Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6045,2,Mod(1,6045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6045.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: | \(48.2695680219\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.41421 | −0.577350 | ||||||||
\(7\) | −0.414214 | −0.156558 | −0.0782790 | − | 0.996931i | \(-0.524942\pi\) | ||||
−0.0782790 | + | 0.996931i | \(0.524942\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.41421 | −0.447214 | ||||||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.585786 | 0.156558 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 7.65685 | 1.85706 | 0.928530 | − | 0.371257i | \(-0.121073\pi\) | ||||
0.928530 | + | 0.371257i | \(0.121073\pi\) | |||||||
\(18\) | −1.41421 | −0.333333 | ||||||||
\(19\) | −7.41421 | −1.70094 | −0.850469 | − | 0.526026i | \(-0.823682\pi\) | ||||
−0.850469 | + | 0.526026i | \(0.823682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.414214 | −0.0903888 | ||||||||
\(22\) | −1.17157 | −0.249780 | ||||||||
\(23\) | −8.82843 | −1.84085 | −0.920427 | − | 0.390914i | \(-0.872159\pi\) | ||||
−0.920427 | + | 0.390914i | \(0.872159\pi\) | |||||||
\(24\) | 2.82843 | 0.577350 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.41421 | −0.277350 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.41421 | 0.819699 | 0.409849 | − | 0.912153i | \(-0.365581\pi\) | ||||
0.409849 | + | 0.912153i | \(0.365581\pi\) | |||||||
\(30\) | −1.41421 | −0.258199 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.828427 | 0.144211 | ||||||||
\(34\) | −10.8284 | −1.85706 | ||||||||
\(35\) | −0.414214 | −0.0700149 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.82843 | −1.45138 | −0.725692 | − | 0.688019i | \(-0.758480\pi\) | ||||
−0.725692 | + | 0.688019i | \(0.758480\pi\) | |||||||
\(38\) | 10.4853 | 1.70094 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 2.82843 | 0.447214 | ||||||||
\(41\) | −8.41421 | −1.31408 | −0.657040 | − | 0.753856i | \(-0.728192\pi\) | ||||
−0.657040 | + | 0.753856i | \(0.728192\pi\) | |||||||
\(42\) | 0.585786 | 0.0903888 | ||||||||
\(43\) | −2.41421 | −0.368164 | −0.184082 | − | 0.982911i | \(-0.558931\pi\) | ||||
−0.184082 | + | 0.982911i | \(0.558931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 12.4853 | 1.84085 | ||||||||
\(47\) | 5.07107 | 0.739691 | 0.369846 | − | 0.929093i | \(-0.379411\pi\) | ||||
0.369846 | + | 0.929093i | \(0.379411\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | −6.82843 | −0.975490 | ||||||||
\(50\) | −1.41421 | −0.200000 | ||||||||
\(51\) | 7.65685 | 1.07217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.242641 | −0.0333293 | −0.0166646 | − | 0.999861i | \(-0.505305\pi\) | ||||
−0.0166646 | + | 0.999861i | \(0.505305\pi\) | |||||||
\(54\) | −1.41421 | −0.192450 | ||||||||
\(55\) | 0.828427 | 0.111705 | ||||||||
\(56\) | −1.17157 | −0.156558 | ||||||||
\(57\) | −7.41421 | −0.982037 | ||||||||
\(58\) | −6.24264 | −0.819699 | ||||||||
\(59\) | 6.07107 | 0.790386 | 0.395193 | − | 0.918598i | \(-0.370678\pi\) | ||||
0.395193 | + | 0.918598i | \(0.370678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.24264 | −1.05536 | −0.527681 | − | 0.849443i | \(-0.676938\pi\) | ||||
−0.527681 | + | 0.849443i | \(0.676938\pi\) | |||||||
\(62\) | −1.41421 | −0.179605 | ||||||||
\(63\) | −0.414214 | −0.0521860 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | −1.17157 | −0.144211 | ||||||||
\(67\) | −8.41421 | −1.02796 | −0.513980 | − | 0.857802i | \(-0.671829\pi\) | ||||
−0.513980 | + | 0.857802i | \(0.671829\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.82843 | −1.06282 | ||||||||
\(70\) | 0.585786 | 0.0700149 | ||||||||
\(71\) | −15.3137 | −1.81740 | −0.908701 | − | 0.417447i | \(-0.862925\pi\) | ||||
−0.908701 | + | 0.417447i | \(0.862925\pi\) | |||||||
\(72\) | 2.82843 | 0.333333 | ||||||||
\(73\) | 1.07107 | 0.125359 | 0.0626795 | − | 0.998034i | \(-0.480035\pi\) | ||||
0.0626795 | + | 0.998034i | \(0.480035\pi\) | |||||||
\(74\) | 12.4853 | 1.45138 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.343146 | −0.0391051 | ||||||||
\(78\) | −1.41421 | −0.160128 | ||||||||
\(79\) | −7.07107 | −0.795557 | −0.397779 | − | 0.917481i | \(-0.630219\pi\) | ||||
−0.397779 | + | 0.917481i | \(0.630219\pi\) | |||||||
\(80\) | −4.00000 | −0.447214 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.8995 | 1.31408 | ||||||||
\(83\) | −6.17157 | −0.677418 | −0.338709 | − | 0.940891i | \(-0.609990\pi\) | ||||
−0.338709 | + | 0.940891i | \(0.609990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.65685 | 0.830502 | ||||||||
\(86\) | 3.41421 | 0.368164 | ||||||||
\(87\) | 4.41421 | 0.473253 | ||||||||
\(88\) | 2.34315 | 0.249780 | ||||||||
\(89\) | −8.82843 | −0.935811 | −0.467906 | − | 0.883778i | \(-0.654991\pi\) | ||||
−0.467906 | + | 0.883778i | \(0.654991\pi\) | |||||||
\(90\) | −1.41421 | −0.149071 | ||||||||
\(91\) | −0.414214 | −0.0434214 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | −7.17157 | −0.739691 | ||||||||
\(95\) | −7.41421 | −0.760682 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.58579 | 0.770220 | 0.385110 | − | 0.922871i | \(-0.374164\pi\) | ||||
0.385110 | + | 0.922871i | \(0.374164\pi\) | |||||||
\(98\) | 9.65685 | 0.975490 | ||||||||
\(99\) | 0.828427 | 0.0832601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.07107 | 0.504590 | 0.252295 | − | 0.967650i | \(-0.418815\pi\) | ||||
0.252295 | + | 0.967650i | \(0.418815\pi\) | |||||||
\(102\) | −10.8284 | −1.07217 | ||||||||
\(103\) | 13.0711 | 1.28793 | 0.643965 | − | 0.765055i | \(-0.277288\pi\) | ||||
0.643965 | + | 0.765055i | \(0.277288\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | −0.414214 | −0.0404231 | ||||||||
\(106\) | 0.343146 | 0.0333293 | ||||||||
\(107\) | 5.82843 | 0.563455 | 0.281728 | − | 0.959494i | \(-0.409093\pi\) | ||||
0.281728 | + | 0.959494i | \(0.409093\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.75736 | −0.359890 | −0.179945 | − | 0.983677i | \(-0.557592\pi\) | ||||
−0.179945 | + | 0.983677i | \(0.557592\pi\) | |||||||
\(110\) | −1.17157 | −0.111705 | ||||||||
\(111\) | −8.82843 | −0.837957 | ||||||||
\(112\) | 1.65685 | 0.156558 | ||||||||
\(113\) | 5.34315 | 0.502641 | 0.251320 | − | 0.967904i | \(-0.419135\pi\) | ||||
0.251320 | + | 0.967904i | \(0.419135\pi\) | |||||||
\(114\) | 10.4853 | 0.982037 | ||||||||
\(115\) | −8.82843 | −0.823255 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −8.58579 | −0.790386 | ||||||||
\(119\) | −3.17157 | −0.290738 | ||||||||
\(120\) | 2.82843 | 0.258199 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 11.6569 | 1.05536 | ||||||||
\(123\) | −8.41421 | −0.758684 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.585786 | 0.0521860 | ||||||||
\(127\) | 0.757359 | 0.0672048 | 0.0336024 | − | 0.999435i | \(-0.489302\pi\) | ||||
0.0336024 | + | 0.999435i | \(0.489302\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | −2.41421 | −0.212560 | ||||||||
\(130\) | −1.41421 | −0.124035 | ||||||||
\(131\) | −15.4142 | −1.34675 | −0.673373 | − | 0.739303i | \(-0.735155\pi\) | ||||
−0.673373 | + | 0.739303i | \(0.735155\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.07107 | 0.266295 | ||||||||
\(134\) | 11.8995 | 1.02796 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 21.6569 | 1.85706 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 12.4853 | 1.06282 | ||||||||
\(139\) | 12.5858 | 1.06751 | 0.533756 | − | 0.845638i | \(-0.320780\pi\) | ||||
0.533756 | + | 0.845638i | \(0.320780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.07107 | 0.427061 | ||||||||
\(142\) | 21.6569 | 1.81740 | ||||||||
\(143\) | 0.828427 | 0.0692766 | ||||||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | 4.41421 | 0.366580 | ||||||||
\(146\) | −1.51472 | −0.125359 | ||||||||
\(147\) | −6.82843 | −0.563199 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0711 | 1.15275 | 0.576373 | − | 0.817186i | \(-0.304467\pi\) | ||||
0.576373 | + | 0.817186i | \(0.304467\pi\) | |||||||
\(150\) | −1.41421 | −0.115470 | ||||||||
\(151\) | −5.82843 | −0.474311 | −0.237155 | − | 0.971472i | \(-0.576215\pi\) | ||||
−0.237155 | + | 0.971472i | \(0.576215\pi\) | |||||||
\(152\) | −20.9706 | −1.70094 | ||||||||
\(153\) | 7.65685 | 0.619020 | ||||||||
\(154\) | 0.485281 | 0.0391051 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | −0.242641 | −0.0192427 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.65685 | 0.288200 | ||||||||
\(162\) | −1.41421 | −0.111111 | ||||||||
\(163\) | 5.17157 | 0.405069 | 0.202534 | − | 0.979275i | \(-0.435082\pi\) | ||||
0.202534 | + | 0.979275i | \(0.435082\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.828427 | 0.0644930 | ||||||||
\(166\) | 8.72792 | 0.677418 | ||||||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | −1.17157 | −0.0903888 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −10.8284 | −0.830502 | ||||||||
\(171\) | −7.41421 | −0.566979 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.171573 | −0.0130444 | −0.00652222 | − | 0.999979i | \(-0.502076\pi\) | ||||
−0.00652222 | + | 0.999979i | \(0.502076\pi\) | |||||||
\(174\) | −6.24264 | −0.473253 | ||||||||
\(175\) | −0.414214 | −0.0313116 | ||||||||
\(176\) | −3.31371 | −0.249780 | ||||||||
\(177\) | 6.07107 | 0.456329 | ||||||||
\(178\) | 12.4853 | 0.935811 | ||||||||
\(179\) | 7.72792 | 0.577612 | 0.288806 | − | 0.957388i | \(-0.406742\pi\) | ||||
0.288806 | + | 0.957388i | \(0.406742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.51472 | 0.558565 | 0.279282 | − | 0.960209i | \(-0.409903\pi\) | ||||
0.279282 | + | 0.960209i | \(0.409903\pi\) | |||||||
\(182\) | 0.585786 | 0.0434214 | ||||||||
\(183\) | −8.24264 | −0.609314 | ||||||||
\(184\) | −24.9706 | −1.84085 | ||||||||
\(185\) | −8.82843 | −0.649079 | ||||||||
\(186\) | −1.41421 | −0.103695 | ||||||||
\(187\) | 6.34315 | 0.463857 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.414214 | −0.0301296 | ||||||||
\(190\) | 10.4853 | 0.760682 | ||||||||
\(191\) | −6.48528 | −0.469258 | −0.234629 | − | 0.972085i | \(-0.575388\pi\) | ||||
−0.234629 | + | 0.972085i | \(0.575388\pi\) | |||||||
\(192\) | 8.00000 | 0.577350 | ||||||||
\(193\) | 7.10051 | 0.511106 | 0.255553 | − | 0.966795i | \(-0.417743\pi\) | ||||
0.255553 | + | 0.966795i | \(0.417743\pi\) | |||||||
\(194\) | −10.7279 | −0.770220 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.82843 | −0.415258 | −0.207629 | − | 0.978208i | \(-0.566575\pi\) | ||||
−0.207629 | + | 0.978208i | \(0.566575\pi\) | |||||||
\(198\) | −1.17157 | −0.0832601 | ||||||||
\(199\) | 12.4853 | 0.885058 | 0.442529 | − | 0.896754i | \(-0.354081\pi\) | ||||
0.442529 | + | 0.896754i | \(0.354081\pi\) | |||||||
\(200\) | 2.82843 | 0.200000 | ||||||||
\(201\) | −8.41421 | −0.593493 | ||||||||
\(202\) | −7.17157 | −0.504590 | ||||||||
\(203\) | −1.82843 | −0.128330 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.41421 | −0.587674 | ||||||||
\(206\) | −18.4853 | −1.28793 | ||||||||
\(207\) | −8.82843 | −0.613618 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | −6.14214 | −0.424860 | ||||||||
\(210\) | 0.585786 | 0.0404231 | ||||||||
\(211\) | −17.4853 | −1.20374 | −0.601868 | − | 0.798595i | \(-0.705577\pi\) | ||||
−0.601868 | + | 0.798595i | \(0.705577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.3137 | −1.04928 | ||||||||
\(214\) | −8.24264 | −0.563455 | ||||||||
\(215\) | −2.41421 | −0.164648 | ||||||||
\(216\) | 2.82843 | 0.192450 | ||||||||
\(217\) | −0.414214 | −0.0281186 | ||||||||
\(218\) | 5.31371 | 0.359890 | ||||||||
\(219\) | 1.07107 | 0.0723761 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.65685 | 0.515056 | ||||||||
\(222\) | 12.4853 | 0.837957 | ||||||||
\(223\) | −19.4142 | −1.30007 | −0.650036 | − | 0.759903i | \(-0.725246\pi\) | ||||
−0.650036 | + | 0.759903i | \(0.725246\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.55635 | −0.502641 | ||||||||
\(227\) | 28.6274 | 1.90007 | 0.950034 | − | 0.312146i | \(-0.101048\pi\) | ||||
0.950034 | + | 0.312146i | \(0.101048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4558 | 1.68217 | 0.841085 | − | 0.540903i | \(-0.181918\pi\) | ||||
0.841085 | + | 0.540903i | \(0.181918\pi\) | |||||||
\(230\) | 12.4853 | 0.823255 | ||||||||
\(231\) | −0.343146 | −0.0225773 | ||||||||
\(232\) | 12.4853 | 0.819699 | ||||||||
\(233\) | −24.7990 | −1.62464 | −0.812318 | − | 0.583215i | \(-0.801795\pi\) | ||||
−0.812318 | + | 0.583215i | \(0.801795\pi\) | |||||||
\(234\) | −1.41421 | −0.0924500 | ||||||||
\(235\) | 5.07107 | 0.330800 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.07107 | −0.459315 | ||||||||
\(238\) | 4.48528 | 0.290738 | ||||||||
\(239\) | 1.75736 | 0.113674 | 0.0568371 | − | 0.998383i | \(-0.481898\pi\) | ||||
0.0568371 | + | 0.998383i | \(0.481898\pi\) | |||||||
\(240\) | −4.00000 | −0.258199 | ||||||||
\(241\) | −16.7990 | −1.08212 | −0.541059 | − | 0.840985i | \(-0.681976\pi\) | ||||
−0.541059 | + | 0.840985i | \(0.681976\pi\) | |||||||
\(242\) | 14.5858 | 0.937610 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.82843 | −0.436252 | ||||||||
\(246\) | 11.8995 | 0.758684 | ||||||||
\(247\) | −7.41421 | −0.471755 | ||||||||
\(248\) | 2.82843 | 0.179605 | ||||||||
\(249\) | −6.17157 | −0.391108 | ||||||||
\(250\) | −1.41421 | −0.0894427 | ||||||||
\(251\) | −18.4142 | −1.16229 | −0.581147 | − | 0.813798i | \(-0.697396\pi\) | ||||
−0.581147 | + | 0.813798i | \(0.697396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.31371 | −0.459809 | ||||||||
\(254\) | −1.07107 | −0.0672048 | ||||||||
\(255\) | 7.65685 | 0.479491 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.3137 | −0.955243 | −0.477621 | − | 0.878566i | \(-0.658501\pi\) | ||||
−0.477621 | + | 0.878566i | \(0.658501\pi\) | |||||||
\(258\) | 3.41421 | 0.212560 | ||||||||
\(259\) | 3.65685 | 0.227226 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.41421 | 0.273233 | ||||||||
\(262\) | 21.7990 | 1.34675 | ||||||||
\(263\) | 2.92893 | 0.180606 | 0.0903028 | − | 0.995914i | \(-0.471217\pi\) | ||||
0.0903028 | + | 0.995914i | \(0.471217\pi\) | |||||||
\(264\) | 2.34315 | 0.144211 | ||||||||
\(265\) | −0.242641 | −0.0149053 | ||||||||
\(266\) | −4.34315 | −0.266295 | ||||||||
\(267\) | −8.82843 | −0.540291 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.6274 | 1.74544 | 0.872722 | − | 0.488217i | \(-0.162353\pi\) | ||||
0.872722 | + | 0.488217i | \(0.162353\pi\) | |||||||
\(270\) | −1.41421 | −0.0860663 | ||||||||
\(271\) | 25.4853 | 1.54812 | 0.774060 | − | 0.633112i | \(-0.218223\pi\) | ||||
0.774060 | + | 0.633112i | \(0.218223\pi\) | |||||||
\(272\) | −30.6274 | −1.85706 | ||||||||
\(273\) | −0.414214 | −0.0250693 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.828427 | 0.0499560 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.41421 | −0.385393 | −0.192696 | − | 0.981258i | \(-0.561723\pi\) | ||||
−0.192696 | + | 0.981258i | \(0.561723\pi\) | |||||||
\(278\) | −17.7990 | −1.06751 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | −1.17157 | −0.0700149 | ||||||||
\(281\) | −2.75736 | −0.164490 | −0.0822451 | − | 0.996612i | \(-0.526209\pi\) | ||||
−0.0822451 | + | 0.996612i | \(0.526209\pi\) | |||||||
\(282\) | −7.17157 | −0.427061 | ||||||||
\(283\) | −9.07107 | −0.539219 | −0.269610 | − | 0.962970i | \(-0.586895\pi\) | ||||
−0.269610 | + | 0.962970i | \(0.586895\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.41421 | −0.439180 | ||||||||
\(286\) | −1.17157 | −0.0692766 | ||||||||
\(287\) | 3.48528 | 0.205730 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | −6.24264 | −0.366580 | ||||||||
\(291\) | 7.58579 | 0.444687 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.585786 | −0.0342220 | −0.0171110 | − | 0.999854i | \(-0.505447\pi\) | ||||
−0.0171110 | + | 0.999854i | \(0.505447\pi\) | |||||||
\(294\) | 9.65685 | 0.563199 | ||||||||
\(295\) | 6.07107 | 0.353471 | ||||||||
\(296\) | −24.9706 | −1.45138 | ||||||||
\(297\) | 0.828427 | 0.0480702 | ||||||||
\(298\) | −19.8995 | −1.15275 | ||||||||
\(299\) | −8.82843 | −0.510561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | 0.0576390 | ||||||||
\(302\) | 8.24264 | 0.474311 | ||||||||
\(303\) | 5.07107 | 0.291325 | ||||||||
\(304\) | 29.6569 | 1.70094 | ||||||||
\(305\) | −8.24264 | −0.471972 | ||||||||
\(306\) | −10.8284 | −0.619020 | ||||||||
\(307\) | −25.3137 | −1.44473 | −0.722365 | − | 0.691512i | \(-0.756945\pi\) | ||||
−0.722365 | + | 0.691512i | \(0.756945\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0711 | 0.743587 | ||||||||
\(310\) | −1.41421 | −0.0803219 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 2.82843 | 0.160128 | ||||||||
\(313\) | −6.41421 | −0.362553 | −0.181276 | − | 0.983432i | \(-0.558023\pi\) | ||||
−0.181276 | + | 0.983432i | \(0.558023\pi\) | |||||||
\(314\) | 14.1421 | 0.798087 | ||||||||
\(315\) | −0.414214 | −0.0233383 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.58579 | 0.257563 | 0.128782 | − | 0.991673i | \(-0.458893\pi\) | ||||
0.128782 | + | 0.991673i | \(0.458893\pi\) | |||||||
\(318\) | 0.343146 | 0.0192427 | ||||||||
\(319\) | 3.65685 | 0.204745 | ||||||||
\(320\) | 8.00000 | 0.447214 | ||||||||
\(321\) | 5.82843 | 0.325311 | ||||||||
\(322\) | −5.17157 | −0.288200 | ||||||||
\(323\) | −56.7696 | −3.15874 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −7.31371 | −0.405069 | ||||||||
\(327\) | −3.75736 | −0.207782 | ||||||||
\(328\) | −23.7990 | −1.31408 | ||||||||
\(329\) | −2.10051 | −0.115805 | ||||||||
\(330\) | −1.17157 | −0.0644930 | ||||||||
\(331\) | −11.8284 | −0.650149 | −0.325075 | − | 0.945688i | \(-0.605389\pi\) | ||||
−0.325075 | + | 0.945688i | \(0.605389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.82843 | −0.483795 | ||||||||
\(334\) | 19.7990 | 1.08335 | ||||||||
\(335\) | −8.41421 | −0.459718 | ||||||||
\(336\) | 1.65685 | 0.0903888 | ||||||||
\(337\) | 22.4853 | 1.22485 | 0.612426 | − | 0.790528i | \(-0.290194\pi\) | ||||
0.612426 | + | 0.790528i | \(0.290194\pi\) | |||||||
\(338\) | −1.41421 | −0.0769231 | ||||||||
\(339\) | 5.34315 | 0.290200 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.828427 | 0.0448618 | ||||||||
\(342\) | 10.4853 | 0.566979 | ||||||||
\(343\) | 5.72792 | 0.309279 | ||||||||
\(344\) | −6.82843 | −0.368164 | ||||||||
\(345\) | −8.82843 | −0.475307 | ||||||||
\(346\) | 0.242641 | 0.0130444 | ||||||||
\(347\) | −25.5563 | −1.37194 | −0.685968 | − | 0.727631i | \(-0.740621\pi\) | ||||
−0.685968 | + | 0.727631i | \(0.740621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.79899 | 0.524528 | 0.262264 | − | 0.964996i | \(-0.415531\pi\) | ||||
0.262264 | + | 0.964996i | \(0.415531\pi\) | |||||||
\(350\) | 0.585786 | 0.0313116 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4853 | 0.717749 | 0.358875 | − | 0.933386i | \(-0.383161\pi\) | ||||
0.358875 | + | 0.933386i | \(0.383161\pi\) | |||||||
\(354\) | −8.58579 | −0.456329 | ||||||||
\(355\) | −15.3137 | −0.812767 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.17157 | −0.167857 | ||||||||
\(358\) | −10.9289 | −0.577612 | ||||||||
\(359\) | −35.2426 | −1.86004 | −0.930018 | − | 0.367515i | \(-0.880209\pi\) | ||||
−0.930018 | + | 0.367515i | \(0.880209\pi\) | |||||||
\(360\) | 2.82843 | 0.149071 | ||||||||
\(361\) | 35.9706 | 1.89319 | ||||||||
\(362\) | −10.6274 | −0.558565 | ||||||||
\(363\) | −10.3137 | −0.541329 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.07107 | 0.0560623 | ||||||||
\(366\) | 11.6569 | 0.609314 | ||||||||
\(367\) | 35.6569 | 1.86127 | 0.930636 | − | 0.365945i | \(-0.119254\pi\) | ||||
0.930636 | + | 0.365945i | \(0.119254\pi\) | |||||||
\(368\) | 35.3137 | 1.84085 | ||||||||
\(369\) | −8.41421 | −0.438026 | ||||||||
\(370\) | 12.4853 | 0.649079 | ||||||||
\(371\) | 0.100505 | 0.00521796 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.51472 | 0.0784292 | 0.0392146 | − | 0.999231i | \(-0.487514\pi\) | ||||
0.0392146 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(374\) | −8.97056 | −0.463857 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 14.3431 | 0.739691 | ||||||||
\(377\) | 4.41421 | 0.227344 | ||||||||
\(378\) | 0.585786 | 0.0301296 | ||||||||
\(379\) | −11.0711 | −0.568683 | −0.284341 | − | 0.958723i | \(-0.591775\pi\) | ||||
−0.284341 | + | 0.958723i | \(0.591775\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.757359 | 0.0388007 | ||||||||
\(382\) | 9.17157 | 0.469258 | ||||||||
\(383\) | −23.4853 | −1.20004 | −0.600021 | − | 0.799984i | \(-0.704841\pi\) | ||||
−0.600021 | + | 0.799984i | \(0.704841\pi\) | |||||||
\(384\) | −11.3137 | −0.577350 | ||||||||
\(385\) | −0.343146 | −0.0174883 | ||||||||
\(386\) | −10.0416 | −0.511106 | ||||||||
\(387\) | −2.41421 | −0.122721 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.0711 | 1.62607 | 0.813034 | − | 0.582216i | \(-0.197814\pi\) | ||||
0.813034 | + | 0.582216i | \(0.197814\pi\) | |||||||
\(390\) | −1.41421 | −0.0716115 | ||||||||
\(391\) | −67.5980 | −3.41858 | ||||||||
\(392\) | −19.3137 | −0.975490 | ||||||||
\(393\) | −15.4142 | −0.777544 | ||||||||
\(394\) | 8.24264 | 0.415258 | ||||||||
\(395\) | −7.07107 | −0.355784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.65685 | −0.183532 | −0.0917661 | − | 0.995781i | \(-0.529251\pi\) | ||||
−0.0917661 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(398\) | −17.6569 | −0.885058 | ||||||||
\(399\) | 3.07107 | 0.153746 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 11.7574 | 0.587135 | 0.293567 | − | 0.955938i | \(-0.405158\pi\) | ||||
0.293567 | + | 0.955938i | \(0.405158\pi\) | |||||||
\(402\) | 11.8995 | 0.593493 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 2.58579 | 0.128330 | ||||||||
\(407\) | −7.31371 | −0.362527 | ||||||||
\(408\) | 21.6569 | 1.07217 | ||||||||
\(409\) | 17.9706 | 0.888587 | 0.444294 | − | 0.895881i | \(-0.353455\pi\) | ||||
0.444294 | + | 0.895881i | \(0.353455\pi\) | |||||||
\(410\) | 11.8995 | 0.587674 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.51472 | −0.123741 | ||||||||
\(414\) | 12.4853 | 0.613618 | ||||||||
\(415\) | −6.17157 | −0.302951 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.5858 | 0.616329 | ||||||||
\(418\) | 8.68629 | 0.424860 | ||||||||
\(419\) | −18.4853 | −0.903065 | −0.451533 | − | 0.892255i | \(-0.649123\pi\) | ||||
−0.451533 | + | 0.892255i | \(0.649123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.686292 | −0.0334478 | −0.0167239 | − | 0.999860i | \(-0.505324\pi\) | ||||
−0.0167239 | + | 0.999860i | \(0.505324\pi\) | |||||||
\(422\) | 24.7279 | 1.20374 | ||||||||
\(423\) | 5.07107 | 0.246564 | ||||||||
\(424\) | −0.686292 | −0.0333293 | ||||||||
\(425\) | 7.65685 | 0.371412 | ||||||||
\(426\) | 21.6569 | 1.04928 | ||||||||
\(427\) | 3.41421 | 0.165225 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.828427 | 0.0399968 | ||||||||
\(430\) | 3.41421 | 0.164648 | ||||||||
\(431\) | −28.2132 | −1.35898 | −0.679491 | − | 0.733684i | \(-0.737799\pi\) | ||||
−0.679491 | + | 0.733684i | \(0.737799\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | 3.72792 | 0.179153 | 0.0895763 | − | 0.995980i | \(-0.471449\pi\) | ||||
0.0895763 | + | 0.995980i | \(0.471449\pi\) | |||||||
\(434\) | 0.585786 | 0.0281186 | ||||||||
\(435\) | 4.41421 | 0.211645 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 65.4558 | 3.13118 | ||||||||
\(438\) | −1.51472 | −0.0723761 | ||||||||
\(439\) | 32.1127 | 1.53266 | 0.766328 | − | 0.642450i | \(-0.222082\pi\) | ||||
0.766328 | + | 0.642450i | \(0.222082\pi\) | |||||||
\(440\) | 2.34315 | 0.111705 | ||||||||
\(441\) | −6.82843 | −0.325163 | ||||||||
\(442\) | −10.8284 | −0.515056 | ||||||||
\(443\) | −39.6274 | −1.88276 | −0.941378 | − | 0.337354i | \(-0.890468\pi\) | ||||
−0.941378 | + | 0.337354i | \(0.890468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.82843 | −0.418508 | ||||||||
\(446\) | 27.4558 | 1.30007 | ||||||||
\(447\) | 14.0711 | 0.665539 | ||||||||
\(448\) | −3.31371 | −0.156558 | ||||||||
\(449\) | −31.6985 | −1.49594 | −0.747972 | − | 0.663730i | \(-0.768972\pi\) | ||||
−0.747972 | + | 0.663730i | \(0.768972\pi\) | |||||||
\(450\) | −1.41421 | −0.0666667 | ||||||||
\(451\) | −6.97056 | −0.328231 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.82843 | −0.273843 | ||||||||
\(454\) | −40.4853 | −1.90007 | ||||||||
\(455\) | −0.414214 | −0.0194186 | ||||||||
\(456\) | −20.9706 | −0.982037 | ||||||||
\(457\) | −36.0416 | −1.68596 | −0.842978 | − | 0.537948i | \(-0.819200\pi\) | ||||
−0.842978 | + | 0.537948i | \(0.819200\pi\) | |||||||
\(458\) | −36.0000 | −1.68217 | ||||||||
\(459\) | 7.65685 | 0.357391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6274 | −0.494968 | −0.247484 | − | 0.968892i | \(-0.579604\pi\) | ||||
−0.247484 | + | 0.968892i | \(0.579604\pi\) | |||||||
\(462\) | 0.485281 | 0.0225773 | ||||||||
\(463\) | −9.17157 | −0.426239 | −0.213120 | − | 0.977026i | \(-0.568362\pi\) | ||||
−0.213120 | + | 0.977026i | \(0.568362\pi\) | |||||||
\(464\) | −17.6569 | −0.819699 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 35.0711 | 1.62464 | ||||||||
\(467\) | −31.1421 | −1.44109 | −0.720543 | − | 0.693410i | \(-0.756107\pi\) | ||||
−0.720543 | + | 0.693410i | \(0.756107\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.48528 | 0.160935 | ||||||||
\(470\) | −7.17157 | −0.330800 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | 17.1716 | 0.790386 | ||||||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | −7.41421 | −0.340187 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.242641 | −0.0111098 | ||||||||
\(478\) | −2.48528 | −0.113674 | ||||||||
\(479\) | 15.5858 | 0.712133 | 0.356066 | − | 0.934461i | \(-0.384118\pi\) | ||||
0.356066 | + | 0.934461i | \(0.384118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.82843 | −0.402542 | ||||||||
\(482\) | 23.7574 | 1.08212 | ||||||||
\(483\) | 3.65685 | 0.166393 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.58579 | 0.344453 | ||||||||
\(486\) | −1.41421 | −0.0641500 | ||||||||
\(487\) | 8.24264 | 0.373510 | 0.186755 | − | 0.982407i | \(-0.440203\pi\) | ||||
0.186755 | + | 0.982407i | \(0.440203\pi\) | |||||||
\(488\) | −23.3137 | −1.05536 | ||||||||
\(489\) | 5.17157 | 0.233867 | ||||||||
\(490\) | 9.65685 | 0.436252 | ||||||||
\(491\) | 32.8995 | 1.48473 | 0.742367 | − | 0.669994i | \(-0.233703\pi\) | ||||
0.742367 | + | 0.669994i | \(0.233703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.7990 | 1.52223 | ||||||||
\(494\) | 10.4853 | 0.471755 | ||||||||
\(495\) | 0.828427 | 0.0372350 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 6.34315 | 0.284529 | ||||||||
\(498\) | 8.72792 | 0.391108 | ||||||||
\(499\) | 20.5147 | 0.918365 | 0.459182 | − | 0.888342i | \(-0.348142\pi\) | ||||
0.459182 | + | 0.888342i | \(0.348142\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.0000 | −0.625474 | ||||||||
\(502\) | 26.0416 | 1.16229 | ||||||||
\(503\) | 32.4558 | 1.44713 | 0.723567 | − | 0.690254i | \(-0.242501\pi\) | ||||
0.723567 | + | 0.690254i | \(0.242501\pi\) | |||||||
\(504\) | −1.17157 | −0.0521860 | ||||||||
\(505\) | 5.07107 | 0.225660 | ||||||||
\(506\) | 10.3431 | 0.459809 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0711 | −0.756662 | −0.378331 | − | 0.925670i | \(-0.623502\pi\) | ||||
−0.378331 | + | 0.925670i | \(0.623502\pi\) | |||||||
\(510\) | −10.8284 | −0.479491 | ||||||||
\(511\) | −0.443651 | −0.0196260 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −7.41421 | −0.327346 | ||||||||
\(514\) | 21.6569 | 0.955243 | ||||||||
\(515\) | 13.0711 | 0.575980 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.20101 | 0.184760 | ||||||||
\(518\) | −5.17157 | −0.227226 | ||||||||
\(519\) | −0.171573 | −0.00753121 | ||||||||
\(520\) | 2.82843 | 0.124035 | ||||||||
\(521\) | 17.0711 | 0.747897 | 0.373949 | − | 0.927449i | \(-0.378004\pi\) | ||||
0.373949 | + | 0.927449i | \(0.378004\pi\) | |||||||
\(522\) | −6.24264 | −0.273233 | ||||||||
\(523\) | −21.1005 | −0.922661 | −0.461330 | − | 0.887228i | \(-0.652628\pi\) | ||||
−0.461330 | + | 0.887228i | \(0.652628\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.414214 | −0.0180778 | ||||||||
\(526\) | −4.14214 | −0.180606 | ||||||||
\(527\) | 7.65685 | 0.333538 | ||||||||
\(528\) | −3.31371 | −0.144211 | ||||||||
\(529\) | 54.9411 | 2.38874 | ||||||||
\(530\) | 0.343146 | 0.0149053 | ||||||||
\(531\) | 6.07107 | 0.263462 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.41421 | −0.364460 | ||||||||
\(534\) | 12.4853 | 0.540291 | ||||||||
\(535\) | 5.82843 | 0.251985 | ||||||||
\(536\) | −23.7990 | −1.02796 | ||||||||
\(537\) | 7.72792 | 0.333484 | ||||||||
\(538\) | −40.4853 | −1.74544 | ||||||||
\(539\) | −5.65685 | −0.243658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | −36.0416 | −1.54812 | ||||||||
\(543\) | 7.51472 | 0.322487 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.75736 | −0.160948 | ||||||||
\(546\) | 0.585786 | 0.0250693 | ||||||||
\(547\) | 14.7279 | 0.629720 | 0.314860 | − | 0.949138i | \(-0.398042\pi\) | ||||
0.314860 | + | 0.949138i | \(0.398042\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.24264 | −0.351787 | ||||||||
\(550\) | −1.17157 | −0.0499560 | ||||||||
\(551\) | −32.7279 | −1.39426 | ||||||||
\(552\) | −24.9706 | −1.06282 | ||||||||
\(553\) | 2.92893 | 0.124551 | ||||||||
\(554\) | 9.07107 | 0.385393 | ||||||||
\(555\) | −8.82843 | −0.374746 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.9706 | −1.73598 | −0.867989 | − | 0.496583i | \(-0.834588\pi\) | ||||
−0.867989 | + | 0.496583i | \(0.834588\pi\) | |||||||
\(558\) | −1.41421 | −0.0598684 | ||||||||
\(559\) | −2.41421 | −0.102110 | ||||||||
\(560\) | 1.65685 | 0.0700149 | ||||||||
\(561\) | 6.34315 | 0.267808 | ||||||||
\(562\) | 3.89949 | 0.164490 | ||||||||
\(563\) | 35.6569 | 1.50276 | 0.751379 | − | 0.659871i | \(-0.229389\pi\) | ||||
0.751379 | + | 0.659871i | \(0.229389\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.34315 | 0.224788 | ||||||||
\(566\) | 12.8284 | 0.539219 | ||||||||
\(567\) | −0.414214 | −0.0173953 | ||||||||
\(568\) | −43.3137 | −1.81740 | ||||||||
\(569\) | −7.51472 | −0.315033 | −0.157517 | − | 0.987516i | \(-0.550349\pi\) | ||||
−0.157517 | + | 0.987516i | \(0.550349\pi\) | |||||||
\(570\) | 10.4853 | 0.439180 | ||||||||
\(571\) | −29.4558 | −1.23269 | −0.616344 | − | 0.787477i | \(-0.711387\pi\) | ||||
−0.616344 | + | 0.787477i | \(0.711387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.48528 | −0.270927 | ||||||||
\(574\) | −4.92893 | −0.205730 | ||||||||
\(575\) | −8.82843 | −0.368171 | ||||||||
\(576\) | 8.00000 | 0.333333 | ||||||||
\(577\) | −7.65685 | −0.318759 | −0.159380 | − | 0.987217i | \(-0.550949\pi\) | ||||
−0.159380 | + | 0.987217i | \(0.550949\pi\) | |||||||
\(578\) | −58.8701 | −2.44867 | ||||||||
\(579\) | 7.10051 | 0.295087 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.55635 | 0.106055 | ||||||||
\(582\) | −10.7279 | −0.444687 | ||||||||
\(583\) | −0.201010 | −0.00832499 | ||||||||
\(584\) | 3.02944 | 0.125359 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 0.828427 | 0.0342220 | ||||||||
\(587\) | −9.14214 | −0.377336 | −0.188668 | − | 0.982041i | \(-0.560417\pi\) | ||||
−0.188668 | + | 0.982041i | \(0.560417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.41421 | −0.305497 | ||||||||
\(590\) | −8.58579 | −0.353471 | ||||||||
\(591\) | −5.82843 | −0.239749 | ||||||||
\(592\) | 35.3137 | 1.45138 | ||||||||
\(593\) | 24.8701 | 1.02129 | 0.510645 | − | 0.859791i | \(-0.329406\pi\) | ||||
0.510645 | + | 0.859791i | \(0.329406\pi\) | |||||||
\(594\) | −1.17157 | −0.0480702 | ||||||||
\(595\) | −3.17157 | −0.130022 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.4853 | 0.510989 | ||||||||
\(598\) | 12.4853 | 0.510561 | ||||||||
\(599\) | −11.5147 | −0.470479 | −0.235239 | − | 0.971937i | \(-0.575587\pi\) | ||||
−0.235239 | + | 0.971937i | \(0.575587\pi\) | |||||||
\(600\) | 2.82843 | 0.115470 | ||||||||
\(601\) | −32.1838 | −1.31280 | −0.656402 | − | 0.754412i | \(-0.727922\pi\) | ||||
−0.656402 | + | 0.754412i | \(0.727922\pi\) | |||||||
\(602\) | −1.41421 | −0.0576390 | ||||||||
\(603\) | −8.41421 | −0.342653 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.3137 | −0.419312 | ||||||||
\(606\) | −7.17157 | −0.291325 | ||||||||
\(607\) | −45.5980 | −1.85076 | −0.925382 | − | 0.379035i | \(-0.876256\pi\) | ||||
−0.925382 | + | 0.379035i | \(0.876256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.82843 | −0.0740916 | ||||||||
\(610\) | 11.6569 | 0.471972 | ||||||||
\(611\) | 5.07107 | 0.205153 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.6274 | −1.15625 | −0.578125 | − | 0.815948i | \(-0.696215\pi\) | ||||
−0.578125 | + | 0.815948i | \(0.696215\pi\) | |||||||
\(614\) | 35.7990 | 1.44473 | ||||||||
\(615\) | −8.41421 | −0.339294 | ||||||||
\(616\) | −0.970563 | −0.0391051 | ||||||||
\(617\) | −14.8284 | −0.596970 | −0.298485 | − | 0.954414i | \(-0.596481\pi\) | ||||
−0.298485 | + | 0.954414i | \(0.596481\pi\) | |||||||
\(618\) | −18.4853 | −0.743587 | ||||||||
\(619\) | 0.798990 | 0.0321141 | 0.0160571 | − | 0.999871i | \(-0.494889\pi\) | ||||
0.0160571 | + | 0.999871i | \(0.494889\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.82843 | −0.354273 | ||||||||
\(622\) | 33.9411 | 1.36092 | ||||||||
\(623\) | 3.65685 | 0.146509 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.07107 | 0.362553 | ||||||||
\(627\) | −6.14214 | −0.245293 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −67.5980 | −2.69531 | ||||||||
\(630\) | 0.585786 | 0.0233383 | ||||||||
\(631\) | −3.85786 | −0.153579 | −0.0767896 | − | 0.997047i | \(-0.524467\pi\) | ||||
−0.0767896 | + | 0.997047i | \(0.524467\pi\) | |||||||
\(632\) | −20.0000 | −0.795557 | ||||||||
\(633\) | −17.4853 | −0.694978 | ||||||||
\(634\) | −6.48528 | −0.257563 | ||||||||
\(635\) | 0.757359 | 0.0300549 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.82843 | −0.270552 | ||||||||
\(638\) | −5.17157 | −0.204745 | ||||||||
\(639\) | −15.3137 | −0.605801 | ||||||||
\(640\) | −11.3137 | −0.447214 | ||||||||
\(641\) | −4.41421 | −0.174351 | −0.0871755 | − | 0.996193i | \(-0.527784\pi\) | ||||
−0.0871755 | + | 0.996193i | \(0.527784\pi\) | |||||||
\(642\) | −8.24264 | −0.325311 | ||||||||
\(643\) | 32.8701 | 1.29627 | 0.648134 | − | 0.761526i | \(-0.275550\pi\) | ||||
0.648134 | + | 0.761526i | \(0.275550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.41421 | −0.0950596 | ||||||||
\(646\) | 80.2843 | 3.15874 | ||||||||
\(647\) | −22.2426 | −0.874448 | −0.437224 | − | 0.899353i | \(-0.644038\pi\) | ||||
−0.437224 | + | 0.899353i | \(0.644038\pi\) | |||||||
\(648\) | 2.82843 | 0.111111 | ||||||||
\(649\) | 5.02944 | 0.197423 | ||||||||
\(650\) | −1.41421 | −0.0554700 | ||||||||
\(651\) | −0.414214 | −0.0162343 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −50.1127 | −1.96106 | −0.980531 | − | 0.196366i | \(-0.937086\pi\) | ||||
−0.980531 | + | 0.196366i | \(0.937086\pi\) | |||||||
\(654\) | 5.31371 | 0.207782 | ||||||||
\(655\) | −15.4142 | −0.602283 | ||||||||
\(656\) | 33.6569 | 1.31408 | ||||||||
\(657\) | 1.07107 | 0.0417863 | ||||||||
\(658\) | 2.97056 | 0.115805 | ||||||||
\(659\) | 33.6985 | 1.31271 | 0.656353 | − | 0.754454i | \(-0.272098\pi\) | ||||
0.656353 | + | 0.754454i | \(0.272098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.1421 | 0.627856 | 0.313928 | − | 0.949447i | \(-0.398355\pi\) | ||||
0.313928 | + | 0.949447i | \(0.398355\pi\) | |||||||
\(662\) | 16.7279 | 0.650149 | ||||||||
\(663\) | 7.65685 | 0.297368 | ||||||||
\(664\) | −17.4558 | −0.677418 | ||||||||
\(665\) | 3.07107 | 0.119091 | ||||||||
\(666\) | 12.4853 | 0.483795 | ||||||||
\(667\) | −38.9706 | −1.50895 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.4142 | −0.750597 | ||||||||
\(670\) | 11.8995 | 0.459718 | ||||||||
\(671\) | −6.82843 | −0.263609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.75736 | 0.337571 | 0.168786 | − | 0.985653i | \(-0.446015\pi\) | ||||
0.168786 | + | 0.985653i | \(0.446015\pi\) | |||||||
\(674\) | −31.7990 | −1.22485 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.6985 | −0.910807 | −0.455403 | − | 0.890285i | \(-0.650505\pi\) | ||||
−0.455403 | + | 0.890285i | \(0.650505\pi\) | |||||||
\(678\) | −7.55635 | −0.290200 | ||||||||
\(679\) | −3.14214 | −0.120584 | ||||||||
\(680\) | 21.6569 | 0.830502 | ||||||||
\(681\) | 28.6274 | 1.09701 | ||||||||
\(682\) | −1.17157 | −0.0448618 | ||||||||
\(683\) | 43.4558 | 1.66279 | 0.831396 | − | 0.555681i | \(-0.187542\pi\) | ||||
0.831396 | + | 0.555681i | \(0.187542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.10051 | −0.309279 | ||||||||
\(687\) | 25.4558 | 0.971201 | ||||||||
\(688\) | 9.65685 | 0.368164 | ||||||||
\(689\) | −0.242641 | −0.00924387 | ||||||||
\(690\) | 12.4853 | 0.475307 | ||||||||
\(691\) | 11.8579 | 0.451094 | 0.225547 | − | 0.974232i | \(-0.427583\pi\) | ||||
0.225547 | + | 0.974232i | \(0.427583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.343146 | −0.0130350 | ||||||||
\(694\) | 36.1421 | 1.37194 | ||||||||
\(695\) | 12.5858 | 0.477406 | ||||||||
\(696\) | 12.4853 | 0.473253 | ||||||||
\(697\) | −64.4264 | −2.44032 | ||||||||
\(698\) | −13.8579 | −0.524528 | ||||||||
\(699\) | −24.7990 | −0.937984 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.9706 | 0.414352 | 0.207176 | − | 0.978304i | \(-0.433573\pi\) | ||||
0.207176 | + | 0.978304i | \(0.433573\pi\) | |||||||
\(702\) | −1.41421 | −0.0533761 | ||||||||
\(703\) | 65.4558 | 2.46871 | ||||||||
\(704\) | 6.62742 | 0.249780 | ||||||||
\(705\) | 5.07107 | 0.190987 | ||||||||
\(706\) | −19.0711 | −0.717749 | ||||||||
\(707\) | −2.10051 | −0.0789976 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.2843 | 0.461345 | 0.230673 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230673 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(710\) | 21.6569 | 0.812767 | ||||||||
\(711\) | −7.07107 | −0.265186 | ||||||||
\(712\) | −24.9706 | −0.935811 | ||||||||
\(713\) | −8.82843 | −0.330627 | ||||||||
\(714\) | 4.48528 | 0.167857 | ||||||||
\(715\) | 0.828427 | 0.0309814 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.75736 | 0.0656298 | ||||||||
\(718\) | 49.8406 | 1.86004 | ||||||||
\(719\) | −2.27208 | −0.0847342 | −0.0423671 | − | 0.999102i | \(-0.513490\pi\) | ||||
−0.0423671 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(720\) | −4.00000 | −0.149071 | ||||||||
\(721\) | −5.41421 | −0.201636 | ||||||||
\(722\) | −50.8701 | −1.89319 | ||||||||
\(723\) | −16.7990 | −0.624761 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.41421 | 0.163940 | ||||||||
\(726\) | 14.5858 | 0.541329 | ||||||||
\(727\) | −24.0416 | −0.891655 | −0.445827 | − | 0.895119i | \(-0.647090\pi\) | ||||
−0.445827 | + | 0.895119i | \(0.647090\pi\) | |||||||
\(728\) | −1.17157 | −0.0434214 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.51472 | −0.0560623 | ||||||||
\(731\) | −18.4853 | −0.683703 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.2426 | −0.415256 | −0.207628 | − | 0.978208i | \(-0.566574\pi\) | ||||
−0.207628 | + | 0.978208i | \(0.566574\pi\) | |||||||
\(734\) | −50.4264 | −1.86127 | ||||||||
\(735\) | −6.82843 | −0.251870 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.97056 | −0.256764 | ||||||||
\(738\) | 11.8995 | 0.438026 | ||||||||
\(739\) | −23.4558 | −0.862837 | −0.431419 | − | 0.902152i | \(-0.641987\pi\) | ||||
−0.431419 | + | 0.902152i | \(0.641987\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.41421 | −0.272368 | ||||||||
\(742\) | −0.142136 | −0.00521796 | ||||||||
\(743\) | −25.4853 | −0.934964 | −0.467482 | − | 0.884003i | \(-0.654839\pi\) | ||||
−0.467482 | + | 0.884003i | \(0.654839\pi\) | |||||||
\(744\) | 2.82843 | 0.103695 | ||||||||
\(745\) | 14.0711 | 0.515524 | ||||||||
\(746\) | −2.14214 | −0.0784292 | ||||||||
\(747\) | −6.17157 | −0.225806 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.41421 | −0.0882134 | ||||||||
\(750\) | −1.41421 | −0.0516398 | ||||||||
\(751\) | 16.4558 | 0.600482 | 0.300241 | − | 0.953863i | \(-0.402933\pi\) | ||||
0.300241 | + | 0.953863i | \(0.402933\pi\) | |||||||
\(752\) | −20.2843 | −0.739691 | ||||||||
\(753\) | −18.4142 | −0.671051 | ||||||||
\(754\) | −6.24264 | −0.227344 | ||||||||
\(755\) | −5.82843 | −0.212118 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0122 | −1.23619 | −0.618097 | − | 0.786102i | \(-0.712096\pi\) | ||||
−0.618097 | + | 0.786102i | \(0.712096\pi\) | |||||||
\(758\) | 15.6569 | 0.568683 | ||||||||
\(759\) | −7.31371 | −0.265471 | ||||||||
\(760\) | −20.9706 | −0.760682 | ||||||||
\(761\) | 49.0711 | 1.77882 | 0.889412 | − | 0.457106i | \(-0.151114\pi\) | ||||
0.889412 | + | 0.457106i | \(0.151114\pi\) | |||||||
\(762\) | −1.07107 | −0.0388007 | ||||||||
\(763\) | 1.55635 | 0.0563436 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.65685 | 0.276834 | ||||||||
\(766\) | 33.2132 | 1.20004 | ||||||||
\(767\) | 6.07107 | 0.219214 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.2132 | −0.476480 | −0.238240 | − | 0.971206i | \(-0.576571\pi\) | ||||
−0.238240 | + | 0.971206i | \(0.576571\pi\) | |||||||
\(770\) | 0.485281 | 0.0174883 | ||||||||
\(771\) | −15.3137 | −0.551510 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.6569 | −0.671040 | −0.335520 | − | 0.942033i | \(-0.608912\pi\) | ||||
−0.335520 | + | 0.942033i | \(0.608912\pi\) | |||||||
\(774\) | 3.41421 | 0.122721 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 21.4558 | 0.770220 | ||||||||
\(777\) | 3.65685 | 0.131189 | ||||||||
\(778\) | −45.3553 | −1.62607 | ||||||||
\(779\) | 62.3848 | 2.23517 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6863 | −0.453951 | ||||||||
\(782\) | 95.5980 | 3.41858 | ||||||||
\(783\) | 4.41421 | 0.157751 | ||||||||
\(784\) | 27.3137 | 0.975490 | ||||||||
\(785\) | −10.0000 | −0.356915 | ||||||||
\(786\) | 21.7990 | 0.777544 | ||||||||
\(787\) | −45.3553 | −1.61674 | −0.808372 | − | 0.588673i | \(-0.799651\pi\) | ||||
−0.808372 | + | 0.588673i | \(0.799651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.92893 | 0.104273 | ||||||||
\(790\) | 10.0000 | 0.355784 | ||||||||
\(791\) | −2.21320 | −0.0786925 | ||||||||
\(792\) | 2.34315 | 0.0832601 | ||||||||
\(793\) | −8.24264 | −0.292705 | ||||||||
\(794\) | 5.17157 | 0.183532 | ||||||||
\(795\) | −0.242641 | −0.00860558 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 54.8701 | 1.94360 | 0.971799 | − | 0.235812i | \(-0.0757751\pi\) | ||||
0.971799 | + | 0.235812i | \(0.0757751\pi\) | |||||||
\(798\) | −4.34315 | −0.153746 | ||||||||
\(799\) | 38.8284 | 1.37365 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.82843 | −0.311937 | ||||||||
\(802\) | −16.6274 | −0.587135 | ||||||||
\(803\) | 0.887302 | 0.0313122 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.65685 | 0.128887 | ||||||||
\(806\) | −1.41421 | −0.0498135 | ||||||||
\(807\) | 28.6274 | 1.00773 | ||||||||
\(808\) | 14.3431 | 0.504590 | ||||||||
\(809\) | −34.5563 | −1.21494 | −0.607468 | − | 0.794344i | \(-0.707815\pi\) | ||||
−0.607468 | + | 0.794344i | \(0.707815\pi\) | |||||||
\(810\) | −1.41421 | −0.0496904 | ||||||||
\(811\) | −50.5269 | −1.77424 | −0.887120 | − | 0.461539i | \(-0.847297\pi\) | ||||
−0.887120 | + | 0.461539i | \(0.847297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.4853 | 0.893808 | ||||||||
\(814\) | 10.3431 | 0.362527 | ||||||||
\(815\) | 5.17157 | 0.181152 | ||||||||
\(816\) | −30.6274 | −1.07217 | ||||||||
\(817\) | 17.8995 | 0.626224 | ||||||||
\(818\) | −25.4142 | −0.888587 | ||||||||
\(819\) | −0.414214 | −0.0144738 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.1421 | 1.68017 | 0.840086 | − | 0.542453i | \(-0.182504\pi\) | ||||
0.840086 | + | 0.542453i | \(0.182504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5858 | 0.473571 | 0.236785 | − | 0.971562i | \(-0.423906\pi\) | ||||
0.236785 | + | 0.971562i | \(0.423906\pi\) | |||||||
\(824\) | 36.9706 | 1.28793 | ||||||||
\(825\) | 0.828427 | 0.0288421 | ||||||||
\(826\) | 3.55635 | 0.123741 | ||||||||
\(827\) | −46.1127 | −1.60350 | −0.801748 | − | 0.597662i | \(-0.796096\pi\) | ||||
−0.801748 | + | 0.597662i | \(0.796096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7990 | −0.687647 | −0.343824 | − | 0.939034i | \(-0.611722\pi\) | ||||
−0.343824 | + | 0.939034i | \(0.611722\pi\) | |||||||
\(830\) | 8.72792 | 0.302951 | ||||||||
\(831\) | −6.41421 | −0.222507 | ||||||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | −52.2843 | −1.81154 | ||||||||
\(834\) | −17.7990 | −0.616329 | ||||||||
\(835\) | −14.0000 | −0.484490 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 26.1421 | 0.903065 | ||||||||
\(839\) | 20.8995 | 0.721531 | 0.360765 | − | 0.932657i | \(-0.382516\pi\) | ||||
0.360765 | + | 0.932657i | \(0.382516\pi\) | |||||||
\(840\) | −1.17157 | −0.0404231 | ||||||||
\(841\) | −9.51472 | −0.328094 | ||||||||
\(842\) | 0.970563 | 0.0334478 | ||||||||
\(843\) | −2.75736 | −0.0949685 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | −7.17157 | −0.246564 | ||||||||
\(847\) | 4.27208 | 0.146790 | ||||||||
\(848\) | 0.970563 | 0.0333293 | ||||||||
\(849\) | −9.07107 | −0.311318 | ||||||||
\(850\) | −10.8284 | −0.371412 | ||||||||
\(851\) | 77.9411 | 2.67179 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.2426 | 0.864292 | 0.432146 | − | 0.901804i | \(-0.357757\pi\) | ||||
0.432146 | + | 0.901804i | \(0.357757\pi\) | |||||||
\(854\) | −4.82843 | −0.165225 | ||||||||
\(855\) | −7.41421 | −0.253561 | ||||||||
\(856\) | 16.4853 | 0.563455 | ||||||||
\(857\) | 56.7696 | 1.93921 | 0.969605 | − | 0.244674i | \(-0.0786808\pi\) | ||||
0.969605 | + | 0.244674i | \(0.0786808\pi\) | |||||||
\(858\) | −1.17157 | −0.0399968 | ||||||||
\(859\) | 12.0000 | 0.409435 | 0.204717 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.48528 | 0.118778 | ||||||||
\(862\) | 39.8995 | 1.35898 | ||||||||
\(863\) | −30.7990 | −1.04841 | −0.524205 | − | 0.851592i | \(-0.675637\pi\) | ||||
−0.524205 | + | 0.851592i | \(0.675637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.171573 | −0.00583365 | ||||||||
\(866\) | −5.27208 | −0.179153 | ||||||||
\(867\) | 41.6274 | 1.41374 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.85786 | −0.198714 | ||||||||
\(870\) | −6.24264 | −0.211645 | ||||||||
\(871\) | −8.41421 | −0.285105 | ||||||||
\(872\) | −10.6274 | −0.359890 | ||||||||
\(873\) | 7.58579 | 0.256740 | ||||||||
\(874\) | −92.5685 | −3.13118 | ||||||||
\(875\) | −0.414214 | −0.0140030 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.1716 | 0.917519 | 0.458759 | − | 0.888561i | \(-0.348294\pi\) | ||||
0.458759 | + | 0.888561i | \(0.348294\pi\) | |||||||
\(878\) | −45.4142 | −1.53266 | ||||||||
\(879\) | −0.585786 | −0.0197581 | ||||||||
\(880\) | −3.31371 | −0.111705 | ||||||||
\(881\) | 23.9289 | 0.806186 | 0.403093 | − | 0.915159i | \(-0.367935\pi\) | ||||
0.403093 | + | 0.915159i | \(0.367935\pi\) | |||||||
\(882\) | 9.65685 | 0.325163 | ||||||||
\(883\) | −56.6985 | −1.90806 | −0.954028 | − | 0.299718i | \(-0.903108\pi\) | ||||
−0.954028 | + | 0.299718i | \(0.903108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.07107 | 0.204077 | ||||||||
\(886\) | 56.0416 | 1.88276 | ||||||||
\(887\) | 10.0294 | 0.336756 | 0.168378 | − | 0.985723i | \(-0.446147\pi\) | ||||
0.168378 | + | 0.985723i | \(0.446147\pi\) | |||||||
\(888\) | −24.9706 | −0.837957 | ||||||||
\(889\) | −0.313708 | −0.0105214 | ||||||||
\(890\) | 12.4853 | 0.418508 | ||||||||
\(891\) | 0.828427 | 0.0277534 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −37.5980 | −1.25817 | ||||||||
\(894\) | −19.8995 | −0.665539 | ||||||||
\(895\) | 7.72792 | 0.258316 | ||||||||
\(896\) | 4.68629 | 0.156558 | ||||||||
\(897\) | −8.82843 | −0.294773 | ||||||||
\(898\) | 44.8284 | 1.49594 | ||||||||
\(899\) | 4.41421 | 0.147222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.85786 | −0.0618944 | ||||||||
\(902\) | 9.85786 | 0.328231 | ||||||||
\(903\) | 1.00000 | 0.0332779 | ||||||||
\(904\) | 15.1127 | 0.502641 | ||||||||
\(905\) | 7.51472 | 0.249798 | ||||||||
\(906\) | 8.24264 | 0.273843 | ||||||||
\(907\) | 25.1716 | 0.835808 | 0.417904 | − | 0.908491i | \(-0.362765\pi\) | ||||
0.417904 | + | 0.908491i | \(0.362765\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.07107 | 0.168197 | ||||||||
\(910\) | 0.585786 | 0.0194186 | ||||||||
\(911\) | 18.2132 | 0.603430 | 0.301715 | − | 0.953398i | \(-0.402441\pi\) | ||||
0.301715 | + | 0.953398i | \(0.402441\pi\) | |||||||
\(912\) | 29.6569 | 0.982037 | ||||||||
\(913\) | −5.11270 | −0.169206 | ||||||||
\(914\) | 50.9706 | 1.68596 | ||||||||
\(915\) | −8.24264 | −0.272493 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.38478 | 0.210844 | ||||||||
\(918\) | −10.8284 | −0.357391 | ||||||||
\(919\) | −21.3431 | −0.704045 | −0.352023 | − | 0.935991i | \(-0.614506\pi\) | ||||
−0.352023 | + | 0.935991i | \(0.614506\pi\) | |||||||
\(920\) | −24.9706 | −0.823255 | ||||||||
\(921\) | −25.3137 | −0.834115 | ||||||||
\(922\) | 15.0294 | 0.494968 | ||||||||
\(923\) | −15.3137 | −0.504057 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.82843 | −0.290277 | ||||||||
\(926\) | 12.9706 | 0.426239 | ||||||||
\(927\) | 13.0711 | 0.429310 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.78680 | −0.0914318 | −0.0457159 | − | 0.998954i | \(-0.514557\pi\) | ||||
−0.0457159 | + | 0.998954i | \(0.514557\pi\) | |||||||
\(930\) | −1.41421 | −0.0463739 | ||||||||
\(931\) | 50.6274 | 1.65925 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 44.0416 | 1.44109 | ||||||||
\(935\) | 6.34315 | 0.207443 | ||||||||
\(936\) | 2.82843 | 0.0924500 | ||||||||
\(937\) | 23.9411 | 0.782122 | 0.391061 | − | 0.920365i | \(-0.372108\pi\) | ||||
0.391061 | + | 0.920365i | \(0.372108\pi\) | |||||||
\(938\) | −4.92893 | −0.160935 | ||||||||
\(939\) | −6.41421 | −0.209320 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.8995 | −1.17029 | −0.585145 | − | 0.810929i | \(-0.698962\pi\) | ||||
−0.585145 | + | 0.810929i | \(0.698962\pi\) | |||||||
\(942\) | 14.1421 | 0.460776 | ||||||||
\(943\) | 74.2843 | 2.41903 | ||||||||
\(944\) | −24.2843 | −0.790386 | ||||||||
\(945\) | −0.414214 | −0.0134744 | ||||||||
\(946\) | 2.82843 | 0.0919601 | ||||||||
\(947\) | −47.6569 | −1.54864 | −0.774320 | − | 0.632794i | \(-0.781908\pi\) | ||||
−0.774320 | + | 0.632794i | \(0.781908\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07107 | 0.0347683 | ||||||||
\(950\) | 10.4853 | 0.340187 | ||||||||
\(951\) | 4.58579 | 0.148704 | ||||||||
\(952\) | −8.97056 | −0.290738 | ||||||||
\(953\) | −30.2426 | −0.979655 | −0.489828 | − | 0.871819i | \(-0.662940\pi\) | ||||
−0.489828 | + | 0.871819i | \(0.662940\pi\) | |||||||
\(954\) | 0.343146 | 0.0111098 | ||||||||
\(955\) | −6.48528 | −0.209859 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.65685 | 0.118209 | ||||||||
\(958\) | −22.0416 | −0.712133 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.00000 | 0.258199 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 12.4853 | 0.402542 | ||||||||
\(963\) | 5.82843 | 0.187818 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.10051 | 0.228573 | ||||||||
\(966\) | −5.17157 | −0.166393 | ||||||||
\(967\) | 33.1716 | 1.06673 | 0.533363 | − | 0.845887i | \(-0.320928\pi\) | ||||
0.533363 | + | 0.845887i | \(0.320928\pi\) | |||||||
\(968\) | −29.1716 | −0.937610 | ||||||||
\(969\) | −56.7696 | −1.82370 | ||||||||
\(970\) | −10.7279 | −0.344453 | ||||||||
\(971\) | −38.9706 | −1.25062 | −0.625312 | − | 0.780374i | \(-0.715028\pi\) | ||||
−0.625312 | + | 0.780374i | \(0.715028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.21320 | −0.167128 | ||||||||
\(974\) | −11.6569 | −0.373510 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | 32.9706 | 1.05536 | ||||||||
\(977\) | −37.4558 | −1.19832 | −0.599159 | − | 0.800630i | \(-0.704498\pi\) | ||||
−0.599159 | + | 0.800630i | \(0.704498\pi\) | |||||||
\(978\) | −7.31371 | −0.233867 | ||||||||
\(979\) | −7.31371 | −0.233747 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.75736 | −0.119963 | ||||||||
\(982\) | −46.5269 | −1.48473 | ||||||||
\(983\) | −14.8579 | −0.473892 | −0.236946 | − | 0.971523i | \(-0.576146\pi\) | ||||
−0.236946 | + | 0.971523i | \(0.576146\pi\) | |||||||
\(984\) | −23.7990 | −0.758684 | ||||||||
\(985\) | −5.82843 | −0.185709 | ||||||||
\(986\) | −47.7990 | −1.52223 | ||||||||
\(987\) | −2.10051 | −0.0668598 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.3137 | 0.677737 | ||||||||
\(990\) | −1.17157 | −0.0372350 | ||||||||
\(991\) | 45.4142 | 1.44263 | 0.721315 | − | 0.692607i | \(-0.243538\pi\) | ||||
0.721315 | + | 0.692607i | \(0.243538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.8284 | −0.375364 | ||||||||
\(994\) | −8.97056 | −0.284529 | ||||||||
\(995\) | 12.4853 | 0.395810 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.2426 | 0.514410 | 0.257205 | − | 0.966357i | \(-0.417199\pi\) | ||||
0.257205 | + | 0.966357i | \(0.417199\pi\) | |||||||
\(998\) | −29.0122 | −0.918365 | ||||||||
\(999\) | −8.82843 | −0.279319 |
(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 | 6045.2.a.p.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6045.2.a.p.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |