Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1668357.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 11x^{3} + x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.61712\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.96737 | 0.879834 | 0.439917 | − | 0.898038i | \(-0.355008\pi\) | ||||
0.439917 | + | 0.898038i | \(0.355008\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −3.61712 | −1.36714 | −0.683572 | − | 0.729883i | \(-0.739575\pi\) | ||||
−0.683572 | + | 0.729883i | \(0.739575\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.96737 | −0.622137 | ||||||||
\(11\) | 0.322205 | 0.0971486 | 0.0485743 | − | 0.998820i | \(-0.484532\pi\) | ||||
0.0485743 | + | 0.998820i | \(0.484532\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.69718 | 0.748063 | 0.374032 | − | 0.927416i | \(-0.377975\pi\) | ||||
0.374032 | + | 0.927416i | \(0.377975\pi\) | |||||||
\(14\) | 3.61712 | 0.966717 | ||||||||
\(15\) | 1.96737 | 0.507972 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.90670 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647909\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647909\pi\) | |||||||
\(20\) | 1.96737 | 0.439917 | ||||||||
\(21\) | −3.61712 | −0.789321 | ||||||||
\(22\) | −0.322205 | −0.0686944 | ||||||||
\(23\) | −4.79401 | −0.999620 | −0.499810 | − | 0.866135i | \(-0.666597\pi\) | ||||
−0.499810 | + | 0.866135i | \(0.666597\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.12946 | −0.225892 | ||||||||
\(26\) | −2.69718 | −0.528961 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.61712 | −0.683572 | ||||||||
\(29\) | −0.708609 | −0.131585 | −0.0657927 | − | 0.997833i | \(-0.520958\pi\) | ||||
−0.0657927 | + | 0.997833i | \(0.520958\pi\) | |||||||
\(30\) | −1.96737 | −0.359191 | ||||||||
\(31\) | 6.38640 | 1.14703 | 0.573516 | − | 0.819194i | \(-0.305579\pi\) | ||||
0.573516 | + | 0.819194i | \(0.305579\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.322205 | 0.0560888 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −7.11622 | −1.20286 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.47640 | −1.39351 | −0.696755 | − | 0.717309i | \(-0.745374\pi\) | ||||
−0.696755 | + | 0.717309i | \(0.745374\pi\) | |||||||
\(38\) | 3.90670 | 0.633750 | ||||||||
\(39\) | 2.69718 | 0.431894 | ||||||||
\(40\) | −1.96737 | −0.311068 | ||||||||
\(41\) | 1.55976 | 0.243594 | 0.121797 | − | 0.992555i | \(-0.461134\pi\) | ||||
0.121797 | + | 0.992555i | \(0.461134\pi\) | |||||||
\(42\) | 3.61712 | 0.558134 | ||||||||
\(43\) | 10.0935 | 1.53925 | 0.769624 | − | 0.638498i | \(-0.220444\pi\) | ||||
0.769624 | + | 0.638498i | \(0.220444\pi\) | |||||||
\(44\) | 0.322205 | 0.0485743 | ||||||||
\(45\) | 1.96737 | 0.293278 | ||||||||
\(46\) | 4.79401 | 0.706838 | ||||||||
\(47\) | 12.0456 | 1.75703 | 0.878516 | − | 0.477712i | \(-0.158534\pi\) | ||||
0.878516 | + | 0.477712i | \(0.158534\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.08358 | 0.869083 | ||||||||
\(50\) | 1.12946 | 0.159730 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 2.69718 | 0.374032 | ||||||||
\(53\) | −1.01479 | −0.139393 | −0.0696963 | − | 0.997568i | \(-0.522203\pi\) | ||||
−0.0696963 | + | 0.997568i | \(0.522203\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.633897 | 0.0854746 | ||||||||
\(56\) | 3.61712 | 0.483358 | ||||||||
\(57\) | −3.90670 | −0.517455 | ||||||||
\(58\) | 0.708609 | 0.0930449 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 1.96737 | 0.253986 | ||||||||
\(61\) | 10.7660 | 1.37844 | 0.689221 | − | 0.724552i | \(-0.257953\pi\) | ||||
0.689221 | + | 0.724552i | \(0.257953\pi\) | |||||||
\(62\) | −6.38640 | −0.811074 | ||||||||
\(63\) | −3.61712 | −0.455715 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.30635 | 0.658171 | ||||||||
\(66\) | −0.322205 | −0.0396608 | ||||||||
\(67\) | 12.2702 | 1.49905 | 0.749524 | − | 0.661977i | \(-0.230282\pi\) | ||||
0.749524 | + | 0.661977i | \(0.230282\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −4.79401 | −0.577131 | ||||||||
\(70\) | 7.11622 | 0.850550 | ||||||||
\(71\) | 7.07215 | 0.839310 | 0.419655 | − | 0.907684i | \(-0.362151\pi\) | ||||
0.419655 | + | 0.907684i | \(0.362151\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.18832 | 0.373164 | 0.186582 | − | 0.982439i | \(-0.440259\pi\) | ||||
0.186582 | + | 0.982439i | \(0.440259\pi\) | |||||||
\(74\) | 8.47640 | 0.985361 | ||||||||
\(75\) | −1.12946 | −0.130419 | ||||||||
\(76\) | −3.90670 | −0.448129 | ||||||||
\(77\) | −1.16546 | −0.132816 | ||||||||
\(78\) | −2.69718 | −0.305396 | ||||||||
\(79\) | −0.0479121 | −0.00539053 | −0.00269526 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269526 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(80\) | 1.96737 | 0.219958 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.55976 | −0.172247 | ||||||||
\(83\) | 0.102752 | 0.0112784 | 0.00563922 | − | 0.999984i | \(-0.498205\pi\) | ||||
0.00563922 | + | 0.999984i | \(0.498205\pi\) | |||||||
\(84\) | −3.61712 | −0.394661 | ||||||||
\(85\) | −1.96737 | −0.213391 | ||||||||
\(86\) | −10.0935 | −1.08841 | ||||||||
\(87\) | −0.708609 | −0.0759709 | ||||||||
\(88\) | −0.322205 | −0.0343472 | ||||||||
\(89\) | 3.15216 | 0.334128 | 0.167064 | − | 0.985946i | \(-0.446571\pi\) | ||||
0.167064 | + | 0.985946i | \(0.446571\pi\) | |||||||
\(90\) | −1.96737 | −0.207379 | ||||||||
\(91\) | −9.75603 | −1.02271 | ||||||||
\(92\) | −4.79401 | −0.499810 | ||||||||
\(93\) | 6.38640 | 0.662239 | ||||||||
\(94\) | −12.0456 | −1.24241 | ||||||||
\(95\) | −7.68591 | −0.788558 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 2.11803 | 0.215054 | 0.107527 | − | 0.994202i | \(-0.465707\pi\) | ||||
0.107527 | + | 0.994202i | \(0.465707\pi\) | |||||||
\(98\) | −6.08358 | −0.614535 | ||||||||
\(99\) | 0.322205 | 0.0323829 | ||||||||
\(100\) | −1.12946 | −0.112946 | ||||||||
\(101\) | −3.31580 | −0.329934 | −0.164967 | − | 0.986299i | \(-0.552752\pi\) | ||||
−0.164967 | + | 0.986299i | \(0.552752\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −5.84405 | −0.575831 | −0.287916 | − | 0.957656i | \(-0.592962\pi\) | ||||
−0.287916 | + | 0.957656i | \(0.592962\pi\) | |||||||
\(104\) | −2.69718 | −0.264480 | ||||||||
\(105\) | −7.11622 | −0.694471 | ||||||||
\(106\) | 1.01479 | 0.0985655 | ||||||||
\(107\) | 15.5098 | 1.49939 | 0.749694 | − | 0.661785i | \(-0.230201\pi\) | ||||
0.749694 | + | 0.661785i | \(0.230201\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 6.44376 | 0.617201 | 0.308600 | − | 0.951192i | \(-0.400139\pi\) | ||||
0.308600 | + | 0.951192i | \(0.400139\pi\) | |||||||
\(110\) | −0.633897 | −0.0604397 | ||||||||
\(111\) | −8.47640 | −0.804544 | ||||||||
\(112\) | −3.61712 | −0.341786 | ||||||||
\(113\) | 15.0555 | 1.41631 | 0.708153 | − | 0.706059i | \(-0.249529\pi\) | ||||
0.708153 | + | 0.706059i | \(0.249529\pi\) | |||||||
\(114\) | 3.90670 | 0.365896 | ||||||||
\(115\) | −9.43158 | −0.879500 | ||||||||
\(116\) | −0.708609 | −0.0657927 | ||||||||
\(117\) | 2.69718 | 0.249354 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 3.61712 | 0.331581 | ||||||||
\(120\) | −1.96737 | −0.179595 | ||||||||
\(121\) | −10.8962 | −0.990562 | ||||||||
\(122\) | −10.7660 | −0.974705 | ||||||||
\(123\) | 1.55976 | 0.140639 | ||||||||
\(124\) | 6.38640 | 0.573516 | ||||||||
\(125\) | −12.0589 | −1.07858 | ||||||||
\(126\) | 3.61712 | 0.322239 | ||||||||
\(127\) | 19.4634 | 1.72710 | 0.863549 | − | 0.504264i | \(-0.168236\pi\) | ||||
0.863549 | + | 0.504264i | \(0.168236\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.0935 | 0.888685 | ||||||||
\(130\) | −5.30635 | −0.465397 | ||||||||
\(131\) | −6.93292 | −0.605732 | −0.302866 | − | 0.953033i | \(-0.597943\pi\) | ||||
−0.302866 | + | 0.953033i | \(0.597943\pi\) | |||||||
\(132\) | 0.322205 | 0.0280444 | ||||||||
\(133\) | 14.1310 | 1.22531 | ||||||||
\(134\) | −12.2702 | −1.05999 | ||||||||
\(135\) | 1.96737 | 0.169324 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −16.3204 | −1.39435 | −0.697175 | − | 0.716901i | \(-0.745560\pi\) | ||||
−0.697175 | + | 0.716901i | \(0.745560\pi\) | |||||||
\(138\) | 4.79401 | 0.408093 | ||||||||
\(139\) | 1.77264 | 0.150354 | 0.0751769 | − | 0.997170i | \(-0.476048\pi\) | ||||
0.0751769 | + | 0.997170i | \(0.476048\pi\) | |||||||
\(140\) | −7.11622 | −0.601430 | ||||||||
\(141\) | 12.0456 | 1.01442 | ||||||||
\(142\) | −7.07215 | −0.593482 | ||||||||
\(143\) | 0.869046 | 0.0726733 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.39410 | −0.115773 | ||||||||
\(146\) | −3.18832 | −0.263867 | ||||||||
\(147\) | 6.08358 | 0.501766 | ||||||||
\(148\) | −8.47640 | −0.696755 | ||||||||
\(149\) | −1.92331 | −0.157564 | −0.0787818 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787818 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(150\) | 1.12946 | 0.0922201 | ||||||||
\(151\) | 19.1004 | 1.55437 | 0.777185 | − | 0.629273i | \(-0.216647\pi\) | ||||
0.777185 | + | 0.629273i | \(0.216647\pi\) | |||||||
\(152\) | 3.90670 | 0.316875 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 1.16546 | 0.0939152 | ||||||||
\(155\) | 12.5644 | 1.00920 | ||||||||
\(156\) | 2.69718 | 0.215947 | ||||||||
\(157\) | −3.76548 | −0.300518 | −0.150259 | − | 0.988647i | \(-0.548011\pi\) | ||||
−0.150259 | + | 0.988647i | \(0.548011\pi\) | |||||||
\(158\) | 0.0479121 | 0.00381168 | ||||||||
\(159\) | −1.01479 | −0.0804784 | ||||||||
\(160\) | −1.96737 | −0.155534 | ||||||||
\(161\) | 17.3405 | 1.36662 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −4.05277 | −0.317437 | −0.158719 | − | 0.987324i | \(-0.550736\pi\) | ||||
−0.158719 | + | 0.987324i | \(0.550736\pi\) | |||||||
\(164\) | 1.55976 | 0.121797 | ||||||||
\(165\) | 0.633897 | 0.0493488 | ||||||||
\(166\) | −0.102752 | −0.00797507 | ||||||||
\(167\) | 8.12354 | 0.628618 | 0.314309 | − | 0.949321i | \(-0.398227\pi\) | ||||
0.314309 | + | 0.949321i | \(0.398227\pi\) | |||||||
\(168\) | 3.61712 | 0.279067 | ||||||||
\(169\) | −5.72522 | −0.440401 | ||||||||
\(170\) | 1.96737 | 0.150890 | ||||||||
\(171\) | −3.90670 | −0.298753 | ||||||||
\(172\) | 10.0935 | 0.769624 | ||||||||
\(173\) | 12.3655 | 0.940133 | 0.470067 | − | 0.882631i | \(-0.344230\pi\) | ||||
0.470067 | + | 0.882631i | \(0.344230\pi\) | |||||||
\(174\) | 0.708609 | 0.0537195 | ||||||||
\(175\) | 4.08540 | 0.308827 | ||||||||
\(176\) | 0.322205 | 0.0242872 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −3.15216 | −0.236264 | ||||||||
\(179\) | 16.6961 | 1.24793 | 0.623963 | − | 0.781454i | \(-0.285522\pi\) | ||||
0.623963 | + | 0.781454i | \(0.285522\pi\) | |||||||
\(180\) | 1.96737 | 0.146639 | ||||||||
\(181\) | −26.2946 | −1.95447 | −0.977233 | − | 0.212169i | \(-0.931947\pi\) | ||||
−0.977233 | + | 0.212169i | \(0.931947\pi\) | |||||||
\(182\) | 9.75603 | 0.723165 | ||||||||
\(183\) | 10.7660 | 0.795843 | ||||||||
\(184\) | 4.79401 | 0.353419 | ||||||||
\(185\) | −16.6762 | −1.22606 | ||||||||
\(186\) | −6.38640 | −0.468274 | ||||||||
\(187\) | −0.322205 | −0.0235620 | ||||||||
\(188\) | 12.0456 | 0.878516 | ||||||||
\(189\) | −3.61712 | −0.263107 | ||||||||
\(190\) | 7.68591 | 0.557595 | ||||||||
\(191\) | 5.70129 | 0.412531 | 0.206265 | − | 0.978496i | \(-0.433869\pi\) | ||||
0.206265 | + | 0.978496i | \(0.433869\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 6.01143 | 0.432712 | 0.216356 | − | 0.976315i | \(-0.430583\pi\) | ||||
0.216356 | + | 0.976315i | \(0.430583\pi\) | |||||||
\(194\) | −2.11803 | −0.152066 | ||||||||
\(195\) | 5.30635 | 0.379995 | ||||||||
\(196\) | 6.08358 | 0.434542 | ||||||||
\(197\) | 8.44024 | 0.601342 | 0.300671 | − | 0.953728i | \(-0.402789\pi\) | ||||
0.300671 | + | 0.953728i | \(0.402789\pi\) | |||||||
\(198\) | −0.322205 | −0.0228981 | ||||||||
\(199\) | −10.3059 | −0.730563 | −0.365282 | − | 0.930897i | \(-0.619027\pi\) | ||||
−0.365282 | + | 0.930897i | \(0.619027\pi\) | |||||||
\(200\) | 1.12946 | 0.0798650 | ||||||||
\(201\) | 12.2702 | 0.865476 | ||||||||
\(202\) | 3.31580 | 0.233299 | ||||||||
\(203\) | 2.56313 | 0.179896 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 3.06863 | 0.214322 | ||||||||
\(206\) | 5.84405 | 0.407174 | ||||||||
\(207\) | −4.79401 | −0.333207 | ||||||||
\(208\) | 2.69718 | 0.187016 | ||||||||
\(209\) | −1.25876 | −0.0870702 | ||||||||
\(210\) | 7.11622 | 0.491066 | ||||||||
\(211\) | −8.45060 | −0.581763 | −0.290882 | − | 0.956759i | \(-0.593949\pi\) | ||||
−0.290882 | + | 0.956759i | \(0.593949\pi\) | |||||||
\(212\) | −1.01479 | −0.0696963 | ||||||||
\(213\) | 7.07215 | 0.484576 | ||||||||
\(214\) | −15.5098 | −1.06023 | ||||||||
\(215\) | 19.8577 | 1.35428 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −23.1004 | −1.56816 | ||||||||
\(218\) | −6.44376 | −0.436427 | ||||||||
\(219\) | 3.18832 | 0.215446 | ||||||||
\(220\) | 0.633897 | 0.0427373 | ||||||||
\(221\) | −2.69718 | −0.181432 | ||||||||
\(222\) | 8.47640 | 0.568898 | ||||||||
\(223\) | 23.4257 | 1.56870 | 0.784349 | − | 0.620320i | \(-0.212997\pi\) | ||||
0.784349 | + | 0.620320i | \(0.212997\pi\) | |||||||
\(224\) | 3.61712 | 0.241679 | ||||||||
\(225\) | −1.12946 | −0.0752974 | ||||||||
\(226\) | −15.0555 | −1.00148 | ||||||||
\(227\) | 23.5348 | 1.56206 | 0.781030 | − | 0.624493i | \(-0.214694\pi\) | ||||
0.781030 | + | 0.624493i | \(0.214694\pi\) | |||||||
\(228\) | −3.90670 | −0.258727 | ||||||||
\(229\) | −29.8732 | −1.97408 | −0.987039 | − | 0.160481i | \(-0.948695\pi\) | ||||
−0.987039 | + | 0.160481i | \(0.948695\pi\) | |||||||
\(230\) | 9.43158 | 0.621900 | ||||||||
\(231\) | −1.16546 | −0.0766814 | ||||||||
\(232\) | 0.708609 | 0.0465225 | ||||||||
\(233\) | 13.5825 | 0.889820 | 0.444910 | − | 0.895575i | \(-0.353236\pi\) | ||||
0.444910 | + | 0.895575i | \(0.353236\pi\) | |||||||
\(234\) | −2.69718 | −0.176320 | ||||||||
\(235\) | 23.6981 | 1.54590 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | −0.0479121 | −0.00311222 | ||||||||
\(238\) | −3.61712 | −0.234463 | ||||||||
\(239\) | 5.64131 | 0.364906 | 0.182453 | − | 0.983215i | \(-0.441596\pi\) | ||||
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(240\) | 1.96737 | 0.126993 | ||||||||
\(241\) | 22.6870 | 1.46140 | 0.730698 | − | 0.682701i | \(-0.239195\pi\) | ||||
0.730698 | + | 0.682701i | \(0.239195\pi\) | |||||||
\(242\) | 10.8962 | 0.700433 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.7660 | 0.689221 | ||||||||
\(245\) | 11.9687 | 0.764649 | ||||||||
\(246\) | −1.55976 | −0.0994468 | ||||||||
\(247\) | −10.5371 | −0.670458 | ||||||||
\(248\) | −6.38640 | −0.405537 | ||||||||
\(249\) | 0.102752 | 0.00651162 | ||||||||
\(250\) | 12.0589 | 0.762672 | ||||||||
\(251\) | −6.93425 | −0.437686 | −0.218843 | − | 0.975760i | \(-0.570228\pi\) | ||||
−0.218843 | + | 0.975760i | \(0.570228\pi\) | |||||||
\(252\) | −3.61712 | −0.227857 | ||||||||
\(253\) | −1.54466 | −0.0971117 | ||||||||
\(254\) | −19.4634 | −1.22124 | ||||||||
\(255\) | −1.96737 | −0.123201 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.25097 | 0.577059 | 0.288530 | − | 0.957471i | \(-0.406834\pi\) | ||||
0.288530 | + | 0.957471i | \(0.406834\pi\) | |||||||
\(258\) | −10.0935 | −0.628395 | ||||||||
\(259\) | 30.6602 | 1.90513 | ||||||||
\(260\) | 5.30635 | 0.329086 | ||||||||
\(261\) | −0.708609 | −0.0438618 | ||||||||
\(262\) | 6.93292 | 0.428317 | ||||||||
\(263\) | −1.77066 | −0.109184 | −0.0545919 | − | 0.998509i | \(-0.517386\pi\) | ||||
−0.0545919 | + | 0.998509i | \(0.517386\pi\) | |||||||
\(264\) | −0.322205 | −0.0198304 | ||||||||
\(265\) | −1.99647 | −0.122642 | ||||||||
\(266\) | −14.1310 | −0.866428 | ||||||||
\(267\) | 3.15216 | 0.192909 | ||||||||
\(268\) | 12.2702 | 0.749524 | ||||||||
\(269\) | 1.30106 | 0.0793269 | 0.0396634 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396634 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(270\) | −1.96737 | −0.119730 | ||||||||
\(271\) | 7.25086 | 0.440458 | 0.220229 | − | 0.975448i | \(-0.429319\pi\) | ||||
0.220229 | + | 0.975448i | \(0.429319\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −9.75603 | −0.590462 | ||||||||
\(274\) | 16.3204 | 0.985954 | ||||||||
\(275\) | −0.363919 | −0.0219451 | ||||||||
\(276\) | −4.79401 | −0.288565 | ||||||||
\(277\) | 12.3108 | 0.739683 | 0.369841 | − | 0.929095i | \(-0.379412\pi\) | ||||
0.369841 | + | 0.929095i | \(0.379412\pi\) | |||||||
\(278\) | −1.77264 | −0.106316 | ||||||||
\(279\) | 6.38640 | 0.382344 | ||||||||
\(280\) | 7.11622 | 0.425275 | ||||||||
\(281\) | −22.8921 | −1.36563 | −0.682813 | − | 0.730593i | \(-0.739244\pi\) | ||||
−0.682813 | + | 0.730593i | \(0.739244\pi\) | |||||||
\(282\) | −12.0456 | −0.717306 | ||||||||
\(283\) | 0.128131 | 0.00761662 | 0.00380831 | − | 0.999993i | \(-0.498788\pi\) | ||||
0.00380831 | + | 0.999993i | \(0.498788\pi\) | |||||||
\(284\) | 7.07215 | 0.419655 | ||||||||
\(285\) | −7.68591 | −0.455274 | ||||||||
\(286\) | −0.869046 | −0.0513878 | ||||||||
\(287\) | −5.64185 | −0.333028 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.39410 | 0.0818641 | ||||||||
\(291\) | 2.11803 | 0.124161 | ||||||||
\(292\) | 3.18832 | 0.186582 | ||||||||
\(293\) | −21.9385 | −1.28166 | −0.640830 | − | 0.767683i | \(-0.721410\pi\) | ||||
−0.640830 | + | 0.767683i | \(0.721410\pi\) | |||||||
\(294\) | −6.08358 | −0.354802 | ||||||||
\(295\) | −1.96737 | −0.114545 | ||||||||
\(296\) | 8.47640 | 0.492681 | ||||||||
\(297\) | 0.322205 | 0.0186963 | ||||||||
\(298\) | 1.92331 | 0.111414 | ||||||||
\(299\) | −12.9303 | −0.747779 | ||||||||
\(300\) | −1.12946 | −0.0652095 | ||||||||
\(301\) | −36.5095 | −2.10437 | ||||||||
\(302\) | −19.1004 | −1.09911 | ||||||||
\(303\) | −3.31580 | −0.190488 | ||||||||
\(304\) | −3.90670 | −0.224064 | ||||||||
\(305\) | 21.1806 | 1.21280 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −12.9495 | −0.739066 | −0.369533 | − | 0.929218i | \(-0.620482\pi\) | ||||
−0.369533 | + | 0.929218i | \(0.620482\pi\) | |||||||
\(308\) | −1.16546 | −0.0664081 | ||||||||
\(309\) | −5.84405 | −0.332456 | ||||||||
\(310\) | −12.5644 | −0.713611 | ||||||||
\(311\) | 26.8328 | 1.52155 | 0.760774 | − | 0.649017i | \(-0.224820\pi\) | ||||
0.760774 | + | 0.649017i | \(0.224820\pi\) | |||||||
\(312\) | −2.69718 | −0.152698 | ||||||||
\(313\) | −16.8957 | −0.955001 | −0.477501 | − | 0.878631i | \(-0.658457\pi\) | ||||
−0.477501 | + | 0.878631i | \(0.658457\pi\) | |||||||
\(314\) | 3.76548 | 0.212499 | ||||||||
\(315\) | −7.11622 | −0.400953 | ||||||||
\(316\) | −0.0479121 | −0.00269526 | ||||||||
\(317\) | 21.1631 | 1.18864 | 0.594318 | − | 0.804230i | \(-0.297422\pi\) | ||||
0.594318 | + | 0.804230i | \(0.297422\pi\) | |||||||
\(318\) | 1.01479 | 0.0569068 | ||||||||
\(319\) | −0.228318 | −0.0127833 | ||||||||
\(320\) | 1.96737 | 0.109979 | ||||||||
\(321\) | 15.5098 | 0.865672 | ||||||||
\(322\) | −17.3405 | −0.966350 | ||||||||
\(323\) | 3.90670 | 0.217374 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.04636 | −0.168982 | ||||||||
\(326\) | 4.05277 | 0.224462 | ||||||||
\(327\) | 6.44376 | 0.356341 | ||||||||
\(328\) | −1.55976 | −0.0861235 | ||||||||
\(329\) | −43.5705 | −2.40212 | ||||||||
\(330\) | −0.633897 | −0.0348949 | ||||||||
\(331\) | −27.4693 | −1.50985 | −0.754924 | − | 0.655812i | \(-0.772326\pi\) | ||||
−0.754924 | + | 0.655812i | \(0.772326\pi\) | |||||||
\(332\) | 0.102752 | 0.00563922 | ||||||||
\(333\) | −8.47640 | −0.464504 | ||||||||
\(334\) | −8.12354 | −0.444500 | ||||||||
\(335\) | 24.1401 | 1.31891 | ||||||||
\(336\) | −3.61712 | −0.197330 | ||||||||
\(337\) | −12.5651 | −0.684465 | −0.342232 | − | 0.939615i | \(-0.611183\pi\) | ||||
−0.342232 | + | 0.939615i | \(0.611183\pi\) | |||||||
\(338\) | 5.72522 | 0.311411 | ||||||||
\(339\) | 15.0555 | 0.817705 | ||||||||
\(340\) | −1.96737 | −0.106696 | ||||||||
\(341\) | 2.05773 | 0.111433 | ||||||||
\(342\) | 3.90670 | 0.211250 | ||||||||
\(343\) | 3.31479 | 0.178982 | ||||||||
\(344\) | −10.0935 | −0.544206 | ||||||||
\(345\) | −9.43158 | −0.507779 | ||||||||
\(346\) | −12.3655 | −0.664775 | ||||||||
\(347\) | −7.80090 | −0.418774 | −0.209387 | − | 0.977833i | \(-0.567147\pi\) | ||||
−0.209387 | + | 0.977833i | \(0.567147\pi\) | |||||||
\(348\) | −0.708609 | −0.0379854 | ||||||||
\(349\) | −25.2540 | −1.35181 | −0.675907 | − | 0.736987i | \(-0.736248\pi\) | ||||
−0.675907 | + | 0.736987i | \(0.736248\pi\) | |||||||
\(350\) | −4.08540 | −0.218374 | ||||||||
\(351\) | 2.69718 | 0.143965 | ||||||||
\(352\) | −0.322205 | −0.0171736 | ||||||||
\(353\) | 4.56034 | 0.242722 | 0.121361 | − | 0.992608i | \(-0.461274\pi\) | ||||
0.121361 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 13.9135 | 0.738454 | ||||||||
\(356\) | 3.15216 | 0.167064 | ||||||||
\(357\) | 3.61712 | 0.191438 | ||||||||
\(358\) | −16.6961 | −0.882417 | ||||||||
\(359\) | 14.4272 | 0.761436 | 0.380718 | − | 0.924691i | \(-0.375677\pi\) | ||||
0.380718 | + | 0.924691i | \(0.375677\pi\) | |||||||
\(360\) | −1.96737 | −0.103689 | ||||||||
\(361\) | −3.73771 | −0.196722 | ||||||||
\(362\) | 26.2946 | 1.38202 | ||||||||
\(363\) | −10.8962 | −0.571901 | ||||||||
\(364\) | −9.75603 | −0.511355 | ||||||||
\(365\) | 6.27259 | 0.328322 | ||||||||
\(366\) | −10.7660 | −0.562746 | ||||||||
\(367\) | −24.9628 | −1.30305 | −0.651525 | − | 0.758628i | \(-0.725870\pi\) | ||||
−0.651525 | + | 0.758628i | \(0.725870\pi\) | |||||||
\(368\) | −4.79401 | −0.249905 | ||||||||
\(369\) | 1.55976 | 0.0811980 | ||||||||
\(370\) | 16.6762 | 0.866954 | ||||||||
\(371\) | 3.67063 | 0.190570 | ||||||||
\(372\) | 6.38640 | 0.331120 | ||||||||
\(373\) | 4.05351 | 0.209883 | 0.104941 | − | 0.994478i | \(-0.466535\pi\) | ||||
0.104941 | + | 0.994478i | \(0.466535\pi\) | |||||||
\(374\) | 0.322205 | 0.0166608 | ||||||||
\(375\) | −12.0589 | −0.622719 | ||||||||
\(376\) | −12.0456 | −0.621205 | ||||||||
\(377\) | −1.91125 | −0.0984342 | ||||||||
\(378\) | 3.61712 | 0.186045 | ||||||||
\(379\) | 2.67315 | 0.137310 | 0.0686552 | − | 0.997640i | \(-0.478129\pi\) | ||||
0.0686552 | + | 0.997640i | \(0.478129\pi\) | |||||||
\(380\) | −7.68591 | −0.394279 | ||||||||
\(381\) | 19.4634 | 0.997141 | ||||||||
\(382\) | −5.70129 | −0.291703 | ||||||||
\(383\) | 12.6525 | 0.646512 | 0.323256 | − | 0.946312i | \(-0.395223\pi\) | ||||
0.323256 | + | 0.946312i | \(0.395223\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.29288 | −0.116856 | ||||||||
\(386\) | −6.01143 | −0.305974 | ||||||||
\(387\) | 10.0935 | 0.513082 | ||||||||
\(388\) | 2.11803 | 0.107527 | ||||||||
\(389\) | 19.4285 | 0.985066 | 0.492533 | − | 0.870294i | \(-0.336071\pi\) | ||||
0.492533 | + | 0.870294i | \(0.336071\pi\) | |||||||
\(390\) | −5.30635 | −0.268697 | ||||||||
\(391\) | 4.79401 | 0.242443 | ||||||||
\(392\) | −6.08358 | −0.307267 | ||||||||
\(393\) | −6.93292 | −0.349720 | ||||||||
\(394\) | −8.44024 | −0.425213 | ||||||||
\(395\) | −0.0942607 | −0.00474277 | ||||||||
\(396\) | 0.322205 | 0.0161914 | ||||||||
\(397\) | −12.0808 | −0.606318 | −0.303159 | − | 0.952940i | \(-0.598041\pi\) | ||||
−0.303159 | + | 0.952940i | \(0.598041\pi\) | |||||||
\(398\) | 10.3059 | 0.516586 | ||||||||
\(399\) | 14.1310 | 0.707435 | ||||||||
\(400\) | −1.12946 | −0.0564731 | ||||||||
\(401\) | −6.06618 | −0.302930 | −0.151465 | − | 0.988463i | \(-0.548399\pi\) | ||||
−0.151465 | + | 0.988463i | \(0.548399\pi\) | |||||||
\(402\) | −12.2702 | −0.611984 | ||||||||
\(403\) | 17.2253 | 0.858052 | ||||||||
\(404\) | −3.31580 | −0.164967 | ||||||||
\(405\) | 1.96737 | 0.0977593 | ||||||||
\(406\) | −2.56313 | −0.127206 | ||||||||
\(407\) | −2.73114 | −0.135378 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 29.2302 | 1.44534 | 0.722670 | − | 0.691194i | \(-0.242915\pi\) | ||||
0.722670 | + | 0.691194i | \(0.242915\pi\) | |||||||
\(410\) | −3.06863 | −0.151549 | ||||||||
\(411\) | −16.3204 | −0.805028 | ||||||||
\(412\) | −5.84405 | −0.287916 | ||||||||
\(413\) | 3.61712 | 0.177987 | ||||||||
\(414\) | 4.79401 | 0.235613 | ||||||||
\(415\) | 0.202150 | 0.00992316 | ||||||||
\(416\) | −2.69718 | −0.132240 | ||||||||
\(417\) | 1.77264 | 0.0868068 | ||||||||
\(418\) | 1.25876 | 0.0615679 | ||||||||
\(419\) | 7.51927 | 0.367341 | 0.183670 | − | 0.982988i | \(-0.441202\pi\) | ||||
0.183670 | + | 0.982988i | \(0.441202\pi\) | |||||||
\(420\) | −7.11622 | −0.347236 | ||||||||
\(421\) | −4.10410 | −0.200022 | −0.100011 | − | 0.994986i | \(-0.531888\pi\) | ||||
−0.100011 | + | 0.994986i | \(0.531888\pi\) | |||||||
\(422\) | 8.45060 | 0.411369 | ||||||||
\(423\) | 12.0456 | 0.585678 | ||||||||
\(424\) | 1.01479 | 0.0492827 | ||||||||
\(425\) | 1.12946 | 0.0547869 | ||||||||
\(426\) | −7.07215 | −0.342647 | ||||||||
\(427\) | −38.9418 | −1.88453 | ||||||||
\(428\) | 15.5098 | 0.749694 | ||||||||
\(429\) | 0.869046 | 0.0419579 | ||||||||
\(430\) | −19.8577 | −0.957622 | ||||||||
\(431\) | −25.4463 | −1.22571 | −0.612853 | − | 0.790197i | \(-0.709978\pi\) | ||||
−0.612853 | + | 0.790197i | \(0.709978\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 26.8467 | 1.29017 | 0.645086 | − | 0.764110i | \(-0.276822\pi\) | ||||
0.645086 | + | 0.764110i | \(0.276822\pi\) | |||||||
\(434\) | 23.1004 | 1.10886 | ||||||||
\(435\) | −1.39410 | −0.0668418 | ||||||||
\(436\) | 6.44376 | 0.308600 | ||||||||
\(437\) | 18.7287 | 0.895917 | ||||||||
\(438\) | −3.18832 | −0.152344 | ||||||||
\(439\) | −2.80058 | −0.133664 | −0.0668322 | − | 0.997764i | \(-0.521289\pi\) | ||||
−0.0668322 | + | 0.997764i | \(0.521289\pi\) | |||||||
\(440\) | −0.633897 | −0.0302198 | ||||||||
\(441\) | 6.08358 | 0.289694 | ||||||||
\(442\) | 2.69718 | 0.128292 | ||||||||
\(443\) | −11.2291 | −0.533509 | −0.266755 | − | 0.963765i | \(-0.585951\pi\) | ||||
−0.266755 | + | 0.963765i | \(0.585951\pi\) | |||||||
\(444\) | −8.47640 | −0.402272 | ||||||||
\(445\) | 6.20145 | 0.293977 | ||||||||
\(446\) | −23.4257 | −1.10924 | ||||||||
\(447\) | −1.92331 | −0.0909693 | ||||||||
\(448\) | −3.61712 | −0.170893 | ||||||||
\(449\) | −5.64645 | −0.266472 | −0.133236 | − | 0.991084i | \(-0.542537\pi\) | ||||
−0.133236 | + | 0.991084i | \(0.542537\pi\) | |||||||
\(450\) | 1.12946 | 0.0532433 | ||||||||
\(451\) | 0.502564 | 0.0236648 | ||||||||
\(452\) | 15.0555 | 0.708153 | ||||||||
\(453\) | 19.1004 | 0.897416 | ||||||||
\(454\) | −23.5348 | −1.10454 | ||||||||
\(455\) | −19.1937 | −0.899815 | ||||||||
\(456\) | 3.90670 | 0.182948 | ||||||||
\(457\) | −25.8898 | −1.21108 | −0.605538 | − | 0.795817i | \(-0.707042\pi\) | ||||
−0.605538 | + | 0.795817i | \(0.707042\pi\) | |||||||
\(458\) | 29.8732 | 1.39588 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −9.43158 | −0.439750 | ||||||||
\(461\) | −12.3982 | −0.577440 | −0.288720 | − | 0.957414i | \(-0.593230\pi\) | ||||
−0.288720 | + | 0.957414i | \(0.593230\pi\) | |||||||
\(462\) | 1.16546 | 0.0542220 | ||||||||
\(463\) | −23.5345 | −1.09374 | −0.546871 | − | 0.837217i | \(-0.684181\pi\) | ||||
−0.546871 | + | 0.837217i | \(0.684181\pi\) | |||||||
\(464\) | −0.708609 | −0.0328964 | ||||||||
\(465\) | 12.5644 | 0.582661 | ||||||||
\(466\) | −13.5825 | −0.629198 | ||||||||
\(467\) | 13.3905 | 0.619637 | 0.309818 | − | 0.950796i | \(-0.399732\pi\) | ||||
0.309818 | + | 0.950796i | \(0.399732\pi\) | |||||||
\(468\) | 2.69718 | 0.124677 | ||||||||
\(469\) | −44.3830 | −2.04942 | ||||||||
\(470\) | −23.6981 | −1.09311 | ||||||||
\(471\) | −3.76548 | −0.173504 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 3.25219 | 0.149536 | ||||||||
\(474\) | 0.0479121 | 0.00220067 | ||||||||
\(475\) | 4.41246 | 0.202458 | ||||||||
\(476\) | 3.61712 | 0.165791 | ||||||||
\(477\) | −1.01479 | −0.0464642 | ||||||||
\(478\) | −5.64131 | −0.258028 | ||||||||
\(479\) | 26.8921 | 1.22873 | 0.614365 | − | 0.789022i | \(-0.289412\pi\) | ||||
0.614365 | + | 0.789022i | \(0.289412\pi\) | |||||||
\(480\) | −1.96737 | −0.0897977 | ||||||||
\(481\) | −22.8624 | −1.04243 | ||||||||
\(482\) | −22.6870 | −1.03336 | ||||||||
\(483\) | 17.3405 | 0.789021 | ||||||||
\(484\) | −10.8962 | −0.495281 | ||||||||
\(485\) | 4.16695 | 0.189211 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −16.0458 | −0.727106 | −0.363553 | − | 0.931574i | \(-0.618436\pi\) | ||||
−0.363553 | + | 0.931574i | \(0.618436\pi\) | |||||||
\(488\) | −10.7660 | −0.487353 | ||||||||
\(489\) | −4.05277 | −0.183273 | ||||||||
\(490\) | −11.9687 | −0.540689 | ||||||||
\(491\) | 33.1658 | 1.49675 | 0.748377 | − | 0.663274i | \(-0.230833\pi\) | ||||
0.748377 | + | 0.663274i | \(0.230833\pi\) | |||||||
\(492\) | 1.55976 | 0.0703195 | ||||||||
\(493\) | 0.708609 | 0.0319141 | ||||||||
\(494\) | 10.5371 | 0.474085 | ||||||||
\(495\) | 0.633897 | 0.0284915 | ||||||||
\(496\) | 6.38640 | 0.286758 | ||||||||
\(497\) | −25.5809 | −1.14746 | ||||||||
\(498\) | −0.102752 | −0.00460441 | ||||||||
\(499\) | −19.1598 | −0.857712 | −0.428856 | − | 0.903373i | \(-0.641083\pi\) | ||||
−0.428856 | + | 0.903373i | \(0.641083\pi\) | |||||||
\(500\) | −12.0589 | −0.539291 | ||||||||
\(501\) | 8.12354 | 0.362933 | ||||||||
\(502\) | 6.93425 | 0.309491 | ||||||||
\(503\) | 5.88667 | 0.262474 | 0.131237 | − | 0.991351i | \(-0.458105\pi\) | ||||
0.131237 | + | 0.991351i | \(0.458105\pi\) | |||||||
\(504\) | 3.61712 | 0.161119 | ||||||||
\(505\) | −6.52339 | −0.290287 | ||||||||
\(506\) | 1.54466 | 0.0686683 | ||||||||
\(507\) | −5.72522 | −0.254266 | ||||||||
\(508\) | 19.4634 | 0.863549 | ||||||||
\(509\) | −18.1966 | −0.806550 | −0.403275 | − | 0.915079i | \(-0.632128\pi\) | ||||
−0.403275 | + | 0.915079i | \(0.632128\pi\) | |||||||
\(510\) | 1.96737 | 0.0871165 | ||||||||
\(511\) | −11.5325 | −0.510169 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.90670 | −0.172485 | ||||||||
\(514\) | −9.25097 | −0.408043 | ||||||||
\(515\) | −11.4974 | −0.506636 | ||||||||
\(516\) | 10.0935 | 0.444342 | ||||||||
\(517\) | 3.88116 | 0.170693 | ||||||||
\(518\) | −30.6602 | −1.34713 | ||||||||
\(519\) | 12.3655 | 0.542786 | ||||||||
\(520\) | −5.30635 | −0.232699 | ||||||||
\(521\) | 35.2454 | 1.54413 | 0.772064 | − | 0.635545i | \(-0.219225\pi\) | ||||
0.772064 | + | 0.635545i | \(0.219225\pi\) | |||||||
\(522\) | 0.708609 | 0.0310150 | ||||||||
\(523\) | −13.7504 | −0.601265 | −0.300632 | − | 0.953740i | \(-0.597198\pi\) | ||||
−0.300632 | + | 0.953740i | \(0.597198\pi\) | |||||||
\(524\) | −6.93292 | −0.302866 | ||||||||
\(525\) | 4.08540 | 0.178302 | ||||||||
\(526\) | 1.77066 | 0.0772046 | ||||||||
\(527\) | −6.38640 | −0.278196 | ||||||||
\(528\) | 0.322205 | 0.0140222 | ||||||||
\(529\) | −0.0174704 | −0.000759583 0 | ||||||||
\(530\) | 1.99647 | 0.0867212 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 14.1310 | 0.612657 | ||||||||
\(533\) | 4.20696 | 0.182224 | ||||||||
\(534\) | −3.15216 | −0.136407 | ||||||||
\(535\) | 30.5135 | 1.31921 | ||||||||
\(536\) | −12.2702 | −0.529994 | ||||||||
\(537\) | 16.6961 | 0.720491 | ||||||||
\(538\) | −1.30106 | −0.0560926 | ||||||||
\(539\) | 1.96016 | 0.0844302 | ||||||||
\(540\) | 1.96737 | 0.0846621 | ||||||||
\(541\) | 23.7807 | 1.02241 | 0.511206 | − | 0.859459i | \(-0.329199\pi\) | ||||
0.511206 | + | 0.859459i | \(0.329199\pi\) | |||||||
\(542\) | −7.25086 | −0.311451 | ||||||||
\(543\) | −26.2946 | −1.12841 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 12.6773 | 0.543034 | ||||||||
\(546\) | 9.75603 | 0.417520 | ||||||||
\(547\) | 20.1274 | 0.860584 | 0.430292 | − | 0.902690i | \(-0.358411\pi\) | ||||
0.430292 | + | 0.902690i | \(0.358411\pi\) | |||||||
\(548\) | −16.3204 | −0.697175 | ||||||||
\(549\) | 10.7660 | 0.459480 | ||||||||
\(550\) | 0.363919 | 0.0155175 | ||||||||
\(551\) | 2.76832 | 0.117934 | ||||||||
\(552\) | 4.79401 | 0.204047 | ||||||||
\(553\) | 0.173304 | 0.00736963 | ||||||||
\(554\) | −12.3108 | −0.523035 | ||||||||
\(555\) | −16.6762 | −0.707865 | ||||||||
\(556\) | 1.77264 | 0.0751769 | ||||||||
\(557\) | −1.30667 | −0.0553654 | −0.0276827 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276827 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(558\) | −6.38640 | −0.270358 | ||||||||
\(559\) | 27.2240 | 1.15145 | ||||||||
\(560\) | −7.11622 | −0.300715 | ||||||||
\(561\) | −0.322205 | −0.0136035 | ||||||||
\(562\) | 22.8921 | 0.965643 | ||||||||
\(563\) | 32.0223 | 1.34958 | 0.674790 | − | 0.738010i | \(-0.264234\pi\) | ||||
0.674790 | + | 0.738010i | \(0.264234\pi\) | |||||||
\(564\) | 12.0456 | 0.507212 | ||||||||
\(565\) | 29.6198 | 1.24611 | ||||||||
\(566\) | −0.128131 | −0.00538576 | ||||||||
\(567\) | −3.61712 | −0.151905 | ||||||||
\(568\) | −7.07215 | −0.296741 | ||||||||
\(569\) | −30.1329 | −1.26324 | −0.631619 | − | 0.775279i | \(-0.717609\pi\) | ||||
−0.631619 | + | 0.775279i | \(0.717609\pi\) | |||||||
\(570\) | 7.68591 | 0.321928 | ||||||||
\(571\) | −27.7915 | −1.16304 | −0.581519 | − | 0.813533i | \(-0.697541\pi\) | ||||
−0.581519 | + | 0.813533i | \(0.697541\pi\) | |||||||
\(572\) | 0.869046 | 0.0363366 | ||||||||
\(573\) | 5.70129 | 0.238175 | ||||||||
\(574\) | 5.64185 | 0.235486 | ||||||||
\(575\) | 5.41465 | 0.225806 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.7594 | −0.780964 | −0.390482 | − | 0.920611i | \(-0.627692\pi\) | ||||
−0.390482 | + | 0.920611i | \(0.627692\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 6.01143 | 0.249826 | ||||||||
\(580\) | −1.39410 | −0.0578867 | ||||||||
\(581\) | −0.371665 | −0.0154193 | ||||||||
\(582\) | −2.11803 | −0.0877953 | ||||||||
\(583\) | −0.326972 | −0.0135418 | ||||||||
\(584\) | −3.18832 | −0.131933 | ||||||||
\(585\) | 5.30635 | 0.219390 | ||||||||
\(586\) | 21.9385 | 0.906270 | ||||||||
\(587\) | 22.0372 | 0.909572 | 0.454786 | − | 0.890601i | \(-0.349716\pi\) | ||||
0.454786 | + | 0.890601i | \(0.349716\pi\) | |||||||
\(588\) | 6.08358 | 0.250883 | ||||||||
\(589\) | −24.9497 | −1.02804 | ||||||||
\(590\) | 1.96737 | 0.0809953 | ||||||||
\(591\) | 8.44024 | 0.347185 | ||||||||
\(592\) | −8.47640 | −0.348378 | ||||||||
\(593\) | 31.9702 | 1.31286 | 0.656428 | − | 0.754388i | \(-0.272066\pi\) | ||||
0.656428 | + | 0.754388i | \(0.272066\pi\) | |||||||
\(594\) | −0.322205 | −0.0132203 | ||||||||
\(595\) | 7.11622 | 0.291736 | ||||||||
\(596\) | −1.92331 | −0.0787818 | ||||||||
\(597\) | −10.3059 | −0.421791 | ||||||||
\(598\) | 12.9303 | 0.528760 | ||||||||
\(599\) | 36.8990 | 1.50765 | 0.753825 | − | 0.657075i | \(-0.228206\pi\) | ||||
0.753825 | + | 0.657075i | \(0.228206\pi\) | |||||||
\(600\) | 1.12946 | 0.0461101 | ||||||||
\(601\) | 29.8024 | 1.21567 | 0.607833 | − | 0.794065i | \(-0.292039\pi\) | ||||
0.607833 | + | 0.794065i | \(0.292039\pi\) | |||||||
\(602\) | 36.5095 | 1.48802 | ||||||||
\(603\) | 12.2702 | 0.499683 | ||||||||
\(604\) | 19.1004 | 0.777185 | ||||||||
\(605\) | −21.4368 | −0.871530 | ||||||||
\(606\) | 3.31580 | 0.134695 | ||||||||
\(607\) | −5.56057 | −0.225697 | −0.112848 | − | 0.993612i | \(-0.535997\pi\) | ||||
−0.112848 | + | 0.993612i | \(0.535997\pi\) | |||||||
\(608\) | 3.90670 | 0.158438 | ||||||||
\(609\) | 2.56313 | 0.103863 | ||||||||
\(610\) | −21.1806 | −0.857579 | ||||||||
\(611\) | 32.4892 | 1.31437 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 42.5174 | 1.71726 | 0.858630 | − | 0.512596i | \(-0.171316\pi\) | ||||
0.858630 | + | 0.512596i | \(0.171316\pi\) | |||||||
\(614\) | 12.9495 | 0.522599 | ||||||||
\(615\) | 3.06863 | 0.123739 | ||||||||
\(616\) | 1.16546 | 0.0469576 | ||||||||
\(617\) | −9.21261 | −0.370886 | −0.185443 | − | 0.982655i | \(-0.559372\pi\) | ||||
−0.185443 | + | 0.982655i | \(0.559372\pi\) | |||||||
\(618\) | 5.84405 | 0.235082 | ||||||||
\(619\) | 18.2750 | 0.734534 | 0.367267 | − | 0.930116i | \(-0.380294\pi\) | ||||
0.367267 | + | 0.930116i | \(0.380294\pi\) | |||||||
\(620\) | 12.5644 | 0.504599 | ||||||||
\(621\) | −4.79401 | −0.192377 | ||||||||
\(622\) | −26.8328 | −1.07590 | ||||||||
\(623\) | −11.4017 | −0.456801 | ||||||||
\(624\) | 2.69718 | 0.107974 | ||||||||
\(625\) | −18.0770 | −0.723080 | ||||||||
\(626\) | 16.8957 | 0.675288 | ||||||||
\(627\) | −1.25876 | −0.0502700 | ||||||||
\(628\) | −3.76548 | −0.150259 | ||||||||
\(629\) | 8.47640 | 0.337976 | ||||||||
\(630\) | 7.11622 | 0.283517 | ||||||||
\(631\) | 18.4487 | 0.734430 | 0.367215 | − | 0.930136i | \(-0.380311\pi\) | ||||
0.367215 | + | 0.930136i | \(0.380311\pi\) | |||||||
\(632\) | 0.0479121 | 0.00190584 | ||||||||
\(633\) | −8.45060 | −0.335881 | ||||||||
\(634\) | −21.1631 | −0.840493 | ||||||||
\(635\) | 38.2917 | 1.51956 | ||||||||
\(636\) | −1.01479 | −0.0402392 | ||||||||
\(637\) | 16.4085 | 0.650129 | ||||||||
\(638\) | 0.228318 | 0.00903919 | ||||||||
\(639\) | 7.07215 | 0.279770 | ||||||||
\(640\) | −1.96737 | −0.0777671 | ||||||||
\(641\) | −18.0312 | −0.712189 | −0.356094 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356094 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(642\) | −15.5098 | −0.612122 | ||||||||
\(643\) | 17.6645 | 0.696620 | 0.348310 | − | 0.937379i | \(-0.386756\pi\) | ||||
0.348310 | + | 0.937379i | \(0.386756\pi\) | |||||||
\(644\) | 17.3405 | 0.683312 | ||||||||
\(645\) | 19.8577 | 0.781895 | ||||||||
\(646\) | −3.90670 | −0.153707 | ||||||||
\(647\) | −17.2650 | −0.678756 | −0.339378 | − | 0.940650i | \(-0.610217\pi\) | ||||
−0.339378 | + | 0.940650i | \(0.610217\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −0.322205 | −0.0126477 | ||||||||
\(650\) | 3.04636 | 0.119488 | ||||||||
\(651\) | −23.1004 | −0.905377 | ||||||||
\(652\) | −4.05277 | −0.158719 | ||||||||
\(653\) | 33.7022 | 1.31887 | 0.659435 | − | 0.751762i | \(-0.270796\pi\) | ||||
0.659435 | + | 0.751762i | \(0.270796\pi\) | |||||||
\(654\) | −6.44376 | −0.251971 | ||||||||
\(655\) | −13.6396 | −0.532944 | ||||||||
\(656\) | 1.55976 | 0.0608985 | ||||||||
\(657\) | 3.18832 | 0.124388 | ||||||||
\(658\) | 43.5705 | 1.69855 | ||||||||
\(659\) | −8.24578 | −0.321210 | −0.160605 | − | 0.987019i | \(-0.551345\pi\) | ||||
−0.160605 | + | 0.987019i | \(0.551345\pi\) | |||||||
\(660\) | 0.633897 | 0.0246744 | ||||||||
\(661\) | 34.8127 | 1.35406 | 0.677029 | − | 0.735957i | \(-0.263267\pi\) | ||||
0.677029 | + | 0.735957i | \(0.263267\pi\) | |||||||
\(662\) | 27.4693 | 1.06762 | ||||||||
\(663\) | −2.69718 | −0.104750 | ||||||||
\(664\) | −0.102752 | −0.00398753 | ||||||||
\(665\) | 27.8009 | 1.07807 | ||||||||
\(666\) | 8.47640 | 0.328454 | ||||||||
\(667\) | 3.39708 | 0.131535 | ||||||||
\(668\) | 8.12354 | 0.314309 | ||||||||
\(669\) | 23.4257 | 0.905688 | ||||||||
\(670\) | −24.1401 | −0.932613 | ||||||||
\(671\) | 3.46885 | 0.133914 | ||||||||
\(672\) | 3.61712 | 0.139534 | ||||||||
\(673\) | 41.1376 | 1.58574 | 0.792870 | − | 0.609391i | \(-0.208586\pi\) | ||||
0.792870 | + | 0.609391i | \(0.208586\pi\) | |||||||
\(674\) | 12.5651 | 0.483990 | ||||||||
\(675\) | −1.12946 | −0.0434730 | ||||||||
\(676\) | −5.72522 | −0.220201 | ||||||||
\(677\) | 6.78056 | 0.260598 | 0.130299 | − | 0.991475i | \(-0.458406\pi\) | ||||
0.130299 | + | 0.991475i | \(0.458406\pi\) | |||||||
\(678\) | −15.0555 | −0.578205 | ||||||||
\(679\) | −7.66118 | −0.294009 | ||||||||
\(680\) | 1.96737 | 0.0754451 | ||||||||
\(681\) | 23.5348 | 0.901856 | ||||||||
\(682\) | −2.05773 | −0.0787947 | ||||||||
\(683\) | 25.8919 | 0.990726 | 0.495363 | − | 0.868686i | \(-0.335035\pi\) | ||||
0.495363 | + | 0.868686i | \(0.335035\pi\) | |||||||
\(684\) | −3.90670 | −0.149376 | ||||||||
\(685\) | −32.1083 | −1.22680 | ||||||||
\(686\) | −3.31479 | −0.126559 | ||||||||
\(687\) | −29.8732 | −1.13973 | ||||||||
\(688\) | 10.0935 | 0.384812 | ||||||||
\(689\) | −2.73708 | −0.104274 | ||||||||
\(690\) | 9.43158 | 0.359054 | ||||||||
\(691\) | −34.2953 | −1.30465 | −0.652327 | − | 0.757937i | \(-0.726207\pi\) | ||||
−0.652327 | + | 0.757937i | \(0.726207\pi\) | |||||||
\(692\) | 12.3655 | 0.470067 | ||||||||
\(693\) | −1.16546 | −0.0442721 | ||||||||
\(694\) | 7.80090 | 0.296118 | ||||||||
\(695\) | 3.48744 | 0.132286 | ||||||||
\(696\) | 0.708609 | 0.0268598 | ||||||||
\(697\) | −1.55976 | −0.0590802 | ||||||||
\(698\) | 25.2540 | 0.955876 | ||||||||
\(699\) | 13.5825 | 0.513738 | ||||||||
\(700\) | 4.08540 | 0.154414 | ||||||||
\(701\) | −0.148640 | −0.00561407 | −0.00280704 | − | 0.999996i | \(-0.500894\pi\) | ||||
−0.00280704 | + | 0.999996i | \(0.500894\pi\) | |||||||
\(702\) | −2.69718 | −0.101799 | ||||||||
\(703\) | 33.1147 | 1.24895 | ||||||||
\(704\) | 0.322205 | 0.0121436 | ||||||||
\(705\) | 23.6981 | 0.892524 | ||||||||
\(706\) | −4.56034 | −0.171631 | ||||||||
\(707\) | 11.9936 | 0.451067 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −51.8127 | −1.94587 | −0.972933 | − | 0.231089i | \(-0.925771\pi\) | ||||
−0.972933 | + | 0.231089i | \(0.925771\pi\) | |||||||
\(710\) | −13.9135 | −0.522166 | ||||||||
\(711\) | −0.0479121 | −0.00179684 | ||||||||
\(712\) | −3.15216 | −0.118132 | ||||||||
\(713\) | −30.6165 | −1.14660 | ||||||||
\(714\) | −3.61712 | −0.135367 | ||||||||
\(715\) | 1.70973 | 0.0639404 | ||||||||
\(716\) | 16.6961 | 0.623963 | ||||||||
\(717\) | 5.64131 | 0.210679 | ||||||||
\(718\) | −14.4272 | −0.538417 | ||||||||
\(719\) | 40.7377 | 1.51926 | 0.759629 | − | 0.650356i | \(-0.225380\pi\) | ||||
0.759629 | + | 0.650356i | \(0.225380\pi\) | |||||||
\(720\) | 1.96737 | 0.0733195 | ||||||||
\(721\) | 21.1386 | 0.787244 | ||||||||
\(722\) | 3.73771 | 0.139103 | ||||||||
\(723\) | 22.6870 | 0.843738 | ||||||||
\(724\) | −26.2946 | −0.977233 | ||||||||
\(725\) | 0.800346 | 0.0297241 | ||||||||
\(726\) | 10.8962 | 0.404395 | ||||||||
\(727\) | −36.1177 | −1.33953 | −0.669766 | − | 0.742572i | \(-0.733606\pi\) | ||||
−0.669766 | + | 0.742572i | \(0.733606\pi\) | |||||||
\(728\) | 9.75603 | 0.361583 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.27259 | −0.232159 | ||||||||
\(731\) | −10.0935 | −0.373322 | ||||||||
\(732\) | 10.7660 | 0.397922 | ||||||||
\(733\) | 51.8615 | 1.91555 | 0.957774 | − | 0.287521i | \(-0.0928312\pi\) | ||||
0.957774 | + | 0.287521i | \(0.0928312\pi\) | |||||||
\(734\) | 24.9628 | 0.921395 | ||||||||
\(735\) | 11.9687 | 0.441470 | ||||||||
\(736\) | 4.79401 | 0.176710 | ||||||||
\(737\) | 3.95354 | 0.145631 | ||||||||
\(738\) | −1.55976 | −0.0574156 | ||||||||
\(739\) | −16.1912 | −0.595603 | −0.297801 | − | 0.954628i | \(-0.596253\pi\) | ||||
−0.297801 | + | 0.954628i | \(0.596253\pi\) | |||||||
\(740\) | −16.6762 | −0.613029 | ||||||||
\(741\) | −10.5371 | −0.387089 | ||||||||
\(742\) | −3.67063 | −0.134753 | ||||||||
\(743\) | 6.64667 | 0.243843 | 0.121921 | − | 0.992540i | \(-0.461094\pi\) | ||||
0.121921 | + | 0.992540i | \(0.461094\pi\) | |||||||
\(744\) | −6.38640 | −0.234137 | ||||||||
\(745\) | −3.78386 | −0.138630 | ||||||||
\(746\) | −4.05351 | −0.148410 | ||||||||
\(747\) | 0.102752 | 0.00375948 | ||||||||
\(748\) | −0.322205 | −0.0117810 | ||||||||
\(749\) | −56.1008 | −2.04988 | ||||||||
\(750\) | 12.0589 | 0.440329 | ||||||||
\(751\) | −15.5930 | −0.568995 | −0.284498 | − | 0.958677i | \(-0.591827\pi\) | ||||
−0.284498 | + | 0.958677i | \(0.591827\pi\) | |||||||
\(752\) | 12.0456 | 0.439258 | ||||||||
\(753\) | −6.93425 | −0.252698 | ||||||||
\(754\) | 1.91125 | 0.0696035 | ||||||||
\(755\) | 37.5775 | 1.36759 | ||||||||
\(756\) | −3.61712 | −0.131554 | ||||||||
\(757\) | 13.4225 | 0.487849 | 0.243924 | − | 0.969794i | \(-0.421565\pi\) | ||||
0.243924 | + | 0.969794i | \(0.421565\pi\) | |||||||
\(758\) | −2.67315 | −0.0970931 | ||||||||
\(759\) | −1.54466 | −0.0560675 | ||||||||
\(760\) | 7.68591 | 0.278797 | ||||||||
\(761\) | −2.63485 | −0.0955134 | −0.0477567 | − | 0.998859i | \(-0.515207\pi\) | ||||
−0.0477567 | + | 0.998859i | \(0.515207\pi\) | |||||||
\(762\) | −19.4634 | −0.705085 | ||||||||
\(763\) | −23.3079 | −0.843802 | ||||||||
\(764\) | 5.70129 | 0.206265 | ||||||||
\(765\) | −1.96737 | −0.0711304 | ||||||||
\(766\) | −12.6525 | −0.457153 | ||||||||
\(767\) | −2.69718 | −0.0973895 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −47.1868 | −1.70160 | −0.850799 | − | 0.525491i | \(-0.823882\pi\) | ||||
−0.850799 | + | 0.525491i | \(0.823882\pi\) | |||||||
\(770\) | 2.29288 | 0.0826298 | ||||||||
\(771\) | 9.25097 | 0.333165 | ||||||||
\(772\) | 6.01143 | 0.216356 | ||||||||
\(773\) | −28.2857 | −1.01737 | −0.508683 | − | 0.860954i | \(-0.669867\pi\) | ||||
−0.508683 | + | 0.860954i | \(0.669867\pi\) | |||||||
\(774\) | −10.0935 | −0.362804 | ||||||||
\(775\) | −7.21319 | −0.259106 | ||||||||
\(776\) | −2.11803 | −0.0760329 | ||||||||
\(777\) | 30.6602 | 1.09993 | ||||||||
\(778\) | −19.4285 | −0.696547 | ||||||||
\(779\) | −6.09352 | −0.218323 | ||||||||
\(780\) | 5.30635 | 0.189998 | ||||||||
\(781\) | 2.27869 | 0.0815378 | ||||||||
\(782\) | −4.79401 | −0.171433 | ||||||||
\(783\) | −0.708609 | −0.0253236 | ||||||||
\(784\) | 6.08358 | 0.217271 | ||||||||
\(785\) | −7.40809 | −0.264406 | ||||||||
\(786\) | 6.93292 | 0.247289 | ||||||||
\(787\) | 17.4523 | 0.622108 | 0.311054 | − | 0.950392i | \(-0.399318\pi\) | ||||
0.311054 | + | 0.950392i | \(0.399318\pi\) | |||||||
\(788\) | 8.44024 | 0.300671 | ||||||||
\(789\) | −1.77066 | −0.0630373 | ||||||||
\(790\) | 0.0942607 | 0.00335364 | ||||||||
\(791\) | −54.4578 | −1.93630 | ||||||||
\(792\) | −0.322205 | −0.0114491 | ||||||||
\(793\) | 29.0378 | 1.03116 | ||||||||
\(794\) | 12.0808 | 0.428732 | ||||||||
\(795\) | −1.99647 | −0.0708076 | ||||||||
\(796\) | −10.3059 | −0.365282 | ||||||||
\(797\) | −29.7203 | −1.05275 | −0.526373 | − | 0.850254i | \(-0.676448\pi\) | ||||
−0.526373 | + | 0.850254i | \(0.676448\pi\) | |||||||
\(798\) | −14.1310 | −0.500232 | ||||||||
\(799\) | −12.0456 | −0.426143 | ||||||||
\(800\) | 1.12946 | 0.0399325 | ||||||||
\(801\) | 3.15216 | 0.111376 | ||||||||
\(802\) | 6.06618 | 0.214204 | ||||||||
\(803\) | 1.02729 | 0.0362524 | ||||||||
\(804\) | 12.2702 | 0.432738 | ||||||||
\(805\) | 34.1152 | 1.20240 | ||||||||
\(806\) | −17.2253 | −0.606735 | ||||||||
\(807\) | 1.30106 | 0.0457994 | ||||||||
\(808\) | 3.31580 | 0.116649 | ||||||||
\(809\) | −19.9190 | −0.700314 | −0.350157 | − | 0.936691i | \(-0.613872\pi\) | ||||
−0.350157 | + | 0.936691i | \(0.613872\pi\) | |||||||
\(810\) | −1.96737 | −0.0691263 | ||||||||
\(811\) | 35.6195 | 1.25077 | 0.625385 | − | 0.780316i | \(-0.284942\pi\) | ||||
0.625385 | + | 0.780316i | \(0.284942\pi\) | |||||||
\(812\) | 2.56313 | 0.0899481 | ||||||||
\(813\) | 7.25086 | 0.254299 | ||||||||
\(814\) | 2.73114 | 0.0957265 | ||||||||
\(815\) | −7.97329 | −0.279292 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −39.4323 | −1.37956 | ||||||||
\(818\) | −29.2302 | −1.02201 | ||||||||
\(819\) | −9.75603 | −0.340903 | ||||||||
\(820\) | 3.06863 | 0.107161 | ||||||||
\(821\) | 35.0511 | 1.22329 | 0.611646 | − | 0.791131i | \(-0.290508\pi\) | ||||
0.611646 | + | 0.791131i | \(0.290508\pi\) | |||||||
\(822\) | 16.3204 | 0.569241 | ||||||||
\(823\) | 5.80101 | 0.202210 | 0.101105 | − | 0.994876i | \(-0.467762\pi\) | ||||
0.101105 | + | 0.994876i | \(0.467762\pi\) | |||||||
\(824\) | 5.84405 | 0.203587 | ||||||||
\(825\) | −0.363919 | −0.0126700 | ||||||||
\(826\) | −3.61712 | −0.125856 | ||||||||
\(827\) | −44.0917 | −1.53322 | −0.766608 | − | 0.642115i | \(-0.778057\pi\) | ||||
−0.766608 | + | 0.642115i | \(0.778057\pi\) | |||||||
\(828\) | −4.79401 | −0.166603 | ||||||||
\(829\) | 7.17727 | 0.249277 | 0.124638 | − | 0.992202i | \(-0.460223\pi\) | ||||
0.124638 | + | 0.992202i | \(0.460223\pi\) | |||||||
\(830\) | −0.202150 | −0.00701674 | ||||||||
\(831\) | 12.3108 | 0.427056 | ||||||||
\(832\) | 2.69718 | 0.0935079 | ||||||||
\(833\) | −6.08358 | −0.210784 | ||||||||
\(834\) | −1.77264 | −0.0613817 | ||||||||
\(835\) | 15.9820 | 0.553080 | ||||||||
\(836\) | −1.25876 | −0.0435351 | ||||||||
\(837\) | 6.38640 | 0.220746 | ||||||||
\(838\) | −7.51927 | −0.259749 | ||||||||
\(839\) | −7.56212 | −0.261073 | −0.130537 | − | 0.991443i | \(-0.541670\pi\) | ||||
−0.130537 | + | 0.991443i | \(0.541670\pi\) | |||||||
\(840\) | 7.11622 | 0.245533 | ||||||||
\(841\) | −28.4979 | −0.982685 | ||||||||
\(842\) | 4.10410 | 0.141437 | ||||||||
\(843\) | −22.8921 | −0.788445 | ||||||||
\(844\) | −8.45060 | −0.290882 | ||||||||
\(845\) | −11.2636 | −0.387480 | ||||||||
\(846\) | −12.0456 | −0.414137 | ||||||||
\(847\) | 39.4128 | 1.35424 | ||||||||
\(848\) | −1.01479 | −0.0348482 | ||||||||
\(849\) | 0.128131 | 0.00439746 | ||||||||
\(850\) | −1.12946 | −0.0387402 | ||||||||
\(851\) | 40.6359 | 1.39298 | ||||||||
\(852\) | 7.07215 | 0.242288 | ||||||||
\(853\) | −4.18783 | −0.143388 | −0.0716942 | − | 0.997427i | \(-0.522841\pi\) | ||||
−0.0716942 | + | 0.997427i | \(0.522841\pi\) | |||||||
\(854\) | 38.9418 | 1.33256 | ||||||||
\(855\) | −7.68591 | −0.262853 | ||||||||
\(856\) | −15.5098 | −0.530113 | ||||||||
\(857\) | 26.8730 | 0.917965 | 0.458982 | − | 0.888445i | \(-0.348214\pi\) | ||||
0.458982 | + | 0.888445i | \(0.348214\pi\) | |||||||
\(858\) | −0.869046 | −0.0296687 | ||||||||
\(859\) | 18.3419 | 0.625816 | 0.312908 | − | 0.949783i | \(-0.398697\pi\) | ||||
0.312908 | + | 0.949783i | \(0.398697\pi\) | |||||||
\(860\) | 19.8577 | 0.677141 | ||||||||
\(861\) | −5.64185 | −0.192274 | ||||||||
\(862\) | 25.4463 | 0.866705 | ||||||||
\(863\) | −48.6135 | −1.65482 | −0.827411 | − | 0.561597i | \(-0.810187\pi\) | ||||
−0.827411 | + | 0.561597i | \(0.810187\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 24.3275 | 0.827161 | ||||||||
\(866\) | −26.8467 | −0.912289 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −23.1004 | −0.784079 | ||||||||
\(869\) | −0.0154375 | −0.000523682 0 | ||||||||
\(870\) | 1.39410 | 0.0472643 | ||||||||
\(871\) | 33.0951 | 1.12138 | ||||||||
\(872\) | −6.44376 | −0.218213 | ||||||||
\(873\) | 2.11803 | 0.0716845 | ||||||||
\(874\) | −18.7287 | −0.633509 | ||||||||
\(875\) | 43.6186 | 1.47458 | ||||||||
\(876\) | 3.18832 | 0.107723 | ||||||||
\(877\) | −0.851478 | −0.0287524 | −0.0143762 | − | 0.999897i | \(-0.504576\pi\) | ||||
−0.0143762 | + | 0.999897i | \(0.504576\pi\) | |||||||
\(878\) | 2.80058 | 0.0945151 | ||||||||
\(879\) | −21.9385 | −0.739967 | ||||||||
\(880\) | 0.633897 | 0.0213687 | ||||||||
\(881\) | 36.3285 | 1.22394 | 0.611969 | − | 0.790881i | \(-0.290378\pi\) | ||||
0.611969 | + | 0.790881i | \(0.290378\pi\) | |||||||
\(882\) | −6.08358 | −0.204845 | ||||||||
\(883\) | −56.4060 | −1.89821 | −0.949107 | − | 0.314955i | \(-0.898011\pi\) | ||||
−0.949107 | + | 0.314955i | \(0.898011\pi\) | |||||||
\(884\) | −2.69718 | −0.0907160 | ||||||||
\(885\) | −1.96737 | −0.0661324 | ||||||||
\(886\) | 11.2291 | 0.377248 | ||||||||
\(887\) | 31.0751 | 1.04340 | 0.521701 | − | 0.853129i | \(-0.325298\pi\) | ||||
0.521701 | + | 0.853129i | \(0.325298\pi\) | |||||||
\(888\) | 8.47640 | 0.284449 | ||||||||
\(889\) | −70.4016 | −2.36119 | ||||||||
\(890\) | −6.20145 | −0.207873 | ||||||||
\(891\) | 0.322205 | 0.0107943 | ||||||||
\(892\) | 23.4257 | 0.784349 | ||||||||
\(893\) | −47.0585 | −1.57475 | ||||||||
\(894\) | 1.92331 | 0.0643250 | ||||||||
\(895\) | 32.8474 | 1.09797 | ||||||||
\(896\) | 3.61712 | 0.120840 | ||||||||
\(897\) | −12.9303 | −0.431730 | ||||||||
\(898\) | 5.64645 | 0.188424 | ||||||||
\(899\) | −4.52546 | −0.150933 | ||||||||
\(900\) | −1.12946 | −0.0376487 | ||||||||
\(901\) | 1.01479 | 0.0338077 | ||||||||
\(902\) | −0.502564 | −0.0167336 | ||||||||
\(903\) | −36.5095 | −1.21496 | ||||||||
\(904\) | −15.0555 | −0.500740 | ||||||||
\(905\) | −51.7313 | −1.71961 | ||||||||
\(906\) | −19.1004 | −0.634569 | ||||||||
\(907\) | −55.9171 | −1.85670 | −0.928349 | − | 0.371711i | \(-0.878771\pi\) | ||||
−0.928349 | + | 0.371711i | \(0.878771\pi\) | |||||||
\(908\) | 23.5348 | 0.781030 | ||||||||
\(909\) | −3.31580 | −0.109978 | ||||||||
\(910\) | 19.1937 | 0.636265 | ||||||||
\(911\) | −41.9901 | −1.39119 | −0.695597 | − | 0.718433i | \(-0.744860\pi\) | ||||
−0.695597 | + | 0.718433i | \(0.744860\pi\) | |||||||
\(912\) | −3.90670 | −0.129364 | ||||||||
\(913\) | 0.0331071 | 0.00109569 | ||||||||
\(914\) | 25.8898 | 0.856359 | ||||||||
\(915\) | 21.1806 | 0.700210 | ||||||||
\(916\) | −29.8732 | −0.987039 | ||||||||
\(917\) | 25.0772 | 0.828123 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −38.2639 | −1.26221 | −0.631106 | − | 0.775697i | \(-0.717399\pi\) | ||||
−0.631106 | + | 0.775697i | \(0.717399\pi\) | |||||||
\(920\) | 9.43158 | 0.310950 | ||||||||
\(921\) | −12.9495 | −0.426700 | ||||||||
\(922\) | 12.3982 | 0.408312 | ||||||||
\(923\) | 19.0749 | 0.627857 | ||||||||
\(924\) | −1.16546 | −0.0383407 | ||||||||
\(925\) | 9.57376 | 0.314783 | ||||||||
\(926\) | 23.5345 | 0.773392 | ||||||||
\(927\) | −5.84405 | −0.191944 | ||||||||
\(928\) | 0.708609 | 0.0232612 | ||||||||
\(929\) | 0.719669 | 0.0236116 | 0.0118058 | − | 0.999930i | \(-0.496242\pi\) | ||||
0.0118058 | + | 0.999930i | \(0.496242\pi\) | |||||||
\(930\) | −12.5644 | −0.412003 | ||||||||
\(931\) | −23.7667 | −0.778923 | ||||||||
\(932\) | 13.5825 | 0.444910 | ||||||||
\(933\) | 26.8328 | 0.878466 | ||||||||
\(934\) | −13.3905 | −0.438149 | ||||||||
\(935\) | −0.633897 | −0.0207306 | ||||||||
\(936\) | −2.69718 | −0.0881601 | ||||||||
\(937\) | −52.1853 | −1.70482 | −0.852410 | − | 0.522874i | \(-0.824860\pi\) | ||||
−0.852410 | + | 0.522874i | \(0.824860\pi\) | |||||||
\(938\) | 44.3830 | 1.44916 | ||||||||
\(939\) | −16.8957 | −0.551370 | ||||||||
\(940\) | 23.6981 | 0.772948 | ||||||||
\(941\) | 6.51151 | 0.212269 | 0.106135 | − | 0.994352i | \(-0.466153\pi\) | ||||
0.106135 | + | 0.994352i | \(0.466153\pi\) | |||||||
\(942\) | 3.76548 | 0.122686 | ||||||||
\(943\) | −7.47752 | −0.243501 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −7.11622 | −0.231490 | ||||||||
\(946\) | −3.25219 | −0.105738 | ||||||||
\(947\) | 50.1578 | 1.62991 | 0.814955 | − | 0.579524i | \(-0.196762\pi\) | ||||
0.814955 | + | 0.579524i | \(0.196762\pi\) | |||||||
\(948\) | −0.0479121 | −0.00155611 | ||||||||
\(949\) | 8.59946 | 0.279150 | ||||||||
\(950\) | −4.41246 | −0.143159 | ||||||||
\(951\) | 21.1631 | 0.686259 | ||||||||
\(952\) | −3.61712 | −0.117232 | ||||||||
\(953\) | 30.9124 | 1.00135 | 0.500676 | − | 0.865635i | \(-0.333085\pi\) | ||||
0.500676 | + | 0.865635i | \(0.333085\pi\) | |||||||
\(954\) | 1.01479 | 0.0328552 | ||||||||
\(955\) | 11.2165 | 0.362958 | ||||||||
\(956\) | 5.64131 | 0.182453 | ||||||||
\(957\) | −0.228318 | −0.00738046 | ||||||||
\(958\) | −26.8921 | −0.868843 | ||||||||
\(959\) | 59.0331 | 1.90628 | ||||||||
\(960\) | 1.96737 | 0.0634965 | ||||||||
\(961\) | 9.78615 | 0.315682 | ||||||||
\(962\) | 22.8624 | 0.737112 | ||||||||
\(963\) | 15.5098 | 0.499796 | ||||||||
\(964\) | 22.6870 | 0.730698 | ||||||||
\(965\) | 11.8267 | 0.380715 | ||||||||
\(966\) | −17.3405 | −0.557922 | ||||||||
\(967\) | −41.9689 | −1.34963 | −0.674815 | − | 0.737987i | \(-0.735776\pi\) | ||||
−0.674815 | + | 0.737987i | \(0.735776\pi\) | |||||||
\(968\) | 10.8962 | 0.350217 | ||||||||
\(969\) | 3.90670 | 0.125501 | ||||||||
\(970\) | −4.16695 | −0.133793 | ||||||||
\(971\) | −6.27634 | −0.201417 | −0.100709 | − | 0.994916i | \(-0.532111\pi\) | ||||
−0.100709 | + | 0.994916i | \(0.532111\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −6.41187 | −0.205555 | ||||||||
\(974\) | 16.0458 | 0.514141 | ||||||||
\(975\) | −3.04636 | −0.0975616 | ||||||||
\(976\) | 10.7660 | 0.344610 | ||||||||
\(977\) | −45.0880 | −1.44249 | −0.721247 | − | 0.692678i | \(-0.756431\pi\) | ||||
−0.721247 | + | 0.692678i | \(0.756431\pi\) | |||||||
\(978\) | 4.05277 | 0.129593 | ||||||||
\(979\) | 1.01564 | 0.0324601 | ||||||||
\(980\) | 11.9687 | 0.382325 | ||||||||
\(981\) | 6.44376 | 0.205734 | ||||||||
\(982\) | −33.1658 | −1.05836 | ||||||||
\(983\) | 9.23375 | 0.294511 | 0.147255 | − | 0.989098i | \(-0.452956\pi\) | ||||
0.147255 | + | 0.989098i | \(0.452956\pi\) | |||||||
\(984\) | −1.55976 | −0.0497234 | ||||||||
\(985\) | 16.6051 | 0.529081 | ||||||||
\(986\) | −0.708609 | −0.0225667 | ||||||||
\(987\) | −43.5705 | −1.38686 | ||||||||
\(988\) | −10.5371 | −0.335229 | ||||||||
\(989\) | −48.3884 | −1.53866 | ||||||||
\(990\) | −0.633897 | −0.0201466 | ||||||||
\(991\) | 18.0309 | 0.572771 | 0.286386 | − | 0.958114i | \(-0.407546\pi\) | ||||
0.286386 | + | 0.958114i | \(0.407546\pi\) | |||||||
\(992\) | −6.38640 | −0.202769 | ||||||||
\(993\) | −27.4693 | −0.871712 | ||||||||
\(994\) | 25.5809 | 0.811376 | ||||||||
\(995\) | −20.2754 | −0.642774 | ||||||||
\(996\) | 0.102752 | 0.00325581 | ||||||||
\(997\) | −31.7402 | −1.00522 | −0.502611 | − | 0.864513i | \(-0.667627\pi\) | ||||
−0.502611 | + | 0.864513i | \(0.667627\pi\) | |||||||
\(998\) | 19.1598 | 0.606494 | ||||||||
\(999\) | −8.47640 | −0.268181 |
(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 | 6018.2.a.p.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.p.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial |