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 | 107.3 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.107 |
Dual form | 1350.2.f.e.593.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 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 | \(-0.172977\pi\) |
−0.517070 | + | 0.855943i | \(0.672977\pi\) | |||||||
\(8\) | −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 | \(-0.613423\pi\) |
0.937184 | + | 0.348836i | \(0.113423\pi\) | |||||||
\(14\) | 1.26795 | 0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.55291 | − | 1.55291i | 0.376637 | − | 0.376637i | −0.493250 | − | 0.869887i | \(-0.664191\pi\) |
0.869887 | + | 0.493250i | \(0.164191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.19615i | − | 1.42149i | −0.703447 | − | 0.710747i | \(-0.748357\pi\) | ||
0.703447 | − | 0.710747i | \(-0.251643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.12132 | + | 2.12132i | 0.452267 | + | 0.452267i | ||||
\(23\) | 2.12132 | + | 2.12132i | 0.442326 | + | 0.442326i | 0.892793 | − | 0.450467i | \(-0.148743\pi\) |
−0.450467 | + | 0.892793i | \(0.648743\pi\) | |||||||
\(24\) | 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 | \(-0.224712\pi\) | ||||
0.760994 | + | 0.648759i | \(0.224712\pi\) | |||||||
\(30\) | 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 | 0.985716 | + | 0.168414i | \(0.0538645\pi\) |
0.168414 | + | 0.985716i | \(0.446136\pi\) | |||||||
\(38\) | −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 | 0.172206 | − | 0.985061i | \(-0.444911\pi\) |
0.985061 | − | 0.172206i | \(-0.0550894\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | 0.442326 | ||||||||
\(47\) | 6.36396 | − | 6.36396i | 0.928279 | − | 0.928279i | −0.0693157 | − | 0.997595i | \(-0.522082\pi\) |
0.997595 | + | 0.0693157i | \(0.0220816\pi\) | |||||||
\(48\) | 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 | 0.805672 | − | 0.592362i | \(-0.201805\pi\) |
−0.592362 | + | 0.805672i | \(0.701805\pi\) | |||||||
\(54\) | 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 | \(-0.837024\pi\) | ||||
−0.871765 | + | 0.489925i | \(0.837024\pi\) | |||||||
\(60\) | 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 | \(-0.292831\pi\) |
−0.795574 | + | 0.605856i | \(0.792831\pi\) | |||||||
\(68\) | −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 | \(-0.583508\pi\) |
0.965784 | + | 0.259348i | \(0.0835076\pi\) | |||||||
\(74\) | 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 | \(-0.805555\pi\) | ||
0.819151 | − | 0.573578i | \(-0.194445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.24264 | + | 4.24264i | 0.468521 | + | 0.468521i | ||||
\(83\) | 3.10583 | + | 3.10583i | 0.340909 | + | 0.340909i | 0.856709 | − | 0.515800i | \(-0.172505\pi\) |
−0.515800 | + | 0.856709i | \(0.672505\pi\) | |||||||
\(84\) | 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 | \(-0.643038\pi\) | ||||
−0.434395 | + | 0.900722i | \(0.643038\pi\) | |||||||
\(90\) | 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 | \(-0.293121\pi\) |
−0.796126 | + | 0.605131i | \(0.793121\pi\) | |||||||
\(98\) | −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 | \(-0.764561\pi\) |
0.674032 | + | 0.738703i | \(0.264561\pi\) | |||||||
\(104\) | −3.00000 | −0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.19615 | 0.213309 | ||||||||
\(107\) | −11.0227 | + | 11.0227i | −1.06561 | + | 1.06561i | −0.0679138 | + | 0.997691i | \(0.521634\pi\) |
−0.997691 | + | 0.0679138i | \(0.978366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.00000i | − | 0.766261i | −0.923694 | − | 0.383131i | \(-0.874846\pi\) | ||
0.923694 | − | 0.383131i | \(-0.125154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.896575 | − | 0.896575i | −0.0847184 | − | 0.0847184i | ||||
\(113\) | 7.34847 | + | 7.34847i | 0.691286 | + | 0.691286i | 0.962515 | − | 0.271229i | \(-0.0874301\pi\) |
−0.271229 | + | 0.962515i | \(0.587430\pi\) | |||||||
\(114\) | 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 | \(-0.0974607\pi\) |
−0.301420 | + | 0.953491i | \(0.597461\pi\) | |||||||
\(128\) | 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 | 0.252496 | − | 0.967598i | \(-0.418748\pi\) |
0.967598 | − | 0.252496i | \(-0.0812516\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1962i | 1.37374i | 0.726780 | + | 0.686870i | \(0.241016\pi\) | ||||
−0.726780 | + | 0.686870i | \(0.758984\pi\) | |||||||
\(140\) | 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 | \(-0.639967\pi\) | ||||
−0.425685 | + | 0.904871i | \(0.639967\pi\) | |||||||
\(150\) | 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 | \(-0.339163\pi\) |
−0.875037 | + | 0.484056i | \(0.839163\pi\) | |||||||
\(158\) | −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 | \(-0.770055\pi\) |
0.661183 | + | 0.750225i | \(0.270055\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.39230 | 0.340909 | ||||||||
\(167\) | −17.9551 | + | 17.9551i | −1.38941 | + | 1.38941i | −0.562838 | + | 0.826567i | \(0.690290\pi\) |
−0.826567 | + | 0.562838i | \(0.809710\pi\) | |||||||
\(168\) | 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 | 0.451595 | − | 0.892223i | \(-0.350855\pi\) |
−0.892223 | + | 0.451595i | \(0.850855\pi\) | |||||||
\(174\) | 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 | \(-0.897857\pi\) | ||||
−0.948955 | + | 0.315412i | \(0.897857\pi\) | |||||||
\(180\) | 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 | −0.399187 | + | 0.916870i | \(0.630708\pi\) |
−0.916870 | + | 0.399187i | \(0.869292\pi\) | |||||||
\(194\) | −2.66025 | −0.190995 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.39230 | −0.385165 | ||||||||
\(197\) | 3.10583 | − | 3.10583i | 0.221281 | − | 0.221281i | −0.587757 | − | 0.809038i | \(-0.699989\pi\) |
0.809038 | + | 0.587757i | \(0.199989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.00000i | − | 0.141776i | −0.997484 | − | 0.0708881i | \(-0.977417\pi\) | ||
0.997484 | − | 0.0708881i | \(-0.0225833\pi\) | |||||||
\(200\) | 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 | −0.000267267 | 1.00000i | \(0.500085\pi\) | |
−1.00000 | 0.000267267i | \(0.999915\pi\) | ||||||||
\(224\) | −1.26795 | −0.0847184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.3923 | 0.691286 | ||||||||
\(227\) | 4.81105 | − | 4.81105i | 0.319320 | − | 0.319320i | −0.529186 | − | 0.848506i | \(-0.677503\pi\) |
0.848506 | + | 0.529186i | \(0.177503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.5885i | 1.16228i | 0.813804 | + | 0.581139i | \(0.197393\pi\) | ||||
−0.813804 | + | 0.581139i | \(0.802607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.79555 | − | 5.79555i | −0.380497 | − | 0.380497i | ||||
\(233\) | 10.0382 | + | 10.0382i | 0.657624 | + | 0.657624i | 0.954817 | − | 0.297193i | \(-0.0960506\pi\) |
−0.297193 | + | 0.954817i | \(0.596051\pi\) | |||||||
\(234\) | 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 | \(-0.635906\pi\) | ||||
−0.414106 | + | 0.910229i | \(0.635906\pi\) | |||||||
\(240\) | 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 | −0.657012 | − | 0.753880i | \(-0.728180\pi\) |
0.753880 | + | 0.657012i | \(0.228180\pi\) | |||||||
\(258\) | 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 | 0.875549 | − | 0.483130i | \(-0.160500\pi\) |
−0.483130 | + | 0.875549i | \(0.660500\pi\) | |||||||
\(264\) | 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 | \(-0.238749\pi\) | ||||
0.731653 | + | 0.681677i | \(0.238749\pi\) | |||||||
\(270\) | 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 | \(-0.473070\pi\) |
−0.996423 | + | 0.0845011i | \(0.973070\pi\) | |||||||
\(278\) | 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 | \(-0.853339\pi\) |
0.444618 | + | 0.895720i | \(0.353339\pi\) | |||||||
\(284\) | 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 | −0.975006 | − | 0.222178i | \(-0.928683\pi\) |
−0.222178 | − | 0.975006i | \(-0.571317\pi\) | |||||||
\(294\) | 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 | \(-0.414563\pi\) |
−0.964195 | + | 0.265196i | \(0.914563\pi\) | |||||||
\(308\) | 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 | \(-0.764468\pi\) |
0.674248 | + | 0.738505i | \(0.264468\pi\) | |||||||
\(314\) | −6.92820 | −0.390981 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.1962 | −0.573578 | ||||||||
\(317\) | 18.5235 | − | 18.5235i | 1.04038 | − | 1.04038i | 0.0412325 | − | 0.999150i | \(-0.486872\pi\) |
0.999150 | − | 0.0412325i | \(-0.0131284\pi\) | |||||||
\(318\) | 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 | \(-0.263943\pi\) |
−0.737392 | + | 0.675465i | \(0.763943\pi\) | |||||||
\(338\) | 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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.3923i | − | 0.770402i | −0.922833 | − | 0.385201i | \(-0.874132\pi\) | ||
0.922833 | − | 0.385201i | \(-0.125868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.12132 | − | 2.12132i | −0.113067 | − | 0.113067i | ||||
\(353\) | −2.68973 | − | 2.68973i | −0.143160 | − | 0.143160i | 0.631895 | − | 0.775054i | \(-0.282278\pi\) |
−0.775054 | + | 0.631895i | \(0.782278\pi\) | |||||||
\(354\) | 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 | \(-0.595471\pi\) | ||||
−0.295455 | + | 0.955357i | \(0.595471\pi\) | |||||||
\(360\) | 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 | \(-0.176364\pi\) |
−0.526147 | + | 0.850393i | \(0.676364\pi\) | |||||||
\(368\) | −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 | −0.272023 | + | 0.962291i | \(0.587693\pi\) |
−0.962291 | + | 0.272023i | \(0.912307\pi\) | |||||||
\(374\) | 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 | \(0.0163577\pi\) | ||||
−0.998680 | + | 0.0513665i | \(0.983642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.10583 | + | 3.10583i | 0.158908 | + | 0.158908i | ||||
\(383\) | −2.12132 | − | 2.12132i | −0.108394 | − | 0.108394i | 0.650830 | − | 0.759224i | \(-0.274421\pi\) |
−0.759224 | + | 0.650830i | \(0.774421\pi\) | |||||||
\(384\) | 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 | \(-0.196074\pi\) | ||||
0.816205 | + | 0.577763i | \(0.196074\pi\) | |||||||
\(390\) | 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 | \(-0.266556\pi\) |
−0.742913 | + | 0.669388i | \(0.766556\pi\) | |||||||
\(398\) | −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 | \(0.192530\pi\) | ||||
−0.822588 | + | 0.568638i | \(0.807470\pi\) | |||||||
\(410\) | 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 | \(-0.581697\pi\) | ||||
−0.253849 | + | 0.967244i | \(0.581697\pi\) | |||||||
\(420\) | 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 | \(-0.598636\pi\) |
0.952372 | + | 0.304939i | \(0.0986362\pi\) | |||||||
\(434\) | −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 | \(0.0813119\pi\) | ||||
−0.967550 | + | 0.252680i | \(0.918688\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.65874 | − | 4.65874i | −0.221594 | − | 0.221594i | ||||
\(443\) | −19.5080 | − | 19.5080i | −0.926852 | − | 0.926852i | 0.0706489 | − | 0.997501i | \(-0.477493\pi\) |
−0.997501 | + | 0.0706489i | \(0.977493\pi\) | |||||||
\(444\) | 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 | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 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 | \(-0.0674645\pi\) |
−0.210363 | + | 0.977623i | \(0.567465\pi\) | |||||||
\(458\) | 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 | \(-0.871675\pi\) |
0.392312 | + | 0.919832i | \(0.371675\pi\) | |||||||
\(464\) | −8.19615 | −0.380497 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.1962 | 0.657624 | ||||||||
\(467\) | −9.88589 | + | 9.88589i | −0.457465 | + | 0.457465i | −0.897822 | − | 0.440358i | \(-0.854852\pi\) |
0.440358 | + | 0.897822i | \(0.354852\pi\) | |||||||
\(468\) | 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 | \(-0.670934\pi\) | ||||
−0.511565 | + | 0.859244i | \(0.670934\pi\) | |||||||
\(480\) | 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 | \(-0.342066\pi\) |
−0.879415 | + | 0.476055i | \(0.842066\pi\) | |||||||
\(488\) | 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 | \(-0.733592\pi\) | ||
0.669734 | − | 0.742601i | \(-0.266408\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.984508 | + | 0.984508i | 0.0439408 | + | 0.0439408i | ||||
\(503\) | 1.13681 | + | 1.13681i | 0.0506879 | + | 0.0506879i | 0.731996 | − | 0.681308i | \(-0.238589\pi\) |
−0.681308 | + | 0.731996i | \(0.738589\pi\) | |||||||
\(504\) | 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 | \(-0.170745\pi\) | ||||
0.859549 | + | 0.511054i | \(0.170745\pi\) | |||||||
\(510\) | 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 | \(-0.714631\pi\) |
0.781155 | + | 0.624337i | \(0.214631\pi\) | |||||||
\(524\) | −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 | 0.987610 | + | 0.156930i | \(0.0501596\pi\) |
0.156930 | + | 0.987610i | \(0.449840\pi\) | |||||||
\(548\) | −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 | −0.914146 | − | 0.405384i | \(-0.867138\pi\) |
0.405384 | + | 0.914146i | \(0.367138\pi\) | |||||||
\(558\) | 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 | 0.271243 | − | 0.962511i | \(-0.412565\pi\) |
−0.962511 | + | 0.271243i | \(0.912565\pi\) | |||||||
\(564\) | 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 | \(-0.655518\pi\) | ||||
−0.469367 | + | 0.883003i | \(0.655518\pi\) | |||||||
\(570\) | 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 | \(-0.267635\pi\) |
−0.745177 | + | 0.666867i | \(0.767635\pi\) | |||||||
\(578\) | 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 | −0.953841 | − | 0.300312i | \(-0.902909\pi\) |
0.300312 | + | 0.953841i | \(0.402909\pi\) | |||||||
\(588\) | 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 | −0.928102 | − | 0.372327i | \(-0.878560\pi\) |
−0.372327 | − | 0.928102i | \(-0.621440\pi\) | |||||||
\(594\) | 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 | \(-0.589671\pi\) | ||||
−0.277998 | + | 0.960582i | \(0.589671\pi\) | |||||||
\(600\) | 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 | \(-0.382023\pi\) |
−0.932098 | + | 0.362207i | \(0.882023\pi\) | |||||||
\(608\) | 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 | \(-0.628371\pi\) |
0.919776 | + | 0.392445i | \(0.128371\pi\) | |||||||
\(614\) | −17.3205 | −0.698999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.80385 | 0.153261 | ||||||||
\(617\) | 4.24264 | − | 4.24264i | 0.170802 | − | 0.170802i | −0.616530 | − | 0.787332i | \(-0.711462\pi\) |
0.787332 | + | 0.616530i | \(0.211462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 42.3923i | − | 1.70389i | −0.523631 | − | 0.851945i | \(-0.675423\pi\) | ||
0.523631 | − | 0.851945i | \(-0.324577\pi\) | |||||||
\(620\) | 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 | \(-0.634506\pi\) |
0.912040 | + | 0.410100i | \(0.134506\pi\) | |||||||
\(644\) | 3.80385 | 0.149893 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.6077 | −0.535388 | ||||||||
\(647\) | −5.22715 | + | 5.22715i | −0.205500 | + | 0.205500i | −0.802352 | − | 0.596851i | \(-0.796418\pi\) |
0.596851 | + | 0.802352i | \(0.296418\pi\) | |||||||
\(648\) | 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 | 0.181464 | − | 0.983398i | \(-0.441916\pi\) |
−0.983398 | + | 0.181464i | \(0.941916\pi\) | |||||||
\(654\) | 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 | \(-0.772566\pi\) | ||||
−0.755417 | + | 0.655244i | \(0.772566\pi\) | |||||||
\(660\) | 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 | \(-0.518321\pi\) |
0.998344 | + | 0.0575247i | \(0.0183208\pi\) | |||||||
\(674\) | −1.60770 | −0.0619261 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.00000 | 0.153846 | ||||||||
\(677\) | −18.1074 | + | 18.1074i | −0.695923 | + | 0.695923i | −0.963529 | − | 0.267606i | \(-0.913768\pi\) |
0.267606 | + | 0.963529i | \(0.413768\pi\) | |||||||
\(678\) | 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 | 0.997268 | + | 0.0738643i | \(0.0235332\pi\) |
0.0738643 | + | 0.997268i | \(0.476467\pi\) | |||||||
\(684\) | 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 | \(0.167888\pi\) | ||||
−0.864100 | + | 0.503320i | \(0.832112\pi\) | |||||||
\(710\) | 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 | \(-0.495229\pi\) | ||||
0.0149892 | + | 0.999888i | \(0.495229\pi\) | |||||||
\(720\) | 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 | 0.993416 | + | 0.114562i | \(0.0365465\pi\) |
0.114562 | + | 0.993416i | \(0.463453\pi\) | |||||||
\(728\) | −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 | \(-0.713382\pi\) |
0.783599 | + | 0.621268i | \(0.213382\pi\) | |||||||
\(734\) | 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 | \(0.306086\pi\) | ||||
−0.572211 | + | 0.820106i | \(0.693914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.96902 | + | 1.96902i | 0.0722849 | + | 0.0722849i | ||||
\(743\) | 11.7434 | + | 11.7434i | 0.430824 | + | 0.430824i | 0.888909 | − | 0.458085i | \(-0.151464\pi\) |
−0.458085 | + | 0.888909i | \(0.651464\pi\) | |||||||
\(744\) | 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 | \(-0.0851000\pi\) |
−0.264176 | + | 0.964474i | \(0.585100\pi\) | |||||||
\(758\) | 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 | \(-0.696978\pi\) | ||
0.580078 | − | 0.814561i | \(-0.303022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.2832 | + | 18.2832i | 0.658028 | + | 0.658028i | ||||
\(773\) | −6.93237 | − | 6.93237i | −0.249340 | − | 0.249340i | 0.571360 | − | 0.820700i | \(-0.306416\pi\) |
−0.820700 | + | 0.571360i | \(0.806416\pi\) | |||||||
\(774\) | 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 | \(-0.386443\pi\) |
−0.937037 | + | 0.349229i | \(0.886443\pi\) | |||||||
\(788\) | −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 | 0.502979 | − | 0.864299i | \(-0.332237\pi\) |
0.864299 | − | 0.502979i | \(-0.167763\pi\) | |||||||
\(798\) | 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 | \(-0.438168\pi\) | ||||
0.193032 | + | 0.981193i | \(0.438168\pi\) | |||||||
\(810\) | 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 | 0.0821144 | − | 0.996623i | \(-0.473833\pi\) |
0.996623 | − | 0.0821144i | \(-0.0261673\pi\) | |||||||
\(824\) | 0.928203 | 0.0323355 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.9808 | −0.590836 | ||||||||
\(827\) | 35.3417 | − | 35.3417i | 1.22895 | − | 1.22895i | 0.264592 | − | 0.964360i | \(-0.414763\pi\) |
0.964360 | − | 0.264592i | \(-0.0852373\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 35.9808i | − | 1.24966i | −0.780759 | − | 0.624832i | \(-0.785168\pi\) | ||
0.780759 | − | 0.624832i | \(-0.214832\pi\) | |||||||
\(830\) | 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 | \(-0.612089\pi\) | ||||
−0.344906 | + | 0.938637i | \(0.612089\pi\) | |||||||
\(840\) | 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 | \(-0.676366\pi\) |
0.850391 | + | 0.526151i | \(0.176366\pi\) | |||||||
\(854\) | −11.6603 | −0.399006 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.5885 | 0.532803 | ||||||||
\(857\) | −8.48528 | + | 8.48528i | −0.289852 | + | 0.289852i | −0.837022 | − | 0.547170i | \(-0.815705\pi\) |
0.547170 | + | 0.837022i | \(0.315705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9808i | 0.511137i | 0.966791 | + | 0.255569i | \(0.0822626\pi\) | ||||
−0.966791 | + | 0.255569i | \(0.917737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.5080 | − | 19.5080i | −0.664445 | − | 0.664445i | ||||
\(863\) | −21.2132 | − | 21.2132i | −0.722106 | − | 0.722106i | 0.246928 | − | 0.969034i | \(-0.420579\pi\) |
−0.969034 | + | 0.246928i | \(0.920579\pi\) | |||||||
\(864\) | 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 | \(-0.0678590\pi\) |
−0.211574 | + | 0.977362i | \(0.567859\pi\) | |||||||
\(878\) | 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 | \(-0.917866\pi\) |
0.255179 | + | 0.966894i | \(0.417866\pi\) | |||||||
\(884\) | −6.58846 | −0.221594 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.5885 | −0.926852 | ||||||||
\(887\) | 15.9861 | − | 15.9861i | 0.536759 | − | 0.536759i | −0.385816 | − | 0.922576i | \(-0.626080\pi\) |
0.922576 | + | 0.385816i | \(0.126080\pi\) | |||||||
\(888\) | 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 | \(-0.210173\pi\) |
−0.613337 | + | 0.789821i | \(0.710173\pi\) | |||||||
\(908\) | −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 | \(-0.982080\pi\) | ||
0.998416 | − | 0.0562682i | \(-0.0179202\pi\) | |||||||
\(920\) | 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 | \(-0.601866\pi\) | ||||
−0.314587 | + | 0.949229i | \(0.601866\pi\) | |||||||
\(930\) | 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 | 0.989655 | + | 0.143468i | \(0.0458253\pi\) |
0.143468 | + | 0.989655i | \(0.454175\pi\) | |||||||
\(938\) | −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 | −0.895535 | − | 0.444991i | \(-0.853207\pi\) |
0.444991 | + | 0.895535i | \(0.353207\pi\) | |||||||
\(948\) | 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 | 0.990755 | + | 0.135664i | \(0.0433167\pi\) |
0.135664 | + | 0.990755i | \(0.456683\pi\) | |||||||
\(954\) | 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 | \(-0.220522\pi\) |
−0.638688 | + | 0.769466i | \(0.720522\pi\) | |||||||
\(968\) | −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 | −0.542174 | − | 0.840266i | \(-0.682399\pi\) |
0.840266 | + | 0.542174i | \(0.182399\pi\) | |||||||
\(978\) | 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 | 0.940105 | − | 0.340884i | \(-0.110726\pi\) |
−0.340884 | + | 0.940105i | \(0.610726\pi\) | |||||||
\(984\) | 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 | \(-0.390623\pi\) |
−0.941542 | + | 0.336896i | \(0.890623\pi\) | |||||||
\(998\) | −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.e.107.3 | yes | 8 | |
3.2 | odd | 2 | 1350.2.f.b.107.1 | ✓ | 8 | ||
5.2 | odd | 4 | 1350.2.f.b.593.4 | yes | 8 | ||
5.3 | odd | 4 | 1350.2.f.b.593.1 | yes | 8 | ||
5.4 | even | 2 | inner | 1350.2.f.e.107.2 | yes | 8 | |
15.2 | even | 4 | inner | 1350.2.f.e.593.2 | yes | 8 | |
15.8 | even | 4 | inner | 1350.2.f.e.593.3 | yes | 8 | |
15.14 | odd | 2 | 1350.2.f.b.107.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.2.f.b.107.1 | ✓ | 8 | 3.2 | odd | 2 | ||
1350.2.f.b.107.4 | yes | 8 | 15.14 | odd | 2 | ||
1350.2.f.b.593.1 | yes | 8 | 5.3 | odd | 4 | ||
1350.2.f.b.593.4 | yes | 8 | 5.2 | odd | 4 | ||
1350.2.f.e.107.2 | yes | 8 | 5.4 | even | 2 | inner | |
1350.2.f.e.107.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1350.2.f.e.593.2 | yes | 8 | 15.2 | even | 4 | inner | |
1350.2.f.e.593.3 | yes | 8 | 15.8 | even | 4 | inner |