Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(107,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.f (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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.4 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.593 |
Dual form | 1350.2.f.b.107.4 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.896575 | + | 0.896575i | −0.338874 | + | 0.338874i | −0.855943 | − | 0.517070i | \(-0.827023\pi\) |
0.517070 | + | 0.855943i | \(0.327023\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000i | 0.904534i | 0.891883 | + | 0.452267i | \(0.149385\pi\) | ||||
−0.891883 | + | 0.452267i | \(0.850615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.12132 | − | 2.12132i | −0.588348 | − | 0.588348i | 0.348836 | − | 0.937184i | \(-0.386577\pi\) |
−0.937184 | + | 0.348836i | \(0.886577\pi\) | |||||||
\(14\) | −1.26795 | −0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.55291 | + | 1.55291i | 0.376637 | + | 0.376637i | 0.869887 | − | 0.493250i | \(-0.164191\pi\) |
−0.493250 | + | 0.869887i | \(0.664191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.19615i | 1.42149i | 0.703447 | + | 0.710747i | \(0.251643\pi\) | ||||
−0.703447 | + | 0.710747i | \(0.748357\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.12132 | + | 2.12132i | −0.452267 | + | 0.452267i | ||||
\(23\) | 2.12132 | − | 2.12132i | 0.442326 | − | 0.442326i | −0.450467 | − | 0.892793i | \(-0.648743\pi\) |
0.892793 | + | 0.450467i | \(0.148743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.00000i | − | 0.588348i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.896575 | − | 0.896575i | −0.169437 | − | 0.169437i | ||||
\(29\) | −8.19615 | −1.52199 | −0.760994 | − | 0.648759i | \(-0.775288\pi\) | ||||
−0.760994 | + | 0.648759i | \(0.775288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.19615i | 0.376637i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.02030 | + | 7.02030i | −1.15413 | + | 1.15413i | −0.168414 | + | 0.985716i | \(0.553864\pi\) |
−0.985716 | + | 0.168414i | \(0.946136\pi\) | |||||||
\(38\) | −4.38134 | + | 4.38134i | −0.710747 | + | 0.710747i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.58871 | − | 7.58871i | −1.15727 | − | 1.15727i | −0.985061 | − | 0.172206i | \(-0.944911\pi\) |
−0.172206 | − | 0.985061i | \(-0.555089\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | 0.442326 | ||||||||
\(47\) | 6.36396 | + | 6.36396i | 0.928279 | + | 0.928279i | 0.997595 | − | 0.0693157i | \(-0.0220816\pi\) |
−0.0693157 | + | 0.997595i | \(0.522082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.39230i | 0.770329i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.12132 | − | 2.12132i | 0.294174 | − | 0.294174i | ||||
\(53\) | 1.55291 | − | 1.55291i | 0.213309 | − | 0.213309i | −0.592362 | − | 0.805672i | \(-0.701805\pi\) |
0.805672 | + | 0.592362i | \(0.201805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.26795i | − | 0.169437i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.79555 | − | 5.79555i | −0.760994 | − | 0.760994i | ||||
\(59\) | 13.3923 | 1.74353 | 0.871765 | − | 0.489925i | \(-0.162976\pi\) | ||||
0.871765 | + | 0.489925i | \(0.162976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.19615 | −1.17745 | −0.588723 | − | 0.808335i | \(-0.700369\pi\) | ||||
−0.588723 | + | 0.808335i | \(0.700369\pi\) | |||||||
\(62\) | −1.41421 | − | 1.41421i | −0.179605 | − | 0.179605i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.55291 | − | 1.55291i | 0.189719 | − | 0.189719i | −0.605856 | − | 0.795574i | \(-0.707169\pi\) |
0.795574 | + | 0.605856i | \(0.207169\pi\) | |||||||
\(68\) | −1.55291 | + | 1.55291i | −0.188319 | + | 0.188319i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.803848i | 0.0953992i | 0.998862 | + | 0.0476996i | \(0.0151890\pi\) | ||||
−0.998862 | + | 0.0476996i | \(0.984811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.03579 | − | 6.03579i | −0.706436 | − | 0.706436i | 0.259348 | − | 0.965784i | \(-0.416492\pi\) |
−0.965784 | + | 0.259348i | \(0.916492\pi\) | |||||||
\(74\) | −9.92820 | −1.15413 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.19615 | −0.710747 | ||||||||
\(77\) | −2.68973 | − | 2.68973i | −0.306523 | − | 0.306523i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1962i | 1.14716i | 0.819151 | + | 0.573578i | \(0.194445\pi\) | ||||
−0.819151 | + | 0.573578i | \(0.805555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.24264 | + | 4.24264i | −0.468521 | + | 0.468521i | ||||
\(83\) | 3.10583 | − | 3.10583i | 0.340909 | − | 0.340909i | −0.515800 | − | 0.856709i | \(-0.672505\pi\) |
0.856709 | + | 0.515800i | \(0.172505\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 10.7321i | − | 1.15727i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.12132 | − | 2.12132i | −0.226134 | − | 0.226134i | ||||
\(89\) | 8.19615 | 0.868790 | 0.434395 | − | 0.900722i | \(-0.356962\pi\) | ||||
0.434395 | + | 0.900722i | \(0.356962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.80385 | 0.398752 | ||||||||
\(92\) | 2.12132 | + | 2.12132i | 0.221163 | + | 0.221163i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.00000i | 0.928279i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.88108 | − | 1.88108i | 0.190995 | − | 0.190995i | −0.605131 | − | 0.796126i | \(-0.706879\pi\) |
0.796126 | + | 0.605131i | \(0.206879\pi\) | |||||||
\(98\) | −3.81294 | + | 3.81294i | −0.385165 | + | 0.385165i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.5885i | 1.84962i | 0.380429 | + | 0.924810i | \(0.375776\pi\) | ||||
−0.380429 | + | 0.924810i | \(0.624224\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.656339 | + | 0.656339i | 0.0646710 | + | 0.0646710i | 0.738703 | − | 0.674032i | \(-0.235439\pi\) |
−0.674032 | + | 0.738703i | \(0.735439\pi\) | |||||||
\(104\) | 3.00000 | 0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.19615 | 0.213309 | ||||||||
\(107\) | −11.0227 | − | 11.0227i | −1.06561 | − | 1.06561i | −0.997691 | − | 0.0679138i | \(-0.978366\pi\) |
−0.0679138 | − | 0.997691i | \(-0.521634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000i | 0.766261i | 0.923694 | + | 0.383131i | \(0.125154\pi\) | ||||
−0.923694 | + | 0.383131i | \(0.874846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.896575 | − | 0.896575i | 0.0847184 | − | 0.0847184i | ||||
\(113\) | 7.34847 | − | 7.34847i | 0.691286 | − | 0.691286i | −0.271229 | − | 0.962515i | \(-0.587430\pi\) |
0.962515 | + | 0.271229i | \(0.0874301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 8.19615i | − | 0.760994i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.46979 | + | 9.46979i | 0.871765 | + | 0.871765i | ||||
\(119\) | −2.78461 | −0.255265 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | −6.50266 | − | 6.50266i | −0.588723 | − | 0.588723i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 2.00000i | − | 0.179605i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | + | 7.34847i | −0.652071 | + | 0.652071i | −0.953491 | − | 0.301420i | \(-0.902539\pi\) |
0.301420 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.3923i | − | 1.17009i | −0.811000 | − | 0.585046i | \(-0.801077\pi\) | ||
0.811000 | − | 0.585046i | \(-0.198923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.55532 | − | 5.55532i | −0.481707 | − | 0.481707i | ||||
\(134\) | 2.19615 | 0.189719 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.19615 | −0.188319 | ||||||||
\(137\) | 14.2808 | + | 14.2808i | 1.22009 | + | 1.22009i | 0.967598 | + | 0.252496i | \(0.0812516\pi\) |
0.252496 | + | 0.967598i | \(0.418748\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.1962i | − | 1.37374i | −0.726780 | − | 0.686870i | \(-0.758984\pi\) | ||
0.726780 | − | 0.686870i | \(-0.241016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.568406 | + | 0.568406i | −0.0476996 | + | 0.0476996i | ||||
\(143\) | 6.36396 | − | 6.36396i | 0.532181 | − | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 8.53590i | − | 0.706436i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.02030 | − | 7.02030i | −0.577065 | − | 0.577065i | ||||
\(149\) | 10.3923 | 0.851371 | 0.425685 | − | 0.904871i | \(-0.360033\pi\) | ||||
0.425685 | + | 0.904871i | \(0.360033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.196152 | 0.0159627 | 0.00798133 | − | 0.999968i | \(-0.497459\pi\) | ||||
0.00798133 | + | 0.999968i | \(0.497459\pi\) | |||||||
\(152\) | −4.38134 | − | 4.38134i | −0.355374 | − | 0.355374i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 3.80385i | − | 0.306523i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.89898 | − | 4.89898i | 0.390981 | − | 0.390981i | −0.484056 | − | 0.875037i | \(-0.660837\pi\) |
0.875037 | + | 0.484056i | \(0.160837\pi\) | |||||||
\(158\) | −7.20977 | + | 7.20977i | −0.573578 | + | 0.573578i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.80385i | 0.299785i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.13681 | + | 1.13681i | 0.0890420 | + | 0.0890420i | 0.750225 | − | 0.661183i | \(-0.229945\pi\) |
−0.661183 | + | 0.750225i | \(0.729945\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.39230 | 0.340909 | ||||||||
\(167\) | −17.9551 | − | 17.9551i | −1.38941 | − | 1.38941i | −0.826567 | − | 0.562838i | \(-0.809710\pi\) |
−0.562838 | − | 0.826567i | \(-0.690290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.00000i | − | 0.307692i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.58871 | − | 7.58871i | 0.578633 | − | 0.578633i | ||||
\(173\) | −5.79555 | + | 5.79555i | −0.440628 | + | 0.440628i | −0.892223 | − | 0.451595i | \(-0.850855\pi\) |
0.451595 | + | 0.892223i | \(0.350855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.00000i | − | 0.226134i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.79555 | + | 5.79555i | 0.434395 | + | 0.434395i | ||||
\(179\) | 25.3923 | 1.89791 | 0.948955 | − | 0.315412i | \(-0.102143\pi\) | ||||
0.948955 | + | 0.315412i | \(0.102143\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5885 | 1.01002 | 0.505011 | − | 0.863113i | \(-0.331488\pi\) | ||||
0.505011 | + | 0.863113i | \(0.331488\pi\) | |||||||
\(182\) | 2.68973 | + | 2.68973i | 0.199376 | + | 0.199376i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000i | 0.221163i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.65874 | + | 4.65874i | −0.340681 | + | 0.340681i | ||||
\(188\) | −6.36396 | + | 6.36396i | −0.464140 | + | 0.464140i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.39230i | 0.317816i | 0.987293 | + | 0.158908i | \(0.0507973\pi\) | ||||
−0.987293 | + | 0.158908i | \(0.949203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.2832 | + | 18.2832i | 1.31606 | + | 1.31606i | 0.916870 | + | 0.399187i | \(0.130708\pi\) |
0.399187 | + | 0.916870i | \(0.369292\pi\) | |||||||
\(194\) | 2.66025 | 0.190995 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.39230 | −0.385165 | ||||||||
\(197\) | 3.10583 | + | 3.10583i | 0.221281 | + | 0.221281i | 0.809038 | − | 0.587757i | \(-0.199989\pi\) |
−0.587757 | + | 0.809038i | \(0.699989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000i | 0.141776i | 0.997484 | + | 0.0708881i | \(0.0225833\pi\) | ||||
−0.997484 | + | 0.0708881i | \(0.977417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.1440 | + | 13.1440i | −0.924810 | + | 0.924810i | ||||
\(203\) | 7.34847 | − | 7.34847i | 0.515761 | − | 0.515761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.928203i | 0.0646710i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.12132 | + | 2.12132i | 0.147087 | + | 0.147087i | ||||
\(209\) | −18.5885 | −1.28579 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 1.55291 | + | 1.55291i | 0.106655 | + | 0.106655i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 15.5885i | − | 1.06561i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.79315 | − | 1.79315i | 0.121727 | − | 0.121727i | ||||
\(218\) | −5.65685 | + | 5.65685i | −0.383131 | + | 0.383131i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.58846i | − | 0.443188i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9372 | + | 14.9372i | 1.00027 | + | 1.00027i | 1.00000 | 0.000267267i | \(8.50736e-5\pi\) | |
0.000267267 | 1.00000i | \(0.499915\pi\) | ||||||||
\(224\) | 1.26795 | 0.0847184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.3923 | 0.691286 | ||||||||
\(227\) | 4.81105 | + | 4.81105i | 0.319320 | + | 0.319320i | 0.848506 | − | 0.529186i | \(-0.177503\pi\) |
−0.529186 | + | 0.848506i | \(0.677503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.5885i | − | 1.16228i | −0.813804 | − | 0.581139i | \(-0.802607\pi\) | ||
0.813804 | − | 0.581139i | \(-0.197393\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.79555 | − | 5.79555i | 0.380497 | − | 0.380497i | ||||
\(233\) | 10.0382 | − | 10.0382i | 0.657624 | − | 0.657624i | −0.297193 | − | 0.954817i | \(-0.596051\pi\) |
0.954817 | + | 0.297193i | \(0.0960506\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.3923i | 0.871765i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.96902 | − | 1.96902i | −0.127632 | − | 0.127632i | ||||
\(239\) | 12.8038 | 0.828212 | 0.414106 | − | 0.910229i | \(-0.364094\pi\) | ||||
0.414106 | + | 0.910229i | \(0.364094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | −0.0322078 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322078 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(242\) | 1.41421 | + | 1.41421i | 0.0909091 | + | 0.0909091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.19615i | − | 0.588723i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.1440 | − | 13.1440i | 0.836334 | − | 0.836334i | ||||
\(248\) | 1.41421 | − | 1.41421i | 0.0898027 | − | 0.0898027i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.39230i | 0.0878815i | 0.999034 | + | 0.0439408i | \(0.0139913\pi\) | ||||
−0.999034 | + | 0.0439408i | \(0.986009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.36396 | + | 6.36396i | 0.400099 | + | 0.400099i | ||||
\(254\) | −10.3923 | −0.652071 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.55291 | + | 1.55291i | 0.0968681 | + | 0.0968681i | 0.753880 | − | 0.657012i | \(-0.228180\pi\) |
−0.657012 | + | 0.753880i | \(0.728180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.5885i | − | 0.782209i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.46979 | − | 9.46979i | 0.585046 | − | 0.585046i | ||||
\(263\) | 6.36396 | − | 6.36396i | 0.392419 | − | 0.392419i | −0.483130 | − | 0.875549i | \(-0.660500\pi\) |
0.875549 | + | 0.483130i | \(0.160500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 7.85641i | − | 0.481707i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.55291 | + | 1.55291i | 0.0948593 | + | 0.0948593i | ||||
\(269\) | −24.0000 | −1.46331 | −0.731653 | − | 0.681677i | \(-0.761251\pi\) | ||||
−0.731653 | + | 0.681677i | \(0.761251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3923 | −1.23874 | −0.619372 | − | 0.785098i | \(-0.712613\pi\) | ||||
−0.619372 | + | 0.785098i | \(0.712613\pi\) | |||||||
\(272\) | −1.55291 | − | 1.55291i | −0.0941593 | − | 0.0941593i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.1962i | 1.22009i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1774 | − | 15.1774i | 0.911922 | − | 0.911922i | −0.0845011 | − | 0.996423i | \(-0.526930\pi\) |
0.996423 | + | 0.0845011i | \(0.0269296\pi\) | |||||||
\(278\) | 11.4524 | − | 11.4524i | 0.686870 | − | 0.686870i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.8038i | 1.30071i | 0.759631 | + | 0.650354i | \(0.225380\pi\) | ||||
−0.759631 | + | 0.650354i | \(0.774620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.58871 | + | 7.58871i | 0.451102 | + | 0.451102i | 0.895720 | − | 0.444618i | \(-0.146661\pi\) |
−0.444618 | + | 0.895720i | \(0.646661\pi\) | |||||||
\(284\) | −0.803848 | −0.0476996 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.00000 | 0.532181 | ||||||||
\(287\) | −5.37945 | − | 5.37945i | −0.317539 | − | 0.317539i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 12.1769i | − | 0.716289i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.03579 | − | 6.03579i | 0.353218 | − | 0.353218i | ||||
\(293\) | −20.4925 | + | 20.4925i | −1.19718 | + | 1.19718i | −0.222178 | + | 0.975006i | \(0.571317\pi\) |
−0.975006 | + | 0.222178i | \(0.928683\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 9.92820i | − | 0.577065i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.34847 | + | 7.34847i | 0.425685 | + | 0.425685i | ||||
\(299\) | −9.00000 | −0.520483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.6077 | 0.784335 | ||||||||
\(302\) | 0.138701 | + | 0.138701i | 0.00798133 | + | 0.00798133i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.19615i | − | 0.355374i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2474 | − | 12.2474i | 0.698999 | − | 0.698999i | −0.265196 | − | 0.964195i | \(-0.585437\pi\) |
0.964195 | + | 0.265196i | \(0.0854366\pi\) | |||||||
\(308\) | 2.68973 | − | 2.68973i | 0.153261 | − | 0.153261i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.803848i | − | 0.0455820i | −0.999740 | − | 0.0227910i | \(-0.992745\pi\) | ||
0.999740 | − | 0.0227910i | \(-0.00725523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.13681 | + | 1.13681i | 0.0642564 | + | 0.0642564i | 0.738505 | − | 0.674248i | \(-0.235532\pi\) |
−0.674248 | + | 0.738505i | \(0.735532\pi\) | |||||||
\(314\) | 6.92820 | 0.390981 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.1962 | −0.573578 | ||||||||
\(317\) | 18.5235 | + | 18.5235i | 1.04038 | + | 1.04038i | 0.999150 | + | 0.0412325i | \(0.0131284\pi\) |
0.0412325 | + | 0.999150i | \(0.486872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 24.5885i | − | 1.37669i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.68973 | + | 2.68973i | −0.149893 | + | 0.149893i | ||||
\(323\) | −9.62209 | + | 9.62209i | −0.535388 | + | 0.535388i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.60770i | 0.0890420i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.24264 | − | 4.24264i | −0.234261 | − | 0.234261i | ||||
\(329\) | −11.4115 | −0.629139 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.7846 | 1.91194 | 0.955968 | − | 0.293472i | \(-0.0948109\pi\) | ||||
0.955968 | + | 0.293472i | \(0.0948109\pi\) | |||||||
\(332\) | 3.10583 | + | 3.10583i | 0.170454 | + | 0.170454i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 25.3923i | − | 1.38941i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.13681 | − | 1.13681i | 0.0619261 | − | 0.0619261i | −0.675465 | − | 0.737392i | \(-0.736057\pi\) |
0.737392 | + | 0.675465i | \(0.236057\pi\) | |||||||
\(338\) | 2.82843 | − | 2.82843i | 0.153846 | − | 0.153846i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.00000i | − | 0.324918i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.1106 | − | 11.1106i | −0.599918 | − | 0.599918i | ||||
\(344\) | 10.7321 | 0.578633 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.19615 | −0.440628 | ||||||||
\(347\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3923i | 0.770402i | 0.922833 | + | 0.385201i | \(0.125868\pi\) | ||||
−0.922833 | + | 0.385201i | \(0.874132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.12132 | − | 2.12132i | 0.113067 | − | 0.113067i | ||||
\(353\) | −2.68973 | + | 2.68973i | −0.143160 | + | 0.143160i | −0.775054 | − | 0.631895i | \(-0.782278\pi\) |
0.631895 | + | 0.775054i | \(0.282278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.19615i | 0.434395i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.9551 | + | 17.9551i | 0.948955 | + | 0.948955i | ||||
\(359\) | 11.1962 | 0.590910 | 0.295455 | − | 0.955357i | \(-0.404529\pi\) | ||||
0.295455 | + | 0.955357i | \(0.404529\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.3923 | −1.02065 | ||||||||
\(362\) | 9.60849 | + | 9.60849i | 0.505011 | + | 0.505011i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.80385i | 0.199376i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.21166 | + | 6.21166i | −0.324246 | + | 0.324246i | −0.850393 | − | 0.526147i | \(-0.823636\pi\) |
0.526147 | + | 0.850393i | \(0.323636\pi\) | |||||||
\(368\) | −2.12132 | + | 2.12132i | −0.110581 | + | 0.110581i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.78461i | 0.144570i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.8386 | + | 23.8386i | 1.23431 | + | 1.23431i | 0.962291 | + | 0.272023i | \(0.0876927\pi\) |
0.272023 | + | 0.962291i | \(0.412307\pi\) | |||||||
\(374\) | −6.58846 | −0.340681 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | 17.3867 | + | 17.3867i | 0.895459 | + | 0.895459i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.00000i | − | 0.102733i | −0.998680 | − | 0.0513665i | \(-0.983642\pi\) | ||
0.998680 | − | 0.0513665i | \(-0.0163577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.10583 | + | 3.10583i | −0.158908 | + | 0.158908i | ||||
\(383\) | −2.12132 | + | 2.12132i | −0.108394 | + | 0.108394i | −0.759224 | − | 0.650830i | \(-0.774421\pi\) |
0.650830 | + | 0.759224i | \(0.274421\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.8564i | 1.31606i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.88108 | + | 1.88108i | 0.0954976 | + | 0.0954976i | ||||
\(389\) | −32.1962 | −1.63241 | −0.816205 | − | 0.577763i | \(-0.803926\pi\) | ||||
−0.816205 | + | 0.577763i | \(0.803926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.58846 | 0.333193 | ||||||||
\(392\) | −3.81294 | − | 3.81294i | −0.192582 | − | 0.192582i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.39230i | 0.221281i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.46498 | − | 1.46498i | 0.0735253 | − | 0.0735253i | −0.669388 | − | 0.742913i | \(-0.733444\pi\) |
0.742913 | + | 0.669388i | \(0.233444\pi\) | |||||||
\(398\) | −1.41421 | + | 1.41421i | −0.0708881 | + | 0.0708881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.80385i | 0.189955i | 0.995479 | + | 0.0949775i | \(0.0302779\pi\) | ||||
−0.995479 | + | 0.0949775i | \(0.969722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.24264 | + | 4.24264i | 0.211341 | + | 0.211341i | ||||
\(404\) | −18.5885 | −0.924810 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.3923 | 0.515761 | ||||||||
\(407\) | −21.0609 | − | 21.0609i | −1.04395 | − | 1.04395i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.0000i | − | 1.13728i | −0.822588 | − | 0.568638i | \(-0.807470\pi\) | ||
0.822588 | − | 0.568638i | \(-0.192530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.656339 | + | 0.656339i | −0.0323355 | + | 0.0323355i | ||||
\(413\) | −12.0072 | + | 12.0072i | −0.590836 | + | 0.590836i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000i | 0.147087i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.1440 | − | 13.1440i | −0.642895 | − | 0.642895i | ||||
\(419\) | 10.3923 | 0.507697 | 0.253849 | − | 0.967244i | \(-0.418303\pi\) | ||||
0.253849 | + | 0.967244i | \(0.418303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.1962 | −0.935563 | −0.467782 | − | 0.883844i | \(-0.654947\pi\) | ||||
−0.467782 | + | 0.883844i | \(0.654947\pi\) | |||||||
\(422\) | −2.82843 | − | 2.82843i | −0.137686 | − | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.19615i | 0.106655i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.24504 | − | 8.24504i | 0.399006 | − | 0.399006i | ||||
\(428\) | 11.0227 | − | 11.0227i | 0.532803 | − | 0.532803i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 27.5885i | − | 1.32889i | −0.747338 | − | 0.664445i | \(-0.768668\pi\) | ||
0.747338 | − | 0.664445i | \(-0.231332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.4722 | − | 13.4722i | −0.647432 | − | 0.647432i | 0.304939 | − | 0.952372i | \(-0.401364\pi\) |
−0.952372 | + | 0.304939i | \(0.901364\pi\) | |||||||
\(434\) | 2.53590 | 0.121727 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | 13.1440 | + | 13.1440i | 0.628764 | + | 0.628764i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10.5885i | − | 0.505359i | −0.967550 | − | 0.252680i | \(-0.918688\pi\) | ||
0.967550 | − | 0.252680i | \(-0.0813119\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.65874 | − | 4.65874i | 0.221594 | − | 0.221594i | ||||
\(443\) | −19.5080 | + | 19.5080i | −0.926852 | + | 0.926852i | −0.997501 | − | 0.0706489i | \(-0.977493\pi\) |
0.0706489 | + | 0.997501i | \(0.477493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.1244i | 1.00027i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.896575 | + | 0.896575i | 0.0423592 | + | 0.0423592i | ||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | 7.34847 | + | 7.34847i | 0.345643 | + | 0.345643i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.80385i | 0.319320i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4022 | + | 16.4022i | −0.767261 | + | 0.767261i | −0.977623 | − | 0.210363i | \(-0.932535\pi\) |
0.210363 | + | 0.977623i | \(0.432535\pi\) | |||||||
\(458\) | 12.4369 | − | 12.4369i | 0.581139 | − | 0.581139i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 32.7846i | − | 1.52693i | −0.645848 | − | 0.763466i | \(-0.723496\pi\) | ||
0.645848 | − | 0.763466i | \(-0.276504\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3509 | + | 11.3509i | 0.527520 | + | 0.527520i | 0.919832 | − | 0.392312i | \(-0.128325\pi\) |
−0.392312 | + | 0.919832i | \(0.628325\pi\) | |||||||
\(464\) | 8.19615 | 0.380497 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.1962 | 0.657624 | ||||||||
\(467\) | −9.88589 | − | 9.88589i | −0.457465 | − | 0.457465i | 0.440358 | − | 0.897822i | \(-0.354852\pi\) |
−0.897822 | + | 0.440358i | \(0.854852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.78461i | 0.128581i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.46979 | + | 9.46979i | −0.435882 | + | 0.435882i | ||||
\(473\) | 22.7661 | − | 22.7661i | 1.04679 | − | 1.04679i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.78461i | − | 0.127632i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.05369 | + | 9.05369i | 0.414106 | + | 0.414106i | ||||
\(479\) | 22.3923 | 1.02313 | 0.511565 | − | 0.859244i | \(-0.329066\pi\) | ||||
0.511565 | + | 0.859244i | \(0.329066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.7846 | 1.35806 | ||||||||
\(482\) | −0.707107 | − | 0.707107i | −0.0322078 | − | 0.0322078i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000i | 0.0909091i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.90138 | − | 8.90138i | 0.403360 | − | 0.403360i | −0.476055 | − | 0.879415i | \(-0.657934\pi\) |
0.879415 | + | 0.476055i | \(0.157934\pi\) | |||||||
\(488\) | 6.50266 | − | 6.50266i | 0.294362 | − | 0.294362i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.60770i | − | 0.0725543i | −0.999342 | − | 0.0362771i | \(-0.988450\pi\) | ||
0.999342 | − | 0.0362771i | \(-0.0115499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7279 | − | 12.7279i | −0.573237 | − | 0.573237i | ||||
\(494\) | 18.5885 | 0.836334 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −0.720710 | − | 0.720710i | −0.0323283 | − | 0.0323283i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.1769i | 1.48520i | 0.669734 | + | 0.742601i | \(0.266408\pi\) | ||||
−0.669734 | + | 0.742601i | \(0.733592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.984508 | + | 0.984508i | −0.0439408 | + | 0.0439408i | ||||
\(503\) | 1.13681 | − | 1.13681i | 0.0506879 | − | 0.0506879i | −0.681308 | − | 0.731996i | \(-0.738589\pi\) |
0.731996 | + | 0.681308i | \(0.238589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000i | 0.400099i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.34847 | − | 7.34847i | −0.326036 | − | 0.326036i | ||||
\(509\) | −38.7846 | −1.71910 | −0.859549 | − | 0.511054i | \(-0.829255\pi\) | ||||
−0.859549 | + | 0.511054i | \(0.829255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8231 | 0.478785 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.19615i | 0.0968681i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.0919 | + | 19.0919i | −0.839660 | + | 0.839660i | ||||
\(518\) | 8.90138 | − | 8.90138i | 0.391104 | − | 0.391104i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.1962i | 1.41054i | 0.708939 | + | 0.705270i | \(0.249174\pi\) | ||||
−0.708939 | + | 0.705270i | \(0.750826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.58630 | − | 3.58630i | −0.156818 | − | 0.156818i | 0.624337 | − | 0.781155i | \(-0.285369\pi\) |
−0.781155 | + | 0.624337i | \(0.785369\pi\) | |||||||
\(524\) | 13.3923 | 0.585046 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | 0.392419 | ||||||||
\(527\) | −3.10583 | − | 3.10583i | −0.135292 | − | 0.135292i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0000i | 0.608696i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.55532 | − | 5.55532i | 0.240854 | − | 0.240854i | ||||
\(533\) | 12.7279 | − | 12.7279i | 0.551308 | − | 0.551308i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.19615i | 0.0948593i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.9706 | − | 16.9706i | −0.731653 | − | 0.731653i | ||||
\(539\) | −16.1769 | −0.696789 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9808 | 0.687067 | 0.343533 | − | 0.939140i | \(-0.388376\pi\) | ||||
0.343533 | + | 0.939140i | \(0.388376\pi\) | |||||||
\(542\) | −14.4195 | − | 14.4195i | −0.619372 | − | 0.619372i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.19615i | − | 0.0941593i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.7685 | + | 26.7685i | −1.14454 | + | 1.14454i | −0.156930 | + | 0.987610i | \(0.550160\pi\) |
−0.987610 | + | 0.156930i | \(0.949840\pi\) | |||||||
\(548\) | −14.2808 | + | 14.2808i | −0.610047 | + | 0.610047i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 50.7846i | − | 2.16350i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.14162 | − | 9.14162i | −0.388741 | − | 0.388741i | ||||
\(554\) | 21.4641 | 0.911922 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.1962 | 0.686870 | ||||||||
\(557\) | −12.0072 | − | 12.0072i | −0.508762 | − | 0.508762i | 0.405384 | − | 0.914146i | \(-0.367138\pi\) |
−0.914146 | + | 0.405384i | \(0.867138\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.1962i | 1.36175i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.4176 | + | 15.4176i | −0.650354 | + | 0.650354i | ||||
\(563\) | −16.4022 | + | 16.4022i | −0.691268 | + | 0.691268i | −0.962511 | − | 0.271243i | \(-0.912565\pi\) |
0.271243 | + | 0.962511i | \(0.412565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.7321i | 0.451102i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.568406 | − | 0.568406i | −0.0238498 | − | 0.0238498i | ||||
\(569\) | 22.3923 | 0.938734 | 0.469367 | − | 0.883003i | \(-0.344482\pi\) | ||||
0.469367 | + | 0.883003i | \(0.344482\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.7846 | −0.786111 | −0.393056 | − | 0.919515i | \(-0.628582\pi\) | ||||
−0.393056 | + | 0.919515i | \(0.628582\pi\) | |||||||
\(572\) | 6.36396 | + | 6.36396i | 0.266091 | + | 0.266091i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 7.60770i | − | 0.317539i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.88108 | − | 1.88108i | 0.0783105 | − | 0.0783105i | −0.666867 | − | 0.745177i | \(-0.732365\pi\) |
0.745177 | + | 0.666867i | \(0.232365\pi\) | |||||||
\(578\) | 8.61038 | − | 8.61038i | 0.358145 | − | 0.358145i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.56922i | 0.231050i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.65874 | + | 4.65874i | 0.192945 | + | 0.192945i | ||||
\(584\) | 8.53590 | 0.353218 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.9808 | −1.19718 | ||||||||
\(587\) | −15.8338 | − | 15.8338i | −0.653529 | − | 0.653529i | 0.300312 | − | 0.953841i | \(-0.402909\pi\) |
−0.953841 | + | 0.300312i | \(0.902909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.3923i | − | 0.510616i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.02030 | − | 7.02030i | 0.288533 | − | 0.288533i | ||||
\(593\) | −31.6675 | + | 31.6675i | −1.30043 | + | 1.30043i | −0.372327 | + | 0.928102i | \(0.621440\pi\) |
−0.928102 | + | 0.372327i | \(0.878560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.3923i | 0.425685i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.36396 | − | 6.36396i | −0.260242 | − | 0.260242i | ||||
\(599\) | 13.6077 | 0.555995 | 0.277998 | − | 0.960582i | \(-0.410329\pi\) | ||||
0.277998 | + | 0.960582i | \(0.410329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.0000 | −0.938190 | −0.469095 | − | 0.883148i | \(-0.655420\pi\) | ||||
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | 9.62209 | + | 9.62209i | 0.392167 | + | 0.392167i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.196152i | 0.00798133i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0406 | − | 14.0406i | 0.569890 | − | 0.569890i | −0.362207 | − | 0.932098i | \(-0.617977\pi\) |
0.932098 | + | 0.362207i | \(0.117977\pi\) | |||||||
\(608\) | 4.38134 | − | 4.38134i | 0.177687 | − | 0.177687i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 27.0000i | − | 1.09230i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0561 | − | 13.0561i | −0.527331 | − | 0.527331i | 0.392445 | − | 0.919776i | \(-0.371629\pi\) |
−0.919776 | + | 0.392445i | \(0.871629\pi\) | |||||||
\(614\) | 17.3205 | 0.698999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.80385 | 0.153261 | ||||||||
\(617\) | 4.24264 | + | 4.24264i | 0.170802 | + | 0.170802i | 0.787332 | − | 0.616530i | \(-0.211462\pi\) |
−0.616530 | + | 0.787332i | \(0.711462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.3923i | 1.70389i | 0.523631 | + | 0.851945i | \(0.324577\pi\) | ||||
−0.523631 | + | 0.851945i | \(0.675423\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.568406 | − | 0.568406i | 0.0227910 | − | 0.0227910i | ||||
\(623\) | −7.34847 | + | 7.34847i | −0.294410 | + | 0.294410i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.60770i | 0.0642564i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.89898 | + | 4.89898i | 0.195491 | + | 0.195491i | ||||
\(629\) | −21.8038 | −0.869376 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.58846 | 0.341901 | 0.170951 | − | 0.985280i | \(-0.445316\pi\) | ||||
0.170951 | + | 0.985280i | \(0.445316\pi\) | |||||||
\(632\) | −7.20977 | − | 7.20977i | −0.286789 | − | 0.286789i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.1962i | 1.04038i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.4388 | − | 11.4388i | 0.453222 | − | 0.453222i | ||||
\(638\) | 17.3867 | − | 17.3867i | 0.688345 | − | 0.688345i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.5885i | 0.497214i | 0.968604 | + | 0.248607i | \(0.0799728\pi\) | ||||
−0.968604 | + | 0.248607i | \(0.920027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.7279 | − | 12.7279i | −0.501940 | − | 0.501940i | 0.410100 | − | 0.912040i | \(-0.365494\pi\) |
−0.912040 | + | 0.410100i | \(0.865494\pi\) | |||||||
\(644\) | −3.80385 | −0.149893 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.6077 | −0.535388 | ||||||||
\(647\) | −5.22715 | − | 5.22715i | −0.205500 | − | 0.205500i | 0.596851 | − | 0.802352i | \(-0.296418\pi\) |
−0.802352 | + | 0.596851i | \(0.796418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.1769i | 1.57708i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.13681 | + | 1.13681i | −0.0445210 | + | 0.0445210i | ||||
\(653\) | −20.4925 | + | 20.4925i | −0.801933 | + | 0.801933i | −0.983398 | − | 0.181464i | \(-0.941916\pi\) |
0.181464 | + | 0.983398i | \(0.441916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 6.00000i | − | 0.234261i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.06918 | − | 8.06918i | −0.314569 | − | 0.314569i | ||||
\(659\) | 38.7846 | 1.51083 | 0.755417 | − | 0.655244i | \(-0.227434\pi\) | ||||
0.755417 | + | 0.655244i | \(0.227434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.3731 | −1.49254 | −0.746270 | − | 0.665644i | \(-0.768157\pi\) | ||||
−0.746270 | + | 0.665644i | \(0.768157\pi\) | |||||||
\(662\) | 24.5964 | + | 24.5964i | 0.955968 | + | 0.955968i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.39230i | 0.170454i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3867 | + | 17.3867i | −0.673214 | + | 0.673214i | ||||
\(668\) | 17.9551 | − | 17.9551i | 0.694703 | − | 0.694703i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 27.5885i | − | 1.06504i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.4070 | − | 24.4070i | −0.940819 | − | 0.940819i | 0.0575247 | − | 0.998344i | \(-0.481679\pi\) |
−0.998344 | + | 0.0575247i | \(0.981679\pi\) | |||||||
\(674\) | 1.60770 | 0.0619261 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.00000 | 0.153846 | ||||||||
\(677\) | −18.1074 | − | 18.1074i | −0.695923 | − | 0.695923i | 0.267606 | − | 0.963529i | \(-0.413768\pi\) |
−0.963529 | + | 0.267606i | \(0.913768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.37307i | 0.129446i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.24264 | − | 4.24264i | 0.162459 | − | 0.162459i | ||||
\(683\) | 27.9933 | − | 27.9933i | 1.07113 | − | 1.07113i | 0.0738643 | − | 0.997268i | \(-0.476467\pi\) |
0.997268 | − | 0.0738643i | \(-0.0235332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 15.7128i | − | 0.599918i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.58871 | + | 7.58871i | 0.289317 | + | 0.289317i | ||||
\(689\) | −6.58846 | −0.251000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | −5.79555 | − | 5.79555i | −0.220314 | − | 0.220314i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.31749 | + | 9.31749i | −0.352925 | + | 0.352925i | ||||
\(698\) | −10.1769 | + | 10.1769i | −0.385201 | + | 0.385201i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30.5885i | − | 1.15531i | −0.816281 | − | 0.577655i | \(-0.803968\pi\) | ||
0.816281 | − | 0.577655i | \(-0.196032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.4988 | − | 43.4988i | −1.64059 | − | 1.64059i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.80385 | −0.143160 | ||||||||
\(707\) | −16.6660 | − | 16.6660i | −0.626788 | − | 0.626788i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 26.8038i | − | 1.00664i | −0.864100 | − | 0.503320i | \(-0.832112\pi\) | ||
0.864100 | − | 0.503320i | \(-0.167888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.79555 | + | 5.79555i | −0.217198 | + | 0.217198i | ||||
\(713\) | −4.24264 | + | 4.24264i | −0.158888 | + | 0.158888i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.3923i | 0.948955i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.91688 | + | 7.91688i | 0.295455 | + | 0.295455i | ||||
\(719\) | −0.803848 | −0.0299785 | −0.0149892 | − | 0.999888i | \(-0.504771\pi\) | ||||
−0.0149892 | + | 0.999888i | \(0.504771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.17691 | −0.0438306 | ||||||||
\(722\) | −13.7124 | − | 13.7124i | −0.510324 | − | 0.510324i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.5885i | 0.505011i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.8744 | + | 29.8744i | −1.10798 | + | 1.10798i | −0.114562 | + | 0.993416i | \(0.536547\pi\) |
−0.993416 | + | 0.114562i | \(0.963453\pi\) | |||||||
\(728\) | −2.68973 | + | 2.68973i | −0.0996879 | + | 0.0996879i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 23.5692i | − | 0.871739i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.39494 | − | 4.39494i | −0.162331 | − | 0.162331i | 0.621268 | − | 0.783599i | \(-0.286618\pi\) |
−0.783599 | + | 0.621268i | \(0.786618\pi\) | |||||||
\(734\) | −8.78461 | −0.324246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 4.65874 | + | 4.65874i | 0.171607 | + | 0.171607i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 44.5885i | − | 1.64021i | −0.572211 | − | 0.820106i | \(-0.693914\pi\) | ||
0.572211 | − | 0.820106i | \(-0.306086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.96902 | + | 1.96902i | −0.0722849 | + | 0.0722849i | ||||
\(743\) | 11.7434 | − | 11.7434i | 0.430824 | − | 0.430824i | −0.458085 | − | 0.888909i | \(-0.651464\pi\) |
0.888909 | + | 0.458085i | \(0.151464\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 33.7128i | 1.23431i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.65874 | − | 4.65874i | −0.170341 | − | 0.170341i | ||||
\(749\) | 19.7654 | 0.722211 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.39230 | 0.306240 | 0.153120 | − | 0.988208i | \(-0.451068\pi\) | ||||
0.153120 | + | 0.988208i | \(0.451068\pi\) | |||||||
\(752\) | −6.36396 | − | 6.36396i | −0.232070 | − | 0.232070i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.5885i | 0.895459i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.2677 | + | 19.2677i | −0.700298 | + | 0.700298i | −0.964474 | − | 0.264176i | \(-0.914900\pi\) |
0.264176 | + | 0.964474i | \(0.414900\pi\) | |||||||
\(758\) | 1.41421 | − | 1.41421i | 0.0513665 | − | 0.0513665i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.3923i | 0.811720i | 0.913935 | + | 0.405860i | \(0.133028\pi\) | ||||
−0.913935 | + | 0.405860i | \(0.866972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.17260 | − | 7.17260i | −0.259666 | − | 0.259666i | ||||
\(764\) | −4.39230 | −0.158908 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00000 | −0.108394 | ||||||||
\(767\) | −28.4094 | − | 28.4094i | −1.02580 | − | 1.02580i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.1769i | 1.62912i | 0.580078 | + | 0.814561i | \(0.303022\pi\) | ||||
−0.580078 | + | 0.814561i | \(0.696978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.2832 | + | 18.2832i | −0.658028 | + | 0.658028i | ||||
\(773\) | −6.93237 | + | 6.93237i | −0.249340 | + | 0.249340i | −0.820700 | − | 0.571360i | \(-0.806416\pi\) |
0.571360 | + | 0.820700i | \(0.306416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.66025i | 0.0954976i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.7661 | − | 22.7661i | −0.816205 | − | 0.816205i | ||||
\(779\) | −37.1769 | −1.33200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.41154 | −0.0862918 | ||||||||
\(782\) | 4.65874 | + | 4.65874i | 0.166596 | + | 0.166596i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 5.39230i | − | 0.192582i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.4901 | − | 16.4901i | 0.587808 | − | 0.587808i | −0.349229 | − | 0.937037i | \(-0.613557\pi\) |
0.937037 | + | 0.349229i | \(0.113557\pi\) | |||||||
\(788\) | −3.10583 | + | 3.10583i | −0.110641 | + | 0.110641i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1769i | 0.468517i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5080 | + | 19.5080i | 0.692749 | + | 0.692749i | ||||
\(794\) | 2.07180 | 0.0735253 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.00000 | −0.0708881 | ||||||||
\(797\) | 38.5999 | + | 38.5999i | 1.36728 | + | 1.36728i | 0.864299 | + | 0.502979i | \(0.167763\pi\) |
0.502979 | + | 0.864299i | \(0.332237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7654i | 0.699249i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.68973 | + | 2.68973i | −0.0949775 | + | 0.0949775i | ||||
\(803\) | 18.1074 | − | 18.1074i | 0.638995 | − | 0.638995i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.00000i | 0.211341i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.1440 | − | 13.1440i | −0.462405 | − | 0.462405i | ||||
\(809\) | −10.9808 | −0.386063 | −0.193032 | − | 0.981193i | \(-0.561832\pi\) | ||||
−0.193032 | + | 0.981193i | \(0.561832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.5885 | −1.14434 | −0.572168 | − | 0.820137i | \(-0.693897\pi\) | ||||
−0.572168 | + | 0.820137i | \(0.693897\pi\) | |||||||
\(812\) | 7.34847 | + | 7.34847i | 0.257881 | + | 0.257881i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 29.7846i | − | 1.04395i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.0208 | − | 47.0208i | 1.64505 | − | 1.64505i | ||||
\(818\) | 16.2635 | − | 16.2635i | 0.568638 | − | 0.568638i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 50.7846i | − | 1.77240i | −0.463308 | − | 0.886198i | \(-0.653337\pi\) | ||
0.463308 | − | 0.886198i | \(-0.346663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.9468 | − | 30.9468i | −1.07874 | − | 1.07874i | −0.996623 | − | 0.0821144i | \(-0.973833\pi\) |
−0.0821144 | − | 0.996623i | \(-0.526167\pi\) | |||||||
\(824\) | −0.928203 | −0.0323355 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.9808 | −0.590836 | ||||||||
\(827\) | 35.3417 | + | 35.3417i | 1.22895 | + | 1.22895i | 0.964360 | + | 0.264592i | \(0.0852373\pi\) |
0.264592 | + | 0.964360i | \(0.414763\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.9808i | 1.24966i | 0.780759 | + | 0.624832i | \(0.214832\pi\) | ||||
−0.780759 | + | 0.624832i | \(0.785168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.12132 | + | 2.12132i | −0.0735436 | + | 0.0735436i | ||||
\(833\) | −8.37379 | + | 8.37379i | −0.290135 | + | 0.290135i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 18.5885i | − | 0.642895i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.34847 | + | 7.34847i | 0.253849 | + | 0.253849i | ||||
\(839\) | 19.9808 | 0.689813 | 0.344906 | − | 0.938637i | \(-0.387911\pi\) | ||||
0.344906 | + | 0.938637i | \(0.387911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.1769 | 1.31645 | ||||||||
\(842\) | −13.5737 | − | 13.5737i | −0.467782 | − | 0.467782i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.00000i | − | 0.137686i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.79315 | + | 1.79315i | −0.0616134 | + | 0.0616134i | ||||
\(848\) | −1.55291 | + | 1.55291i | −0.0533273 | + | 0.0533273i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.7846i | 1.02100i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.46979 | − | 9.46979i | −0.324239 | − | 0.324239i | 0.526151 | − | 0.850391i | \(-0.323634\pi\) |
−0.850391 | + | 0.526151i | \(0.823634\pi\) | |||||||
\(854\) | 11.6603 | 0.399006 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.5885 | 0.532803 | ||||||||
\(857\) | −8.48528 | − | 8.48528i | −0.289852 | − | 0.289852i | 0.547170 | − | 0.837022i | \(-0.315705\pi\) |
−0.837022 | + | 0.547170i | \(0.815705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14.9808i | − | 0.511137i | −0.966791 | − | 0.255569i | \(-0.917737\pi\) | ||
0.966791 | − | 0.255569i | \(-0.0822626\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.5080 | − | 19.5080i | 0.664445 | − | 0.664445i | ||||
\(863\) | −21.2132 | + | 21.2132i | −0.722106 | + | 0.722106i | −0.969034 | − | 0.246928i | \(-0.920579\pi\) |
0.246928 | + | 0.969034i | \(0.420579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 19.0526i | − | 0.647432i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.79315 | + | 1.79315i | 0.0608635 | + | 0.0608635i | ||||
\(869\) | −30.5885 | −1.03764 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.58846 | −0.223241 | ||||||||
\(872\) | −5.65685 | − | 5.65685i | −0.191565 | − | 0.191565i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.5885i | 0.628764i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6782 | + | 22.6782i | −0.765788 | + | 0.765788i | −0.977362 | − | 0.211574i | \(-0.932141\pi\) |
0.211574 | + | 0.977362i | \(0.432141\pi\) | |||||||
\(878\) | 7.48717 | − | 7.48717i | 0.252680 | − | 0.252680i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.5692i | 1.80479i | 0.430907 | + | 0.902396i | \(0.358194\pi\) | ||||
−0.430907 | + | 0.902396i | \(0.641806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.1488 | + | 21.1488i | 0.711715 | + | 0.711715i | 0.966894 | − | 0.255179i | \(-0.0821344\pi\) |
−0.255179 | + | 0.966894i | \(0.582134\pi\) | |||||||
\(884\) | 6.58846 | 0.221594 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.5885 | −0.926852 | ||||||||
\(887\) | 15.9861 | + | 15.9861i | 0.536759 | + | 0.536759i | 0.922576 | − | 0.385816i | \(-0.126080\pi\) |
−0.385816 | + | 0.922576i | \(0.626080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.1769i | − | 0.441940i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.9372 | + | 14.9372i | −0.500134 | + | 0.500134i | ||||
\(893\) | −39.4321 | + | 39.4321i | −1.31954 | + | 1.31954i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.26795i | 0.0423592i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.24264 | − | 4.24264i | −0.141579 | − | 0.141579i | ||||
\(899\) | 16.3923 | 0.546714 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.82309 | 0.160680 | ||||||||
\(902\) | −12.7279 | − | 12.7279i | −0.423793 | − | 0.423793i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.3923i | 0.345643i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.31508 | + | 5.31508i | −0.176484 | + | 0.176484i | −0.789821 | − | 0.613337i | \(-0.789827\pi\) |
0.613337 | + | 0.789821i | \(0.289827\pi\) | |||||||
\(908\) | −4.81105 | + | 4.81105i | −0.159660 | + | 0.159660i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.1962i | 1.56368i | 0.623480 | + | 0.781839i | \(0.285718\pi\) | ||||
−0.623480 | + | 0.781839i | \(0.714282\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.31749 | + | 9.31749i | 0.308364 | + | 0.308364i | ||||
\(914\) | −23.1962 | −0.767261 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.5885 | 0.581139 | ||||||||
\(917\) | 12.0072 | + | 12.0072i | 0.396513 | + | 0.396513i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.41154i | 0.112536i | 0.998416 | + | 0.0562682i | \(0.0179202\pi\) | ||||
−0.998416 | + | 0.0562682i | \(0.982080\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.1822 | − | 23.1822i | 0.763466 | − | 0.763466i | ||||
\(923\) | 1.70522 | − | 1.70522i | 0.0561279 | − | 0.0561279i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.0526i | 0.527520i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.79555 | + | 5.79555i | 0.190248 | + | 0.190248i | ||||
\(929\) | 19.1769 | 0.629174 | 0.314587 | − | 0.949229i | \(-0.398134\pi\) | ||||
0.314587 | + | 0.949229i | \(0.398134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.4115 | −1.09502 | ||||||||
\(932\) | 10.0382 | + | 10.0382i | 0.328812 | + | 0.328812i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 13.9808i | − | 0.457465i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.6854 | + | 34.6854i | −1.13312 | + | 1.13312i | −0.143468 | + | 0.989655i | \(0.545825\pi\) |
−0.989655 | + | 0.143468i | \(0.954175\pi\) | |||||||
\(938\) | −1.96902 | + | 1.96902i | −0.0642907 | + | 0.0642907i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 27.3731i | − | 0.892336i | −0.894949 | − | 0.446168i | \(-0.852788\pi\) | ||
0.894949 | − | 0.446168i | \(-0.147212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.7279 | + | 12.7279i | 0.414478 | + | 0.414478i | ||||
\(944\) | −13.3923 | −0.435882 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.1962 | 1.04679 | ||||||||
\(947\) | −13.8647 | − | 13.8647i | −0.450543 | − | 0.450543i | 0.444991 | − | 0.895535i | \(-0.353207\pi\) |
−0.895535 | + | 0.444991i | \(0.853207\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.6077i | 0.831261i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.96902 | − | 1.96902i | 0.0638162 | − | 0.0638162i | ||||
\(953\) | 34.7733 | − | 34.7733i | 1.12642 | − | 1.12642i | 0.135664 | − | 0.990755i | \(-0.456683\pi\) |
0.990755 | − | 0.135664i | \(-0.0433167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.8038i | 0.414106i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.8338 | + | 15.8338i | 0.511565 | + | 0.511565i | ||||
\(959\) | −25.6077 | −0.826916 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 21.0609 | + | 21.0609i | 0.679031 | + | 0.679031i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.00000i | − | 0.0322078i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.06678 | + | 4.06678i | −0.130779 | + | 0.130779i | −0.769466 | − | 0.638688i | \(-0.779478\pi\) |
0.638688 | + | 0.769466i | \(0.279478\pi\) | |||||||
\(968\) | −1.41421 | + | 1.41421i | −0.0454545 | + | 0.0454545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 17.7846i | − | 0.570735i | −0.958418 | − | 0.285368i | \(-0.907884\pi\) | ||
0.958418 | − | 0.285368i | \(-0.0921157\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.5211 | + | 14.5211i | 0.465524 | + | 0.465524i | ||||
\(974\) | 12.5885 | 0.403360 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.19615 | 0.294362 | ||||||||
\(977\) | 9.31749 | + | 9.31749i | 0.298093 | + | 0.298093i | 0.840266 | − | 0.542174i | \(-0.182399\pi\) |
−0.542174 | + | 0.840266i | \(0.682399\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.5885i | 0.785851i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.13681 | − | 1.13681i | 0.0362771 | − | 0.0362771i | ||||
\(983\) | 18.7873 | − | 18.7873i | 0.599221 | − | 0.599221i | −0.340884 | − | 0.940105i | \(-0.610726\pi\) |
0.940105 | + | 0.340884i | \(0.110726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 18.0000i | − | 0.573237i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.1440 | + | 13.1440i | 0.418167 | + | 0.418167i | ||||
\(989\) | −32.1962 | −1.02378 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.5692 | 1.57462 | 0.787309 | − | 0.616559i | \(-0.211474\pi\) | ||||
0.787309 | + | 0.616559i | \(0.211474\pi\) | |||||||
\(992\) | 1.41421 | + | 1.41421i | 0.0449013 | + | 0.0449013i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 1.01924i | − | 0.0323283i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0919 | − | 19.0919i | 0.604646 | − | 0.604646i | −0.336896 | − | 0.941542i | \(-0.609377\pi\) |
0.941542 | + | 0.336896i | \(0.109377\pi\) | |||||||
\(998\) | −23.4596 | + | 23.4596i | −0.742601 | + | 0.742601i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.2.f.b.593.4 | yes | 8 | |
3.2 | odd | 2 | 1350.2.f.e.593.2 | yes | 8 | ||
5.2 | odd | 4 | 1350.2.f.e.107.2 | yes | 8 | ||
5.3 | odd | 4 | 1350.2.f.e.107.3 | yes | 8 | ||
5.4 | even | 2 | inner | 1350.2.f.b.593.1 | yes | 8 | |
15.2 | even | 4 | inner | 1350.2.f.b.107.4 | yes | 8 | |
15.8 | even | 4 | inner | 1350.2.f.b.107.1 | ✓ | 8 | |
15.14 | odd | 2 | 1350.2.f.e.593.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.2.f.b.107.1 | ✓ | 8 | 15.8 | even | 4 | inner | |
1350.2.f.b.107.4 | yes | 8 | 15.2 | even | 4 | inner | |
1350.2.f.b.593.1 | yes | 8 | 5.4 | even | 2 | inner | |
1350.2.f.b.593.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1350.2.f.e.107.2 | yes | 8 | 5.2 | odd | 4 | ||
1350.2.f.e.107.3 | yes | 8 | 5.3 | odd | 4 | ||
1350.2.f.e.593.2 | yes | 8 | 3.2 | odd | 2 | ||
1350.2.f.e.593.3 | yes | 8 | 15.14 | odd | 2 |