Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(657,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.657");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.x (of order \(4\), degree \(2\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 657.2 | ||
Character | \(\chi\) | \(=\) | 1400.657 |
Dual form | 1400.2.x.b.993.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −2.16341 | − | 2.16341i | −1.24904 | − | 1.24904i | −0.956143 | − | 0.292900i | \(-0.905380\pi\) |
−0.292900 | − | 0.956143i | \(-0.594620\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61380 | + | 0.409966i | 0.987922 | + | 0.154953i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.36066i | 2.12022i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.796216 | 0.240068 | 0.120034 | − | 0.992770i | \(-0.461700\pi\) | ||||
0.120034 | + | 0.992770i | \(0.461700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.25130 | − | 3.25130i | −0.901750 | − | 0.901750i | 0.0938379 | − | 0.995587i | \(-0.470086\pi\) |
−0.995587 | + | 0.0938379i | \(0.970086\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.52106 | + | 2.52106i | −0.611447 | + | 0.611447i | −0.943323 | − | 0.331876i | \(-0.892318\pi\) |
0.331876 | + | 0.943323i | \(0.392318\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.29803 | 0.527203 | 0.263602 | − | 0.964632i | \(-0.415090\pi\) | ||||
0.263602 | + | 0.964632i | \(0.415090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.76778 | − | 6.54163i | −1.04041 | − | 1.42750i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.08441 | − | 2.08441i | 0.434630 | − | 0.434630i | −0.455570 | − | 0.890200i | \(-0.650565\pi\) |
0.890200 | + | 0.455570i | \(0.150565\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.27046 | − | 7.27046i | 1.39920 | − | 1.39920i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 10.0797i | − | 1.87176i | −0.352319 | − | 0.935880i | \(-0.614607\pi\) | ||
0.352319 | − | 0.935880i | \(-0.385393\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.63347i | − | 0.652590i | −0.945268 | − | 0.326295i | \(-0.894200\pi\) | ||
0.945268 | − | 0.326295i | \(-0.105800\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.72254 | − | 1.72254i | −0.299856 | − | 0.299856i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.30001 | − | 7.30001i | −1.20011 | − | 1.20011i | −0.974131 | − | 0.225982i | \(-0.927441\pi\) |
−0.225982 | − | 0.974131i | \(-0.572559\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.0678i | 2.25265i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.81026i | 0.438889i | 0.975625 | + | 0.219444i | \(0.0704245\pi\) | ||||
−0.975625 | + | 0.219444i | \(0.929576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.33689 | + | 2.33689i | −0.356373 | + | 0.356373i | −0.862474 | − | 0.506101i | \(-0.831086\pi\) |
0.506101 | + | 0.862474i | \(0.331086\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.09923 | − | 4.09923i | 0.597934 | − | 0.597934i | −0.341829 | − | 0.939762i | \(-0.611046\pi\) |
0.939762 | + | 0.341829i | \(0.111046\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.66386 | + | 2.14314i | 0.951979 | + | 0.306162i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.9082 | 1.52745 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.50379 | + | 6.50379i | −0.893364 | + | 0.893364i | −0.994838 | − | 0.101474i | \(-0.967644\pi\) |
0.101474 | + | 0.994838i | \(0.467644\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.97156 | − | 4.97156i | −0.658500 | − | 0.658500i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.4005 | −1.48422 | −0.742112 | − | 0.670276i | \(-0.766176\pi\) | ||||
−0.742112 | + | 0.670276i | \(0.766176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.35941i | − | 0.430128i | −0.976600 | − | 0.215064i | \(-0.931004\pi\) | ||
0.976600 | − | 0.215064i | \(-0.0689960\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.60765 | + | 16.6255i | −0.328533 | + | 2.09461i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.49153 | + | 2.49153i | 0.304389 | + | 0.304389i | 0.842728 | − | 0.538339i | \(-0.180948\pi\) |
−0.538339 | + | 0.842728i | \(0.680948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.01885 | −1.08574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.93777 | −0.348650 | −0.174325 | − | 0.984688i | \(-0.555774\pi\) | ||||
−0.174325 | + | 0.984688i | \(0.555774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.93694 | − | 4.93694i | −0.577826 | − | 0.577826i | 0.356478 | − | 0.934304i | \(-0.383977\pi\) |
−0.934304 | + | 0.356478i | \(0.883977\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.08115 | + | 0.326422i | 0.237169 | + | 0.0371992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.53223i | − | 0.734933i | −0.930037 | − | 0.367467i | \(-0.880225\pi\) | ||
0.930037 | − | 0.367467i | \(-0.119775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.3760 | −1.37511 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.14828 | − | 1.14828i | −0.126040 | − | 0.126040i | 0.641273 | − | 0.767313i | \(-0.278407\pi\) |
−0.767313 | + | 0.641273i | \(0.778407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.8066 | + | 21.8066i | −2.33791 | + | 2.33791i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0949 | −1.49405 | −0.747026 | − | 0.664795i | \(-0.768519\pi\) | ||||
−0.747026 | + | 0.664795i | \(0.768519\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.16532 | − | 9.83117i | −0.751130 | − | 1.03059i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.86067 | + | 7.86067i | −0.815114 | + | 0.815114i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.30685 | + | 4.30685i | −0.437295 | + | 0.437295i | −0.891101 | − | 0.453806i | \(-0.850066\pi\) |
0.453806 | + | 0.891101i | \(0.350066\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.06446i | 0.508997i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6450i | 1.15872i | 0.815072 | + | 0.579360i | \(0.196697\pi\) | ||||
−0.815072 | + | 0.579360i | \(0.803303\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.54280 | + | 3.54280i | 0.349082 | + | 0.349082i | 0.859768 | − | 0.510685i | \(-0.170608\pi\) |
−0.510685 | + | 0.859768i | \(0.670608\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.21284 | + | 9.21284i | 0.890639 | + | 0.890639i | 0.994583 | − | 0.103944i | \(-0.0331462\pi\) |
−0.103944 | + | 0.994583i | \(0.533146\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.01531i | − | 0.576162i | −0.957606 | − | 0.288081i | \(-0.906983\pi\) | ||
0.957606 | − | 0.288081i | \(-0.0930173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.5858i | 2.99799i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.56399 | + | 3.56399i | −0.335272 | + | 0.335272i | −0.854585 | − | 0.519312i | \(-0.826188\pi\) |
0.519312 | + | 0.854585i | \(0.326188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.6804 | − | 20.6804i | 1.91191 | − | 1.91191i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.62309 | + | 5.55599i | −0.698807 | + | 0.509317i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3660 | −0.942367 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.07973 | − | 6.07973i | 0.548191 | − | 0.548191i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2615 | − | 14.2615i | −1.26551 | − | 1.26551i | −0.948384 | − | 0.317123i | \(-0.897283\pi\) |
−0.317123 | − | 0.948384i | \(-0.602717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.1113 | 0.890250 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.24139i | − | 0.720054i | −0.932942 | − | 0.360027i | \(-0.882768\pi\) | ||
0.932942 | − | 0.360027i | \(-0.117232\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00657 | + | 0.942113i | 0.520836 | + | 0.0816915i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.79622 | − | 5.79622i | −0.495204 | − | 0.495204i | 0.414737 | − | 0.909941i | \(-0.363874\pi\) |
−0.909941 | + | 0.414737i | \(0.863874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.89813 | −0.669911 | −0.334955 | − | 0.942234i | \(-0.608721\pi\) | ||||
−0.334955 | + | 0.942234i | \(0.608721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.7366 | −1.49369 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.58874 | − | 2.58874i | −0.216481 | − | 0.216481i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.78015 | − | 19.0531i | −0.806654 | − | 1.57147i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.09736i | 0.417592i | 0.977959 | + | 0.208796i | \(0.0669545\pi\) | ||||
−0.977959 | + | 0.208796i | \(0.933045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.4201 | 1.09211 | 0.546057 | − | 0.837748i | \(-0.316128\pi\) | ||||
0.546057 | + | 0.837748i | \(0.316128\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.0356 | − | 16.0356i | −1.29640 | − | 1.29640i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.73434 | + | 2.73434i | −0.218224 | + | 0.218224i | −0.807750 | − | 0.589525i | \(-0.799315\pi\) |
0.589525 | + | 0.807750i | \(0.299315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.1407 | 2.23170 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.30276 | − | 4.59368i | 0.496727 | − | 0.362033i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.4971 | − | 15.4971i | 1.21383 | − | 1.21383i | 0.244068 | − | 0.969758i | \(-0.421518\pi\) |
0.969758 | − | 0.244068i | \(-0.0784820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.74279 | − | 4.74279i | 0.367008 | − | 0.367008i | −0.499377 | − | 0.866385i | \(-0.666438\pi\) |
0.866385 | + | 0.499377i | \(0.166438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.14196i | 0.626305i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6169i | 1.11779i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5915 | + | 10.5915i | 0.805253 | + | 0.805253i | 0.983911 | − | 0.178658i | \(-0.0571756\pi\) |
−0.178658 | + | 0.983911i | \(0.557176\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.6640 | + | 24.6640i | 1.85386 | + | 1.85386i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.0880i | − | 1.35196i | −0.736918 | − | 0.675982i | \(-0.763720\pi\) | ||
0.736918 | − | 0.675982i | \(-0.236280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.0287i | − | 1.04274i | −0.853329 | − | 0.521372i | \(-0.825420\pi\) | ||
0.853329 | − | 0.521372i | \(-0.174580\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.26776 | + | 7.26776i | −0.537248 | + | 0.537248i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00731 | + | 2.00731i | −0.146789 | + | 0.146789i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.9841 | − | 16.0229i | 1.59911 | − | 1.16549i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.39084 | 0.390068 | 0.195034 | − | 0.980796i | \(-0.437518\pi\) | ||||
0.195034 | + | 0.980796i | \(0.437518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.66005 | − | 3.66005i | 0.263456 | − | 0.263456i | −0.563000 | − | 0.826457i | \(-0.690353\pi\) |
0.826457 | + | 0.563000i | \(0.190353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.16340 | + | 9.16340i | 0.652865 | + | 0.652865i | 0.953682 | − | 0.300817i | \(-0.0972593\pi\) |
−0.300817 | + | 0.953682i | \(0.597259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9276 | −1.12908 | −0.564539 | − | 0.825406i | \(-0.690946\pi\) | ||||
−0.564539 | + | 0.825406i | \(0.690946\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 10.7804i | − | 0.760391i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.13235 | − | 26.3464i | 0.290034 | − | 1.84915i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.2582 | + | 13.2582i | 0.921510 | + | 0.921510i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.82972 | 0.126565 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.20382 | 0.289403 | 0.144701 | − | 0.989475i | \(-0.453778\pi\) | ||||
0.144701 | + | 0.989475i | \(0.453778\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.35560 | + | 6.35560i | 0.435479 | + | 0.435479i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.48960 | − | 9.49715i | 0.101121 | − | 0.644708i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.3612i | 1.44346i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3935 | 1.10274 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.79408 | + | 8.79408i | 0.588895 | + | 0.588895i | 0.937332 | − | 0.348437i | \(-0.113288\pi\) |
−0.348437 | + | 0.937332i | \(0.613288\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9267 | + | 12.9267i | −0.857973 | + | 0.857973i | −0.991099 | − | 0.133126i | \(-0.957498\pi\) |
0.133126 | + | 0.991099i | \(0.457498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.2917 | 1.01050 | 0.505252 | − | 0.862972i | \(-0.331400\pi\) | ||||
0.505252 | + | 0.862972i | \(0.331400\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.79618 | − | 5.20855i | −0.249770 | − | 0.342697i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.89086 | − | 6.89086i | 0.451435 | − | 0.451435i | −0.444395 | − | 0.895831i | \(-0.646581\pi\) |
0.895831 | + | 0.444395i | \(0.146581\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.1319 | + | 14.1319i | −0.917963 | + | 0.917963i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.40870i | 0.285175i | 0.989782 | + | 0.142588i | \(0.0455423\pi\) | ||||
−0.989782 | + | 0.142588i | \(0.954458\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.82692i | − | 0.633008i | −0.948591 | − | 0.316504i | \(-0.897491\pi\) | ||
0.948591 | − | 0.316504i | \(-0.102509\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.96286 | + | 4.96286i | 0.318368 | + | 0.318368i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.47158 | − | 7.47158i | −0.475405 | − | 0.475405i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.96840i | 0.314860i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.723170i | 0.0456461i | 0.999740 | + | 0.0228230i | \(0.00726543\pi\) | ||||
−0.999740 | + | 0.0228230i | \(0.992735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.65964 | − | 1.65964i | 0.104341 | − | 0.104341i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.32060 | − | 6.32060i | 0.394268 | − | 0.394268i | −0.481938 | − | 0.876206i | \(-0.660067\pi\) |
0.876206 | + | 0.481938i | \(0.160067\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0880 | − | 22.0735i | −0.999658 | − | 1.37158i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 64.1137 | 3.96854 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.22755 | + | 6.22755i | −0.384007 | + | 0.384007i | −0.872543 | − | 0.488537i | \(-0.837531\pi\) |
0.488537 | + | 0.872543i | \(0.337531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.4929 | + | 30.4929i | 1.86613 | + | 1.86613i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.12088 | −0.190283 | −0.0951417 | − | 0.995464i | \(-0.530330\pi\) | ||||
−0.0951417 | + | 0.995464i | \(0.530330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.17480i | − | 0.314347i | −0.987571 | − | 0.157173i | \(-0.949762\pi\) | ||
0.987571 | − | 0.157173i | \(-0.0502382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.76732 | + | 36.7703i | −0.349054 | + | 2.22544i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9267 | − | 18.9267i | −1.13719 | − | 1.13719i | −0.988951 | − | 0.148242i | \(-0.952638\pi\) |
−0.148242 | − | 0.988951i | \(-0.547362\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.1112 | 1.38363 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2646 | −0.612333 | −0.306166 | − | 0.951978i | \(-0.599046\pi\) | ||||
−0.306166 | + | 0.951978i | \(0.599046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.3112 | − | 23.3112i | −1.38571 | − | 1.38571i | −0.834110 | − | 0.551598i | \(-0.814018\pi\) |
−0.551598 | − | 0.834110i | \(-0.685982\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.15211 | + | 7.34545i | −0.0680070 | + | 0.433588i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.28850i | 0.252265i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.6349 | 1.09240 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.53673 | + | 7.53673i | 0.440301 | + | 0.440301i | 0.892113 | − | 0.451812i | \(-0.149222\pi\) |
−0.451812 | + | 0.892113i | \(0.649222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.78886 | − | 5.78886i | 0.335904 | − | 0.335904i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.5541 | −0.783854 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.06621 | + | 5.15011i | −0.407289 | + | 0.296848i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.1929 | − | 25.1929i | 1.44729 | − | 1.44729i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.09625 | − | 5.09625i | 0.290858 | − | 0.290858i | −0.546561 | − | 0.837419i | \(-0.684063\pi\) |
0.837419 | + | 0.546561i | \(0.184063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 15.3290i | − | 0.872038i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.88013i | − | 0.503546i | −0.967786 | − | 0.251773i | \(-0.918986\pi\) | ||
0.967786 | − | 0.251773i | \(-0.0810136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.50060 | + | 6.50060i | 0.367436 | + | 0.367436i | 0.866541 | − | 0.499105i | \(-0.166338\pi\) |
−0.499105 | + | 0.866541i | \(0.666338\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.87753 | − | 3.87753i | −0.217784 | − | 0.217784i | 0.589780 | − | 0.807564i | \(-0.299214\pi\) |
−0.807564 | + | 0.589780i | \(0.799214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.02565i | − | 0.449350i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 39.8623i | − | 2.22489i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.79346 | + | 5.79346i | −0.322357 | + | 0.322357i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.0136 | + | 13.0136i | −0.719652 | + | 0.719652i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.3951 | − | 9.03400i | 0.683363 | − | 0.498060i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.56299 | 0.360735 | 0.180367 | − | 0.983599i | \(-0.442271\pi\) | ||||
0.180367 | + | 0.983599i | \(0.442271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 46.4328 | − | 46.4328i | 2.54450 | − | 2.54450i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.62582 | − | 3.62582i | −0.197511 | − | 0.197511i | 0.601421 | − | 0.798932i | \(-0.294601\pi\) |
−0.798932 | + | 0.601421i | \(0.794601\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.4207 | 0.837540 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.89303i | − | 0.156666i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.5393 | + | 8.33367i | 0.893041 | + | 0.449976i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.698071 | + | 0.698071i | 0.0374744 | + | 0.0374744i | 0.725596 | − | 0.688121i | \(-0.241564\pi\) |
−0.688121 | + | 0.725596i | \(0.741564\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.36446 | 0.0730378 | 0.0365189 | − | 0.999333i | \(-0.488373\pi\) | ||||
0.0365189 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −47.2770 | −2.52346 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.57760 | − | 8.57760i | −0.456539 | − | 0.456539i | 0.440978 | − | 0.897518i | \(-0.354632\pi\) |
−0.897518 | + | 0.440978i | \(0.854632\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.5117 | + | 4.47198i | 1.50900 | + | 0.236682i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.0825i | 1.05992i | 0.848024 | + | 0.529958i | \(0.177792\pi\) | ||||
−0.848024 | + | 0.529958i | \(0.822208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7191 | −0.722057 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.4260 | + | 22.4260i | 1.17706 | + | 1.17706i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.7210 | − | 18.7210i | 0.977228 | − | 0.977228i | −0.0225182 | − | 0.999746i | \(-0.507168\pi\) |
0.999746 | + | 0.0225182i | \(0.00716838\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.8751 | −0.930540 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.6659 | + | 14.3332i | −1.02100 | + | 0.744145i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2070 | − | 14.2070i | 0.735612 | − | 0.735612i | −0.236113 | − | 0.971726i | \(-0.575874\pi\) |
0.971726 | + | 0.236113i | \(0.0758736\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −32.7723 | + | 32.7723i | −1.68786 | + | 1.68786i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 32.8094i | − | 1.68530i | −0.538459 | − | 0.842652i | \(-0.680993\pi\) | ||
0.538459 | − | 0.842652i | \(-0.319007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 61.7070i | 3.16135i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.07047 | − | 4.07047i | −0.207991 | − | 0.207991i | 0.595422 | − | 0.803413i | \(-0.296985\pi\) |
−0.803413 | + | 0.595422i | \(0.796985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.8642 | − | 14.8642i | −0.755588 | − | 0.755588i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.60774i | − | 0.385728i | −0.981226 | − | 0.192864i | \(-0.938222\pi\) | ||
0.981226 | − | 0.192864i | \(-0.0617776\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5099i | 0.531506i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.8295 | + | 17.8295i | −0.899378 | + | 0.899378i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7106 | + | 18.7106i | −0.939059 | + | 0.939059i | −0.998247 | − | 0.0591880i | \(-0.981149\pi\) |
0.0591880 | + | 0.998247i | \(0.481149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.9565 | − | 15.0328i | −0.548510 | − | 0.752582i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.07435 | 0.203463 | 0.101732 | − | 0.994812i | \(-0.467562\pi\) | ||||
0.101732 | + | 0.994812i | \(0.467562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.8135 | + | 11.8135i | −0.588473 | + | 0.588473i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.81238 | − | 5.81238i | −0.288109 | − | 0.288109i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.30032 | −0.360978 | −0.180489 | − | 0.983577i | \(-0.557768\pi\) | ||||
−0.180489 | + | 0.983577i | \(0.557768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.0791i | 1.23706i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −29.7987 | − | 4.67383i | −1.46630 | − | 0.229984i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.0869 | + | 17.0869i | 0.836748 | + | 0.836748i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.4444 | 1.87813 | 0.939066 | − | 0.343737i | \(-0.111693\pi\) | ||||
0.939066 | + | 0.343737i | \(0.111693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.4603 | −0.899698 | −0.449849 | − | 0.893105i | \(-0.648522\pi\) | ||||
−0.449849 | + | 0.893105i | \(0.648522\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.0738 | + | 26.0738i | 1.26775 | + | 1.26775i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.37724 | − | 8.78080i | 0.0666495 | − | 0.424933i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.2010i | 0.540789i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3985 | 0.886227 | 0.443113 | − | 0.896466i | \(-0.353874\pi\) | ||||
0.443113 | + | 0.896466i | \(0.353874\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6373 | + | 13.6373i | 0.655368 | + | 0.655368i | 0.954280 | − | 0.298913i | \(-0.0966240\pi\) |
−0.298913 | + | 0.954280i | \(0.596624\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.79003 | − | 4.79003i | 0.229138 | − | 0.229138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8974 | 0.663285 | 0.331642 | − | 0.943405i | \(-0.392397\pi\) | ||||
0.331642 | + | 0.943405i | \(0.392397\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.6317 | + | 42.3865i | −0.649131 | + | 2.01840i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.8725 | + | 18.8725i | −0.896659 | + | 0.896659i | −0.995139 | − | 0.0984802i | \(-0.968602\pi\) |
0.0984802 | + | 0.995139i | \(0.468602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.0277 | − | 11.0277i | 0.521591 | − | 0.521591i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.54414i | − | 0.261644i | −0.991406 | − | 0.130822i | \(-0.958238\pi\) | ||
0.991406 | − | 0.130822i | \(-0.0417617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.23757i | 0.105363i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.0332 | − | 29.0332i | −1.36410 | − | 1.36410i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7321 | + | 20.7321i | 0.969806 | + | 0.969806i | 0.999557 | − | 0.0297514i | \(-0.00947155\pi\) |
−0.0297514 | + | 0.999557i | \(0.509472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.6586i | 1.71108i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0221i | 0.885950i | 0.896534 | + | 0.442975i | \(0.146077\pi\) | ||||
−0.896534 | + | 0.442975i | \(0.853923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5483 | − | 14.5483i | 0.676115 | − | 0.676115i | −0.283004 | − | 0.959119i | \(-0.591331\pi\) |
0.959119 | + | 0.283004i | \(0.0913309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.09112 | + | 6.09112i | −0.281863 | + | 0.281863i | −0.833852 | − | 0.551989i | \(-0.813869\pi\) |
0.551989 | + | 0.833852i | \(0.313869\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.49092 | + | 7.53381i | 0.253547 | + | 0.347879i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8310 | 0.545143 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.86067 | + | 1.86067i | −0.0855538 | + | 0.0855538i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −41.3684 | − | 41.3684i | −1.89413 | − | 1.89413i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.2499 | −0.788169 | −0.394085 | − | 0.919074i | \(-0.628938\pi\) | ||||
−0.394085 | + | 0.919074i | \(0.628938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.4691i | 2.16440i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.5734 | − | 3.69742i | −1.07263 | − | 0.168239i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.7915 | + | 19.7915i | 0.896839 | + | 0.896839i | 0.995155 | − | 0.0983164i | \(-0.0313457\pi\) |
−0.0983164 | + | 0.995155i | \(0.531346\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −67.0530 | −3.03224 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.8114 | 1.75153 | 0.875767 | − | 0.482735i | \(-0.160357\pi\) | ||||
0.875767 | + | 0.482735i | \(0.160357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.4116 | + | 25.4116i | 1.14448 | + | 1.14448i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.67874 | − | 1.20439i | −0.344439 | − | 0.0540242i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.21748i | − | 0.367865i | −0.982939 | − | 0.183932i | \(-0.941117\pi\) | ||
0.982939 | − | 0.183932i | \(-0.0588828\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.5212 | −0.916818 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.7880 | − | 13.7880i | −0.614775 | − | 0.614775i | 0.329411 | − | 0.944187i | \(-0.393150\pi\) |
−0.944187 | + | 0.329411i | \(0.893150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.6144 | − | 17.6144i | 0.782282 | − | 0.782282i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.30389 | −0.146442 | −0.0732212 | − | 0.997316i | \(-0.523328\pi\) | ||||
−0.0732212 | + | 0.997316i | \(0.523328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.8802 | − | 14.9281i | −0.481311 | − | 0.660382i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.7077 | − | 16.7077i | 0.737663 | − | 0.737663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.26387 | − | 3.26387i | 0.143545 | − | 0.143545i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 45.8272i | − | 2.01159i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17.8887i | − | 0.783717i | −0.920025 | − | 0.391859i | \(-0.871832\pi\) | ||
0.920025 | − | 0.391859i | \(-0.128168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.57838 | + | 8.57838i | 0.375106 | + | 0.375106i | 0.869333 | − | 0.494227i | \(-0.164549\pi\) |
−0.494227 | + | 0.869333i | \(0.664549\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.16020 | + | 9.16020i | 0.399025 | + | 0.399025i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.3105i | 0.622194i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 72.5149i | − | 3.14688i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.13701 | − | 9.13701i | 0.395768 | − | 0.395768i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −39.1318 | + | 39.1318i | −1.68866 | + | 1.68866i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.30587 | + | 1.70640i | 0.228540 | + | 0.0734998i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.47422 | 0.407328 | 0.203664 | − | 0.979041i | \(-0.434715\pi\) | ||||
0.203664 | + | 0.979041i | \(0.434715\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.3498 | + | 30.3498i | −1.30243 | + | 1.30243i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.34561 | − | 7.34561i | −0.314076 | − | 0.314076i | 0.532411 | − | 0.846486i | \(-0.321286\pi\) |
−0.846486 | + | 0.532411i | \(0.821286\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.3680 | 0.911965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.1635i | − | 0.986798i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.67799 | − | 17.0739i | 0.113880 | − | 0.726056i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.79776 | − | 8.79776i | −0.372773 | − | 0.372773i | 0.495713 | − | 0.868486i | \(-0.334907\pi\) |
−0.868486 | + | 0.495713i | \(0.834907\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.1959 | 0.642718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.68525 | 0.366692 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.78671 | + | 2.78671i | 0.117446 | + | 0.117446i | 0.763387 | − | 0.645941i | \(-0.223535\pi\) |
−0.645941 | + | 0.763387i | \(0.723535\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −32.3483 | − | 5.07373i | −1.35850 | − | 0.213077i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 0.247978i | − | 0.0103958i | −0.999986 | − | 0.00519788i | \(-0.998345\pi\) | ||
0.999986 | − | 0.00519788i | \(-0.00165455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.7125 | −1.66192 | −0.830959 | − | 0.556334i | \(-0.812208\pi\) | ||||
−0.830959 | + | 0.556334i | \(0.812208\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.6626 | − | 11.6626i | −0.487212 | − | 0.487212i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2036 | − | 28.2036i | 1.17413 | − | 1.17413i | 0.192916 | − | 0.981215i | \(-0.438205\pi\) |
0.981215 | − | 0.192916i | \(-0.0617945\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.8364 | −0.658136 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.53062 | − | 3.47213i | −0.104988 | − | 0.144048i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.17842 | + | 5.17842i | −0.214468 | + | 0.214468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.6383 | + | 24.6383i | −1.01693 | + | 1.01693i | −0.0170778 | + | 0.999854i | \(0.505436\pi\) |
−0.999854 | + | 0.0170778i | \(0.994564\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.34981i | − | 0.344048i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 39.6483i | − | 1.63091i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.6964 | + | 29.6964i | 1.21948 | + | 1.21948i | 0.967813 | + | 0.251670i | \(0.0809798\pi\) |
0.251670 | + | 0.967813i | \(0.419020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.4579 | + | 34.4579i | 1.41027 | + | 1.41027i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.4830i | 1.16378i | 0.813267 | + | 0.581891i | \(0.197687\pi\) | ||||
−0.813267 | + | 0.581891i | \(0.802313\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11.7809i | − | 0.480555i | −0.970704 | − | 0.240277i | \(-0.922762\pi\) | ||
0.970704 | − | 0.240277i | \(-0.0772384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.8478 | + | 15.8478i | −0.645372 | + | 0.645372i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.0405 | − | 28.0405i | 1.13813 | − | 1.13813i | 0.149344 | − | 0.988785i | \(-0.452284\pi\) |
0.988785 | − | 0.149344i | \(-0.0477161\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −65.9379 | + | 48.0579i | −2.67194 | + | 1.94741i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.6557 | −1.07837 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.8251 | + | 28.8251i | −1.16423 | + | 1.16423i | −0.180695 | + | 0.983539i | \(0.557835\pi\) |
−0.983539 | + | 0.180695i | \(0.942165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.96881 | − | 6.96881i | −0.280554 | − | 0.280554i | 0.552776 | − | 0.833330i | \(-0.313568\pi\) |
−0.833330 | + | 0.552776i | \(0.813568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.2636 | 0.814464 | 0.407232 | − | 0.913325i | \(-0.366494\pi\) | ||||
0.407232 | + | 0.913325i | \(0.366494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 30.3093i | − | 1.21627i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.8411 | − | 5.77841i | −1.47601 | − | 0.231507i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.95844 | − | 3.95844i | −0.158085 | − | 0.158085i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.8075 | 1.46761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.95896 | 0.117794 | 0.0588972 | − | 0.998264i | \(-0.481242\pi\) | ||||
0.0588972 | + | 0.998264i | \(0.481242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.09457 | − | 9.09457i | −0.361477 | − | 0.361477i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.6982 | − | 28.6342i | −0.582365 | − | 1.13453i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 18.6862i | − | 0.739213i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.8186 | 0.940776 | 0.470388 | − | 0.882460i | \(-0.344114\pi\) | ||||
0.470388 | + | 0.882460i | \(0.344114\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3400 | + | 25.3400i | 0.999312 | + | 0.999312i | 1.00000 | 0.000687568i | \(-0.000218860\pi\) | |
−0.000687568 | 1.00000i | \(0.500219\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.4265 | − | 16.4265i | 0.645792 | − | 0.645792i | −0.306181 | − | 0.951973i | \(-0.599051\pi\) |
0.951973 | + | 0.306181i | \(0.0990513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.07729 | −0.356315 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.7688 | + | 17.3236i | −0.931573 | + | 0.678965i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.4103 | − | 22.4103i | 0.876984 | − | 0.876984i | −0.116237 | − | 0.993221i | \(-0.537083\pi\) |
0.993221 | + | 0.116237i | \(0.0370833\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.4022 | − | 31.4022i | 1.22512 | − | 1.22512i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.0537i | 1.75504i | 0.479537 | + | 0.877521i | \(0.340805\pi\) | ||||
−0.479537 | + | 0.877521i | \(0.659195\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 28.5466i | − | 1.11033i | −0.831739 | − | 0.555167i | \(-0.812655\pi\) | ||
0.831739 | − | 0.555167i | \(-0.187345\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.4658 | − | 35.4658i | −1.37738 | − | 1.37738i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.0103 | − | 21.0103i | −0.813522 | − | 0.813522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 38.0503i | − | 1.47111i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.67481i | − | 0.103260i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.86064 | + | 1.86064i | −0.0717223 | + | 0.0717223i | −0.742058 | − | 0.670336i | \(-0.766150\pi\) |
0.670336 | + | 0.742058i | \(0.266150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.24734 | − | 2.24734i | 0.0863723 | − | 0.0863723i | −0.662601 | − | 0.748973i | \(-0.730547\pi\) |
0.748973 | + | 0.662601i | \(0.230547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0229 | + | 9.49157i | −0.499773 | + | 0.364253i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 55.9313 | 2.14329 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.1882 | − | 23.1882i | 0.887271 | − | 0.887271i | −0.106989 | − | 0.994260i | \(-0.534121\pi\) |
0.994260 | + | 0.106989i | \(0.0341210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.0821 | − | 33.0821i | −1.26216 | − | 1.26216i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.2916 | 1.61118 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 26.5659i | − | 1.01061i | −0.862940 | − | 0.505307i | \(-0.831379\pi\) | ||
0.862940 | − | 0.505307i | \(-0.168621\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.07626 | + | 13.2375i | −0.0788704 | + | 0.502849i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.08484 | − | 7.08484i | −0.268357 | − | 0.268357i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.8155 | −1.12772 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.7343 | 0.934201 | 0.467100 | − | 0.884204i | \(-0.345299\pi\) | ||||
0.467100 | + | 0.884204i | \(0.345299\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.7756 | − | 16.7756i | −0.632704 | − | 0.632704i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.77405 | + | 30.4376i | −0.179547 | + | 1.14473i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.16805i | − | 0.0814230i | −0.999171 | − | 0.0407115i | \(-0.987038\pi\) | ||
0.999171 | − | 0.0407115i | \(-0.0129625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.5492 | 1.55822 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.57364 | − | 7.57364i | −0.283635 | − | 0.283635i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.53781 | − | 9.53781i | 0.356196 | − | 0.356196i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.9675 | −1.49054 | −0.745269 | − | 0.666764i | \(-0.767679\pi\) | ||||
−0.745269 | + | 0.666764i | \(0.767679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.80772 | + | 10.7126i | 0.290775 | + | 0.398957i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.2596 | + | 21.2596i | −0.790654 | + | 0.790654i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.2654 | − | 10.2654i | 0.380722 | − | 0.380722i | −0.490641 | − | 0.871362i | \(-0.663237\pi\) |
0.871362 | + | 0.490641i | \(0.163237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.6545i | 0.579798i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.7829i | − | 0.435806i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.1656 | − | 34.1656i | −1.26194 | − | 1.26194i | −0.950154 | − | 0.311781i | \(-0.899074\pi\) |
−0.311781 | − | 0.950154i | \(-0.600926\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.98380 | + | 1.98380i | 0.0730742 | + | 0.0730742i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.7193i | 1.01967i | 0.860272 | + | 0.509835i | \(0.170293\pi\) | ||||
−0.860272 | + | 0.509835i | \(0.829707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.3281i | 1.18760i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.8434 | + | 18.8434i | −0.691299 | + | 0.691299i | −0.962518 | − | 0.271219i | \(-0.912573\pi\) |
0.271219 | + | 0.962518i | \(0.412573\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.30382 | − | 7.30382i | 0.267233 | − | 0.267233i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.3035 | + | 27.8574i | 0.741875 | + | 1.01789i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.96211 | −0.144580 | −0.0722898 | − | 0.997384i | \(-0.523031\pi\) | ||||
−0.0722898 | + | 0.997384i | \(0.523031\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.56451 | − | 1.56451i | 0.0570139 | − | 0.0570139i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.4177 | + | 12.4177i | 0.451328 | + | 0.451328i | 0.895795 | − | 0.444467i | \(-0.146607\pi\) |
−0.444467 | + | 0.895795i | \(0.646607\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.18096 | −0.260652 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.1007i | 0.656148i | 0.944652 | + | 0.328074i | \(0.106400\pi\) | ||||
−0.944652 | + | 0.328074i | \(0.893600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.46607 | − | 15.7228i | 0.0892779 | − | 0.569204i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.0666 | + | 37.0666i | 1.33840 | + | 1.33840i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.5274 | 0.776299 | 0.388149 | − | 0.921596i | \(-0.373114\pi\) | ||||
0.388149 | + | 0.921596i | \(0.373114\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.3480 | −0.984915 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.4318 | + | 12.4318i | 0.447143 | + | 0.447143i | 0.894403 | − | 0.447261i | \(-0.147600\pi\) |
−0.447261 | + | 0.894403i | \(0.647600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.9491 | + | 82.5587i | −0.464546 | + | 2.96178i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.45805i | 0.231384i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.33910 | −0.0836997 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −73.2843 | − | 73.2843i | −2.61897 | − | 2.61897i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.9985 | − | 23.9985i | 0.855455 | − | 0.855455i | −0.135343 | − | 0.990799i | \(-0.543214\pi\) |
0.990799 | + | 0.135343i | \(0.0432138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.9454 | 0.959283 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.7767 | + | 7.85444i | −0.383174 | + | 0.279272i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9225 | + | 10.9225i | −0.387868 | + | 0.387868i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.6111 | − | 14.6111i | 0.517552 | − | 0.517552i | −0.399278 | − | 0.916830i | \(-0.630739\pi\) |
0.916830 | + | 0.399278i | \(0.130739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.6688i | 0.731210i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 89.6525i | − | 3.16772i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.93087 | − | 3.93087i | −0.138718 | − | 0.138718i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.75173 | + | 6.75173i | 0.237672 | + | 0.237672i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.5234i | 0.369983i | 0.982740 | + | 0.184991i | \(0.0592258\pi\) | ||||
−0.982740 | + | 0.184991i | \(0.940774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.8109i | 1.08192i | 0.841050 | + | 0.540958i | \(0.181938\pi\) | ||||
−0.841050 | + | 0.540958i | \(0.818062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.1952 | + | 11.1952i | −0.392633 | + | 0.392633i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.37024 | + | 5.37024i | −0.187881 | + | 0.187881i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 62.5327 | − | 45.5761i | 2.18507 | − | 1.59256i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.63075 | 0.196515 | 0.0982573 | − | 0.995161i | \(-0.468673\pi\) | ||||
0.0982573 | + | 0.995161i | \(0.468673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.8777 | − | 32.8777i | 1.14604 | − | 1.14604i | 0.158720 | − | 0.987324i | \(-0.449263\pi\) |
0.987324 | − | 0.158720i | \(-0.0507368\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.06998 | + | 4.06998i | 0.141527 | + | 0.141527i | 0.774321 | − | 0.632794i | \(-0.218092\pi\) |
−0.632794 | + | 0.774321i | \(0.718092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.8830 | −0.898955 | −0.449478 | − | 0.893292i | \(-0.648390\pi\) | ||||
−0.449478 | + | 0.893292i | \(0.648390\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 81.8922i | 2.84081i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.2030 | + | 11.3970i | −0.769287 | + | 0.394883i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.4170 | − | 26.4170i | −0.913105 | − | 0.913105i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.6763 | 0.610253 | 0.305126 | − | 0.952312i | \(-0.401301\pi\) | ||||
0.305126 | + | 0.952312i | \(0.401301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −72.6011 | −2.50348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.2064 | + | 22.2064i | 0.764830 | + | 0.764830i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.0947 | − | 4.24973i | −0.930985 | − | 0.146022i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 100.863i | 3.46162i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.4324 | −1.04321 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.0308 | + | 40.0308i | 1.37063 | + | 1.37063i | 0.859511 | + | 0.511117i | \(0.170768\pi\) |
0.511117 | + | 0.859511i | \(0.329232\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.8266 | − | 30.8266i | 1.05302 | − | 1.05302i | 0.0545034 | − | 0.998514i | \(-0.482642\pi\) |
0.998514 | − | 0.0545034i | \(-0.0173576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.9929 | 1.60338 | 0.801689 | − | 0.597741i | \(-0.203935\pi\) | ||||
0.801689 | + | 0.597741i | \(0.203935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.3837 | − | 13.3987i | 0.626514 | − | 0.456626i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.4965 | − | 22.4965i | 0.765789 | − | 0.765789i | −0.211573 | − | 0.977362i | \(-0.567859\pi\) |
0.977362 | + | 0.211573i | \(0.0678586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.27776 | − | 9.27776i | 0.315089 | − | 0.315089i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.20106i | − | 0.176434i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 16.2015i | − | 0.548966i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.3944 | − | 27.3944i | −0.927160 | − | 0.927160i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0005 | − | 19.0005i | −0.641602 | − | 0.641602i | 0.309347 | − | 0.950949i | \(-0.399890\pi\) |
−0.950949 | + | 0.309347i | \(0.899890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 32.6100i | − | 1.09991i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.8855i | 0.636268i | 0.948046 | + | 0.318134i | \(0.103056\pi\) | ||||
−0.948046 | + | 0.318134i | \(0.896944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.94189 | + | 2.94189i | −0.0990023 | + | 0.0990023i | −0.754873 | − | 0.655871i | \(-0.772302\pi\) |
0.655871 | + | 0.754873i | \(0.272302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.662275 | − | 0.662275i | 0.0222370 | − | 0.0222370i | −0.695901 | − | 0.718138i | \(-0.744995\pi\) |
0.718138 | + | 0.695901i | \(0.244995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.4300 | − | 43.1235i | −1.05413 | − | 1.44632i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.85394 | −0.330120 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.42013 | − | 9.42013i | 0.315233 | − | 0.315233i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.3230 | + | 29.3230i | 0.979068 | + | 0.979068i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.6244 | −1.22149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 32.7929i | − | 1.09249i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.4289 | + | 4.14529i | 0.879498 | + | 0.137947i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.0100 | − | 32.0100i | −1.06288 | − | 1.06288i | −0.997886 | − | 0.0649902i | \(-0.979298\pi\) |
−0.0649902 | − | 0.997886i | \(-0.520702\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −74.0698 | −2.45674 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.6612 | −1.41343 | −0.706714 | − | 0.707499i | \(-0.749823\pi\) | ||||
−0.706714 | + | 0.707499i | \(0.749823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.914280 | − | 0.914280i | −0.0302583 | − | 0.0302583i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.37869 | − | 21.5413i | 0.111574 | − | 0.711357i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.3500i | − | 1.00115i | −0.865692 | − | 0.500577i | \(-0.833121\pi\) | ||
0.865692 | − | 0.500577i | \(-0.166879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.0505 | −0.726589 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.55160 | + | 9.55160i | 0.314395 | + | 0.314395i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.5345 | + | 22.5345i | −0.740130 | + | 0.740130i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.7434 | −0.549334 | −0.274667 | − | 0.961539i | \(-0.588568\pi\) | ||||
−0.274667 | + | 0.961539i | \(0.588568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.3137 | + | 4.92498i | 0.501887 | + | 0.161410i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.2113 | + | 19.2113i | −0.628951 | + | 0.628951i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0760 | − | 31.0760i | 1.01521 | − | 1.01521i | 0.0153259 | − | 0.999883i | \(-0.495121\pi\) |
0.999883 | − | 0.0153259i | \(-0.00487859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 28.1269i | − | 0.917886i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.0141i | 1.46742i | 0.679464 | + | 0.733709i | \(0.262212\pi\) | ||||
−0.679464 | + | 0.733709i | \(0.737788\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.85773 | + | 5.85773i | 0.190754 | + | 0.190754i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.7267 | − | 18.7267i | −0.608535 | − | 0.608535i | 0.334028 | − | 0.942563i | \(-0.391592\pi\) |
−0.942563 | + | 0.334028i | \(0.891592\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.1030i | 1.04211i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.7773i | 0.544042i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.06721 | − | 3.06721i | 0.0993566 | − | 0.0993566i | −0.655681 | − | 0.755038i | \(-0.727618\pi\) |
0.755038 | + | 0.655681i | \(0.227618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.3627 | + | 17.3627i | −0.561258 | + | 0.561258i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.7739 | − | 17.5264i | −0.412490 | − | 0.565956i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7979 | 0.574126 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −58.5997 | + | 58.5997i | −1.88835 | + | 1.88835i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0904 | + | 20.0904i | 0.646063 | + | 0.646063i | 0.952039 | − | 0.305976i | \(-0.0989828\pi\) |
−0.305976 | + | 0.952039i | \(0.598983\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.0672 | 0.805276 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.8425i | 1.40697i | 0.710708 | + | 0.703487i | \(0.248375\pi\) | ||||
−0.710708 | + | 0.703487i | \(0.751625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.6441 | − | 3.23797i | −0.661820 | − | 0.103804i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.5360 | − | 25.5360i | −0.816968 | − | 0.816968i | 0.168700 | − | 0.985667i | \(-0.446043\pi\) |
−0.985667 | + | 0.168700i | \(0.946043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.2225 | −0.358674 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.2613 | 1.22159 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.5331 | + | 13.5331i | 0.431639 | + | 0.431639i | 0.889186 | − | 0.457547i | \(-0.151272\pi\) |
−0.457547 | + | 0.889186i | \(0.651272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −46.3598 | − | 7.27140i | −1.47565 | − | 0.231451i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.74209i | 0.309780i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.6536 | −0.529019 | −0.264510 | − | 0.964383i | \(-0.585210\pi\) | ||||
−0.264510 | + | 0.964383i | \(0.585210\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.1984 | − | 14.1984i | −0.450573 | − | 0.450573i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.7663 | + | 31.7663i | −1.00605 | + | 1.00605i | −0.00606773 | + | 0.999982i | \(0.501931\pi\) |
−0.999982 | + | 0.00606773i | \(0.998069\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −106.149 | −3.35840 |
(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 | 1400.2.x.b.657.2 | 24 | ||
5.2 | odd | 4 | 280.2.x.a.153.2 | yes | 24 | ||
5.3 | odd | 4 | inner | 1400.2.x.b.993.11 | 24 | ||
5.4 | even | 2 | 280.2.x.a.97.11 | yes | 24 | ||
7.6 | odd | 2 | inner | 1400.2.x.b.657.11 | 24 | ||
20.7 | even | 4 | 560.2.bj.d.433.11 | 24 | |||
20.19 | odd | 2 | 560.2.bj.d.97.2 | 24 | |||
35.13 | even | 4 | inner | 1400.2.x.b.993.2 | 24 | ||
35.27 | even | 4 | 280.2.x.a.153.11 | yes | 24 | ||
35.34 | odd | 2 | 280.2.x.a.97.2 | ✓ | 24 | ||
140.27 | odd | 4 | 560.2.bj.d.433.2 | 24 | |||
140.139 | even | 2 | 560.2.bj.d.97.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.x.a.97.2 | ✓ | 24 | 35.34 | odd | 2 | ||
280.2.x.a.97.11 | yes | 24 | 5.4 | even | 2 | ||
280.2.x.a.153.2 | yes | 24 | 5.2 | odd | 4 | ||
280.2.x.a.153.11 | yes | 24 | 35.27 | even | 4 | ||
560.2.bj.d.97.2 | 24 | 20.19 | odd | 2 | |||
560.2.bj.d.97.11 | 24 | 140.139 | even | 2 | |||
560.2.bj.d.433.2 | 24 | 140.27 | odd | 4 | |||
560.2.bj.d.433.11 | 24 | 20.7 | even | 4 | |||
1400.2.x.b.657.2 | 24 | 1.1 | even | 1 | trivial | ||
1400.2.x.b.657.11 | 24 | 7.6 | odd | 2 | inner | ||
1400.2.x.b.993.2 | 24 | 35.13 | even | 4 | inner | ||
1400.2.x.b.993.11 | 24 | 5.3 | odd | 4 | inner |