Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
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: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.38197 | 0.416678 | 0.208339 | − | 0.978057i | \(-0.433194\pi\) | ||||
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | −2.61803 | −0.726112 | −0.363056 | − | 0.931767i | \(-0.618267\pi\) | ||||
−0.363056 | + | 0.931767i | \(0.618267\pi\) | |||||||
\(14\) | 3.23607 | 0.864876 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.85410 | 0.692221 | 0.346111 | − | 0.938194i | \(-0.387502\pi\) | ||||
0.346111 | + | 0.938194i | \(0.387502\pi\) | |||||||
\(18\) | −2.61803 | −0.617077 | ||||||||
\(19\) | −1.61803 | −0.371202 | −0.185601 | − | 0.982625i | \(-0.559423\pi\) | ||||
−0.185601 | + | 0.982625i | \(0.559423\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 1.38197 | 0.294636 | ||||||||
\(23\) | −0.472136 | −0.0984472 | −0.0492236 | − | 0.998788i | \(-0.515675\pi\) | ||||
−0.0492236 | + | 0.998788i | \(0.515675\pi\) | |||||||
\(24\) | −1.85410 | −0.378467 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.61803 | −0.513439 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | −3.23607 | −0.611559 | ||||||||
\(29\) | 4.09017 | 0.759525 | 0.379763 | − | 0.925084i | \(-0.376006\pi\) | ||||
0.379763 | + | 0.925084i | \(0.376006\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4721 | −1.88085 | −0.940426 | − | 0.340000i | \(-0.889573\pi\) | ||||
−0.940426 | + | 0.340000i | \(0.889573\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0.854102 | 0.148680 | ||||||||
\(34\) | 2.85410 | 0.489474 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.61803 | 0.436339 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | −1.61803 | −0.262480 | ||||||||
\(39\) | −1.61803 | −0.259093 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.09017 | 1.10730 | 0.553649 | − | 0.832750i | \(-0.313235\pi\) | ||||
0.553649 | + | 0.832750i | \(0.313235\pi\) | |||||||
\(42\) | 2.00000 | 0.308607 | ||||||||
\(43\) | −2.47214 | −0.376997 | −0.188499 | − | 0.982073i | \(-0.560362\pi\) | ||||
−0.188499 | + | 0.982073i | \(0.560362\pi\) | |||||||
\(44\) | −1.38197 | −0.208339 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.472136 | −0.0696126 | ||||||||
\(47\) | 1.14590 | 0.167146 | 0.0835732 | − | 0.996502i | \(-0.473367\pi\) | ||||
0.0835732 | + | 0.996502i | \(0.473367\pi\) | |||||||
\(48\) | −0.618034 | −0.0892055 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.76393 | 0.247000 | ||||||||
\(52\) | 2.61803 | 0.363056 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | −3.47214 | −0.472498 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.70820 | −1.29731 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 4.09017 | 0.537066 | ||||||||
\(59\) | −7.23607 | −0.942056 | −0.471028 | − | 0.882118i | \(-0.656117\pi\) | ||||
−0.471028 | + | 0.882118i | \(0.656117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.85410 | −0.237393 | −0.118697 | − | 0.992931i | \(-0.537872\pi\) | ||||
−0.118697 | + | 0.992931i | \(0.537872\pi\) | |||||||
\(62\) | −10.4721 | −1.32996 | ||||||||
\(63\) | −8.47214 | −1.06739 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.854102 | 0.105133 | ||||||||
\(67\) | −11.7984 | −1.44140 | −0.720700 | − | 0.693247i | \(-0.756180\pi\) | ||||
−0.720700 | + | 0.693247i | \(0.756180\pi\) | |||||||
\(68\) | −2.85410 | −0.346111 | ||||||||
\(69\) | −0.291796 | −0.0351281 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.79837 | 1.16285 | 0.581427 | − | 0.813599i | \(-0.302495\pi\) | ||||
0.581427 | + | 0.813599i | \(0.302495\pi\) | |||||||
\(72\) | 7.85410 | 0.925615 | ||||||||
\(73\) | 10.0902 | 1.18097 | 0.590483 | − | 0.807050i | \(-0.298937\pi\) | ||||
0.590483 | + | 0.807050i | \(0.298937\pi\) | |||||||
\(74\) | −4.47214 | −0.519875 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.61803 | 0.185601 | ||||||||
\(77\) | 4.47214 | 0.509647 | ||||||||
\(78\) | −1.61803 | −0.183206 | ||||||||
\(79\) | −16.6525 | −1.87355 | −0.936775 | − | 0.349932i | \(-0.886205\pi\) | ||||
−0.936775 | + | 0.349932i | \(0.886205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 7.09017 | 0.782978 | ||||||||
\(83\) | −15.6180 | −1.71430 | −0.857151 | − | 0.515065i | \(-0.827768\pi\) | ||||
−0.857151 | + | 0.515065i | \(0.827768\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.47214 | −0.266577 | ||||||||
\(87\) | 2.52786 | 0.271015 | ||||||||
\(88\) | −4.14590 | −0.441954 | ||||||||
\(89\) | 7.52786 | 0.797952 | 0.398976 | − | 0.916961i | \(-0.369366\pi\) | ||||
0.398976 | + | 0.916961i | \(0.369366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.47214 | −0.888121 | ||||||||
\(92\) | 0.472136 | 0.0492236 | ||||||||
\(93\) | −6.47214 | −0.671129 | ||||||||
\(94\) | 1.14590 | 0.118190 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.09017 | 0.315389 | ||||||||
\(97\) | −17.2361 | −1.75006 | −0.875029 | − | 0.484071i | \(-0.839158\pi\) | ||||
−0.875029 | + | 0.484071i | \(0.839158\pi\) | |||||||
\(98\) | 3.47214 | 0.350739 | ||||||||
\(99\) | −3.61803 | −0.363626 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.23607 | 0.720016 | 0.360008 | − | 0.932949i | \(-0.382774\pi\) | ||||
0.360008 | + | 0.932949i | \(0.382774\pi\) | |||||||
\(102\) | 1.76393 | 0.174655 | ||||||||
\(103\) | −12.6525 | −1.24669 | −0.623343 | − | 0.781949i | \(-0.714226\pi\) | ||||
−0.623343 | + | 0.781949i | \(0.714226\pi\) | |||||||
\(104\) | 7.85410 | 0.770158 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −3.09017 | −0.298738 | −0.149369 | − | 0.988782i | \(-0.547724\pi\) | ||||
−0.149369 | + | 0.988782i | \(0.547724\pi\) | |||||||
\(108\) | 3.47214 | 0.334106 | ||||||||
\(109\) | −5.52786 | −0.529473 | −0.264737 | − | 0.964321i | \(-0.585285\pi\) | ||||
−0.264737 | + | 0.964321i | \(0.585285\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.76393 | −0.262341 | ||||||||
\(112\) | −3.23607 | −0.305780 | ||||||||
\(113\) | 19.1246 | 1.79909 | 0.899546 | − | 0.436826i | \(-0.143897\pi\) | ||||
0.899546 | + | 0.436826i | \(0.143897\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.09017 | −0.379763 | ||||||||
\(117\) | 6.85410 | 0.633662 | ||||||||
\(118\) | −7.23607 | −0.666134 | ||||||||
\(119\) | 9.23607 | 0.846669 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | −1.85410 | −0.167863 | ||||||||
\(123\) | 4.38197 | 0.395109 | ||||||||
\(124\) | 10.4721 | 0.940426 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.47214 | −0.754758 | ||||||||
\(127\) | −10.0000 | −0.887357 | −0.443678 | − | 0.896186i | \(-0.646327\pi\) | ||||
−0.443678 | + | 0.896186i | \(0.646327\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | −1.52786 | −0.134521 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6180 | −1.53929 | −0.769647 | − | 0.638469i | \(-0.779568\pi\) | ||||
−0.769647 | + | 0.638469i | \(0.779568\pi\) | |||||||
\(132\) | −0.854102 | −0.0743400 | ||||||||
\(133\) | −5.23607 | −0.454025 | ||||||||
\(134\) | −11.7984 | −1.01922 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.56231 | −0.734212 | ||||||||
\(137\) | −13.0902 | −1.11837 | −0.559184 | − | 0.829043i | \(-0.688886\pi\) | ||||
−0.559184 | + | 0.829043i | \(0.688886\pi\) | |||||||
\(138\) | −0.291796 | −0.0248393 | ||||||||
\(139\) | 13.0902 | 1.11029 | 0.555147 | − | 0.831752i | \(-0.312662\pi\) | ||||
0.555147 | + | 0.831752i | \(0.312662\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.708204 | 0.0596415 | ||||||||
\(142\) | 9.79837 | 0.822261 | ||||||||
\(143\) | −3.61803 | −0.302555 | ||||||||
\(144\) | 2.61803 | 0.218169 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0902 | 0.835068 | ||||||||
\(147\) | 2.14590 | 0.176991 | ||||||||
\(148\) | 4.47214 | 0.367607 | ||||||||
\(149\) | 12.9443 | 1.06044 | 0.530218 | − | 0.847861i | \(-0.322110\pi\) | ||||
0.530218 | + | 0.847861i | \(0.322110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.94427 | 0.565117 | 0.282558 | − | 0.959250i | \(-0.408817\pi\) | ||||
0.282558 | + | 0.959250i | \(0.408817\pi\) | |||||||
\(152\) | 4.85410 | 0.393720 | ||||||||
\(153\) | −7.47214 | −0.604086 | ||||||||
\(154\) | 4.47214 | 0.360375 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.61803 | 0.129546 | ||||||||
\(157\) | 5.32624 | 0.425080 | 0.212540 | − | 0.977152i | \(-0.431826\pi\) | ||||
0.212540 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(158\) | −16.6525 | −1.32480 | ||||||||
\(159\) | −2.47214 | −0.196053 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.52786 | −0.120413 | ||||||||
\(162\) | 5.70820 | 0.448479 | ||||||||
\(163\) | 13.8885 | 1.08783 | 0.543917 | − | 0.839139i | \(-0.316940\pi\) | ||||
0.543917 | + | 0.839139i | \(0.316940\pi\) | |||||||
\(164\) | −7.09017 | −0.553649 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.6180 | −1.21219 | ||||||||
\(167\) | 4.29180 | 0.332109 | 0.166055 | − | 0.986117i | \(-0.446897\pi\) | ||||
0.166055 | + | 0.986117i | \(0.446897\pi\) | |||||||
\(168\) | −6.00000 | −0.462910 | ||||||||
\(169\) | −6.14590 | −0.472761 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.23607 | 0.323940 | ||||||||
\(172\) | 2.47214 | 0.188499 | ||||||||
\(173\) | −6.32624 | −0.480975 | −0.240487 | − | 0.970652i | \(-0.577307\pi\) | ||||
−0.240487 | + | 0.970652i | \(0.577307\pi\) | |||||||
\(174\) | 2.52786 | 0.191637 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.38197 | −0.104170 | ||||||||
\(177\) | −4.47214 | −0.336146 | ||||||||
\(178\) | 7.52786 | 0.564237 | ||||||||
\(179\) | 4.94427 | 0.369552 | 0.184776 | − | 0.982781i | \(-0.440844\pi\) | ||||
0.184776 | + | 0.982781i | \(0.440844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.38197 | −0.251380 | −0.125690 | − | 0.992070i | \(-0.540114\pi\) | ||||
−0.125690 | + | 0.992070i | \(0.540114\pi\) | |||||||
\(182\) | −8.47214 | −0.627996 | ||||||||
\(183\) | −1.14590 | −0.0847072 | ||||||||
\(184\) | 1.41641 | 0.104419 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.47214 | −0.474560 | ||||||||
\(187\) | 3.94427 | 0.288434 | ||||||||
\(188\) | −1.14590 | −0.0835732 | ||||||||
\(189\) | −11.2361 | −0.817304 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.6525 | −1.49436 | −0.747180 | − | 0.664621i | \(-0.768593\pi\) | ||||
−0.747180 | + | 0.664621i | \(0.768593\pi\) | |||||||
\(192\) | 4.32624 | 0.312219 | ||||||||
\(193\) | −0.472136 | −0.0339851 | −0.0169925 | − | 0.999856i | \(-0.505409\pi\) | ||||
−0.0169925 | + | 0.999856i | \(0.505409\pi\) | |||||||
\(194\) | −17.2361 | −1.23748 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.47214 | −0.248010 | ||||||||
\(197\) | −14.9443 | −1.06474 | −0.532368 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532368 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(198\) | −3.61803 | −0.257122 | ||||||||
\(199\) | −23.8541 | −1.69097 | −0.845486 | − | 0.533997i | \(-0.820689\pi\) | ||||
−0.845486 | + | 0.533997i | \(0.820689\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.29180 | −0.514324 | ||||||||
\(202\) | 7.23607 | 0.509128 | ||||||||
\(203\) | 13.2361 | 0.928990 | ||||||||
\(204\) | −1.76393 | −0.123500 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.6525 | −0.881540 | ||||||||
\(207\) | 1.23607 | 0.0859127 | ||||||||
\(208\) | 2.61803 | 0.181528 | ||||||||
\(209\) | −2.23607 | −0.154672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.2361 | −1.04889 | −0.524447 | − | 0.851443i | \(-0.675728\pi\) | ||||
−0.524447 | + | 0.851443i | \(0.675728\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | 6.05573 | 0.414932 | ||||||||
\(214\) | −3.09017 | −0.211240 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 10.4164 | 0.708747 | ||||||||
\(217\) | −33.8885 | −2.30050 | ||||||||
\(218\) | −5.52786 | −0.374394 | ||||||||
\(219\) | 6.23607 | 0.421394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.47214 | −0.502630 | ||||||||
\(222\) | −2.76393 | −0.185503 | ||||||||
\(223\) | 4.38197 | 0.293438 | 0.146719 | − | 0.989178i | \(-0.453129\pi\) | ||||
0.146719 | + | 0.989178i | \(0.453129\pi\) | |||||||
\(224\) | 16.1803 | 1.08109 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.1246 | 1.27215 | ||||||||
\(227\) | 21.5967 | 1.43343 | 0.716713 | − | 0.697368i | \(-0.245646\pi\) | ||||
0.716713 | + | 0.697368i | \(0.245646\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −4.03444 | −0.266603 | −0.133302 | − | 0.991076i | \(-0.542558\pi\) | ||||
−0.133302 | + | 0.991076i | \(0.542558\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.76393 | 0.181853 | ||||||||
\(232\) | −12.2705 | −0.805598 | ||||||||
\(233\) | −2.94427 | −0.192886 | −0.0964428 | − | 0.995339i | \(-0.530746\pi\) | ||||
−0.0964428 | + | 0.995339i | \(0.530746\pi\) | |||||||
\(234\) | 6.85410 | 0.448067 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.23607 | 0.471028 | ||||||||
\(237\) | −10.2918 | −0.668524 | ||||||||
\(238\) | 9.23607 | 0.598685 | ||||||||
\(239\) | −1.52786 | −0.0988293 | −0.0494147 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494147 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −9.09017 | −0.584338 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 1.85410 | 0.118697 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.38197 | 0.279384 | ||||||||
\(247\) | 4.23607 | 0.269535 | ||||||||
\(248\) | 31.4164 | 1.99494 | ||||||||
\(249\) | −9.65248 | −0.611701 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.70820 | −0.360299 | −0.180149 | − | 0.983639i | \(-0.557658\pi\) | ||||
−0.180149 | + | 0.983639i | \(0.557658\pi\) | |||||||
\(252\) | 8.47214 | 0.533694 | ||||||||
\(253\) | −0.652476 | −0.0410208 | ||||||||
\(254\) | −10.0000 | −0.627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −31.1246 | −1.94150 | −0.970750 | − | 0.240093i | \(-0.922822\pi\) | ||||
−0.970750 | + | 0.240093i | \(0.922822\pi\) | |||||||
\(258\) | −1.52786 | −0.0951207 | ||||||||
\(259\) | −14.4721 | −0.899255 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.7082 | −0.662821 | ||||||||
\(262\) | −17.6180 | −1.08845 | ||||||||
\(263\) | −5.52786 | −0.340863 | −0.170431 | − | 0.985370i | \(-0.554516\pi\) | ||||
−0.170431 | + | 0.985370i | \(0.554516\pi\) | |||||||
\(264\) | −2.56231 | −0.157699 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.23607 | −0.321044 | ||||||||
\(267\) | 4.65248 | 0.284727 | ||||||||
\(268\) | 11.7984 | 0.720700 | ||||||||
\(269\) | −11.7082 | −0.713862 | −0.356931 | − | 0.934131i | \(-0.616177\pi\) | ||||
−0.356931 | + | 0.934131i | \(0.616177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.1803 | −1.71183 | −0.855917 | − | 0.517113i | \(-0.827007\pi\) | ||||
−0.855917 | + | 0.517113i | \(0.827007\pi\) | |||||||
\(272\) | −2.85410 | −0.173055 | ||||||||
\(273\) | −5.23607 | −0.316901 | ||||||||
\(274\) | −13.0902 | −0.790806 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.291796 | 0.0175641 | ||||||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | 13.0902 | 0.785096 | ||||||||
\(279\) | 27.4164 | 1.64138 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0344 | 1.19515 | 0.597577 | − | 0.801811i | \(-0.296130\pi\) | ||||
0.597577 | + | 0.801811i | \(0.296130\pi\) | |||||||
\(282\) | 0.708204 | 0.0421729 | ||||||||
\(283\) | 11.2361 | 0.667915 | 0.333957 | − | 0.942588i | \(-0.391616\pi\) | ||||
0.333957 | + | 0.942588i | \(0.391616\pi\) | |||||||
\(284\) | −9.79837 | −0.581427 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.61803 | −0.213939 | ||||||||
\(287\) | 22.9443 | 1.35436 | ||||||||
\(288\) | −13.0902 | −0.771346 | ||||||||
\(289\) | −8.85410 | −0.520830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.6525 | −0.624459 | ||||||||
\(292\) | −10.0902 | −0.590483 | ||||||||
\(293\) | 21.3262 | 1.24589 | 0.622946 | − | 0.782265i | \(-0.285936\pi\) | ||||
0.622946 | + | 0.782265i | \(0.285936\pi\) | |||||||
\(294\) | 2.14590 | 0.125151 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.4164 | 0.779813 | ||||||||
\(297\) | −4.79837 | −0.278430 | ||||||||
\(298\) | 12.9443 | 0.749842 | ||||||||
\(299\) | 1.23607 | 0.0714837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 6.94427 | 0.399598 | ||||||||
\(303\) | 4.47214 | 0.256917 | ||||||||
\(304\) | 1.61803 | 0.0928006 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.47214 | −0.427154 | ||||||||
\(307\) | 16.2918 | 0.929822 | 0.464911 | − | 0.885357i | \(-0.346086\pi\) | ||||
0.464911 | + | 0.885357i | \(0.346086\pi\) | |||||||
\(308\) | −4.47214 | −0.254824 | ||||||||
\(309\) | −7.81966 | −0.444845 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2148 | 1.20298 | 0.601490 | − | 0.798880i | \(-0.294574\pi\) | ||||
0.601490 | + | 0.798880i | \(0.294574\pi\) | |||||||
\(312\) | 4.85410 | 0.274809 | ||||||||
\(313\) | 25.7082 | 1.45311 | 0.726557 | − | 0.687106i | \(-0.241119\pi\) | ||||
0.726557 | + | 0.687106i | \(0.241119\pi\) | |||||||
\(314\) | 5.32624 | 0.300577 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.6525 | 0.936775 | ||||||||
\(317\) | 14.0344 | 0.788253 | 0.394126 | − | 0.919056i | \(-0.371047\pi\) | ||||
0.394126 | + | 0.919056i | \(0.371047\pi\) | |||||||
\(318\) | −2.47214 | −0.138631 | ||||||||
\(319\) | 5.65248 | 0.316478 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.90983 | −0.106596 | ||||||||
\(322\) | −1.52786 | −0.0851445 | ||||||||
\(323\) | −4.61803 | −0.256954 | ||||||||
\(324\) | −5.70820 | −0.317122 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.8885 | 0.769215 | ||||||||
\(327\) | −3.41641 | −0.188928 | ||||||||
\(328\) | −21.2705 | −1.17447 | ||||||||
\(329\) | 3.70820 | 0.204440 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.18034 | 0.449632 | 0.224816 | − | 0.974401i | \(-0.427822\pi\) | ||||
0.224816 | + | 0.974401i | \(0.427822\pi\) | |||||||
\(332\) | 15.6180 | 0.857151 | ||||||||
\(333\) | 11.7082 | 0.641606 | ||||||||
\(334\) | 4.29180 | 0.234837 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | −0.109109 | ||||||||
\(337\) | 4.65248 | 0.253437 | 0.126718 | − | 0.991939i | \(-0.459556\pi\) | ||||
0.126718 | + | 0.991939i | \(0.459556\pi\) | |||||||
\(338\) | −6.14590 | −0.334293 | ||||||||
\(339\) | 11.8197 | 0.641956 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.4721 | −0.783710 | ||||||||
\(342\) | 4.23607 | 0.229060 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | 7.41641 | 0.399866 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.32624 | −0.340101 | ||||||||
\(347\) | 11.7984 | 0.633370 | 0.316685 | − | 0.948531i | \(-0.397430\pi\) | ||||
0.316685 | + | 0.948531i | \(0.397430\pi\) | |||||||
\(348\) | −2.52786 | −0.135508 | ||||||||
\(349\) | 23.5066 | 1.25828 | 0.629139 | − | 0.777293i | \(-0.283408\pi\) | ||||
0.629139 | + | 0.777293i | \(0.283408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.09017 | 0.485197 | ||||||||
\(352\) | 6.90983 | 0.368295 | ||||||||
\(353\) | −30.3262 | −1.61410 | −0.807051 | − | 0.590481i | \(-0.798938\pi\) | ||||
−0.807051 | + | 0.590481i | \(0.798938\pi\) | |||||||
\(354\) | −4.47214 | −0.237691 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.52786 | −0.398976 | ||||||||
\(357\) | 5.70820 | 0.302110 | ||||||||
\(358\) | 4.94427 | 0.261313 | ||||||||
\(359\) | 4.29180 | 0.226512 | 0.113256 | − | 0.993566i | \(-0.463872\pi\) | ||||
0.113256 | + | 0.993566i | \(0.463872\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3820 | −0.862209 | ||||||||
\(362\) | −3.38197 | −0.177752 | ||||||||
\(363\) | −5.61803 | −0.294870 | ||||||||
\(364\) | 8.47214 | 0.444061 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.14590 | −0.0598970 | ||||||||
\(367\) | −16.1803 | −0.844607 | −0.422303 | − | 0.906455i | \(-0.638778\pi\) | ||||
−0.422303 | + | 0.906455i | \(0.638778\pi\) | |||||||
\(368\) | 0.472136 | 0.0246118 | ||||||||
\(369\) | −18.5623 | −0.966315 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.9443 | −0.672033 | ||||||||
\(372\) | 6.47214 | 0.335565 | ||||||||
\(373\) | 14.8541 | 0.769116 | 0.384558 | − | 0.923101i | \(-0.374354\pi\) | ||||
0.384558 | + | 0.923101i | \(0.374354\pi\) | |||||||
\(374\) | 3.94427 | 0.203953 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.43769 | −0.177286 | ||||||||
\(377\) | −10.7082 | −0.551501 | ||||||||
\(378\) | −11.2361 | −0.577921 | ||||||||
\(379\) | 5.74265 | 0.294980 | 0.147490 | − | 0.989064i | \(-0.452881\pi\) | ||||
0.147490 | + | 0.989064i | \(0.452881\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.18034 | −0.316628 | ||||||||
\(382\) | −20.6525 | −1.05667 | ||||||||
\(383\) | −24.4721 | −1.25047 | −0.625234 | − | 0.780437i | \(-0.714996\pi\) | ||||
−0.625234 | + | 0.780437i | \(0.714996\pi\) | |||||||
\(384\) | −1.85410 | −0.0946167 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.472136 | −0.0240311 | ||||||||
\(387\) | 6.47214 | 0.328997 | ||||||||
\(388\) | 17.2361 | 0.875029 | ||||||||
\(389\) | −10.2918 | −0.521815 | −0.260907 | − | 0.965364i | \(-0.584022\pi\) | ||||
−0.260907 | + | 0.965364i | \(0.584022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.34752 | −0.0681472 | ||||||||
\(392\) | −10.4164 | −0.526108 | ||||||||
\(393\) | −10.8885 | −0.549254 | ||||||||
\(394\) | −14.9443 | −0.752882 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.61803 | 0.181813 | ||||||||
\(397\) | 31.3050 | 1.57115 | 0.785575 | − | 0.618766i | \(-0.212367\pi\) | ||||
0.785575 | + | 0.618766i | \(0.212367\pi\) | |||||||
\(398\) | −23.8541 | −1.19570 | ||||||||
\(399\) | −3.23607 | −0.162006 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.7984 | −0.888808 | −0.444404 | − | 0.895826i | \(-0.646585\pi\) | ||||
−0.444404 | + | 0.895826i | \(0.646585\pi\) | |||||||
\(402\) | −7.29180 | −0.363682 | ||||||||
\(403\) | 27.4164 | 1.36571 | ||||||||
\(404\) | −7.23607 | −0.360008 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.2361 | 0.656895 | ||||||||
\(407\) | −6.18034 | −0.306348 | ||||||||
\(408\) | −5.29180 | −0.261983 | ||||||||
\(409\) | 32.9443 | 1.62899 | 0.814495 | − | 0.580171i | \(-0.197014\pi\) | ||||
0.814495 | + | 0.580171i | \(0.197014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.09017 | −0.399059 | ||||||||
\(412\) | 12.6525 | 0.623343 | ||||||||
\(413\) | −23.4164 | −1.15225 | ||||||||
\(414\) | 1.23607 | 0.0607494 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13.0902 | −0.641798 | ||||||||
\(417\) | 8.09017 | 0.396177 | ||||||||
\(418\) | −2.23607 | −0.109370 | ||||||||
\(419\) | 3.20163 | 0.156410 | 0.0782048 | − | 0.996937i | \(-0.475081\pi\) | ||||
0.0782048 | + | 0.996937i | \(0.475081\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.3607 | −0.504949 | −0.252474 | − | 0.967604i | \(-0.581244\pi\) | ||||
−0.252474 | + | 0.967604i | \(0.581244\pi\) | |||||||
\(422\) | −15.2361 | −0.741680 | ||||||||
\(423\) | −3.00000 | −0.145865 | ||||||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.05573 | 0.293401 | ||||||||
\(427\) | −6.00000 | −0.290360 | ||||||||
\(428\) | 3.09017 | 0.149369 | ||||||||
\(429\) | −2.23607 | −0.107958 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.4508 | −1.61127 | −0.805635 | − | 0.592412i | \(-0.798176\pi\) | ||||
−0.805635 | + | 0.592412i | \(0.798176\pi\) | |||||||
\(432\) | 3.47214 | 0.167053 | ||||||||
\(433\) | 12.6525 | 0.608039 | 0.304020 | − | 0.952666i | \(-0.401671\pi\) | ||||
0.304020 | + | 0.952666i | \(0.401671\pi\) | |||||||
\(434\) | −33.8885 | −1.62670 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.52786 | 0.264737 | ||||||||
\(437\) | 0.763932 | 0.0365438 | ||||||||
\(438\) | 6.23607 | 0.297971 | ||||||||
\(439\) | 4.14590 | 0.197873 | 0.0989365 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989365 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.09017 | −0.432865 | ||||||||
\(442\) | −7.47214 | −0.355413 | ||||||||
\(443\) | 2.94427 | 0.139887 | 0.0699433 | − | 0.997551i | \(-0.477718\pi\) | ||||
0.0699433 | + | 0.997551i | \(0.477718\pi\) | |||||||
\(444\) | 2.76393 | 0.131170 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.38197 | 0.207492 | ||||||||
\(447\) | 8.00000 | 0.378387 | ||||||||
\(448\) | 22.6525 | 1.07023 | ||||||||
\(449\) | −8.76393 | −0.413596 | −0.206798 | − | 0.978384i | \(-0.566304\pi\) | ||||
−0.206798 | + | 0.978384i | \(0.566304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.79837 | 0.461387 | ||||||||
\(452\) | −19.1246 | −0.899546 | ||||||||
\(453\) | 4.29180 | 0.201646 | ||||||||
\(454\) | 21.5967 | 1.01359 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | 0.140488 | ||||||||
\(457\) | 6.65248 | 0.311190 | 0.155595 | − | 0.987821i | \(-0.450271\pi\) | ||||
0.155595 | + | 0.987821i | \(0.450271\pi\) | |||||||
\(458\) | −4.03444 | −0.188517 | ||||||||
\(459\) | −9.90983 | −0.462551 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.0000 | −1.67669 | −0.838344 | − | 0.545142i | \(-0.816476\pi\) | ||||
−0.838344 | + | 0.545142i | \(0.816476\pi\) | |||||||
\(462\) | 2.76393 | 0.128590 | ||||||||
\(463\) | 17.7082 | 0.822970 | 0.411485 | − | 0.911417i | \(-0.365010\pi\) | ||||
0.411485 | + | 0.911417i | \(0.365010\pi\) | |||||||
\(464\) | −4.09017 | −0.189881 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.94427 | −0.136391 | ||||||||
\(467\) | 24.3262 | 1.12568 | 0.562842 | − | 0.826564i | \(-0.309708\pi\) | ||||
0.562842 | + | 0.826564i | \(0.309708\pi\) | |||||||
\(468\) | −6.85410 | −0.316831 | ||||||||
\(469\) | −38.1803 | −1.76300 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.29180 | 0.151678 | ||||||||
\(472\) | 21.7082 | 0.999201 | ||||||||
\(473\) | −3.41641 | −0.157087 | ||||||||
\(474\) | −10.2918 | −0.472718 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.23607 | −0.423334 | ||||||||
\(477\) | 10.4721 | 0.479486 | ||||||||
\(478\) | −1.52786 | −0.0698829 | ||||||||
\(479\) | −21.0557 | −0.962061 | −0.481030 | − | 0.876704i | \(-0.659737\pi\) | ||||
−0.481030 | + | 0.876704i | \(0.659737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.7082 | 0.533848 | ||||||||
\(482\) | 1.00000 | 0.0455488 | ||||||||
\(483\) | −0.944272 | −0.0429659 | ||||||||
\(484\) | 9.09017 | 0.413190 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.9443 | 0.632525 | ||||||||
\(487\) | 8.32624 | 0.377298 | 0.188649 | − | 0.982045i | \(-0.439589\pi\) | ||||
0.188649 | + | 0.982045i | \(0.439589\pi\) | |||||||
\(488\) | 5.56231 | 0.251794 | ||||||||
\(489\) | 8.58359 | 0.388163 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.4164 | 1.05677 | 0.528384 | − | 0.849006i | \(-0.322798\pi\) | ||||
0.528384 | + | 0.849006i | \(0.322798\pi\) | |||||||
\(492\) | −4.38197 | −0.197554 | ||||||||
\(493\) | 11.6738 | 0.525760 | ||||||||
\(494\) | 4.23607 | 0.190590 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.4721 | 0.470213 | ||||||||
\(497\) | 31.7082 | 1.42231 | ||||||||
\(498\) | −9.65248 | −0.432538 | ||||||||
\(499\) | −21.3050 | −0.953741 | −0.476870 | − | 0.878974i | \(-0.658229\pi\) | ||||
−0.476870 | + | 0.878974i | \(0.658229\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.65248 | 0.118504 | ||||||||
\(502\) | −5.70820 | −0.254770 | ||||||||
\(503\) | −4.65248 | −0.207444 | −0.103722 | − | 0.994606i | \(-0.533075\pi\) | ||||
−0.103722 | + | 0.994606i | \(0.533075\pi\) | |||||||
\(504\) | 25.4164 | 1.13214 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.652476 | −0.0290061 | ||||||||
\(507\) | −3.79837 | −0.168692 | ||||||||
\(508\) | 10.0000 | 0.443678 | ||||||||
\(509\) | 32.0344 | 1.41990 | 0.709951 | − | 0.704251i | \(-0.248717\pi\) | ||||
0.709951 | + | 0.704251i | \(0.248717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.6525 | 1.44446 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 5.61803 | 0.248042 | ||||||||
\(514\) | −31.1246 | −1.37285 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.52786 | 0.0672605 | ||||||||
\(517\) | 1.58359 | 0.0696463 | ||||||||
\(518\) | −14.4721 | −0.635869 | ||||||||
\(519\) | −3.90983 | −0.171622 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.23607 | −0.0541531 | −0.0270766 | − | 0.999633i | \(-0.508620\pi\) | ||||
−0.0270766 | + | 0.999633i | \(0.508620\pi\) | |||||||
\(522\) | −10.7082 | −0.468685 | ||||||||
\(523\) | 13.5623 | 0.593038 | 0.296519 | − | 0.955027i | \(-0.404174\pi\) | ||||
0.296519 | + | 0.955027i | \(0.404174\pi\) | |||||||
\(524\) | 17.6180 | 0.769647 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.52786 | −0.241026 | ||||||||
\(527\) | −29.8885 | −1.30197 | ||||||||
\(528\) | −0.854102 | −0.0371700 | ||||||||
\(529\) | −22.7771 | −0.990308 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.9443 | 0.822111 | ||||||||
\(532\) | 5.23607 | 0.227012 | ||||||||
\(533\) | −18.5623 | −0.804023 | ||||||||
\(534\) | 4.65248 | 0.201332 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 35.3951 | 1.52884 | ||||||||
\(537\) | 3.05573 | 0.131864 | ||||||||
\(538\) | −11.7082 | −0.504777 | ||||||||
\(539\) | 4.79837 | 0.206681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2016 | 0.438602 | 0.219301 | − | 0.975657i | \(-0.429622\pi\) | ||||
0.219301 | + | 0.975657i | \(0.429622\pi\) | |||||||
\(542\) | −28.1803 | −1.21045 | ||||||||
\(543\) | −2.09017 | −0.0896978 | ||||||||
\(544\) | 14.2705 | 0.611843 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.23607 | −0.224083 | ||||||||
\(547\) | 3.70820 | 0.158551 | 0.0792757 | − | 0.996853i | \(-0.474739\pi\) | ||||
0.0792757 | + | 0.996853i | \(0.474739\pi\) | |||||||
\(548\) | 13.0902 | 0.559184 | ||||||||
\(549\) | 4.85410 | 0.207168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.61803 | −0.281938 | ||||||||
\(552\) | 0.875388 | 0.0372590 | ||||||||
\(553\) | −53.8885 | −2.29157 | ||||||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.0902 | −0.555147 | ||||||||
\(557\) | 10.1115 | 0.428436 | 0.214218 | − | 0.976786i | \(-0.431280\pi\) | ||||
0.214218 | + | 0.976786i | \(0.431280\pi\) | |||||||
\(558\) | 27.4164 | 1.16063 | ||||||||
\(559\) | 6.47214 | 0.273742 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.43769 | 0.102920 | ||||||||
\(562\) | 20.0344 | 0.845102 | ||||||||
\(563\) | −41.2705 | −1.73934 | −0.869672 | − | 0.493629i | \(-0.835670\pi\) | ||||
−0.869672 | + | 0.493629i | \(0.835670\pi\) | |||||||
\(564\) | −0.708204 | −0.0298208 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.2361 | 0.472287 | ||||||||
\(567\) | 18.4721 | 0.775757 | ||||||||
\(568\) | −29.3951 | −1.23339 | ||||||||
\(569\) | −14.5066 | −0.608147 | −0.304074 | − | 0.952649i | \(-0.598347\pi\) | ||||
−0.304074 | + | 0.952649i | \(0.598347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.3262 | −0.641383 | −0.320692 | − | 0.947184i | \(-0.603915\pi\) | ||||
−0.320692 | + | 0.947184i | \(0.603915\pi\) | |||||||
\(572\) | 3.61803 | 0.151278 | ||||||||
\(573\) | −12.7639 | −0.533221 | ||||||||
\(574\) | 22.9443 | 0.957675 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −18.3262 | −0.763593 | ||||||||
\(577\) | −16.1459 | −0.672163 | −0.336081 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336081 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(578\) | −8.85410 | −0.368282 | ||||||||
\(579\) | −0.291796 | −0.0121266 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.5410 | −2.09679 | ||||||||
\(582\) | −10.6525 | −0.441559 | ||||||||
\(583\) | −5.52786 | −0.228941 | ||||||||
\(584\) | −30.2705 | −1.25260 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3262 | 0.880979 | ||||||||
\(587\) | 11.5279 | 0.475806 | 0.237903 | − | 0.971289i | \(-0.423540\pi\) | ||||
0.237903 | + | 0.971289i | \(0.423540\pi\) | |||||||
\(588\) | −2.14590 | −0.0884953 | ||||||||
\(589\) | 16.9443 | 0.698177 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.23607 | −0.379921 | ||||||||
\(592\) | 4.47214 | 0.183804 | ||||||||
\(593\) | −12.8328 | −0.526981 | −0.263490 | − | 0.964662i | \(-0.584874\pi\) | ||||
−0.263490 | + | 0.964662i | \(0.584874\pi\) | |||||||
\(594\) | −4.79837 | −0.196880 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.9443 | −0.530218 | ||||||||
\(597\) | −14.7426 | −0.603376 | ||||||||
\(598\) | 1.23607 | 0.0505466 | ||||||||
\(599\) | −36.4508 | −1.48934 | −0.744671 | − | 0.667432i | \(-0.767393\pi\) | ||||
−0.744671 | + | 0.667432i | \(0.767393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.74265 | −0.152666 | −0.0763329 | − | 0.997082i | \(-0.524321\pi\) | ||||
−0.0763329 | + | 0.997082i | \(0.524321\pi\) | |||||||
\(602\) | −8.00000 | −0.326056 | ||||||||
\(603\) | 30.8885 | 1.25788 | ||||||||
\(604\) | −6.94427 | −0.282558 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.47214 | 0.181668 | ||||||||
\(607\) | 0.360680 | 0.0146395 | 0.00731977 | − | 0.999973i | \(-0.497670\pi\) | ||||
0.00731977 | + | 0.999973i | \(0.497670\pi\) | |||||||
\(608\) | −8.09017 | −0.328100 | ||||||||
\(609\) | 8.18034 | 0.331484 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | −0.121367 | ||||||||
\(612\) | 7.47214 | 0.302043 | ||||||||
\(613\) | 33.6869 | 1.36060 | 0.680301 | − | 0.732933i | \(-0.261849\pi\) | ||||
0.680301 | + | 0.732933i | \(0.261849\pi\) | |||||||
\(614\) | 16.2918 | 0.657483 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.4164 | −0.540562 | ||||||||
\(617\) | 36.9443 | 1.48732 | 0.743660 | − | 0.668558i | \(-0.233088\pi\) | ||||
0.743660 | + | 0.668558i | \(0.233088\pi\) | |||||||
\(618\) | −7.81966 | −0.314553 | ||||||||
\(619\) | 41.0344 | 1.64931 | 0.824657 | − | 0.565634i | \(-0.191368\pi\) | ||||
0.824657 | + | 0.565634i | \(0.191368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.63932 | 0.0657837 | ||||||||
\(622\) | 21.2148 | 0.850635 | ||||||||
\(623\) | 24.3607 | 0.975990 | ||||||||
\(624\) | 1.61803 | 0.0647732 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.7082 | 1.02751 | ||||||||
\(627\) | −1.38197 | −0.0551904 | ||||||||
\(628\) | −5.32624 | −0.212540 | ||||||||
\(629\) | −12.7639 | −0.508931 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0902 | 1.11825 | 0.559126 | − | 0.829083i | \(-0.311137\pi\) | ||||
0.559126 | + | 0.829083i | \(0.311137\pi\) | |||||||
\(632\) | 49.9574 | 1.98720 | ||||||||
\(633\) | −9.41641 | −0.374269 | ||||||||
\(634\) | 14.0344 | 0.557379 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.47214 | 0.0980266 | ||||||||
\(637\) | −9.09017 | −0.360166 | ||||||||
\(638\) | 5.65248 | 0.223784 | ||||||||
\(639\) | −25.6525 | −1.01480 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.8541 | −0.823688 | −0.411844 | − | 0.911254i | \(-0.635115\pi\) | ||||
−0.411844 | + | 0.911254i | \(0.635115\pi\) | |||||||
\(642\) | −1.90983 | −0.0753750 | ||||||||
\(643\) | −12.0000 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(644\) | 1.52786 | 0.0602063 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.61803 | −0.181694 | ||||||||
\(647\) | 26.1803 | 1.02926 | 0.514628 | − | 0.857414i | \(-0.327930\pi\) | ||||
0.514628 | + | 0.857414i | \(0.327930\pi\) | |||||||
\(648\) | −17.1246 | −0.672718 | ||||||||
\(649\) | −10.0000 | −0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.9443 | −0.820871 | ||||||||
\(652\) | −13.8885 | −0.543917 | ||||||||
\(653\) | −2.67376 | −0.104632 | −0.0523162 | − | 0.998631i | \(-0.516660\pi\) | ||||
−0.0523162 | + | 0.998631i | \(0.516660\pi\) | |||||||
\(654\) | −3.41641 | −0.133592 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.09017 | −0.276825 | ||||||||
\(657\) | −26.4164 | −1.03060 | ||||||||
\(658\) | 3.70820 | 0.144561 | ||||||||
\(659\) | −19.2361 | −0.749331 | −0.374665 | − | 0.927160i | \(-0.622242\pi\) | ||||
−0.374665 | + | 0.927160i | \(0.622242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0689 | 0.702798 | 0.351399 | − | 0.936226i | \(-0.385706\pi\) | ||||
0.351399 | + | 0.936226i | \(0.385706\pi\) | |||||||
\(662\) | 8.18034 | 0.317938 | ||||||||
\(663\) | −4.61803 | −0.179350 | ||||||||
\(664\) | 46.8541 | 1.81829 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.7082 | 0.453684 | ||||||||
\(667\) | −1.93112 | −0.0747731 | ||||||||
\(668\) | −4.29180 | −0.166055 | ||||||||
\(669\) | 2.70820 | 0.104705 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.56231 | −0.0989167 | ||||||||
\(672\) | 10.0000 | 0.385758 | ||||||||
\(673\) | 36.6525 | 1.41285 | 0.706425 | − | 0.707788i | \(-0.250307\pi\) | ||||
0.706425 | + | 0.707788i | \(0.250307\pi\) | |||||||
\(674\) | 4.65248 | 0.179207 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.14590 | 0.236381 | ||||||||
\(677\) | 14.6180 | 0.561817 | 0.280908 | − | 0.959735i | \(-0.409364\pi\) | ||||
0.280908 | + | 0.959735i | \(0.409364\pi\) | |||||||
\(678\) | 11.8197 | 0.453931 | ||||||||
\(679\) | −55.7771 | −2.14053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.3475 | 0.511478 | ||||||||
\(682\) | −14.4721 | −0.554167 | ||||||||
\(683\) | 28.3607 | 1.08519 | 0.542596 | − | 0.839994i | \(-0.317442\pi\) | ||||
0.542596 | + | 0.839994i | \(0.317442\pi\) | |||||||
\(684\) | −4.23607 | −0.161970 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.4164 | −0.435880 | ||||||||
\(687\) | −2.49342 | −0.0951300 | ||||||||
\(688\) | 2.47214 | 0.0942493 | ||||||||
\(689\) | 10.4721 | 0.398957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.81966 | −0.221390 | −0.110695 | − | 0.993854i | \(-0.535308\pi\) | ||||
−0.110695 | + | 0.993854i | \(0.535308\pi\) | |||||||
\(692\) | 6.32624 | 0.240487 | ||||||||
\(693\) | −11.7082 | −0.444758 | ||||||||
\(694\) | 11.7984 | 0.447860 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.58359 | −0.287455 | ||||||||
\(697\) | 20.2361 | 0.766496 | ||||||||
\(698\) | 23.5066 | 0.889737 | ||||||||
\(699\) | −1.81966 | −0.0688259 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.8197 | −0.446422 | −0.223211 | − | 0.974770i | \(-0.571654\pi\) | ||||
−0.223211 | + | 0.974770i | \(0.571654\pi\) | |||||||
\(702\) | 9.09017 | 0.343086 | ||||||||
\(703\) | 7.23607 | 0.272913 | ||||||||
\(704\) | 9.67376 | 0.364594 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.3262 | −1.14134 | ||||||||
\(707\) | 23.4164 | 0.880665 | ||||||||
\(708\) | 4.47214 | 0.168073 | ||||||||
\(709\) | −9.52786 | −0.357826 | −0.178913 | − | 0.983865i | \(-0.557258\pi\) | ||||
−0.178913 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.5967 | 1.63501 | ||||||||
\(712\) | −22.5836 | −0.846356 | ||||||||
\(713\) | 4.94427 | 0.185164 | ||||||||
\(714\) | 5.70820 | 0.213624 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.94427 | −0.184776 | ||||||||
\(717\) | −0.944272 | −0.0352645 | ||||||||
\(718\) | 4.29180 | 0.160168 | ||||||||
\(719\) | −33.5967 | −1.25295 | −0.626474 | − | 0.779443i | \(-0.715502\pi\) | ||||
−0.626474 | + | 0.779443i | \(0.715502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.9443 | −1.52484 | ||||||||
\(722\) | −16.3820 | −0.609674 | ||||||||
\(723\) | 0.618034 | 0.0229849 | ||||||||
\(724\) | 3.38197 | 0.125690 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.61803 | −0.208505 | ||||||||
\(727\) | 20.2016 | 0.749237 | 0.374618 | − | 0.927179i | \(-0.377774\pi\) | ||||
0.374618 | + | 0.927179i | \(0.377774\pi\) | |||||||
\(728\) | 25.4164 | 0.941995 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.05573 | −0.260966 | ||||||||
\(732\) | 1.14590 | 0.0423536 | ||||||||
\(733\) | −4.18034 | −0.154404 | −0.0772022 | − | 0.997015i | \(-0.524599\pi\) | ||||
−0.0772022 | + | 0.997015i | \(0.524599\pi\) | |||||||
\(734\) | −16.1803 | −0.597227 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.36068 | −0.0870158 | ||||||||
\(737\) | −16.3050 | −0.600601 | ||||||||
\(738\) | −18.5623 | −0.683288 | ||||||||
\(739\) | −2.76393 | −0.101673 | −0.0508364 | − | 0.998707i | \(-0.516189\pi\) | ||||
−0.0508364 | + | 0.998707i | \(0.516189\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.61803 | 0.0961759 | ||||||||
\(742\) | −12.9443 | −0.475199 | ||||||||
\(743\) | 45.9230 | 1.68475 | 0.842375 | − | 0.538891i | \(-0.181157\pi\) | ||||
0.842375 | + | 0.538891i | \(0.181157\pi\) | |||||||
\(744\) | 19.4164 | 0.711840 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.8541 | 0.543847 | ||||||||
\(747\) | 40.8885 | 1.49603 | ||||||||
\(748\) | −3.94427 | −0.144217 | ||||||||
\(749\) | −10.0000 | −0.365392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8541 | 0.578524 | 0.289262 | − | 0.957250i | \(-0.406590\pi\) | ||||
0.289262 | + | 0.957250i | \(0.406590\pi\) | |||||||
\(752\) | −1.14590 | −0.0417866 | ||||||||
\(753\) | −3.52786 | −0.128563 | ||||||||
\(754\) | −10.7082 | −0.389970 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.2361 | 0.408652 | ||||||||
\(757\) | 1.14590 | 0.0416484 | 0.0208242 | − | 0.999783i | \(-0.493371\pi\) | ||||
0.0208242 | + | 0.999783i | \(0.493371\pi\) | |||||||
\(758\) | 5.74265 | 0.208582 | ||||||||
\(759\) | −0.403252 | −0.0146371 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.8328 | 1.04519 | 0.522594 | − | 0.852581i | \(-0.324964\pi\) | ||||
0.522594 | + | 0.852581i | \(0.324964\pi\) | |||||||
\(762\) | −6.18034 | −0.223890 | ||||||||
\(763\) | −17.8885 | −0.647609 | ||||||||
\(764\) | 20.6525 | 0.747180 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.4721 | −0.884214 | ||||||||
\(767\) | 18.9443 | 0.684038 | ||||||||
\(768\) | −10.5066 | −0.379123 | ||||||||
\(769\) | 23.4164 | 0.844417 | 0.422209 | − | 0.906499i | \(-0.361255\pi\) | ||||
0.422209 | + | 0.906499i | \(0.361255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2361 | −0.692770 | ||||||||
\(772\) | 0.472136 | 0.0169925 | ||||||||
\(773\) | 39.0132 | 1.40321 | 0.701603 | − | 0.712568i | \(-0.252468\pi\) | ||||
0.701603 | + | 0.712568i | \(0.252468\pi\) | |||||||
\(774\) | 6.47214 | 0.232636 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 51.7082 | 1.85622 | ||||||||
\(777\) | −8.94427 | −0.320874 | ||||||||
\(778\) | −10.2918 | −0.368979 | ||||||||
\(779\) | −11.4721 | −0.411032 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.5410 | 0.484536 | ||||||||
\(782\) | −1.34752 | −0.0481874 | ||||||||
\(783\) | −14.2016 | −0.507525 | ||||||||
\(784\) | −3.47214 | −0.124005 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.8885 | −0.388381 | ||||||||
\(787\) | −36.0344 | −1.28449 | −0.642245 | − | 0.766500i | \(-0.721997\pi\) | ||||
−0.642245 | + | 0.766500i | \(0.721997\pi\) | |||||||
\(788\) | 14.9443 | 0.532368 | ||||||||
\(789\) | −3.41641 | −0.121627 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.8885 | 2.20050 | ||||||||
\(792\) | 10.8541 | 0.385684 | ||||||||
\(793\) | 4.85410 | 0.172374 | ||||||||
\(794\) | 31.3050 | 1.11097 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.8541 | 0.845486 | ||||||||
\(797\) | 4.96556 | 0.175889 | 0.0879445 | − | 0.996125i | \(-0.471970\pi\) | ||||
0.0879445 | + | 0.996125i | \(0.471970\pi\) | |||||||
\(798\) | −3.23607 | −0.114556 | ||||||||
\(799\) | 3.27051 | 0.115702 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.7082 | −0.696355 | ||||||||
\(802\) | −17.7984 | −0.628482 | ||||||||
\(803\) | 13.9443 | 0.492083 | ||||||||
\(804\) | 7.29180 | 0.257162 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27.4164 | 0.965702 | ||||||||
\(807\) | −7.23607 | −0.254722 | ||||||||
\(808\) | −21.7082 | −0.763692 | ||||||||
\(809\) | 1.88854 | 0.0663977 | 0.0331988 | − | 0.999449i | \(-0.489431\pi\) | ||||
0.0331988 | + | 0.999449i | \(0.489431\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.5066 | 0.439165 | 0.219583 | − | 0.975594i | \(-0.429530\pi\) | ||||
0.219583 | + | 0.975594i | \(0.429530\pi\) | |||||||
\(812\) | −13.2361 | −0.464495 | ||||||||
\(813\) | −17.4164 | −0.610820 | ||||||||
\(814\) | −6.18034 | −0.216621 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.76393 | −0.0617500 | ||||||||
\(817\) | 4.00000 | 0.139942 | ||||||||
\(818\) | 32.9443 | 1.15187 | ||||||||
\(819\) | 22.1803 | 0.775044 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.4508 | −1.65605 | −0.828023 | − | 0.560694i | \(-0.810534\pi\) | ||||
−0.828023 | + | 0.560694i | \(0.810534\pi\) | |||||||
\(822\) | −8.09017 | −0.282177 | ||||||||
\(823\) | −12.5836 | −0.438636 | −0.219318 | − | 0.975653i | \(-0.570383\pi\) | ||||
−0.219318 | + | 0.975653i | \(0.570383\pi\) | |||||||
\(824\) | 37.9574 | 1.32231 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.4164 | −0.814761 | ||||||||
\(827\) | 6.94427 | 0.241476 | 0.120738 | − | 0.992684i | \(-0.461474\pi\) | ||||
0.120738 | + | 0.992684i | \(0.461474\pi\) | |||||||
\(828\) | −1.23607 | −0.0429563 | ||||||||
\(829\) | 13.7984 | 0.479237 | 0.239619 | − | 0.970867i | \(-0.422978\pi\) | ||||
0.239619 | + | 0.970867i | \(0.422978\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.94427 | −0.171515 | ||||||||
\(832\) | −18.3262 | −0.635348 | ||||||||
\(833\) | 9.90983 | 0.343355 | ||||||||
\(834\) | 8.09017 | 0.280140 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.23607 | 0.0773360 | ||||||||
\(837\) | 36.3607 | 1.25681 | ||||||||
\(838\) | 3.20163 | 0.110598 | ||||||||
\(839\) | 11.8885 | 0.410438 | 0.205219 | − | 0.978716i | \(-0.434209\pi\) | ||||
0.205219 | + | 0.978716i | \(0.434209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.2705 | −0.423121 | ||||||||
\(842\) | −10.3607 | −0.357053 | ||||||||
\(843\) | 12.3820 | 0.426458 | ||||||||
\(844\) | 15.2361 | 0.524447 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | −29.4164 | −1.01076 | ||||||||
\(848\) | 4.00000 | 0.137361 | ||||||||
\(849\) | 6.94427 | 0.238327 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.11146 | 0.0723798 | ||||||||
\(852\) | −6.05573 | −0.207466 | ||||||||
\(853\) | −26.9787 | −0.923734 | −0.461867 | − | 0.886949i | \(-0.652820\pi\) | ||||
−0.461867 | + | 0.886949i | \(0.652820\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.27051 | 0.316860 | ||||||||
\(857\) | −33.7082 | −1.15145 | −0.575725 | − | 0.817643i | \(-0.695280\pi\) | ||||
−0.575725 | + | 0.817643i | \(0.695280\pi\) | |||||||
\(858\) | −2.23607 | −0.0763381 | ||||||||
\(859\) | 5.25735 | 0.179379 | 0.0896893 | − | 0.995970i | \(-0.471413\pi\) | ||||
0.0896893 | + | 0.995970i | \(0.471413\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.1803 | 0.483265 | ||||||||
\(862\) | −33.4508 | −1.13934 | ||||||||
\(863\) | −18.7639 | −0.638732 | −0.319366 | − | 0.947632i | \(-0.603470\pi\) | ||||
−0.319366 | + | 0.947632i | \(0.603470\pi\) | |||||||
\(864\) | −17.3607 | −0.590622 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.6525 | 0.429949 | ||||||||
\(867\) | −5.47214 | −0.185843 | ||||||||
\(868\) | 33.8885 | 1.15025 | ||||||||
\(869\) | −23.0132 | −0.780668 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.8885 | 1.04662 | ||||||||
\(872\) | 16.5836 | 0.561591 | ||||||||
\(873\) | 45.1246 | 1.52724 | ||||||||
\(874\) | 0.763932 | 0.0258404 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.23607 | −0.210697 | ||||||||
\(877\) | 34.5410 | 1.16637 | 0.583184 | − | 0.812340i | \(-0.301807\pi\) | ||||
0.583184 | + | 0.812340i | \(0.301807\pi\) | |||||||
\(878\) | 4.14590 | 0.139917 | ||||||||
\(879\) | 13.1803 | 0.444562 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.7984 | 1.00393 | 0.501966 | − | 0.864887i | \(-0.332610\pi\) | ||||
0.501966 | + | 0.864887i | \(0.332610\pi\) | |||||||
\(882\) | −9.09017 | −0.306082 | ||||||||
\(883\) | 37.5623 | 1.26407 | 0.632036 | − | 0.774939i | \(-0.282219\pi\) | ||||
0.632036 | + | 0.774939i | \(0.282219\pi\) | |||||||
\(884\) | 7.47214 | 0.251315 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.94427 | 0.0989147 | ||||||||
\(887\) | −4.97871 | −0.167169 | −0.0835844 | − | 0.996501i | \(-0.526637\pi\) | ||||
−0.0835844 | + | 0.996501i | \(0.526637\pi\) | |||||||
\(888\) | 8.29180 | 0.278254 | ||||||||
\(889\) | −32.3607 | −1.08534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.88854 | 0.264276 | ||||||||
\(892\) | −4.38197 | −0.146719 | ||||||||
\(893\) | −1.85410 | −0.0620452 | ||||||||
\(894\) | 8.00000 | 0.267560 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.70820 | −0.324328 | ||||||||
\(897\) | 0.763932 | 0.0255069 | ||||||||
\(898\) | −8.76393 | −0.292456 | ||||||||
\(899\) | −42.8328 | −1.42855 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4164 | −0.380336 | ||||||||
\(902\) | 9.79837 | 0.326250 | ||||||||
\(903\) | −4.94427 | −0.164535 | ||||||||
\(904\) | −57.3738 | −1.90823 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.29180 | 0.142585 | ||||||||
\(907\) | 5.81966 | 0.193239 | 0.0966193 | − | 0.995321i | \(-0.469197\pi\) | ||||
0.0966193 | + | 0.995321i | \(0.469197\pi\) | |||||||
\(908\) | −21.5967 | −0.716713 | ||||||||
\(909\) | −18.9443 | −0.628342 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.34752 | 0.0446455 | 0.0223227 | − | 0.999751i | \(-0.492894\pi\) | ||||
0.0223227 | + | 0.999751i | \(0.492894\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −21.5836 | −0.714313 | ||||||||
\(914\) | 6.65248 | 0.220044 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.03444 | 0.133302 | ||||||||
\(917\) | −57.0132 | −1.88274 | ||||||||
\(918\) | −9.90983 | −0.327073 | ||||||||
\(919\) | 2.94427 | 0.0971226 | 0.0485613 | − | 0.998820i | \(-0.484536\pi\) | ||||
0.0485613 | + | 0.998820i | \(0.484536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0689 | 0.331781 | ||||||||
\(922\) | −36.0000 | −1.18560 | ||||||||
\(923\) | −25.6525 | −0.844362 | ||||||||
\(924\) | −2.76393 | −0.0909267 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.7082 | 0.581928 | ||||||||
\(927\) | 33.1246 | 1.08795 | ||||||||
\(928\) | 20.4508 | 0.671332 | ||||||||
\(929\) | 6.76393 | 0.221917 | 0.110959 | − | 0.993825i | \(-0.464608\pi\) | ||||
0.110959 | + | 0.993825i | \(0.464608\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.61803 | −0.184124 | ||||||||
\(932\) | 2.94427 | 0.0964428 | ||||||||
\(933\) | 13.1115 | 0.429250 | ||||||||
\(934\) | 24.3262 | 0.795979 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −20.5623 | −0.672100 | ||||||||
\(937\) | −20.3607 | −0.665154 | −0.332577 | − | 0.943076i | \(-0.607918\pi\) | ||||
−0.332577 | + | 0.943076i | \(0.607918\pi\) | |||||||
\(938\) | −38.1803 | −1.24663 | ||||||||
\(939\) | 15.8885 | 0.518503 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.65248 | 0.216865 | 0.108432 | − | 0.994104i | \(-0.465417\pi\) | ||||
0.108432 | + | 0.994104i | \(0.465417\pi\) | |||||||
\(942\) | 3.29180 | 0.107253 | ||||||||
\(943\) | −3.34752 | −0.109010 | ||||||||
\(944\) | 7.23607 | 0.235514 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.41641 | −0.111077 | ||||||||
\(947\) | 37.1246 | 1.20639 | 0.603194 | − | 0.797595i | \(-0.293895\pi\) | ||||
0.603194 | + | 0.797595i | \(0.293895\pi\) | |||||||
\(948\) | 10.2918 | 0.334262 | ||||||||
\(949\) | −26.4164 | −0.857513 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.67376 | 0.281266 | ||||||||
\(952\) | −27.7082 | −0.898028 | ||||||||
\(953\) | 25.3820 | 0.822203 | 0.411101 | − | 0.911590i | \(-0.365144\pi\) | ||||
0.411101 | + | 0.911590i | \(0.365144\pi\) | |||||||
\(954\) | 10.4721 | 0.339048 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.52786 | 0.0494147 | ||||||||
\(957\) | 3.49342 | 0.112926 | ||||||||
\(958\) | −21.0557 | −0.680280 | ||||||||
\(959\) | −42.3607 | −1.36790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.6656 | 2.53760 | ||||||||
\(962\) | 11.7082 | 0.377488 | ||||||||
\(963\) | 8.09017 | 0.260702 | ||||||||
\(964\) | −1.00000 | −0.0322078 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.944272 | −0.0303815 | ||||||||
\(967\) | −7.05573 | −0.226897 | −0.113448 | − | 0.993544i | \(-0.536190\pi\) | ||||
−0.113448 | + | 0.993544i | \(0.536190\pi\) | |||||||
\(968\) | 27.2705 | 0.876507 | ||||||||
\(969\) | −2.85410 | −0.0916870 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.7214 | 1.69191 | 0.845954 | − | 0.533255i | \(-0.179031\pi\) | ||||
0.845954 | + | 0.533255i | \(0.179031\pi\) | |||||||
\(972\) | −13.9443 | −0.447263 | ||||||||
\(973\) | 42.3607 | 1.35802 | ||||||||
\(974\) | 8.32624 | 0.266790 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.85410 | 0.0593484 | ||||||||
\(977\) | 5.05573 | 0.161747 | 0.0808735 | − | 0.996724i | \(-0.474229\pi\) | ||||
0.0808735 | + | 0.996724i | \(0.474229\pi\) | |||||||
\(978\) | 8.58359 | 0.274473 | ||||||||
\(979\) | 10.4033 | 0.332489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4721 | 0.462060 | ||||||||
\(982\) | 23.4164 | 0.747248 | ||||||||
\(983\) | 0.403252 | 0.0128617 | 0.00643087 | − | 0.999979i | \(-0.497953\pi\) | ||||
0.00643087 | + | 0.999979i | \(0.497953\pi\) | |||||||
\(984\) | −13.1459 | −0.419076 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.6738 | 0.371768 | ||||||||
\(987\) | 2.29180 | 0.0729487 | ||||||||
\(988\) | −4.23607 | −0.134767 | ||||||||
\(989\) | 1.16718 | 0.0371143 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.4164 | 1.63330 | 0.816648 | − | 0.577136i | \(-0.195830\pi\) | ||||
0.816648 | + | 0.577136i | \(0.195830\pi\) | |||||||
\(992\) | −52.3607 | −1.66245 | ||||||||
\(993\) | 5.05573 | 0.160439 | ||||||||
\(994\) | 31.7082 | 1.00572 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.65248 | 0.305850 | ||||||||
\(997\) | 27.8541 | 0.882148 | 0.441074 | − | 0.897471i | \(-0.354598\pi\) | ||||
0.441074 | + | 0.897471i | \(0.354598\pi\) | |||||||
\(998\) | −21.3050 | −0.674396 | ||||||||
\(999\) | 15.5279 | 0.491280 |
(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 | 6025.2.a.d.1.2 | 2 | ||
5.2 | odd | 4 | 1205.2.b.b.724.3 | yes | 4 | ||
5.3 | odd | 4 | 1205.2.b.b.724.2 | ✓ | 4 | ||
5.4 | even | 2 | 6025.2.a.a.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.b.724.2 | ✓ | 4 | 5.3 | odd | 4 | ||
1205.2.b.b.724.3 | yes | 4 | 5.2 | odd | 4 | ||
6025.2.a.a.1.1 | 2 | 5.4 | even | 2 | |||
6025.2.a.d.1.2 | 2 | 1.1 | even | 1 | trivial |