Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [928,2,Mod(191,928)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(928, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("928.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 928 = 2^{5} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 928.k (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: | \(7.41011730757\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 23x^{8} + 153x^{6} + 273x^{4} + 103x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 447.2 | ||
Root | \(-0.356878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 928.447 |
Dual form | 928.2.k.e.191.2 |
$q$-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 \(\left(\mathbb{Z}/928\mathbb{Z}\right)^\times\).
\(n\) | \(321\) | \(581\) | \(639\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.13340 | + | 1.13340i | −0.654368 | + | 0.654368i | −0.954042 | − | 0.299674i | \(-0.903122\pi\) |
0.299674 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.87777i | 0.839765i | 0.907578 | + | 0.419883i | \(0.137929\pi\) | ||||
−0.907578 | + | 0.419883i | \(0.862071\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.61854i | 1.74564i | 0.488038 | + | 0.872822i | \(0.337713\pi\) | ||||
−0.488038 | + | 0.872822i | \(0.662287\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.430814i | 0.143605i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.65429 | + | 3.65429i | −1.10181 | + | 1.10181i | −0.107619 | + | 0.994192i | \(0.534323\pi\) |
−0.994192 | + | 0.107619i | \(0.965677\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.02701i | − | 0.562192i | −0.959680 | − | 0.281096i | \(-0.909302\pi\) | ||
0.959680 | − | 0.281096i | \(-0.0906980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.12826 | − | 2.12826i | −0.549516 | − | 0.549516i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.117094 | − | 0.117094i | −0.0283994 | − | 0.0283994i | 0.692764 | − | 0.721164i | \(-0.256393\pi\) |
−0.721164 | + | 0.692764i | \(0.756393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.13944 | − | 5.13944i | 1.17907 | − | 1.17907i | 0.199085 | − | 0.979982i | \(-0.436203\pi\) |
0.979982 | − | 0.199085i | \(-0.0637971\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.23465 | − | 5.23465i | −1.14229 | − | 1.14229i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.35174i | 1.32443i | 0.749314 | + | 0.662215i | \(0.230383\pi\) | ||||
−0.749314 | + | 0.662215i | \(0.769617\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.47397 | 0.294794 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.88848 | − | 3.88848i | −0.748338 | − | 0.748338i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.38389 | + | 0.117094i | −0.999764 | + | 0.0217438i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.45813 | − | 3.45813i | 0.621098 | − | 0.621098i | −0.324714 | − | 0.945812i | \(-0.605268\pi\) |
0.945812 | + | 0.324714i | \(0.105268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 8.28354i | − | 1.44198i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.67257 | −1.46593 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.78256 | − | 6.78256i | 1.11505 | − | 1.11505i | 0.122588 | − | 0.992458i | \(-0.460881\pi\) |
0.992458 | − | 0.122588i | \(-0.0391194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.29741 | + | 2.29741i | 0.367881 | + | 0.367881i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.99487 | − | 3.99487i | 0.623893 | − | 0.623893i | −0.322631 | − | 0.946525i | \(-0.604567\pi\) |
0.946525 | + | 0.322631i | \(0.104567\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.36805 | + | 6.36805i | −0.971118 | + | 0.971118i | −0.999594 | − | 0.0284761i | \(-0.990935\pi\) |
0.0284761 | + | 0.999594i | \(0.490935\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.808970 | −0.120594 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.12826 | + | 4.12826i | 0.602169 | + | 0.602169i | 0.940888 | − | 0.338718i | \(-0.109993\pi\) |
−0.338718 | + | 0.940888i | \(0.609993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.3309 | −2.04728 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.265428 | 0.0371674 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.67647 | 0.642363 | 0.321182 | − | 0.947018i | \(-0.395920\pi\) | ||||
0.321182 | + | 0.947018i | \(0.395920\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.86193 | − | 6.86193i | −0.925262 | − | 0.925262i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.6501i | 1.54309i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.40380i | 0.182759i | 0.995816 | + | 0.0913796i | \(0.0291277\pi\) | ||||
−0.995816 | + | 0.0913796i | \(0.970872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.85319 | + | 4.85319i | 0.621388 | + | 0.621388i | 0.945886 | − | 0.324499i | \(-0.105196\pi\) |
−0.324499 | + | 0.945886i | \(0.605196\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.98973 | −0.250683 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.80627 | 0.472110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.5233 | −1.77431 | −0.887153 | − | 0.461475i | \(-0.847321\pi\) | ||||
−0.887153 | + | 0.461475i | \(0.847321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.19906 | − | 7.19906i | −0.866665 | − | 0.866665i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.02234 | 0.240008 | 0.120004 | − | 0.992773i | \(-0.461709\pi\) | ||||
0.120004 | + | 0.992773i | \(0.461709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2101 | + | 10.2101i | −1.19500 | + | 1.19500i | −0.219353 | + | 0.975646i | \(0.570395\pi\) |
−0.975646 | + | 0.219353i | \(0.929605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.67060 | + | 1.67060i | −0.192904 | + | 0.192904i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.8775 | − | 16.8775i | −1.92337 | − | 1.92337i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.68131 | − | 3.68131i | 0.414179 | − | 0.414179i | −0.469012 | − | 0.883192i | \(-0.655390\pi\) |
0.883192 | + | 0.469012i | \(0.155390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.52196 | 0.835773 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.22364i | − | 0.792897i | −0.918057 | − | 0.396449i | \(-0.870242\pi\) | ||
0.918057 | − | 0.396449i | \(-0.129758\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.219876 | − | 0.219876i | 0.0238489 | − | 0.0238489i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.96938 | − | 6.23481i | 0.639985 | − | 0.668442i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.43325 | − | 4.43325i | −0.469923 | − | 0.469923i | 0.431966 | − | 0.901890i | \(-0.357820\pi\) |
−0.901890 | + | 0.431966i | \(0.857820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.36185 | 0.981388 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.83888i | 0.812854i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.65069 | + | 9.65069i | 0.990140 | + | 0.990140i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.88021 | + | 6.88021i | −0.698579 | + | 0.698579i | −0.964104 | − | 0.265525i | \(-0.914455\pi\) |
0.265525 | + | 0.964104i | \(0.414455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.57432 | − | 1.57432i | −0.158225 | − | 0.158225i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.20887 | + | 3.20887i | 0.319294 | + | 0.319294i | 0.848496 | − | 0.529202i | \(-0.177509\pi\) |
−0.529202 | + | 0.848496i | \(0.677509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.18245i | − | 0.510642i | −0.966856 | − | 0.255321i | \(-0.917819\pi\) | ||
0.966856 | − | 0.255321i | \(-0.0821812\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.82948 | − | 9.82948i | 0.959259 | − | 0.959259i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0878i | 1.07190i | 0.844249 | + | 0.535951i | \(0.180047\pi\) | ||||
−0.844249 | + | 0.535951i | \(0.819953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.68734i | 0.544749i | 0.962191 | + | 0.272374i | \(0.0878089\pi\) | ||||
−0.962191 | + | 0.272374i | \(0.912191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.3747i | 1.45930i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.37409 | − | 3.37409i | 0.317407 | − | 0.317407i | −0.530363 | − | 0.847771i | \(-0.677944\pi\) |
0.847771 | + | 0.530363i | \(0.177944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.9271 | −1.11221 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.873266 | 0.0807334 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.540803 | − | 0.540803i | 0.0495753 | − | 0.0495753i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 15.7077i | − | 1.42797i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.05555i | 0.816512i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1566i | 1.08732i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8011 | − | 12.8011i | 1.13592 | − | 1.13592i | 0.146742 | − | 0.989175i | \(-0.453121\pi\) |
0.989175 | − | 0.146742i | \(-0.0468788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 14.4351i | − | 1.27094i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.31102 | − | 5.31102i | −0.464026 | − | 0.464026i | 0.435947 | − | 0.899973i | \(-0.356414\pi\) |
−0.899973 | + | 0.435947i | \(0.856414\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.7367 | + | 23.7367i | 2.05823 | + | 2.05823i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.30168 | − | 7.30168i | 0.628429 | − | 0.628429i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.46539 | + | 9.46539i | 0.808683 | + | 0.808683i | 0.984435 | − | 0.175751i | \(-0.0562355\pi\) |
−0.175751 | + | 0.984435i | \(0.556235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.86283i | − | 0.836555i | −0.908319 | − | 0.418277i | \(-0.862634\pi\) | ||
0.908319 | − | 0.418277i | \(-0.137366\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.35794 | −0.788081 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.40730 | + | 7.40730i | 0.619430 | + | 0.619430i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.219876 | − | 10.1097i | −0.0182597 | − | 0.839567i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.2427 | − | 16.2427i | 1.33967 | − | 1.33967i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.2223i | 1.16514i | 0.812782 | + | 0.582568i | \(0.197952\pi\) | ||||
−0.812782 | + | 0.582568i | \(0.802048\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3872 | −1.08944 | −0.544719 | − | 0.838618i | \(-0.683364\pi\) | ||||
−0.544719 | + | 0.838618i | \(0.683364\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0504456 | − | 0.0504456i | 0.00407829 | − | 0.00407829i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.49358 | + | 6.49358i | 0.521577 | + | 0.521577i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.15558 | − | 7.15558i | 0.571077 | − | 0.571077i | −0.361352 | − | 0.932429i | \(-0.617685\pi\) |
0.932429 | + | 0.361352i | \(0.117685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.30031 | + | 5.30031i | −0.420342 | + | 0.420342i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −29.3358 | −2.31198 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.50628 | − | 2.50628i | −0.196307 | − | 0.196307i | 0.602108 | − | 0.798415i | \(-0.294328\pi\) |
−0.798415 | + | 0.602108i | \(0.794328\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.5546 | 1.21092 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2463 | 1.41194 | 0.705969 | − | 0.708243i | \(-0.250512\pi\) | ||||
0.705969 | + | 0.708243i | \(0.250512\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.89122 | 0.683940 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.21414 | + | 2.21414i | 0.169320 | + | 0.169320i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.2028i | 1.23188i | 0.787794 | + | 0.615939i | \(0.211223\pi\) | ||||
−0.787794 | + | 0.615939i | \(0.788777\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.80760i | 0.514606i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.59107 | − | 1.59107i | −0.119592 | − | 0.119592i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.43472 | −0.107236 | −0.0536180 | − | 0.998562i | \(-0.517075\pi\) | ||||
−0.0536180 | + | 0.998562i | \(0.517075\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.11486 | −0.0828666 | −0.0414333 | − | 0.999141i | \(-0.513192\pi\) | ||||
−0.0414333 | + | 0.999141i | \(0.513192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0012 | −0.813232 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.7361 | + | 12.7361i | 0.936377 | + | 0.936377i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.855790 | 0.0625816 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.9591 | − | 17.9591i | 1.30633 | − | 1.30633i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.82058 | + | 7.82058i | −0.565877 | + | 0.565877i | −0.930971 | − | 0.365093i | \(-0.881037\pi\) |
0.365093 | + | 0.930971i | \(0.381037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9652 | + | 10.9652i | 0.789289 | + | 0.789289i | 0.981378 | − | 0.192089i | \(-0.0615261\pi\) |
−0.192089 | + | 0.981378i | \(0.561526\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.31402 | + | 4.31402i | −0.308934 | + | 0.308934i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.22392 | −0.443436 | −0.221718 | − | 0.975111i | \(-0.571166\pi\) | ||||
−0.221718 | + | 0.975111i | \(0.571166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.403965i | − | 0.0286363i | −0.999897 | − | 0.0143182i | \(-0.995442\pi\) | ||
0.999897 | − | 0.0143182i | \(-0.00455777\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.4607 | − | 16.4607i | 1.16105 | − | 1.16105i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.540803 | − | 24.8657i | −0.0379569 | − | 1.74523i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.50145 | + | 7.50145i | 0.523924 | + | 0.523924i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.73642 | −0.190194 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.5620i | 2.59822i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.13629 | + | 8.13629i | 0.560126 | + | 0.560126i | 0.929343 | − | 0.369217i | \(-0.120374\pi\) |
−0.369217 | + | 0.929343i | \(0.620374\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.29212 | + | 2.29212i | −0.157053 | + | 0.157053i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.9577 | − | 11.9577i | −0.815511 | − | 0.815511i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.9715 | + | 15.9715i | 1.08422 | + | 1.08422i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 23.1442i | − | 1.56394i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.237351 | + | 0.237351i | −0.0159659 | + | 0.0159659i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.71556i | 0.583637i | 0.956474 | + | 0.291819i | \(0.0942604\pi\) | ||||
−0.956474 | + | 0.291819i | \(0.905740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.635008i | 0.0423338i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0214i | 0.797889i | 0.916975 | + | 0.398945i | \(0.130623\pi\) | ||||
−0.916975 | + | 0.398945i | \(0.869377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.94281 | + | 2.94281i | −0.194466 | + | 0.194466i | −0.797623 | − | 0.603157i | \(-0.793909\pi\) |
0.603157 | + | 0.797623i | \(0.293909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 38.2579 | 2.51718 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.1681 | −1.51779 | −0.758897 | − | 0.651211i | \(-0.774261\pi\) | ||||
−0.758897 | + | 0.651211i | \(0.774261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.75194 | + | 7.75194i | −0.505681 | + | 0.505681i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.34478i | 0.542052i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.5443i | − | 1.45827i | −0.684370 | − | 0.729135i | \(-0.739923\pi\) | ||
0.684370 | − | 0.729135i | \(-0.260077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.29184i | 0.0832148i | 0.999134 | + | 0.0416074i | \(0.0132479\pi\) | ||||
−0.999134 | + | 0.0416074i | \(0.986752\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.14006 | − | 3.14006i | 0.201435 | − | 0.201435i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 26.9102i | − | 1.71923i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4177 | − | 10.4177i | −0.662863 | − | 0.662863i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.18727 | + | 8.18727i | 0.518847 | + | 0.518847i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.1769 | − | 10.1769i | 0.642359 | − | 0.642359i | −0.308776 | − | 0.951135i | \(-0.599919\pi\) |
0.951135 | + | 0.308776i | \(0.0999193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.2111 | − | 23.2111i | −1.45927 | − | 1.45927i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.498413i | 0.0312119i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.16708 | −0.0728003 | −0.0364001 | − | 0.999337i | \(-0.511589\pi\) | ||||
−0.0364001 | + | 0.999337i | \(0.511589\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.3255 | + | 31.3255i | 1.94647 | + | 1.94647i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0504456 | − | 2.31946i | −0.00312251 | − | 0.143571i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.35144 | + | 4.35144i | −0.268321 | + | 0.268321i | −0.828424 | − | 0.560102i | \(-0.810762\pi\) |
0.560102 | + | 0.828424i | \(0.310762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.78135i | 0.539434i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0493 | 0.615006 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4925 | + | 10.4925i | −0.639742 | + | 0.639742i | −0.950492 | − | 0.310750i | \(-0.899420\pi\) |
0.310750 | + | 0.950492i | \(0.399420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.74634 | − | 9.74634i | −0.592048 | − | 0.592048i | 0.346136 | − | 0.938184i | \(-0.387494\pi\) |
−0.938184 | + | 0.346136i | \(0.887494\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.6107 | + | 10.6107i | −0.642189 | + | 0.642189i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.38633 | + | 5.38633i | −0.324808 | + | 0.324808i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0550 | 1.08482 | 0.542408 | − | 0.840115i | \(-0.317513\pi\) | ||||
0.542408 | + | 0.840115i | \(0.317513\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.48981 | + | 1.48981i | 0.0891926 | + | 0.0891926i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.3507 | −0.915748 | −0.457874 | − | 0.889017i | \(-0.651389\pi\) | ||||
−0.457874 | + | 0.889017i | \(0.651389\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.78389 | 0.165485 | 0.0827425 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827425 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −21.8762 | −1.29583 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.4505 | + | 18.4505i | 1.08910 | + | 1.08910i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.9726i | − | 0.998387i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 15.5960i | − | 0.914256i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.11953 | + | 2.11953i | 0.123824 | + | 0.123824i | 0.766303 | − | 0.642479i | \(-0.222094\pi\) |
−0.642479 | + | 0.766303i | \(0.722094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.63602 | −0.153475 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.4193 | 1.64905 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.8751 | 0.744585 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.4111 | − | 29.4111i | −1.69523 | − | 1.69523i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.27385 | −0.417872 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.11319 | + | 9.11319i | −0.521820 | + | 0.521820i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.74951 | − | 9.74951i | 0.556434 | − | 0.556434i | −0.371856 | − | 0.928290i | \(-0.621279\pi\) |
0.928290 | + | 0.371856i | \(0.121279\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.87379 | + | 5.87379i | 0.334148 | + | 0.334148i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7465 | + | 12.7465i | −0.722788 | + | 0.722788i | −0.969172 | − | 0.246384i | \(-0.920757\pi\) |
0.246384 | + | 0.969172i | \(0.420757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.166591 | 0.00941625 | 0.00470813 | − | 0.999989i | \(-0.498501\pi\) | ||||
0.00470813 | + | 0.999989i | \(0.498501\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.73626i | − | 0.210515i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.8755 | − | 10.8755i | 0.610831 | − | 0.610831i | −0.332332 | − | 0.943163i | \(-0.607835\pi\) |
0.943163 | + | 0.332332i | \(0.107835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.2464 | − | 20.1022i | 1.07759 | − | 1.12551i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.5669 | − | 12.5669i | −0.701419 | − | 0.701419i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.20359 | −0.0669697 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.98776i | − | 0.165731i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.44603 | − | 6.44603i | −0.356466 | − | 0.356466i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.0666 | + | 19.0666i | −1.05117 | + | 1.05117i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2753 | − | 20.2753i | −1.11443 | − | 1.11443i | −0.992544 | − | 0.121885i | \(-0.961106\pi\) |
−0.121885 | − | 0.992544i | \(-0.538894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.92202 | + | 2.92202i | 0.160126 | + | 0.160126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 27.2715i | − | 1.49000i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3139 | + | 13.3139i | −0.725255 | + | 0.725255i | −0.969671 | − | 0.244415i | \(-0.921404\pi\) |
0.244415 | + | 0.969671i | \(0.421404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.64837i | 0.415402i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.2740i | 1.36867i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 33.8582i | − | 1.82817i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5182 | − | 13.5182i | 0.727795 | − | 0.727795i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0375 | 1.29040 | 0.645200 | − | 0.764014i | \(-0.276774\pi\) | ||||
0.645200 | + | 0.764014i | \(0.276774\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.69411 | −0.0906839 | −0.0453419 | − | 0.998972i | \(-0.514438\pi\) | ||||
−0.0453419 | + | 0.998972i | \(0.514438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.88200 | + | 7.88200i | −0.420710 | + | 0.420710i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 15.2039i | − | 0.809220i | −0.914489 | − | 0.404610i | \(-0.867407\pi\) | ||
0.914489 | − | 0.404610i | \(-0.132593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.79750i | 0.201550i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.22589i | 0.0648810i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.55485 | + | 7.55485i | −0.398730 | + | 0.398730i | −0.877785 | − | 0.479055i | \(-0.840979\pi\) |
0.479055 | + | 0.877785i | \(0.340979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 33.8276i | − | 1.78040i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.8031 | + | 17.8031i | 0.934421 | + | 0.934421i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.1722 | − | 19.1722i | −1.00352 | − | 1.00352i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5582 | + | 21.5582i | −1.12533 | + | 1.12533i | −0.134402 | + | 0.990927i | \(0.542911\pi\) |
−0.990927 | + | 0.134402i | \(0.957089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.72104 | + | 1.72104i | 0.0895940 | + | 0.0895940i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.5985i | 1.12134i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.51653 | 0.0785228 | 0.0392614 | − | 0.999229i | \(-0.487500\pi\) | ||||
0.0392614 | + | 0.999229i | \(0.487500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7783 | − | 13.7783i | −0.711510 | − | 0.711510i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.237351 | + | 10.9132i | 0.0122242 | + | 0.562060i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7612 | + | 17.7612i | −0.912329 | + | 0.912329i | −0.996455 | − | 0.0841260i | \(-0.973190\pi\) |
0.0841260 | + | 0.996455i | \(0.473190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.0176i | 1.48662i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.7163 | −1.56953 | −0.784766 | − | 0.619793i | \(-0.787217\pi\) | ||||
−0.784766 | + | 0.619793i | \(0.787217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.6921 | − | 31.6921i | 1.61518 | − | 1.61518i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.74344 | − | 2.74344i | −0.139457 | − | 0.139457i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.9093 | − | 13.9093i | 0.705229 | − | 0.705229i | −0.260299 | − | 0.965528i | \(-0.583821\pi\) |
0.965528 | + | 0.260299i | \(0.0838211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.743750 | − | 0.743750i | 0.0376131 | − | 0.0376131i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0390 | 0.607288 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.91265 | + | 6.91265i | 0.347813 | + | 0.347813i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.2779 | 1.16828 | 0.584141 | − | 0.811652i | \(-0.301431\pi\) | ||||
0.584141 | + | 0.811652i | \(0.301431\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −53.8063 | −2.69368 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.3061 | −1.16385 | −0.581924 | − | 0.813243i | \(-0.697700\pi\) | ||||
−0.581924 | + | 0.813243i | \(0.697700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.00968 | − | 7.00968i | −0.349177 | − | 0.349177i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.1245i | 0.701853i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.5709i | 2.45714i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1630 | + | 13.1630i | 0.650869 | + | 0.650869i | 0.953202 | − | 0.302333i | \(-0.0977656\pi\) |
−0.302333 | + | 0.953202i | \(0.597766\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.4561 | −1.05835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.48351 | −0.319033 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.5643 | 0.665848 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.1785 | + | 11.1785i | 0.547415 | + | 0.547415i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.70332 | −0.278626 | −0.139313 | − | 0.990248i | \(-0.544489\pi\) | ||||
−0.139313 | + | 0.990248i | \(0.544489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.4789 | + | 15.4789i | −0.754397 | + | 0.754397i | −0.975297 | − | 0.220899i | \(-0.929101\pi\) |
0.220899 | + | 0.975297i | \(0.429101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.77851 | + | 1.77851i | −0.0864743 | + | 0.0864743i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.172593 | − | 0.172593i | −0.00837199 | − | 0.00837199i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.4147 | + | 22.4147i | −1.08472 | + | 1.08472i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.7909 | −0.810670 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 9.59910i | − | 0.462372i | −0.972910 | − | 0.231186i | \(-0.925739\pi\) | ||
0.972910 | − | 0.231186i | \(-0.0742606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7314 | − | 11.7314i | 0.563776 | − | 0.563776i | −0.366602 | − | 0.930378i | \(-0.619479\pi\) |
0.930378 | + | 0.366602i | \(0.119479\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.7076 | + | 11.2091i | 0.561334 | + | 0.537437i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.6444 | + | 32.6444i | 1.56159 | + | 1.56159i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5216 | 0.502170 | 0.251085 | − | 0.967965i | \(-0.419213\pi\) | ||||
0.251085 | + | 0.967965i | \(0.419213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 6.17396i | − | 0.293998i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.38252 | + | 3.38252i | 0.160708 | + | 0.160708i | 0.782881 | − | 0.622172i | \(-0.213750\pi\) |
−0.622172 | + | 0.782881i | \(0.713750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.32463 | − | 8.32463i | 0.394625 | − | 0.394625i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.1195 | − | 16.1195i | −0.762429 | − | 0.762429i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.41696 | + | 7.41696i | 0.350028 | + | 0.350028i | 0.860120 | − | 0.510092i | \(-0.170389\pi\) |
−0.510092 | + | 0.860120i | \(0.670389\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.1968i | 1.37482i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.1731 | − | 15.1731i | 0.712894 | − | 0.712894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.5794i | 0.824136i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.96799i | 0.279171i | 0.990210 | + | 0.139585i | \(0.0445770\pi\) | ||||
−0.990210 | + | 0.139585i | \(0.955423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.910634i | 0.0425048i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.39522 | − | 8.39522i | 0.391005 | − | 0.391005i | −0.484041 | − | 0.875045i | \(-0.660831\pi\) |
0.875045 | + | 0.484041i | \(0.160831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2011 | 0.474087 | 0.237043 | − | 0.971499i | \(-0.423822\pi\) | ||||
0.237043 | + | 0.971499i | \(0.423822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.7196 | −0.682606 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.03744 | + | 3.03744i | −0.140556 | + | 0.140556i | −0.773884 | − | 0.633328i | \(-0.781689\pi\) |
0.633328 | + | 0.773884i | \(0.281689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 67.0766i | − | 3.09731i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.2203i | 0.747390i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 46.5414i | − | 2.13998i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.57538 | − | 7.57538i | 0.347582 | − | 0.347582i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.01469i | 0.0922463i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00259 | + | 9.00259i | 0.411339 | + | 0.411339i | 0.882205 | − | 0.470866i | \(-0.156058\pi\) |
−0.470866 | + | 0.882205i | \(0.656058\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7483 | − | 13.7483i | −0.626870 | − | 0.626870i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 33.2492 | − | 33.2492i | 1.51289 | − | 1.51289i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.9195 | − | 12.9195i | −0.586642 | − | 0.586642i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.90676i | 0.312975i | 0.987680 | + | 0.156488i | \(0.0500171\pi\) | ||||
−0.987680 | + | 0.156488i | \(0.949983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.68123 | 0.256914 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.2194 | − | 15.2194i | −0.686842 | − | 0.686842i | 0.274690 | − | 0.961533i | \(-0.411425\pi\) |
−0.961533 | + | 0.274690i | \(0.911425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.644131 | + | 0.616710i | 0.0290102 | + | 0.0277752i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.95621 | − | 2.95621i | 0.132872 | − | 0.132872i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.34027i | 0.418968i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.94029 | 0.400222 | 0.200111 | − | 0.979773i | \(-0.435870\pi\) | ||||
0.200111 | + | 0.979773i | \(0.435870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.6803 | + | 20.6803i | −0.923927 | + | 0.923927i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0347 | + | 24.0347i | 1.07166 | + | 1.07166i | 0.997226 | + | 0.0744288i | \(0.0237133\pi\) |
0.0744288 | + | 0.997226i | \(0.476287\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.02552 | + | 6.02552i | −0.268132 | + | 0.268132i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.0773 | + | 10.0773i | −0.447548 | + | 0.447548i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.6977 | −0.961735 | −0.480867 | − | 0.876793i | \(-0.659678\pi\) | ||||
−0.480867 | + | 0.876793i | \(0.659678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −47.1556 | − | 47.1556i | −2.08604 | − | 2.08604i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −39.9692 | −1.76468 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.73147 | 0.428820 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.1718 | −1.32695 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.3643 | − | 18.3643i | −0.806102 | − | 0.806102i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.3550i | − | 1.24226i | −0.783709 | − | 0.621128i | \(-0.786675\pi\) | ||
0.783709 | − | 0.621128i | \(-0.213325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.2190i | 1.36511i | 0.730833 | + | 0.682556i | \(0.239132\pi\) | ||||
−0.730833 | + | 0.682556i | \(0.760868\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.71573 | − | 7.71573i | −0.336742 | − | 0.336742i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.809851 | −0.0352777 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3447 | −0.754115 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.604777 | −0.0262451 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.09765 | − | 8.09765i | −0.350748 | − | 0.350748i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.8204 | −0.900146 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.62611 | − | 1.62611i | 0.0701718 | − | 0.0701718i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 52.3694 | − | 52.3694i | 2.25571 | − | 2.25571i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.803209 | + | 0.803209i | 0.0345326 | + | 0.0345326i | 0.724162 | − | 0.689630i | \(-0.242227\pi\) |
−0.689630 | + | 0.724162i | \(0.742227\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.26358 | − | 1.26358i | 0.0542252 | − | 0.0542252i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.6795 | −0.457461 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.4159i | − | 0.744649i | −0.928103 | − | 0.372325i | \(-0.878561\pi\) | ||
0.928103 | − | 0.372325i | \(-0.121439\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.09082 | + | 2.09082i | −0.0892341 | + | 0.0892341i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.0684 | + | 28.2720i | −1.15315 | + | 1.20443i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.0023 | + | 17.0023i | 0.723010 | + | 0.723010i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28.8702 | −1.22547 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.46415i | 0.189152i | 0.995518 | + | 0.0945761i | \(0.0301496\pi\) | ||||
−0.995518 | + | 0.0945761i | \(0.969850\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.9081 | + | 12.9081i | 0.545955 | + | 0.545955i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.969952 | + | 0.969952i | −0.0409514 | + | 0.0409514i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.7864 | + | 19.7864i | 0.833896 | + | 0.833896i | 0.988047 | − | 0.154152i | \(-0.0492644\pi\) |
−0.154152 | + | 0.988047i | \(0.549264\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.33576 | + | 6.33576i | 0.266548 | + | 0.266548i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34.7405i | 1.45896i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.5991 | + | 14.5991i | −0.612026 | + | 0.612026i | −0.943474 | − | 0.331448i | \(-0.892463\pi\) |
0.331448 | + | 0.943474i | \(0.392463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.89118i | 0.204689i | 0.994749 | + | 0.102345i | \(0.0326345\pi\) | ||||
−0.994749 | + | 0.102345i | \(0.967366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 17.7277i | − | 0.740584i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.36229i | 0.390435i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.6225 | + | 18.6225i | −0.775265 | + | 0.775265i | −0.979022 | − | 0.203757i | \(-0.934685\pi\) |
0.203757 | + | 0.979022i | \(0.434685\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.8558 | −1.03297 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.3627 | 1.38412 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.0892 | + | 17.0892i | −0.707763 | + | 0.707763i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.63979i | 0.0677971i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.8014i | 1.27131i | 0.771973 | + | 0.635656i | \(0.219270\pi\) | ||||
−0.771973 | + | 0.635656i | \(0.780730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 35.5457i | − | 1.46463i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.05418 | − | 7.05418i | 0.290170 | − | 0.290170i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.859810i | 0.0353082i | 0.999844 | + | 0.0176541i | \(0.00561976\pi\) | ||||
−0.999844 | + | 0.0176541i | \(0.994380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01550 | + | 1.01550i | 0.0416316 | + | 0.0416316i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.457854 | + | 0.457854i | 0.0187387 | + | 0.0187387i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.8795 | − | 14.8795i | 0.607960 | − | 0.607960i | −0.334453 | − | 0.942413i | \(-0.608551\pi\) |
0.942413 | + | 0.334453i | \(0.108551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7547 | + | 12.7547i | 0.520274 | + | 0.520274i | 0.917654 | − | 0.397380i | \(-0.130081\pi\) |
−0.397380 | + | 0.917654i | \(0.630081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.25685i | − | 0.254799i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.4955 | 1.19916 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.6300 | + | 25.6300i | 1.04029 | + | 1.04029i | 0.999153 | + | 0.0411375i | \(0.0130982\pi\) |
0.0411375 | + | 0.999153i | \(0.486902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.7957 | + | 27.5698i | 1.16686 | + | 1.11719i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.36805 | − | 8.36805i | 0.338535 | − | 0.338535i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3524i | 1.18553i | 0.805374 | + | 0.592767i | \(0.201964\pi\) | ||||
−0.805374 | + | 0.592767i | \(0.798036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.0043 | −0.685678 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.4589 | − | 32.4589i | 1.30675 | − | 1.30675i | 0.382999 | − | 0.923749i | \(-0.374891\pi\) |
0.923749 | − | 0.382999i | \(-0.125109\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.45209 | − | 7.45209i | −0.299525 | − | 0.299525i | 0.541303 | − | 0.840828i | \(-0.317931\pi\) |
−0.840828 | + | 0.541303i | \(0.817931\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.6986 | − | 24.6986i | 0.991122 | − | 0.991122i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.4751 | − | 20.4751i | 0.820319 | − | 0.820319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.4575 | −0.618302 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −42.5727 | − | 42.5727i | −1.70019 | − | 1.70019i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.58839 | −0.0633333 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9343 | 0.475097 | 0.237548 | − | 0.971376i | \(-0.423656\pi\) | ||||
0.237548 | + | 0.971376i | \(0.423656\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.4433 | −0.733057 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.0376 | + | 24.0376i | 0.953904 | + | 0.953904i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.0490i | 1.15096i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.871253i | 0.0344662i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.7465 | − | 19.7465i | −0.779940 | − | 0.779940i | 0.199880 | − | 0.979820i | \(-0.435945\pi\) |
−0.979820 | + | 0.199880i | \(0.935945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.5916 | 0.772616 | 0.386308 | − | 0.922370i | \(-0.373750\pi\) | ||||
0.386308 | + | 0.922370i | \(0.373750\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.1058 | 1.06729 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.5461 | 0.650495 | 0.325247 | − | 0.945629i | \(-0.394552\pi\) | ||||
0.325247 | + | 0.945629i | \(0.394552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.12990 | − | 5.12990i | −0.201366 | − | 0.201366i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.2042 | −1.41895 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.9120 | + | 35.9120i | −1.40535 | + | 1.40535i | −0.623617 | + | 0.781730i | \(0.714337\pi\) |
−0.781730 | + | 0.623617i | \(0.785663\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.97288 | − | 9.97288i | 0.389673 | − | 0.389673i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.39864 | − | 4.39864i | −0.171607 | − | 0.171607i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.6276 | + | 21.6276i | −0.842492 | + | 0.842492i | −0.989182 | − | 0.146690i | \(-0.953138\pi\) |
0.146690 | + | 0.989182i | \(0.453138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.74975 | −0.0680575 | −0.0340287 | − | 0.999421i | \(-0.510834\pi\) | ||||
−0.0340287 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.538026i | − | 0.0208952i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −44.5721 | + | 44.5721i | −1.72843 | + | 1.72843i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.743750 | − | 34.1971i | −0.0287981 | − | 1.32412i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.87821 | − | 9.87821i | −0.381914 | − | 0.381914i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.4700 | −1.36930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 48.7095i | − | 1.87761i | −0.344446 | − | 0.938806i | \(-0.611933\pi\) | ||
0.344446 | − | 0.938806i | \(-0.388067\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.73151 | − | 5.73151i | −0.220606 | − | 0.220606i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.2703 | − | 11.2703i | 0.433153 | − | 0.433153i | −0.456547 | − | 0.889699i | \(-0.650914\pi\) |
0.889699 | + | 0.456547i | \(0.150914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.7765 | − | 31.7765i | −1.21947 | − | 1.21947i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6251 | − | 13.6251i | −0.522113 | − | 0.522113i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.0026i | 1.26281i | 0.775454 | + | 0.631404i | \(0.217521\pi\) | ||||
−0.775454 | + | 0.631404i | \(0.782479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.7739 | + | 17.7739i | −0.679104 | + | 0.679104i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.67075i | − | 0.254505i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.47928i | − | 0.361132i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0492i | 0.914873i | 0.889242 | + | 0.457437i | \(0.151232\pi\) | ||||
−0.889242 | + | 0.457437i | \(0.848768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.27106 | − | 7.27106i | 0.276205 | − | 0.276205i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.5202 | 0.702509 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.935548 | −0.0354364 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.2587 | − | 26.2587i | 0.993196 | − | 0.993196i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.2843i | 0.652819i | 0.945228 | + | 0.326410i | \(0.105839\pi\) | ||||
−0.945228 | + | 0.326410i | \(0.894161\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 69.7170i | − | 2.62943i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 17.5721i | − | 0.661803i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.8203 | + | 14.8203i | −0.557374 | + | 0.557374i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.1739i | 1.47121i | 0.677413 | + | 0.735603i | \(0.263101\pi\) | ||||
−0.677413 | + | 0.735603i | \(0.736899\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.58596 | + | 1.58596i | 0.0594781 | + | 0.0594781i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.9652 | + | 21.9652i | 0.822601 | + | 0.822601i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.9092 | + | 13.9092i | −0.520176 | + | 0.520176i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.5517 | + | 25.5517i | 0.954245 | + | 0.954245i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.6490i | 1.32948i | 0.747073 | + | 0.664742i | \(0.231459\pi\) | ||||
−0.747073 | + | 0.664742i | \(0.768541\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.9354 | 0.891400 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.46417 | − | 1.46417i | −0.0544531 | − | 0.0544531i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.93570 | + | 0.172593i | −0.294725 | + | 0.00640994i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.7780 | − | 35.7780i | 1.32693 | − | 1.32693i | 0.418902 | − | 0.908031i | \(-0.362415\pi\) |
0.908031 | − | 0.418902i | \(-0.137585\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.6838i | 1.09940i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.49132 | 0.0551584 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.91038 | + | 2.91038i | −0.107497 | + | 0.107497i | −0.758810 | − | 0.651312i | \(-0.774219\pi\) |
0.651312 | + | 0.758810i | \(0.274219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 30.5000 | + | 30.5000i | 1.12501 | + | 1.12501i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.0725 | − | 53.0725i | 1.95495 | − | 1.95495i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.2116 | − | 29.2116i | 1.07457 | − | 1.07457i | 0.0775789 | − | 0.996986i | \(-0.475281\pi\) |
0.996986 | − | 0.0775789i | \(-0.0247190\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.6148 | 0.867513 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.4269 | − | 25.4269i | −0.932822 | − | 0.932822i | 0.0650595 | − | 0.997881i | \(-0.479276\pi\) |
−0.997881 | + | 0.0650595i | \(0.979276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.7063 | −0.978441 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.11204 | 0.113864 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −51.2097 | −1.87116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.8866 | − | 17.8866i | −0.652690 | − | 0.652690i | 0.300950 | − | 0.953640i | \(-0.402696\pi\) |
−0.953640 | + | 0.300950i | \(0.902696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.0689i | 0.840678i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 25.1382i | − | 0.914873i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.6836 | + | 13.6836i | 0.497338 | + | 0.497338i | 0.910608 | − | 0.413270i | \(-0.135614\pi\) |
−0.413270 | + | 0.910608i | \(0.635614\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 52.6149 | 1.90980 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.0021 | 1.30508 | 0.652538 | − | 0.757756i | \(-0.273704\pi\) | ||||
0.652538 | + | 0.757756i | \(0.273704\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.2672 | −0.950938 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0947254 | + | 0.0947254i | 0.00342481 | + | 0.00342481i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.84552 | 0.102746 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.9265 | − | 26.9265i | 0.970994 | − | 0.970994i | −0.0285966 | − | 0.999591i | \(-0.509104\pi\) |
0.999591 | + | 0.0285966i | \(0.00910382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.32276 | − | 1.32276i | 0.0476382 | − | 0.0476382i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.3516 | − | 33.3516i | −1.19957 | − | 1.19957i | −0.974294 | − | 0.225281i | \(-0.927670\pi\) |
−0.225281 | − | 0.974294i | \(-0.572330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.09719 | − | 5.09719i | 0.183096 | − | 0.183096i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −71.0086 | −2.54742 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 41.0627i | − | 1.47122i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.39023 | + | 7.39023i | −0.264443 | + | 0.264443i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.3905 | + | 20.4798i | 0.764433 | + | 0.731890i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.4365 | + | 13.4365i | 0.479571 | + | 0.479571i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.46870 | −0.230584 | −0.115292 | − | 0.993332i | \(-0.536780\pi\) | ||||
−0.115292 | + | 0.993332i | \(0.536780\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 9.86384i | − | 0.351162i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.5834 | + | 15.5834i | 0.554080 | + | 0.554080i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.83749 | − | 9.83749i | 0.349339 | − | 0.349339i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.95278 | − | 9.95278i | −0.352989 | − | 0.352989i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.6210 | + | 23.6210i | 0.836698 | + | 0.836698i | 0.988423 | − | 0.151725i | \(-0.0484828\pi\) |
−0.151725 | + | 0.988423i | \(0.548483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.966789i | − | 0.0342025i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.90990 | − | 1.90990i | 0.0674832 | − | 0.0674832i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 74.6212i | − | 2.63332i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 55.0859i | − | 1.94152i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 23.7845i | − | 0.837254i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.92186 | − | 9.92186i | 0.348834 | − | 0.348834i | −0.510841 | − | 0.859675i | \(-0.670666\pi\) |
0.859675 | + | 0.510841i | \(0.170666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.3418 | 0.644068 | 0.322034 | − | 0.946728i | \(-0.395634\pi\) | ||||
0.322034 | + | 0.946728i | \(0.395634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.0930 | 0.774835 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.70622 | − | 4.70622i | 0.164852 | − | 0.164852i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65.4564i | 2.29003i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.03321i | 0.140932i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 21.2252i | − | 0.740765i | −0.928879 | − | 0.370382i | \(-0.879227\pi\) | ||
0.928879 | − | 0.370382i | \(-0.120773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.92578 | + | 2.92578i | −0.101986 | + | 0.101986i | −0.756259 | − | 0.654272i | \(-0.772975\pi\) |
0.654272 | + | 0.756259i | \(0.272975\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 12.2097i | − | 0.425088i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2586 | + | 29.2586i | 1.01742 | + | 1.01742i | 0.999846 | + | 0.0175740i | \(0.00559427\pi\) |
0.0175740 | + | 0.999846i | \(0.494406\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.1371 | + | 16.1371i | 0.560466 | + | 0.560466i | 0.929440 | − | 0.368974i | \(-0.120291\pi\) |
−0.368974 | + | 0.929440i | \(0.620291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.4635 | + | 20.4635i | −0.709870 | + | 0.709870i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.67806 | + | 1.67806i | 0.0581414 | + | 0.0581414i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.2623i | 1.18570i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.8937 | −0.929584 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.55730 | − | 2.55730i | −0.0882879 | − | 0.0882879i | 0.661584 | − | 0.749871i | \(-0.269885\pi\) |
−0.749871 | + | 0.661584i | \(0.769885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9726 | − | 1.26084i | 0.999054 | − | 0.0434773i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.3985 | − | 17.3985i | 0.599236 | − | 0.599236i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.6957i | 0.574349i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 72.5467 | 2.49274 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.15526 | + | 3.15526i | −0.108288 | + | 0.108288i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.0811 | + | 43.0811i | 1.47680 | + | 1.47680i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.5144 | + | 13.5144i | −0.462725 | + | 0.462725i | −0.899548 | − | 0.436822i | \(-0.856104\pi\) |
0.436822 | + | 0.899548i | \(0.356104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.15765 | + | 4.15765i | −0.142189 | + | 0.142189i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.5099 | 1.21300 | 0.606498 | − | 0.795085i | \(-0.292574\pi\) | ||||
0.606498 | + | 0.795085i | \(0.292574\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5054 | + | 15.5054i | 0.529036 | + | 0.529036i | 0.920285 | − | 0.391249i | \(-0.127957\pi\) |
−0.391249 | + | 0.920285i | \(0.627957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −41.8235 | −1.42534 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.9502 | 0.815276 | 0.407638 | − | 0.913144i | \(-0.366353\pi\) | ||||
0.407638 | + | 0.913144i | \(0.366353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.4252 | −1.03449 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.2367 | + | 19.2367i | 0.653313 | + | 0.653313i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.9051i | 0.912695i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.4390i | 0.997502i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.96409 | − | 2.96409i | −0.100319 | − | 0.100319i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −56.1460 | −1.89808 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.15943 | −0.309292 | −0.154646 | − | 0.987970i | \(-0.549424\pi\) | ||||
−0.154646 | + | 0.987970i | \(0.549424\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.80454 | −0.162053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.60816 | + | 1.60816i | 0.0541803 | + | 0.0541803i | 0.733678 | − | 0.679498i | \(-0.237802\pi\) |
−0.679498 | + | 0.733678i | \(0.737802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5780 | −0.726156 | −0.363078 | − | 0.931759i | \(-0.618274\pi\) | ||||
−0.363078 | + | 0.931759i | \(0.618274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.98766 | − | 2.98766i | 0.100429 | − | 0.100429i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.9686 | − | 18.9686i | 0.636904 | − | 0.636904i | −0.312887 | − | 0.949790i | \(-0.601296\pi\) |
0.949790 | + | 0.312887i | \(0.101296\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 59.1226 | + | 59.1226i | 1.98291 | + | 1.98291i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.4874 | + | 27.4874i | −0.920864 | + | 0.920864i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.4339 | 1.42000 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.69408i | − | 0.0900530i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.5926 | + | 14.5926i | −0.487232 | + | 0.487232i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.2133 | + | 19.0231i | −0.607446 | + | 0.634457i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.547586 | − | 0.547586i | −0.0182427 | − | 0.0182427i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 66.6690 | 2.21861 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.09344i | − | 0.0695885i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.6167 | − | 17.6167i | −0.584953 | − | 0.584953i | 0.351307 | − | 0.936260i | \(-0.385737\pi\) |
−0.936260 | + | 0.351307i | \(0.885737\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.38242 | + | 1.38242i | −0.0458521 | + | 0.0458521i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.266941 | − | 0.266941i | −0.00884414 | − | 0.00884414i | 0.702671 | − | 0.711515i | \(-0.251991\pi\) |
−0.711515 | + | 0.702671i | \(0.751991\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.3973 | + | 26.3973i | 0.873623 | + | 0.873623i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 20.6578i | − | 0.682924i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.5292 | − | 24.5292i | 0.810024 | − | 0.810024i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29.2241i | − | 0.964016i | −0.876167 | − | 0.482008i | \(-0.839908\pi\) | ||
0.876167 | − | 0.482008i | \(-0.160092\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.1002i | 0.728225i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.09931i | − | 0.134931i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.99730 | − | 9.99730i | 0.328709 | − | 0.328709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.23267 | 0.0733306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.693550 | 0.0227546 | 0.0113773 | − | 0.999935i | \(-0.496378\pi\) | ||||
0.0113773 | + | 0.999935i | \(0.496378\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −73.6529 | + | 73.6529i | −2.41388 | + | 2.41388i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 28.8937i | − | 0.945939i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.60698i | 0.0525538i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0078i | 0.947642i | 0.880621 | + | 0.473821i | \(0.157126\pi\) | ||||
−0.880621 | + | 0.473821i | \(0.842874\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.188814 | + | 0.188814i | −0.00616170 | + | 0.00616170i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.9516i | − | 0.878596i | −0.898341 | − | 0.439298i | \(-0.855227\pi\) | ||
0.898341 | − | 0.439298i | \(-0.144773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3744 | + | 25.3744i | 0.826303 | + | 0.826303i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.7231 | + | 33.7231i | 1.09701 | + | 1.09701i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.1687 | − | 26.1687i | 0.850369 | − | 0.850369i | −0.139809 | − | 0.990178i | \(-0.544649\pi\) |
0.990178 | + | 0.139809i | \(0.0446489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.6960 | + | 20.6960i | 0.671819 | + | 0.671819i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.6526i | 0.799417i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.8766 | −1.64806 | −0.824028 | − | 0.566549i | \(-0.808278\pi\) | ||||
−0.824028 | + | 0.566549i | \(0.808278\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.6853 | − | 14.6853i | −0.475204 | − | 0.475204i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.969952 | + | 44.5977i | 0.0313541 | + | 1.44164i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.7163 | + | 43.7163i | −1.41167 | + | 1.41167i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.08268i | 0.228474i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.77680 | −0.153930 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.5901 | + | 20.5901i | −0.662817 | + | 0.662817i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.66999 | − | 6.66999i | −0.214493 | − | 0.214493i | 0.591680 | − | 0.806173i | \(-0.298465\pi\) |
−0.806173 | + | 0.591680i | \(0.798465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.36415 | − | 1.36415i | 0.0438228 | − | 0.0438228i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.20264 | − | 3.20264i | 0.102778 | − | 0.102778i | −0.653848 | − | 0.756626i | \(-0.726846\pi\) |
0.756626 | + | 0.653848i | \(0.226846\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.5519 | 1.46033 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.38633 | + | 3.38633i | 0.108449 | + | 0.108449i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.4986 | 0.975737 | 0.487868 | − | 0.872917i | \(-0.337775\pi\) | ||||
0.487868 | + | 0.872917i | \(0.337775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.4008 | 1.03553 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.45019 | −0.0782284 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.79423 | + | 4.79423i | 0.152912 | + | 0.152912i | 0.779417 | − | 0.626505i | \(-0.215515\pi\) |
−0.626505 | + | 0.779417i | \(0.715515\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 11.6871i | − | 0.372382i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 43.2200i | − | 1.37571i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.4482 | − | 40.4482i | −1.28618 | − | 1.28618i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9596 | 0.634037 | 0.317018 | − | 0.948419i | \(-0.397318\pi\) | ||||
0.317018 | + | 0.948419i | \(0.397318\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.9599 | 1.45849 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.758555 | 0.0240478 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0474 | + | 18.0474i | 0.571566 | + | 0.571566i | 0.932566 | − | 0.361000i | \(-0.117564\pi\) |
−0.361000 | + | 0.932566i | \(0.617564\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −52.7477 | −1.66886 |
(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 | 928.2.k.e.447.2 | yes | 10 | |
4.3 | odd | 2 | 928.2.k.f.447.4 | yes | 10 | ||
29.17 | odd | 4 | 928.2.k.f.191.4 | yes | 10 | ||
116.75 | even | 4 | inner | 928.2.k.e.191.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.2.k.e.191.2 | ✓ | 10 | 116.75 | even | 4 | inner | |
928.2.k.e.447.2 | yes | 10 | 1.1 | even | 1 | trivial | |
928.2.k.f.191.4 | yes | 10 | 29.17 | odd | 4 | ||
928.2.k.f.447.4 | yes | 10 | 4.3 | odd | 2 |