Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4704,2,Mod(1567,4704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4704, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4704.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4704.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: | \(37.5616291108\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 24x^{14} + 218x^{12} + 968x^{10} + 2241x^{8} + 2672x^{6} + 1512x^{4} + 320x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.14 | ||
Root | \(1.60698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4704.1567 |
Dual form | 4704.2.b.e.1567.3 |
$q$-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 \(\left(\mathbb{Z}/4704\mathbb{Z}\right)^\times\).
\(n\) | \(1471\) | \(1765\) | \(3137\) | \(4609\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.70012i | 1.20753i | 0.797163 | + | 0.603764i | \(0.206333\pi\) | ||||
−0.797163 | + | 0.603764i | \(0.793667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.41762i | − 0.427428i | −0.976896 | − | 0.213714i | \(-0.931444\pi\) | ||||
0.976896 | − | 0.213714i | \(-0.0685561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.69489i | − 1.57948i | −0.613442 | − | 0.789739i | \(-0.710216\pi\) | ||||
0.613442 | − | 0.789739i | \(-0.289784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.70012i | 0.697167i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.95966i | 0.475286i | 0.971353 | + | 0.237643i | \(0.0763749\pi\) | ||||
−0.971353 | + | 0.237643i | \(0.923625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.723292 | 0.165934 | 0.0829672 | − | 0.996552i | \(-0.473560\pi\) | ||||
0.0829672 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 0.649746i | − 0.135481i | −0.997703 | − | 0.0677407i | \(-0.978421\pi\) | ||||
0.997703 | − | 0.0677407i | \(-0.0215791\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.29063 | −0.458126 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.06459 | 1.12617 | 0.563083 | − | 0.826400i | \(-0.309615\pi\) | ||||
0.563083 | + | 0.826400i | \(0.309615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.99520 | 0.897164 | 0.448582 | − | 0.893742i | \(-0.351929\pi\) | ||||
0.448582 | + | 0.893742i | \(0.351929\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.41762i | − 0.246776i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.15370 | 0.189667 | 0.0948336 | − | 0.995493i | \(-0.469768\pi\) | ||||
0.0948336 | + | 0.995493i | \(0.469768\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 5.69489i | − 0.911913i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 1.58141i | − 0.246975i | −0.992346 | − | 0.123487i | \(-0.960592\pi\) | ||||
0.992346 | − | 0.123487i | \(-0.0394078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.8193i | − 1.64993i | −0.565185 | − | 0.824965i | \(-0.691195\pi\) | ||||
0.565185 | − | 0.824965i | \(-0.308805\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.70012i | 0.402510i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.62969 | −1.40464 | −0.702318 | − | 0.711864i | \(-0.747851\pi\) | ||||
−0.702318 | + | 0.711864i | \(0.747851\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.95966i | 0.274407i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.5241 | 1.72032 | 0.860158 | − | 0.510027i | \(-0.170365\pi\) | ||||
0.860158 | + | 0.510027i | \(0.170365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.82774 | 0.516132 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.723292 | 0.0958023 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.868280 | −0.113040 | −0.0565202 | − | 0.998401i | \(-0.518001\pi\) | ||||
−0.0565202 | + | 0.998401i | \(0.518001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.6101i | 1.74259i | 0.490756 | + | 0.871297i | \(0.336721\pi\) | ||||
−0.490756 | + | 0.871297i | \(0.663279\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.3769 | 1.90727 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.0530875i | − 0.00648567i | −0.999995 | − | 0.00324283i | \(-0.998968\pi\) | ||||
0.999995 | − | 0.00324283i | \(-0.00103223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 0.649746i | − 0.0782202i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0593i | 1.66853i | 0.551362 | + | 0.834266i | \(0.314108\pi\) | ||||
−0.551362 | + | 0.834266i | \(0.685892\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 15.6484i | − 1.83151i | −0.401735 | − | 0.915756i | \(-0.631593\pi\) | ||||
0.401735 | − | 0.915756i | \(-0.368407\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.29063 | −0.264499 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 11.4936i | − 1.29313i | −0.762861 | − | 0.646563i | \(-0.776206\pi\) | ||||
0.762861 | − | 0.646563i | \(-0.223794\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.95860 | 0.324749 | 0.162375 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162375 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.29130 | −0.573922 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.06459 | 0.650192 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 8.24185i | − 0.873634i | −0.899550 | − | 0.436817i | \(-0.856106\pi\) | ||||
0.899550 | − | 0.436817i | \(-0.143894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.99520 | 0.517978 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.95297i | 0.200371i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01880i | 0.103444i | 0.998662 | + | 0.0517218i | \(0.0164709\pi\) | ||||
−0.998662 | + | 0.0517218i | \(0.983529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1.41762i | − 0.142476i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.9466i | 1.18873i | 0.804196 | + | 0.594364i | \(0.202596\pi\) | ||||
−0.804196 | + | 0.594364i | \(0.797404\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.5903 | 1.73322 | 0.866610 | − | 0.498986i | \(-0.166294\pi\) | ||||
0.866610 | + | 0.498986i | \(0.166294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 14.5752i | − 1.40903i | −0.709687 | − | 0.704517i | \(-0.751164\pi\) | ||||
0.709687 | − | 0.704517i | \(-0.248836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.41674 | 0.518829 | 0.259415 | − | 0.965766i | \(-0.416470\pi\) | ||||
0.259415 | + | 0.965766i | \(0.416470\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.15370 | 0.109504 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.65726 | −0.532190 | −0.266095 | − | 0.963947i | \(-0.585733\pi\) | ||||
−0.266095 | + | 0.963947i | \(0.585733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.75439 | 0.163598 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 5.69489i | − 0.526493i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.99035 | 0.817305 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.58141i | − 0.142591i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.31562i | 0.654329i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 11.7616i | − 1.04367i | −0.853046 | − | 0.521835i | \(-0.825247\pi\) | ||||
0.853046 | − | 0.521835i | \(-0.174753\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 10.8193i | − 0.952587i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.6203 | 1.80161 | 0.900804 | − | 0.434226i | \(-0.142978\pi\) | ||||
0.900804 | + | 0.434226i | \(0.142978\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.70012i | 0.232389i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5698 | 1.67196 | 0.835979 | − | 0.548762i | \(-0.184901\pi\) | ||||
0.835979 | + | 0.548762i | \(0.184901\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.4109 | −1.64641 | −0.823205 | − | 0.567745i | \(-0.807816\pi\) | ||||
−0.823205 | + | 0.567745i | \(0.807816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.62969 | −0.810967 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.07319 | −0.675114 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3751i | 1.35988i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.2112 | −1.57385 | −0.786923 | − | 0.617051i | \(-0.788327\pi\) | ||||
−0.786923 | + | 0.617051i | \(0.788327\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1.67704i | − 0.136475i | −0.997669 | − | 0.0682376i | \(-0.978262\pi\) | ||||
0.997669 | − | 0.0682376i | \(-0.0217376\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.95966i | 0.158429i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.4876i | 1.08335i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.87226i | 0.628275i | 0.949378 | + | 0.314137i | \(0.101715\pi\) | ||||
−0.949378 | + | 0.314137i | \(0.898285\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.5241 | 0.993225 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.56484i | 0.279220i | 0.990207 | + | 0.139610i | \(0.0445849\pi\) | ||||
−0.990207 | + | 0.139610i | \(0.955415\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.82774 | 0.297989 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9594 | 0.848063 | 0.424031 | − | 0.905647i | \(-0.360615\pi\) | ||||
0.424031 | + | 0.905647i | \(0.360615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.4318 | −1.49475 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.723292 | 0.0553115 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9366i | 1.43972i | 0.694118 | + | 0.719861i | \(0.255795\pi\) | ||||
−0.694118 | + | 0.719861i | \(0.744205\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.868280 | −0.0652640 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.90622i | 0.441451i | 0.975336 | + | 0.220726i | \(0.0708425\pi\) | ||||
−0.975336 | + | 0.220726i | \(0.929157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.5302i | 1.82331i | 0.410953 | + | 0.911656i | \(0.365196\pi\) | ||||
−0.410953 | + | 0.911656i | \(0.634804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6101i | 1.00609i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.11513i | 0.229029i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.77805 | 0.203151 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 7.88475i | − 0.570520i | −0.958450 | − | 0.285260i | \(-0.907920\pi\) | ||||
0.958450 | − | 0.285260i | \(-0.0920800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7493 | −0.773750 | −0.386875 | − | 0.922132i | \(-0.626446\pi\) | ||||
−0.386875 | + | 0.922132i | \(0.626446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.3769 | 1.10116 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.22489 | 0.443505 | 0.221753 | − | 0.975103i | \(-0.428822\pi\) | ||||
0.221753 | + | 0.975103i | \(0.428822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.28223 | 0.303559 | 0.151780 | − | 0.988414i | \(-0.451500\pi\) | ||||
0.151780 | + | 0.988414i | \(0.451500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 0.0530875i | − 0.00374450i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.26999 | 0.298229 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 0.649746i | − 0.0451605i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1.02535i | − 0.0709251i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2858i | 1.19001i | 0.803723 | + | 0.595003i | \(0.202849\pi\) | ||||
−0.803723 | + | 0.595003i | \(0.797151\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.0593i | 0.963328i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.2134 | 1.99234 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 15.6484i | − 1.05742i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.1600 | 0.750705 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.40635 | 0.295071 | 0.147535 | − | 0.989057i | \(-0.452866\pi\) | ||||
0.147535 | + | 0.989057i | \(0.452866\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.29063 | −0.152709 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.22077 | 0.412887 | 0.206444 | − | 0.978458i | \(-0.433811\pi\) | ||||
0.206444 | + | 0.978458i | \(0.433811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5332i | 0.762138i | 0.924547 | + | 0.381069i | \(0.124444\pi\) | ||||
−0.924547 | + | 0.381069i | \(0.875556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.27693 | 0.607752 | 0.303876 | − | 0.952712i | \(-0.401719\pi\) | ||||
0.303876 | + | 0.952712i | \(0.401719\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 26.0013i | − 1.69614i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 11.4936i | − 0.746587i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.55540i | 0.229980i | 0.993367 | + | 0.114990i | \(0.0366835\pi\) | ||||
−0.993367 | + | 0.114990i | \(0.963316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 8.59044i | − 0.553359i | −0.960962 | − | 0.276679i | \(-0.910766\pi\) | ||||
0.960962 | − | 0.276679i | \(-0.0892340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.11907i | − 0.262090i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.95860 | 0.187494 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6135 | 0.669918 | 0.334959 | − | 0.942233i | \(-0.391277\pi\) | ||||
0.334959 | + | 0.942233i | \(0.391277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.921093 | −0.0579086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.29130 | −0.331354 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.8261i | 0.987203i | 0.869688 | + | 0.493601i | \(0.164320\pi\) | ||||
−0.869688 | + | 0.493601i | \(0.835680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.06459 | 0.375389 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 0.437527i | − 0.0269790i | −0.999909 | − | 0.0134895i | \(-0.995706\pi\) | ||||
0.999909 | − | 0.0134895i | \(-0.00429398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.8165i | 2.07733i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8.24185i | − 0.504393i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 0.496114i | − 0.0302486i | −0.999886 | − | 0.0151243i | \(-0.995186\pi\) | ||||
0.999886 | − | 0.0151243i | \(-0.00481440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.37679 | −0.205125 | −0.102563 | − | 0.994727i | \(-0.532704\pi\) | ||||
−0.102563 | + | 0.994727i | \(0.532704\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.24724i | 0.195816i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.9336 | 0.656934 | 0.328467 | − | 0.944515i | \(-0.393468\pi\) | ||||
0.328467 | + | 0.944515i | \(0.393468\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.99520 | 0.299055 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.4932 | −1.58045 | −0.790226 | − | 0.612815i | \(-0.790037\pi\) | ||||
−0.790226 | + | 0.612815i | \(0.790037\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.17861 | 0.129505 | 0.0647524 | − | 0.997901i | \(-0.479374\pi\) | ||||
0.0647524 | + | 0.997901i | \(0.479374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.95297i | 0.115684i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.1598 | 0.774103 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.01880i | 0.0597231i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.82696i | 0.398835i | 0.979915 | + | 0.199418i | \(0.0639050\pi\) | ||||
−0.979915 | + | 0.199418i | \(0.936095\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 2.34446i | − 0.136500i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1.41762i | − 0.0822586i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.70023 | −0.213990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.9466i | 0.686312i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −36.7489 | −2.10423 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.9855 | −0.741122 | −0.370561 | − | 0.928808i | \(-0.620835\pi\) | ||||
−0.370561 | + | 0.928808i | \(0.620835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.5903 | 1.00068 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.7636 | −1.85786 | −0.928928 | − | 0.370261i | \(-0.879268\pi\) | ||||
−0.928928 | + | 0.370261i | \(0.879268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.15065i | 0.517225i | 0.965981 | + | 0.258613i | \(0.0832653\pi\) | ||||
−0.965981 | + | 0.258613i | \(0.916735\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.5872 | 1.38096 | 0.690479 | − | 0.723353i | \(-0.257400\pi\) | ||||
0.690479 | + | 0.723353i | \(0.257400\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 8.59728i | − 0.481355i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 14.5752i | − 0.813506i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.41740i | 0.0788664i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0449i | 0.723600i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.41674 | 0.299546 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 20.2118i | − 1.11094i | −0.831537 | − | 0.555470i | \(-0.812539\pi\) | ||||
0.831537 | − | 0.555470i | \(-0.187461\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.15370 | 0.0632224 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.143342 | 0.00783163 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4425 | −0.841209 | −0.420605 | − | 0.907244i | \(-0.638182\pi\) | ||||
−0.420605 | + | 0.907244i | \(0.638182\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.65726 | −0.307260 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7.08129i | − 0.383474i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.75439 | 0.0944532 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 22.9682i | − 1.23300i | −0.787356 | − | 0.616498i | \(-0.788551\pi\) | ||||
0.787356 | − | 0.616498i | \(-0.211449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.24157i | 0.119988i | 0.998199 | + | 0.0599941i | \(0.0191082\pi\) | ||||
−0.998199 | + | 0.0599941i | \(0.980892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 5.69489i | − 0.303971i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7735i | 0.679863i | 0.940450 | + | 0.339932i | \(0.110404\pi\) | ||||
−0.940450 | + | 0.339932i | \(0.889596\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.9618 | −2.01480 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 22.4512i | − 1.18493i | −0.805597 | − | 0.592464i | \(-0.798155\pi\) | ||||
0.805597 | − | 0.592464i | \(-0.201845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4768 | −0.972466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.99035 | 0.471871 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 42.2526 | 2.21160 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.97020 | 0.207243 | 0.103621 | − | 0.994617i | \(-0.466957\pi\) | ||||
0.103621 | + | 0.994617i | \(0.466957\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 1.58141i | − 0.0823249i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0774 | 0.936014 | 0.468007 | − | 0.883725i | \(-0.344972\pi\) | ||||
0.468007 | + | 0.883725i | \(0.344972\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.31562i | 0.377777i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 34.5372i | − 1.77876i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.69206i | 0.497848i | 0.968523 | + | 0.248924i | \(0.0800769\pi\) | ||||
−0.968523 | + | 0.248924i | \(0.919923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 11.7616i | − 0.602564i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.8602 | −0.708222 | −0.354111 | − | 0.935203i | \(-0.615217\pi\) | ||||
−0.354111 | + | 0.935203i | \(0.615217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 10.8193i | − 0.549976i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.3052 | 0.978814 | 0.489407 | − | 0.872055i | \(-0.337213\pi\) | ||||
0.489407 | + | 0.872055i | \(0.337213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.27328 | 0.0643925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.6203 | 1.04016 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 31.0339 | 1.56149 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 0.531536i | − 0.0266770i | −0.999911 | − | 0.0133385i | \(-0.995754\pi\) | ||||
0.999911 | − | 0.0133385i | \(-0.00424591\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.749230 | −0.0374147 | −0.0187074 | − | 0.999825i | \(-0.505955\pi\) | ||||
−0.0187074 | + | 0.999825i | \(0.505955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 28.4471i | − 1.41705i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.70012i | 0.134170i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.63551i | − 0.0810692i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 10.0341i | − 0.496156i | −0.968740 | − | 0.248078i | \(-0.920201\pi\) | ||||
0.968740 | − | 0.248078i | \(-0.0797990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.5698 | 0.965305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.98858i | 0.392144i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.4109 | −0.950555 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.20727 | 0.107832 | 0.0539160 | − | 0.998545i | \(-0.482830\pi\) | ||||
0.0539160 | + | 0.998545i | \(0.482830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.3916 | −1.04256 | −0.521280 | − | 0.853386i | \(-0.674545\pi\) | ||||
−0.521280 | + | 0.853386i | \(0.674545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.62969 | −0.468212 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 4.48884i | − 0.217741i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.07319 | −0.389777 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 32.7031i | − 1.57525i | −0.616153 | − | 0.787626i | \(-0.711310\pi\) | ||||
0.616153 | − | 0.787626i | \(-0.288690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 3.18695i | − 0.153155i | −0.997064 | − | 0.0765775i | \(-0.975601\pi\) | ||||
0.997064 | − | 0.0765775i | \(-0.0243993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.3751i | 0.785126i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 0.469956i | − 0.0224810i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.6702 | −0.509262 | −0.254631 | − | 0.967038i | \(-0.581954\pi\) | ||||
−0.254631 | + | 0.967038i | \(0.581954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.2559i | 1.24746i | 0.781641 | + | 0.623729i | \(0.214383\pi\) | ||||
−0.781641 | + | 0.623729i | \(0.785617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.2539 | 1.05494 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.2112 | −0.908661 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3240 | 0.487220 | 0.243610 | − | 0.969873i | \(-0.421668\pi\) | ||||
0.243610 | + | 0.969873i | \(0.421668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.24184 | −0.105564 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.67704i | − 0.0787940i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.2002 | −1.17881 | −0.589407 | − | 0.807836i | \(-0.700638\pi\) | ||||
−0.589407 | + | 0.807836i | \(0.700638\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.95966i | 0.0914689i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 20.7224i | − 0.965140i | −0.875857 | − | 0.482570i | \(-0.839703\pi\) | ||||
0.875857 | − | 0.482570i | \(-0.160297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 39.6594i | − 1.84313i | −0.388227 | − | 0.921564i | \(-0.626912\pi\) | ||||
0.388227 | − | 0.921564i | \(-0.373088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.4876i | 0.625474i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.1962 | 1.53614 | 0.768068 | − | 0.640369i | \(-0.221219\pi\) | ||||
0.768068 | + | 0.640369i | \(0.221219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.87226i | 0.362735i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.3377 | −0.705227 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.65679 | −0.0760189 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.5241 | 0.573439 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.1873 | 0.831000 | 0.415500 | − | 0.909593i | \(-0.363607\pi\) | ||||
0.415500 | + | 0.909593i | \(0.363607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 6.57020i | − 0.299575i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.75088 | −0.124911 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.9614i | − 1.08579i | −0.839799 | − | 0.542897i | \(-0.817327\pi\) | ||||
0.839799 | − | 0.542897i | \(-0.182673\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.56484i | 0.161208i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 11.5449i | − 0.521016i | −0.965472 | − | 0.260508i | \(-0.916110\pi\) | ||||
0.965472 | − | 0.260508i | \(-0.0838900\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.8845i | 0.535251i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.82774 | 0.172044 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 22.1819i | − 0.993000i | −0.868037 | − | 0.496500i | \(-0.834618\pi\) | ||||
0.868037 | − | 0.496500i | \(-0.165382\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.9594 | 0.489629 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.53547 | 0.0684631 | 0.0342316 | − | 0.999414i | \(-0.489102\pi\) | ||||
0.0342316 | + | 0.999414i | \(0.489102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.2571 | −1.43542 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.4318 | −0.862997 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 9.70502i | − 0.430167i | −0.976596 | − | 0.215084i | \(-0.930998\pi\) | ||||
0.976596 | − | 0.215084i | \(-0.0690024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.723292 | 0.0319341 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 47.4958i | 2.09291i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6512i | 0.600381i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.9366i | 0.831224i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 26.6360i | − 1.16695i | −0.812133 | − | 0.583473i | \(-0.801694\pi\) | ||||
0.812133 | − | 0.583473i | \(-0.198306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.48803 | −0.414882 | −0.207441 | − | 0.978247i | \(-0.566514\pi\) | ||||
−0.207441 | + | 0.978247i | \(0.566514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.78887i | 0.426410i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5778 | 0.981645 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.868280 | −0.0376802 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.00595 | −0.390091 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.3546 | 1.70145 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.90622i | 0.254872i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.0579 | −1.16331 | −0.581654 | − | 0.813436i | \(-0.697594\pi\) | ||||
−0.581654 | + | 0.813436i | \(0.697594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.5302i | 1.05269i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.6258i | 0.626501i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 32.3241i | − 1.38208i | −0.722818 | − | 0.691039i | \(-0.757153\pi\) | ||||
0.722818 | − | 0.691039i | \(-0.242847\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.6101i | 0.580865i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.38647 | 0.186870 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.11513i | 0.132230i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.13372 | −0.175151 | −0.0875757 | − | 0.996158i | \(-0.527912\pi\) | ||||
−0.0875757 | + | 0.996158i | \(0.527912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −61.6148 | −2.60603 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.77805 | 0.117289 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.1077 | −1.35318 | −0.676589 | − | 0.736361i | \(-0.736542\pi\) | ||||
−0.676589 | + | 0.736361i | \(0.736542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 15.2753i | − 0.642635i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.83749 | 0.370487 | 0.185243 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185243 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6970i | 1.11724i | 0.829425 | + | 0.558618i | \(0.188668\pi\) | ||||
−0.829425 | + | 0.558618i | \(0.811332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7.88475i | − 0.329390i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.48833i | 0.0620675i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.6269i | 0.858710i | 0.903136 | + | 0.429355i | \(0.141259\pi\) | ||||
−0.903136 | + | 0.429355i | \(0.858741\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.7493 | −0.446725 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 17.7544i | − 0.735312i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.3769 | 0.635755 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.8831 | −1.27468 | −0.637341 | − | 0.770582i | \(-0.719966\pi\) | ||||
−0.637341 | + | 0.770582i | \(0.719966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.61299 | 0.148871 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.22489 | 0.256058 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 30.6091i | − 1.25697i | −0.777823 | − | 0.628483i | \(-0.783676\pi\) | ||||
0.777823 | − | 0.628483i | \(-0.216324\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.28223 | 0.175260 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.72452i | 0.111321i | 0.998450 | + | 0.0556605i | \(0.0177264\pi\) | ||||
−0.998450 | + | 0.0556605i | \(0.982274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 28.9310i | − 1.18012i | −0.807360 | − | 0.590059i | \(-0.799104\pi\) | ||||
0.807360 | − | 0.590059i | \(-0.200896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 0.0530875i | − 0.00216189i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.2750i | 0.986919i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.3046 | −1.35179 | −0.675896 | − | 0.736997i | \(-0.736243\pi\) | ||||
−0.675896 | + | 0.736997i | \(0.736243\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.8401i | 2.21859i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.85667 | −0.0749902 | −0.0374951 | − | 0.999297i | \(-0.511938\pi\) | ||||
−0.0374951 | + | 0.999297i | \(0.511938\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.26999 | 0.172183 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.4264 | 1.10415 | 0.552073 | − | 0.833796i | \(-0.313837\pi\) | ||||
0.552073 | + | 0.833796i | \(0.313837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.20947 | 0.0888061 | 0.0444031 | − | 0.999014i | \(-0.485861\pi\) | ||||
0.0444031 | + | 0.999014i | \(0.485861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 0.649746i | − 0.0260734i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2062 | −1.24825 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.02535i | − 0.0409486i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.26086i | 0.0901462i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7387i | 0.785784i | 0.919585 | + | 0.392892i | \(0.128525\pi\) | ||||
−0.919585 | + | 0.392892i | \(0.871475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.2858i | 0.687051i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.7576 | 1.26026 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0593i | 0.556177i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.9726 | −0.749372 | −0.374686 | − | 0.927152i | \(-0.622249\pi\) | ||||
−0.374686 | + | 0.927152i | \(0.622249\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.5988 | 0.694027 | 0.347013 | − | 0.937860i | \(-0.387196\pi\) | ||||
0.347013 | + | 0.937860i | \(0.387196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.2134 | 1.15028 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.03295 | 0.237180 | 0.118590 | − | 0.992943i | \(-0.462163\pi\) | ||||
0.118590 | + | 0.992943i | \(0.462163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.23089i | 0.0483167i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.59067 | −0.0622478 | −0.0311239 | − | 0.999516i | \(-0.509909\pi\) | ||||
−0.0311239 | + | 0.999516i | \(0.509909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55.6773i | 2.17549i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 15.6484i | − 0.610504i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 8.83213i | − 0.344051i | −0.985093 | − | 0.172025i | \(-0.944969\pi\) | ||||
0.985093 | − | 0.172025i | \(-0.0550311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.46020i | 0.0567953i | 0.999597 | + | 0.0283976i | \(0.00904047\pi\) | ||||
−0.999597 | + | 0.0283976i | \(0.990960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.1600 | 0.433419 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.94044i | − 0.152575i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.40635 | 0.170359 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.2939 | 0.744835 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7279 | −1.22302 | −0.611510 | − | 0.791237i | \(-0.709438\pi\) | ||||
−0.611510 | + | 0.791237i | \(0.709438\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.29063 | −0.0881664 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.31504i | − 0.242707i | −0.992609 | − | 0.121353i | \(-0.961277\pi\) | ||||
0.992609 | − | 0.121353i | \(-0.0387234\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.22077 | 0.238381 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3.46801i | − 0.132700i | −0.997796 | − | 0.0663499i | \(-0.978865\pi\) | ||||
0.997796 | − | 0.0663499i | \(-0.0211354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 52.8406i | 2.01894i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.5332i | 0.440020i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 71.3234i | − 2.71720i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.57217 | −0.326101 | −0.163050 | − | 0.986618i | \(-0.552133\pi\) | ||||
−0.163050 | + | 0.986618i | \(0.552133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 52.4116i | − 1.98809i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.09902 | 0.117384 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.27693 | 0.350886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.08683 | −0.229896 | −0.114948 | − | 0.993371i | \(-0.536670\pi\) | ||||
−0.114948 | + | 0.993371i | \(0.536670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.834462 | 0.0314723 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 26.0013i | − 0.979266i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.8567 | −1.38418 | −0.692092 | − | 0.721810i | \(-0.743311\pi\) | ||||
−0.692092 | + | 0.721810i | \(0.743311\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 11.4936i | − 0.431042i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 3.24561i | − 0.121549i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 21.7986i | − 0.815220i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.55540i | 0.132779i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.5835 | −1.69998 | −0.849988 | − | 0.526802i | \(-0.823391\pi\) | ||||
−0.849988 | + | 0.526802i | \(0.823391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8.59044i | − 0.319482i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.8917 | −0.515926 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.02124 | 0.334579 | 0.167290 | − | 0.985908i | \(-0.446498\pi\) | ||||
0.167290 | + | 0.985908i | \(0.446498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.2021 | 0.784188 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.0705i | 1.14762i | 0.818990 | + | 0.573808i | \(0.194535\pi\) | ||||
−0.818990 | + | 0.573808i | \(0.805465\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0752578 | −0.00277216 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.7370i | 1.38818i | 0.719890 | + | 0.694089i | \(0.244192\pi\) | ||||
−0.719890 | + | 0.694089i | \(0.755808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 4.11907i | − 0.151318i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 43.6664i | − 1.60197i | −0.598687 | − | 0.800983i | \(-0.704311\pi\) | ||||
0.598687 | − | 0.800983i | \(-0.295689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 51.8726i | − 1.90047i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.95860 | 0.108250 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.8611i | 1.70999i | 0.518639 | + | 0.854993i | \(0.326439\pi\) | ||||
−0.518639 | + | 0.854993i | \(0.673561\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.6135 | 0.386778 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.52819 | 0.164798 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1824 | 0.733543 | 0.366771 | − | 0.930311i | \(-0.380463\pi\) | ||||
0.366771 | + | 0.930311i | \(0.380463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.921093 | −0.0334336 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 4.46892i | − 0.161998i | −0.996714 | − | 0.0809991i | \(-0.974189\pi\) | ||||
0.996714 | − | 0.0809991i | \(-0.0258111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.29130 | −0.191307 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.94476i | 0.178545i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.5449i | 0.921173i | 0.887615 | + | 0.460587i | \(0.152361\pi\) | ||||
−0.887615 | + | 0.460587i | \(0.847639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.8261i | 0.569962i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.1119i | 0.651442i | 0.945466 | + | 0.325721i | \(0.105607\pi\) | ||||
−0.945466 | + | 0.325721i | \(0.894393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.4422 | −0.411014 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.14382i | − 0.0409816i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.9307 | 0.713178 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.06459 | 0.216731 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.2560 | −0.758660 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.6272 | −1.59079 | −0.795394 | − | 0.606093i | \(-0.792736\pi\) | ||||
−0.795394 | + | 0.606093i | \(0.792736\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 0.437527i | − 0.0155764i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 77.5081 | 2.75239 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.8165i | 1.19935i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 24.9941i | − 0.885335i | −0.896686 | − | 0.442668i | \(-0.854032\pi\) | ||||
0.896686 | − | 0.442668i | \(-0.145968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 18.8709i | − 0.667604i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 8.24185i | − 0.291211i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.1835 | −0.782840 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 0.496114i | − 0.0174640i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.6868 | 0.938258 | 0.469129 | − | 0.883130i | \(-0.344568\pi\) | ||||
0.469129 | + | 0.883130i | \(0.344568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.1884 | −0.427994 | −0.213997 | − | 0.976834i | \(-0.568648\pi\) | ||||
−0.213997 | + | 0.976834i | \(0.568648\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.37679 | −0.118429 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.62549 | −0.337166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 7.82551i | − 0.273780i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.0914 | 0.561594 | 0.280797 | − | 0.959767i | \(-0.409401\pi\) | ||||
0.280797 | + | 0.959767i | \(0.409401\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 18.4743i | − 0.643973i | −0.946744 | − | 0.321986i | \(-0.895649\pi\) | ||||
0.946744 | − | 0.321986i | \(-0.104351\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.24724i | 0.113054i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.1954i | 1.74547i | 0.488198 | + | 0.872733i | \(0.337654\pi\) | ||||
−0.488198 | + | 0.872733i | \(0.662346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 20.4162i | − 0.709084i | −0.935040 | − | 0.354542i | \(-0.884637\pi\) | ||||
0.935040 | − | 0.354542i | \(-0.115363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.9336 | 0.379281 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.5916i | 1.02406i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.99520 | 0.172659 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.8855 | 0.721048 | 0.360524 | − | 0.932750i | \(-0.382598\pi\) | ||||
0.360524 | + | 0.932750i | \(0.382598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.77923 | 0.268249 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.4932 | −0.912475 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 52.4681i | − 1.80496i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.17861 | 0.0747696 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 0.749613i | − 0.0256964i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 23.6666i | − 0.810329i | −0.914244 | − | 0.405165i | \(-0.867214\pi\) | ||||
0.914244 | − | 0.405165i | \(-0.132786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.95297i | 0.0667902i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.13263i | 0.107009i | 0.998568 | + | 0.0535043i | \(0.0170391\pi\) | ||||
−0.998568 | + | 0.0535043i | \(0.982961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3010 | 0.624423 | 0.312211 | − | 0.950013i | \(-0.398930\pi\) | ||||
0.312211 | + | 0.950013i | \(0.398930\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.92199i | 0.167546i | 0.996485 | + | 0.0837732i | \(0.0266971\pi\) | ||||
−0.996485 | + | 0.0837732i | \(0.973303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −51.1310 | −1.73851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.1598 | 0.446929 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.2935 | −0.552719 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.302327 | −0.0102440 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.01880i | 0.0344812i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.7764 | −1.34316 | −0.671578 | − | 0.740934i | \(-0.734383\pi\) | ||||
−0.671578 | + | 0.740934i | \(0.734383\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.82696i | 0.230268i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.2750i | 0.716774i | 0.933573 | + | 0.358387i | \(0.116673\pi\) | ||||
−0.933573 | + | 0.358387i | \(0.883327\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 22.6054i | − 0.760733i | −0.924836 | − | 0.380366i | \(-0.875798\pi\) | ||||
0.924836 | − | 0.380366i | \(-0.124202\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.34446i | − 0.0788081i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.6324 | −1.06211 | −0.531057 | − | 0.847336i | \(-0.678205\pi\) | ||||
−0.531057 | + | 0.847336i | \(0.678205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.41762i | − 0.0474920i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.96508 | −0.233077 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.9475 | −0.533065 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.70023 | −0.123547 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.2938 | 1.01036 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.5429i | 0.817643i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −66.2343 | −2.20170 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 17.9573i | − 0.596264i | −0.954525 | − | 0.298132i | \(-0.903636\pi\) | ||||
0.954525 | − | 0.298132i | \(-0.0963635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.9466i | 0.396242i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.5199i | 1.27622i | 0.769945 | + | 0.638110i | \(0.220284\pi\) | ||||
−0.769945 | + | 0.638110i | \(0.779716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 4.19418i | − 0.138807i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36.7489 | −1.21488 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.77085i | 0.124389i | 0.998064 | + | 0.0621944i | \(0.0198099\pi\) | ||||
−0.998064 | + | 0.0621944i | \(0.980190\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.9855 | −0.427887 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80.0662 | 2.63541 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.64270 | −0.0868915 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.5903 | 0.577740 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 11.0167i | − 0.361448i | −0.983534 | − | 0.180724i | \(-0.942156\pi\) | ||||
0.983534 | − | 0.180724i | \(-0.0578440\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.7636 | −1.07263 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.50105i | 0.245310i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.09549i | 0.166462i | 0.996530 | + | 0.0832312i | \(0.0265240\pi\) | ||||
−0.996530 | + | 0.0832312i | \(0.973476\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.15065i | 0.298620i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 10.3499i | − 0.337397i | −0.985668 | − | 0.168698i | \(-0.946044\pi\) | ||||
0.985668 | − | 0.168698i | \(-0.0539563\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.02751 | −0.0334605 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.8596i | 1.52273i | 0.648321 | + | 0.761367i | \(0.275471\pi\) | ||||
−0.648321 | + | 0.761367i | \(0.724529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −89.1162 | −2.89284 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.5872 | 0.797296 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.3560 | 1.33965 | 0.669825 | − | 0.742519i | \(-0.266369\pi\) | ||||
0.669825 | + | 0.742519i | \(0.266369\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.2897 | 0.688920 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 8.59728i | − 0.277911i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.04797 | −0.195096 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 14.5752i | − 0.469678i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 29.0243i | − 0.934326i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.6169i | 0.759467i | 0.925096 | + | 0.379733i | \(0.123984\pi\) | ||||
−0.925096 | + | 0.379733i | \(0.876016\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.41740i | 0.0455335i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.3328 | 1.48689 | 0.743446 | − | 0.668796i | \(-0.233190\pi\) | ||||
0.743446 | + | 0.668796i | \(0.233190\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.0449i | 0.417771i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.3404 | −0.394804 | −0.197402 | − | 0.980323i | \(-0.563250\pi\) | ||||
−0.197402 | + | 0.980323i | \(0.563250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.6838 | −0.373416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.41674 | 0.172943 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.1901 | −0.612069 | −0.306034 | − | 0.952020i | \(-0.599002\pi\) | ||||
−0.306034 | + | 0.952020i | \(0.599002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.8079i | 0.535545i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.02980 | −0.223535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.99448i | 0.317485i | 0.987320 | + | 0.158743i | \(0.0507440\pi\) | ||||
−0.987320 | + | 0.158743i | \(0.949256\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 20.2118i | − 0.641401i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.5625i | 0.366556i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.5449i | − 1.22073i | −0.792120 | − | 0.610365i | \(-0.791023\pi\) | ||||
0.792120 | − | 0.610365i | \(-0.208977\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.15370 | 0.0365015 |
(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 | 4704.2.b.e.1567.14 | 16 | ||
4.3 | odd | 2 | 4704.2.b.d.1567.14 | 16 | |||
7.2 | even | 3 | 672.2.bl.a.31.7 | ✓ | 16 | ||
7.3 | odd | 6 | 672.2.bl.b.607.7 | yes | 16 | ||
7.6 | odd | 2 | 4704.2.b.d.1567.3 | 16 | |||
21.2 | odd | 6 | 2016.2.cs.a.703.2 | 16 | |||
21.17 | even | 6 | 2016.2.cs.c.1279.2 | 16 | |||
28.3 | even | 6 | 672.2.bl.a.607.7 | yes | 16 | ||
28.23 | odd | 6 | 672.2.bl.b.31.7 | yes | 16 | ||
28.27 | even | 2 | inner | 4704.2.b.e.1567.3 | 16 | ||
56.3 | even | 6 | 1344.2.bl.l.1279.2 | 16 | |||
56.37 | even | 6 | 1344.2.bl.l.703.2 | 16 | |||
56.45 | odd | 6 | 1344.2.bl.k.1279.2 | 16 | |||
56.51 | odd | 6 | 1344.2.bl.k.703.2 | 16 | |||
84.23 | even | 6 | 2016.2.cs.c.703.2 | 16 | |||
84.59 | odd | 6 | 2016.2.cs.a.1279.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.bl.a.31.7 | ✓ | 16 | 7.2 | even | 3 | ||
672.2.bl.a.607.7 | yes | 16 | 28.3 | even | 6 | ||
672.2.bl.b.31.7 | yes | 16 | 28.23 | odd | 6 | ||
672.2.bl.b.607.7 | yes | 16 | 7.3 | odd | 6 | ||
1344.2.bl.k.703.2 | 16 | 56.51 | odd | 6 | |||
1344.2.bl.k.1279.2 | 16 | 56.45 | odd | 6 | |||
1344.2.bl.l.703.2 | 16 | 56.37 | even | 6 | |||
1344.2.bl.l.1279.2 | 16 | 56.3 | even | 6 | |||
2016.2.cs.a.703.2 | 16 | 21.2 | odd | 6 | |||
2016.2.cs.a.1279.2 | 16 | 84.59 | odd | 6 | |||
2016.2.cs.c.703.2 | 16 | 84.23 | even | 6 | |||
2016.2.cs.c.1279.2 | 16 | 21.17 | even | 6 | |||
4704.2.b.d.1567.3 | 16 | 7.6 | odd | 2 | |||
4704.2.b.d.1567.14 | 16 | 4.3 | odd | 2 | |||
4704.2.b.e.1567.3 | 16 | 28.27 | even | 2 | inner | ||
4704.2.b.e.1567.14 | 16 | 1.1 | even | 1 | trivial |