | + | 0.837166i | −0.546948 | + | 0.837166i | ||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.17811 | + | 0.0976210i | 1.17811 | + | 0.0976210i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.38167 | −2.38167 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.73897 | − | 0.941085i | 1.73897 | − | 0.941085i | ||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 1.62310 | + | 1.06042i | 1.62310 | + | 1.06042i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.58487 | −1.58487 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 0.202885i | − | 0.202885i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.106888 | + | 0.640542i | −0.106888 | + | 0.640542i | ||||
\(705\) | −0.887461 | −0.887461 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.689512 | −0.689512 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.879474 | + | 0.475947i | −0.879474 | + | 0.475947i | ||||
\(719\) | −1.97272 | −1.97272 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(720\) | −0.685923 | + | 0.300874i | −0.685923 | + | 0.300874i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.879474 | + | 0.475947i | −0.879474 | + | 0.475947i | ||||
\(723\) | 1.34377i | 1.34377i | ||||||||
\(724\) | −0.796894 | − | 0.520637i | −0.796894 | − | 0.520637i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.338101 | − | 0.624756i | −0.338101 | − | 0.624756i | ||||
\(727\) | 1.89163 | 1.89163 | 0.945817 | − | 0.324699i | \(-0.105263\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.104645 | −0.104645 | ||||||||
\(730\) | −1.23185 | − | 2.27625i | −1.23185 | − | 2.27625i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.83155i | 1.83155i | 0.401695 | + | 0.915773i | \(0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(734\) | −1.66364 | + | 0.900319i | −1.66364 | + | 0.900319i | ||||
\(735\) | 1.80756 | 1.80756 | ||||||||
\(736\) | −0.863238 | − | 0.671885i | −0.863238 | − | 0.671885i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.883144 | − | 0.477934i | 0.883144 | − | 0.477934i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | −0.264933 | + | 0.405511i | −0.264933 | + | 0.405511i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.35456 | −1.35456 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.46369 | −2.46369 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.436767 | − | 0.285354i | −0.436767 | − | 0.285354i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.262554 | + | 0.142087i | −0.262554 | + | 0.142087i | ||||
\(751\) | −0.490971 | −0.490971 | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(752\) | 0.197221 | + | 0.449618i | 0.197221 | + | 0.449618i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.78344i | − | 2.78344i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(758\) | 0.871720 | + | 1.61080i | 0.871720 | + | 1.61080i | ||||
\(759\) | −0.872643 | −0.872643 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | −0.287054 | − | 0.530429i | −0.287054 | − | 0.530429i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.439413 | + | 0.672572i | −0.439413 | + | 0.672572i | ||||
\(765\) | − | 0.601747i | − | 0.601747i | ||||||
\(766\) | 0.145253 | − | 0.0786068i | 0.145253 | − | 0.0786068i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.903782 | + | 0.831990i | 0.903782 | + | 0.831990i | ||||
\(769\) | −1.89163 | −1.89163 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.03463 | − | 1.58361i | 1.03463 | − | 1.58361i | ||||
\(773\) | 0.329189i | 0.329189i | 0.986361 | + | 0.164595i | \(0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.156677 | − | 0.289513i | −0.156677 | − | 0.289513i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.772905 | − | 0.418275i | 0.772905 | − | 0.418275i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.401695 | − | 0.915773i | −0.401695 | − | 0.915773i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.15336 | − | 1.16534i | 2.15336 | − | 1.16534i | ||||
\(787\) | − | 1.93880i | − | 1.93880i | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||
0.245485 | − | 0.969400i | \(-0.421053\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.948644 | + | 1.75294i | 0.948644 | + | 1.75294i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.329434 | + | 0.0272977i | 0.329434 | + | 0.0272977i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.83155i | 1.83155i | 0.401695 | + | 0.915773i | \(0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.394442 | −0.394442 | ||||||||
\(800\) | 0.919474 | + | 0.715655i | 0.919474 | + | 0.715655i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.14226i | 1.14226i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.98636 | + | 0.164595i | 1.98636 | + | 0.164595i | ||||
\(809\) | −1.09390 | −1.09390 | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(810\) | −0.875358 | − | 1.61752i | −0.875358 | − | 1.61752i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.188010 | − | 0.101746i | 0.188010 | − | 0.101746i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.903782 | + | 0.396436i | −0.903782 | + | 0.396436i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.73496 | − | 0.938912i | 1.73496 | − | 0.938912i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.43009 | − | 1.58766i | −2.43009 | − | 1.58766i | ||||
\(821\) | 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 | ||||||||
\(825\) | 0.929492 | 0.929492 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | −0.304554 | + | 0.466155i | −0.304554 | + | 0.466155i | ||||
\(829\) | − | 0.649399i | − | 0.649399i | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||
0.945817 | − | 0.324699i | \(-0.105263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.803391 | 0.803391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.453052 | − | 0.837166i | −0.453052 | − | 0.837166i | ||||
\(839\) | −1.75895 | −1.75895 | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.93880i | − | 1.93880i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.47145i | − | 1.47145i | ||||||
\(846\) | 0.219797 | − | 0.118948i | 0.219797 | − | 0.118948i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.44846 | 2.44846 | ||||||||
\(850\) | −0.823256 | + | 0.445524i | −0.823256 | + | 0.445524i | ||||
\(851\) | 0.360099i | 0.360099i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.93880i | 1.93880i | 0.245485 | + | 0.969400i | \(0.421053\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.328065 | − | 0.0271842i | −0.328065 | − | 0.0271842i | ||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.329189i | − | 0.329189i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||
0.986361 | − | 0.164595i | \(-0.0526316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.706561 | − | 0.382372i | 0.706561 | − | 0.382372i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −0.370445 | + | 0.475947i | −0.370445 | + | 0.475947i | ||||
\(865\) | −2.85284 | −2.85284 | ||||||||
\(866\) | 1.19130 | − | 0.644701i | 1.19130 | − | 0.644701i | ||||
\(867\) | 0.435554i | 0.435554i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 0.879652i | − | 0.879652i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.80890 | + | 1.18181i | 1.80890 | + | 1.18181i | ||||
\(877\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(878\) | −0.145253 | + | 0.0786068i | −0.145253 | + | 0.0786068i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.383843 | − | 0.875073i | −0.383843 | − | 0.875073i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −0.447678 | + | 0.242271i | −0.447678 | + | 0.242271i | ||||
\(883\) | − | 0.649399i | − | 0.649399i | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||
0.945817 | − | 0.324699i | \(-0.105263\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.57828 | 1.57828 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(888\) | 0.0333938 | − | 0.403003i | 0.0333938 | − | 0.403003i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.811696i | 0.811696i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 1.80890 | − | 0.978925i | 1.80890 | − | 0.978925i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.54695 | − | 0.837166i | 1.54695 | − | 0.837166i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.324395 | − | 0.496523i | 0.324395 | − | 0.496523i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.609729 | + | 1.12668i | 0.609729 | + | 1.12668i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.40066 | 1.40066 | ||||||||
\(906\) | 1.10597 | + | 2.04366i | 1.10597 | + | 2.04366i | ||||
\(907\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1.01458i | − | 1.01458i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.165159 | 0.165159 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
0.0825793 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.706561 | − | 0.382372i | 0.706561 | − | 0.382372i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.62310 | − | 1.06042i | −1.62310 | − | 1.06042i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.230617 | − | 0.426142i | −0.230617 | − | 0.426142i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 1.60411 | + | 0.132921i | 1.60411 | + | 0.132921i | ||||
\(921\) | −2.05679 | −2.05679 | ||||||||
\(922\) | −0.584666 | − | 1.08037i | −0.584666 | − | 1.08037i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 0.383558i | − | 0.383558i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.0903332 | − | 0.138265i | 0.0903332 | − | 0.138265i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.922767 | − | 1.70512i | −0.922767 | − | 1.70512i | ||||
\(935\) | 0.767685 | 0.767685 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.35456 | 1.35456 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.604801 | − | 0.395136i | −0.604801 | − | 0.395136i | ||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.15795 | −2.15795 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.99317i | − | 1.99317i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||
0.0825793 | − | 0.996584i | \(-0.473684\pi\) | |||||||
\(948\) | −1.39303 | − | 0.910111i | −1.39303 | − | 0.910111i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.797738 | 0.797738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.57828 | 1.57828 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.18215i | − | 1.18215i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.38806 | + | 0.751179i | −1.38806 | + | 0.751179i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.78291 | − | 0.297515i | −1.78291 | − | 0.297515i | ||||
\(961\) | 1.00000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.167567i | 0.167567i | ||||||||
\(964\) | −0.598305 | + | 0.915773i | −0.598305 | + | 0.915773i | ||||
\(965\) | 2.78344i | 2.78344i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0.0477541 | − | 0.576306i | 0.0477541 | − | 0.576306i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.67433i | − | 1.67433i | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||
0.546948 | − | 0.837166i | \(-0.315789\pi\) | |||||||
\(972\) | 0.780499 | + | 0.509925i | 0.780499 | + | 0.509925i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.38806 | + | 0.751179i | −1.38806 | + | 0.751179i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.23185 | + | 0.804806i | 1.23185 | + | 0.804806i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.156677 | + | 0.289513i | 0.156677 | + | 0.289513i | ||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | 2.41507 | + | 0.200118i | 2.41507 | + | 0.200118i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −0.427781 | + | 0.231504i | −0.427781 | + | 0.231504i | ||||
\(991\) | 1.75895 | 1.75895 | 0.879474 | − | 0.475947i | \(-0.157895\pi\) | ||||
0.879474 | + | 0.475947i | \(0.157895\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.80756 | −1.80756 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.198541 | 0.198541 |
(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.717.15 | ✓ | 18 | |
8.5 | even | 2 | inner | 2872.1.b.e.717.16 | yes | 18 | |
359.358 | odd | 2 | CM | 2872.1.b.e.717.15 | ✓ | 18 | |
2872.717 | odd | 2 | inner | 2872.1.b.e.717.16 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2872.1.b.e.717.15 | ✓ | 18 | 1.1 | even | 1 | trivial | |
2872.1.b.e.717.15 | ✓ | 18 | 359.358 | odd | 2 | CM | |
2872.1.b.e.717.16 | yes | 18 | 8.5 | even | 2 | inner | |
2872.1.b.e.717.16 | yes | 18 | 2872.717 | odd | 2 | inner |