Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(601,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.601");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.bg (of order \(3\), 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: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.1 | ||
Root | \(1.28078 - 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.841 |
Dual form | 1560.2.bg.f.601.1 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.28078 | − | 3.95042i | −0.862052 | − | 1.49312i | −0.869944 | − | 0.493150i | \(-0.835845\pi\) |
0.00789196 | − | 0.999969i | \(-0.497488\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.219224 | + | 0.379706i | −0.0660984 | + | 0.114486i | −0.897181 | − | 0.441664i | \(-0.854388\pi\) |
0.831082 | + | 0.556149i | \(0.187722\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.84233 | − | 2.21837i | −0.788320 | − | 0.615265i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.56155 | − | 2.70469i | −0.358245 | − | 0.620498i | 0.629423 | − | 0.777063i | \(-0.283291\pi\) |
−0.987668 | + | 0.156565i | \(0.949958\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.56155 | −0.995412 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.219224 | + | 0.379706i | −0.0457113 | + | 0.0791743i | −0.887976 | − | 0.459890i | \(-0.847889\pi\) |
0.842265 | + | 0.539064i | \(0.181222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.34233 | + | 7.52113i | −0.806350 | + | 1.39664i | 0.109025 | + | 0.994039i | \(0.465227\pi\) |
−0.915376 | + | 0.402601i | \(0.868106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.12311 | −0.740532 | −0.370266 | − | 0.928926i | \(-0.620733\pi\) | ||||
−0.370266 | + | 0.928926i | \(0.620733\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.219224 | + | 0.379706i | 0.0381619 | + | 0.0660984i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.28078 | − | 3.95042i | −0.385522 | − | 0.667743i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.219224 | + | 0.379706i | −0.0360401 | + | 0.0624233i | −0.883483 | − | 0.468463i | \(-0.844808\pi\) |
0.847443 | + | 0.530887i | \(0.178141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.34233 | + | 1.35234i | −0.535201 | + | 0.216548i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | − | 1.73205i | 0.156174 | − | 0.270501i | −0.777312 | − | 0.629115i | \(-0.783417\pi\) |
0.933486 | + | 0.358614i | \(0.116751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.06155 | − | 1.83866i | −0.161885 | − | 0.280394i | 0.773660 | − | 0.633602i | \(-0.218424\pi\) |
−0.935545 | + | 0.353208i | \(0.885091\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.43845 | 0.355684 | 0.177842 | − | 0.984059i | \(-0.443088\pi\) | ||||
0.177842 | + | 0.984059i | \(0.443088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90388 | + | 11.9579i | −0.986269 | + | 1.70827i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.12311 | −0.978434 | −0.489217 | − | 0.872162i | \(-0.662717\pi\) | ||||
−0.489217 | + | 0.872162i | \(0.662717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.219224 | + | 0.379706i | −0.0295601 | + | 0.0511996i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.12311 | −0.413665 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.34233 | − | 7.52113i | −0.565323 | − | 0.979168i | −0.997020 | − | 0.0771494i | \(-0.975418\pi\) |
0.431696 | − | 0.902019i | \(-0.357915\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.842329 | + | 1.45896i | 0.107849 | + | 0.186800i | 0.914899 | − | 0.403683i | \(-0.132270\pi\) |
−0.807050 | + | 0.590484i | \(0.798937\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.28078 | + | 3.95042i | −0.287351 | + | 0.497706i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.84233 | − | 2.21837i | −0.352548 | − | 0.275155i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.28078 | − | 5.68247i | 0.400811 | − | 0.694224i | −0.593013 | − | 0.805193i | \(-0.702062\pi\) |
0.993824 | + | 0.110968i | \(0.0353952\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.219224 | + | 0.379706i | 0.0263914 | + | 0.0457113i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.56155 | 1.00205 | 0.501027 | − | 0.865432i | \(-0.332956\pi\) | ||||
0.501027 | + | 0.865432i | \(0.332956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.2462 | −1.94035 | −0.970175 | − | 0.242405i | \(-0.922064\pi\) | ||||
−0.970175 | + | 0.242405i | \(0.922064\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.3693 | 1.46747 | 0.733737 | − | 0.679434i | \(-0.237775\pi\) | ||||
0.733737 | + | 0.679434i | \(0.237775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | + | 1.73205i | 0.108465 | + | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.34233 | + | 7.52113i | 0.465547 | + | 0.806350i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.00000 | + | 1.73205i | −0.106000 | + | 0.183597i | −0.914146 | − | 0.405385i | \(-0.867138\pi\) |
0.808146 | + | 0.588982i | \(0.200471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.28078 | + | 16.2880i | −0.239090 | + | 1.70745i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.06155 | + | 3.57071i | −0.213773 | + | 0.370266i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.56155 | − | 2.70469i | −0.160212 | − | 0.277495i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.28078 | − | 10.8786i | −0.637716 | − | 1.10456i | −0.985933 | − | 0.167143i | \(-0.946546\pi\) |
0.348216 | − | 0.937414i | \(-0.386787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.438447 | 0.0440656 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.12311 | − | 7.14143i | 0.410264 | − | 0.710599i | −0.584654 | − | 0.811283i | \(-0.698770\pi\) |
0.994918 | + | 0.100684i | \(0.0321031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.561553 | 0.0553314 | 0.0276657 | − | 0.999617i | \(-0.491193\pi\) | ||||
0.0276657 | + | 0.999617i | \(0.491193\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.56155 | −0.445162 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.56155 | − | 9.63289i | 0.537656 | − | 0.931247i | −0.461374 | − | 0.887206i | \(-0.652643\pi\) |
0.999030 | − | 0.0440411i | \(-0.0140233\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.80776 | −0.268935 | −0.134468 | − | 0.990918i | \(-0.542932\pi\) | ||||
−0.134468 | + | 0.990918i | \(0.542932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.219224 | + | 0.379706i | 0.0208078 | + | 0.0360401i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.34233 | − | 16.1814i | −0.878852 | − | 1.52222i | −0.852602 | − | 0.522562i | \(-0.824976\pi\) |
−0.0262509 | − | 0.999655i | \(-0.508357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.219224 | + | 0.379706i | −0.0204427 | + | 0.0354078i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | + | 3.57071i | −0.0462250 | + | 0.330113i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.56155 | − | 7.90084i | 0.418157 | − | 0.724269i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.40388 | + | 9.35980i | 0.491262 | + | 0.850891i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | − | 1.73205i | −0.0901670 | − | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.84233 | − | 8.38716i | 0.429687 | − | 0.744240i | −0.567158 | − | 0.823609i | \(-0.691957\pi\) |
0.996845 | + | 0.0793688i | \(0.0252905\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.12311 | −0.186929 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.56155 | 0.136434 | 0.0682168 | − | 0.997671i | \(-0.478269\pi\) | ||||
0.0682168 | + | 0.997671i | \(0.478269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.12311 | + | 12.3376i | −0.617652 | + | 1.06980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.219224 | + | 0.379706i | 0.0187295 | + | 0.0324405i | 0.875238 | − | 0.483692i | \(-0.160705\pi\) |
−0.856509 | + | 0.516133i | \(0.827371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.40388 | − | 2.43160i | −0.119076 | − | 0.206245i | 0.800326 | − | 0.599565i | \(-0.204660\pi\) |
−0.919402 | + | 0.393320i | \(0.871326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.21922 | − | 2.11176i | 0.102677 | − | 0.177842i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.46543 | − | 0.592932i | 0.122546 | − | 0.0495834i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.34233 | + | 7.52113i | −0.360611 | + | 0.624596i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.90388 | + | 11.9579i | 0.569423 | + | 0.986269i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.46543 | − | 12.9305i | −0.611592 | − | 1.05931i | −0.990972 | − | 0.134068i | \(-0.957196\pi\) |
0.379380 | − | 0.925241i | \(-0.376137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.00000 | − | 1.73205i | 0.0808452 | − | 0.140028i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.12311 | −0.331176 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.24621 | −0.418693 | −0.209347 | − | 0.977841i | \(-0.567134\pi\) | ||||
−0.209347 | + | 0.977841i | \(0.567134\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.56155 | + | 6.16879i | −0.282450 | + | 0.489217i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.93845 | − | 10.2857i | −0.465135 | − | 0.805638i | 0.534073 | − | 0.845439i | \(-0.320661\pi\) |
−0.999208 | + | 0.0398011i | \(0.987328\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.219224 | + | 0.379706i | 0.0170665 | + | 0.0295601i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.7808 | + | 22.1370i | −0.989006 | + | 1.71301i | −0.366440 | + | 0.930442i | \(0.619424\pi\) |
−0.622566 | + | 0.782567i | \(0.713910\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.15767 | + | 12.6107i | 0.242898 | + | 0.970052i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.56155 | + | 2.70469i | −0.119415 | + | 0.206833i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | + | 3.46410i | 0.152057 | + | 0.263371i | 0.931984 | − | 0.362500i | \(-0.118077\pi\) |
−0.779926 | + | 0.625871i | \(0.784744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.28078 | − | 3.95042i | −0.172410 | − | 0.298624i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.68466 | −0.652779 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.90388 | − | 8.49377i | 0.366533 | − | 0.634854i | −0.622488 | − | 0.782630i | \(-0.713878\pi\) |
0.989021 | + | 0.147775i | \(0.0472112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.12311 | 0.380797 | 0.190399 | − | 0.981707i | \(-0.439022\pi\) | ||||
0.190399 | + | 0.981707i | \(0.439022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.68466 | 0.124534 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.219224 | + | 0.379706i | −0.0161176 | + | 0.0279166i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.876894 | −0.0641249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.28078 | + | 3.95042i | 0.165902 | + | 0.287351i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0000 | − | 17.3205i | −0.723575 | − | 1.25327i | −0.959558 | − | 0.281511i | \(-0.909164\pi\) |
0.235983 | − | 0.971757i | \(-0.424169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.52699 | + | 16.5012i | −0.685768 | + | 1.18778i | 0.287427 | + | 0.957802i | \(0.407200\pi\) |
−0.973195 | + | 0.229982i | \(0.926133\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.34233 | + | 1.35234i | −0.239349 | + | 0.0968434i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | − | 6.92820i | 0.284988 | − | 0.493614i | −0.687618 | − | 0.726073i | \(-0.741344\pi\) |
0.972606 | + | 0.232458i | \(0.0746770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.71922 | − | 8.17394i | −0.334537 | − | 0.579435i | 0.648859 | − | 0.760909i | \(-0.275247\pi\) |
−0.983396 | + | 0.181474i | \(0.941913\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.28078 | − | 5.68247i | −0.231408 | − | 0.400811i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 39.6155 | 2.78046 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00000 | − | 1.73205i | 0.0698430 | − | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.438447 | 0.0304742 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.36932 | 0.0947176 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5270 | + | 19.9653i | −0.793551 | + | 1.37447i | 0.130205 | + | 0.991487i | \(0.458436\pi\) |
−0.923755 | + | 0.382983i | \(0.874897\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.06155 | − | 1.83866i | −0.0723973 | − | 0.125396i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.40388 | + | 16.2880i | 0.638377 | + | 1.10570i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.28078 | − | 7.41452i | 0.289268 | − | 0.501027i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00000 | − | 7.14143i | 0.0672673 | − | 0.480384i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8078 | − | 20.4516i | 0.790706 | − | 1.36954i | −0.134824 | − | 0.990870i | \(-0.543047\pi\) |
0.925530 | − | 0.378674i | \(-0.123620\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.315342 | − | 0.546188i | −0.0209300 | − | 0.0362517i | 0.855371 | − | 0.518016i | \(-0.173329\pi\) |
−0.876301 | + | 0.481765i | \(0.839996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.7386 | −1.89910 | −0.949551 | − | 0.313612i | \(-0.898461\pi\) | ||||
−0.949551 | + | 0.313612i | \(0.898461\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | − | 1.73205i | 0.0657952 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0540 | 1.05173 | 0.525865 | − | 0.850568i | \(-0.323742\pi\) | ||||
0.525865 | + | 0.850568i | \(0.323742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.43845 | 0.159067 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.62311 | + | 14.9357i | −0.560131 | + | 0.970175i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4654 | + | 25.0549i | 0.931801 | + | 1.61393i | 0.780242 | + | 0.625478i | \(0.215096\pi\) |
0.151558 | + | 0.988448i | \(0.451571\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.90388 | + | 11.9579i | −0.441073 | + | 0.763961i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.56155 | + | 11.1517i | −0.0993592 | + | 0.709567i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.68466 | − | 11.5782i | 0.423623 | − | 0.733737i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.21922 | − | 5.57586i | −0.203196 | − | 0.351945i | 0.746361 | − | 0.665542i | \(-0.231799\pi\) |
−0.949556 | + | 0.313597i | \(0.898466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0961180 | − | 0.166481i | −0.00604288 | − | 0.0104666i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.21922 | + | 10.7720i | −0.387945 | + | 0.671940i | −0.992173 | − | 0.124872i | \(-0.960148\pi\) |
0.604228 | + | 0.796811i | \(0.293481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.68466 | 0.537567 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4654 | − | 21.5908i | 0.768652 | − | 1.33134i | −0.169643 | − | 0.985506i | \(-0.554261\pi\) |
0.938294 | − | 0.345838i | \(-0.112405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.12311 | −0.437569 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.00000 | + | 1.73205i | 0.0611990 | + | 0.106000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.12311 | − | 7.14143i | −0.251390 | − | 0.435421i | 0.712519 | − | 0.701653i | \(-0.247554\pi\) |
−0.963909 | + | 0.266233i | \(0.914221\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.8693 | − | 20.5583i | 0.721010 | − | 1.24883i | −0.239586 | − | 0.970875i | \(-0.577012\pi\) |
0.960595 | − | 0.277950i | \(-0.0896550\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.9654 | + | 10.1192i | 0.784704 | + | 0.612443i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.219224 | + | 0.379706i | −0.0132197 | + | 0.0228972i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.78078 | − | 13.4767i | −0.467502 | − | 0.809736i | 0.531809 | − | 0.846864i | \(-0.321512\pi\) |
−0.999311 | + | 0.0371279i | \(0.988179\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.06155 | + | 3.57071i | 0.123422 | + | 0.213773i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8617 | 1.54278 | 0.771391 | − | 0.636361i | \(-0.219561\pi\) | ||||
0.771391 | + | 0.636361i | \(0.219561\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.50000 | + | 2.59808i | −0.0891657 | + | 0.154440i | −0.907159 | − | 0.420789i | \(-0.861753\pi\) |
0.817993 | + | 0.575228i | \(0.195087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.12311 | −0.184997 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.12311 | −0.538520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.5616 | −0.736371 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.43845 | + | 4.22351i | 0.142456 | + | 0.246740i | 0.928421 | − | 0.371530i | \(-0.121167\pi\) |
−0.785965 | + | 0.618271i | \(0.787834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.34233 | − | 7.52113i | −0.252820 | − | 0.437897i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.219224 | − | 0.379706i | 0.0127206 | − | 0.0220328i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.46543 | − | 0.592932i | 0.0847483 | − | 0.0342901i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.84233 | + | 8.38716i | −0.279107 | + | 0.483428i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.12311 | − | 7.14143i | −0.236866 | − | 0.410264i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.842329 | + | 1.45896i | 0.0482316 | + | 0.0835396i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9309 | 0.795077 | 0.397538 | − | 0.917586i | \(-0.369865\pi\) | ||||
0.397538 | + | 0.917586i | \(0.369865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.280776 | − | 0.486319i | 0.0159728 | − | 0.0276657i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3693 | 1.09833 | 0.549167 | − | 0.835713i | \(-0.314945\pi\) | ||||
0.549167 | + | 0.835713i | \(0.314945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0540 | 1.30309 | 0.651544 | − | 0.758611i | \(-0.274122\pi\) | ||||
0.651544 | + | 0.758611i | \(0.274122\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.28078 | + | 3.95042i | −0.128507 | + | 0.222581i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.2462 | 1.02481 | 0.512405 | − | 0.858744i | \(-0.328755\pi\) | ||||
0.512405 | + | 0.858744i | \(0.328755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.90388 | − | 3.29762i | −0.106597 | − | 0.184631i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.56155 | − | 9.63289i | −0.310416 | − | 0.537656i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.12311 | − | 5.40938i | 0.173774 | − | 0.300986i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.84233 | − | 2.21837i | −0.157664 | − | 0.123053i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.40388 | + | 2.43160i | −0.0776349 | + | 0.134468i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.56155 | − | 9.63289i | −0.306618 | − | 0.531079i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.71922 | − | 4.70983i | −0.149462 | − | 0.258876i | 0.781567 | − | 0.623822i | \(-0.214421\pi\) |
−0.931029 | + | 0.364946i | \(0.881088\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.438447 | 0.0240268 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.28078 | − | 5.68247i | 0.179248 | − | 0.310467i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.19224 | −0.0649452 | −0.0324726 | − | 0.999473i | \(-0.510338\pi\) | ||||
−0.0324726 | + | 0.999473i | \(0.510338\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.6847 | −1.01481 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.903882 | − | 1.56557i | 0.0489480 | − | 0.0847803i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31.0540 | 1.67676 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.219224 | + | 0.379706i | 0.0118026 | + | 0.0204427i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.68466 | + | 11.5782i | 0.358851 | + | 0.621549i | 0.987769 | − | 0.155923i | \(-0.0498352\pi\) |
−0.628918 | + | 0.777472i | \(0.716502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.15767 | − | 7.20130i | 0.222555 | − | 0.385477i | −0.733028 | − | 0.680198i | \(-0.761894\pi\) |
0.955583 | + | 0.294722i | \(0.0952270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.84233 | + | 2.21837i | 0.151712 | + | 0.118408i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1231 | − | 24.4619i | 0.751697 | − | 1.30198i | −0.195303 | − | 0.980743i | \(-0.562569\pi\) |
0.947000 | − | 0.321234i | \(-0.104098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.56155 | − | 7.90084i | −0.241423 | − | 0.418157i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.1231 | 1.32595 | 0.662973 | − | 0.748643i | \(-0.269294\pi\) | ||||
0.662973 | + | 0.748643i | \(0.269294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.62311 | − | 8.00745i | 0.243321 | − | 0.421445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8078 | 0.567260 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.56155 | 0.448132 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0885 | − | 20.9380i | 0.631017 | − | 1.09295i | −0.356328 | − | 0.934361i | \(-0.615971\pi\) |
0.987344 | − | 0.158592i | \(-0.0506954\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.2462 | + | 28.1393i | 0.843461 | + | 1.46092i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.62311 | + | 8.00745i | 0.239375 | + | 0.414610i | 0.960535 | − | 0.278158i | \(-0.0897240\pi\) |
−0.721160 | + | 0.692769i | \(0.756391\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.0270 | − | 11.7446i | 1.49497 | − | 0.604880i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0885 | + | 19.2059i | −0.569580 | + | 0.986542i | 0.427027 | + | 0.904239i | \(0.359561\pi\) |
−0.996607 | + | 0.0823029i | \(0.973773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.84233 | − | 8.38716i | −0.248080 | − | 0.429687i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.0270 | + | 17.3673i | 0.512355 | + | 0.887425i | 0.999897 | + | 0.0143257i | \(0.00456018\pi\) |
−0.487542 | + | 0.873099i | \(0.662106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.06155 | + | 1.83866i | −0.0539618 | + | 0.0934645i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.3002 | −1.23207 | −0.616034 | − | 0.787719i | \(-0.711262\pi\) | ||||
−0.616034 | + | 0.787719i | \(0.711262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.876894 | −0.0443465 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.780776 | − | 1.35234i | 0.0393850 | − | 0.0682168i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.2462 | −0.867751 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.93845 | + | 3.35749i | 0.0972879 | + | 0.168508i | 0.910561 | − | 0.413374i | \(-0.135650\pi\) |
−0.813273 | + | 0.581882i | \(0.802317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.12311 | + | 12.3376i | 0.356601 | + | 0.617652i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1231 | − | 19.2658i | 0.555461 | − | 0.962087i | −0.442406 | − | 0.896815i | \(-0.645875\pi\) |
0.997867 | − | 0.0652725i | \(-0.0207917\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7192 | + | 9.14657i | 0.583776 | + | 0.455623i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0961180 | − | 0.166481i | −0.00476439 | − | 0.00825217i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.59612 | − | 11.4248i | −0.326157 | − | 0.564921i | 0.655589 | − | 0.755118i | \(-0.272420\pi\) |
−0.981746 | + | 0.190198i | \(0.939087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.438447 | 0.0216270 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.8078 | + | 34.3081i | −0.974676 | + | 1.68819i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.3693 | 0.656274 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.80776 | −0.137497 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.43845 | + | 5.95557i | −0.167979 | + | 0.290948i | −0.937709 | − | 0.347421i | \(-0.887057\pi\) |
0.769730 | + | 0.638369i | \(0.220391\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1922 | −0.740424 | −0.370212 | − | 0.928947i | \(-0.620715\pi\) | ||||
−0.370212 | + | 0.928947i | \(0.620715\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.21922 | − | 2.11176i | −0.0592807 | − | 0.102677i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.84233 | − | 6.65511i | 0.185943 | − | 0.322063i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.219224 | − | 1.56557i | 0.0105842 | − | 0.0755864i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.2462 | + | 17.7470i | −0.493543 | + | 0.854841i | −0.999972 | − | 0.00744035i | \(-0.997632\pi\) |
0.506430 | + | 0.862281i | \(0.330965\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.2116 | + | 26.3473i | 0.731025 | + | 1.26617i | 0.956445 | + | 0.291911i | \(0.0942911\pi\) |
−0.225420 | + | 0.974262i | \(0.572376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.34233 | + | 7.52113i | 0.208199 | + | 0.360611i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.36932 | 0.0655033 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.6501 | + | 21.9106i | −0.603756 | + | 1.04574i | 0.388491 | + | 0.921453i | \(0.372997\pi\) |
−0.992247 | + | 0.124283i | \(0.960337\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.8078 | 0.657513 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.63068 | −0.220010 | −0.110005 | − | 0.993931i | \(-0.535087\pi\) | ||||
−0.110005 | + | 0.993931i | \(0.535087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | + | 1.73205i | −0.0474045 | + | 0.0821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.9309 | −0.706206 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.68466 | − | 2.91791i | −0.0795039 | − | 0.137705i | 0.823532 | − | 0.567270i | \(-0.192000\pi\) |
−0.903036 | + | 0.429565i | \(0.858667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.438447 | + | 0.759413i | 0.0206457 | + | 0.0357594i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | − | 13.8564i | 0.375873 | − | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.28078 | + | 16.2880i | −0.106924 | + | 0.763593i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.9654 | − | 20.7247i | 0.559719 | − | 0.969462i | −0.437800 | − | 0.899072i | \(-0.644242\pi\) |
0.997520 | − | 0.0703902i | \(-0.0224244\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.09612 | + | 5.36263i | 0.144201 | + | 0.249763i | 0.929074 | − | 0.369893i | \(-0.120606\pi\) |
−0.784874 | + | 0.619656i | \(0.787272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.8078 | −0.874071 | −0.437035 | − | 0.899444i | \(-0.643972\pi\) | ||||
−0.437035 | + | 0.899444i | \(0.643972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.06155 | + | 3.57071i | −0.0956022 | + | 0.165588i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.6155 | −0.907698 | −0.453849 | − | 0.891079i | \(-0.649950\pi\) | ||||
−0.453849 | + | 0.891079i | \(0.649950\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.9309 | −1.38208 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.62311 | + | 4.54335i | −0.120866 | + | 0.209347i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.930870 | 0.0428014 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.56155 | − | 2.70469i | −0.0716490 | − | 0.124100i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.56155 | + | 6.16879i | 0.163072 | + | 0.282450i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.9309 | + | 31.0572i | −0.819282 | + | 1.41904i | 0.0869294 | + | 0.996214i | \(0.472295\pi\) |
−0.906212 | + | 0.422824i | \(0.861039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.46543 | − | 0.592932i | 0.0668181 | − | 0.0270354i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | − | 1.73205i | 0.0455016 | − | 0.0788110i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.28078 | − | 10.8786i | −0.285195 | − | 0.493973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.31534 | − | 2.27824i | −0.0596038 | − | 0.103237i | 0.834684 | − | 0.550729i | \(-0.185650\pi\) |
−0.894288 | + | 0.447493i | \(0.852317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.8769 | −0.537092 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2462 | + | 24.6752i | −0.642923 | + | 1.11357i | 0.341855 | + | 0.939753i | \(0.388945\pi\) |
−0.984777 | + | 0.173822i | \(0.944388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.3693 | −0.782275 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.438447 | 0.0197067 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4924 | −0.738302 | −0.369151 | − | 0.929369i | \(-0.620352\pi\) | ||||
−0.369151 | + | 0.929369i | \(0.620352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.7808 | + | 22.1370i | 0.571003 | + | 0.989006i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.31534 | − | 7.47439i | −0.192412 | − | 0.333267i | 0.753637 | − | 0.657290i | \(-0.228298\pi\) |
−0.946049 | + | 0.324024i | \(0.894964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.12311 | − | 7.14143i | 0.183476 | − | 0.317789i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5000 | + | 3.57071i | 0.555144 | + | 0.158581i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.3423 | − | 26.5737i | 0.680037 | − | 1.17786i | −0.294932 | − | 0.955518i | \(-0.595297\pi\) |
0.974969 | − | 0.222340i | \(-0.0713695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.5270 | − | 33.8217i | −0.863823 | − | 1.49619i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.56155 | + | 2.70469i | 0.0689442 | + | 0.119415i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.561553 | 0.0247450 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.534565 | + | 0.925894i | −0.0235101 | + | 0.0407208i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.00000 | 0.175581 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7386 | 1.08382 | 0.541910 | − | 0.840437i | \(-0.317702\pi\) | ||||
0.541910 | + | 0.840437i | \(0.317702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.21922 | + | 15.9682i | −0.403129 | + | 0.698239i | −0.994102 | − | 0.108452i | \(-0.965411\pi\) |
0.590973 | + | 0.806691i | \(0.298744\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.56155 | −0.199082 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.12311 | − | 7.14143i | −0.179605 | − | 0.311086i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4039 | + | 19.7521i | 0.495821 | + | 0.858787i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.34233 | + | 7.52113i | −0.188441 | + | 0.326389i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.68466 | + | 2.70469i | −0.289545 | + | 0.117153i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.56155 | − | 9.63289i | 0.240447 | − | 0.416466i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.90388 | − | 8.49377i | −0.211618 | − | 0.366533i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.02699 | − | 5.24290i | −0.130382 | − | 0.225828i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.0540 | 1.85103 | 0.925517 | − | 0.378705i | \(-0.123630\pi\) | ||||
0.925517 | + | 0.378705i | \(0.123630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.56155 | − | 4.43674i | 0.109927 | − | 0.190399i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.80776 | −0.120271 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.3153 | 0.697594 | 0.348797 | − | 0.937198i | \(-0.386590\pi\) | ||||
0.348797 | + | 0.937198i | \(0.386590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.842329 | − | 1.45896i | 0.0359497 | − | 0.0622668i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.1231 | 1.15548 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.3348 | + | 68.1298i | 1.67268 | + | 2.89717i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.219224 | + | 0.379706i | 0.00930552 | + | 0.0161176i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.31534 | + | 9.20644i | −0.225218 | + | 0.390089i | −0.956385 | − | 0.292109i | \(-0.905643\pi\) |
0.731167 | + | 0.682199i | \(0.238976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.06155 | + | 7.58100i | −0.0448989 | + | 0.320642i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.438447 | + | 0.759413i | −0.0185113 | + | 0.0320624i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8078 | + | 18.7196i | 0.455493 | + | 0.788937i | 0.998716 | − | 0.0506512i | \(-0.0161297\pi\) |
−0.543223 | + | 0.839588i | \(0.682796\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.34233 | − | 16.1814i | −0.393035 | − | 0.680756i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.56155 | 0.191567 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.4384 | + | 25.0081i | −0.605291 | + | 1.04840i | 0.386714 | + | 0.922200i | \(0.373610\pi\) |
−0.992005 | + | 0.126195i | \(0.959723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.2311 | −1.80916 | −0.904582 | − | 0.426300i | \(-0.859817\pi\) | ||||
−0.904582 | + | 0.426300i | \(0.859817\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0000 | −0.835512 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.219224 | + | 0.379706i | −0.00914226 | + | 0.0158349i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9848 | 1.12339 | 0.561697 | − | 0.827343i | \(-0.310149\pi\) | ||||
0.561697 | + | 0.827343i | \(0.310149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.52699 | + | 16.5012i | 0.395928 | + | 0.685768i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.4924 | − | 52.8144i | −1.26504 | − | 2.19111i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.56155 | − | 2.70469i | 0.0646729 | − | 0.112017i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | + | 3.57071i | −0.0206725 | + | 0.147631i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.6847 | − | 35.8269i | 0.853747 | − | 1.47873i | −0.0240552 | − | 0.999711i | \(-0.507658\pi\) |
0.877802 | − | 0.479023i | \(-0.159009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.43845 | + | 11.1517i | 0.265292 | + | 0.459499i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.00000 | − | 6.92820i | −0.164538 | − | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.3002 | −0.422978 | −0.211489 | − | 0.977380i | \(-0.567831\pi\) | ||||
−0.211489 | + | 0.977380i | \(0.567831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.56155 | − | 7.90084i | 0.187005 | − | 0.323903i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.43845 | −0.386290 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.3693 | −0.873127 | −0.436563 | − | 0.899674i | \(-0.643805\pi\) | ||||
−0.436563 | + | 0.899674i | \(0.643805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.4654 | − | 42.3754i | 0.997966 | − | 1.72853i | 0.443774 | − | 0.896139i | \(-0.353639\pi\) |
0.554192 | − | 0.832389i | \(-0.313027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.56155 | −0.267207 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.40388 | + | 9.35980i | 0.219699 | + | 0.380530i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.31534 | + | 5.74234i | 0.134566 | + | 0.233074i | 0.925431 | − | 0.378915i | \(-0.123703\pi\) |
−0.790866 | + | 0.611990i | \(0.790369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.8078 | − | 34.3081i | 0.802651 | − | 1.39023i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.93087 | − | 5.40938i | −0.280393 | − | 0.218840i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.307764 | + | 0.533063i | −0.0124305 | + | 0.0215302i | −0.872174 | − | 0.489196i | \(-0.837290\pi\) |
0.859743 | + | 0.510726i | \(0.170624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.00000 | − | 1.73205i | −0.0403239 | − | 0.0698430i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.78078 | − | 16.9408i | −0.393759 | − | 0.682011i | 0.599183 | − | 0.800612i | \(-0.295492\pi\) |
−0.992942 | + | 0.118601i | \(0.962159\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.4233 | −1.14243 | −0.571214 | − | 0.820801i | \(-0.693527\pi\) | ||||
−0.571214 | + | 0.820801i | \(0.693527\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.219224 | − | 0.379706i | 0.00879714 | − | 0.0152371i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.12311 | 0.365510 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.684658 | − | 1.18586i | 0.0273426 | − | 0.0473588i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.876894 | −0.0349641 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.28078 | − | 5.68247i | −0.130606 | − | 0.226216i | 0.793305 | − | 0.608825i | \(-0.208359\pi\) |
−0.923910 | + | 0.382609i | \(0.875026\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.5270 | + | 19.9653i | 0.458157 | + | 0.793551i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.84233 | − | 8.38716i | 0.192162 | − | 0.332834i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.1501 | − | 18.6729i | 1.82853 | − | 0.739845i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0000 | − | 29.4449i | −0.671460 | − | 1.16300i | −0.977490 | − | 0.210981i | \(-0.932334\pi\) |
0.306031 | − | 0.952022i | \(-0.400999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.0885 | − | 41.7226i | −0.949959 | − | 1.64538i | −0.745503 | − | 0.666502i | \(-0.767791\pi\) |
−0.204456 | − | 0.978876i | \(-0.565543\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.12311 | −0.0835972 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0540 | + | 33.0025i | −0.749089 | + | 1.29746i | 0.199171 | + | 0.979965i | \(0.436175\pi\) |
−0.948260 | + | 0.317496i | \(0.897158\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.80776 | 0.149468 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.8078 | 0.737134 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.1231 | − | 20.9978i | 0.474414 | − | 0.821709i | −0.525157 | − | 0.851005i | \(-0.675993\pi\) |
0.999571 | + | 0.0292966i | \(0.00932673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.56155 | 0.0610149 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.28078 | − | 7.41452i | −0.167009 | − | 0.289268i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.58854 | − | 11.4117i | −0.256653 | − | 0.444536i | 0.708690 | − | 0.705520i | \(-0.249286\pi\) |
−0.965343 | + | 0.260984i | \(0.915953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.28078 | − | 12.6107i | 0.283189 | − | 0.490498i | −0.688979 | − | 0.724781i | \(-0.741941\pi\) |
0.972168 | + | 0.234283i | \(0.0752742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.68466 | − | 4.43674i | −0.220774 | − | 0.172309i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.12311 | + | 12.3376i | −0.276222 | + | 0.478431i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.90388 | − | 3.29762i | −0.0737186 | − | 0.127684i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.8078 | − | 20.4516i | −0.456515 | − | 0.790706i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.738634 | −0.0285146 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.1577 | + | 17.5936i | −0.391549 | + | 0.678184i | −0.992654 | − | 0.120987i | \(-0.961394\pi\) |
0.601105 | + | 0.799170i | \(0.294727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.24621 | −0.240061 | −0.120031 | − | 0.992770i | \(-0.538299\pi\) | ||||
−0.120031 | + | 0.992770i | \(0.538299\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.6501 | + | 49.6234i | −1.09949 | + | 1.90437i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.630683 | −0.0241678 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.87689 | − | 8.44703i | −0.186609 | − | 0.323217i | 0.757508 | − | 0.652825i | \(-0.226416\pi\) |
−0.944118 | + | 0.329609i | \(0.893083\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.219224 | + | 0.379706i | 0.00837610 | + | 0.0145078i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.3693 | + | 24.8884i | −0.548224 | + | 0.949551i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.2462 | + | 15.8017i | 0.771319 | + | 0.601996i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.6501 | + | 27.1068i | −0.595358 | + | 1.03119i | 0.398139 | + | 0.917325i | \(0.369656\pi\) |
−0.993496 | + | 0.113864i | \(0.963677\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | − | 1.73205i | −0.0379869 | − | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.40388 | − | 2.43160i | −0.0532523 | − | 0.0922357i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.02699 | − | 13.9032i | 0.303609 | − | 0.525865i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.3153 | −0.880608 | −0.440304 | − | 0.897849i | \(-0.645129\pi\) | ||||
−0.440304 | + | 0.897849i | \(0.645129\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.36932 | 0.0516448 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.21922 | − | 2.11176i | 0.0459186 | − | 0.0795334i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.6155 | −1.41468 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5961 | + | 20.0851i | 0.435501 | + | 0.754310i | 0.997336 | − | 0.0729388i | \(-0.0232378\pi\) |
−0.561835 | + | 0.827249i | \(0.689904\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.62311 | + | 14.9357i | 0.323392 | + | 0.560131i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.903882 | − | 1.56557i | 0.0338506 | − | 0.0586310i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.46543 | − | 0.592932i | 0.0548042 | − | 0.0221744i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.00000 | − | 3.46410i | 0.0746914 | − | 0.129369i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.2462 | − | 45.4598i | −0.978819 | − | 1.69536i | −0.666711 | − | 0.745317i | \(-0.732298\pi\) |
−0.312108 | − | 0.950047i | \(-0.601035\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.28078 | − | 2.21837i | −0.0476986 | − | 0.0826164i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.9309 | 1.07595 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.34233 | + | 7.52113i | −0.161270 | + | 0.279328i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.3153 | −0.456751 | −0.228375 | − | 0.973573i | \(-0.573341\pi\) | ||||
−0.228375 | + | 0.973573i | \(0.573341\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.12311 | − | 3.67733i | 0.0785259 | − | 0.136011i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.4233 | −1.64081 | −0.820406 | − | 0.571782i | \(-0.806252\pi\) | ||||
−0.820406 | + | 0.571782i | \(0.806252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.90388 | + | 11.9579i | 0.254654 | + | 0.441073i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.43845 | + | 2.49146i | 0.0529859 | + | 0.0917742i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.75379 | − | 13.4300i | 0.285228 | − | 0.494029i | −0.687437 | − | 0.726244i | \(-0.741264\pi\) |
0.972664 | + | 0.232215i | \(0.0745974\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.87689 | + | 6.92820i | 0.326101 | + | 0.254514i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.09612 | − | 3.63058i | 0.0768991 | − | 0.133193i | −0.825011 | − | 0.565116i | \(-0.808831\pi\) |
0.901911 | + | 0.431923i | \(0.142165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.46543 | − | 12.9305i | −0.273512 | − | 0.473737i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.68466 | − | 11.5782i | −0.244579 | − | 0.423623i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50.7386 | −1.85395 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.02699 | − | 12.1711i | 0.256418 | − | 0.444130i | −0.708861 | − | 0.705348i | \(-0.750791\pi\) |
0.965280 | + | 0.261218i | \(0.0841242\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.43845 | −0.234630 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.4924 | − | 26.8337i | 0.563082 | − | 0.975286i | −0.434144 | − | 0.900844i | \(-0.642949\pi\) |
0.997225 | − | 0.0744424i | \(-0.0237177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.192236 | −0.00697772 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1231 | + | 33.1222i | 0.693212 | + | 1.20068i | 0.970780 | + | 0.239972i | \(0.0771384\pi\) |
−0.277568 | + | 0.960706i | \(0.589528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.40388 | + | 11.0918i | 0.231836 | + | 0.401552i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.00000 | − | 1.73205i | 0.0361551 | − | 0.0626224i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.34233 | + | 31.0104i | −0.156792 | + | 1.11972i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9039 | − | 18.8861i | 0.393204 | − | 0.681049i | −0.599666 | − | 0.800250i | \(-0.704700\pi\) |
0.992870 | + | 0.119201i | \(0.0380333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.21922 | + | 10.7720i | 0.223980 | + | 0.387945i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5616 | + | 39.0778i | 0.811483 | + | 1.40553i | 0.911826 | + | 0.410576i | \(0.134672\pi\) |
−0.100344 | + | 0.994953i | \(0.531994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.12311 | −0.148106 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.00000 | − | 1.73205i | 0.0358748 | − | 0.0621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.24621 | −0.223794 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.34233 | − | 7.52113i | 0.155182 | − | 0.268783i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.24621 | −0.187245 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1847 | − | 41.8891i | −0.862090 | − | 1.49318i | −0.869908 | − | 0.493214i | \(-0.835822\pi\) |
0.00781794 | − | 0.999969i | \(-0.497511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.4654 | − | 21.5908i | −0.443781 | − | 0.768652i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.6155 | + | 73.8123i | −1.51523 | + | 2.62446i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.842329 | − | 6.01543i | 0.0299120 | − | 0.213614i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.56155 | + | 6.16879i | −0.126315 | + | 0.218784i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.6847 | − | 44.4871i | −0.909797 | − | 1.57582i | −0.814345 | − | 0.580381i | \(-0.802904\pi\) |
−0.0954523 | − | 0.995434i | \(-0.530430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.43845 | + | 4.22351i | 0.0862661 | + | 0.149417i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.87689 | + | 3.25088i | −0.0662342 | + | 0.114721i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.24621 | −0.290280 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.5616 | − | 44.2739i | 0.898696 | − | 1.55659i | 0.0695342 | − | 0.997580i | \(-0.477849\pi\) |
0.829162 | − | 0.559008i | \(-0.188818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.8078 | −1.29250 | −0.646248 | − | 0.763128i | \(-0.723663\pi\) | ||||
−0.646248 | + | 0.763128i | \(0.723663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.8693 | − | 20.5583i | −0.416275 | − | 0.721010i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.93845 | − | 10.2857i | −0.208015 | − | 0.360292i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.31534 | + | 5.74234i | −0.115989 | + | 0.200899i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.2462 | − | 6.16879i | 0.532746 | − | 0.215555i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.34233 | − | 5.78908i | 0.116648 | − | 0.202040i | −0.801789 | − | 0.597607i | \(-0.796118\pi\) |
0.918437 | + | 0.395566i | \(0.129452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.9309 | − | 29.3251i | −0.590173 | − | 1.02221i | −0.994209 | − | 0.107466i | \(-0.965726\pi\) |
0.404036 | − | 0.914743i | \(-0.367607\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.219224 | + | 0.379706i | 0.00763239 | + | 0.0132197i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.26137 | 0.252502 | 0.126251 | − | 0.991998i | \(-0.459705\pi\) | ||||
0.126251 | + | 0.991998i | \(0.459705\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.8423 | + | 43.0282i | −0.862810 | + | 1.49443i | 0.00639587 | + | 0.999980i | \(0.497964\pi\) |
−0.869206 | + | 0.494451i | \(0.835369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.5616 | −0.539824 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.6155 | −0.956821 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.7808 | + | 22.1370i | −0.442297 | + | 0.766081i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.12311 | 0.142515 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.87689 | + | 10.1791i | 0.202893 | + | 0.351421i | 0.949459 | − | 0.313890i | \(-0.101632\pi\) |
−0.746566 | + | 0.665311i | \(0.768299\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.2116 | − | 40.2038i | −0.800402 | − | 1.38634i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.9309 | − | 22.3969i | 0.445363 | − | 0.771391i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.15767 | + | 12.6107i | 0.108627 | + | 0.433820i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.6501 | − | 42.6952i | 0.846987 | − | 1.46702i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.50000 | + | 2.59808i | 0.0514799 | + | 0.0891657i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0961180 | − | 0.166481i | −0.00329488 | − | 0.00570690i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.38447 | 0.321318 | 0.160659 | − | 0.987010i | \(-0.448638\pi\) | ||||
0.160659 | + | 0.987010i | \(0.448638\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.56155 | + | 2.70469i | −0.0534040 | + | 0.0924984i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.42329 | −0.253575 | −0.126787 | − | 0.991930i | \(-0.540467\pi\) | ||||
−0.126787 | + | 0.991930i | \(0.540467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.8078 | −0.641713 | −0.320856 | − | 0.947128i | \(-0.603971\pi\) | ||||
−0.320856 | + | 0.947128i | \(0.603971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.56155 | + | 7.90084i | −0.155457 | + | 0.269260i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.69981 | 0.0578623 | 0.0289312 | − | 0.999581i | \(-0.490790\pi\) | ||||
0.0289312 | + | 0.999581i | \(0.490790\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | + | 3.46410i | 0.0680020 | + | 0.117783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.50000 | − | 11.2583i | −0.220752 | − | 0.382353i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.78078 | − | 6.54850i | 0.128254 | − | 0.222143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.9309 | + | 8.87348i | −0.743099 | + | 0.300666i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.28078 | + | 10.8786i | −0.212572 | + | 0.368186i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.28078 | − | 3.95042i | −0.0771043 | − | 0.133549i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.3423 | + | 23.1096i | 0.450538 | + | 0.780355i | 0.998419 | − | 0.0562008i | \(-0.0178987\pi\) |
−0.547881 | + | 0.836556i | \(0.684565\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.87689 | 0.164494 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.4384 | + | 35.4004i | −0.688589 | + | 1.19267i | 0.283706 | + | 0.958911i | \(0.408436\pi\) |
−0.972294 | + | 0.233759i | \(0.924897\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1231 | 0.677196 | 0.338598 | − | 0.940931i | \(-0.390047\pi\) | ||||
0.338598 | + | 0.940931i | \(0.390047\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.68466 | −0.291932 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.3963 | + | 38.7915i | −0.751994 | + | 1.30249i | 0.194860 | + | 0.980831i | \(0.437575\pi\) |
−0.946855 | + | 0.321661i | \(0.895759\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.1771 | −1.48165 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.219224 | − | 0.379706i | −0.00734427 | − | 0.0127206i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.80776 | − | 6.59524i | −0.127422 | − | 0.220701i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.90388 | − | 8.49377i | 0.163919 | − | 0.283916i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.219224 | − | 1.56557i | 0.00731966 | − | 0.0522728i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9039 | − | 31.0104i | 0.597128 | − | 1.03426i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.12311 | − | 12.3376i | −0.237305 | − | 0.411024i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.84233 | + | 8.38716i | 0.161143 | + | 0.279107i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.12311 | 0.170298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.7808 | + | 35.9934i | −0.690014 | + | 1.19514i | 0.281818 | + | 0.959468i | \(0.409062\pi\) |
−0.971833 | + | 0.235672i | \(0.924271\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.24621 | −0.273510 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.61553 | −0.119788 | −0.0598939 | − | 0.998205i | \(-0.519076\pi\) | ||||
−0.0598939 | + | 0.998205i | \(0.519076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.93087 | + | 5.07642i | −0.0969976 | + | 0.168005i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.68466 | 0.0556931 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.56155 | − | 6.16879i | −0.117613 | − | 0.203711i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.4924 | + | 28.5657i | 0.544035 | + | 0.942296i | 0.998667 | + | 0.0516167i | \(0.0164374\pi\) |
−0.454632 | + | 0.890679i | \(0.650229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.96543 | − | 12.0645i | 0.229519 | − | 0.397538i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.219224 | + | 0.379706i | −0.00720803 | + | 0.0124847i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.280776 | − | 0.486319i | −0.00922191 | − | 0.0159728i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.6155 | + | 44.3674i | 0.840418 | + | 1.45565i | 0.889542 | + | 0.456854i | \(0.151024\pi\) |
−0.0491233 | + | 0.998793i | \(0.515643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.1231 | 1.41330 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.68466 | − | 16.7743i | 0.317061 | − | 0.549167i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.876894 | −0.0286775 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.75379 | −0.253305 | −0.126653 | − | 0.991947i | \(-0.540423\pi\) | ||||
−0.126653 | + | 0.991947i | \(0.540423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.5270 | − | 19.9653i | 0.376169 | − | 0.651544i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.3542 | −1.11991 | −0.559957 | − | 0.828522i | \(-0.689182\pi\) | ||||
−0.559957 | + | 0.828522i | \(0.689182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.438447 | + | 0.759413i | 0.0142778 | + | 0.0247299i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.28078 | + | 3.95042i | 0.0741937 | + | 0.128507i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.6847 | + | 47.9512i | −0.899631 | + | 1.55821i | −0.0716636 | + | 0.997429i | \(0.522831\pi\) |
−0.827967 | + | 0.560777i | \(0.810503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.3348 | − | 18.9927i | −0.789939 | − | 0.616529i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.12311 | − | 15.8017i | 0.295837 | − | 0.512405i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.9039 | − | 36.2066i | −0.677143 | − | 1.17285i | −0.975838 | − | 0.218498i | \(-0.929884\pi\) |
0.298694 | − | 0.954349i | \(-0.403449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0000 | − | 17.3205i | −0.323592 | − | 0.560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.80776 | −0.123088 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.00000 | − | 1.73205i | 0.0322917 | − | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | −0.451613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.1231 | −0.358437 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.52699 | + | 16.5012i | −0.306685 | + | 0.531193i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.24621 | −0.200865 | −0.100432 | − | 0.994944i | \(-0.532023\pi\) | ||||
−0.100432 | + | 0.994944i | \(0.532023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.12311 | − | 5.40938i | −0.100329 | − | 0.173774i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.75379 | − | 3.03765i | −0.0562818 | − | 0.0974829i | 0.836512 | − | 0.547949i | \(-0.184591\pi\) |
−0.892794 | + | 0.450466i | \(0.851258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.40388 | + | 11.0918i | −0.205299 | + | 0.355588i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.34233 | + | 1.35234i | −0.107040 | + | 0.0433097i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.1501 | + | 45.2933i | −0.836616 | + | 1.44906i | 0.0560926 | + | 0.998426i | \(0.482136\pi\) |
−0.892708 | + | 0.450635i | \(0.851198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.438447 | − | 0.759413i | −0.0140128 | − | 0.0242709i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40388 | + | 2.43160i | 0.0448225 | + | 0.0776349i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.8078 | 0.695560 | 0.347780 | − | 0.937576i | \(-0.386936\pi\) | ||||
0.347780 | + | 0.937576i | \(0.386936\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00000 | − | 6.92820i | 0.127451 | − | 0.220751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.1231 | −0.354052 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.930870 | 0.0295999 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.6577 | + | 20.1917i | −0.370318 | + | 0.641410i | −0.989614 | − | 0.143748i | \(-0.954085\pi\) |
0.619296 | + | 0.785157i | \(0.287418\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.43845 | −0.172584 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.71922 | − | 8.17394i | −0.149609 | − | 0.259131i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.7732 | + | 29.0520i | 0.531213 | + | 0.920087i | 0.999336 | + | 0.0364243i | \(0.0115968\pi\) |
−0.468124 | + | 0.883663i | \(0.655070\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.219224 | − | 0.379706i | 0.00693593 | − | 0.0120134i |
(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 | 1560.2.bg.f.841.1 | yes | 4 | |
13.3 | even | 3 | inner | 1560.2.bg.f.601.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.bg.f.601.1 | ✓ | 4 | 13.3 | even | 3 | inner | |
1560.2.bg.f.841.1 | yes | 4 | 1.1 | even | 1 | trivial |