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: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 12x^{6} + 7x^{5} + 41x^{4} - 6x^{3} - 28x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.57663\) 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 | ||||||||
\(3\) | 1.57663 | 0.910270 | 0.455135 | − | 0.890422i | \(-0.349591\pi\) | ||||
0.455135 | + | 0.890422i | \(0.349591\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.57663 | −0.643658 | ||||||||
\(7\) | 0.800428 | 0.302533 | 0.151267 | − | 0.988493i | \(-0.451665\pi\) | ||||
0.151267 | + | 0.988493i | \(0.451665\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.514223 | −0.171408 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.57663 | 0.455135 | ||||||||
\(13\) | −1.02499 | −0.284281 | −0.142141 | − | 0.989846i | \(-0.545399\pi\) | ||||
−0.142141 | + | 0.989846i | \(0.545399\pi\) | |||||||
\(14\) | −0.800428 | −0.213923 | ||||||||
\(15\) | 1.57663 | 0.407085 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.32510 | −1.29153 | −0.645763 | − | 0.763538i | \(-0.723461\pi\) | ||||
−0.645763 | + | 0.763538i | \(0.723461\pi\) | |||||||
\(18\) | 0.514223 | 0.121204 | ||||||||
\(19\) | −2.64922 | −0.607773 | −0.303886 | − | 0.952708i | \(-0.598284\pi\) | ||||
−0.303886 | + | 0.952708i | \(0.598284\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.26198 | 0.275387 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.02499 | −0.630754 | −0.315377 | − | 0.948966i | \(-0.602131\pi\) | ||||
−0.315377 | + | 0.948966i | \(0.602131\pi\) | |||||||
\(24\) | −1.57663 | −0.321829 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.02499 | 0.201017 | ||||||||
\(27\) | −5.54065 | −1.06630 | ||||||||
\(28\) | 0.800428 | 0.151267 | ||||||||
\(29\) | −0.208061 | −0.0386359 | −0.0193180 | − | 0.999813i | \(-0.506149\pi\) | ||||
−0.0193180 | + | 0.999813i | \(0.506149\pi\) | |||||||
\(30\) | −1.57663 | −0.287853 | ||||||||
\(31\) | 1.97566 | 0.354839 | 0.177419 | − | 0.984135i | \(-0.443225\pi\) | ||||
0.177419 | + | 0.984135i | \(0.443225\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.57663 | 0.274457 | ||||||||
\(34\) | 5.32510 | 0.913247 | ||||||||
\(35\) | 0.800428 | 0.135297 | ||||||||
\(36\) | −0.514223 | −0.0857039 | ||||||||
\(37\) | −6.73970 | −1.10800 | −0.554000 | − | 0.832517i | \(-0.686899\pi\) | ||||
−0.554000 | + | 0.832517i | \(0.686899\pi\) | |||||||
\(38\) | 2.64922 | 0.429760 | ||||||||
\(39\) | −1.61604 | −0.258773 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 10.4726 | 1.63555 | 0.817774 | − | 0.575539i | \(-0.195208\pi\) | ||||
0.817774 | + | 0.575539i | \(0.195208\pi\) | |||||||
\(42\) | −1.26198 | −0.194728 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −0.514223 | −0.0766559 | ||||||||
\(46\) | 3.02499 | 0.446011 | ||||||||
\(47\) | 3.55198 | 0.518110 | 0.259055 | − | 0.965863i | \(-0.416589\pi\) | ||||
0.259055 | + | 0.965863i | \(0.416589\pi\) | |||||||
\(48\) | 1.57663 | 0.227568 | ||||||||
\(49\) | −6.35931 | −0.908474 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −8.39573 | −1.17564 | ||||||||
\(52\) | −1.02499 | −0.142141 | ||||||||
\(53\) | −9.61400 | −1.32058 | −0.660292 | − | 0.751009i | \(-0.729568\pi\) | ||||
−0.660292 | + | 0.751009i | \(0.729568\pi\) | |||||||
\(54\) | 5.54065 | 0.753986 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −0.800428 | −0.106962 | ||||||||
\(57\) | −4.17685 | −0.553237 | ||||||||
\(58\) | 0.208061 | 0.0273197 | ||||||||
\(59\) | −11.8754 | −1.54605 | −0.773023 | − | 0.634378i | \(-0.781256\pi\) | ||||
−0.773023 | + | 0.634378i | \(0.781256\pi\) | |||||||
\(60\) | 1.57663 | 0.203543 | ||||||||
\(61\) | −2.97971 | −0.381513 | −0.190757 | − | 0.981637i | \(-0.561094\pi\) | ||||
−0.190757 | + | 0.981637i | \(0.561094\pi\) | |||||||
\(62\) | −1.97566 | −0.250909 | ||||||||
\(63\) | −0.411599 | −0.0518566 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.02499 | −0.127135 | ||||||||
\(66\) | −1.57663 | −0.194070 | ||||||||
\(67\) | −10.5520 | −1.28913 | −0.644567 | − | 0.764548i | \(-0.722962\pi\) | ||||
−0.644567 | + | 0.764548i | \(0.722962\pi\) | |||||||
\(68\) | −5.32510 | −0.645763 | ||||||||
\(69\) | −4.76931 | −0.574157 | ||||||||
\(70\) | −0.800428 | −0.0956695 | ||||||||
\(71\) | −6.73861 | −0.799726 | −0.399863 | − | 0.916575i | \(-0.630942\pi\) | ||||
−0.399863 | + | 0.916575i | \(0.630942\pi\) | |||||||
\(72\) | 0.514223 | 0.0606018 | ||||||||
\(73\) | 1.32907 | 0.155556 | 0.0777780 | − | 0.996971i | \(-0.475217\pi\) | ||||
0.0777780 | + | 0.996971i | \(0.475217\pi\) | |||||||
\(74\) | 6.73970 | 0.783474 | ||||||||
\(75\) | 1.57663 | 0.182054 | ||||||||
\(76\) | −2.64922 | −0.303886 | ||||||||
\(77\) | 0.800428 | 0.0912173 | ||||||||
\(78\) | 1.61604 | 0.182980 | ||||||||
\(79\) | 8.33391 | 0.937638 | 0.468819 | − | 0.883294i | \(-0.344680\pi\) | ||||
0.468819 | + | 0.883294i | \(0.344680\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.19290 | −0.799212 | ||||||||
\(82\) | −10.4726 | −1.15651 | ||||||||
\(83\) | 10.2036 | 1.11999 | 0.559994 | − | 0.828496i | \(-0.310803\pi\) | ||||
0.559994 | + | 0.828496i | \(0.310803\pi\) | |||||||
\(84\) | 1.26198 | 0.137694 | ||||||||
\(85\) | −5.32510 | −0.577588 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | −0.328036 | −0.0351691 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 9.34345 | 0.990404 | 0.495202 | − | 0.868778i | \(-0.335094\pi\) | ||||
0.495202 | + | 0.868778i | \(0.335094\pi\) | |||||||
\(90\) | 0.514223 | 0.0542039 | ||||||||
\(91\) | −0.820432 | −0.0860046 | ||||||||
\(92\) | −3.02499 | −0.315377 | ||||||||
\(93\) | 3.11489 | 0.322999 | ||||||||
\(94\) | −3.55198 | −0.366359 | ||||||||
\(95\) | −2.64922 | −0.271804 | ||||||||
\(96\) | −1.57663 | −0.160915 | ||||||||
\(97\) | 0.294217 | 0.0298732 | 0.0149366 | − | 0.999888i | \(-0.495245\pi\) | ||||
0.0149366 | + | 0.999888i | \(0.495245\pi\) | |||||||
\(98\) | 6.35931 | 0.642388 | ||||||||
\(99\) | −0.514223 | −0.0516814 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.14270 | 0.113702 | 0.0568512 | − | 0.998383i | \(-0.481894\pi\) | ||||
0.0568512 | + | 0.998383i | \(0.481894\pi\) | |||||||
\(102\) | 8.39573 | 0.831302 | ||||||||
\(103\) | −9.50752 | −0.936804 | −0.468402 | − | 0.883516i | \(-0.655170\pi\) | ||||
−0.468402 | + | 0.883516i | \(0.655170\pi\) | |||||||
\(104\) | 1.02499 | 0.100509 | ||||||||
\(105\) | 1.26198 | 0.123157 | ||||||||
\(106\) | 9.61400 | 0.933794 | ||||||||
\(107\) | 4.79302 | 0.463359 | 0.231679 | − | 0.972792i | \(-0.425578\pi\) | ||||
0.231679 | + | 0.972792i | \(0.425578\pi\) | |||||||
\(108\) | −5.54065 | −0.533149 | ||||||||
\(109\) | −17.2100 | −1.64842 | −0.824209 | − | 0.566286i | \(-0.808380\pi\) | ||||
−0.824209 | + | 0.566286i | \(0.808380\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −10.6260 | −1.00858 | ||||||||
\(112\) | 0.800428 | 0.0756334 | ||||||||
\(113\) | −12.6986 | −1.19458 | −0.597292 | − | 0.802024i | \(-0.703756\pi\) | ||||
−0.597292 | + | 0.802024i | \(0.703756\pi\) | |||||||
\(114\) | 4.17685 | 0.391198 | ||||||||
\(115\) | −3.02499 | −0.282082 | ||||||||
\(116\) | −0.208061 | −0.0193180 | ||||||||
\(117\) | 0.527074 | 0.0487281 | ||||||||
\(118\) | 11.8754 | 1.09322 | ||||||||
\(119\) | −4.26236 | −0.390730 | ||||||||
\(120\) | −1.57663 | −0.143926 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.97971 | 0.269771 | ||||||||
\(123\) | 16.5115 | 1.48879 | ||||||||
\(124\) | 1.97566 | 0.177419 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.411599 | 0.0366682 | ||||||||
\(127\) | 19.3137 | 1.71381 | 0.856907 | − | 0.515471i | \(-0.172383\pi\) | ||||
0.856907 | + | 0.515471i | \(0.172383\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.57663 | −0.138815 | ||||||||
\(130\) | 1.02499 | 0.0898977 | ||||||||
\(131\) | −2.23687 | −0.195436 | −0.0977180 | − | 0.995214i | \(-0.531154\pi\) | ||||
−0.0977180 | + | 0.995214i | \(0.531154\pi\) | |||||||
\(132\) | 1.57663 | 0.137228 | ||||||||
\(133\) | −2.12051 | −0.183872 | ||||||||
\(134\) | 10.5520 | 0.911555 | ||||||||
\(135\) | −5.54065 | −0.476863 | ||||||||
\(136\) | 5.32510 | 0.456623 | ||||||||
\(137\) | 15.3916 | 1.31499 | 0.657496 | − | 0.753458i | \(-0.271616\pi\) | ||||
0.657496 | + | 0.753458i | \(0.271616\pi\) | |||||||
\(138\) | 4.76931 | 0.405990 | ||||||||
\(139\) | −16.6321 | −1.41072 | −0.705358 | − | 0.708851i | \(-0.749214\pi\) | ||||
−0.705358 | + | 0.708851i | \(0.749214\pi\) | |||||||
\(140\) | 0.800428 | 0.0676485 | ||||||||
\(141\) | 5.60018 | 0.471620 | ||||||||
\(142\) | 6.73861 | 0.565492 | ||||||||
\(143\) | −1.02499 | −0.0857141 | ||||||||
\(144\) | −0.514223 | −0.0428520 | ||||||||
\(145\) | −0.208061 | −0.0172785 | ||||||||
\(146\) | −1.32907 | −0.109995 | ||||||||
\(147\) | −10.0263 | −0.826957 | ||||||||
\(148\) | −6.73970 | −0.554000 | ||||||||
\(149\) | −13.1363 | −1.07617 | −0.538083 | − | 0.842892i | \(-0.680851\pi\) | ||||
−0.538083 | + | 0.842892i | \(0.680851\pi\) | |||||||
\(150\) | −1.57663 | −0.128732 | ||||||||
\(151\) | 5.38185 | 0.437969 | 0.218984 | − | 0.975728i | \(-0.429726\pi\) | ||||
0.218984 | + | 0.975728i | \(0.429726\pi\) | |||||||
\(152\) | 2.64922 | 0.214880 | ||||||||
\(153\) | 2.73829 | 0.221378 | ||||||||
\(154\) | −0.800428 | −0.0645003 | ||||||||
\(155\) | 1.97566 | 0.158689 | ||||||||
\(156\) | −1.61604 | −0.129386 | ||||||||
\(157\) | −15.7870 | −1.25994 | −0.629969 | − | 0.776620i | \(-0.716932\pi\) | ||||
−0.629969 | + | 0.776620i | \(0.716932\pi\) | |||||||
\(158\) | −8.33391 | −0.663010 | ||||||||
\(159\) | −15.1578 | −1.20209 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.42129 | −0.190824 | ||||||||
\(162\) | 7.19290 | 0.565128 | ||||||||
\(163\) | −17.6800 | −1.38481 | −0.692403 | − | 0.721511i | \(-0.743448\pi\) | ||||
−0.692403 | + | 0.721511i | \(0.743448\pi\) | |||||||
\(164\) | 10.4726 | 0.817774 | ||||||||
\(165\) | 1.57663 | 0.122741 | ||||||||
\(166\) | −10.2036 | −0.791952 | ||||||||
\(167\) | 4.11462 | 0.318399 | 0.159199 | − | 0.987246i | \(-0.449109\pi\) | ||||
0.159199 | + | 0.987246i | \(0.449109\pi\) | |||||||
\(168\) | −1.26198 | −0.0973641 | ||||||||
\(169\) | −11.9494 | −0.919184 | ||||||||
\(170\) | 5.32510 | 0.408416 | ||||||||
\(171\) | 1.36229 | 0.104177 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | −17.3731 | −1.32085 | −0.660426 | − | 0.750891i | \(-0.729624\pi\) | ||||
−0.660426 | + | 0.750891i | \(0.729624\pi\) | |||||||
\(174\) | 0.328036 | 0.0248683 | ||||||||
\(175\) | 0.800428 | 0.0605067 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −18.7232 | −1.40732 | ||||||||
\(178\) | −9.34345 | −0.700321 | ||||||||
\(179\) | 3.11052 | 0.232491 | 0.116246 | − | 0.993220i | \(-0.462914\pi\) | ||||
0.116246 | + | 0.993220i | \(0.462914\pi\) | |||||||
\(180\) | −0.514223 | −0.0383280 | ||||||||
\(181\) | 19.5553 | 1.45353 | 0.726766 | − | 0.686885i | \(-0.241023\pi\) | ||||
0.726766 | + | 0.686885i | \(0.241023\pi\) | |||||||
\(182\) | 0.820432 | 0.0608145 | ||||||||
\(183\) | −4.69792 | −0.347280 | ||||||||
\(184\) | 3.02499 | 0.223005 | ||||||||
\(185\) | −6.73970 | −0.495513 | ||||||||
\(186\) | −3.11489 | −0.228395 | ||||||||
\(187\) | −5.32510 | −0.389410 | ||||||||
\(188\) | 3.55198 | 0.259055 | ||||||||
\(189\) | −4.43489 | −0.322591 | ||||||||
\(190\) | 2.64922 | 0.192195 | ||||||||
\(191\) | 11.5515 | 0.835840 | 0.417920 | − | 0.908484i | \(-0.362759\pi\) | ||||
0.417920 | + | 0.908484i | \(0.362759\pi\) | |||||||
\(192\) | 1.57663 | 0.113784 | ||||||||
\(193\) | 15.7250 | 1.13191 | 0.565955 | − | 0.824436i | \(-0.308508\pi\) | ||||
0.565955 | + | 0.824436i | \(0.308508\pi\) | |||||||
\(194\) | −0.294217 | −0.0211235 | ||||||||
\(195\) | −1.61604 | −0.115727 | ||||||||
\(196\) | −6.35931 | −0.454237 | ||||||||
\(197\) | −12.6214 | −0.899236 | −0.449618 | − | 0.893221i | \(-0.648440\pi\) | ||||
−0.449618 | + | 0.893221i | \(0.648440\pi\) | |||||||
\(198\) | 0.514223 | 0.0365443 | ||||||||
\(199\) | 8.27011 | 0.586253 | 0.293126 | − | 0.956074i | \(-0.405304\pi\) | ||||
0.293126 | + | 0.956074i | \(0.405304\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −16.6367 | −1.17346 | ||||||||
\(202\) | −1.14270 | −0.0803998 | ||||||||
\(203\) | −0.166538 | −0.0116887 | ||||||||
\(204\) | −8.39573 | −0.587819 | ||||||||
\(205\) | 10.4726 | 0.731440 | ||||||||
\(206\) | 9.50752 | 0.662420 | ||||||||
\(207\) | 1.55552 | 0.108116 | ||||||||
\(208\) | −1.02499 | −0.0710703 | ||||||||
\(209\) | −2.64922 | −0.183250 | ||||||||
\(210\) | −1.26198 | −0.0870851 | ||||||||
\(211\) | −4.00515 | −0.275726 | −0.137863 | − | 0.990451i | \(-0.544023\pi\) | ||||
−0.137863 | + | 0.990451i | \(0.544023\pi\) | |||||||
\(212\) | −9.61400 | −0.660292 | ||||||||
\(213\) | −10.6243 | −0.727967 | ||||||||
\(214\) | −4.79302 | −0.327644 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 5.54065 | 0.376993 | ||||||||
\(217\) | 1.58137 | 0.107351 | ||||||||
\(218\) | 17.2100 | 1.16561 | ||||||||
\(219\) | 2.09546 | 0.141598 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 5.45818 | 0.367157 | ||||||||
\(222\) | 10.6260 | 0.713173 | ||||||||
\(223\) | −9.48329 | −0.635048 | −0.317524 | − | 0.948250i | \(-0.602851\pi\) | ||||
−0.317524 | + | 0.948250i | \(0.602851\pi\) | |||||||
\(224\) | −0.800428 | −0.0534809 | ||||||||
\(225\) | −0.514223 | −0.0342816 | ||||||||
\(226\) | 12.6986 | 0.844698 | ||||||||
\(227\) | 12.2245 | 0.811372 | 0.405686 | − | 0.914013i | \(-0.367033\pi\) | ||||
0.405686 | + | 0.914013i | \(0.367033\pi\) | |||||||
\(228\) | −4.17685 | −0.276619 | ||||||||
\(229\) | 16.0960 | 1.06365 | 0.531826 | − | 0.846854i | \(-0.321506\pi\) | ||||
0.531826 | + | 0.846854i | \(0.321506\pi\) | |||||||
\(230\) | 3.02499 | 0.199462 | ||||||||
\(231\) | 1.26198 | 0.0830324 | ||||||||
\(232\) | 0.208061 | 0.0136599 | ||||||||
\(233\) | 23.9182 | 1.56693 | 0.783466 | − | 0.621435i | \(-0.213450\pi\) | ||||
0.783466 | + | 0.621435i | \(0.213450\pi\) | |||||||
\(234\) | −0.527074 | −0.0344559 | ||||||||
\(235\) | 3.55198 | 0.231706 | ||||||||
\(236\) | −11.8754 | −0.773023 | ||||||||
\(237\) | 13.1395 | 0.853504 | ||||||||
\(238\) | 4.26236 | 0.276288 | ||||||||
\(239\) | 20.7070 | 1.33942 | 0.669711 | − | 0.742622i | \(-0.266418\pi\) | ||||
0.669711 | + | 0.742622i | \(0.266418\pi\) | |||||||
\(240\) | 1.57663 | 0.101771 | ||||||||
\(241\) | −13.8160 | −0.889968 | −0.444984 | − | 0.895539i | \(-0.646791\pi\) | ||||
−0.444984 | + | 0.895539i | \(0.646791\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 5.28136 | 0.338799 | ||||||||
\(244\) | −2.97971 | −0.190757 | ||||||||
\(245\) | −6.35931 | −0.406282 | ||||||||
\(246\) | −16.5115 | −1.05273 | ||||||||
\(247\) | 2.71543 | 0.172778 | ||||||||
\(248\) | −1.97566 | −0.125454 | ||||||||
\(249\) | 16.0873 | 1.01949 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −5.08380 | −0.320887 | −0.160443 | − | 0.987045i | \(-0.551292\pi\) | ||||
−0.160443 | + | 0.987045i | \(0.551292\pi\) | |||||||
\(252\) | −0.411599 | −0.0259283 | ||||||||
\(253\) | −3.02499 | −0.190180 | ||||||||
\(254\) | −19.3137 | −1.21185 | ||||||||
\(255\) | −8.39573 | −0.525761 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.8556 | −1.05142 | −0.525712 | − | 0.850663i | \(-0.676201\pi\) | ||||
−0.525712 | + | 0.850663i | \(0.676201\pi\) | |||||||
\(258\) | 1.57663 | 0.0981570 | ||||||||
\(259\) | −5.39465 | −0.335207 | ||||||||
\(260\) | −1.02499 | −0.0635673 | ||||||||
\(261\) | 0.106990 | 0.00662250 | ||||||||
\(262\) | 2.23687 | 0.138194 | ||||||||
\(263\) | 11.0417 | 0.680861 | 0.340431 | − | 0.940270i | \(-0.389427\pi\) | ||||
0.340431 | + | 0.940270i | \(0.389427\pi\) | |||||||
\(264\) | −1.57663 | −0.0970351 | ||||||||
\(265\) | −9.61400 | −0.590583 | ||||||||
\(266\) | 2.12051 | 0.130017 | ||||||||
\(267\) | 14.7312 | 0.901536 | ||||||||
\(268\) | −10.5520 | −0.644567 | ||||||||
\(269\) | 5.90487 | 0.360026 | 0.180013 | − | 0.983664i | \(-0.442386\pi\) | ||||
0.180013 | + | 0.983664i | \(0.442386\pi\) | |||||||
\(270\) | 5.54065 | 0.337193 | ||||||||
\(271\) | −0.109692 | −0.00666330 | −0.00333165 | − | 0.999994i | \(-0.501060\pi\) | ||||
−0.00333165 | + | 0.999994i | \(0.501060\pi\) | |||||||
\(272\) | −5.32510 | −0.322882 | ||||||||
\(273\) | −1.29352 | −0.0782875 | ||||||||
\(274\) | −15.3916 | −0.929840 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −4.76931 | −0.287078 | ||||||||
\(277\) | −10.1828 | −0.611825 | −0.305913 | − | 0.952060i | \(-0.598962\pi\) | ||||
−0.305913 | + | 0.952060i | \(0.598962\pi\) | |||||||
\(278\) | 16.6321 | 0.997527 | ||||||||
\(279\) | −1.01593 | −0.0608221 | ||||||||
\(280\) | −0.800428 | −0.0478347 | ||||||||
\(281\) | 12.0954 | 0.721549 | 0.360774 | − | 0.932653i | \(-0.382512\pi\) | ||||
0.360774 | + | 0.932653i | \(0.382512\pi\) | |||||||
\(282\) | −5.60018 | −0.333486 | ||||||||
\(283\) | 3.46228 | 0.205811 | 0.102906 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102906 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(284\) | −6.73861 | −0.399863 | ||||||||
\(285\) | −4.17685 | −0.247415 | ||||||||
\(286\) | 1.02499 | 0.0606090 | ||||||||
\(287\) | 8.38258 | 0.494808 | ||||||||
\(288\) | 0.514223 | 0.0303009 | ||||||||
\(289\) | 11.3567 | 0.668040 | ||||||||
\(290\) | 0.208061 | 0.0122177 | ||||||||
\(291\) | 0.463873 | 0.0271927 | ||||||||
\(292\) | 1.32907 | 0.0777780 | ||||||||
\(293\) | −32.8264 | −1.91774 | −0.958869 | − | 0.283848i | \(-0.908389\pi\) | ||||
−0.958869 | + | 0.283848i | \(0.908389\pi\) | |||||||
\(294\) | 10.0263 | 0.584747 | ||||||||
\(295\) | −11.8754 | −0.691413 | ||||||||
\(296\) | 6.73970 | 0.391737 | ||||||||
\(297\) | −5.54065 | −0.321501 | ||||||||
\(298\) | 13.1363 | 0.760964 | ||||||||
\(299\) | 3.10059 | 0.179312 | ||||||||
\(300\) | 1.57663 | 0.0910270 | ||||||||
\(301\) | −0.800428 | −0.0461359 | ||||||||
\(302\) | −5.38185 | −0.309691 | ||||||||
\(303\) | 1.80161 | 0.103500 | ||||||||
\(304\) | −2.64922 | −0.151943 | ||||||||
\(305\) | −2.97971 | −0.170618 | ||||||||
\(306\) | −2.73829 | −0.156538 | ||||||||
\(307\) | 15.8101 | 0.902327 | 0.451164 | − | 0.892441i | \(-0.351009\pi\) | ||||
0.451164 | + | 0.892441i | \(0.351009\pi\) | |||||||
\(308\) | 0.800428 | 0.0456086 | ||||||||
\(309\) | −14.9899 | −0.852745 | ||||||||
\(310\) | −1.97566 | −0.112210 | ||||||||
\(311\) | −7.41195 | −0.420293 | −0.210147 | − | 0.977670i | \(-0.567394\pi\) | ||||
−0.210147 | + | 0.977670i | \(0.567394\pi\) | |||||||
\(312\) | 1.61604 | 0.0914900 | ||||||||
\(313\) | 14.8333 | 0.838426 | 0.419213 | − | 0.907888i | \(-0.362306\pi\) | ||||
0.419213 | + | 0.907888i | \(0.362306\pi\) | |||||||
\(314\) | 15.7870 | 0.890911 | ||||||||
\(315\) | −0.411599 | −0.0231910 | ||||||||
\(316\) | 8.33391 | 0.468819 | ||||||||
\(317\) | 18.5511 | 1.04193 | 0.520967 | − | 0.853577i | \(-0.325571\pi\) | ||||
0.520967 | + | 0.853577i | \(0.325571\pi\) | |||||||
\(318\) | 15.1578 | 0.850005 | ||||||||
\(319\) | −0.208061 | −0.0116492 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 7.55684 | 0.421782 | ||||||||
\(322\) | 2.42129 | 0.134933 | ||||||||
\(323\) | 14.1074 | 0.784954 | ||||||||
\(324\) | −7.19290 | −0.399606 | ||||||||
\(325\) | −1.02499 | −0.0568563 | ||||||||
\(326\) | 17.6800 | 0.979206 | ||||||||
\(327\) | −27.1338 | −1.50051 | ||||||||
\(328\) | −10.4726 | −0.578254 | ||||||||
\(329\) | 2.84311 | 0.156745 | ||||||||
\(330\) | −1.57663 | −0.0867909 | ||||||||
\(331\) | 11.7965 | 0.648393 | 0.324196 | − | 0.945990i | \(-0.394906\pi\) | ||||
0.324196 | + | 0.945990i | \(0.394906\pi\) | |||||||
\(332\) | 10.2036 | 0.559994 | ||||||||
\(333\) | 3.46571 | 0.189920 | ||||||||
\(334\) | −4.11462 | −0.225142 | ||||||||
\(335\) | −10.5520 | −0.576518 | ||||||||
\(336\) | 1.26198 | 0.0688468 | ||||||||
\(337\) | 10.8501 | 0.591043 | 0.295521 | − | 0.955336i | \(-0.404507\pi\) | ||||
0.295521 | + | 0.955336i | \(0.404507\pi\) | |||||||
\(338\) | 11.9494 | 0.649961 | ||||||||
\(339\) | −20.0210 | −1.08739 | ||||||||
\(340\) | −5.32510 | −0.288794 | ||||||||
\(341\) | 1.97566 | 0.106988 | ||||||||
\(342\) | −1.36229 | −0.0736642 | ||||||||
\(343\) | −10.6932 | −0.577377 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | −4.76931 | −0.256771 | ||||||||
\(346\) | 17.3731 | 0.933984 | ||||||||
\(347\) | −21.8988 | −1.17559 | −0.587794 | − | 0.809011i | \(-0.700003\pi\) | ||||
−0.587794 | + | 0.809011i | \(0.700003\pi\) | |||||||
\(348\) | −0.328036 | −0.0175846 | ||||||||
\(349\) | 4.86814 | 0.260585 | 0.130293 | − | 0.991476i | \(-0.458408\pi\) | ||||
0.130293 | + | 0.991476i | \(0.458408\pi\) | |||||||
\(350\) | −0.800428 | −0.0427847 | ||||||||
\(351\) | 5.67911 | 0.303129 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −3.25663 | −0.173333 | −0.0866664 | − | 0.996237i | \(-0.527621\pi\) | ||||
−0.0866664 | + | 0.996237i | \(0.527621\pi\) | |||||||
\(354\) | 18.7232 | 0.995126 | ||||||||
\(355\) | −6.73861 | −0.357648 | ||||||||
\(356\) | 9.34345 | 0.495202 | ||||||||
\(357\) | −6.72018 | −0.355670 | ||||||||
\(358\) | −3.11052 | −0.164396 | ||||||||
\(359\) | 9.66427 | 0.510061 | 0.255030 | − | 0.966933i | \(-0.417915\pi\) | ||||
0.255030 | + | 0.966933i | \(0.417915\pi\) | |||||||
\(360\) | 0.514223 | 0.0271020 | ||||||||
\(361\) | −11.9816 | −0.630613 | ||||||||
\(362\) | −19.5553 | −1.02780 | ||||||||
\(363\) | 1.57663 | 0.0827519 | ||||||||
\(364\) | −0.820432 | −0.0430023 | ||||||||
\(365\) | 1.32907 | 0.0695668 | ||||||||
\(366\) | 4.69792 | 0.245564 | ||||||||
\(367\) | −27.2816 | −1.42409 | −0.712043 | − | 0.702136i | \(-0.752230\pi\) | ||||
−0.712043 | + | 0.702136i | \(0.752230\pi\) | |||||||
\(368\) | −3.02499 | −0.157689 | ||||||||
\(369\) | −5.38527 | −0.280346 | ||||||||
\(370\) | 6.73970 | 0.350380 | ||||||||
\(371\) | −7.69532 | −0.399521 | ||||||||
\(372\) | 3.11489 | 0.161500 | ||||||||
\(373\) | −26.5850 | −1.37652 | −0.688259 | − | 0.725465i | \(-0.741625\pi\) | ||||
−0.688259 | + | 0.725465i | \(0.741625\pi\) | |||||||
\(374\) | 5.32510 | 0.275354 | ||||||||
\(375\) | 1.57663 | 0.0814171 | ||||||||
\(376\) | −3.55198 | −0.183179 | ||||||||
\(377\) | 0.213260 | 0.0109835 | ||||||||
\(378\) | 4.43489 | 0.228106 | ||||||||
\(379\) | −17.8037 | −0.914514 | −0.457257 | − | 0.889335i | \(-0.651168\pi\) | ||||
−0.457257 | + | 0.889335i | \(0.651168\pi\) | |||||||
\(380\) | −2.64922 | −0.135902 | ||||||||
\(381\) | 30.4506 | 1.56003 | ||||||||
\(382\) | −11.5515 | −0.591028 | ||||||||
\(383\) | 17.7357 | 0.906253 | 0.453126 | − | 0.891446i | \(-0.350309\pi\) | ||||
0.453126 | + | 0.891446i | \(0.350309\pi\) | |||||||
\(384\) | −1.57663 | −0.0804573 | ||||||||
\(385\) | 0.800428 | 0.0407936 | ||||||||
\(386\) | −15.7250 | −0.800381 | ||||||||
\(387\) | 0.514223 | 0.0261394 | ||||||||
\(388\) | 0.294217 | 0.0149366 | ||||||||
\(389\) | −29.6312 | −1.50236 | −0.751180 | − | 0.660098i | \(-0.770515\pi\) | ||||
−0.751180 | + | 0.660098i | \(0.770515\pi\) | |||||||
\(390\) | 1.61604 | 0.0818312 | ||||||||
\(391\) | 16.1084 | 0.814636 | ||||||||
\(392\) | 6.35931 | 0.321194 | ||||||||
\(393\) | −3.52672 | −0.177900 | ||||||||
\(394\) | 12.6214 | 0.635856 | ||||||||
\(395\) | 8.33391 | 0.419324 | ||||||||
\(396\) | −0.514223 | −0.0258407 | ||||||||
\(397\) | −0.874875 | −0.0439087 | −0.0219543 | − | 0.999759i | \(-0.506989\pi\) | ||||
−0.0219543 | + | 0.999759i | \(0.506989\pi\) | |||||||
\(398\) | −8.27011 | −0.414543 | ||||||||
\(399\) | −3.34327 | −0.167373 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 16.7273 | 0.835322 | 0.417661 | − | 0.908603i | \(-0.362850\pi\) | ||||
0.417661 | + | 0.908603i | \(0.362850\pi\) | |||||||
\(402\) | 16.6367 | 0.829761 | ||||||||
\(403\) | −2.02503 | −0.100874 | ||||||||
\(404\) | 1.14270 | 0.0568512 | ||||||||
\(405\) | −7.19290 | −0.357418 | ||||||||
\(406\) | 0.166538 | 0.00826513 | ||||||||
\(407\) | −6.73970 | −0.334075 | ||||||||
\(408\) | 8.39573 | 0.415651 | ||||||||
\(409\) | 11.4333 | 0.565341 | 0.282670 | − | 0.959217i | \(-0.408780\pi\) | ||||
0.282670 | + | 0.959217i | \(0.408780\pi\) | |||||||
\(410\) | −10.4726 | −0.517206 | ||||||||
\(411\) | 24.2669 | 1.19700 | ||||||||
\(412\) | −9.50752 | −0.468402 | ||||||||
\(413\) | −9.50541 | −0.467731 | ||||||||
\(414\) | −1.55552 | −0.0764497 | ||||||||
\(415\) | 10.2036 | 0.500874 | ||||||||
\(416\) | 1.02499 | 0.0502543 | ||||||||
\(417\) | −26.2227 | −1.28413 | ||||||||
\(418\) | 2.64922 | 0.129578 | ||||||||
\(419\) | −0.915714 | −0.0447356 | −0.0223678 | − | 0.999750i | \(-0.507120\pi\) | ||||
−0.0223678 | + | 0.999750i | \(0.507120\pi\) | |||||||
\(420\) | 1.26198 | 0.0615785 | ||||||||
\(421\) | 23.5860 | 1.14951 | 0.574757 | − | 0.818324i | \(-0.305097\pi\) | ||||
0.574757 | + | 0.818324i | \(0.305097\pi\) | |||||||
\(422\) | 4.00515 | 0.194968 | ||||||||
\(423\) | −1.82651 | −0.0888080 | ||||||||
\(424\) | 9.61400 | 0.466897 | ||||||||
\(425\) | −5.32510 | −0.258305 | ||||||||
\(426\) | 10.6243 | 0.514750 | ||||||||
\(427\) | −2.38505 | −0.115420 | ||||||||
\(428\) | 4.79302 | 0.231679 | ||||||||
\(429\) | −1.61604 | −0.0780230 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | 26.1671 | 1.26043 | 0.630213 | − | 0.776423i | \(-0.282968\pi\) | ||||
0.630213 | + | 0.776423i | \(0.282968\pi\) | |||||||
\(432\) | −5.54065 | −0.266574 | ||||||||
\(433\) | −15.9409 | −0.766072 | −0.383036 | − | 0.923733i | \(-0.625121\pi\) | ||||
−0.383036 | + | 0.923733i | \(0.625121\pi\) | |||||||
\(434\) | −1.58137 | −0.0759083 | ||||||||
\(435\) | −0.328036 | −0.0157281 | ||||||||
\(436\) | −17.2100 | −0.824209 | ||||||||
\(437\) | 8.01386 | 0.383355 | ||||||||
\(438\) | −2.09546 | −0.100125 | ||||||||
\(439\) | −30.0150 | −1.43254 | −0.716268 | − | 0.697825i | \(-0.754151\pi\) | ||||
−0.716268 | + | 0.697825i | \(0.754151\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 3.27011 | 0.155719 | ||||||||
\(442\) | −5.45818 | −0.259619 | ||||||||
\(443\) | 24.5171 | 1.16484 | 0.582421 | − | 0.812887i | \(-0.302105\pi\) | ||||
0.582421 | + | 0.812887i | \(0.302105\pi\) | |||||||
\(444\) | −10.6260 | −0.504290 | ||||||||
\(445\) | 9.34345 | 0.442922 | ||||||||
\(446\) | 9.48329 | 0.449047 | ||||||||
\(447\) | −20.7111 | −0.979602 | ||||||||
\(448\) | 0.800428 | 0.0378167 | ||||||||
\(449\) | 26.7819 | 1.26391 | 0.631957 | − | 0.775003i | \(-0.282252\pi\) | ||||
0.631957 | + | 0.775003i | \(0.282252\pi\) | |||||||
\(450\) | 0.514223 | 0.0242407 | ||||||||
\(451\) | 10.4726 | 0.493136 | ||||||||
\(452\) | −12.6986 | −0.597292 | ||||||||
\(453\) | 8.48521 | 0.398670 | ||||||||
\(454\) | −12.2245 | −0.573726 | ||||||||
\(455\) | −0.820432 | −0.0384624 | ||||||||
\(456\) | 4.17685 | 0.195599 | ||||||||
\(457\) | −6.46219 | −0.302289 | −0.151144 | − | 0.988512i | \(-0.548296\pi\) | ||||
−0.151144 | + | 0.988512i | \(0.548296\pi\) | |||||||
\(458\) | −16.0960 | −0.752116 | ||||||||
\(459\) | 29.5045 | 1.37715 | ||||||||
\(460\) | −3.02499 | −0.141041 | ||||||||
\(461\) | 26.6725 | 1.24226 | 0.621132 | − | 0.783706i | \(-0.286673\pi\) | ||||
0.621132 | + | 0.783706i | \(0.286673\pi\) | |||||||
\(462\) | −1.26198 | −0.0587128 | ||||||||
\(463\) | −16.9910 | −0.789638 | −0.394819 | − | 0.918759i | \(-0.629193\pi\) | ||||
−0.394819 | + | 0.918759i | \(0.629193\pi\) | |||||||
\(464\) | −0.208061 | −0.00965898 | ||||||||
\(465\) | 3.11489 | 0.144450 | ||||||||
\(466\) | −23.9182 | −1.10799 | ||||||||
\(467\) | −24.6468 | −1.14052 | −0.570258 | − | 0.821465i | \(-0.693157\pi\) | ||||
−0.570258 | + | 0.821465i | \(0.693157\pi\) | |||||||
\(468\) | 0.527074 | 0.0243640 | ||||||||
\(469\) | −8.44613 | −0.390006 | ||||||||
\(470\) | −3.55198 | −0.163841 | ||||||||
\(471\) | −24.8903 | −1.14688 | ||||||||
\(472\) | 11.8754 | 0.546610 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −13.1395 | −0.603519 | ||||||||
\(475\) | −2.64922 | −0.121555 | ||||||||
\(476\) | −4.26236 | −0.195365 | ||||||||
\(477\) | 4.94374 | 0.226358 | ||||||||
\(478\) | −20.7070 | −0.947114 | ||||||||
\(479\) | −31.3134 | −1.43074 | −0.715372 | − | 0.698744i | \(-0.753743\pi\) | ||||
−0.715372 | + | 0.698744i | \(0.753743\pi\) | |||||||
\(480\) | −1.57663 | −0.0719632 | ||||||||
\(481\) | 6.90813 | 0.314984 | ||||||||
\(482\) | 13.8160 | 0.629302 | ||||||||
\(483\) | −3.81749 | −0.173702 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.294217 | 0.0133597 | ||||||||
\(486\) | −5.28136 | −0.239567 | ||||||||
\(487\) | 3.47565 | 0.157497 | 0.0787484 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787484 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(488\) | 2.97971 | 0.134885 | ||||||||
\(489\) | −27.8749 | −1.26055 | ||||||||
\(490\) | 6.35931 | 0.287285 | ||||||||
\(491\) | −2.76700 | −0.124873 | −0.0624365 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624365 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(492\) | 16.5115 | 0.744396 | ||||||||
\(493\) | 1.10794 | 0.0498993 | ||||||||
\(494\) | −2.71543 | −0.122173 | ||||||||
\(495\) | −0.514223 | −0.0231126 | ||||||||
\(496\) | 1.97566 | 0.0887097 | ||||||||
\(497\) | −5.39378 | −0.241944 | ||||||||
\(498\) | −16.0873 | −0.720890 | ||||||||
\(499\) | 29.7798 | 1.33313 | 0.666564 | − | 0.745448i | \(-0.267764\pi\) | ||||
0.666564 | + | 0.745448i | \(0.267764\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 6.48724 | 0.289829 | ||||||||
\(502\) | 5.08380 | 0.226901 | ||||||||
\(503\) | 27.3250 | 1.21836 | 0.609181 | − | 0.793031i | \(-0.291498\pi\) | ||||
0.609181 | + | 0.793031i | \(0.291498\pi\) | |||||||
\(504\) | 0.411599 | 0.0183341 | ||||||||
\(505\) | 1.14270 | 0.0508493 | ||||||||
\(506\) | 3.02499 | 0.134477 | ||||||||
\(507\) | −18.8398 | −0.836706 | ||||||||
\(508\) | 19.3137 | 0.856907 | ||||||||
\(509\) | −32.3336 | −1.43316 | −0.716581 | − | 0.697503i | \(-0.754294\pi\) | ||||
−0.716581 | + | 0.697503i | \(0.754294\pi\) | |||||||
\(510\) | 8.39573 | 0.371769 | ||||||||
\(511\) | 1.06383 | 0.0470609 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.6784 | 0.648067 | ||||||||
\(514\) | 16.8556 | 0.743469 | ||||||||
\(515\) | −9.50752 | −0.418951 | ||||||||
\(516\) | −1.57663 | −0.0694075 | ||||||||
\(517\) | 3.55198 | 0.156216 | ||||||||
\(518\) | 5.39465 | 0.237027 | ||||||||
\(519\) | −27.3910 | −1.20233 | ||||||||
\(520\) | 1.02499 | 0.0449488 | ||||||||
\(521\) | 2.19231 | 0.0960470 | 0.0480235 | − | 0.998846i | \(-0.484708\pi\) | ||||
0.0480235 | + | 0.998846i | \(0.484708\pi\) | |||||||
\(522\) | −0.106990 | −0.00468281 | ||||||||
\(523\) | −22.2363 | −0.972326 | −0.486163 | − | 0.873868i | \(-0.661604\pi\) | ||||
−0.486163 | + | 0.873868i | \(0.661604\pi\) | |||||||
\(524\) | −2.23687 | −0.0977180 | ||||||||
\(525\) | 1.26198 | 0.0550774 | ||||||||
\(526\) | −11.0417 | −0.481442 | ||||||||
\(527\) | −10.5206 | −0.458284 | ||||||||
\(528\) | 1.57663 | 0.0686142 | ||||||||
\(529\) | −13.8494 | −0.602149 | ||||||||
\(530\) | 9.61400 | 0.417605 | ||||||||
\(531\) | 6.10661 | 0.265004 | ||||||||
\(532\) | −2.12051 | −0.0919358 | ||||||||
\(533\) | −10.7343 | −0.464956 | ||||||||
\(534\) | −14.7312 | −0.637482 | ||||||||
\(535\) | 4.79302 | 0.207220 | ||||||||
\(536\) | 10.5520 | 0.455777 | ||||||||
\(537\) | 4.90416 | 0.211630 | ||||||||
\(538\) | −5.90487 | −0.254577 | ||||||||
\(539\) | −6.35931 | −0.273915 | ||||||||
\(540\) | −5.54065 | −0.238431 | ||||||||
\(541\) | −4.52948 | −0.194737 | −0.0973687 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973687 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(542\) | 0.109692 | 0.00471167 | ||||||||
\(543\) | 30.8315 | 1.32311 | ||||||||
\(544\) | 5.32510 | 0.228312 | ||||||||
\(545\) | −17.2100 | −0.737195 | ||||||||
\(546\) | 1.29352 | 0.0553576 | ||||||||
\(547\) | −25.8318 | −1.10449 | −0.552243 | − | 0.833683i | \(-0.686228\pi\) | ||||
−0.552243 | + | 0.833683i | \(0.686228\pi\) | |||||||
\(548\) | 15.3916 | 0.657496 | ||||||||
\(549\) | 1.53224 | 0.0653943 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 0.551199 | 0.0234818 | ||||||||
\(552\) | 4.76931 | 0.202995 | ||||||||
\(553\) | 6.67070 | 0.283667 | ||||||||
\(554\) | 10.1828 | 0.432626 | ||||||||
\(555\) | −10.6260 | −0.451050 | ||||||||
\(556\) | −16.6321 | −0.705358 | ||||||||
\(557\) | −14.6117 | −0.619118 | −0.309559 | − | 0.950880i | \(-0.600181\pi\) | ||||
−0.309559 | + | 0.950880i | \(0.600181\pi\) | |||||||
\(558\) | 1.01593 | 0.0430078 | ||||||||
\(559\) | 1.02499 | 0.0433525 | ||||||||
\(560\) | 0.800428 | 0.0338243 | ||||||||
\(561\) | −8.39573 | −0.354468 | ||||||||
\(562\) | −12.0954 | −0.510212 | ||||||||
\(563\) | −29.5053 | −1.24350 | −0.621750 | − | 0.783216i | \(-0.713578\pi\) | ||||
−0.621750 | + | 0.783216i | \(0.713578\pi\) | |||||||
\(564\) | 5.60018 | 0.235810 | ||||||||
\(565\) | −12.6986 | −0.534234 | ||||||||
\(566\) | −3.46228 | −0.145531 | ||||||||
\(567\) | −5.75740 | −0.241788 | ||||||||
\(568\) | 6.73861 | 0.282746 | ||||||||
\(569\) | 20.9018 | 0.876251 | 0.438125 | − | 0.898914i | \(-0.355643\pi\) | ||||
0.438125 | + | 0.898914i | \(0.355643\pi\) | |||||||
\(570\) | 4.17685 | 0.174949 | ||||||||
\(571\) | −4.47120 | −0.187114 | −0.0935569 | − | 0.995614i | \(-0.529824\pi\) | ||||
−0.0935569 | + | 0.995614i | \(0.529824\pi\) | |||||||
\(572\) | −1.02499 | −0.0428570 | ||||||||
\(573\) | 18.2126 | 0.760840 | ||||||||
\(574\) | −8.38258 | −0.349882 | ||||||||
\(575\) | −3.02499 | −0.126151 | ||||||||
\(576\) | −0.514223 | −0.0214260 | ||||||||
\(577\) | −38.6359 | −1.60843 | −0.804217 | − | 0.594335i | \(-0.797415\pi\) | ||||
−0.804217 | + | 0.594335i | \(0.797415\pi\) | |||||||
\(578\) | −11.3567 | −0.472375 | ||||||||
\(579\) | 24.7926 | 1.03034 | ||||||||
\(580\) | −0.208061 | −0.00863925 | ||||||||
\(581\) | 8.16724 | 0.338834 | ||||||||
\(582\) | −0.463873 | −0.0192281 | ||||||||
\(583\) | −9.61400 | −0.398171 | ||||||||
\(584\) | −1.32907 | −0.0549974 | ||||||||
\(585\) | 0.527074 | 0.0217918 | ||||||||
\(586\) | 32.8264 | 1.35605 | ||||||||
\(587\) | 5.43021 | 0.224129 | 0.112064 | − | 0.993701i | \(-0.464254\pi\) | ||||
0.112064 | + | 0.993701i | \(0.464254\pi\) | |||||||
\(588\) | −10.0263 | −0.413478 | ||||||||
\(589\) | −5.23395 | −0.215661 | ||||||||
\(590\) | 11.8754 | 0.488903 | ||||||||
\(591\) | −19.8993 | −0.818548 | ||||||||
\(592\) | −6.73970 | −0.277000 | ||||||||
\(593\) | 14.8798 | 0.611039 | 0.305520 | − | 0.952186i | \(-0.401170\pi\) | ||||
0.305520 | + | 0.952186i | \(0.401170\pi\) | |||||||
\(594\) | 5.54065 | 0.227335 | ||||||||
\(595\) | −4.26236 | −0.174740 | ||||||||
\(596\) | −13.1363 | −0.538083 | ||||||||
\(597\) | 13.0389 | 0.533649 | ||||||||
\(598\) | −3.10059 | −0.126793 | ||||||||
\(599\) | 1.29419 | 0.0528791 | 0.0264396 | − | 0.999650i | \(-0.491583\pi\) | ||||
0.0264396 | + | 0.999650i | \(0.491583\pi\) | |||||||
\(600\) | −1.57663 | −0.0643658 | ||||||||
\(601\) | 12.1106 | 0.494002 | 0.247001 | − | 0.969015i | \(-0.420555\pi\) | ||||
0.247001 | + | 0.969015i | \(0.420555\pi\) | |||||||
\(602\) | 0.800428 | 0.0326230 | ||||||||
\(603\) | 5.42609 | 0.220968 | ||||||||
\(604\) | 5.38185 | 0.218984 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −1.80161 | −0.0731855 | ||||||||
\(607\) | −25.9256 | −1.05229 | −0.526143 | − | 0.850396i | \(-0.676362\pi\) | ||||
−0.526143 | + | 0.850396i | \(0.676362\pi\) | |||||||
\(608\) | 2.64922 | 0.107440 | ||||||||
\(609\) | −0.262569 | −0.0106398 | ||||||||
\(610\) | 2.97971 | 0.120645 | ||||||||
\(611\) | −3.64075 | −0.147289 | ||||||||
\(612\) | 2.73829 | 0.110689 | ||||||||
\(613\) | 10.8232 | 0.437143 | 0.218571 | − | 0.975821i | \(-0.429860\pi\) | ||||
0.218571 | + | 0.975821i | \(0.429860\pi\) | |||||||
\(614\) | −15.8101 | −0.638042 | ||||||||
\(615\) | 16.5115 | 0.665808 | ||||||||
\(616\) | −0.800428 | −0.0322502 | ||||||||
\(617\) | −2.94986 | −0.118757 | −0.0593785 | − | 0.998236i | \(-0.518912\pi\) | ||||
−0.0593785 | + | 0.998236i | \(0.518912\pi\) | |||||||
\(618\) | 14.9899 | 0.602982 | ||||||||
\(619\) | 10.5819 | 0.425323 | 0.212662 | − | 0.977126i | \(-0.431787\pi\) | ||||
0.212662 | + | 0.977126i | \(0.431787\pi\) | |||||||
\(620\) | 1.97566 | 0.0793444 | ||||||||
\(621\) | 16.7604 | 0.672572 | ||||||||
\(622\) | 7.41195 | 0.297192 | ||||||||
\(623\) | 7.47876 | 0.299630 | ||||||||
\(624\) | −1.61604 | −0.0646932 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.8333 | −0.592856 | ||||||||
\(627\) | −4.17685 | −0.166807 | ||||||||
\(628\) | −15.7870 | −0.629969 | ||||||||
\(629\) | 35.8896 | 1.43101 | ||||||||
\(630\) | 0.411599 | 0.0163985 | ||||||||
\(631\) | −21.4951 | −0.855706 | −0.427853 | − | 0.903848i | \(-0.640730\pi\) | ||||
−0.427853 | + | 0.903848i | \(0.640730\pi\) | |||||||
\(632\) | −8.33391 | −0.331505 | ||||||||
\(633\) | −6.31466 | −0.250985 | ||||||||
\(634\) | −18.5511 | −0.736759 | ||||||||
\(635\) | 19.3137 | 0.766441 | ||||||||
\(636\) | −15.1578 | −0.601044 | ||||||||
\(637\) | 6.51824 | 0.258262 | ||||||||
\(638\) | 0.208061 | 0.00823721 | ||||||||
\(639\) | 3.46515 | 0.137079 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −9.38771 | −0.370792 | −0.185396 | − | 0.982664i | \(-0.559357\pi\) | ||||
−0.185396 | + | 0.982664i | \(0.559357\pi\) | |||||||
\(642\) | −7.55684 | −0.298245 | ||||||||
\(643\) | 10.4007 | 0.410164 | 0.205082 | − | 0.978745i | \(-0.434254\pi\) | ||||
0.205082 | + | 0.978745i | \(0.434254\pi\) | |||||||
\(644\) | −2.42129 | −0.0954121 | ||||||||
\(645\) | −1.57663 | −0.0620799 | ||||||||
\(646\) | −14.1074 | −0.555046 | ||||||||
\(647\) | −43.1859 | −1.69781 | −0.848907 | − | 0.528542i | \(-0.822739\pi\) | ||||
−0.848907 | + | 0.528542i | \(0.822739\pi\) | |||||||
\(648\) | 7.19290 | 0.282564 | ||||||||
\(649\) | −11.8754 | −0.466151 | ||||||||
\(650\) | 1.02499 | 0.0402035 | ||||||||
\(651\) | 2.49325 | 0.0977181 | ||||||||
\(652\) | −17.6800 | −0.692403 | ||||||||
\(653\) | 3.31176 | 0.129599 | 0.0647996 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0647996 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(654\) | 27.1338 | 1.06102 | ||||||||
\(655\) | −2.23687 | −0.0874016 | ||||||||
\(656\) | 10.4726 | 0.408887 | ||||||||
\(657\) | −0.683440 | −0.0266635 | ||||||||
\(658\) | −2.84311 | −0.110836 | ||||||||
\(659\) | −32.0509 | −1.24853 | −0.624264 | − | 0.781214i | \(-0.714601\pi\) | ||||
−0.624264 | + | 0.781214i | \(0.714601\pi\) | |||||||
\(660\) | 1.57663 | 0.0613704 | ||||||||
\(661\) | −17.2999 | −0.672887 | −0.336444 | − | 0.941704i | \(-0.609224\pi\) | ||||
−0.336444 | + | 0.941704i | \(0.609224\pi\) | |||||||
\(662\) | −11.7965 | −0.458483 | ||||||||
\(663\) | 8.60555 | 0.334212 | ||||||||
\(664\) | −10.2036 | −0.395976 | ||||||||
\(665\) | −2.12051 | −0.0822298 | ||||||||
\(666\) | −3.46571 | −0.134294 | ||||||||
\(667\) | 0.629382 | 0.0243698 | ||||||||
\(668\) | 4.11462 | 0.159199 | ||||||||
\(669\) | −14.9517 | −0.578066 | ||||||||
\(670\) | 10.5520 | 0.407660 | ||||||||
\(671\) | −2.97971 | −0.115031 | ||||||||
\(672\) | −1.26198 | −0.0486820 | ||||||||
\(673\) | −27.9517 | −1.07746 | −0.538729 | − | 0.842479i | \(-0.681095\pi\) | ||||
−0.538729 | + | 0.842479i | \(0.681095\pi\) | |||||||
\(674\) | −10.8501 | −0.417930 | ||||||||
\(675\) | −5.54065 | −0.213260 | ||||||||
\(676\) | −11.9494 | −0.459592 | ||||||||
\(677\) | −13.5715 | −0.521594 | −0.260797 | − | 0.965394i | \(-0.583985\pi\) | ||||
−0.260797 | + | 0.965394i | \(0.583985\pi\) | |||||||
\(678\) | 20.0210 | 0.768903 | ||||||||
\(679\) | 0.235500 | 0.00903764 | ||||||||
\(680\) | 5.32510 | 0.204208 | ||||||||
\(681\) | 19.2736 | 0.738568 | ||||||||
\(682\) | −1.97566 | −0.0756519 | ||||||||
\(683\) | −9.40214 | −0.359763 | −0.179881 | − | 0.983688i | \(-0.557571\pi\) | ||||
−0.179881 | + | 0.983688i | \(0.557571\pi\) | |||||||
\(684\) | 1.36229 | 0.0520885 | ||||||||
\(685\) | 15.3916 | 0.588082 | ||||||||
\(686\) | 10.6932 | 0.408267 | ||||||||
\(687\) | 25.3775 | 0.968211 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | 9.85426 | 0.375418 | ||||||||
\(690\) | 4.76931 | 0.181564 | ||||||||
\(691\) | 15.2503 | 0.580150 | 0.290075 | − | 0.957004i | \(-0.406320\pi\) | ||||
0.290075 | + | 0.957004i | \(0.406320\pi\) | |||||||
\(692\) | −17.3731 | −0.660426 | ||||||||
\(693\) | −0.411599 | −0.0156354 | ||||||||
\(694\) | 21.8988 | 0.831266 | ||||||||
\(695\) | −16.6321 | −0.630891 | ||||||||
\(696\) | 0.328036 | 0.0124342 | ||||||||
\(697\) | −55.7677 | −2.11235 | ||||||||
\(698\) | −4.86814 | −0.184262 | ||||||||
\(699\) | 37.7102 | 1.42633 | ||||||||
\(700\) | 0.800428 | 0.0302533 | ||||||||
\(701\) | −37.1132 | −1.40174 | −0.700872 | − | 0.713287i | \(-0.747206\pi\) | ||||
−0.700872 | + | 0.713287i | \(0.747206\pi\) | |||||||
\(702\) | −5.67911 | −0.214344 | ||||||||
\(703\) | 17.8549 | 0.673412 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 5.60018 | 0.210915 | ||||||||
\(706\) | 3.25663 | 0.122565 | ||||||||
\(707\) | 0.914646 | 0.0343988 | ||||||||
\(708\) | −18.7232 | −0.703660 | ||||||||
\(709\) | 36.6980 | 1.37822 | 0.689110 | − | 0.724657i | \(-0.258002\pi\) | ||||
0.689110 | + | 0.724657i | \(0.258002\pi\) | |||||||
\(710\) | 6.73861 | 0.252896 | ||||||||
\(711\) | −4.28549 | −0.160718 | ||||||||
\(712\) | −9.34345 | −0.350161 | ||||||||
\(713\) | −5.97635 | −0.223816 | ||||||||
\(714\) | 6.72018 | 0.251497 | ||||||||
\(715\) | −1.02499 | −0.0383325 | ||||||||
\(716\) | 3.11052 | 0.116246 | ||||||||
\(717\) | 32.6473 | 1.21924 | ||||||||
\(718\) | −9.66427 | −0.360667 | ||||||||
\(719\) | −30.0585 | −1.12099 | −0.560497 | − | 0.828156i | \(-0.689390\pi\) | ||||
−0.560497 | + | 0.828156i | \(0.689390\pi\) | |||||||
\(720\) | −0.514223 | −0.0191640 | ||||||||
\(721\) | −7.61009 | −0.283414 | ||||||||
\(722\) | 11.9816 | 0.445910 | ||||||||
\(723\) | −21.7828 | −0.810112 | ||||||||
\(724\) | 19.5553 | 0.726766 | ||||||||
\(725\) | −0.208061 | −0.00772718 | ||||||||
\(726\) | −1.57663 | −0.0585144 | ||||||||
\(727\) | −2.91194 | −0.107998 | −0.0539989 | − | 0.998541i | \(-0.517197\pi\) | ||||
−0.0539989 | + | 0.998541i | \(0.517197\pi\) | |||||||
\(728\) | 0.820432 | 0.0304072 | ||||||||
\(729\) | 29.9055 | 1.10761 | ||||||||
\(730\) | −1.32907 | −0.0491912 | ||||||||
\(731\) | 5.32510 | 0.196956 | ||||||||
\(732\) | −4.69792 | −0.173640 | ||||||||
\(733\) | 31.7751 | 1.17364 | 0.586821 | − | 0.809717i | \(-0.300379\pi\) | ||||
0.586821 | + | 0.809717i | \(0.300379\pi\) | |||||||
\(734\) | 27.2816 | 1.00698 | ||||||||
\(735\) | −10.0263 | −0.369826 | ||||||||
\(736\) | 3.02499 | 0.111503 | ||||||||
\(737\) | −10.5520 | −0.388688 | ||||||||
\(738\) | 5.38527 | 0.198234 | ||||||||
\(739\) | 3.10556 | 0.114240 | 0.0571200 | − | 0.998367i | \(-0.481808\pi\) | ||||
0.0571200 | + | 0.998367i | \(0.481808\pi\) | |||||||
\(740\) | −6.73970 | −0.247756 | ||||||||
\(741\) | 4.28123 | 0.157275 | ||||||||
\(742\) | 7.69532 | 0.282504 | ||||||||
\(743\) | 16.5595 | 0.607508 | 0.303754 | − | 0.952750i | \(-0.401760\pi\) | ||||
0.303754 | + | 0.952750i | \(0.401760\pi\) | |||||||
\(744\) | −3.11489 | −0.114197 | ||||||||
\(745\) | −13.1363 | −0.481276 | ||||||||
\(746\) | 26.5850 | 0.973345 | ||||||||
\(747\) | −5.24692 | −0.191975 | ||||||||
\(748\) | −5.32510 | −0.194705 | ||||||||
\(749\) | 3.83647 | 0.140182 | ||||||||
\(750\) | −1.57663 | −0.0575706 | ||||||||
\(751\) | 49.7609 | 1.81580 | 0.907900 | − | 0.419186i | \(-0.137684\pi\) | ||||
0.907900 | + | 0.419186i | \(0.137684\pi\) | |||||||
\(752\) | 3.55198 | 0.129527 | ||||||||
\(753\) | −8.01530 | −0.292094 | ||||||||
\(754\) | −0.213260 | −0.00776649 | ||||||||
\(755\) | 5.38185 | 0.195866 | ||||||||
\(756\) | −4.43489 | −0.161295 | ||||||||
\(757\) | 33.0266 | 1.20037 | 0.600186 | − | 0.799861i | \(-0.295093\pi\) | ||||
0.600186 | + | 0.799861i | \(0.295093\pi\) | |||||||
\(758\) | 17.8037 | 0.646659 | ||||||||
\(759\) | −4.76931 | −0.173115 | ||||||||
\(760\) | 2.64922 | 0.0960973 | ||||||||
\(761\) | 35.4359 | 1.28455 | 0.642276 | − | 0.766474i | \(-0.277991\pi\) | ||||
0.642276 | + | 0.766474i | \(0.277991\pi\) | |||||||
\(762\) | −30.4506 | −1.10311 | ||||||||
\(763\) | −13.7754 | −0.498701 | ||||||||
\(764\) | 11.5515 | 0.417920 | ||||||||
\(765\) | 2.73829 | 0.0990031 | ||||||||
\(766\) | −17.7357 | −0.640817 | ||||||||
\(767\) | 12.1722 | 0.439512 | ||||||||
\(768\) | 1.57663 | 0.0568919 | ||||||||
\(769\) | −13.3462 | −0.481277 | −0.240639 | − | 0.970615i | \(-0.577357\pi\) | ||||
−0.240639 | + | 0.970615i | \(0.577357\pi\) | |||||||
\(770\) | −0.800428 | −0.0288454 | ||||||||
\(771\) | −26.5751 | −0.957080 | ||||||||
\(772\) | 15.7250 | 0.565955 | ||||||||
\(773\) | 39.3147 | 1.41405 | 0.707026 | − | 0.707188i | \(-0.250036\pi\) | ||||
0.707026 | + | 0.707188i | \(0.250036\pi\) | |||||||
\(774\) | −0.514223 | −0.0184834 | ||||||||
\(775\) | 1.97566 | 0.0709678 | ||||||||
\(776\) | −0.294217 | −0.0105618 | ||||||||
\(777\) | −8.50539 | −0.305129 | ||||||||
\(778\) | 29.6312 | 1.06233 | ||||||||
\(779\) | −27.7443 | −0.994041 | ||||||||
\(780\) | −1.61604 | −0.0578634 | ||||||||
\(781\) | −6.73861 | −0.241127 | ||||||||
\(782\) | −16.1084 | −0.576034 | ||||||||
\(783\) | 1.15279 | 0.0411974 | ||||||||
\(784\) | −6.35931 | −0.227118 | ||||||||
\(785\) | −15.7870 | −0.563461 | ||||||||
\(786\) | 3.52672 | 0.125794 | ||||||||
\(787\) | −37.5439 | −1.33830 | −0.669148 | − | 0.743129i | \(-0.733341\pi\) | ||||
−0.669148 | + | 0.743129i | \(0.733341\pi\) | |||||||
\(788\) | −12.6214 | −0.449618 | ||||||||
\(789\) | 17.4088 | 0.619768 | ||||||||
\(790\) | −8.33391 | −0.296507 | ||||||||
\(791\) | −10.1643 | −0.361401 | ||||||||
\(792\) | 0.514223 | 0.0182721 | ||||||||
\(793\) | 3.05418 | 0.108457 | ||||||||
\(794\) | 0.874875 | 0.0310481 | ||||||||
\(795\) | −15.1578 | −0.537590 | ||||||||
\(796\) | 8.27011 | 0.293126 | ||||||||
\(797\) | −23.2800 | −0.824620 | −0.412310 | − | 0.911044i | \(-0.635278\pi\) | ||||
−0.412310 | + | 0.911044i | \(0.635278\pi\) | |||||||
\(798\) | 3.34327 | 0.118350 | ||||||||
\(799\) | −18.9146 | −0.669152 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −4.80462 | −0.169763 | ||||||||
\(802\) | −16.7273 | −0.590662 | ||||||||
\(803\) | 1.32907 | 0.0469019 | ||||||||
\(804\) | −16.6367 | −0.586730 | ||||||||
\(805\) | −2.42129 | −0.0853392 | ||||||||
\(806\) | 2.02503 | 0.0713287 | ||||||||
\(807\) | 9.30982 | 0.327721 | ||||||||
\(808\) | −1.14270 | −0.0401999 | ||||||||
\(809\) | 3.65160 | 0.128383 | 0.0641917 | − | 0.997938i | \(-0.479553\pi\) | ||||
0.0641917 | + | 0.997938i | \(0.479553\pi\) | |||||||
\(810\) | 7.19290 | 0.252733 | ||||||||
\(811\) | −11.2086 | −0.393589 | −0.196794 | − | 0.980445i | \(-0.563053\pi\) | ||||
−0.196794 | + | 0.980445i | \(0.563053\pi\) | |||||||
\(812\) | −0.166538 | −0.00584433 | ||||||||
\(813\) | −0.172944 | −0.00606541 | ||||||||
\(814\) | 6.73970 | 0.236226 | ||||||||
\(815\) | −17.6800 | −0.619304 | ||||||||
\(816\) | −8.39573 | −0.293909 | ||||||||
\(817\) | 2.64922 | 0.0926844 | ||||||||
\(818\) | −11.4333 | −0.399756 | ||||||||
\(819\) | 0.421885 | 0.0147419 | ||||||||
\(820\) | 10.4726 | 0.365720 | ||||||||
\(821\) | 41.0787 | 1.43366 | 0.716828 | − | 0.697250i | \(-0.245593\pi\) | ||||
0.716828 | + | 0.697250i | \(0.245593\pi\) | |||||||
\(822\) | −24.2669 | −0.846406 | ||||||||
\(823\) | −0.499858 | −0.0174240 | −0.00871198 | − | 0.999962i | \(-0.502773\pi\) | ||||
−0.00871198 | + | 0.999962i | \(0.502773\pi\) | |||||||
\(824\) | 9.50752 | 0.331210 | ||||||||
\(825\) | 1.57663 | 0.0548914 | ||||||||
\(826\) | 9.50541 | 0.330736 | ||||||||
\(827\) | 13.0330 | 0.453203 | 0.226602 | − | 0.973988i | \(-0.427238\pi\) | ||||
0.226602 | + | 0.973988i | \(0.427238\pi\) | |||||||
\(828\) | 1.55552 | 0.0540581 | ||||||||
\(829\) | 37.6377 | 1.30721 | 0.653606 | − | 0.756835i | \(-0.273255\pi\) | ||||
0.653606 | + | 0.756835i | \(0.273255\pi\) | |||||||
\(830\) | −10.2036 | −0.354172 | ||||||||
\(831\) | −16.0546 | −0.556927 | ||||||||
\(832\) | −1.02499 | −0.0355352 | ||||||||
\(833\) | 33.8640 | 1.17332 | ||||||||
\(834\) | 26.2227 | 0.908019 | ||||||||
\(835\) | 4.11462 | 0.142392 | ||||||||
\(836\) | −2.64922 | −0.0916252 | ||||||||
\(837\) | −10.9464 | −0.378364 | ||||||||
\(838\) | 0.915714 | 0.0316328 | ||||||||
\(839\) | −10.6040 | −0.366089 | −0.183045 | − | 0.983105i | \(-0.558595\pi\) | ||||
−0.183045 | + | 0.983105i | \(0.558595\pi\) | |||||||
\(840\) | −1.26198 | −0.0435425 | ||||||||
\(841\) | −28.9567 | −0.998507 | ||||||||
\(842\) | −23.5860 | −0.812829 | ||||||||
\(843\) | 19.0700 | 0.656805 | ||||||||
\(844\) | −4.00515 | −0.137863 | ||||||||
\(845\) | −11.9494 | −0.411072 | ||||||||
\(846\) | 1.82651 | 0.0627968 | ||||||||
\(847\) | 0.800428 | 0.0275030 | ||||||||
\(848\) | −9.61400 | −0.330146 | ||||||||
\(849\) | 5.45875 | 0.187344 | ||||||||
\(850\) | 5.32510 | 0.182649 | ||||||||
\(851\) | 20.3875 | 0.698876 | ||||||||
\(852\) | −10.6243 | −0.363984 | ||||||||
\(853\) | 44.7626 | 1.53264 | 0.766322 | − | 0.642457i | \(-0.222085\pi\) | ||||
0.766322 | + | 0.642457i | \(0.222085\pi\) | |||||||
\(854\) | 2.38505 | 0.0816146 | ||||||||
\(855\) | 1.36229 | 0.0465894 | ||||||||
\(856\) | −4.79302 | −0.163822 | ||||||||
\(857\) | 40.9407 | 1.39851 | 0.699254 | − | 0.714873i | \(-0.253516\pi\) | ||||
0.699254 | + | 0.714873i | \(0.253516\pi\) | |||||||
\(858\) | 1.61604 | 0.0551706 | ||||||||
\(859\) | −11.5373 | −0.393647 | −0.196824 | − | 0.980439i | \(-0.563063\pi\) | ||||
−0.196824 | + | 0.980439i | \(0.563063\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 13.2163 | 0.450409 | ||||||||
\(862\) | −26.1671 | −0.891255 | ||||||||
\(863\) | −11.7277 | −0.399215 | −0.199608 | − | 0.979876i | \(-0.563967\pi\) | ||||
−0.199608 | + | 0.979876i | \(0.563967\pi\) | |||||||
\(864\) | 5.54065 | 0.188497 | ||||||||
\(865\) | −17.3731 | −0.590703 | ||||||||
\(866\) | 15.9409 | 0.541695 | ||||||||
\(867\) | 17.9053 | 0.608097 | ||||||||
\(868\) | 1.58137 | 0.0536753 | ||||||||
\(869\) | 8.33391 | 0.282709 | ||||||||
\(870\) | 0.328036 | 0.0111215 | ||||||||
\(871\) | 10.8157 | 0.366477 | ||||||||
\(872\) | 17.2100 | 0.582803 | ||||||||
\(873\) | −0.151293 | −0.00512050 | ||||||||
\(874\) | −8.01386 | −0.271073 | ||||||||
\(875\) | 0.800428 | 0.0270594 | ||||||||
\(876\) | 2.09546 | 0.0707990 | ||||||||
\(877\) | −2.53727 | −0.0856775 | −0.0428388 | − | 0.999082i | \(-0.513640\pi\) | ||||
−0.0428388 | + | 0.999082i | \(0.513640\pi\) | |||||||
\(878\) | 30.0150 | 1.01296 | ||||||||
\(879\) | −51.7552 | −1.74566 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 8.32215 | 0.280380 | 0.140190 | − | 0.990125i | \(-0.455229\pi\) | ||||
0.140190 | + | 0.990125i | \(0.455229\pi\) | |||||||
\(882\) | −3.27011 | −0.110110 | ||||||||
\(883\) | −11.3446 | −0.381777 | −0.190888 | − | 0.981612i | \(-0.561137\pi\) | ||||
−0.190888 | + | 0.981612i | \(0.561137\pi\) | |||||||
\(884\) | 5.45818 | 0.183578 | ||||||||
\(885\) | −18.7232 | −0.629373 | ||||||||
\(886\) | −24.5171 | −0.823668 | ||||||||
\(887\) | 32.8951 | 1.10451 | 0.552254 | − | 0.833676i | \(-0.313768\pi\) | ||||
0.552254 | + | 0.833676i | \(0.313768\pi\) | |||||||
\(888\) | 10.6260 | 0.356587 | ||||||||
\(889\) | 15.4592 | 0.518486 | ||||||||
\(890\) | −9.34345 | −0.313193 | ||||||||
\(891\) | −7.19290 | −0.240971 | ||||||||
\(892\) | −9.48329 | −0.317524 | ||||||||
\(893\) | −9.40998 | −0.314893 | ||||||||
\(894\) | 20.7111 | 0.692683 | ||||||||
\(895\) | 3.11052 | 0.103973 | ||||||||
\(896\) | −0.800428 | −0.0267404 | ||||||||
\(897\) | 4.88850 | 0.163222 | ||||||||
\(898\) | −26.7819 | −0.893723 | ||||||||
\(899\) | −0.411057 | −0.0137095 | ||||||||
\(900\) | −0.514223 | −0.0171408 | ||||||||
\(901\) | 51.1955 | 1.70557 | ||||||||
\(902\) | −10.4726 | −0.348700 | ||||||||
\(903\) | −1.26198 | −0.0419962 | ||||||||
\(904\) | 12.6986 | 0.422349 | ||||||||
\(905\) | 19.5553 | 0.650039 | ||||||||
\(906\) | −8.48521 | −0.281902 | ||||||||
\(907\) | −14.7363 | −0.489312 | −0.244656 | − | 0.969610i | \(-0.578675\pi\) | ||||
−0.244656 | + | 0.969610i | \(0.578675\pi\) | |||||||
\(908\) | 12.2245 | 0.405686 | ||||||||
\(909\) | −0.587601 | −0.0194895 | ||||||||
\(910\) | 0.820432 | 0.0271971 | ||||||||
\(911\) | 23.9691 | 0.794131 | 0.397065 | − | 0.917790i | \(-0.370029\pi\) | ||||
0.397065 | + | 0.917790i | \(0.370029\pi\) | |||||||
\(912\) | −4.17685 | −0.138309 | ||||||||
\(913\) | 10.2036 | 0.337689 | ||||||||
\(914\) | 6.46219 | 0.213750 | ||||||||
\(915\) | −4.69792 | −0.155308 | ||||||||
\(916\) | 16.0960 | 0.531826 | ||||||||
\(917\) | −1.79045 | −0.0591259 | ||||||||
\(918\) | −29.5045 | −0.973793 | ||||||||
\(919\) | 31.9385 | 1.05355 | 0.526777 | − | 0.850004i | \(-0.323400\pi\) | ||||
0.526777 | + | 0.850004i | \(0.323400\pi\) | |||||||
\(920\) | 3.02499 | 0.0997310 | ||||||||
\(921\) | 24.9267 | 0.821362 | ||||||||
\(922\) | −26.6725 | −0.878413 | ||||||||
\(923\) | 6.90702 | 0.227347 | ||||||||
\(924\) | 1.26198 | 0.0415162 | ||||||||
\(925\) | −6.73970 | −0.221600 | ||||||||
\(926\) | 16.9910 | 0.558359 | ||||||||
\(927\) | 4.88899 | 0.160575 | ||||||||
\(928\) | 0.208061 | 0.00682993 | ||||||||
\(929\) | −25.9985 | −0.852984 | −0.426492 | − | 0.904491i | \(-0.640251\pi\) | ||||
−0.426492 | + | 0.904491i | \(0.640251\pi\) | |||||||
\(930\) | −3.11489 | −0.102141 | ||||||||
\(931\) | 16.8472 | 0.552145 | ||||||||
\(932\) | 23.9182 | 0.783466 | ||||||||
\(933\) | −11.6859 | −0.382581 | ||||||||
\(934\) | 24.6468 | 0.806467 | ||||||||
\(935\) | −5.32510 | −0.174149 | ||||||||
\(936\) | −0.527074 | −0.0172280 | ||||||||
\(937\) | −42.1033 | −1.37545 | −0.687727 | − | 0.725969i | \(-0.741391\pi\) | ||||
−0.687727 | + | 0.725969i | \(0.741391\pi\) | |||||||
\(938\) | 8.44613 | 0.275776 | ||||||||
\(939\) | 23.3866 | 0.763194 | ||||||||
\(940\) | 3.55198 | 0.115853 | ||||||||
\(941\) | 45.0237 | 1.46773 | 0.733865 | − | 0.679296i | \(-0.237715\pi\) | ||||
0.733865 | + | 0.679296i | \(0.237715\pi\) | |||||||
\(942\) | 24.8903 | 0.810969 | ||||||||
\(943\) | −31.6796 | −1.03163 | ||||||||
\(944\) | −11.8754 | −0.386512 | ||||||||
\(945\) | −4.43489 | −0.144267 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 32.0104 | 1.04020 | 0.520100 | − | 0.854106i | \(-0.325895\pi\) | ||||
0.520100 | + | 0.854106i | \(0.325895\pi\) | |||||||
\(948\) | 13.1395 | 0.426752 | ||||||||
\(949\) | −1.36229 | −0.0442217 | ||||||||
\(950\) | 2.64922 | 0.0859520 | ||||||||
\(951\) | 29.2483 | 0.948442 | ||||||||
\(952\) | 4.26236 | 0.138144 | ||||||||
\(953\) | 52.4310 | 1.69841 | 0.849203 | − | 0.528066i | \(-0.177083\pi\) | ||||
0.849203 | + | 0.528066i | \(0.177083\pi\) | |||||||
\(954\) | −4.94374 | −0.160060 | ||||||||
\(955\) | 11.5515 | 0.373799 | ||||||||
\(956\) | 20.7070 | 0.669711 | ||||||||
\(957\) | −0.328036 | −0.0106039 | ||||||||
\(958\) | 31.3134 | 1.01169 | ||||||||
\(959\) | 12.3199 | 0.397829 | ||||||||
\(960\) | 1.57663 | 0.0508857 | ||||||||
\(961\) | −27.0968 | −0.874089 | ||||||||
\(962\) | −6.90813 | −0.222727 | ||||||||
\(963\) | −2.46468 | −0.0794233 | ||||||||
\(964\) | −13.8160 | −0.444984 | ||||||||
\(965\) | 15.7250 | 0.506205 | ||||||||
\(966\) | 3.81749 | 0.122826 | ||||||||
\(967\) | −26.7669 | −0.860764 | −0.430382 | − | 0.902647i | \(-0.641621\pi\) | ||||
−0.430382 | + | 0.902647i | \(0.641621\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 22.2421 | 0.714520 | ||||||||
\(970\) | −0.294217 | −0.00944674 | ||||||||
\(971\) | 42.0144 | 1.34831 | 0.674153 | − | 0.738592i | \(-0.264509\pi\) | ||||
0.674153 | + | 0.738592i | \(0.264509\pi\) | |||||||
\(972\) | 5.28136 | 0.169400 | ||||||||
\(973\) | −13.3128 | −0.426789 | ||||||||
\(974\) | −3.47565 | −0.111367 | ||||||||
\(975\) | −1.61604 | −0.0517546 | ||||||||
\(976\) | −2.97971 | −0.0953783 | ||||||||
\(977\) | −15.6696 | −0.501316 | −0.250658 | − | 0.968076i | \(-0.580647\pi\) | ||||
−0.250658 | + | 0.968076i | \(0.580647\pi\) | |||||||
\(978\) | 27.8749 | 0.891342 | ||||||||
\(979\) | 9.34345 | 0.298618 | ||||||||
\(980\) | −6.35931 | −0.203141 | ||||||||
\(981\) | 8.84978 | 0.282552 | ||||||||
\(982\) | 2.76700 | 0.0882985 | ||||||||
\(983\) | −15.7881 | −0.503562 | −0.251781 | − | 0.967784i | \(-0.581016\pi\) | ||||
−0.251781 | + | 0.967784i | \(0.581016\pi\) | |||||||
\(984\) | −16.5115 | −0.526367 | ||||||||
\(985\) | −12.6214 | −0.402151 | ||||||||
\(986\) | −1.10794 | −0.0352841 | ||||||||
\(987\) | 4.48254 | 0.142681 | ||||||||
\(988\) | 2.71543 | 0.0863892 | ||||||||
\(989\) | 3.02499 | 0.0961891 | ||||||||
\(990\) | 0.514223 | 0.0163431 | ||||||||
\(991\) | −7.31945 | −0.232510 | −0.116255 | − | 0.993219i | \(-0.537089\pi\) | ||||
−0.116255 | + | 0.993219i | \(0.537089\pi\) | |||||||
\(992\) | −1.97566 | −0.0627272 | ||||||||
\(993\) | 18.5987 | 0.590213 | ||||||||
\(994\) | 5.39378 | 0.171080 | ||||||||
\(995\) | 8.27011 | 0.262180 | ||||||||
\(996\) | 16.0873 | 0.509746 | ||||||||
\(997\) | −26.1994 | −0.829744 | −0.414872 | − | 0.909880i | \(-0.636174\pi\) | ||||
−0.414872 | + | 0.909880i | \(0.636174\pi\) | |||||||
\(998\) | −29.7798 | −0.942663 | ||||||||
\(999\) | 37.3423 | 1.18146 |
(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.w.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.w.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial |