Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(1151,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1151 |
Dual form | 2304.2.f.b.1151.3 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.585786 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.828427i | 0.313116i | 0.987669 | + | 0.156558i | \(0.0500398\pi\) | ||||
−0.987669 | + | 0.156558i | \(0.949960\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.82843i | − 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843i | 0.784465i | 0.919866 | + | 0.392232i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392232i | \(0.871703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.58579i | − 0.627145i | −0.949564 | − | 0.313573i | \(-0.898474\pi\) | ||||
0.949564 | − | 0.313573i | \(-0.101526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.82843 | 1.42383 | 0.711913 | − | 0.702268i | \(-0.247829\pi\) | ||||
0.711913 | + | 0.702268i | \(0.247829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.41421 | 0.634004 | 0.317002 | − | 0.948425i | \(-0.397324\pi\) | ||||
0.317002 | + | 0.948425i | \(0.397324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.82843i | − 1.58563i | −0.609461 | − | 0.792816i | \(-0.708614\pi\) | ||||
0.609461 | − | 0.792816i | \(-0.291386\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 0.485281i | − 0.0820275i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.65685i | − 1.25878i | −0.777090 | − | 0.629390i | \(-0.783305\pi\) | ||||
0.777090 | − | 0.629390i | \(-0.216695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.41421i | 0.845558i | 0.906233 | + | 0.422779i | \(0.138945\pi\) | ||||
−0.906233 | + | 0.422779i | \(0.861055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65685 | 0.252668 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.48528 | 0.654246 | 0.327123 | − | 0.944982i | \(-0.393921\pi\) | ||||
0.327123 | + | 0.944982i | \(0.393921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.31371 | 0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.07107 | −1.24601 | −0.623003 | − | 0.782219i | \(-0.714088\pi\) | ||||
−0.623003 | + | 0.782219i | \(0.714088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.65685i | 0.223410i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 13.6569i | − 1.77797i | −0.457935 | − | 0.888985i | \(-0.651411\pi\) | ||||
0.457935 | − | 0.888985i | \(-0.348589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.65685i | 0.468212i | 0.972211 | + | 0.234106i | \(0.0752163\pi\) | ||||
−0.972211 | + | 0.234106i | \(0.924784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 1.65685i | − 0.205507i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4853 | 1.48173 | 0.740865 | − | 0.671654i | \(-0.234416\pi\) | ||||
0.740865 | + | 0.671654i | \(0.234416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.34315 | 0.267026 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 10.4853i | − 1.17969i | −0.807518 | − | 0.589843i | \(-0.799190\pi\) | ||||
0.807518 | − | 0.589843i | \(-0.200810\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 10.8284i | − 1.18857i | −0.804253 | − | 0.594287i | \(-0.797434\pi\) | ||||
0.804253 | − | 0.594287i | \(-0.202566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.51472i | 0.164294i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.75736i | 0.398279i | 0.979971 | + | 0.199140i | \(0.0638147\pi\) | ||||
−0.979971 | + | 0.199140i | \(0.936185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.34315 | −0.245628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.31371 | 0.339979 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.34315 | 0.237910 | 0.118955 | − | 0.992900i | \(-0.462046\pi\) | ||||
0.118955 | + | 0.992900i | \(0.462046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7279 | 1.46548 | 0.732742 | − | 0.680507i | \(-0.238240\pi\) | ||||
0.732742 | + | 0.680507i | \(0.238240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8.82843i | − 0.869891i | −0.900457 | − | 0.434945i | \(-0.856768\pi\) | ||||
0.900457 | − | 0.434945i | \(-0.143232\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 11.3137i | − 1.09374i | −0.837218 | − | 0.546869i | \(-0.815820\pi\) | ||||
0.837218 | − | 0.546869i | \(-0.184180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.17157i | 0.495347i | 0.968844 | + | 0.247673i | \(0.0796660\pi\) | ||||
−0.968844 | + | 0.247673i | \(0.920334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 3.75736i | − 0.353463i | −0.984259 | − | 0.176731i | \(-0.943448\pi\) | ||||
0.984259 | − | 0.176731i | \(-0.0565524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.14214 | 0.196369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 0.828427i | − 0.0735110i | −0.999324 | − | 0.0367555i | \(-0.988298\pi\) | ||||
0.999324 | − | 0.0367555i | \(-0.0117023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 5.65685i | − 0.494242i | −0.968985 | − | 0.247121i | \(-0.920516\pi\) | ||||
0.968985 | − | 0.247121i | \(-0.0794845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.68629i | − 0.406353i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 13.4142i | − 1.14605i | −0.819537 | − | 0.573027i | \(-0.805769\pi\) | ||||
0.819537 | − | 0.573027i | \(-0.194231\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.7279 | −1.53425 | −0.767126 | − | 0.641497i | \(-0.778314\pi\) | ||||
−0.767126 | + | 0.641497i | \(0.778314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 10.4853i | − 0.853280i | −0.904422 | − | 0.426640i | \(-0.859697\pi\) | ||||
0.904422 | − | 0.426640i | \(-0.140303\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.17157i | 0.415391i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 11.6569i | − 0.930318i | −0.885227 | − | 0.465159i | \(-0.845997\pi\) | ||||
0.885227 | − | 0.465159i | \(-0.154003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.65685i | 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.65685 | 0.756383 | 0.378192 | − | 0.925727i | \(-0.376546\pi\) | ||||
0.378192 | + | 0.925727i | \(0.376546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.65685 | 0.437741 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.4142 | −1.78015 | −0.890075 | − | 0.455814i | \(-0.849348\pi\) | ||||
−0.890075 | + | 0.455814i | \(0.849348\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.85786i | − 0.291627i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.31371i | − 0.247678i | −0.992302 | − | 0.123839i | \(-0.960479\pi\) | ||||
0.992302 | − | 0.123839i | \(-0.0395207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1421i | 1.64581i | 0.568178 | + | 0.822906i | \(0.307649\pi\) | ||||
−0.568178 | + | 0.822906i | \(0.692351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.48528i | 0.329764i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.31371 | −0.534831 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6569 | 1.56703 | 0.783517 | − | 0.621370i | \(-0.213423\pi\) | ||||
0.783517 | + | 0.621370i | \(0.213423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.3137 | −1.24627 | −0.623134 | − | 0.782115i | \(-0.714141\pi\) | ||||
−0.623134 | + | 0.782115i | \(0.714141\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.3848 | 1.45236 | 0.726178 | − | 0.687507i | \(-0.241295\pi\) | ||||
0.726178 | + | 0.687507i | \(0.241295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 0.828427i | − 0.0587256i | −0.999569 | − | 0.0293628i | \(-0.990652\pi\) | ||||
0.999569 | − | 0.0293628i | \(-0.00934782\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.82843i | 0.198517i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3.17157i | − 0.221512i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000i | 1.10674i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.686292 | −0.0472463 | −0.0236231 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236231 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.970563 | −0.0661918 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.31371 | 0.496487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.31371 | 0.491973 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7990i | 1.45977i | 0.683571 | + | 0.729884i | \(0.260426\pi\) | ||||
−0.683571 | + | 0.729884i | \(0.739574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 21.1716i | − 1.40521i | −0.711582 | − | 0.702603i | \(-0.752021\pi\) | ||||
0.711582 | − | 0.702603i | \(-0.247979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 10.8284i | − 0.715563i | −0.933805 | − | 0.357781i | \(-0.883533\pi\) | ||||
0.933805 | − | 0.357781i | \(-0.116467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.89949i | 0.124440i | 0.998062 | + | 0.0622200i | \(0.0198181\pi\) | ||||
−0.998062 | + | 0.0622200i | \(0.980182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.62742 | −0.171394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9706 | −0.835507 | −0.417754 | − | 0.908560i | \(-0.637183\pi\) | ||||
−0.417754 | + | 0.908560i | \(0.637183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.69848 | −0.236288 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 16.0000i | − 1.01806i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.51472i | 0.474325i | 0.971470 | + | 0.237162i | \(0.0762174\pi\) | ||||
−0.971470 | + | 0.237162i | \(0.923783\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 19.3137i | − 1.21424i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 9.89949i | − 0.617514i | −0.951141 | − | 0.308757i | \(-0.900087\pi\) | ||||
0.951141 | − | 0.308757i | \(-0.0999129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.34315 | 0.394144 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.6569 | −1.82872 | −0.914360 | − | 0.404902i | \(-0.867306\pi\) | ||||
−0.914360 | + | 0.404902i | \(0.867306\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.31371 | 0.326419 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.38478 | −0.267345 | −0.133672 | − | 0.991026i | \(-0.542677\pi\) | ||||
−0.133672 | + | 0.991026i | \(0.542677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4853i | 1.12290i | 0.827510 | + | 0.561450i | \(0.189756\pi\) | ||||
−0.827510 | + | 0.561450i | \(0.810244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1716i | 0.794276i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8284i | 1.61196i | 0.591940 | + | 0.805982i | \(0.298362\pi\) | ||||
−0.591940 | + | 0.805982i | \(0.701638\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 25.8995i | − 1.54503i | −0.634994 | − | 0.772517i | \(-0.718997\pi\) | ||||
0.634994 | − | 0.772517i | \(-0.281003\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.3137 | −1.14808 | −0.574040 | − | 0.818827i | \(-0.694625\pi\) | ||||
−0.574040 | + | 0.818827i | \(0.694625\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.48528 | −0.264758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3137 | 0.606689 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.8701 | 1.45292 | 0.726462 | − | 0.687206i | \(-0.241163\pi\) | ||||
0.726462 | + | 0.687206i | \(0.241163\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000i | 0.465778i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.3137i | 1.11694i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.37258i | 0.0791144i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 2.14214i | − 0.122658i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3137 | 1.33058 | 0.665292 | − | 0.746583i | \(-0.268307\pi\) | ||||
0.665292 | + | 0.746583i | \(0.268307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.34315 | −0.132868 | −0.0664338 | − | 0.997791i | \(-0.521162\pi\) | ||||
−0.0664338 | + | 0.997791i | \(0.521162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3137 | 0.752535 | 0.376268 | − | 0.926511i | \(-0.377207\pi\) | ||||
0.376268 | + | 0.926511i | \(0.377207\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.75736 | −0.323366 | −0.161683 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161683 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 9.65685i | − 0.540680i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6274i | 0.813891i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 13.1716i | − 0.730627i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.71573i | 0.204855i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.02944 | 0.384059 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.686292 | 0.0373847 | 0.0186923 | − | 0.999825i | \(-0.494050\pi\) | ||||
0.0186923 | + | 0.999825i | \(0.494050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.9706 | −1.35223 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0294i | 0.595534i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.485281i | 0.0260513i | 0.999915 | + | 0.0130256i | \(0.00414631\pi\) | ||||
−0.999915 | + | 0.0130256i | \(0.995854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.343146i | 0.0183682i | 0.999958 | + | 0.00918409i | \(0.00292343\pi\) | ||||
−0.999958 | + | 0.00918409i | \(0.997077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.8701i | 1.85595i | 0.372648 | + | 0.927973i | \(0.378450\pi\) | ||||
−0.372648 | + | 0.927973i | \(0.621550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.31371 | −0.388171 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.51472 | 0.185500 | 0.0927499 | − | 0.995689i | \(-0.470434\pi\) | ||||
0.0927499 | + | 0.995689i | \(0.470434\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.34315 | 0.122646 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1716i | 0.791950i | 0.918261 | + | 0.395975i | \(0.129593\pi\) | ||||
−0.918261 | + | 0.395975i | \(0.870407\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 7.51472i | − 0.390145i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9706i | 0.982259i | 0.871087 | + | 0.491129i | \(0.163416\pi\) | ||||
−0.871087 | + | 0.491129i | \(0.836584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.65685i | 0.497353i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.2843 | 1.86380 | 0.931899 | − | 0.362718i | \(-0.118151\pi\) | ||||
0.931899 | + | 0.362718i | \(0.118151\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.6274 | −1.56499 | −0.782494 | − | 0.622658i | \(-0.786053\pi\) | ||||
−0.782494 | + | 0.622658i | \(0.786053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.37258 | −0.0699533 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.5563 | 1.70137 | 0.850687 | − | 0.525672i | \(-0.176186\pi\) | ||||
0.850687 | + | 0.525672i | \(0.176186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 17.6569i | − 0.892946i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.14214i | 0.309044i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.9706i | 0.751351i | 0.926751 | + | 0.375676i | \(0.122589\pi\) | ||||
−0.926751 | + | 0.375676i | \(0.877411\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 10.5858i | − 0.528629i | −0.964437 | − | 0.264314i | \(-0.914854\pi\) | ||||
0.964437 | − | 0.264314i | \(-0.0851457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.9706 | 1.24387 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.6569 | −1.07349 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.6569 | −1.07086 | −0.535431 | − | 0.844579i | \(-0.679851\pi\) | ||||
−0.535431 | + | 0.844579i | \(0.679851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3137 | 0.556711 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.34315i | 0.311373i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.7990i | 1.35807i | 0.734106 | + | 0.679035i | \(0.237601\pi\) | ||||
−0.734106 | + | 0.679035i | \(0.762399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 24.4853i | − 1.19334i | −0.802487 | − | 0.596670i | \(-0.796490\pi\) | ||||
0.802487 | − | 0.596670i | \(-0.203510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0416i | 0.584105i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.02944 | −0.146605 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5147 | −0.554644 | −0.277322 | − | 0.960777i | \(-0.589447\pi\) | ||||
−0.277322 | + | 0.960777i | \(0.589447\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6274 | −0.799063 | −0.399531 | − | 0.916720i | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.6274 | −1.84780 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.1421i | 1.72497i | 0.506083 | + | 0.862485i | \(0.331093\pi\) | ||||
−0.506083 | + | 0.862485i | \(0.668907\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.4558i | 1.58954i | 0.606914 | + | 0.794768i | \(0.292407\pi\) | ||||
−0.606914 | + | 0.794768i | \(0.707593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.20101i | − 0.104338i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 40.7279i | − 1.92207i | −0.276428 | − | 0.961035i | \(-0.589151\pi\) | ||||
0.276428 | − | 0.961035i | \(-0.410849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.3137 | 0.721094 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.37258 | 0.0643477 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.9706 | −1.16807 | −0.584037 | − | 0.811727i | \(-0.698528\pi\) | ||||
−0.584037 | + | 0.811727i | \(0.698528\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.8995 | −1.29941 | −0.649705 | − | 0.760187i | \(-0.725107\pi\) | ||||
−0.649705 | + | 0.760187i | \(0.725107\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 5.79899i | − 0.269502i | −0.990879 | − | 0.134751i | \(-0.956977\pi\) | ||||
0.990879 | − | 0.134751i | \(-0.0430234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.1421i | 1.02462i | 0.858802 | + | 0.512308i | \(0.171209\pi\) | ||||
−0.858802 | + | 0.512308i | \(0.828791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 9.94113i | − 0.459039i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4.68629i | − 0.215476i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.3431 | 1.20871 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8284 | −0.677528 | −0.338764 | − | 0.940871i | \(-0.610009\pi\) | ||||
−0.338764 | + | 0.940871i | \(0.610009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.6569 | 0.987468 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.37258 | −0.0623258 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1716i | 1.05000i | 0.851101 | + | 0.525002i | \(0.175935\pi\) | ||||
−0.851101 | + | 0.525002i | \(0.824065\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12.6863i | − 0.572524i | −0.958151 | − | 0.286262i | \(-0.907587\pi\) | ||||
0.958151 | − | 0.286262i | \(-0.0924128\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.82843i | − 0.397612i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3431i | 0.463953i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.6274 | −1.72920 | −0.864600 | − | 0.502460i | \(-0.832428\pi\) | ||||
−0.864600 | + | 0.502460i | \(0.832428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.7990 | −1.06114 | −0.530572 | − | 0.847640i | \(-0.678023\pi\) | ||||
−0.530572 | + | 0.847640i | \(0.678023\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.62742 | −0.383915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.7279 | 1.71658 | 0.858292 | − | 0.513161i | \(-0.171526\pi\) | ||||
0.858292 | + | 0.513161i | \(0.171526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 3.31371i | − 0.146590i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.17157i | 0.227887i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 12.6863i | − 0.557942i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 11.0711i | − 0.485032i | −0.970147 | − | 0.242516i | \(-0.922027\pi\) | ||||
0.970147 | − | 0.242516i | \(-0.0779727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.3431 | 1.50172 | 0.750860 | − | 0.660461i | \(-0.229639\pi\) | ||||
0.750860 | + | 0.660461i | \(0.229639\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.8284 | −0.994422 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.3137 | −0.663310 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.62742i | 0.286528i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 17.8579i | − 0.769193i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.79899i | 0.163331i | 0.996660 | + | 0.0816657i | \(0.0260240\pi\) | ||||
−0.996660 | + | 0.0816657i | \(0.973976\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 3.02944i | − 0.129767i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.65685 | −0.0708420 | −0.0354210 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354210 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.3137 | −0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.68629 | 0.369379 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.07107 | 0.214868 | 0.107434 | − | 0.994212i | \(-0.465737\pi\) | ||||
0.107434 | + | 0.994212i | \(0.465737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.68629i | 0.198209i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.4558i | 1.07284i | 0.843952 | + | 0.536418i | \(0.180223\pi\) | ||||
−0.843952 | + | 0.536418i | \(0.819777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.20101i | 0.0925972i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.8995i | 0.918075i | 0.888417 | + | 0.459037i | \(0.151806\pi\) | ||||
−0.888417 | + | 0.459037i | \(0.848194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0000 | −1.00437 | −0.502184 | − | 0.864761i | \(-0.667470\pi\) | ||||
−0.502184 | + | 0.864761i | \(0.667470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.7990 | −1.32611 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.68629 | −0.278354 | −0.139177 | − | 0.990268i | \(-0.544446\pi\) | ||||
−0.139177 | + | 0.990268i | \(0.544446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.97056 | 0.372162 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.6569i | 1.06260i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.3431i | 0.757103i | 0.925580 | + | 0.378551i | \(0.123578\pi\) | ||||
−0.925580 | + | 0.378551i | \(0.876422\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.9411i | 2.05779i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 0.928932i | − 0.0381467i | −0.999818 | − | 0.0190733i | \(-0.993928\pi\) | ||||
0.999818 | − | 0.0190733i | \(-0.00607160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.25483 | −0.0514432 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5147 | 1.12422 | 0.562110 | − | 0.827062i | \(-0.309990\pi\) | ||||
0.562110 | + | 0.827062i | \(0.309990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.31371 | 0.0535873 | 0.0267936 | − | 0.999641i | \(-0.491470\pi\) | ||||
0.0267936 | + | 0.999641i | \(0.491470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.75736 | −0.0714468 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.8284i | − 1.00775i | −0.863775 | − | 0.503877i | \(-0.831906\pi\) | ||||
0.863775 | − | 0.503877i | \(-0.168094\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.6863i | 0.513232i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 0.343146i | − 0.0138595i | −0.999976 | − | 0.00692976i | \(-0.997794\pi\) | ||||
0.999976 | − | 0.00692976i | \(-0.00220583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4142i | 1.34521i | 0.740004 | + | 0.672603i | \(0.234824\pi\) | ||||
−0.740004 | + | 0.672603i | \(0.765176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9411 | 1.36421 | 0.682105 | − | 0.731255i | \(-0.261065\pi\) | ||||
0.682105 | + | 0.731255i | \(0.261065\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.11270 | −0.124708 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.7990 | −0.789437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4853i | 0.735887i | 0.929848 | + | 0.367944i | \(0.119938\pi\) | ||||
−0.929848 | + | 0.367944i | \(0.880062\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.485281i | 0.0192578i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.8579i | 0.707554i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 14.8701i | − 0.587332i | −0.955908 | − | 0.293666i | \(-0.905125\pi\) | ||||
0.955908 | − | 0.293666i | \(-0.0948753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.65685 | 0.380829 | 0.190415 | − | 0.981704i | \(-0.439017\pi\) | ||||
0.190415 | + | 0.981704i | \(0.439017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.7990 | 0.621122 | 0.310561 | − | 0.950553i | \(-0.399483\pi\) | ||||
0.310561 | + | 0.950553i | \(0.399483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.6274 | −1.51626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.27208 | 0.206312 | 0.103156 | − | 0.994665i | \(-0.467106\pi\) | ||||
0.103156 | + | 0.994665i | \(0.467106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.31371i | 0.129477i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.97056i | 0.349444i | 0.984618 | + | 0.174722i | \(0.0559026\pi\) | ||||
−0.984618 | + | 0.174722i | \(0.944097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.65685i | 0.142235i | 0.997468 | + | 0.0711176i | \(0.0226566\pi\) | ||||
−0.997468 | + | 0.0711176i | \(0.977343\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.74517i | 0.106453i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.3137 | 0.902710 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.3431 | 0.399293 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000 | 0.693849 | 0.346925 | − | 0.937893i | \(-0.387226\pi\) | ||||
0.346925 | + | 0.937893i | \(0.387226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.7279 | 0.719773 | 0.359886 | − | 0.932996i | \(-0.382815\pi\) | ||||
0.359886 | + | 0.932996i | \(0.382815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.94113i | 0.0744936i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.1421i | 0.847245i | 0.905839 | + | 0.423623i | \(0.139242\pi\) | ||||
−0.905839 | + | 0.423623i | \(0.860758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.85786i | 0.300234i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 25.6569i | − 0.977448i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.02944 | 0.115245 | 0.0576226 | − | 0.998338i | \(-0.481648\pi\) | ||||
0.0576226 | + | 0.998338i | \(0.481648\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.02944 | 0.266642 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0000 | 0.530288 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.7574 | 0.519608 | 0.259804 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259804 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.3137i | 1.63361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2010i | 0.458866i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 48.0833i | − 1.80580i | −0.429846 | − | 0.902902i | \(-0.641432\pi\) | ||||
0.429846 | − | 0.902902i | \(-0.358568\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 60.2843i | − 2.25766i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.68629 | −0.175257 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.4853 | −1.06232 | −0.531161 | − | 0.847271i | \(-0.678244\pi\) | ||||
−0.531161 | + | 0.847271i | \(0.678244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.31371 | 0.272377 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.8995 | −0.590492 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.82843i | − 0.327428i | −0.986508 | − | 0.163714i | \(-0.947653\pi\) | ||||
0.986508 | − | 0.163714i | \(-0.0523475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 4.28427i | − 0.158459i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 24.4853i | − 0.904385i | −0.891920 | − | 0.452192i | \(-0.850642\pi\) | ||||
0.891920 | − | 0.452192i | \(-0.149358\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.9411i | 1.25024i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00000 | −0.294285 | −0.147142 | − | 0.989115i | \(-0.547008\pi\) | ||||
−0.147142 | + | 0.989115i | \(0.547008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.9706 | −0.622590 | −0.311295 | − | 0.950313i | \(-0.600763\pi\) | ||||
−0.311295 | + | 0.950313i | \(0.600763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.9706 | 0.401930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.37258 | 0.342467 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 40.8284i | − 1.48985i | −0.667148 | − | 0.744925i | \(-0.732485\pi\) | ||||
0.667148 | − | 0.744925i | \(-0.267515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.14214i | 0.223535i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.485281i | 0.0176379i | 0.999961 | + | 0.00881893i | \(0.00280719\pi\) | ||||
−0.999961 | + | 0.00881893i | \(0.997193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.6985i | 0.931569i | 0.884898 | + | 0.465785i | \(0.154228\pi\) | ||||
−0.884898 | + | 0.465785i | \(0.845772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.28427 | −0.155101 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.6274 | 1.39476 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3137 | −0.768592 | −0.384296 | − | 0.923210i | \(-0.625556\pi\) | ||||
−0.384296 | + | 0.923210i | \(0.625556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.5858 | 0.452679 | 0.226340 | − | 0.974048i | \(-0.427324\pi\) | ||||
0.226340 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.1127i | 1.47681i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 30.6274i | − 1.09734i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 35.3137i | − 1.26362i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.82843i | 0.243717i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.3431 | −0.939032 | −0.469516 | − | 0.882924i | \(-0.655572\pi\) | ||||
−0.469516 | + | 0.882924i | \(0.655572\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.11270 | 0.110675 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3431 | −0.367296 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.0711 | −0.463001 | −0.231500 | − | 0.972835i | \(-0.574363\pi\) | ||||
−0.231500 | + | 0.972835i | \(0.574363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 11.5980i | − 0.410307i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.3137i | 0.399252i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.31371i | − 0.116793i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.6690i | 1.50016i | 0.661345 | + | 0.750082i | \(0.269986\pi\) | ||||
−0.661345 | + | 0.750082i | \(0.730014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.5980 | −1.10956 | −0.554778 | − | 0.831999i | \(-0.687197\pi\) | ||||
−0.554778 | + | 0.831999i | \(0.687197\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.65685 | −0.198151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.37258 | −0.327905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4142 | 0.398359 | 0.199179 | − | 0.979963i | \(-0.436172\pi\) | ||||
0.199179 | + | 0.979963i | \(0.436172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 52.4264i | − 1.82747i | −0.406311 | − | 0.913735i | \(-0.633185\pi\) | ||||
0.406311 | − | 0.913735i | \(-0.366815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 15.0294i | − 0.522625i | −0.965254 | − | 0.261312i | \(-0.915845\pi\) | ||||
0.965254 | − | 0.261312i | \(-0.0841553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 4.20101i | − 0.145907i | −0.997335 | − | 0.0729536i | \(-0.976758\pi\) | ||||
0.997335 | − | 0.0729536i | \(-0.0232425\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 16.3259i | − 0.565659i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.31371 | −0.114676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.51472 | 0.121342 | 0.0606708 | − | 0.998158i | \(-0.480676\pi\) | ||||
0.0606708 | + | 0.998158i | \(0.480676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.3431 | −0.598040 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.92893 | −0.100758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.48528i | 0.0853953i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 52.2843i | − 1.79228i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.2843i | 1.44779i | 0.689912 | + | 0.723893i | \(0.257649\pi\) | ||||
−0.689912 | + | 0.723893i | \(0.742351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 21.8995i | − 0.748072i | −0.927414 | − | 0.374036i | \(-0.877974\pi\) | ||||
0.927414 | − | 0.374036i | \(-0.122026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.65685 | 0.0565311 | 0.0282656 | − | 0.999600i | \(-0.491002\pi\) | ||||
0.0282656 | + | 0.999600i | \(0.491002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.970563 | 0.0330383 | 0.0165192 | − | 0.999864i | \(-0.494742\pi\) | ||||
0.0165192 | + | 0.999864i | \(0.494742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7157 | 0.466349 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.6569 | −1.00604 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 33.9411i | − 1.15005i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.68629i | 0.158426i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.97056i | 0.235379i | 0.993050 | + | 0.117690i | \(0.0375488\pi\) | ||||
−0.993050 | + | 0.117690i | \(0.962451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7279i | 0.428815i | 0.976744 | + | 0.214407i | \(0.0687820\pi\) | ||||
−0.976744 | + | 0.214407i | \(0.931218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.2843 | 1.35567 | 0.677837 | − | 0.735212i | \(-0.262918\pi\) | ||||
0.677837 | + | 0.735212i | \(0.262918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.34315 | 0.0786751 | 0.0393376 | − | 0.999226i | \(-0.487475\pi\) | ||||
0.0393376 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.686292 | 0.0230175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.3726 | −0.849061 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.94113i | 0.0648847i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 30.1421i | − 1.00530i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.4558i | 0.781427i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 12.9706i | − 0.431156i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3431 | −0.476256 | −0.238128 | − | 0.971234i | \(-0.576534\pi\) | ||||
−0.238128 | + | 0.971234i | \(0.576534\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5980 | 0.781836 | 0.390918 | − | 0.920426i | \(-0.372158\pi\) | ||||
0.390918 | + | 0.920426i | \(0.372158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.6274 | −1.01362 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.68629 | 0.154755 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.4558i | 0.773737i | 0.922135 | + | 0.386868i | \(0.126443\pi\) | ||||
−0.922135 | + | 0.386868i | \(0.873557\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.3137i | 1.16236i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.6569i | 1.17239i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.7279i | 0.548825i | 0.961612 | + | 0.274413i | \(0.0884834\pi\) | ||||
−0.961612 | + | 0.274413i | \(0.911517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.7157 | −1.17054 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.28427 | 0.140111 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.6274 | 1.84994 | 0.924969 | − | 0.380044i | \(-0.124091\pi\) | ||||
0.924969 | + | 0.380044i | \(0.124091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.2721 | −0.693450 | −0.346725 | − | 0.937967i | \(-0.612706\pi\) | ||||
−0.346725 | + | 0.937967i | \(0.612706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.9706i | 1.20393i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 31.5980i | − 1.02680i | −0.858151 | − | 0.513398i | \(-0.828386\pi\) | ||||
0.858151 | − | 0.513398i | \(-0.171614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 11.3137i | − 0.367259i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 4.44365i | − 0.143944i | −0.997407 | − | 0.0719720i | \(-0.977071\pi\) | ||||
0.997407 | − | 0.0719720i | \(-0.0229292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.6863 | −0.410519 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1127 | 0.358848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −46.9411 | −1.51423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.1421 | 0.326487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 46.0833i | − 1.48194i | −0.671539 | − | 0.740969i | \(-0.734367\pi\) | ||||
0.671539 | − | 0.740969i | \(-0.265633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 21.1716i | − 0.679428i | −0.940529 | − | 0.339714i | \(-0.889670\pi\) | ||||
0.940529 | − | 0.339714i | \(-0.110330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.94113i | − 0.318698i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.5269i | 0.400771i | 0.979717 | + | 0.200386i | \(0.0642195\pi\) | ||||
−0.979717 | + | 0.200386i | \(0.935780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6274 | 0.339654 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.3431 | −1.09538 | −0.547688 | − | 0.836683i | \(-0.684492\pi\) | ||||
−0.547688 | + | 0.836683i | \(0.684492\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9411 | −0.380476 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3137 | 0.359755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7990i | 0.438339i | 0.975687 | + | 0.219170i | \(0.0703348\pi\) | ||||
−0.975687 | + | 0.219170i | \(0.929665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.485281i | 0.0153845i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.5980i | 0.557334i | 0.960388 | + | 0.278667i | \(0.0898925\pi\) | ||||
−0.960388 | + | 0.278667i | \(0.910107\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2304.2.f.b.1151.4 | 4 | ||
3.2 | odd | 2 | 2304.2.f.g.1151.2 | 4 | |||
4.3 | odd | 2 | 2304.2.f.a.1151.3 | 4 | |||
8.3 | odd | 2 | 2304.2.f.g.1151.1 | 4 | |||
8.5 | even | 2 | 2304.2.f.h.1151.2 | 4 | |||
12.11 | even | 2 | 2304.2.f.h.1151.1 | 4 | |||
16.3 | odd | 4 | 1152.2.c.d.1151.3 | yes | 4 | ||
16.5 | even | 4 | 1152.2.c.b.1151.2 | yes | 4 | ||
16.11 | odd | 4 | 1152.2.c.c.1151.2 | yes | 4 | ||
16.13 | even | 4 | 1152.2.c.a.1151.3 | yes | 4 | ||
24.5 | odd | 2 | 2304.2.f.a.1151.4 | 4 | |||
24.11 | even | 2 | inner | 2304.2.f.b.1151.3 | 4 | ||
48.5 | odd | 4 | 1152.2.c.c.1151.3 | yes | 4 | ||
48.11 | even | 4 | 1152.2.c.b.1151.3 | yes | 4 | ||
48.29 | odd | 4 | 1152.2.c.d.1151.2 | yes | 4 | ||
48.35 | even | 4 | 1152.2.c.a.1151.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.c.a.1151.2 | ✓ | 4 | 48.35 | even | 4 | ||
1152.2.c.a.1151.3 | yes | 4 | 16.13 | even | 4 | ||
1152.2.c.b.1151.2 | yes | 4 | 16.5 | even | 4 | ||
1152.2.c.b.1151.3 | yes | 4 | 48.11 | even | 4 | ||
1152.2.c.c.1151.2 | yes | 4 | 16.11 | odd | 4 | ||
1152.2.c.c.1151.3 | yes | 4 | 48.5 | odd | 4 | ||
1152.2.c.d.1151.2 | yes | 4 | 48.29 | odd | 4 | ||
1152.2.c.d.1151.3 | yes | 4 | 16.3 | odd | 4 | ||
2304.2.f.a.1151.3 | 4 | 4.3 | odd | 2 | |||
2304.2.f.a.1151.4 | 4 | 24.5 | odd | 2 | |||
2304.2.f.b.1151.3 | 4 | 24.11 | even | 2 | inner | ||
2304.2.f.b.1151.4 | 4 | 1.1 | even | 1 | trivial | ||
2304.2.f.g.1151.1 | 4 | 8.3 | odd | 2 | |||
2304.2.f.g.1151.2 | 4 | 3.2 | odd | 2 | |||
2304.2.f.h.1151.1 | 4 | 12.11 | even | 2 | |||
2304.2.f.h.1151.2 | 4 | 8.5 | even | 2 |