Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(1,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("483.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 1.38197 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.23607 | −0.707107 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | −1.61803 | −0.448762 | −0.224381 | − | 0.974502i | \(-0.572036\pi\) | ||||
−0.224381 | + | 0.974502i | \(0.572036\pi\) | |||||||
\(14\) | −1.61803 | −0.432438 | ||||||||
\(15\) | 1.38197 | 0.356822 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 3.47214 | 0.842117 | 0.421058 | − | 0.907034i | \(-0.361659\pi\) | ||||
0.421058 | + | 0.907034i | \(0.361659\pi\) | |||||||
\(18\) | −1.61803 | −0.381374 | ||||||||
\(19\) | −0.236068 | −0.0541577 | −0.0270789 | − | 0.999633i | \(-0.508621\pi\) | ||||
−0.0270789 | + | 0.999633i | \(0.508621\pi\) | |||||||
\(20\) | 0.854102 | 0.190983 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.61803 | −0.344966 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | −3.09017 | −0.618034 | ||||||||
\(26\) | 2.61803 | 0.513439 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.618034 | 0.116797 | ||||||||
\(29\) | 6.23607 | 1.15801 | 0.579004 | − | 0.815324i | \(-0.303441\pi\) | ||||
0.579004 | + | 0.815324i | \(0.303441\pi\) | |||||||
\(30\) | −2.23607 | −0.408248 | ||||||||
\(31\) | 4.70820 | 0.845618 | 0.422809 | − | 0.906219i | \(-0.361044\pi\) | ||||
0.422809 | + | 0.906219i | \(0.361044\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −5.61803 | −0.963485 | ||||||||
\(35\) | 1.38197 | 0.233595 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | −4.23607 | −0.696405 | −0.348203 | − | 0.937419i | \(-0.613208\pi\) | ||||
−0.348203 | + | 0.937419i | \(0.613208\pi\) | |||||||
\(38\) | 0.381966 | 0.0619631 | ||||||||
\(39\) | −1.61803 | −0.259093 | ||||||||
\(40\) | 3.09017 | 0.488599 | ||||||||
\(41\) | 5.47214 | 0.854604 | 0.427302 | − | 0.904109i | \(-0.359464\pi\) | ||||
0.427302 | + | 0.904109i | \(0.359464\pi\) | |||||||
\(42\) | −1.61803 | −0.249668 | ||||||||
\(43\) | 2.85410 | 0.435246 | 0.217623 | − | 0.976033i | \(-0.430170\pi\) | ||||
0.217623 | + | 0.976033i | \(0.430170\pi\) | |||||||
\(44\) | 0.618034 | 0.0931721 | ||||||||
\(45\) | 1.38197 | 0.206011 | ||||||||
\(46\) | −1.61803 | −0.238566 | ||||||||
\(47\) | −1.70820 | −0.249167 | −0.124584 | − | 0.992209i | \(-0.539759\pi\) | ||||
−0.124584 | + | 0.992209i | \(0.539759\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 3.47214 | 0.486196 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 11.0902 | 1.52335 | 0.761676 | − | 0.647958i | \(-0.224377\pi\) | ||||
0.761676 | + | 0.647958i | \(0.224377\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 1.38197 | 0.186344 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | −0.236068 | −0.0312680 | ||||||||
\(58\) | −10.0902 | −1.32490 | ||||||||
\(59\) | −1.38197 | −0.179917 | −0.0899583 | − | 0.995946i | \(-0.528673\pi\) | ||||
−0.0899583 | + | 0.995946i | \(0.528673\pi\) | |||||||
\(60\) | 0.854102 | 0.110264 | ||||||||
\(61\) | −1.14590 | −0.146717 | −0.0733586 | − | 0.997306i | \(-0.523372\pi\) | ||||
−0.0733586 | + | 0.997306i | \(0.523372\pi\) | |||||||
\(62\) | −7.61803 | −0.967491 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −2.23607 | −0.277350 | ||||||||
\(66\) | −1.61803 | −0.199166 | ||||||||
\(67\) | 3.09017 | 0.377524 | 0.188762 | − | 0.982023i | \(-0.439552\pi\) | ||||
0.188762 | + | 0.982023i | \(0.439552\pi\) | |||||||
\(68\) | 2.14590 | 0.260228 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −2.23607 | −0.267261 | ||||||||
\(71\) | 5.32624 | 0.632108 | 0.316054 | − | 0.948741i | \(-0.397642\pi\) | ||||
0.316054 | + | 0.948741i | \(0.397642\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 6.23607 | 0.729877 | 0.364938 | − | 0.931032i | \(-0.381090\pi\) | ||||
0.364938 | + | 0.931032i | \(0.381090\pi\) | |||||||
\(74\) | 6.85410 | 0.796773 | ||||||||
\(75\) | −3.09017 | −0.356822 | ||||||||
\(76\) | −0.145898 | −0.0167357 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 2.61803 | 0.296434 | ||||||||
\(79\) | −9.76393 | −1.09853 | −0.549264 | − | 0.835649i | \(-0.685092\pi\) | ||||
−0.549264 | + | 0.835649i | \(0.685092\pi\) | |||||||
\(80\) | −6.70820 | −0.750000 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.85410 | −0.977772 | ||||||||
\(83\) | −0.0557281 | −0.00611695 | −0.00305848 | − | 0.999995i | \(-0.500974\pi\) | ||||
−0.00305848 | + | 0.999995i | \(0.500974\pi\) | |||||||
\(84\) | 0.618034 | 0.0674330 | ||||||||
\(85\) | 4.79837 | 0.520457 | ||||||||
\(86\) | −4.61803 | −0.497975 | ||||||||
\(87\) | 6.23607 | 0.668577 | ||||||||
\(88\) | 2.23607 | 0.238366 | ||||||||
\(89\) | −6.56231 | −0.695603 | −0.347802 | − | 0.937568i | \(-0.613072\pi\) | ||||
−0.347802 | + | 0.937568i | \(0.613072\pi\) | |||||||
\(90\) | −2.23607 | −0.235702 | ||||||||
\(91\) | −1.61803 | −0.169616 | ||||||||
\(92\) | 0.618034 | 0.0644345 | ||||||||
\(93\) | 4.70820 | 0.488218 | ||||||||
\(94\) | 2.76393 | 0.285078 | ||||||||
\(95\) | −0.326238 | −0.0334713 | ||||||||
\(96\) | 3.38197 | 0.345170 | ||||||||
\(97\) | −6.70820 | −0.681115 | −0.340557 | − | 0.940224i | \(-0.610616\pi\) | ||||
−0.340557 | + | 0.940224i | \(0.610616\pi\) | |||||||
\(98\) | −1.61803 | −0.163446 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.90983 | −0.190983 | ||||||||
\(101\) | −9.09017 | −0.904506 | −0.452253 | − | 0.891890i | \(-0.649380\pi\) | ||||
−0.452253 | + | 0.891890i | \(0.649380\pi\) | |||||||
\(102\) | −5.61803 | −0.556268 | ||||||||
\(103\) | −9.52786 | −0.938808 | −0.469404 | − | 0.882983i | \(-0.655531\pi\) | ||||
−0.469404 | + | 0.882983i | \(0.655531\pi\) | |||||||
\(104\) | −3.61803 | −0.354777 | ||||||||
\(105\) | 1.38197 | 0.134866 | ||||||||
\(106\) | −17.9443 | −1.74290 | ||||||||
\(107\) | −14.0902 | −1.36215 | −0.681074 | − | 0.732215i | \(-0.738487\pi\) | ||||
−0.681074 | + | 0.732215i | \(0.738487\pi\) | |||||||
\(108\) | 0.618034 | 0.0594703 | ||||||||
\(109\) | 4.61803 | 0.442327 | 0.221164 | − | 0.975237i | \(-0.429014\pi\) | ||||
0.221164 | + | 0.975237i | \(0.429014\pi\) | |||||||
\(110\) | −2.23607 | −0.213201 | ||||||||
\(111\) | −4.23607 | −0.402070 | ||||||||
\(112\) | −4.85410 | −0.458670 | ||||||||
\(113\) | 2.90983 | 0.273734 | 0.136867 | − | 0.990589i | \(-0.456297\pi\) | ||||
0.136867 | + | 0.990589i | \(0.456297\pi\) | |||||||
\(114\) | 0.381966 | 0.0357744 | ||||||||
\(115\) | 1.38197 | 0.128869 | ||||||||
\(116\) | 3.85410 | 0.357844 | ||||||||
\(117\) | −1.61803 | −0.149587 | ||||||||
\(118\) | 2.23607 | 0.205847 | ||||||||
\(119\) | 3.47214 | 0.318290 | ||||||||
\(120\) | 3.09017 | 0.282093 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 1.85410 | 0.167863 | ||||||||
\(123\) | 5.47214 | 0.493406 | ||||||||
\(124\) | 2.90983 | 0.261310 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | −1.61803 | −0.144146 | ||||||||
\(127\) | −1.14590 | −0.101682 | −0.0508410 | − | 0.998707i | \(-0.516190\pi\) | ||||
−0.0508410 | + | 0.998707i | \(0.516190\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | 2.85410 | 0.251290 | ||||||||
\(130\) | 3.61803 | 0.317323 | ||||||||
\(131\) | −16.7082 | −1.45980 | −0.729901 | − | 0.683553i | \(-0.760434\pi\) | ||||
−0.729901 | + | 0.683553i | \(0.760434\pi\) | |||||||
\(132\) | 0.618034 | 0.0537930 | ||||||||
\(133\) | −0.236068 | −0.0204697 | ||||||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | 1.38197 | 0.118941 | ||||||||
\(136\) | 7.76393 | 0.665752 | ||||||||
\(137\) | −7.18034 | −0.613458 | −0.306729 | − | 0.951797i | \(-0.599235\pi\) | ||||
−0.306729 | + | 0.951797i | \(0.599235\pi\) | |||||||
\(138\) | −1.61803 | −0.137736 | ||||||||
\(139\) | −8.03444 | −0.681472 | −0.340736 | − | 0.940159i | \(-0.610676\pi\) | ||||
−0.340736 | + | 0.940159i | \(0.610676\pi\) | |||||||
\(140\) | 0.854102 | 0.0721848 | ||||||||
\(141\) | −1.70820 | −0.143857 | ||||||||
\(142\) | −8.61803 | −0.723209 | ||||||||
\(143\) | −1.61803 | −0.135307 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 8.61803 | 0.715689 | ||||||||
\(146\) | −10.0902 | −0.835068 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −2.61803 | −0.215201 | ||||||||
\(149\) | −9.70820 | −0.795327 | −0.397664 | − | 0.917531i | \(-0.630179\pi\) | ||||
−0.397664 | + | 0.917531i | \(0.630179\pi\) | |||||||
\(150\) | 5.00000 | 0.408248 | ||||||||
\(151\) | −22.6525 | −1.84343 | −0.921716 | − | 0.387865i | \(-0.873213\pi\) | ||||
−0.921716 | + | 0.387865i | \(0.873213\pi\) | |||||||
\(152\) | −0.527864 | −0.0428154 | ||||||||
\(153\) | 3.47214 | 0.280706 | ||||||||
\(154\) | −1.61803 | −0.130385 | ||||||||
\(155\) | 6.50658 | 0.522621 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 13.2361 | 1.05635 | 0.528177 | − | 0.849135i | \(-0.322876\pi\) | ||||
0.528177 | + | 0.849135i | \(0.322876\pi\) | |||||||
\(158\) | 15.7984 | 1.25685 | ||||||||
\(159\) | 11.0902 | 0.879508 | ||||||||
\(160\) | 4.67376 | 0.369493 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −1.61803 | −0.127125 | ||||||||
\(163\) | 13.2705 | 1.03943 | 0.519713 | − | 0.854341i | \(-0.326039\pi\) | ||||
0.519713 | + | 0.854341i | \(0.326039\pi\) | |||||||
\(164\) | 3.38197 | 0.264087 | ||||||||
\(165\) | 1.38197 | 0.107586 | ||||||||
\(166\) | 0.0901699 | 0.00699854 | ||||||||
\(167\) | −2.70820 | −0.209567 | −0.104784 | − | 0.994495i | \(-0.533415\pi\) | ||||
−0.104784 | + | 0.994495i | \(0.533415\pi\) | |||||||
\(168\) | 2.23607 | 0.172516 | ||||||||
\(169\) | −10.3820 | −0.798613 | ||||||||
\(170\) | −7.76393 | −0.595466 | ||||||||
\(171\) | −0.236068 | −0.0180526 | ||||||||
\(172\) | 1.76393 | 0.134499 | ||||||||
\(173\) | 20.4164 | 1.55223 | 0.776115 | − | 0.630591i | \(-0.217187\pi\) | ||||
0.776115 | + | 0.630591i | \(0.217187\pi\) | |||||||
\(174\) | −10.0902 | −0.764934 | ||||||||
\(175\) | −3.09017 | −0.233595 | ||||||||
\(176\) | −4.85410 | −0.365892 | ||||||||
\(177\) | −1.38197 | −0.103875 | ||||||||
\(178\) | 10.6180 | 0.795855 | ||||||||
\(179\) | 10.7984 | 0.807108 | 0.403554 | − | 0.914956i | \(-0.367775\pi\) | ||||
0.403554 | + | 0.914956i | \(0.367775\pi\) | |||||||
\(180\) | 0.854102 | 0.0636610 | ||||||||
\(181\) | 19.1803 | 1.42566 | 0.712832 | − | 0.701335i | \(-0.247412\pi\) | ||||
0.712832 | + | 0.701335i | \(0.247412\pi\) | |||||||
\(182\) | 2.61803 | 0.194062 | ||||||||
\(183\) | −1.14590 | −0.0847072 | ||||||||
\(184\) | 2.23607 | 0.164845 | ||||||||
\(185\) | −5.85410 | −0.430402 | ||||||||
\(186\) | −7.61803 | −0.558581 | ||||||||
\(187\) | 3.47214 | 0.253908 | ||||||||
\(188\) | −1.05573 | −0.0769969 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0.527864 | 0.0382953 | ||||||||
\(191\) | −8.18034 | −0.591909 | −0.295954 | − | 0.955202i | \(-0.595638\pi\) | ||||
−0.295954 | + | 0.955202i | \(0.595638\pi\) | |||||||
\(192\) | 4.23607 | 0.305712 | ||||||||
\(193\) | 5.23607 | 0.376900 | 0.188450 | − | 0.982083i | \(-0.439654\pi\) | ||||
0.188450 | + | 0.982083i | \(0.439654\pi\) | |||||||
\(194\) | 10.8541 | 0.779279 | ||||||||
\(195\) | −2.23607 | −0.160128 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | −8.56231 | −0.610039 | −0.305020 | − | 0.952346i | \(-0.598663\pi\) | ||||
−0.305020 | + | 0.952346i | \(0.598663\pi\) | |||||||
\(198\) | −1.61803 | −0.114989 | ||||||||
\(199\) | 21.5623 | 1.52851 | 0.764256 | − | 0.644913i | \(-0.223107\pi\) | ||||
0.764256 | + | 0.644913i | \(0.223107\pi\) | |||||||
\(200\) | −6.90983 | −0.488599 | ||||||||
\(201\) | 3.09017 | 0.217964 | ||||||||
\(202\) | 14.7082 | 1.03487 | ||||||||
\(203\) | 6.23607 | 0.437686 | ||||||||
\(204\) | 2.14590 | 0.150243 | ||||||||
\(205\) | 7.56231 | 0.528174 | ||||||||
\(206\) | 15.4164 | 1.07411 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 7.85410 | 0.544584 | ||||||||
\(209\) | −0.236068 | −0.0163292 | ||||||||
\(210\) | −2.23607 | −0.154303 | ||||||||
\(211\) | −26.8885 | −1.85108 | −0.925542 | − | 0.378645i | \(-0.876390\pi\) | ||||
−0.925542 | + | 0.378645i | \(0.876390\pi\) | |||||||
\(212\) | 6.85410 | 0.470742 | ||||||||
\(213\) | 5.32624 | 0.364948 | ||||||||
\(214\) | 22.7984 | 1.55846 | ||||||||
\(215\) | 3.94427 | 0.268997 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | 4.70820 | 0.319614 | ||||||||
\(218\) | −7.47214 | −0.506077 | ||||||||
\(219\) | 6.23607 | 0.421394 | ||||||||
\(220\) | 0.854102 | 0.0575835 | ||||||||
\(221\) | −5.61803 | −0.377910 | ||||||||
\(222\) | 6.85410 | 0.460017 | ||||||||
\(223\) | −0.618034 | −0.0413866 | −0.0206933 | − | 0.999786i | \(-0.506587\pi\) | ||||
−0.0206933 | + | 0.999786i | \(0.506587\pi\) | |||||||
\(224\) | 3.38197 | 0.225967 | ||||||||
\(225\) | −3.09017 | −0.206011 | ||||||||
\(226\) | −4.70820 | −0.313185 | ||||||||
\(227\) | −22.9787 | −1.52515 | −0.762575 | − | 0.646899i | \(-0.776065\pi\) | ||||
−0.762575 | + | 0.646899i | \(0.776065\pi\) | |||||||
\(228\) | −0.145898 | −0.00966233 | ||||||||
\(229\) | 3.20163 | 0.211569 | 0.105785 | − | 0.994389i | \(-0.466265\pi\) | ||||
0.105785 | + | 0.994389i | \(0.466265\pi\) | |||||||
\(230\) | −2.23607 | −0.147442 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 13.9443 | 0.915486 | ||||||||
\(233\) | 24.3262 | 1.59366 | 0.796832 | − | 0.604200i | \(-0.206507\pi\) | ||||
0.796832 | + | 0.604200i | \(0.206507\pi\) | |||||||
\(234\) | 2.61803 | 0.171146 | ||||||||
\(235\) | −2.36068 | −0.153994 | ||||||||
\(236\) | −0.854102 | −0.0555973 | ||||||||
\(237\) | −9.76393 | −0.634236 | ||||||||
\(238\) | −5.61803 | −0.364163 | ||||||||
\(239\) | −8.79837 | −0.569119 | −0.284560 | − | 0.958658i | \(-0.591847\pi\) | ||||
−0.284560 | + | 0.958658i | \(0.591847\pi\) | |||||||
\(240\) | −6.70820 | −0.433013 | ||||||||
\(241\) | −16.7082 | −1.07627 | −0.538135 | − | 0.842859i | \(-0.680871\pi\) | ||||
−0.538135 | + | 0.842859i | \(0.680871\pi\) | |||||||
\(242\) | 16.1803 | 1.04011 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.708204 | −0.0453381 | ||||||||
\(245\) | 1.38197 | 0.0882906 | ||||||||
\(246\) | −8.85410 | −0.564517 | ||||||||
\(247\) | 0.381966 | 0.0243039 | ||||||||
\(248\) | 10.5279 | 0.668520 | ||||||||
\(249\) | −0.0557281 | −0.00353162 | ||||||||
\(250\) | 18.0902 | 1.14412 | ||||||||
\(251\) | 4.29180 | 0.270896 | 0.135448 | − | 0.990784i | \(-0.456753\pi\) | ||||
0.135448 | + | 0.990784i | \(0.456753\pi\) | |||||||
\(252\) | 0.618034 | 0.0389325 | ||||||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | 1.85410 | 0.116337 | ||||||||
\(255\) | 4.79837 | 0.300486 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 10.2918 | 0.641985 | 0.320992 | − | 0.947082i | \(-0.395984\pi\) | ||||
0.320992 | + | 0.947082i | \(0.395984\pi\) | |||||||
\(258\) | −4.61803 | −0.287506 | ||||||||
\(259\) | −4.23607 | −0.263216 | ||||||||
\(260\) | −1.38197 | −0.0857059 | ||||||||
\(261\) | 6.23607 | 0.386003 | ||||||||
\(262\) | 27.0344 | 1.67019 | ||||||||
\(263\) | −9.65248 | −0.595197 | −0.297599 | − | 0.954691i | \(-0.596186\pi\) | ||||
−0.297599 | + | 0.954691i | \(0.596186\pi\) | |||||||
\(264\) | 2.23607 | 0.137620 | ||||||||
\(265\) | 15.3262 | 0.941483 | ||||||||
\(266\) | 0.381966 | 0.0234198 | ||||||||
\(267\) | −6.56231 | −0.401607 | ||||||||
\(268\) | 1.90983 | 0.116661 | ||||||||
\(269\) | −26.7426 | −1.63053 | −0.815264 | − | 0.579090i | \(-0.803408\pi\) | ||||
−0.815264 | + | 0.579090i | \(0.803408\pi\) | |||||||
\(270\) | −2.23607 | −0.136083 | ||||||||
\(271\) | −6.52786 | −0.396540 | −0.198270 | − | 0.980147i | \(-0.563532\pi\) | ||||
−0.198270 | + | 0.980147i | \(0.563532\pi\) | |||||||
\(272\) | −16.8541 | −1.02193 | ||||||||
\(273\) | −1.61803 | −0.0979279 | ||||||||
\(274\) | 11.6180 | 0.701871 | ||||||||
\(275\) | −3.09017 | −0.186344 | ||||||||
\(276\) | 0.618034 | 0.0372013 | ||||||||
\(277\) | −8.67376 | −0.521156 | −0.260578 | − | 0.965453i | \(-0.583913\pi\) | ||||
−0.260578 | + | 0.965453i | \(0.583913\pi\) | |||||||
\(278\) | 13.0000 | 0.779688 | ||||||||
\(279\) | 4.70820 | 0.281873 | ||||||||
\(280\) | 3.09017 | 0.184673 | ||||||||
\(281\) | 16.6525 | 0.993403 | 0.496702 | − | 0.867921i | \(-0.334544\pi\) | ||||
0.496702 | + | 0.867921i | \(0.334544\pi\) | |||||||
\(282\) | 2.76393 | 0.164590 | ||||||||
\(283\) | 9.67376 | 0.575045 | 0.287523 | − | 0.957774i | \(-0.407168\pi\) | ||||
0.287523 | + | 0.957774i | \(0.407168\pi\) | |||||||
\(284\) | 3.29180 | 0.195332 | ||||||||
\(285\) | −0.326238 | −0.0193247 | ||||||||
\(286\) | 2.61803 | 0.154808 | ||||||||
\(287\) | 5.47214 | 0.323010 | ||||||||
\(288\) | 3.38197 | 0.199284 | ||||||||
\(289\) | −4.94427 | −0.290840 | ||||||||
\(290\) | −13.9443 | −0.818836 | ||||||||
\(291\) | −6.70820 | −0.393242 | ||||||||
\(292\) | 3.85410 | 0.225544 | ||||||||
\(293\) | 30.8328 | 1.80127 | 0.900636 | − | 0.434574i | \(-0.143101\pi\) | ||||
0.900636 | + | 0.434574i | \(0.143101\pi\) | |||||||
\(294\) | −1.61803 | −0.0943657 | ||||||||
\(295\) | −1.90983 | −0.111195 | ||||||||
\(296\) | −9.47214 | −0.550557 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 15.7082 | 0.909952 | ||||||||
\(299\) | −1.61803 | −0.0935733 | ||||||||
\(300\) | −1.90983 | −0.110264 | ||||||||
\(301\) | 2.85410 | 0.164508 | ||||||||
\(302\) | 36.6525 | 2.10911 | ||||||||
\(303\) | −9.09017 | −0.522217 | ||||||||
\(304\) | 1.14590 | 0.0657218 | ||||||||
\(305\) | −1.58359 | −0.0906762 | ||||||||
\(306\) | −5.61803 | −0.321162 | ||||||||
\(307\) | 6.12461 | 0.349550 | 0.174775 | − | 0.984608i | \(-0.444080\pi\) | ||||
0.174775 | + | 0.984608i | \(0.444080\pi\) | |||||||
\(308\) | 0.618034 | 0.0352158 | ||||||||
\(309\) | −9.52786 | −0.542021 | ||||||||
\(310\) | −10.5279 | −0.597942 | ||||||||
\(311\) | 27.5066 | 1.55975 | 0.779877 | − | 0.625932i | \(-0.215281\pi\) | ||||
0.779877 | + | 0.625932i | \(0.215281\pi\) | |||||||
\(312\) | −3.61803 | −0.204831 | ||||||||
\(313\) | −1.88854 | −0.106747 | −0.0533734 | − | 0.998575i | \(-0.516997\pi\) | ||||
−0.0533734 | + | 0.998575i | \(0.516997\pi\) | |||||||
\(314\) | −21.4164 | −1.20860 | ||||||||
\(315\) | 1.38197 | 0.0778650 | ||||||||
\(316\) | −6.03444 | −0.339464 | ||||||||
\(317\) | 11.0902 | 0.622886 | 0.311443 | − | 0.950265i | \(-0.399188\pi\) | ||||
0.311443 | + | 0.950265i | \(0.399188\pi\) | |||||||
\(318\) | −17.9443 | −1.00626 | ||||||||
\(319\) | 6.23607 | 0.349153 | ||||||||
\(320\) | 5.85410 | 0.327254 | ||||||||
\(321\) | −14.0902 | −0.786437 | ||||||||
\(322\) | −1.61803 | −0.0901695 | ||||||||
\(323\) | −0.819660 | −0.0456071 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 5.00000 | 0.277350 | ||||||||
\(326\) | −21.4721 | −1.18923 | ||||||||
\(327\) | 4.61803 | 0.255378 | ||||||||
\(328\) | 12.2361 | 0.675624 | ||||||||
\(329\) | −1.70820 | −0.0941763 | ||||||||
\(330\) | −2.23607 | −0.123091 | ||||||||
\(331\) | −27.8885 | −1.53289 | −0.766447 | − | 0.642308i | \(-0.777977\pi\) | ||||
−0.766447 | + | 0.642308i | \(0.777977\pi\) | |||||||
\(332\) | −0.0344419 | −0.00189024 | ||||||||
\(333\) | −4.23607 | −0.232135 | ||||||||
\(334\) | 4.38197 | 0.239771 | ||||||||
\(335\) | 4.27051 | 0.233323 | ||||||||
\(336\) | −4.85410 | −0.264813 | ||||||||
\(337\) | −19.0344 | −1.03687 | −0.518436 | − | 0.855116i | \(-0.673486\pi\) | ||||
−0.518436 | + | 0.855116i | \(0.673486\pi\) | |||||||
\(338\) | 16.7984 | 0.913711 | ||||||||
\(339\) | 2.90983 | 0.158040 | ||||||||
\(340\) | 2.96556 | 0.160830 | ||||||||
\(341\) | 4.70820 | 0.254964 | ||||||||
\(342\) | 0.381966 | 0.0206544 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.38197 | 0.344093 | ||||||||
\(345\) | 1.38197 | 0.0744025 | ||||||||
\(346\) | −33.0344 | −1.77594 | ||||||||
\(347\) | −20.7082 | −1.11167 | −0.555837 | − | 0.831291i | \(-0.687602\pi\) | ||||
−0.555837 | + | 0.831291i | \(0.687602\pi\) | |||||||
\(348\) | 3.85410 | 0.206602 | ||||||||
\(349\) | 4.79837 | 0.256851 | 0.128426 | − | 0.991719i | \(-0.459008\pi\) | ||||
0.128426 | + | 0.991719i | \(0.459008\pi\) | |||||||
\(350\) | 5.00000 | 0.267261 | ||||||||
\(351\) | −1.61803 | −0.0863643 | ||||||||
\(352\) | 3.38197 | 0.180259 | ||||||||
\(353\) | −20.4164 | −1.08666 | −0.543328 | − | 0.839521i | \(-0.682836\pi\) | ||||
−0.543328 | + | 0.839521i | \(0.682836\pi\) | |||||||
\(354\) | 2.23607 | 0.118846 | ||||||||
\(355\) | 7.36068 | 0.390664 | ||||||||
\(356\) | −4.05573 | −0.214953 | ||||||||
\(357\) | 3.47214 | 0.183765 | ||||||||
\(358\) | −17.4721 | −0.923431 | ||||||||
\(359\) | −11.5623 | −0.610235 | −0.305118 | − | 0.952315i | \(-0.598696\pi\) | ||||
−0.305118 | + | 0.952315i | \(0.598696\pi\) | |||||||
\(360\) | 3.09017 | 0.162866 | ||||||||
\(361\) | −18.9443 | −0.997067 | ||||||||
\(362\) | −31.0344 | −1.63113 | ||||||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | −1.00000 | −0.0524142 | ||||||||
\(365\) | 8.61803 | 0.451089 | ||||||||
\(366\) | 1.85410 | 0.0969155 | ||||||||
\(367\) | −20.2705 | −1.05811 | −0.529056 | − | 0.848587i | \(-0.677454\pi\) | ||||
−0.529056 | + | 0.848587i | \(0.677454\pi\) | |||||||
\(368\) | −4.85410 | −0.253038 | ||||||||
\(369\) | 5.47214 | 0.284868 | ||||||||
\(370\) | 9.47214 | 0.492433 | ||||||||
\(371\) | 11.0902 | 0.575773 | ||||||||
\(372\) | 2.90983 | 0.150868 | ||||||||
\(373\) | −6.12461 | −0.317120 | −0.158560 | − | 0.987349i | \(-0.550685\pi\) | ||||
−0.158560 | + | 0.987349i | \(0.550685\pi\) | |||||||
\(374\) | −5.61803 | −0.290502 | ||||||||
\(375\) | −11.1803 | −0.577350 | ||||||||
\(376\) | −3.81966 | −0.196984 | ||||||||
\(377\) | −10.0902 | −0.519670 | ||||||||
\(378\) | −1.61803 | −0.0832227 | ||||||||
\(379\) | −34.4721 | −1.77071 | −0.885357 | − | 0.464911i | \(-0.846086\pi\) | ||||
−0.885357 | + | 0.464911i | \(0.846086\pi\) | |||||||
\(380\) | −0.201626 | −0.0103432 | ||||||||
\(381\) | −1.14590 | −0.0587061 | ||||||||
\(382\) | 13.2361 | 0.677216 | ||||||||
\(383\) | 13.9443 | 0.712519 | 0.356260 | − | 0.934387i | \(-0.384052\pi\) | ||||
0.356260 | + | 0.934387i | \(0.384052\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | 1.38197 | 0.0704315 | ||||||||
\(386\) | −8.47214 | −0.431220 | ||||||||
\(387\) | 2.85410 | 0.145082 | ||||||||
\(388\) | −4.14590 | −0.210476 | ||||||||
\(389\) | −2.05573 | −0.104230 | −0.0521148 | − | 0.998641i | \(-0.516596\pi\) | ||||
−0.0521148 | + | 0.998641i | \(0.516596\pi\) | |||||||
\(390\) | 3.61803 | 0.183206 | ||||||||
\(391\) | 3.47214 | 0.175593 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | −16.7082 | −0.842817 | ||||||||
\(394\) | 13.8541 | 0.697960 | ||||||||
\(395\) | −13.4934 | −0.678928 | ||||||||
\(396\) | 0.618034 | 0.0310574 | ||||||||
\(397\) | −0.180340 | −0.00905100 | −0.00452550 | − | 0.999990i | \(-0.501441\pi\) | ||||
−0.00452550 | + | 0.999990i | \(0.501441\pi\) | |||||||
\(398\) | −34.8885 | −1.74880 | ||||||||
\(399\) | −0.236068 | −0.0118182 | ||||||||
\(400\) | 15.0000 | 0.750000 | ||||||||
\(401\) | −5.00000 | −0.249688 | −0.124844 | − | 0.992176i | \(-0.539843\pi\) | ||||
−0.124844 | + | 0.992176i | \(0.539843\pi\) | |||||||
\(402\) | −5.00000 | −0.249377 | ||||||||
\(403\) | −7.61803 | −0.379481 | ||||||||
\(404\) | −5.61803 | −0.279508 | ||||||||
\(405\) | 1.38197 | 0.0686704 | ||||||||
\(406\) | −10.0902 | −0.500767 | ||||||||
\(407\) | −4.23607 | −0.209974 | ||||||||
\(408\) | 7.76393 | 0.384372 | ||||||||
\(409\) | 10.8885 | 0.538404 | 0.269202 | − | 0.963084i | \(-0.413240\pi\) | ||||
0.269202 | + | 0.963084i | \(0.413240\pi\) | |||||||
\(410\) | −12.2361 | −0.604296 | ||||||||
\(411\) | −7.18034 | −0.354180 | ||||||||
\(412\) | −5.88854 | −0.290108 | ||||||||
\(413\) | −1.38197 | −0.0680021 | ||||||||
\(414\) | −1.61803 | −0.0795220 | ||||||||
\(415\) | −0.0770143 | −0.00378048 | ||||||||
\(416\) | −5.47214 | −0.268294 | ||||||||
\(417\) | −8.03444 | −0.393448 | ||||||||
\(418\) | 0.381966 | 0.0186826 | ||||||||
\(419\) | 25.0902 | 1.22574 | 0.612868 | − | 0.790186i | \(-0.290016\pi\) | ||||
0.612868 | + | 0.790186i | \(0.290016\pi\) | |||||||
\(420\) | 0.854102 | 0.0416759 | ||||||||
\(421\) | −9.43769 | −0.459965 | −0.229983 | − | 0.973195i | \(-0.573867\pi\) | ||||
−0.229983 | + | 0.973195i | \(0.573867\pi\) | |||||||
\(422\) | 43.5066 | 2.11787 | ||||||||
\(423\) | −1.70820 | −0.0830557 | ||||||||
\(424\) | 24.7984 | 1.20432 | ||||||||
\(425\) | −10.7295 | −0.520457 | ||||||||
\(426\) | −8.61803 | −0.417545 | ||||||||
\(427\) | −1.14590 | −0.0554539 | ||||||||
\(428\) | −8.70820 | −0.420927 | ||||||||
\(429\) | −1.61803 | −0.0781194 | ||||||||
\(430\) | −6.38197 | −0.307766 | ||||||||
\(431\) | −22.2705 | −1.07273 | −0.536366 | − | 0.843985i | \(-0.680203\pi\) | ||||
−0.536366 | + | 0.843985i | \(0.680203\pi\) | |||||||
\(432\) | −4.85410 | −0.233543 | ||||||||
\(433\) | 25.2361 | 1.21277 | 0.606384 | − | 0.795172i | \(-0.292619\pi\) | ||||
0.606384 | + | 0.795172i | \(0.292619\pi\) | |||||||
\(434\) | −7.61803 | −0.365677 | ||||||||
\(435\) | 8.61803 | 0.413203 | ||||||||
\(436\) | 2.85410 | 0.136687 | ||||||||
\(437\) | −0.236068 | −0.0112927 | ||||||||
\(438\) | −10.0902 | −0.482127 | ||||||||
\(439\) | −13.1803 | −0.629063 | −0.314532 | − | 0.949247i | \(-0.601847\pi\) | ||||
−0.314532 | + | 0.949247i | \(0.601847\pi\) | |||||||
\(440\) | 3.09017 | 0.147318 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 9.09017 | 0.432375 | ||||||||
\(443\) | 26.8328 | 1.27487 | 0.637433 | − | 0.770506i | \(-0.279996\pi\) | ||||
0.637433 | + | 0.770506i | \(0.279996\pi\) | |||||||
\(444\) | −2.61803 | −0.124246 | ||||||||
\(445\) | −9.06888 | −0.429906 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | −9.70820 | −0.459182 | ||||||||
\(448\) | 4.23607 | 0.200135 | ||||||||
\(449\) | 6.72949 | 0.317584 | 0.158792 | − | 0.987312i | \(-0.449240\pi\) | ||||
0.158792 | + | 0.987312i | \(0.449240\pi\) | |||||||
\(450\) | 5.00000 | 0.235702 | ||||||||
\(451\) | 5.47214 | 0.257673 | ||||||||
\(452\) | 1.79837 | 0.0845884 | ||||||||
\(453\) | −22.6525 | −1.06431 | ||||||||
\(454\) | 37.1803 | 1.74496 | ||||||||
\(455\) | −2.23607 | −0.104828 | ||||||||
\(456\) | −0.527864 | −0.0247195 | ||||||||
\(457\) | 39.7426 | 1.85908 | 0.929541 | − | 0.368718i | \(-0.120203\pi\) | ||||
0.929541 | + | 0.368718i | \(0.120203\pi\) | |||||||
\(458\) | −5.18034 | −0.242061 | ||||||||
\(459\) | 3.47214 | 0.162065 | ||||||||
\(460\) | 0.854102 | 0.0398227 | ||||||||
\(461\) | 10.3262 | 0.480941 | 0.240470 | − | 0.970656i | \(-0.422698\pi\) | ||||
0.240470 | + | 0.970656i | \(0.422698\pi\) | |||||||
\(462\) | −1.61803 | −0.0752778 | ||||||||
\(463\) | −26.1246 | −1.21411 | −0.607057 | − | 0.794658i | \(-0.707650\pi\) | ||||
−0.607057 | + | 0.794658i | \(0.707650\pi\) | |||||||
\(464\) | −30.2705 | −1.40527 | ||||||||
\(465\) | 6.50658 | 0.301735 | ||||||||
\(466\) | −39.3607 | −1.82335 | ||||||||
\(467\) | 2.88854 | 0.133666 | 0.0668329 | − | 0.997764i | \(-0.478711\pi\) | ||||
0.0668329 | + | 0.997764i | \(0.478711\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 3.09017 | 0.142691 | ||||||||
\(470\) | 3.81966 | 0.176188 | ||||||||
\(471\) | 13.2361 | 0.609886 | ||||||||
\(472\) | −3.09017 | −0.142237 | ||||||||
\(473\) | 2.85410 | 0.131232 | ||||||||
\(474\) | 15.7984 | 0.725643 | ||||||||
\(475\) | 0.729490 | 0.0334713 | ||||||||
\(476\) | 2.14590 | 0.0983571 | ||||||||
\(477\) | 11.0902 | 0.507784 | ||||||||
\(478\) | 14.2361 | 0.651143 | ||||||||
\(479\) | −9.29180 | −0.424553 | −0.212276 | − | 0.977210i | \(-0.568088\pi\) | ||||
−0.212276 | + | 0.977210i | \(0.568088\pi\) | |||||||
\(480\) | 4.67376 | 0.213327 | ||||||||
\(481\) | 6.85410 | 0.312520 | ||||||||
\(482\) | 27.0344 | 1.23139 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | −6.18034 | −0.280925 | ||||||||
\(485\) | −9.27051 | −0.420952 | ||||||||
\(486\) | −1.61803 | −0.0733955 | ||||||||
\(487\) | 10.1246 | 0.458790 | 0.229395 | − | 0.973333i | \(-0.426325\pi\) | ||||
0.229395 | + | 0.973333i | \(0.426325\pi\) | |||||||
\(488\) | −2.56231 | −0.115990 | ||||||||
\(489\) | 13.2705 | 0.600113 | ||||||||
\(490\) | −2.23607 | −0.101015 | ||||||||
\(491\) | −22.5623 | −1.01822 | −0.509111 | − | 0.860701i | \(-0.670026\pi\) | ||||
−0.509111 | + | 0.860701i | \(0.670026\pi\) | |||||||
\(492\) | 3.38197 | 0.152471 | ||||||||
\(493\) | 21.6525 | 0.975178 | ||||||||
\(494\) | −0.618034 | −0.0278067 | ||||||||
\(495\) | 1.38197 | 0.0621148 | ||||||||
\(496\) | −22.8541 | −1.02618 | ||||||||
\(497\) | 5.32624 | 0.238914 | ||||||||
\(498\) | 0.0901699 | 0.00404061 | ||||||||
\(499\) | −3.56231 | −0.159471 | −0.0797354 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797354 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(500\) | −6.90983 | −0.309017 | ||||||||
\(501\) | −2.70820 | −0.120994 | ||||||||
\(502\) | −6.94427 | −0.309938 | ||||||||
\(503\) | 34.6869 | 1.54661 | 0.773307 | − | 0.634032i | \(-0.218601\pi\) | ||||
0.773307 | + | 0.634032i | \(0.218601\pi\) | |||||||
\(504\) | 2.23607 | 0.0996024 | ||||||||
\(505\) | −12.5623 | −0.559015 | ||||||||
\(506\) | −1.61803 | −0.0719304 | ||||||||
\(507\) | −10.3820 | −0.461079 | ||||||||
\(508\) | −0.708204 | −0.0314215 | ||||||||
\(509\) | 35.2361 | 1.56181 | 0.780906 | − | 0.624649i | \(-0.214758\pi\) | ||||
0.780906 | + | 0.624649i | \(0.214758\pi\) | |||||||
\(510\) | −7.76393 | −0.343793 | ||||||||
\(511\) | 6.23607 | 0.275867 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | −0.236068 | −0.0104227 | ||||||||
\(514\) | −16.6525 | −0.734509 | ||||||||
\(515\) | −13.1672 | −0.580215 | ||||||||
\(516\) | 1.76393 | 0.0776528 | ||||||||
\(517\) | −1.70820 | −0.0751267 | ||||||||
\(518\) | 6.85410 | 0.301152 | ||||||||
\(519\) | 20.4164 | 0.896181 | ||||||||
\(520\) | −5.00000 | −0.219265 | ||||||||
\(521\) | 5.41641 | 0.237297 | 0.118649 | − | 0.992936i | \(-0.462144\pi\) | ||||
0.118649 | + | 0.992936i | \(0.462144\pi\) | |||||||
\(522\) | −10.0902 | −0.441635 | ||||||||
\(523\) | −37.4164 | −1.63611 | −0.818053 | − | 0.575143i | \(-0.804946\pi\) | ||||
−0.818053 | + | 0.575143i | \(0.804946\pi\) | |||||||
\(524\) | −10.3262 | −0.451104 | ||||||||
\(525\) | −3.09017 | −0.134866 | ||||||||
\(526\) | 15.6180 | 0.680979 | ||||||||
\(527\) | 16.3475 | 0.712109 | ||||||||
\(528\) | −4.85410 | −0.211248 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −24.7984 | −1.07717 | ||||||||
\(531\) | −1.38197 | −0.0599722 | ||||||||
\(532\) | −0.145898 | −0.00632548 | ||||||||
\(533\) | −8.85410 | −0.383514 | ||||||||
\(534\) | 10.6180 | 0.459487 | ||||||||
\(535\) | −19.4721 | −0.841854 | ||||||||
\(536\) | 6.90983 | 0.298459 | ||||||||
\(537\) | 10.7984 | 0.465984 | ||||||||
\(538\) | 43.2705 | 1.86552 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0.854102 | 0.0367547 | ||||||||
\(541\) | −2.29180 | −0.0985320 | −0.0492660 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492660 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(542\) | 10.5623 | 0.453690 | ||||||||
\(543\) | 19.1803 | 0.823107 | ||||||||
\(544\) | 11.7426 | 0.503462 | ||||||||
\(545\) | 6.38197 | 0.273373 | ||||||||
\(546\) | 2.61803 | 0.112042 | ||||||||
\(547\) | −32.1459 | −1.37446 | −0.687230 | − | 0.726440i | \(-0.741173\pi\) | ||||
−0.687230 | + | 0.726440i | \(0.741173\pi\) | |||||||
\(548\) | −4.43769 | −0.189569 | ||||||||
\(549\) | −1.14590 | −0.0489057 | ||||||||
\(550\) | 5.00000 | 0.213201 | ||||||||
\(551\) | −1.47214 | −0.0627151 | ||||||||
\(552\) | 2.23607 | 0.0951734 | ||||||||
\(553\) | −9.76393 | −0.415205 | ||||||||
\(554\) | 14.0344 | 0.596266 | ||||||||
\(555\) | −5.85410 | −0.248493 | ||||||||
\(556\) | −4.96556 | −0.210587 | ||||||||
\(557\) | 17.2361 | 0.730316 | 0.365158 | − | 0.930946i | \(-0.381015\pi\) | ||||
0.365158 | + | 0.930946i | \(0.381015\pi\) | |||||||
\(558\) | −7.61803 | −0.322497 | ||||||||
\(559\) | −4.61803 | −0.195322 | ||||||||
\(560\) | −6.70820 | −0.283473 | ||||||||
\(561\) | 3.47214 | 0.146594 | ||||||||
\(562\) | −26.9443 | −1.13658 | ||||||||
\(563\) | −15.2148 | −0.641227 | −0.320613 | − | 0.947210i | \(-0.603889\pi\) | ||||
−0.320613 | + | 0.947210i | \(0.603889\pi\) | |||||||
\(564\) | −1.05573 | −0.0444542 | ||||||||
\(565\) | 4.02129 | 0.169177 | ||||||||
\(566\) | −15.6525 | −0.657923 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 11.9098 | 0.499725 | ||||||||
\(569\) | −9.88854 | −0.414549 | −0.207275 | − | 0.978283i | \(-0.566459\pi\) | ||||
−0.207275 | + | 0.978283i | \(0.566459\pi\) | |||||||
\(570\) | 0.527864 | 0.0221098 | ||||||||
\(571\) | 24.5967 | 1.02934 | 0.514671 | − | 0.857388i | \(-0.327914\pi\) | ||||
0.514671 | + | 0.857388i | \(0.327914\pi\) | |||||||
\(572\) | −1.00000 | −0.0418121 | ||||||||
\(573\) | −8.18034 | −0.341739 | ||||||||
\(574\) | −8.85410 | −0.369563 | ||||||||
\(575\) | −3.09017 | −0.128869 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | 40.2492 | 1.67560 | 0.837799 | − | 0.545979i | \(-0.183842\pi\) | ||||
0.837799 | + | 0.545979i | \(0.183842\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | 5.23607 | 0.217604 | ||||||||
\(580\) | 5.32624 | 0.221160 | ||||||||
\(581\) | −0.0557281 | −0.00231199 | ||||||||
\(582\) | 10.8541 | 0.449917 | ||||||||
\(583\) | 11.0902 | 0.459308 | ||||||||
\(584\) | 13.9443 | 0.577018 | ||||||||
\(585\) | −2.23607 | −0.0924500 | ||||||||
\(586\) | −49.8885 | −2.06088 | ||||||||
\(587\) | 20.2016 | 0.833810 | 0.416905 | − | 0.908950i | \(-0.363115\pi\) | ||||
0.416905 | + | 0.908950i | \(0.363115\pi\) | |||||||
\(588\) | 0.618034 | 0.0254873 | ||||||||
\(589\) | −1.11146 | −0.0457968 | ||||||||
\(590\) | 3.09017 | 0.127220 | ||||||||
\(591\) | −8.56231 | −0.352206 | ||||||||
\(592\) | 20.5623 | 0.845106 | ||||||||
\(593\) | −4.87539 | −0.200208 | −0.100104 | − | 0.994977i | \(-0.531918\pi\) | ||||
−0.100104 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(594\) | −1.61803 | −0.0663887 | ||||||||
\(595\) | 4.79837 | 0.196714 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 21.5623 | 0.882486 | ||||||||
\(598\) | 2.61803 | 0.107059 | ||||||||
\(599\) | −9.61803 | −0.392982 | −0.196491 | − | 0.980506i | \(-0.562955\pi\) | ||||
−0.196491 | + | 0.980506i | \(0.562955\pi\) | |||||||
\(600\) | −6.90983 | −0.282093 | ||||||||
\(601\) | −28.6869 | −1.17016 | −0.585082 | − | 0.810974i | \(-0.698938\pi\) | ||||
−0.585082 | + | 0.810974i | \(0.698938\pi\) | |||||||
\(602\) | −4.61803 | −0.188217 | ||||||||
\(603\) | 3.09017 | 0.125841 | ||||||||
\(604\) | −14.0000 | −0.569652 | ||||||||
\(605\) | −13.8197 | −0.561849 | ||||||||
\(606\) | 14.7082 | 0.597480 | ||||||||
\(607\) | −31.5066 | −1.27881 | −0.639406 | − | 0.768869i | \(-0.720820\pi\) | ||||
−0.639406 | + | 0.768869i | \(0.720820\pi\) | |||||||
\(608\) | −0.798374 | −0.0323783 | ||||||||
\(609\) | 6.23607 | 0.252698 | ||||||||
\(610\) | 2.56231 | 0.103745 | ||||||||
\(611\) | 2.76393 | 0.111817 | ||||||||
\(612\) | 2.14590 | 0.0867428 | ||||||||
\(613\) | 31.8328 | 1.28572 | 0.642858 | − | 0.765986i | \(-0.277749\pi\) | ||||
0.642858 | + | 0.765986i | \(0.277749\pi\) | |||||||
\(614\) | −9.90983 | −0.399928 | ||||||||
\(615\) | 7.56231 | 0.304942 | ||||||||
\(616\) | 2.23607 | 0.0900937 | ||||||||
\(617\) | 34.7426 | 1.39869 | 0.699343 | − | 0.714786i | \(-0.253476\pi\) | ||||
0.699343 | + | 0.714786i | \(0.253476\pi\) | |||||||
\(618\) | 15.4164 | 0.620139 | ||||||||
\(619\) | 16.0902 | 0.646719 | 0.323359 | − | 0.946276i | \(-0.395188\pi\) | ||||
0.323359 | + | 0.946276i | \(0.395188\pi\) | |||||||
\(620\) | 4.02129 | 0.161499 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −44.5066 | −1.78455 | ||||||||
\(623\) | −6.56231 | −0.262913 | ||||||||
\(624\) | 7.85410 | 0.314416 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.05573 | 0.122131 | ||||||||
\(627\) | −0.236068 | −0.00942765 | ||||||||
\(628\) | 8.18034 | 0.326431 | ||||||||
\(629\) | −14.7082 | −0.586454 | ||||||||
\(630\) | −2.23607 | −0.0890871 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | −21.8328 | −0.868463 | ||||||||
\(633\) | −26.8885 | −1.06872 | ||||||||
\(634\) | −17.9443 | −0.712658 | ||||||||
\(635\) | −1.58359 | −0.0628429 | ||||||||
\(636\) | 6.85410 | 0.271783 | ||||||||
\(637\) | −1.61803 | −0.0641088 | ||||||||
\(638\) | −10.0902 | −0.399474 | ||||||||
\(639\) | 5.32624 | 0.210703 | ||||||||
\(640\) | −18.8197 | −0.743912 | ||||||||
\(641\) | −0.201626 | −0.00796375 | −0.00398188 | − | 0.999992i | \(-0.501267\pi\) | ||||
−0.00398188 | + | 0.999992i | \(0.501267\pi\) | |||||||
\(642\) | 22.7984 | 0.899780 | ||||||||
\(643\) | 33.0344 | 1.30275 | 0.651376 | − | 0.758755i | \(-0.274192\pi\) | ||||
0.651376 | + | 0.758755i | \(0.274192\pi\) | |||||||
\(644\) | 0.618034 | 0.0243540 | ||||||||
\(645\) | 3.94427 | 0.155306 | ||||||||
\(646\) | 1.32624 | 0.0521801 | ||||||||
\(647\) | 6.72949 | 0.264564 | 0.132282 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132282 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | −1.38197 | −0.0542469 | ||||||||
\(650\) | −8.09017 | −0.317323 | ||||||||
\(651\) | 4.70820 | 0.184529 | ||||||||
\(652\) | 8.20163 | 0.321200 | ||||||||
\(653\) | −7.09017 | −0.277460 | −0.138730 | − | 0.990330i | \(-0.544302\pi\) | ||||
−0.138730 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(654\) | −7.47214 | −0.292184 | ||||||||
\(655\) | −23.0902 | −0.902208 | ||||||||
\(656\) | −26.5623 | −1.03708 | ||||||||
\(657\) | 6.23607 | 0.243292 | ||||||||
\(658\) | 2.76393 | 0.107749 | ||||||||
\(659\) | −18.0557 | −0.703351 | −0.351676 | − | 0.936122i | \(-0.614388\pi\) | ||||
−0.351676 | + | 0.936122i | \(0.614388\pi\) | |||||||
\(660\) | 0.854102 | 0.0332459 | ||||||||
\(661\) | −7.65248 | −0.297647 | −0.148823 | − | 0.988864i | \(-0.547549\pi\) | ||||
−0.148823 | + | 0.988864i | \(0.547549\pi\) | |||||||
\(662\) | 45.1246 | 1.75382 | ||||||||
\(663\) | −5.61803 | −0.218186 | ||||||||
\(664\) | −0.124612 | −0.00483588 | ||||||||
\(665\) | −0.326238 | −0.0126510 | ||||||||
\(666\) | 6.85410 | 0.265591 | ||||||||
\(667\) | 6.23607 | 0.241462 | ||||||||
\(668\) | −1.67376 | −0.0647598 | ||||||||
\(669\) | −0.618034 | −0.0238946 | ||||||||
\(670\) | −6.90983 | −0.266950 | ||||||||
\(671\) | −1.14590 | −0.0442369 | ||||||||
\(672\) | 3.38197 | 0.130462 | ||||||||
\(673\) | −7.58359 | −0.292326 | −0.146163 | − | 0.989261i | \(-0.546692\pi\) | ||||
−0.146163 | + | 0.989261i | \(0.546692\pi\) | |||||||
\(674\) | 30.7984 | 1.18631 | ||||||||
\(675\) | −3.09017 | −0.118941 | ||||||||
\(676\) | −6.41641 | −0.246785 | ||||||||
\(677\) | 18.6738 | 0.717691 | 0.358845 | − | 0.933397i | \(-0.383170\pi\) | ||||
0.358845 | + | 0.933397i | \(0.383170\pi\) | |||||||
\(678\) | −4.70820 | −0.180817 | ||||||||
\(679\) | −6.70820 | −0.257437 | ||||||||
\(680\) | 10.7295 | 0.411457 | ||||||||
\(681\) | −22.9787 | −0.880546 | ||||||||
\(682\) | −7.61803 | −0.291710 | ||||||||
\(683\) | −26.1246 | −0.999630 | −0.499815 | − | 0.866132i | \(-0.666599\pi\) | ||||
−0.499815 | + | 0.866132i | \(0.666599\pi\) | |||||||
\(684\) | −0.145898 | −0.00557855 | ||||||||
\(685\) | −9.92299 | −0.379138 | ||||||||
\(686\) | −1.61803 | −0.0617768 | ||||||||
\(687\) | 3.20163 | 0.122150 | ||||||||
\(688\) | −13.8541 | −0.528183 | ||||||||
\(689\) | −17.9443 | −0.683622 | ||||||||
\(690\) | −2.23607 | −0.0851257 | ||||||||
\(691\) | −18.3820 | −0.699283 | −0.349641 | − | 0.936884i | \(-0.613697\pi\) | ||||
−0.349641 | + | 0.936884i | \(0.613697\pi\) | |||||||
\(692\) | 12.6180 | 0.479666 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 33.5066 | 1.27189 | ||||||||
\(695\) | −11.1033 | −0.421173 | ||||||||
\(696\) | 13.9443 | 0.528556 | ||||||||
\(697\) | 19.0000 | 0.719676 | ||||||||
\(698\) | −7.76393 | −0.293869 | ||||||||
\(699\) | 24.3262 | 0.920103 | ||||||||
\(700\) | −1.90983 | −0.0721848 | ||||||||
\(701\) | −3.09017 | −0.116714 | −0.0583571 | − | 0.998296i | \(-0.518586\pi\) | ||||
−0.0583571 | + | 0.998296i | \(0.518586\pi\) | |||||||
\(702\) | 2.61803 | 0.0988113 | ||||||||
\(703\) | 1.00000 | 0.0377157 | ||||||||
\(704\) | 4.23607 | 0.159653 | ||||||||
\(705\) | −2.36068 | −0.0889083 | ||||||||
\(706\) | 33.0344 | 1.24327 | ||||||||
\(707\) | −9.09017 | −0.341871 | ||||||||
\(708\) | −0.854102 | −0.0320991 | ||||||||
\(709\) | 42.2705 | 1.58750 | 0.793751 | − | 0.608243i | \(-0.208125\pi\) | ||||
0.793751 | + | 0.608243i | \(0.208125\pi\) | |||||||
\(710\) | −11.9098 | −0.446968 | ||||||||
\(711\) | −9.76393 | −0.366176 | ||||||||
\(712\) | −14.6738 | −0.549922 | ||||||||
\(713\) | 4.70820 | 0.176324 | ||||||||
\(714\) | −5.61803 | −0.210250 | ||||||||
\(715\) | −2.23607 | −0.0836242 | ||||||||
\(716\) | 6.67376 | 0.249410 | ||||||||
\(717\) | −8.79837 | −0.328581 | ||||||||
\(718\) | 18.7082 | 0.698184 | ||||||||
\(719\) | −2.88854 | −0.107725 | −0.0538623 | − | 0.998548i | \(-0.517153\pi\) | ||||
−0.0538623 | + | 0.998548i | \(0.517153\pi\) | |||||||
\(720\) | −6.70820 | −0.250000 | ||||||||
\(721\) | −9.52786 | −0.354836 | ||||||||
\(722\) | 30.6525 | 1.14077 | ||||||||
\(723\) | −16.7082 | −0.621385 | ||||||||
\(724\) | 11.8541 | 0.440554 | ||||||||
\(725\) | −19.2705 | −0.715689 | ||||||||
\(726\) | 16.1803 | 0.600509 | ||||||||
\(727\) | −15.5410 | −0.576385 | −0.288192 | − | 0.957573i | \(-0.593054\pi\) | ||||
−0.288192 | + | 0.957573i | \(0.593054\pi\) | |||||||
\(728\) | −3.61803 | −0.134093 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.9443 | −0.516101 | ||||||||
\(731\) | 9.90983 | 0.366528 | ||||||||
\(732\) | −0.708204 | −0.0261760 | ||||||||
\(733\) | 42.7639 | 1.57952 | 0.789761 | − | 0.613415i | \(-0.210205\pi\) | ||||
0.789761 | + | 0.613415i | \(0.210205\pi\) | |||||||
\(734\) | 32.7984 | 1.21061 | ||||||||
\(735\) | 1.38197 | 0.0509746 | ||||||||
\(736\) | 3.38197 | 0.124661 | ||||||||
\(737\) | 3.09017 | 0.113828 | ||||||||
\(738\) | −8.85410 | −0.325924 | ||||||||
\(739\) | −22.5279 | −0.828701 | −0.414350 | − | 0.910117i | \(-0.635991\pi\) | ||||
−0.414350 | + | 0.910117i | \(0.635991\pi\) | |||||||
\(740\) | −3.61803 | −0.133002 | ||||||||
\(741\) | 0.381966 | 0.0140319 | ||||||||
\(742\) | −17.9443 | −0.658755 | ||||||||
\(743\) | 13.3820 | 0.490937 | 0.245468 | − | 0.969405i | \(-0.421058\pi\) | ||||
0.245468 | + | 0.969405i | \(0.421058\pi\) | |||||||
\(744\) | 10.5279 | 0.385970 | ||||||||
\(745\) | −13.4164 | −0.491539 | ||||||||
\(746\) | 9.90983 | 0.362825 | ||||||||
\(747\) | −0.0557281 | −0.00203898 | ||||||||
\(748\) | 2.14590 | 0.0784618 | ||||||||
\(749\) | −14.0902 | −0.514844 | ||||||||
\(750\) | 18.0902 | 0.660560 | ||||||||
\(751\) | −45.4508 | −1.65853 | −0.829263 | − | 0.558859i | \(-0.811239\pi\) | ||||
−0.829263 | + | 0.558859i | \(0.811239\pi\) | |||||||
\(752\) | 8.29180 | 0.302371 | ||||||||
\(753\) | 4.29180 | 0.156402 | ||||||||
\(754\) | 16.3262 | 0.594567 | ||||||||
\(755\) | −31.3050 | −1.13930 | ||||||||
\(756\) | 0.618034 | 0.0224777 | ||||||||
\(757\) | 22.3475 | 0.812235 | 0.406117 | − | 0.913821i | \(-0.366882\pi\) | ||||
0.406117 | + | 0.913821i | \(0.366882\pi\) | |||||||
\(758\) | 55.7771 | 2.02592 | ||||||||
\(759\) | 1.00000 | 0.0362977 | ||||||||
\(760\) | −0.729490 | −0.0264614 | ||||||||
\(761\) | 6.11146 | 0.221540 | 0.110770 | − | 0.993846i | \(-0.464668\pi\) | ||||
0.110770 | + | 0.993846i | \(0.464668\pi\) | |||||||
\(762\) | 1.85410 | 0.0671670 | ||||||||
\(763\) | 4.61803 | 0.167184 | ||||||||
\(764\) | −5.05573 | −0.182910 | ||||||||
\(765\) | 4.79837 | 0.173486 | ||||||||
\(766\) | −22.5623 | −0.815209 | ||||||||
\(767\) | 2.23607 | 0.0807397 | ||||||||
\(768\) | 13.5623 | 0.489388 | ||||||||
\(769\) | 20.6525 | 0.744747 | 0.372374 | − | 0.928083i | \(-0.378544\pi\) | ||||
0.372374 | + | 0.928083i | \(0.378544\pi\) | |||||||
\(770\) | −2.23607 | −0.0805823 | ||||||||
\(771\) | 10.2918 | 0.370650 | ||||||||
\(772\) | 3.23607 | 0.116469 | ||||||||
\(773\) | 28.5967 | 1.02855 | 0.514277 | − | 0.857624i | \(-0.328060\pi\) | ||||
0.514277 | + | 0.857624i | \(0.328060\pi\) | |||||||
\(774\) | −4.61803 | −0.165992 | ||||||||
\(775\) | −14.5492 | −0.522621 | ||||||||
\(776\) | −15.0000 | −0.538469 | ||||||||
\(777\) | −4.23607 | −0.151968 | ||||||||
\(778\) | 3.32624 | 0.119251 | ||||||||
\(779\) | −1.29180 | −0.0462834 | ||||||||
\(780\) | −1.38197 | −0.0494823 | ||||||||
\(781\) | 5.32624 | 0.190588 | ||||||||
\(782\) | −5.61803 | −0.200900 | ||||||||
\(783\) | 6.23607 | 0.222859 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | 18.2918 | 0.652862 | ||||||||
\(786\) | 27.0344 | 0.964287 | ||||||||
\(787\) | −10.7984 | −0.384920 | −0.192460 | − | 0.981305i | \(-0.561647\pi\) | ||||
−0.192460 | + | 0.981305i | \(0.561647\pi\) | |||||||
\(788\) | −5.29180 | −0.188512 | ||||||||
\(789\) | −9.65248 | −0.343637 | ||||||||
\(790\) | 21.8328 | 0.776777 | ||||||||
\(791\) | 2.90983 | 0.103462 | ||||||||
\(792\) | 2.23607 | 0.0794552 | ||||||||
\(793\) | 1.85410 | 0.0658411 | ||||||||
\(794\) | 0.291796 | 0.0103555 | ||||||||
\(795\) | 15.3262 | 0.543566 | ||||||||
\(796\) | 13.3262 | 0.472336 | ||||||||
\(797\) | −33.1246 | −1.17333 | −0.586667 | − | 0.809828i | \(-0.699560\pi\) | ||||
−0.586667 | + | 0.809828i | \(0.699560\pi\) | |||||||
\(798\) | 0.381966 | 0.0135215 | ||||||||
\(799\) | −5.93112 | −0.209828 | ||||||||
\(800\) | −10.4508 | −0.369493 | ||||||||
\(801\) | −6.56231 | −0.231868 | ||||||||
\(802\) | 8.09017 | 0.285674 | ||||||||
\(803\) | 6.23607 | 0.220066 | ||||||||
\(804\) | 1.90983 | 0.0673545 | ||||||||
\(805\) | 1.38197 | 0.0487079 | ||||||||
\(806\) | 12.3262 | 0.434173 | ||||||||
\(807\) | −26.7426 | −0.941386 | ||||||||
\(808\) | −20.3262 | −0.715075 | ||||||||
\(809\) | −40.2705 | −1.41584 | −0.707918 | − | 0.706295i | \(-0.750365\pi\) | ||||
−0.707918 | + | 0.706295i | \(0.750365\pi\) | |||||||
\(810\) | −2.23607 | −0.0785674 | ||||||||
\(811\) | 50.3050 | 1.76645 | 0.883223 | − | 0.468953i | \(-0.155369\pi\) | ||||
0.883223 | + | 0.468953i | \(0.155369\pi\) | |||||||
\(812\) | 3.85410 | 0.135252 | ||||||||
\(813\) | −6.52786 | −0.228942 | ||||||||
\(814\) | 6.85410 | 0.240236 | ||||||||
\(815\) | 18.3394 | 0.642401 | ||||||||
\(816\) | −16.8541 | −0.590012 | ||||||||
\(817\) | −0.673762 | −0.0235720 | ||||||||
\(818\) | −17.6180 | −0.616000 | ||||||||
\(819\) | −1.61803 | −0.0565387 | ||||||||
\(820\) | 4.67376 | 0.163215 | ||||||||
\(821\) | 36.5410 | 1.27529 | 0.637645 | − | 0.770330i | \(-0.279909\pi\) | ||||
0.637645 | + | 0.770330i | \(0.279909\pi\) | |||||||
\(822\) | 11.6180 | 0.405225 | ||||||||
\(823\) | −8.21478 | −0.286349 | −0.143175 | − | 0.989697i | \(-0.545731\pi\) | ||||
−0.143175 | + | 0.989697i | \(0.545731\pi\) | |||||||
\(824\) | −21.3050 | −0.742193 | ||||||||
\(825\) | −3.09017 | −0.107586 | ||||||||
\(826\) | 2.23607 | 0.0778028 | ||||||||
\(827\) | 5.85410 | 0.203567 | 0.101784 | − | 0.994807i | \(-0.467545\pi\) | ||||
0.101784 | + | 0.994807i | \(0.467545\pi\) | |||||||
\(828\) | 0.618034 | 0.0214782 | ||||||||
\(829\) | −32.7771 | −1.13840 | −0.569198 | − | 0.822201i | \(-0.692746\pi\) | ||||
−0.569198 | + | 0.822201i | \(0.692746\pi\) | |||||||
\(830\) | 0.124612 | 0.00432534 | ||||||||
\(831\) | −8.67376 | −0.300889 | ||||||||
\(832\) | −6.85410 | −0.237623 | ||||||||
\(833\) | 3.47214 | 0.120302 | ||||||||
\(834\) | 13.0000 | 0.450153 | ||||||||
\(835\) | −3.74265 | −0.129520 | ||||||||
\(836\) | −0.145898 | −0.00504599 | ||||||||
\(837\) | 4.70820 | 0.162739 | ||||||||
\(838\) | −40.5967 | −1.40239 | ||||||||
\(839\) | 45.9787 | 1.58736 | 0.793681 | − | 0.608335i | \(-0.208162\pi\) | ||||
0.793681 | + | 0.608335i | \(0.208162\pi\) | |||||||
\(840\) | 3.09017 | 0.106621 | ||||||||
\(841\) | 9.88854 | 0.340984 | ||||||||
\(842\) | 15.2705 | 0.526257 | ||||||||
\(843\) | 16.6525 | 0.573542 | ||||||||
\(844\) | −16.6180 | −0.572016 | ||||||||
\(845\) | −14.3475 | −0.493570 | ||||||||
\(846\) | 2.76393 | 0.0950259 | ||||||||
\(847\) | −10.0000 | −0.343604 | ||||||||
\(848\) | −53.8328 | −1.84863 | ||||||||
\(849\) | 9.67376 | 0.332003 | ||||||||
\(850\) | 17.3607 | 0.595466 | ||||||||
\(851\) | −4.23607 | −0.145211 | ||||||||
\(852\) | 3.29180 | 0.112775 | ||||||||
\(853\) | −36.0689 | −1.23498 | −0.617488 | − | 0.786581i | \(-0.711849\pi\) | ||||
−0.617488 | + | 0.786581i | \(0.711849\pi\) | |||||||
\(854\) | 1.85410 | 0.0634461 | ||||||||
\(855\) | −0.326238 | −0.0111571 | ||||||||
\(856\) | −31.5066 | −1.07687 | ||||||||
\(857\) | −39.1246 | −1.33647 | −0.668236 | − | 0.743950i | \(-0.732950\pi\) | ||||
−0.668236 | + | 0.743950i | \(0.732950\pi\) | |||||||
\(858\) | 2.61803 | 0.0893782 | ||||||||
\(859\) | −46.3607 | −1.58181 | −0.790903 | − | 0.611942i | \(-0.790389\pi\) | ||||
−0.790903 | + | 0.611942i | \(0.790389\pi\) | |||||||
\(860\) | 2.43769 | 0.0831247 | ||||||||
\(861\) | 5.47214 | 0.186490 | ||||||||
\(862\) | 36.0344 | 1.22734 | ||||||||
\(863\) | 30.1803 | 1.02735 | 0.513675 | − | 0.857985i | \(-0.328284\pi\) | ||||
0.513675 | + | 0.857985i | \(0.328284\pi\) | |||||||
\(864\) | 3.38197 | 0.115057 | ||||||||
\(865\) | 28.2148 | 0.959331 | ||||||||
\(866\) | −40.8328 | −1.38756 | ||||||||
\(867\) | −4.94427 | −0.167916 | ||||||||
\(868\) | 2.90983 | 0.0987661 | ||||||||
\(869\) | −9.76393 | −0.331219 | ||||||||
\(870\) | −13.9443 | −0.472755 | ||||||||
\(871\) | −5.00000 | −0.169419 | ||||||||
\(872\) | 10.3262 | 0.349691 | ||||||||
\(873\) | −6.70820 | −0.227038 | ||||||||
\(874\) | 0.381966 | 0.0129202 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | 3.85410 | 0.130218 | ||||||||
\(877\) | 20.0000 | 0.675352 | 0.337676 | − | 0.941262i | \(-0.390359\pi\) | ||||
0.337676 | + | 0.941262i | \(0.390359\pi\) | |||||||
\(878\) | 21.3262 | 0.719726 | ||||||||
\(879\) | 30.8328 | 1.03997 | ||||||||
\(880\) | −6.70820 | −0.226134 | ||||||||
\(881\) | −47.7082 | −1.60733 | −0.803665 | − | 0.595082i | \(-0.797120\pi\) | ||||
−0.803665 | + | 0.595082i | \(0.797120\pi\) | |||||||
\(882\) | −1.61803 | −0.0544820 | ||||||||
\(883\) | 16.0902 | 0.541477 | 0.270739 | − | 0.962653i | \(-0.412732\pi\) | ||||
0.270739 | + | 0.962653i | \(0.412732\pi\) | |||||||
\(884\) | −3.47214 | −0.116781 | ||||||||
\(885\) | −1.90983 | −0.0641982 | ||||||||
\(886\) | −43.4164 | −1.45860 | ||||||||
\(887\) | 49.9787 | 1.67812 | 0.839060 | − | 0.544038i | \(-0.183105\pi\) | ||||
0.839060 | + | 0.544038i | \(0.183105\pi\) | |||||||
\(888\) | −9.47214 | −0.317864 | ||||||||
\(889\) | −1.14590 | −0.0384322 | ||||||||
\(890\) | 14.6738 | 0.491866 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −0.381966 | −0.0127892 | ||||||||
\(893\) | 0.403252 | 0.0134943 | ||||||||
\(894\) | 15.7082 | 0.525361 | ||||||||
\(895\) | 14.9230 | 0.498820 | ||||||||
\(896\) | −13.6180 | −0.454947 | ||||||||
\(897\) | −1.61803 | −0.0540246 | ||||||||
\(898\) | −10.8885 | −0.363355 | ||||||||
\(899\) | 29.3607 | 0.979233 | ||||||||
\(900\) | −1.90983 | −0.0636610 | ||||||||
\(901\) | 38.5066 | 1.28284 | ||||||||
\(902\) | −8.85410 | −0.294809 | ||||||||
\(903\) | 2.85410 | 0.0949786 | ||||||||
\(904\) | 6.50658 | 0.216406 | ||||||||
\(905\) | 26.5066 | 0.881108 | ||||||||
\(906\) | 36.6525 | 1.21770 | ||||||||
\(907\) | 31.2705 | 1.03832 | 0.519160 | − | 0.854677i | \(-0.326245\pi\) | ||||
0.519160 | + | 0.854677i | \(0.326245\pi\) | |||||||
\(908\) | −14.2016 | −0.471298 | ||||||||
\(909\) | −9.09017 | −0.301502 | ||||||||
\(910\) | 3.61803 | 0.119937 | ||||||||
\(911\) | 35.0132 | 1.16004 | 0.580019 | − | 0.814603i | \(-0.303045\pi\) | ||||
0.580019 | + | 0.814603i | \(0.303045\pi\) | |||||||
\(912\) | 1.14590 | 0.0379445 | ||||||||
\(913\) | −0.0557281 | −0.00184433 | ||||||||
\(914\) | −64.3050 | −2.12702 | ||||||||
\(915\) | −1.58359 | −0.0523519 | ||||||||
\(916\) | 1.97871 | 0.0653785 | ||||||||
\(917\) | −16.7082 | −0.551754 | ||||||||
\(918\) | −5.61803 | −0.185423 | ||||||||
\(919\) | 56.1935 | 1.85365 | 0.926826 | − | 0.375491i | \(-0.122526\pi\) | ||||
0.926826 | + | 0.375491i | \(0.122526\pi\) | |||||||
\(920\) | 3.09017 | 0.101880 | ||||||||
\(921\) | 6.12461 | 0.201813 | ||||||||
\(922\) | −16.7082 | −0.550255 | ||||||||
\(923\) | −8.61803 | −0.283666 | ||||||||
\(924\) | 0.618034 | 0.0203318 | ||||||||
\(925\) | 13.0902 | 0.430402 | ||||||||
\(926\) | 42.2705 | 1.38910 | ||||||||
\(927\) | −9.52786 | −0.312936 | ||||||||
\(928\) | 21.0902 | 0.692319 | ||||||||
\(929\) | 29.9230 | 0.981741 | 0.490871 | − | 0.871232i | \(-0.336679\pi\) | ||||
0.490871 | + | 0.871232i | \(0.336679\pi\) | |||||||
\(930\) | −10.5279 | −0.345222 | ||||||||
\(931\) | −0.236068 | −0.00773682 | ||||||||
\(932\) | 15.0344 | 0.492470 | ||||||||
\(933\) | 27.5066 | 0.900525 | ||||||||
\(934\) | −4.67376 | −0.152930 | ||||||||
\(935\) | 4.79837 | 0.156924 | ||||||||
\(936\) | −3.61803 | −0.118259 | ||||||||
\(937\) | −23.3607 | −0.763160 | −0.381580 | − | 0.924336i | \(-0.624620\pi\) | ||||
−0.381580 | + | 0.924336i | \(0.624620\pi\) | |||||||
\(938\) | −5.00000 | −0.163256 | ||||||||
\(939\) | −1.88854 | −0.0616303 | ||||||||
\(940\) | −1.45898 | −0.0475867 | ||||||||
\(941\) | 44.3607 | 1.44612 | 0.723058 | − | 0.690787i | \(-0.242736\pi\) | ||||
0.723058 | + | 0.690787i | \(0.242736\pi\) | |||||||
\(942\) | −21.4164 | −0.697784 | ||||||||
\(943\) | 5.47214 | 0.178197 | ||||||||
\(944\) | 6.70820 | 0.218333 | ||||||||
\(945\) | 1.38197 | 0.0449554 | ||||||||
\(946\) | −4.61803 | −0.150145 | ||||||||
\(947\) | −53.4164 | −1.73580 | −0.867900 | − | 0.496739i | \(-0.834531\pi\) | ||||
−0.867900 | + | 0.496739i | \(0.834531\pi\) | |||||||
\(948\) | −6.03444 | −0.195990 | ||||||||
\(949\) | −10.0902 | −0.327541 | ||||||||
\(950\) | −1.18034 | −0.0382953 | ||||||||
\(951\) | 11.0902 | 0.359623 | ||||||||
\(952\) | 7.76393 | 0.251630 | ||||||||
\(953\) | −33.9787 | −1.10068 | −0.550339 | − | 0.834941i | \(-0.685502\pi\) | ||||
−0.550339 | + | 0.834941i | \(0.685502\pi\) | |||||||
\(954\) | −17.9443 | −0.580967 | ||||||||
\(955\) | −11.3050 | −0.365820 | ||||||||
\(956\) | −5.43769 | −0.175868 | ||||||||
\(957\) | 6.23607 | 0.201583 | ||||||||
\(958\) | 15.0344 | 0.485741 | ||||||||
\(959\) | −7.18034 | −0.231865 | ||||||||
\(960\) | 5.85410 | 0.188940 | ||||||||
\(961\) | −8.83282 | −0.284930 | ||||||||
\(962\) | −11.0902 | −0.357561 | ||||||||
\(963\) | −14.0902 | −0.454049 | ||||||||
\(964\) | −10.3262 | −0.332586 | ||||||||
\(965\) | 7.23607 | 0.232937 | ||||||||
\(966\) | −1.61803 | −0.0520594 | ||||||||
\(967\) | −7.88854 | −0.253678 | −0.126839 | − | 0.991923i | \(-0.540483\pi\) | ||||
−0.126839 | + | 0.991923i | \(0.540483\pi\) | |||||||
\(968\) | −22.3607 | −0.718699 | ||||||||
\(969\) | −0.819660 | −0.0263313 | ||||||||
\(970\) | 15.0000 | 0.481621 | ||||||||
\(971\) | 20.9656 | 0.672817 | 0.336408 | − | 0.941716i | \(-0.390788\pi\) | ||||
0.336408 | + | 0.941716i | \(0.390788\pi\) | |||||||
\(972\) | 0.618034 | 0.0198234 | ||||||||
\(973\) | −8.03444 | −0.257572 | ||||||||
\(974\) | −16.3820 | −0.524912 | ||||||||
\(975\) | 5.00000 | 0.160128 | ||||||||
\(976\) | 5.56231 | 0.178045 | ||||||||
\(977\) | 39.2148 | 1.25459 | 0.627296 | − | 0.778781i | \(-0.284162\pi\) | ||||
0.627296 | + | 0.778781i | \(0.284162\pi\) | |||||||
\(978\) | −21.4721 | −0.686603 | ||||||||
\(979\) | −6.56231 | −0.209732 | ||||||||
\(980\) | 0.854102 | 0.0272833 | ||||||||
\(981\) | 4.61803 | 0.147442 | ||||||||
\(982\) | 36.5066 | 1.16497 | ||||||||
\(983\) | 5.00000 | 0.159475 | 0.0797376 | − | 0.996816i | \(-0.474592\pi\) | ||||
0.0797376 | + | 0.996816i | \(0.474592\pi\) | |||||||
\(984\) | 12.2361 | 0.390072 | ||||||||
\(985\) | −11.8328 | −0.377025 | ||||||||
\(986\) | −35.0344 | −1.11572 | ||||||||
\(987\) | −1.70820 | −0.0543727 | ||||||||
\(988\) | 0.236068 | 0.00751032 | ||||||||
\(989\) | 2.85410 | 0.0907552 | ||||||||
\(990\) | −2.23607 | −0.0710669 | ||||||||
\(991\) | −48.3820 | −1.53690 | −0.768452 | − | 0.639908i | \(-0.778973\pi\) | ||||
−0.768452 | + | 0.639908i | \(0.778973\pi\) | |||||||
\(992\) | 15.9230 | 0.505555 | ||||||||
\(993\) | −27.8885 | −0.885016 | ||||||||
\(994\) | −8.61803 | −0.273347 | ||||||||
\(995\) | 29.7984 | 0.944672 | ||||||||
\(996\) | −0.0344419 | −0.00109133 | ||||||||
\(997\) | −22.3050 | −0.706405 | −0.353202 | − | 0.935547i | \(-0.614907\pi\) | ||||
−0.353202 | + | 0.935547i | \(0.614907\pi\) | |||||||
\(998\) | 5.76393 | 0.182454 | ||||||||
\(999\) | −4.23607 | −0.134023 |
(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 | 483.2.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1449.2.a.g.1.2 | 2 | |||
4.3 | odd | 2 | 7728.2.a.be.1.1 | 2 | |||
7.6 | odd | 2 | 3381.2.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1449.2.a.g.1.2 | 2 | 3.2 | odd | 2 | |||
3381.2.a.o.1.1 | 2 | 7.6 | odd | 2 | |||
7728.2.a.be.1.1 | 2 | 4.3 | odd | 2 |