Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | ||||||||
\(3\) | 1.56155 | 0.901563 | 0.450781 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450781 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.56155 | −0.637501 | ||||||||
\(7\) | 3.12311 | 1.18042 | 0.590211 | − | 0.807249i | \(-0.299044\pi\) | ||||
0.590211 | + | 0.807249i | \(0.299044\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.56155 | 0.450781 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −3.12311 | −0.834685 | ||||||||
\(15\) | 1.56155 | 0.403191 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0.561553 | 0.132359 | ||||||||
\(19\) | −7.12311 | −1.63415 | −0.817076 | − | 0.576530i | \(-0.804407\pi\) | ||||
−0.817076 | + | 0.576530i | \(0.804407\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 4.87689 | 1.06423 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | −1.56155 | −0.318751 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | −5.56155 | −1.07032 | ||||||||
\(28\) | 3.12311 | 0.590211 | ||||||||
\(29\) | −5.56155 | −1.03275 | −0.516377 | − | 0.856361i | \(-0.672720\pi\) | ||||
−0.516377 | + | 0.856361i | \(0.672720\pi\) | |||||||
\(30\) | −1.56155 | −0.285099 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.56155 | −0.271831 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 3.12311 | 0.527901 | ||||||||
\(36\) | −0.561553 | −0.0935921 | ||||||||
\(37\) | −1.12311 | −0.184637 | −0.0923187 | − | 0.995730i | \(-0.529428\pi\) | ||||
−0.0923187 | + | 0.995730i | \(0.529428\pi\) | |||||||
\(38\) | 7.12311 | 1.15552 | ||||||||
\(39\) | −6.24621 | −1.00019 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.12311 | −0.175400 | −0.0876998 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0876998 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(42\) | −4.87689 | −0.752521 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 1.56155 | 0.225391 | ||||||||
\(49\) | 2.75379 | 0.393398 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −6.24621 | −0.874645 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | −3.56155 | −0.489217 | −0.244608 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244608 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(54\) | 5.56155 | 0.756831 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −3.12311 | −0.417343 | ||||||||
\(57\) | −11.1231 | −1.47329 | ||||||||
\(58\) | 5.56155 | 0.730268 | ||||||||
\(59\) | 6.24621 | 0.813187 | 0.406594 | − | 0.913609i | \(-0.366716\pi\) | ||||
0.406594 | + | 0.913609i | \(0.366716\pi\) | |||||||
\(60\) | 1.56155 | 0.201596 | ||||||||
\(61\) | −5.56155 | −0.712084 | −0.356042 | − | 0.934470i | \(-0.615874\pi\) | ||||
−0.356042 | + | 0.934470i | \(0.615874\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.75379 | −0.220957 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 1.56155 | 0.192214 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 9.36932 | 1.12793 | ||||||||
\(70\) | −3.12311 | −0.373283 | ||||||||
\(71\) | −1.12311 | −0.133288 | −0.0666441 | − | 0.997777i | \(-0.521229\pi\) | ||||
−0.0666441 | + | 0.997777i | \(0.521229\pi\) | |||||||
\(72\) | 0.561553 | 0.0661796 | ||||||||
\(73\) | 1.31534 | 0.153949 | 0.0769745 | − | 0.997033i | \(-0.475474\pi\) | ||||
0.0769745 | + | 0.997033i | \(0.475474\pi\) | |||||||
\(74\) | 1.12311 | 0.130558 | ||||||||
\(75\) | 1.56155 | 0.180313 | ||||||||
\(76\) | −7.12311 | −0.817076 | ||||||||
\(77\) | −3.12311 | −0.355911 | ||||||||
\(78\) | 6.24621 | 0.707244 | ||||||||
\(79\) | −13.5616 | −1.52579 | −0.762897 | − | 0.646520i | \(-0.776224\pi\) | ||||
−0.762897 | + | 0.646520i | \(0.776224\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 1.12311 | 0.124026 | ||||||||
\(83\) | −2.43845 | −0.267654 | −0.133827 | − | 0.991005i | \(-0.542727\pi\) | ||||
−0.133827 | + | 0.991005i | \(0.542727\pi\) | |||||||
\(84\) | 4.87689 | 0.532113 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | −8.68466 | −0.931093 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −7.36932 | −0.781146 | −0.390573 | − | 0.920572i | \(-0.627723\pi\) | ||||
−0.390573 | + | 0.920572i | \(0.627723\pi\) | |||||||
\(90\) | 0.561553 | 0.0591929 | ||||||||
\(91\) | −12.4924 | −1.30956 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | −7.12311 | −0.730815 | ||||||||
\(96\) | −1.56155 | −0.159375 | ||||||||
\(97\) | −15.5616 | −1.58004 | −0.790018 | − | 0.613083i | \(-0.789929\pi\) | ||||
−0.790018 | + | 0.613083i | \(0.789929\pi\) | |||||||
\(98\) | −2.75379 | −0.278175 | ||||||||
\(99\) | 0.561553 | 0.0564382 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.4924 | −1.44205 | −0.721025 | − | 0.692909i | \(-0.756329\pi\) | ||||
−0.721025 | + | 0.692909i | \(0.756329\pi\) | |||||||
\(102\) | 6.24621 | 0.618467 | ||||||||
\(103\) | 8.24621 | 0.812523 | 0.406262 | − | 0.913757i | \(-0.366832\pi\) | ||||
0.406262 | + | 0.913757i | \(0.366832\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 4.87689 | 0.475936 | ||||||||
\(106\) | 3.56155 | 0.345929 | ||||||||
\(107\) | 3.80776 | 0.368110 | 0.184055 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184055 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(108\) | −5.56155 | −0.535161 | ||||||||
\(109\) | 1.12311 | 0.107574 | 0.0537870 | − | 0.998552i | \(-0.482871\pi\) | ||||
0.0537870 | + | 0.998552i | \(0.482871\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | −1.75379 | −0.166462 | ||||||||
\(112\) | 3.12311 | 0.295106 | ||||||||
\(113\) | 5.12311 | 0.481941 | 0.240971 | − | 0.970532i | \(-0.422534\pi\) | ||||
0.240971 | + | 0.970532i | \(0.422534\pi\) | |||||||
\(114\) | 11.1231 | 1.04177 | ||||||||
\(115\) | 6.00000 | 0.559503 | ||||||||
\(116\) | −5.56155 | −0.516377 | ||||||||
\(117\) | 2.24621 | 0.207662 | ||||||||
\(118\) | −6.24621 | −0.575010 | ||||||||
\(119\) | −12.4924 | −1.14518 | ||||||||
\(120\) | −1.56155 | −0.142550 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.56155 | 0.503519 | ||||||||
\(123\) | −1.75379 | −0.158134 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.75379 | 0.156240 | ||||||||
\(127\) | −3.80776 | −0.337884 | −0.168942 | − | 0.985626i | \(-0.554035\pi\) | ||||
−0.168942 | + | 0.985626i | \(0.554035\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.56155 | 0.137487 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | 6.24621 | 0.545734 | 0.272867 | − | 0.962052i | \(-0.412028\pi\) | ||||
0.272867 | + | 0.962052i | \(0.412028\pi\) | |||||||
\(132\) | −1.56155 | −0.135916 | ||||||||
\(133\) | −22.2462 | −1.92899 | ||||||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | −5.56155 | −0.478662 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | −5.12311 | −0.437696 | −0.218848 | − | 0.975759i | \(-0.570230\pi\) | ||||
−0.218848 | + | 0.975759i | \(0.570230\pi\) | |||||||
\(138\) | −9.36932 | −0.797569 | ||||||||
\(139\) | −4.68466 | −0.397348 | −0.198674 | − | 0.980066i | \(-0.563663\pi\) | ||||
−0.198674 | + | 0.980066i | \(0.563663\pi\) | |||||||
\(140\) | 3.12311 | 0.263951 | ||||||||
\(141\) | −3.12311 | −0.263013 | ||||||||
\(142\) | 1.12311 | 0.0942489 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | −0.561553 | −0.0467961 | ||||||||
\(145\) | −5.56155 | −0.461862 | ||||||||
\(146\) | −1.31534 | −0.108858 | ||||||||
\(147\) | 4.30019 | 0.354673 | ||||||||
\(148\) | −1.12311 | −0.0923187 | ||||||||
\(149\) | 4.68466 | 0.383782 | 0.191891 | − | 0.981416i | \(-0.438538\pi\) | ||||
0.191891 | + | 0.981416i | \(0.438538\pi\) | |||||||
\(150\) | −1.56155 | −0.127500 | ||||||||
\(151\) | 21.3693 | 1.73901 | 0.869505 | − | 0.493924i | \(-0.164438\pi\) | ||||
0.869505 | + | 0.493924i | \(0.164438\pi\) | |||||||
\(152\) | 7.12311 | 0.577760 | ||||||||
\(153\) | 2.24621 | 0.181595 | ||||||||
\(154\) | 3.12311 | 0.251667 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.24621 | −0.500097 | ||||||||
\(157\) | 7.75379 | 0.618820 | 0.309410 | − | 0.950929i | \(-0.399869\pi\) | ||||
0.309410 | + | 0.950929i | \(0.399869\pi\) | |||||||
\(158\) | 13.5616 | 1.07890 | ||||||||
\(159\) | −5.56155 | −0.441060 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 18.7386 | 1.47681 | ||||||||
\(162\) | 7.00000 | 0.549972 | ||||||||
\(163\) | 4.68466 | 0.366931 | 0.183465 | − | 0.983026i | \(-0.441268\pi\) | ||||
0.183465 | + | 0.983026i | \(0.441268\pi\) | |||||||
\(164\) | −1.12311 | −0.0876998 | ||||||||
\(165\) | −1.56155 | −0.121567 | ||||||||
\(166\) | 2.43845 | 0.189260 | ||||||||
\(167\) | 15.8078 | 1.22324 | 0.611621 | − | 0.791151i | \(-0.290518\pi\) | ||||
0.611621 | + | 0.791151i | \(0.290518\pi\) | |||||||
\(168\) | −4.87689 | −0.376261 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −2.24621 | −0.170776 | −0.0853881 | − | 0.996348i | \(-0.527213\pi\) | ||||
−0.0853881 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(174\) | 8.68466 | 0.658382 | ||||||||
\(175\) | 3.12311 | 0.236085 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 9.75379 | 0.733140 | ||||||||
\(178\) | 7.36932 | 0.552354 | ||||||||
\(179\) | 8.43845 | 0.630719 | 0.315360 | − | 0.948972i | \(-0.397875\pi\) | ||||
0.315360 | + | 0.948972i | \(0.397875\pi\) | |||||||
\(180\) | −0.561553 | −0.0418557 | ||||||||
\(181\) | −16.0540 | −1.19328 | −0.596641 | − | 0.802508i | \(-0.703498\pi\) | ||||
−0.596641 | + | 0.802508i | \(0.703498\pi\) | |||||||
\(182\) | 12.4924 | 0.926000 | ||||||||
\(183\) | −8.68466 | −0.641988 | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −1.12311 | −0.0825724 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | −17.3693 | −1.26343 | ||||||||
\(190\) | 7.12311 | 0.516764 | ||||||||
\(191\) | −9.31534 | −0.674034 | −0.337017 | − | 0.941498i | \(-0.609418\pi\) | ||||
−0.337017 | + | 0.941498i | \(0.609418\pi\) | |||||||
\(192\) | 1.56155 | 0.112695 | ||||||||
\(193\) | −14.2462 | −1.02546 | −0.512732 | − | 0.858548i | \(-0.671367\pi\) | ||||
−0.512732 | + | 0.858548i | \(0.671367\pi\) | |||||||
\(194\) | 15.5616 | 1.11725 | ||||||||
\(195\) | −6.24621 | −0.447300 | ||||||||
\(196\) | 2.75379 | 0.196699 | ||||||||
\(197\) | −1.75379 | −0.124952 | −0.0624761 | − | 0.998046i | \(-0.519900\pi\) | ||||
−0.0624761 | + | 0.998046i | \(0.519900\pi\) | |||||||
\(198\) | −0.561553 | −0.0399078 | ||||||||
\(199\) | −1.12311 | −0.0796148 | −0.0398074 | − | 0.999207i | \(-0.512674\pi\) | ||||
−0.0398074 | + | 0.999207i | \(0.512674\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 3.12311 | 0.220287 | ||||||||
\(202\) | 14.4924 | 1.01968 | ||||||||
\(203\) | −17.3693 | −1.21909 | ||||||||
\(204\) | −6.24621 | −0.437322 | ||||||||
\(205\) | −1.12311 | −0.0784411 | ||||||||
\(206\) | −8.24621 | −0.574541 | ||||||||
\(207\) | −3.36932 | −0.234184 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 7.12311 | 0.492716 | ||||||||
\(210\) | −4.87689 | −0.336538 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | −3.56155 | −0.244608 | ||||||||
\(213\) | −1.75379 | −0.120168 | ||||||||
\(214\) | −3.80776 | −0.260293 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 5.56155 | 0.378416 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.12311 | −0.0760663 | ||||||||
\(219\) | 2.05398 | 0.138795 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 16.0000 | 1.07628 | ||||||||
\(222\) | 1.75379 | 0.117707 | ||||||||
\(223\) | −18.9309 | −1.26770 | −0.633852 | − | 0.773454i | \(-0.718527\pi\) | ||||
−0.633852 | + | 0.773454i | \(0.718527\pi\) | |||||||
\(224\) | −3.12311 | −0.208671 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | −5.12311 | −0.340784 | ||||||||
\(227\) | −5.36932 | −0.356374 | −0.178187 | − | 0.983997i | \(-0.557023\pi\) | ||||
−0.178187 | + | 0.983997i | \(0.557023\pi\) | |||||||
\(228\) | −11.1231 | −0.736646 | ||||||||
\(229\) | −3.56155 | −0.235354 | −0.117677 | − | 0.993052i | \(-0.537545\pi\) | ||||
−0.117677 | + | 0.993052i | \(0.537545\pi\) | |||||||
\(230\) | −6.00000 | −0.395628 | ||||||||
\(231\) | −4.87689 | −0.320876 | ||||||||
\(232\) | 5.56155 | 0.365134 | ||||||||
\(233\) | 3.56155 | 0.233325 | 0.116663 | − | 0.993172i | \(-0.462780\pi\) | ||||
0.116663 | + | 0.993172i | \(0.462780\pi\) | |||||||
\(234\) | −2.24621 | −0.146839 | ||||||||
\(235\) | −2.00000 | −0.130466 | ||||||||
\(236\) | 6.24621 | 0.406594 | ||||||||
\(237\) | −21.1771 | −1.37560 | ||||||||
\(238\) | 12.4924 | 0.809763 | ||||||||
\(239\) | 0.684658 | 0.0442869 | 0.0221434 | − | 0.999755i | \(-0.492951\pi\) | ||||
0.0221434 | + | 0.999755i | \(0.492951\pi\) | |||||||
\(240\) | 1.56155 | 0.100798 | ||||||||
\(241\) | 16.8769 | 1.08714 | 0.543568 | − | 0.839365i | \(-0.317073\pi\) | ||||
0.543568 | + | 0.839365i | \(0.317073\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 5.75379 | 0.369106 | ||||||||
\(244\) | −5.56155 | −0.356042 | ||||||||
\(245\) | 2.75379 | 0.175933 | ||||||||
\(246\) | 1.75379 | 0.111817 | ||||||||
\(247\) | 28.4924 | 1.81293 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.80776 | −0.241307 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 25.3693 | 1.60130 | 0.800649 | − | 0.599134i | \(-0.204488\pi\) | ||||
0.800649 | + | 0.599134i | \(0.204488\pi\) | |||||||
\(252\) | −1.75379 | −0.110478 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 3.80776 | 0.238920 | ||||||||
\(255\) | −6.24621 | −0.391153 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.4924 | 0.654499 | 0.327250 | − | 0.944938i | \(-0.393878\pi\) | ||||
0.327250 | + | 0.944938i | \(0.393878\pi\) | |||||||
\(258\) | −1.56155 | −0.0972180 | ||||||||
\(259\) | −3.50758 | −0.217950 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 3.12311 | 0.193315 | ||||||||
\(262\) | −6.24621 | −0.385892 | ||||||||
\(263\) | 22.2462 | 1.37176 | 0.685880 | − | 0.727715i | \(-0.259417\pi\) | ||||
0.685880 | + | 0.727715i | \(0.259417\pi\) | |||||||
\(264\) | 1.56155 | 0.0961069 | ||||||||
\(265\) | −3.56155 | −0.218784 | ||||||||
\(266\) | 22.2462 | 1.36400 | ||||||||
\(267\) | −11.5076 | −0.704252 | ||||||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | 8.05398 | 0.491060 | 0.245530 | − | 0.969389i | \(-0.421038\pi\) | ||||
0.245530 | + | 0.969389i | \(0.421038\pi\) | |||||||
\(270\) | 5.56155 | 0.338465 | ||||||||
\(271\) | −9.75379 | −0.592500 | −0.296250 | − | 0.955110i | \(-0.595736\pi\) | ||||
−0.296250 | + | 0.955110i | \(0.595736\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | −19.5076 | −1.18065 | ||||||||
\(274\) | 5.12311 | 0.309498 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 9.36932 | 0.563967 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 4.68466 | 0.280967 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.12311 | −0.186641 | ||||||||
\(281\) | 21.6155 | 1.28947 | 0.644737 | − | 0.764404i | \(-0.276967\pi\) | ||||
0.644737 | + | 0.764404i | \(0.276967\pi\) | |||||||
\(282\) | 3.12311 | 0.185978 | ||||||||
\(283\) | 9.56155 | 0.568375 | 0.284188 | − | 0.958769i | \(-0.408276\pi\) | ||||
0.284188 | + | 0.958769i | \(0.408276\pi\) | |||||||
\(284\) | −1.12311 | −0.0666441 | ||||||||
\(285\) | −11.1231 | −0.658876 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | −3.50758 | −0.207046 | ||||||||
\(288\) | 0.561553 | 0.0330898 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 5.56155 | 0.326586 | ||||||||
\(291\) | −24.3002 | −1.42450 | ||||||||
\(292\) | 1.31534 | 0.0769745 | ||||||||
\(293\) | −2.24621 | −0.131225 | −0.0656125 | − | 0.997845i | \(-0.520900\pi\) | ||||
−0.0656125 | + | 0.997845i | \(0.520900\pi\) | |||||||
\(294\) | −4.30019 | −0.250792 | ||||||||
\(295\) | 6.24621 | 0.363668 | ||||||||
\(296\) | 1.12311 | 0.0652792 | ||||||||
\(297\) | 5.56155 | 0.322714 | ||||||||
\(298\) | −4.68466 | −0.271375 | ||||||||
\(299\) | −24.0000 | −1.38796 | ||||||||
\(300\) | 1.56155 | 0.0901563 | ||||||||
\(301\) | 3.12311 | 0.180013 | ||||||||
\(302\) | −21.3693 | −1.22967 | ||||||||
\(303\) | −22.6307 | −1.30010 | ||||||||
\(304\) | −7.12311 | −0.408538 | ||||||||
\(305\) | −5.56155 | −0.318454 | ||||||||
\(306\) | −2.24621 | −0.128407 | ||||||||
\(307\) | 27.8078 | 1.58707 | 0.793536 | − | 0.608523i | \(-0.208238\pi\) | ||||
0.793536 | + | 0.608523i | \(0.208238\pi\) | |||||||
\(308\) | −3.12311 | −0.177955 | ||||||||
\(309\) | 12.8769 | 0.732541 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.12311 | −0.403914 | −0.201957 | − | 0.979394i | \(-0.564730\pi\) | ||||
−0.201957 | + | 0.979394i | \(0.564730\pi\) | |||||||
\(312\) | 6.24621 | 0.353622 | ||||||||
\(313\) | −13.1231 | −0.741762 | −0.370881 | − | 0.928680i | \(-0.620944\pi\) | ||||
−0.370881 | + | 0.928680i | \(0.620944\pi\) | |||||||
\(314\) | −7.75379 | −0.437572 | ||||||||
\(315\) | −1.75379 | −0.0988148 | ||||||||
\(316\) | −13.5616 | −0.762897 | ||||||||
\(317\) | −7.56155 | −0.424699 | −0.212350 | − | 0.977194i | \(-0.568112\pi\) | ||||
−0.212350 | + | 0.977194i | \(0.568112\pi\) | |||||||
\(318\) | 5.56155 | 0.311876 | ||||||||
\(319\) | 5.56155 | 0.311387 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 5.94602 | 0.331875 | ||||||||
\(322\) | −18.7386 | −1.04426 | ||||||||
\(323\) | 28.4924 | 1.58536 | ||||||||
\(324\) | −7.00000 | −0.388889 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | −4.68466 | −0.259459 | ||||||||
\(327\) | 1.75379 | 0.0969847 | ||||||||
\(328\) | 1.12311 | 0.0620131 | ||||||||
\(329\) | −6.24621 | −0.344365 | ||||||||
\(330\) | 1.56155 | 0.0859607 | ||||||||
\(331\) | −14.8769 | −0.817708 | −0.408854 | − | 0.912600i | \(-0.634071\pi\) | ||||
−0.408854 | + | 0.912600i | \(0.634071\pi\) | |||||||
\(332\) | −2.43845 | −0.133827 | ||||||||
\(333\) | 0.630683 | 0.0345612 | ||||||||
\(334\) | −15.8078 | −0.864962 | ||||||||
\(335\) | 2.00000 | 0.109272 | ||||||||
\(336\) | 4.87689 | 0.266056 | ||||||||
\(337\) | −29.3693 | −1.59985 | −0.799924 | − | 0.600101i | \(-0.795127\pi\) | ||||
−0.799924 | + | 0.600101i | \(0.795127\pi\) | |||||||
\(338\) | −3.00000 | −0.163178 | ||||||||
\(339\) | 8.00000 | 0.434500 | ||||||||
\(340\) | −4.00000 | −0.216930 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | −13.2614 | −0.716046 | ||||||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | 9.36932 | 0.504427 | ||||||||
\(346\) | 2.24621 | 0.120757 | ||||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | −8.68466 | −0.465547 | ||||||||
\(349\) | 3.12311 | 0.167176 | 0.0835880 | − | 0.996500i | \(-0.473362\pi\) | ||||
0.0835880 | + | 0.996500i | \(0.473362\pi\) | |||||||
\(350\) | −3.12311 | −0.166937 | ||||||||
\(351\) | 22.2462 | 1.18741 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 12.4384 | 0.662032 | 0.331016 | − | 0.943625i | \(-0.392609\pi\) | ||||
0.331016 | + | 0.943625i | \(0.392609\pi\) | |||||||
\(354\) | −9.75379 | −0.518408 | ||||||||
\(355\) | −1.12311 | −0.0596083 | ||||||||
\(356\) | −7.36932 | −0.390573 | ||||||||
\(357\) | −19.5076 | −1.03245 | ||||||||
\(358\) | −8.43845 | −0.445986 | ||||||||
\(359\) | −16.6847 | −0.880583 | −0.440291 | − | 0.897855i | \(-0.645125\pi\) | ||||
−0.440291 | + | 0.897855i | \(0.645125\pi\) | |||||||
\(360\) | 0.561553 | 0.0295964 | ||||||||
\(361\) | 31.7386 | 1.67045 | ||||||||
\(362\) | 16.0540 | 0.843778 | ||||||||
\(363\) | 1.56155 | 0.0819603 | ||||||||
\(364\) | −12.4924 | −0.654781 | ||||||||
\(365\) | 1.31534 | 0.0688481 | ||||||||
\(366\) | 8.68466 | 0.453954 | ||||||||
\(367\) | 30.4924 | 1.59169 | 0.795846 | − | 0.605499i | \(-0.207027\pi\) | ||||
0.795846 | + | 0.605499i | \(0.207027\pi\) | |||||||
\(368\) | 6.00000 | 0.312772 | ||||||||
\(369\) | 0.630683 | 0.0328321 | ||||||||
\(370\) | 1.12311 | 0.0583875 | ||||||||
\(371\) | −11.1231 | −0.577483 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.9309 | −1.08376 | −0.541880 | − | 0.840456i | \(-0.682287\pi\) | ||||
−0.541880 | + | 0.840456i | \(0.682287\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 1.56155 | 0.0806382 | ||||||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | 22.2462 | 1.14574 | ||||||||
\(378\) | 17.3693 | 0.893381 | ||||||||
\(379\) | 23.6155 | 1.21305 | 0.606524 | − | 0.795065i | \(-0.292563\pi\) | ||||
0.606524 | + | 0.795065i | \(0.292563\pi\) | |||||||
\(380\) | −7.12311 | −0.365408 | ||||||||
\(381\) | −5.94602 | −0.304624 | ||||||||
\(382\) | 9.31534 | 0.476614 | ||||||||
\(383\) | 33.1771 | 1.69527 | 0.847635 | − | 0.530580i | \(-0.178026\pi\) | ||||
0.847635 | + | 0.530580i | \(0.178026\pi\) | |||||||
\(384\) | −1.56155 | −0.0796877 | ||||||||
\(385\) | −3.12311 | −0.159168 | ||||||||
\(386\) | 14.2462 | 0.725113 | ||||||||
\(387\) | −0.561553 | −0.0285453 | ||||||||
\(388\) | −15.5616 | −0.790018 | ||||||||
\(389\) | −20.7386 | −1.05149 | −0.525745 | − | 0.850642i | \(-0.676213\pi\) | ||||
−0.525745 | + | 0.850642i | \(0.676213\pi\) | |||||||
\(390\) | 6.24621 | 0.316289 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | −2.75379 | −0.139087 | ||||||||
\(393\) | 9.75379 | 0.492014 | ||||||||
\(394\) | 1.75379 | 0.0883546 | ||||||||
\(395\) | −13.5616 | −0.682356 | ||||||||
\(396\) | 0.561553 | 0.0282191 | ||||||||
\(397\) | −20.4384 | −1.02578 | −0.512888 | − | 0.858455i | \(-0.671424\pi\) | ||||
−0.512888 | + | 0.858455i | \(0.671424\pi\) | |||||||
\(398\) | 1.12311 | 0.0562962 | ||||||||
\(399\) | −34.7386 | −1.73911 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 22.6847 | 1.13282 | 0.566409 | − | 0.824124i | \(-0.308332\pi\) | ||||
0.566409 | + | 0.824124i | \(0.308332\pi\) | |||||||
\(402\) | −3.12311 | −0.155766 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.4924 | −0.721025 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 17.3693 | 0.862025 | ||||||||
\(407\) | 1.12311 | 0.0556703 | ||||||||
\(408\) | 6.24621 | 0.309234 | ||||||||
\(409\) | −21.5616 | −1.06615 | −0.533075 | − | 0.846068i | \(-0.678964\pi\) | ||||
−0.533075 | + | 0.846068i | \(0.678964\pi\) | |||||||
\(410\) | 1.12311 | 0.0554662 | ||||||||
\(411\) | −8.00000 | −0.394611 | ||||||||
\(412\) | 8.24621 | 0.406262 | ||||||||
\(413\) | 19.5076 | 0.959905 | ||||||||
\(414\) | 3.36932 | 0.165593 | ||||||||
\(415\) | −2.43845 | −0.119699 | ||||||||
\(416\) | 4.00000 | 0.196116 | ||||||||
\(417\) | −7.31534 | −0.358234 | ||||||||
\(418\) | −7.12311 | −0.348402 | ||||||||
\(419\) | −20.0540 | −0.979701 | −0.489850 | − | 0.871807i | \(-0.662949\pi\) | ||||
−0.489850 | + | 0.871807i | \(0.662949\pi\) | |||||||
\(420\) | 4.87689 | 0.237968 | ||||||||
\(421\) | −30.8769 | −1.50485 | −0.752424 | − | 0.658679i | \(-0.771115\pi\) | ||||
−0.752424 | + | 0.658679i | \(0.771115\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.12311 | 0.0546073 | ||||||||
\(424\) | 3.56155 | 0.172964 | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | 1.75379 | 0.0849713 | ||||||||
\(427\) | −17.3693 | −0.840560 | ||||||||
\(428\) | 3.80776 | 0.184055 | ||||||||
\(429\) | 6.24621 | 0.301570 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | 26.7386 | 1.28795 | 0.643977 | − | 0.765045i | \(-0.277283\pi\) | ||||
0.643977 | + | 0.765045i | \(0.277283\pi\) | |||||||
\(432\) | −5.56155 | −0.267580 | ||||||||
\(433\) | 31.3693 | 1.50751 | 0.753757 | − | 0.657154i | \(-0.228240\pi\) | ||||
0.753757 | + | 0.657154i | \(0.228240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.68466 | −0.416398 | ||||||||
\(436\) | 1.12311 | 0.0537870 | ||||||||
\(437\) | −42.7386 | −2.04447 | ||||||||
\(438\) | −2.05398 | −0.0981427 | ||||||||
\(439\) | 20.4924 | 0.978050 | 0.489025 | − | 0.872270i | \(-0.337353\pi\) | ||||
0.489025 | + | 0.872270i | \(0.337353\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | −1.54640 | −0.0736380 | ||||||||
\(442\) | −16.0000 | −0.761042 | ||||||||
\(443\) | 16.2462 | 0.771881 | 0.385940 | − | 0.922524i | \(-0.373877\pi\) | ||||
0.385940 | + | 0.922524i | \(0.373877\pi\) | |||||||
\(444\) | −1.75379 | −0.0832311 | ||||||||
\(445\) | −7.36932 | −0.349339 | ||||||||
\(446\) | 18.9309 | 0.896403 | ||||||||
\(447\) | 7.31534 | 0.346004 | ||||||||
\(448\) | 3.12311 | 0.147553 | ||||||||
\(449\) | 34.0000 | 1.60456 | 0.802280 | − | 0.596948i | \(-0.203620\pi\) | ||||
0.802280 | + | 0.596948i | \(0.203620\pi\) | |||||||
\(450\) | 0.561553 | 0.0264719 | ||||||||
\(451\) | 1.12311 | 0.0528850 | ||||||||
\(452\) | 5.12311 | 0.240971 | ||||||||
\(453\) | 33.3693 | 1.56783 | ||||||||
\(454\) | 5.36932 | 0.251995 | ||||||||
\(455\) | −12.4924 | −0.585654 | ||||||||
\(456\) | 11.1231 | 0.520887 | ||||||||
\(457\) | −42.4924 | −1.98771 | −0.993856 | − | 0.110682i | \(-0.964696\pi\) | ||||
−0.993856 | + | 0.110682i | \(0.964696\pi\) | |||||||
\(458\) | 3.56155 | 0.166420 | ||||||||
\(459\) | 22.2462 | 1.03836 | ||||||||
\(460\) | 6.00000 | 0.279751 | ||||||||
\(461\) | −7.36932 | −0.343223 | −0.171612 | − | 0.985165i | \(-0.554897\pi\) | ||||
−0.171612 | + | 0.985165i | \(0.554897\pi\) | |||||||
\(462\) | 4.87689 | 0.226894 | ||||||||
\(463\) | −2.24621 | −0.104390 | −0.0521951 | − | 0.998637i | \(-0.516622\pi\) | ||||
−0.0521951 | + | 0.998637i | \(0.516622\pi\) | |||||||
\(464\) | −5.56155 | −0.258189 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.56155 | −0.164986 | ||||||||
\(467\) | −18.7386 | −0.867121 | −0.433560 | − | 0.901125i | \(-0.642743\pi\) | ||||
−0.433560 | + | 0.901125i | \(0.642743\pi\) | |||||||
\(468\) | 2.24621 | 0.103831 | ||||||||
\(469\) | 6.24621 | 0.288423 | ||||||||
\(470\) | 2.00000 | 0.0922531 | ||||||||
\(471\) | 12.1080 | 0.557905 | ||||||||
\(472\) | −6.24621 | −0.287505 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 21.1771 | 0.972696 | ||||||||
\(475\) | −7.12311 | −0.326831 | ||||||||
\(476\) | −12.4924 | −0.572589 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | −0.684658 | −0.0313155 | ||||||||
\(479\) | 8.68466 | 0.396812 | 0.198406 | − | 0.980120i | \(-0.436424\pi\) | ||||
0.198406 | + | 0.980120i | \(0.436424\pi\) | |||||||
\(480\) | −1.56155 | −0.0712748 | ||||||||
\(481\) | 4.49242 | 0.204837 | ||||||||
\(482\) | −16.8769 | −0.768721 | ||||||||
\(483\) | 29.2614 | 1.33144 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −15.5616 | −0.706614 | ||||||||
\(486\) | −5.75379 | −0.260997 | ||||||||
\(487\) | −6.49242 | −0.294200 | −0.147100 | − | 0.989122i | \(-0.546994\pi\) | ||||
−0.147100 | + | 0.989122i | \(0.546994\pi\) | |||||||
\(488\) | 5.56155 | 0.251760 | ||||||||
\(489\) | 7.31534 | 0.330811 | ||||||||
\(490\) | −2.75379 | −0.124403 | ||||||||
\(491\) | 3.12311 | 0.140944 | 0.0704719 | − | 0.997514i | \(-0.477549\pi\) | ||||
0.0704719 | + | 0.997514i | \(0.477549\pi\) | |||||||
\(492\) | −1.75379 | −0.0790669 | ||||||||
\(493\) | 22.2462 | 1.00192 | ||||||||
\(494\) | −28.4924 | −1.28193 | ||||||||
\(495\) | 0.561553 | 0.0252399 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.50758 | −0.157336 | ||||||||
\(498\) | 3.80776 | 0.170630 | ||||||||
\(499\) | −3.56155 | −0.159437 | −0.0797185 | − | 0.996817i | \(-0.525402\pi\) | ||||
−0.0797185 | + | 0.996817i | \(0.525402\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 24.6847 | 1.10283 | ||||||||
\(502\) | −25.3693 | −1.13229 | ||||||||
\(503\) | −26.7386 | −1.19222 | −0.596108 | − | 0.802904i | \(-0.703287\pi\) | ||||
−0.596108 | + | 0.802904i | \(0.703287\pi\) | |||||||
\(504\) | 1.75379 | 0.0781200 | ||||||||
\(505\) | −14.4924 | −0.644904 | ||||||||
\(506\) | 6.00000 | 0.266733 | ||||||||
\(507\) | 4.68466 | 0.208053 | ||||||||
\(508\) | −3.80776 | −0.168942 | ||||||||
\(509\) | −16.7386 | −0.741927 | −0.370963 | − | 0.928647i | \(-0.620972\pi\) | ||||
−0.370963 | + | 0.928647i | \(0.620972\pi\) | |||||||
\(510\) | 6.24621 | 0.276587 | ||||||||
\(511\) | 4.10795 | 0.181725 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 39.6155 | 1.74907 | ||||||||
\(514\) | −10.4924 | −0.462801 | ||||||||
\(515\) | 8.24621 | 0.363371 | ||||||||
\(516\) | 1.56155 | 0.0687435 | ||||||||
\(517\) | 2.00000 | 0.0879599 | ||||||||
\(518\) | 3.50758 | 0.154114 | ||||||||
\(519\) | −3.50758 | −0.153966 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | 22.9848 | 1.00698 | 0.503492 | − | 0.864000i | \(-0.332048\pi\) | ||||
0.503492 | + | 0.864000i | \(0.332048\pi\) | |||||||
\(522\) | −3.12311 | −0.136695 | ||||||||
\(523\) | −10.2462 | −0.448036 | −0.224018 | − | 0.974585i | \(-0.571917\pi\) | ||||
−0.224018 | + | 0.974585i | \(0.571917\pi\) | |||||||
\(524\) | 6.24621 | 0.272867 | ||||||||
\(525\) | 4.87689 | 0.212845 | ||||||||
\(526\) | −22.2462 | −0.969981 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.56155 | −0.0679579 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 3.56155 | 0.154704 | ||||||||
\(531\) | −3.50758 | −0.152216 | ||||||||
\(532\) | −22.2462 | −0.964496 | ||||||||
\(533\) | 4.49242 | 0.194588 | ||||||||
\(534\) | 11.5076 | 0.497982 | ||||||||
\(535\) | 3.80776 | 0.164624 | ||||||||
\(536\) | −2.00000 | −0.0863868 | ||||||||
\(537\) | 13.1771 | 0.568633 | ||||||||
\(538\) | −8.05398 | −0.347232 | ||||||||
\(539\) | −2.75379 | −0.118614 | ||||||||
\(540\) | −5.56155 | −0.239331 | ||||||||
\(541\) | 20.7386 | 0.891624 | 0.445812 | − | 0.895127i | \(-0.352915\pi\) | ||||
0.445812 | + | 0.895127i | \(0.352915\pi\) | |||||||
\(542\) | 9.75379 | 0.418961 | ||||||||
\(543\) | −25.0691 | −1.07582 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 1.12311 | 0.0481086 | ||||||||
\(546\) | 19.5076 | 0.834847 | ||||||||
\(547\) | −45.5616 | −1.94807 | −0.974036 | − | 0.226395i | \(-0.927306\pi\) | ||||
−0.974036 | + | 0.226395i | \(0.927306\pi\) | |||||||
\(548\) | −5.12311 | −0.218848 | ||||||||
\(549\) | 3.12311 | 0.133291 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 39.6155 | 1.68768 | ||||||||
\(552\) | −9.36932 | −0.398785 | ||||||||
\(553\) | −42.3542 | −1.80108 | ||||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | −1.75379 | −0.0744442 | ||||||||
\(556\) | −4.68466 | −0.198674 | ||||||||
\(557\) | −15.1231 | −0.640787 | −0.320393 | − | 0.947285i | \(-0.603815\pi\) | ||||
−0.320393 | + | 0.947285i | \(0.603815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 3.12311 | 0.131975 | ||||||||
\(561\) | 6.24621 | 0.263715 | ||||||||
\(562\) | −21.6155 | −0.911796 | ||||||||
\(563\) | −1.75379 | −0.0739134 | −0.0369567 | − | 0.999317i | \(-0.511766\pi\) | ||||
−0.0369567 | + | 0.999317i | \(0.511766\pi\) | |||||||
\(564\) | −3.12311 | −0.131506 | ||||||||
\(565\) | 5.12311 | 0.215531 | ||||||||
\(566\) | −9.56155 | −0.401902 | ||||||||
\(567\) | −21.8617 | −0.918107 | ||||||||
\(568\) | 1.12311 | 0.0471245 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 11.1231 | 0.465896 | ||||||||
\(571\) | −6.63068 | −0.277485 | −0.138743 | − | 0.990328i | \(-0.544306\pi\) | ||||
−0.138743 | + | 0.990328i | \(0.544306\pi\) | |||||||
\(572\) | 4.00000 | 0.167248 | ||||||||
\(573\) | −14.5464 | −0.607684 | ||||||||
\(574\) | 3.50758 | 0.146403 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | −0.561553 | −0.0233980 | ||||||||
\(577\) | 5.61553 | 0.233777 | 0.116889 | − | 0.993145i | \(-0.462708\pi\) | ||||
0.116889 | + | 0.993145i | \(0.462708\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −22.2462 | −0.924521 | ||||||||
\(580\) | −5.56155 | −0.230931 | ||||||||
\(581\) | −7.61553 | −0.315945 | ||||||||
\(582\) | 24.3002 | 1.00728 | ||||||||
\(583\) | 3.56155 | 0.147504 | ||||||||
\(584\) | −1.31534 | −0.0544292 | ||||||||
\(585\) | 2.24621 | 0.0928694 | ||||||||
\(586\) | 2.24621 | 0.0927901 | ||||||||
\(587\) | −46.2462 | −1.90879 | −0.954393 | − | 0.298554i | \(-0.903496\pi\) | ||||
−0.954393 | + | 0.298554i | \(0.903496\pi\) | |||||||
\(588\) | 4.30019 | 0.177337 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −6.24621 | −0.257152 | ||||||||
\(591\) | −2.73863 | −0.112652 | ||||||||
\(592\) | −1.12311 | −0.0461594 | ||||||||
\(593\) | 26.1922 | 1.07559 | 0.537793 | − | 0.843077i | \(-0.319258\pi\) | ||||
0.537793 | + | 0.843077i | \(0.319258\pi\) | |||||||
\(594\) | −5.56155 | −0.228193 | ||||||||
\(595\) | −12.4924 | −0.512139 | ||||||||
\(596\) | 4.68466 | 0.191891 | ||||||||
\(597\) | −1.75379 | −0.0717778 | ||||||||
\(598\) | 24.0000 | 0.981433 | ||||||||
\(599\) | 5.75379 | 0.235093 | 0.117547 | − | 0.993067i | \(-0.462497\pi\) | ||||
0.117547 | + | 0.993067i | \(0.462497\pi\) | |||||||
\(600\) | −1.56155 | −0.0637501 | ||||||||
\(601\) | −0.876894 | −0.0357693 | −0.0178846 | − | 0.999840i | \(-0.505693\pi\) | ||||
−0.0178846 | + | 0.999840i | \(0.505693\pi\) | |||||||
\(602\) | −3.12311 | −0.127288 | ||||||||
\(603\) | −1.12311 | −0.0457364 | ||||||||
\(604\) | 21.3693 | 0.869505 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 22.6307 | 0.919309 | ||||||||
\(607\) | −1.36932 | −0.0555789 | −0.0277894 | − | 0.999614i | \(-0.508847\pi\) | ||||
−0.0277894 | + | 0.999614i | \(0.508847\pi\) | |||||||
\(608\) | 7.12311 | 0.288880 | ||||||||
\(609\) | −27.1231 | −1.09908 | ||||||||
\(610\) | 5.56155 | 0.225181 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 2.24621 | 0.0907977 | ||||||||
\(613\) | −47.1231 | −1.90328 | −0.951642 | − | 0.307209i | \(-0.900605\pi\) | ||||
−0.951642 | + | 0.307209i | \(0.900605\pi\) | |||||||
\(614\) | −27.8078 | −1.12223 | ||||||||
\(615\) | −1.75379 | −0.0707196 | ||||||||
\(616\) | 3.12311 | 0.125834 | ||||||||
\(617\) | −46.4924 | −1.87171 | −0.935857 | − | 0.352379i | \(-0.885373\pi\) | ||||
−0.935857 | + | 0.352379i | \(0.885373\pi\) | |||||||
\(618\) | −12.8769 | −0.517985 | ||||||||
\(619\) | 18.2462 | 0.733377 | 0.366689 | − | 0.930344i | \(-0.380491\pi\) | ||||
0.366689 | + | 0.930344i | \(0.380491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33.3693 | −1.33906 | ||||||||
\(622\) | 7.12311 | 0.285611 | ||||||||
\(623\) | −23.0152 | −0.922083 | ||||||||
\(624\) | −6.24621 | −0.250049 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.1231 | 0.524505 | ||||||||
\(627\) | 11.1231 | 0.444214 | ||||||||
\(628\) | 7.75379 | 0.309410 | ||||||||
\(629\) | 4.49242 | 0.179125 | ||||||||
\(630\) | 1.75379 | 0.0698726 | ||||||||
\(631\) | −46.6847 | −1.85849 | −0.929243 | − | 0.369468i | \(-0.879540\pi\) | ||||
−0.929243 | + | 0.369468i | \(0.879540\pi\) | |||||||
\(632\) | 13.5616 | 0.539450 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.56155 | 0.300308 | ||||||||
\(635\) | −3.80776 | −0.151107 | ||||||||
\(636\) | −5.56155 | −0.220530 | ||||||||
\(637\) | −11.0152 | −0.436436 | ||||||||
\(638\) | −5.56155 | −0.220184 | ||||||||
\(639\) | 0.630683 | 0.0249494 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 26.0000 | 1.02694 | 0.513469 | − | 0.858108i | \(-0.328360\pi\) | ||||
0.513469 | + | 0.858108i | \(0.328360\pi\) | |||||||
\(642\) | −5.94602 | −0.234671 | ||||||||
\(643\) | 2.49242 | 0.0982915 | 0.0491458 | − | 0.998792i | \(-0.484350\pi\) | ||||
0.0491458 | + | 0.998792i | \(0.484350\pi\) | |||||||
\(644\) | 18.7386 | 0.738406 | ||||||||
\(645\) | 1.56155 | 0.0614861 | ||||||||
\(646\) | −28.4924 | −1.12102 | ||||||||
\(647\) | 21.5616 | 0.847672 | 0.423836 | − | 0.905739i | \(-0.360683\pi\) | ||||
0.423836 | + | 0.905739i | \(0.360683\pi\) | |||||||
\(648\) | 7.00000 | 0.274986 | ||||||||
\(649\) | −6.24621 | −0.245185 | ||||||||
\(650\) | 4.00000 | 0.156893 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.68466 | 0.183465 | ||||||||
\(653\) | 22.9848 | 0.899466 | 0.449733 | − | 0.893163i | \(-0.351519\pi\) | ||||
0.449733 | + | 0.893163i | \(0.351519\pi\) | |||||||
\(654\) | −1.75379 | −0.0685786 | ||||||||
\(655\) | 6.24621 | 0.244060 | ||||||||
\(656\) | −1.12311 | −0.0438499 | ||||||||
\(657\) | −0.738634 | −0.0288168 | ||||||||
\(658\) | 6.24621 | 0.243503 | ||||||||
\(659\) | −30.4384 | −1.18571 | −0.592857 | − | 0.805308i | \(-0.702000\pi\) | ||||
−0.592857 | + | 0.805308i | \(0.702000\pi\) | |||||||
\(660\) | −1.56155 | −0.0607834 | ||||||||
\(661\) | 12.4384 | 0.483800 | 0.241900 | − | 0.970301i | \(-0.422229\pi\) | ||||
0.241900 | + | 0.970301i | \(0.422229\pi\) | |||||||
\(662\) | 14.8769 | 0.578207 | ||||||||
\(663\) | 24.9848 | 0.970331 | ||||||||
\(664\) | 2.43845 | 0.0946301 | ||||||||
\(665\) | −22.2462 | −0.862671 | ||||||||
\(666\) | −0.630683 | −0.0244385 | ||||||||
\(667\) | −33.3693 | −1.29207 | ||||||||
\(668\) | 15.8078 | 0.611621 | ||||||||
\(669\) | −29.5616 | −1.14292 | ||||||||
\(670\) | −2.00000 | −0.0772667 | ||||||||
\(671\) | 5.56155 | 0.214701 | ||||||||
\(672\) | −4.87689 | −0.188130 | ||||||||
\(673\) | −28.0540 | −1.08140 | −0.540701 | − | 0.841215i | \(-0.681841\pi\) | ||||
−0.540701 | + | 0.841215i | \(0.681841\pi\) | |||||||
\(674\) | 29.3693 | 1.13126 | ||||||||
\(675\) | −5.56155 | −0.214064 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 2.68466 | 0.103180 | 0.0515899 | − | 0.998668i | \(-0.483571\pi\) | ||||
0.0515899 | + | 0.998668i | \(0.483571\pi\) | |||||||
\(678\) | −8.00000 | −0.307238 | ||||||||
\(679\) | −48.6004 | −1.86511 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | −8.38447 | −0.321294 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.61553 | −0.214872 | −0.107436 | − | 0.994212i | \(-0.534264\pi\) | ||||
−0.107436 | + | 0.994212i | \(0.534264\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | −5.12311 | −0.195744 | ||||||||
\(686\) | 13.2614 | 0.506321 | ||||||||
\(687\) | −5.56155 | −0.212186 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 14.2462 | 0.542737 | ||||||||
\(690\) | −9.36932 | −0.356684 | ||||||||
\(691\) | 26.3002 | 1.00051 | 0.500253 | − | 0.865879i | \(-0.333240\pi\) | ||||
0.500253 | + | 0.865879i | \(0.333240\pi\) | |||||||
\(692\) | −2.24621 | −0.0853881 | ||||||||
\(693\) | 1.75379 | 0.0666209 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | −4.68466 | −0.177699 | ||||||||
\(696\) | 8.68466 | 0.329191 | ||||||||
\(697\) | 4.49242 | 0.170163 | ||||||||
\(698\) | −3.12311 | −0.118211 | ||||||||
\(699\) | 5.56155 | 0.210357 | ||||||||
\(700\) | 3.12311 | 0.118042 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | −22.2462 | −0.839629 | ||||||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −3.12311 | −0.117623 | ||||||||
\(706\) | −12.4384 | −0.468127 | ||||||||
\(707\) | −45.2614 | −1.70223 | ||||||||
\(708\) | 9.75379 | 0.366570 | ||||||||
\(709\) | 8.05398 | 0.302473 | 0.151237 | − | 0.988498i | \(-0.451674\pi\) | ||||
0.151237 | + | 0.988498i | \(0.451674\pi\) | |||||||
\(710\) | 1.12311 | 0.0421494 | ||||||||
\(711\) | 7.61553 | 0.285605 | ||||||||
\(712\) | 7.36932 | 0.276177 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 19.5076 | 0.730053 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 8.43845 | 0.315360 | ||||||||
\(717\) | 1.06913 | 0.0399274 | ||||||||
\(718\) | 16.6847 | 0.622666 | ||||||||
\(719\) | 0.876894 | 0.0327026 | 0.0163513 | − | 0.999866i | \(-0.494795\pi\) | ||||
0.0163513 | + | 0.999866i | \(0.494795\pi\) | |||||||
\(720\) | −0.561553 | −0.0209278 | ||||||||
\(721\) | 25.7538 | 0.959121 | ||||||||
\(722\) | −31.7386 | −1.18119 | ||||||||
\(723\) | 26.3542 | 0.980122 | ||||||||
\(724\) | −16.0540 | −0.596641 | ||||||||
\(725\) | −5.56155 | −0.206551 | ||||||||
\(726\) | −1.56155 | −0.0579547 | ||||||||
\(727\) | 17.1771 | 0.637063 | 0.318531 | − | 0.947912i | \(-0.396810\pi\) | ||||
0.318531 | + | 0.947912i | \(0.396810\pi\) | |||||||
\(728\) | 12.4924 | 0.463000 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | −1.31534 | −0.0486830 | ||||||||
\(731\) | −4.00000 | −0.147945 | ||||||||
\(732\) | −8.68466 | −0.320994 | ||||||||
\(733\) | 11.0691 | 0.408848 | 0.204424 | − | 0.978882i | \(-0.434468\pi\) | ||||
0.204424 | + | 0.978882i | \(0.434468\pi\) | |||||||
\(734\) | −30.4924 | −1.12550 | ||||||||
\(735\) | 4.30019 | 0.158615 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | −2.00000 | −0.0736709 | ||||||||
\(738\) | −0.630683 | −0.0232158 | ||||||||
\(739\) | −14.7386 | −0.542169 | −0.271085 | − | 0.962555i | \(-0.587382\pi\) | ||||
−0.271085 | + | 0.962555i | \(0.587382\pi\) | |||||||
\(740\) | −1.12311 | −0.0412862 | ||||||||
\(741\) | 44.4924 | 1.63447 | ||||||||
\(742\) | 11.1231 | 0.408342 | ||||||||
\(743\) | −42.3542 | −1.55382 | −0.776912 | − | 0.629610i | \(-0.783215\pi\) | ||||
−0.776912 | + | 0.629610i | \(0.783215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.68466 | 0.171633 | ||||||||
\(746\) | 20.9309 | 0.766334 | ||||||||
\(747\) | 1.36932 | 0.0501007 | ||||||||
\(748\) | 4.00000 | 0.146254 | ||||||||
\(749\) | 11.8920 | 0.434526 | ||||||||
\(750\) | −1.56155 | −0.0570198 | ||||||||
\(751\) | −19.1771 | −0.699782 | −0.349891 | − | 0.936790i | \(-0.613781\pi\) | ||||
−0.349891 | + | 0.936790i | \(0.613781\pi\) | |||||||
\(752\) | −2.00000 | −0.0729325 | ||||||||
\(753\) | 39.6155 | 1.44367 | ||||||||
\(754\) | −22.2462 | −0.810159 | ||||||||
\(755\) | 21.3693 | 0.777709 | ||||||||
\(756\) | −17.3693 | −0.631716 | ||||||||
\(757\) | −46.0000 | −1.67190 | −0.835949 | − | 0.548807i | \(-0.815082\pi\) | ||||
−0.835949 | + | 0.548807i | \(0.815082\pi\) | |||||||
\(758\) | −23.6155 | −0.857755 | ||||||||
\(759\) | −9.36932 | −0.340085 | ||||||||
\(760\) | 7.12311 | 0.258382 | ||||||||
\(761\) | 22.9309 | 0.831243 | 0.415622 | − | 0.909538i | \(-0.363564\pi\) | ||||
0.415622 | + | 0.909538i | \(0.363564\pi\) | |||||||
\(762\) | 5.94602 | 0.215402 | ||||||||
\(763\) | 3.50758 | 0.126983 | ||||||||
\(764\) | −9.31534 | −0.337017 | ||||||||
\(765\) | 2.24621 | 0.0812119 | ||||||||
\(766\) | −33.1771 | −1.19874 | ||||||||
\(767\) | −24.9848 | −0.902150 | ||||||||
\(768\) | 1.56155 | 0.0563477 | ||||||||
\(769\) | 6.00000 | 0.216366 | 0.108183 | − | 0.994131i | \(-0.465497\pi\) | ||||
0.108183 | + | 0.994131i | \(0.465497\pi\) | |||||||
\(770\) | 3.12311 | 0.112549 | ||||||||
\(771\) | 16.3845 | 0.590072 | ||||||||
\(772\) | −14.2462 | −0.512732 | ||||||||
\(773\) | −41.6155 | −1.49681 | −0.748403 | − | 0.663244i | \(-0.769179\pi\) | ||||
−0.748403 | + | 0.663244i | \(0.769179\pi\) | |||||||
\(774\) | 0.561553 | 0.0201846 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.5616 | 0.558627 | ||||||||
\(777\) | −5.47727 | −0.196496 | ||||||||
\(778\) | 20.7386 | 0.743516 | ||||||||
\(779\) | 8.00000 | 0.286630 | ||||||||
\(780\) | −6.24621 | −0.223650 | ||||||||
\(781\) | 1.12311 | 0.0401879 | ||||||||
\(782\) | 24.0000 | 0.858238 | ||||||||
\(783\) | 30.9309 | 1.10538 | ||||||||
\(784\) | 2.75379 | 0.0983496 | ||||||||
\(785\) | 7.75379 | 0.276745 | ||||||||
\(786\) | −9.75379 | −0.347906 | ||||||||
\(787\) | 42.2462 | 1.50591 | 0.752957 | − | 0.658069i | \(-0.228627\pi\) | ||||
0.752957 | + | 0.658069i | \(0.228627\pi\) | |||||||
\(788\) | −1.75379 | −0.0624761 | ||||||||
\(789\) | 34.7386 | 1.23673 | ||||||||
\(790\) | 13.5616 | 0.482498 | ||||||||
\(791\) | 16.0000 | 0.568895 | ||||||||
\(792\) | −0.561553 | −0.0199539 | ||||||||
\(793\) | 22.2462 | 0.789986 | ||||||||
\(794\) | 20.4384 | 0.725333 | ||||||||
\(795\) | −5.56155 | −0.197248 | ||||||||
\(796\) | −1.12311 | −0.0398074 | ||||||||
\(797\) | −4.73863 | −0.167851 | −0.0839255 | − | 0.996472i | \(-0.526746\pi\) | ||||
−0.0839255 | + | 0.996472i | \(0.526746\pi\) | |||||||
\(798\) | 34.7386 | 1.22973 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 4.13826 | 0.146218 | ||||||||
\(802\) | −22.6847 | −0.801023 | ||||||||
\(803\) | −1.31534 | −0.0464174 | ||||||||
\(804\) | 3.12311 | 0.110143 | ||||||||
\(805\) | 18.7386 | 0.660450 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.5767 | 0.442721 | ||||||||
\(808\) | 14.4924 | 0.509842 | ||||||||
\(809\) | −7.36932 | −0.259091 | −0.129546 | − | 0.991573i | \(-0.541352\pi\) | ||||
−0.129546 | + | 0.991573i | \(0.541352\pi\) | |||||||
\(810\) | 7.00000 | 0.245955 | ||||||||
\(811\) | 24.8769 | 0.873546 | 0.436773 | − | 0.899572i | \(-0.356121\pi\) | ||||
0.436773 | + | 0.899572i | \(0.356121\pi\) | |||||||
\(812\) | −17.3693 | −0.609544 | ||||||||
\(813\) | −15.2311 | −0.534176 | ||||||||
\(814\) | −1.12311 | −0.0393648 | ||||||||
\(815\) | 4.68466 | 0.164096 | ||||||||
\(816\) | −6.24621 | −0.218661 | ||||||||
\(817\) | −7.12311 | −0.249206 | ||||||||
\(818\) | 21.5616 | 0.753882 | ||||||||
\(819\) | 7.01515 | 0.245129 | ||||||||
\(820\) | −1.12311 | −0.0392205 | ||||||||
\(821\) | −33.6155 | −1.17319 | −0.586595 | − | 0.809880i | \(-0.699532\pi\) | ||||
−0.586595 | + | 0.809880i | \(0.699532\pi\) | |||||||
\(822\) | 8.00000 | 0.279032 | ||||||||
\(823\) | −29.2311 | −1.01893 | −0.509465 | − | 0.860491i | \(-0.670157\pi\) | ||||
−0.509465 | + | 0.860491i | \(0.670157\pi\) | |||||||
\(824\) | −8.24621 | −0.287270 | ||||||||
\(825\) | −1.56155 | −0.0543663 | ||||||||
\(826\) | −19.5076 | −0.678755 | ||||||||
\(827\) | 14.4384 | 0.502074 | 0.251037 | − | 0.967977i | \(-0.419228\pi\) | ||||
0.251037 | + | 0.967977i | \(0.419228\pi\) | |||||||
\(828\) | −3.36932 | −0.117092 | ||||||||
\(829\) | 51.8617 | 1.80123 | 0.900616 | − | 0.434615i | \(-0.143116\pi\) | ||||
0.900616 | + | 0.434615i | \(0.143116\pi\) | |||||||
\(830\) | 2.43845 | 0.0846397 | ||||||||
\(831\) | −34.3542 | −1.19173 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | −11.0152 | −0.381653 | ||||||||
\(834\) | 7.31534 | 0.253310 | ||||||||
\(835\) | 15.8078 | 0.547050 | ||||||||
\(836\) | 7.12311 | 0.246358 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.0540 | 0.692753 | ||||||||
\(839\) | −22.1922 | −0.766161 | −0.383081 | − | 0.923715i | \(-0.625137\pi\) | ||||
−0.383081 | + | 0.923715i | \(0.625137\pi\) | |||||||
\(840\) | −4.87689 | −0.168269 | ||||||||
\(841\) | 1.93087 | 0.0665817 | ||||||||
\(842\) | 30.8769 | 1.06409 | ||||||||
\(843\) | 33.7538 | 1.16254 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | −1.12311 | −0.0386132 | ||||||||
\(847\) | 3.12311 | 0.107311 | ||||||||
\(848\) | −3.56155 | −0.122304 | ||||||||
\(849\) | 14.9309 | 0.512426 | ||||||||
\(850\) | 4.00000 | 0.137199 | ||||||||
\(851\) | −6.73863 | −0.230997 | ||||||||
\(852\) | −1.75379 | −0.0600838 | ||||||||
\(853\) | 19.1231 | 0.654763 | 0.327381 | − | 0.944892i | \(-0.393834\pi\) | ||||
0.327381 | + | 0.944892i | \(0.393834\pi\) | |||||||
\(854\) | 17.3693 | 0.594366 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | −3.80776 | −0.130147 | ||||||||
\(857\) | −44.4924 | −1.51983 | −0.759916 | − | 0.650021i | \(-0.774760\pi\) | ||||
−0.759916 | + | 0.650021i | \(0.774760\pi\) | |||||||
\(858\) | −6.24621 | −0.213242 | ||||||||
\(859\) | −19.8617 | −0.677674 | −0.338837 | − | 0.940845i | \(-0.610033\pi\) | ||||
−0.338837 | + | 0.940845i | \(0.610033\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | −5.47727 | −0.186665 | ||||||||
\(862\) | −26.7386 | −0.910721 | ||||||||
\(863\) | 22.5464 | 0.767488 | 0.383744 | − | 0.923439i | \(-0.374634\pi\) | ||||
0.383744 | + | 0.923439i | \(0.374634\pi\) | |||||||
\(864\) | 5.56155 | 0.189208 | ||||||||
\(865\) | −2.24621 | −0.0763735 | ||||||||
\(866\) | −31.3693 | −1.06597 | ||||||||
\(867\) | −1.56155 | −0.0530331 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.5616 | 0.460044 | ||||||||
\(870\) | 8.68466 | 0.294437 | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | −1.12311 | −0.0380332 | ||||||||
\(873\) | 8.73863 | 0.295758 | ||||||||
\(874\) | 42.7386 | 1.44566 | ||||||||
\(875\) | 3.12311 | 0.105580 | ||||||||
\(876\) | 2.05398 | 0.0693974 | ||||||||
\(877\) | 54.7386 | 1.84839 | 0.924196 | − | 0.381918i | \(-0.124736\pi\) | ||||
0.924196 | + | 0.381918i | \(0.124736\pi\) | |||||||
\(878\) | −20.4924 | −0.691586 | ||||||||
\(879\) | −3.50758 | −0.118308 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 36.4384 | 1.22764 | 0.613821 | − | 0.789445i | \(-0.289632\pi\) | ||||
0.613821 | + | 0.789445i | \(0.289632\pi\) | |||||||
\(882\) | 1.54640 | 0.0520699 | ||||||||
\(883\) | −19.3693 | −0.651829 | −0.325915 | − | 0.945399i | \(-0.605672\pi\) | ||||
−0.325915 | + | 0.945399i | \(0.605672\pi\) | |||||||
\(884\) | 16.0000 | 0.538138 | ||||||||
\(885\) | 9.75379 | 0.327870 | ||||||||
\(886\) | −16.2462 | −0.545802 | ||||||||
\(887\) | −26.7386 | −0.897795 | −0.448898 | − | 0.893583i | \(-0.648183\pi\) | ||||
−0.448898 | + | 0.893583i | \(0.648183\pi\) | |||||||
\(888\) | 1.75379 | 0.0588533 | ||||||||
\(889\) | −11.8920 | −0.398847 | ||||||||
\(890\) | 7.36932 | 0.247020 | ||||||||
\(891\) | 7.00000 | 0.234509 | ||||||||
\(892\) | −18.9309 | −0.633852 | ||||||||
\(893\) | 14.2462 | 0.476731 | ||||||||
\(894\) | −7.31534 | −0.244662 | ||||||||
\(895\) | 8.43845 | 0.282066 | ||||||||
\(896\) | −3.12311 | −0.104336 | ||||||||
\(897\) | −37.4773 | −1.25133 | ||||||||
\(898\) | −34.0000 | −1.13459 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.561553 | −0.0187184 | ||||||||
\(901\) | 14.2462 | 0.474610 | ||||||||
\(902\) | −1.12311 | −0.0373953 | ||||||||
\(903\) | 4.87689 | 0.162293 | ||||||||
\(904\) | −5.12311 | −0.170392 | ||||||||
\(905\) | −16.0540 | −0.533652 | ||||||||
\(906\) | −33.3693 | −1.10862 | ||||||||
\(907\) | 18.9848 | 0.630381 | 0.315191 | − | 0.949028i | \(-0.397932\pi\) | ||||
0.315191 | + | 0.949028i | \(0.397932\pi\) | |||||||
\(908\) | −5.36932 | −0.178187 | ||||||||
\(909\) | 8.13826 | 0.269929 | ||||||||
\(910\) | 12.4924 | 0.414120 | ||||||||
\(911\) | 33.8078 | 1.12010 | 0.560051 | − | 0.828458i | \(-0.310782\pi\) | ||||
0.560051 | + | 0.828458i | \(0.310782\pi\) | |||||||
\(912\) | −11.1231 | −0.368323 | ||||||||
\(913\) | 2.43845 | 0.0807008 | ||||||||
\(914\) | 42.4924 | 1.40552 | ||||||||
\(915\) | −8.68466 | −0.287106 | ||||||||
\(916\) | −3.56155 | −0.117677 | ||||||||
\(917\) | 19.5076 | 0.644197 | ||||||||
\(918\) | −22.2462 | −0.734234 | ||||||||
\(919\) | 17.0691 | 0.563059 | 0.281529 | − | 0.959553i | \(-0.409158\pi\) | ||||
0.281529 | + | 0.959553i | \(0.409158\pi\) | |||||||
\(920\) | −6.00000 | −0.197814 | ||||||||
\(921\) | 43.4233 | 1.43085 | ||||||||
\(922\) | 7.36932 | 0.242696 | ||||||||
\(923\) | 4.49242 | 0.147870 | ||||||||
\(924\) | −4.87689 | −0.160438 | ||||||||
\(925\) | −1.12311 | −0.0369275 | ||||||||
\(926\) | 2.24621 | 0.0738151 | ||||||||
\(927\) | −4.63068 | −0.152092 | ||||||||
\(928\) | 5.56155 | 0.182567 | ||||||||
\(929\) | −8.63068 | −0.283164 | −0.141582 | − | 0.989927i | \(-0.545219\pi\) | ||||
−0.141582 | + | 0.989927i | \(0.545219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.6155 | −0.642873 | ||||||||
\(932\) | 3.56155 | 0.116663 | ||||||||
\(933\) | −11.1231 | −0.364154 | ||||||||
\(934\) | 18.7386 | 0.613147 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | −2.24621 | −0.0734197 | ||||||||
\(937\) | 2.68466 | 0.0877040 | 0.0438520 | − | 0.999038i | \(-0.486037\pi\) | ||||
0.0438520 | + | 0.999038i | \(0.486037\pi\) | |||||||
\(938\) | −6.24621 | −0.203946 | ||||||||
\(939\) | −20.4924 | −0.668745 | ||||||||
\(940\) | −2.00000 | −0.0652328 | ||||||||
\(941\) | 57.6155 | 1.87821 | 0.939106 | − | 0.343627i | \(-0.111656\pi\) | ||||
0.939106 | + | 0.343627i | \(0.111656\pi\) | |||||||
\(942\) | −12.1080 | −0.394498 | ||||||||
\(943\) | −6.73863 | −0.219440 | ||||||||
\(944\) | 6.24621 | 0.203297 | ||||||||
\(945\) | −17.3693 | −0.565024 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −3.26137 | −0.105980 | −0.0529901 | − | 0.998595i | \(-0.516875\pi\) | ||||
−0.0529901 | + | 0.998595i | \(0.516875\pi\) | |||||||
\(948\) | −21.1771 | −0.687800 | ||||||||
\(949\) | −5.26137 | −0.170791 | ||||||||
\(950\) | 7.12311 | 0.231104 | ||||||||
\(951\) | −11.8078 | −0.382893 | ||||||||
\(952\) | 12.4924 | 0.404882 | ||||||||
\(953\) | 49.8078 | 1.61343 | 0.806716 | − | 0.590940i | \(-0.201243\pi\) | ||||
0.806716 | + | 0.590940i | \(0.201243\pi\) | |||||||
\(954\) | −2.00000 | −0.0647524 | ||||||||
\(955\) | −9.31534 | −0.301437 | ||||||||
\(956\) | 0.684658 | 0.0221434 | ||||||||
\(957\) | 8.68466 | 0.280735 | ||||||||
\(958\) | −8.68466 | −0.280589 | ||||||||
\(959\) | −16.0000 | −0.516667 | ||||||||
\(960\) | 1.56155 | 0.0503989 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −4.49242 | −0.144842 | ||||||||
\(963\) | −2.13826 | −0.0689045 | ||||||||
\(964\) | 16.8769 | 0.543568 | ||||||||
\(965\) | −14.2462 | −0.458602 | ||||||||
\(966\) | −29.2614 | −0.941469 | ||||||||
\(967\) | −39.4233 | −1.26777 | −0.633884 | − | 0.773428i | \(-0.718540\pi\) | ||||
−0.633884 | + | 0.773428i | \(0.718540\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 44.4924 | 1.42930 | ||||||||
\(970\) | 15.5616 | 0.499651 | ||||||||
\(971\) | 24.9848 | 0.801802 | 0.400901 | − | 0.916121i | \(-0.368697\pi\) | ||||
0.400901 | + | 0.916121i | \(0.368697\pi\) | |||||||
\(972\) | 5.75379 | 0.184553 | ||||||||
\(973\) | −14.6307 | −0.469038 | ||||||||
\(974\) | 6.49242 | 0.208031 | ||||||||
\(975\) | −6.24621 | −0.200039 | ||||||||
\(976\) | −5.56155 | −0.178021 | ||||||||
\(977\) | −31.5616 | −1.00974 | −0.504872 | − | 0.863194i | \(-0.668460\pi\) | ||||
−0.504872 | + | 0.863194i | \(0.668460\pi\) | |||||||
\(978\) | −7.31534 | −0.233919 | ||||||||
\(979\) | 7.36932 | 0.235524 | ||||||||
\(980\) | 2.75379 | 0.0879666 | ||||||||
\(981\) | −0.630683 | −0.0201362 | ||||||||
\(982\) | −3.12311 | −0.0996623 | ||||||||
\(983\) | 1.26137 | 0.0402313 | 0.0201157 | − | 0.999798i | \(-0.493597\pi\) | ||||
0.0201157 | + | 0.999798i | \(0.493597\pi\) | |||||||
\(984\) | 1.75379 | 0.0559087 | ||||||||
\(985\) | −1.75379 | −0.0558804 | ||||||||
\(986\) | −22.2462 | −0.708464 | ||||||||
\(987\) | −9.75379 | −0.310467 | ||||||||
\(988\) | 28.4924 | 0.906465 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | −0.561553 | −0.0178473 | ||||||||
\(991\) | −59.1771 | −1.87982 | −0.939911 | − | 0.341420i | \(-0.889092\pi\) | ||||
−0.939911 | + | 0.341420i | \(0.889092\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.2311 | −0.737215 | ||||||||
\(994\) | 3.50758 | 0.111254 | ||||||||
\(995\) | −1.12311 | −0.0356048 | ||||||||
\(996\) | −3.80776 | −0.120654 | ||||||||
\(997\) | −36.7386 | −1.16352 | −0.581762 | − | 0.813359i | \(-0.697637\pi\) | ||||
−0.581762 | + | 0.813359i | \(0.697637\pi\) | |||||||
\(998\) | 3.56155 | 0.112739 | ||||||||
\(999\) | 6.24621 | 0.197621 |
(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 | 4730.2.a.m.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.m.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |