Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.27539\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.55242 | −1.14148 | −0.570739 | − | 0.821132i | \(-0.693343\pi\) | ||||
−0.570739 | + | 0.821132i | \(0.693343\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.37822 | 0.520917 | 0.260459 | − | 0.965485i | \(-0.416126\pi\) | ||||
0.260459 | + | 0.965485i | \(0.416126\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.55242 | 0.807147 | ||||||||
\(11\) | 4.10597 | 1.23800 | 0.618998 | − | 0.785392i | \(-0.287539\pi\) | ||||
0.618998 | + | 0.785392i | \(0.287539\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.37822 | −0.368344 | ||||||||
\(15\) | 2.55242 | 0.659033 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.57390 | 0.866797 | 0.433399 | − | 0.901202i | \(-0.357314\pi\) | ||||
0.433399 | + | 0.901202i | \(0.357314\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.378218 | 0.0867691 | 0.0433846 | − | 0.999058i | \(-0.486186\pi\) | ||||
0.0433846 | + | 0.999058i | \(0.486186\pi\) | |||||||
\(20\) | −2.55242 | −0.570739 | ||||||||
\(21\) | −1.37822 | −0.300752 | ||||||||
\(22\) | −4.10597 | −0.875396 | ||||||||
\(23\) | 3.65040 | 0.761161 | 0.380580 | − | 0.924748i | \(-0.375724\pi\) | ||||
0.380580 | + | 0.924748i | \(0.375724\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.51486 | 0.302972 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.37822 | 0.260459 | ||||||||
\(29\) | −0.329406 | −0.0611692 | −0.0305846 | − | 0.999532i | \(-0.509737\pi\) | ||||
−0.0305846 | + | 0.999532i | \(0.509737\pi\) | |||||||
\(30\) | −2.55242 | −0.466006 | ||||||||
\(31\) | −7.41763 | −1.33225 | −0.666123 | − | 0.745842i | \(-0.732047\pi\) | ||||
−0.666123 | + | 0.745842i | \(0.732047\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.10597 | −0.714757 | ||||||||
\(34\) | −3.57390 | −0.612918 | ||||||||
\(35\) | −3.51779 | −0.594616 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.88409 | −1.13174 | −0.565869 | − | 0.824495i | \(-0.691459\pi\) | ||||
−0.565869 | + | 0.824495i | \(0.691459\pi\) | |||||||
\(38\) | −0.378218 | −0.0613550 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.55242 | 0.403573 | ||||||||
\(41\) | −7.85728 | −1.22710 | −0.613550 | − | 0.789656i | \(-0.710259\pi\) | ||||
−0.613550 | + | 0.789656i | \(0.710259\pi\) | |||||||
\(42\) | 1.37822 | 0.212664 | ||||||||
\(43\) | −2.74031 | −0.417893 | −0.208947 | − | 0.977927i | \(-0.567003\pi\) | ||||
−0.208947 | + | 0.977927i | \(0.567003\pi\) | |||||||
\(44\) | 4.10597 | 0.618998 | ||||||||
\(45\) | −2.55242 | −0.380493 | ||||||||
\(46\) | −3.65040 | −0.538222 | ||||||||
\(47\) | −2.13101 | −0.310840 | −0.155420 | − | 0.987849i | \(-0.549673\pi\) | ||||
−0.155420 | + | 0.987849i | \(0.549673\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.10052 | −0.728645 | ||||||||
\(50\) | −1.51486 | −0.214234 | ||||||||
\(51\) | −3.57390 | −0.500446 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −10.1230 | −1.39050 | −0.695251 | − | 0.718767i | \(-0.744707\pi\) | ||||
−0.695251 | + | 0.718767i | \(0.744707\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −10.4802 | −1.41315 | ||||||||
\(56\) | −1.37822 | −0.184172 | ||||||||
\(57\) | −0.378218 | −0.0500962 | ||||||||
\(58\) | 0.329406 | 0.0432532 | ||||||||
\(59\) | 8.34165 | 1.08599 | 0.542995 | − | 0.839736i | \(-0.317290\pi\) | ||||
0.542995 | + | 0.839736i | \(0.317290\pi\) | |||||||
\(60\) | 2.55242 | 0.329516 | ||||||||
\(61\) | −0.317128 | −0.0406041 | −0.0203020 | − | 0.999794i | \(-0.506463\pi\) | ||||
−0.0203020 | + | 0.999794i | \(0.506463\pi\) | |||||||
\(62\) | 7.41763 | 0.942040 | ||||||||
\(63\) | 1.37822 | 0.173639 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.55242 | −0.316589 | ||||||||
\(66\) | 4.10597 | 0.505410 | ||||||||
\(67\) | 3.12773 | 0.382113 | 0.191056 | − | 0.981579i | \(-0.438809\pi\) | ||||
0.191056 | + | 0.981579i | \(0.438809\pi\) | |||||||
\(68\) | 3.57390 | 0.433399 | ||||||||
\(69\) | −3.65040 | −0.439456 | ||||||||
\(70\) | 3.51779 | 0.420457 | ||||||||
\(71\) | 8.40081 | 0.996992 | 0.498496 | − | 0.866892i | \(-0.333886\pi\) | ||||
0.498496 | + | 0.866892i | \(0.333886\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 2.15179 | 0.251848 | 0.125924 | − | 0.992040i | \(-0.459810\pi\) | ||||
0.125924 | + | 0.992040i | \(0.459810\pi\) | |||||||
\(74\) | 6.88409 | 0.800259 | ||||||||
\(75\) | −1.51486 | −0.174921 | ||||||||
\(76\) | 0.378218 | 0.0433846 | ||||||||
\(77\) | 5.65892 | 0.644894 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −5.79457 | −0.651940 | −0.325970 | − | 0.945380i | \(-0.605691\pi\) | ||||
−0.325970 | + | 0.945380i | \(0.605691\pi\) | |||||||
\(80\) | −2.55242 | −0.285370 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.85728 | 0.867691 | ||||||||
\(83\) | −1.11990 | −0.122925 | −0.0614625 | − | 0.998109i | \(-0.519576\pi\) | ||||
−0.0614625 | + | 0.998109i | \(0.519576\pi\) | |||||||
\(84\) | −1.37822 | −0.150376 | ||||||||
\(85\) | −9.12209 | −0.989430 | ||||||||
\(86\) | 2.74031 | 0.295495 | ||||||||
\(87\) | 0.329406 | 0.0353161 | ||||||||
\(88\) | −4.10597 | −0.437698 | ||||||||
\(89\) | 0.259370 | 0.0274932 | 0.0137466 | − | 0.999906i | \(-0.495624\pi\) | ||||
0.0137466 | + | 0.999906i | \(0.495624\pi\) | |||||||
\(90\) | 2.55242 | 0.269049 | ||||||||
\(91\) | 1.37822 | 0.144476 | ||||||||
\(92\) | 3.65040 | 0.380580 | ||||||||
\(93\) | 7.41763 | 0.769173 | ||||||||
\(94\) | 2.13101 | 0.219797 | ||||||||
\(95\) | −0.965372 | −0.0990451 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 4.63686 | 0.470802 | 0.235401 | − | 0.971898i | \(-0.424360\pi\) | ||||
0.235401 | + | 0.971898i | \(0.424360\pi\) | |||||||
\(98\) | 5.10052 | 0.515230 | ||||||||
\(99\) | 4.10597 | 0.412665 | ||||||||
\(100\) | 1.51486 | 0.151486 | ||||||||
\(101\) | −15.5977 | −1.55203 | −0.776014 | − | 0.630715i | \(-0.782762\pi\) | ||||
−0.776014 | + | 0.630715i | \(0.782762\pi\) | |||||||
\(102\) | 3.57390 | 0.353868 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 3.51779 | 0.343302 | ||||||||
\(106\) | 10.1230 | 0.983233 | ||||||||
\(107\) | 10.0618 | 0.972714 | 0.486357 | − | 0.873760i | \(-0.338325\pi\) | ||||
0.486357 | + | 0.873760i | \(0.338325\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 11.4816 | 1.09974 | 0.549869 | − | 0.835251i | \(-0.314678\pi\) | ||||
0.549869 | + | 0.835251i | \(0.314678\pi\) | |||||||
\(110\) | 10.4802 | 0.999245 | ||||||||
\(111\) | 6.88409 | 0.653409 | ||||||||
\(112\) | 1.37822 | 0.130229 | ||||||||
\(113\) | 4.69080 | 0.441273 | 0.220637 | − | 0.975356i | \(-0.429186\pi\) | ||||
0.220637 | + | 0.975356i | \(0.429186\pi\) | |||||||
\(114\) | 0.378218 | 0.0354233 | ||||||||
\(115\) | −9.31736 | −0.868848 | ||||||||
\(116\) | −0.329406 | −0.0305846 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −8.34165 | −0.767911 | ||||||||
\(119\) | 4.92561 | 0.451530 | ||||||||
\(120\) | −2.55242 | −0.233003 | ||||||||
\(121\) | 5.85898 | 0.532635 | ||||||||
\(122\) | 0.317128 | 0.0287114 | ||||||||
\(123\) | 7.85728 | 0.708467 | ||||||||
\(124\) | −7.41763 | −0.666123 | ||||||||
\(125\) | 8.89555 | 0.795642 | ||||||||
\(126\) | −1.37822 | −0.122781 | ||||||||
\(127\) | −18.9176 | −1.67867 | −0.839335 | − | 0.543615i | \(-0.817055\pi\) | ||||
−0.839335 | + | 0.543615i | \(0.817055\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.74031 | 0.241271 | ||||||||
\(130\) | 2.55242 | 0.223862 | ||||||||
\(131\) | 14.9131 | 1.30297 | 0.651483 | − | 0.758663i | \(-0.274147\pi\) | ||||
0.651483 | + | 0.758663i | \(0.274147\pi\) | |||||||
\(132\) | −4.10597 | −0.357379 | ||||||||
\(133\) | 0.521267 | 0.0451995 | ||||||||
\(134\) | −3.12773 | −0.270194 | ||||||||
\(135\) | 2.55242 | 0.219678 | ||||||||
\(136\) | −3.57390 | −0.306459 | ||||||||
\(137\) | 17.1905 | 1.46868 | 0.734341 | − | 0.678781i | \(-0.237491\pi\) | ||||
0.734341 | + | 0.678781i | \(0.237491\pi\) | |||||||
\(138\) | 3.65040 | 0.310743 | ||||||||
\(139\) | 18.1741 | 1.54150 | 0.770752 | − | 0.637135i | \(-0.219881\pi\) | ||||
0.770752 | + | 0.637135i | \(0.219881\pi\) | |||||||
\(140\) | −3.51779 | −0.297308 | ||||||||
\(141\) | 2.13101 | 0.179463 | ||||||||
\(142\) | −8.40081 | −0.704980 | ||||||||
\(143\) | 4.10597 | 0.343358 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.840784 | 0.0698233 | ||||||||
\(146\) | −2.15179 | −0.178083 | ||||||||
\(147\) | 5.10052 | 0.420683 | ||||||||
\(148\) | −6.88409 | −0.565869 | ||||||||
\(149\) | −7.54334 | −0.617975 | −0.308987 | − | 0.951066i | \(-0.599990\pi\) | ||||
−0.308987 | + | 0.951066i | \(0.599990\pi\) | |||||||
\(150\) | 1.51486 | 0.123688 | ||||||||
\(151\) | −22.2535 | −1.81096 | −0.905481 | − | 0.424386i | \(-0.860490\pi\) | ||||
−0.905481 | + | 0.424386i | \(0.860490\pi\) | |||||||
\(152\) | −0.378218 | −0.0306775 | ||||||||
\(153\) | 3.57390 | 0.288932 | ||||||||
\(154\) | −5.65892 | −0.456009 | ||||||||
\(155\) | 18.9329 | 1.52073 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −11.8126 | −0.942746 | −0.471373 | − | 0.881934i | \(-0.656242\pi\) | ||||
−0.471373 | + | 0.881934i | \(0.656242\pi\) | |||||||
\(158\) | 5.79457 | 0.460992 | ||||||||
\(159\) | 10.1230 | 0.802806 | ||||||||
\(160\) | 2.55242 | 0.201787 | ||||||||
\(161\) | 5.03104 | 0.396502 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.81167 | −0.455205 | −0.227603 | − | 0.973754i | \(-0.573089\pi\) | ||||
−0.227603 | + | 0.973754i | \(0.573089\pi\) | |||||||
\(164\) | −7.85728 | −0.613550 | ||||||||
\(165\) | 10.4802 | 0.815880 | ||||||||
\(166\) | 1.11990 | 0.0869211 | ||||||||
\(167\) | −8.49879 | −0.657656 | −0.328828 | − | 0.944390i | \(-0.606654\pi\) | ||||
−0.328828 | + | 0.944390i | \(0.606654\pi\) | |||||||
\(168\) | 1.37822 | 0.106332 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 9.12209 | 0.699632 | ||||||||
\(171\) | 0.378218 | 0.0289230 | ||||||||
\(172\) | −2.74031 | −0.208947 | ||||||||
\(173\) | −16.5832 | −1.26080 | −0.630398 | − | 0.776272i | \(-0.717108\pi\) | ||||
−0.630398 | + | 0.776272i | \(0.717108\pi\) | |||||||
\(174\) | −0.329406 | −0.0249722 | ||||||||
\(175\) | 2.08781 | 0.157823 | ||||||||
\(176\) | 4.10597 | 0.309499 | ||||||||
\(177\) | −8.34165 | −0.626997 | ||||||||
\(178\) | −0.259370 | −0.0194406 | ||||||||
\(179\) | −14.9667 | −1.11866 | −0.559331 | − | 0.828945i | \(-0.688942\pi\) | ||||
−0.559331 | + | 0.828945i | \(0.688942\pi\) | |||||||
\(180\) | −2.55242 | −0.190246 | ||||||||
\(181\) | −15.9377 | −1.18464 | −0.592319 | − | 0.805704i | \(-0.701787\pi\) | ||||
−0.592319 | + | 0.805704i | \(0.701787\pi\) | |||||||
\(182\) | −1.37822 | −0.102160 | ||||||||
\(183\) | 0.317128 | 0.0234428 | ||||||||
\(184\) | −3.65040 | −0.269111 | ||||||||
\(185\) | 17.5711 | 1.29185 | ||||||||
\(186\) | −7.41763 | −0.543887 | ||||||||
\(187\) | 14.6743 | 1.07309 | ||||||||
\(188\) | −2.13101 | −0.155420 | ||||||||
\(189\) | −1.37822 | −0.100251 | ||||||||
\(190\) | 0.965372 | 0.0700354 | ||||||||
\(191\) | 14.0461 | 1.01634 | 0.508170 | − | 0.861257i | \(-0.330322\pi\) | ||||
0.508170 | + | 0.861257i | \(0.330322\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −9.70946 | −0.698902 | −0.349451 | − | 0.936955i | \(-0.613632\pi\) | ||||
−0.349451 | + | 0.936955i | \(0.613632\pi\) | |||||||
\(194\) | −4.63686 | −0.332907 | ||||||||
\(195\) | 2.55242 | 0.182783 | ||||||||
\(196\) | −5.10052 | −0.364323 | ||||||||
\(197\) | 10.6953 | 0.762006 | 0.381003 | − | 0.924574i | \(-0.375579\pi\) | ||||
0.381003 | + | 0.924574i | \(0.375579\pi\) | |||||||
\(198\) | −4.10597 | −0.291799 | ||||||||
\(199\) | −4.21109 | −0.298516 | −0.149258 | − | 0.988798i | \(-0.547689\pi\) | ||||
−0.149258 | + | 0.988798i | \(0.547689\pi\) | |||||||
\(200\) | −1.51486 | −0.107117 | ||||||||
\(201\) | −3.12773 | −0.220613 | ||||||||
\(202\) | 15.5977 | 1.09745 | ||||||||
\(203\) | −0.453994 | −0.0318641 | ||||||||
\(204\) | −3.57390 | −0.250223 | ||||||||
\(205\) | 20.0551 | 1.40071 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 3.65040 | 0.253720 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 1.55295 | 0.107420 | ||||||||
\(210\) | −3.51779 | −0.242751 | ||||||||
\(211\) | −21.1987 | −1.45938 | −0.729690 | − | 0.683778i | \(-0.760336\pi\) | ||||
−0.729690 | + | 0.683778i | \(0.760336\pi\) | |||||||
\(212\) | −10.1230 | −0.695251 | ||||||||
\(213\) | −8.40081 | −0.575614 | ||||||||
\(214\) | −10.0618 | −0.687813 | ||||||||
\(215\) | 6.99442 | 0.477016 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −10.2231 | −0.693990 | ||||||||
\(218\) | −11.4816 | −0.777632 | ||||||||
\(219\) | −2.15179 | −0.145405 | ||||||||
\(220\) | −10.4802 | −0.706573 | ||||||||
\(221\) | 3.57390 | 0.240406 | ||||||||
\(222\) | −6.88409 | −0.462030 | ||||||||
\(223\) | 9.75733 | 0.653399 | 0.326700 | − | 0.945128i | \(-0.394063\pi\) | ||||
0.326700 | + | 0.945128i | \(0.394063\pi\) | |||||||
\(224\) | −1.37822 | −0.0920861 | ||||||||
\(225\) | 1.51486 | 0.100991 | ||||||||
\(226\) | −4.69080 | −0.312027 | ||||||||
\(227\) | 26.6880 | 1.77135 | 0.885673 | − | 0.464310i | \(-0.153698\pi\) | ||||
0.885673 | + | 0.464310i | \(0.153698\pi\) | |||||||
\(228\) | −0.378218 | −0.0250481 | ||||||||
\(229\) | −21.0379 | −1.39022 | −0.695112 | − | 0.718902i | \(-0.744645\pi\) | ||||
−0.695112 | + | 0.718902i | \(0.744645\pi\) | |||||||
\(230\) | 9.31736 | 0.614368 | ||||||||
\(231\) | −5.65892 | −0.372330 | ||||||||
\(232\) | 0.329406 | 0.0216266 | ||||||||
\(233\) | −8.73734 | −0.572402 | −0.286201 | − | 0.958170i | \(-0.592393\pi\) | ||||
−0.286201 | + | 0.958170i | \(0.592393\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 5.43923 | 0.354816 | ||||||||
\(236\) | 8.34165 | 0.542995 | ||||||||
\(237\) | 5.79457 | 0.376398 | ||||||||
\(238\) | −4.92561 | −0.319280 | ||||||||
\(239\) | −17.3130 | −1.11988 | −0.559942 | − | 0.828532i | \(-0.689177\pi\) | ||||
−0.559942 | + | 0.828532i | \(0.689177\pi\) | |||||||
\(240\) | 2.55242 | 0.164758 | ||||||||
\(241\) | 19.3299 | 1.24515 | 0.622574 | − | 0.782561i | \(-0.286087\pi\) | ||||
0.622574 | + | 0.782561i | \(0.286087\pi\) | |||||||
\(242\) | −5.85898 | −0.376630 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.317128 | −0.0203020 | ||||||||
\(245\) | 13.0187 | 0.831732 | ||||||||
\(246\) | −7.85728 | −0.500962 | ||||||||
\(247\) | 0.378218 | 0.0240654 | ||||||||
\(248\) | 7.41763 | 0.471020 | ||||||||
\(249\) | 1.11990 | 0.0709708 | ||||||||
\(250\) | −8.89555 | −0.562604 | ||||||||
\(251\) | 11.1871 | 0.706125 | 0.353063 | − | 0.935600i | \(-0.385140\pi\) | ||||
0.353063 | + | 0.935600i | \(0.385140\pi\) | |||||||
\(252\) | 1.37822 | 0.0868196 | ||||||||
\(253\) | 14.9884 | 0.942314 | ||||||||
\(254\) | 18.9176 | 1.18700 | ||||||||
\(255\) | 9.12209 | 0.571248 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.3163 | −1.57919 | −0.789594 | − | 0.613629i | \(-0.789709\pi\) | ||||
−0.789594 | + | 0.613629i | \(0.789709\pi\) | |||||||
\(258\) | −2.74031 | −0.170604 | ||||||||
\(259\) | −9.48777 | −0.589542 | ||||||||
\(260\) | −2.55242 | −0.158295 | ||||||||
\(261\) | −0.329406 | −0.0203897 | ||||||||
\(262\) | −14.9131 | −0.921336 | ||||||||
\(263\) | −22.2746 | −1.37351 | −0.686754 | − | 0.726890i | \(-0.740965\pi\) | ||||
−0.686754 | + | 0.726890i | \(0.740965\pi\) | |||||||
\(264\) | 4.10597 | 0.252705 | ||||||||
\(265\) | 25.8382 | 1.58723 | ||||||||
\(266\) | −0.521267 | −0.0319609 | ||||||||
\(267\) | −0.259370 | −0.0158732 | ||||||||
\(268\) | 3.12773 | 0.191056 | ||||||||
\(269\) | 23.4427 | 1.42933 | 0.714663 | − | 0.699469i | \(-0.246580\pi\) | ||||
0.714663 | + | 0.699469i | \(0.246580\pi\) | |||||||
\(270\) | −2.55242 | −0.155335 | ||||||||
\(271\) | 14.7770 | 0.897638 | 0.448819 | − | 0.893623i | \(-0.351845\pi\) | ||||
0.448819 | + | 0.893623i | \(0.351845\pi\) | |||||||
\(272\) | 3.57390 | 0.216699 | ||||||||
\(273\) | −1.37822 | −0.0834135 | ||||||||
\(274\) | −17.1905 | −1.03851 | ||||||||
\(275\) | 6.21997 | 0.375078 | ||||||||
\(276\) | −3.65040 | −0.219728 | ||||||||
\(277\) | 0.941275 | 0.0565557 | 0.0282779 | − | 0.999600i | \(-0.490998\pi\) | ||||
0.0282779 | + | 0.999600i | \(0.490998\pi\) | |||||||
\(278\) | −18.1741 | −1.09001 | ||||||||
\(279\) | −7.41763 | −0.444082 | ||||||||
\(280\) | 3.51779 | 0.210228 | ||||||||
\(281\) | −8.44093 | −0.503543 | −0.251772 | − | 0.967787i | \(-0.581013\pi\) | ||||
−0.251772 | + | 0.967787i | \(0.581013\pi\) | |||||||
\(282\) | −2.13101 | −0.126900 | ||||||||
\(283\) | 0.458757 | 0.0272703 | 0.0136351 | − | 0.999907i | \(-0.495660\pi\) | ||||
0.0136351 | + | 0.999907i | \(0.495660\pi\) | |||||||
\(284\) | 8.40081 | 0.498496 | ||||||||
\(285\) | 0.965372 | 0.0571837 | ||||||||
\(286\) | −4.10597 | −0.242791 | ||||||||
\(287\) | −10.8290 | −0.639218 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −4.22727 | −0.248663 | ||||||||
\(290\) | −0.840784 | −0.0493726 | ||||||||
\(291\) | −4.63686 | −0.271818 | ||||||||
\(292\) | 2.15179 | 0.125924 | ||||||||
\(293\) | −5.81927 | −0.339965 | −0.169983 | − | 0.985447i | \(-0.554371\pi\) | ||||
−0.169983 | + | 0.985447i | \(0.554371\pi\) | |||||||
\(294\) | −5.10052 | −0.297468 | ||||||||
\(295\) | −21.2914 | −1.23963 | ||||||||
\(296\) | 6.88409 | 0.400130 | ||||||||
\(297\) | −4.10597 | −0.238252 | ||||||||
\(298\) | 7.54334 | 0.436974 | ||||||||
\(299\) | 3.65040 | 0.211108 | ||||||||
\(300\) | −1.51486 | −0.0874605 | ||||||||
\(301\) | −3.77674 | −0.217688 | ||||||||
\(302\) | 22.2535 | 1.28054 | ||||||||
\(303\) | 15.5977 | 0.896064 | ||||||||
\(304\) | 0.378218 | 0.0216923 | ||||||||
\(305\) | 0.809445 | 0.0463487 | ||||||||
\(306\) | −3.57390 | −0.204306 | ||||||||
\(307\) | −15.4051 | −0.879214 | −0.439607 | − | 0.898190i | \(-0.644882\pi\) | ||||
−0.439607 | + | 0.898190i | \(0.644882\pi\) | |||||||
\(308\) | 5.65892 | 0.322447 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −18.9329 | −1.07532 | ||||||||
\(311\) | 21.3489 | 1.21058 | 0.605292 | − | 0.796004i | \(-0.293056\pi\) | ||||
0.605292 | + | 0.796004i | \(0.293056\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −0.467785 | −0.0264408 | −0.0132204 | − | 0.999913i | \(-0.504208\pi\) | ||||
−0.0132204 | + | 0.999913i | \(0.504208\pi\) | |||||||
\(314\) | 11.8126 | 0.666622 | ||||||||
\(315\) | −3.51779 | −0.198205 | ||||||||
\(316\) | −5.79457 | −0.325970 | ||||||||
\(317\) | 17.6599 | 0.991881 | 0.495941 | − | 0.868356i | \(-0.334823\pi\) | ||||
0.495941 | + | 0.868356i | \(0.334823\pi\) | |||||||
\(318\) | −10.1230 | −0.567670 | ||||||||
\(319\) | −1.35253 | −0.0757273 | ||||||||
\(320\) | −2.55242 | −0.142685 | ||||||||
\(321\) | −10.0618 | −0.561597 | ||||||||
\(322\) | −5.03104 | −0.280369 | ||||||||
\(323\) | 1.35171 | 0.0752112 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.51486 | 0.0840293 | ||||||||
\(326\) | 5.81167 | 0.321879 | ||||||||
\(327\) | −11.4816 | −0.634934 | ||||||||
\(328\) | 7.85728 | 0.433846 | ||||||||
\(329\) | −2.93699 | −0.161922 | ||||||||
\(330\) | −10.4802 | −0.576914 | ||||||||
\(331\) | −14.5394 | −0.799155 | −0.399578 | − | 0.916699i | \(-0.630843\pi\) | ||||
−0.399578 | + | 0.916699i | \(0.630843\pi\) | |||||||
\(332\) | −1.11990 | −0.0614625 | ||||||||
\(333\) | −6.88409 | −0.377246 | ||||||||
\(334\) | 8.49879 | 0.465033 | ||||||||
\(335\) | −7.98328 | −0.436173 | ||||||||
\(336\) | −1.37822 | −0.0751879 | ||||||||
\(337\) | −27.2491 | −1.48435 | −0.742177 | − | 0.670204i | \(-0.766207\pi\) | ||||
−0.742177 | + | 0.670204i | \(0.766207\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −4.69080 | −0.254769 | ||||||||
\(340\) | −9.12209 | −0.494715 | ||||||||
\(341\) | −30.4566 | −1.64932 | ||||||||
\(342\) | −0.378218 | −0.0204517 | ||||||||
\(343\) | −16.6771 | −0.900481 | ||||||||
\(344\) | 2.74031 | 0.147748 | ||||||||
\(345\) | 9.31736 | 0.501630 | ||||||||
\(346\) | 16.5832 | 0.891517 | ||||||||
\(347\) | −6.74311 | −0.361989 | −0.180994 | − | 0.983484i | \(-0.557932\pi\) | ||||
−0.180994 | + | 0.983484i | \(0.557932\pi\) | |||||||
\(348\) | 0.329406 | 0.0176580 | ||||||||
\(349\) | −9.28940 | −0.497250 | −0.248625 | − | 0.968600i | \(-0.579979\pi\) | ||||
−0.248625 | + | 0.968600i | \(0.579979\pi\) | |||||||
\(350\) | −2.08781 | −0.111598 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −4.10597 | −0.218849 | ||||||||
\(353\) | 9.67070 | 0.514719 | 0.257360 | − | 0.966316i | \(-0.417147\pi\) | ||||
0.257360 | + | 0.966316i | \(0.417147\pi\) | |||||||
\(354\) | 8.34165 | 0.443354 | ||||||||
\(355\) | −21.4424 | −1.13804 | ||||||||
\(356\) | 0.259370 | 0.0137466 | ||||||||
\(357\) | −4.92561 | −0.260691 | ||||||||
\(358\) | 14.9667 | 0.791013 | ||||||||
\(359\) | −3.21503 | −0.169683 | −0.0848413 | − | 0.996394i | \(-0.527038\pi\) | ||||
−0.0848413 | + | 0.996394i | \(0.527038\pi\) | |||||||
\(360\) | 2.55242 | 0.134524 | ||||||||
\(361\) | −18.8570 | −0.992471 | ||||||||
\(362\) | 15.9377 | 0.837666 | ||||||||
\(363\) | −5.85898 | −0.307517 | ||||||||
\(364\) | 1.37822 | 0.0722382 | ||||||||
\(365\) | −5.49228 | −0.287479 | ||||||||
\(366\) | −0.317128 | −0.0165766 | ||||||||
\(367\) | 13.5101 | 0.705224 | 0.352612 | − | 0.935770i | \(-0.385294\pi\) | ||||
0.352612 | + | 0.935770i | \(0.385294\pi\) | |||||||
\(368\) | 3.65040 | 0.190290 | ||||||||
\(369\) | −7.85728 | −0.409034 | ||||||||
\(370\) | −17.5711 | −0.913478 | ||||||||
\(371\) | −13.9517 | −0.724336 | ||||||||
\(372\) | 7.41763 | 0.384586 | ||||||||
\(373\) | −8.16869 | −0.422959 | −0.211479 | − | 0.977382i | \(-0.567828\pi\) | ||||
−0.211479 | + | 0.977382i | \(0.567828\pi\) | |||||||
\(374\) | −14.6743 | −0.758790 | ||||||||
\(375\) | −8.89555 | −0.459364 | ||||||||
\(376\) | 2.13101 | 0.109898 | ||||||||
\(377\) | −0.329406 | −0.0169653 | ||||||||
\(378\) | 1.37822 | 0.0708879 | ||||||||
\(379\) | −5.83245 | −0.299593 | −0.149797 | − | 0.988717i | \(-0.547862\pi\) | ||||
−0.149797 | + | 0.988717i | \(0.547862\pi\) | |||||||
\(380\) | −0.965372 | −0.0495225 | ||||||||
\(381\) | 18.9176 | 0.969180 | ||||||||
\(382\) | −14.0461 | −0.718661 | ||||||||
\(383\) | 10.4854 | 0.535779 | 0.267890 | − | 0.963450i | \(-0.413674\pi\) | ||||
0.267890 | + | 0.963450i | \(0.413674\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −14.4440 | −0.736132 | ||||||||
\(386\) | 9.70946 | 0.494199 | ||||||||
\(387\) | −2.74031 | −0.139298 | ||||||||
\(388\) | 4.63686 | 0.235401 | ||||||||
\(389\) | −1.54358 | −0.0782628 | −0.0391314 | − | 0.999234i | \(-0.512459\pi\) | ||||
−0.0391314 | + | 0.999234i | \(0.512459\pi\) | |||||||
\(390\) | −2.55242 | −0.129247 | ||||||||
\(391\) | 13.0461 | 0.659772 | ||||||||
\(392\) | 5.10052 | 0.257615 | ||||||||
\(393\) | −14.9131 | −0.752268 | ||||||||
\(394\) | −10.6953 | −0.538820 | ||||||||
\(395\) | 14.7902 | 0.744176 | ||||||||
\(396\) | 4.10597 | 0.206333 | ||||||||
\(397\) | 25.3759 | 1.27358 | 0.636790 | − | 0.771038i | \(-0.280262\pi\) | ||||
0.636790 | + | 0.771038i | \(0.280262\pi\) | |||||||
\(398\) | 4.21109 | 0.211083 | ||||||||
\(399\) | −0.521267 | −0.0260960 | ||||||||
\(400\) | 1.51486 | 0.0757430 | ||||||||
\(401\) | −18.4808 | −0.922887 | −0.461444 | − | 0.887170i | \(-0.652668\pi\) | ||||
−0.461444 | + | 0.887170i | \(0.652668\pi\) | |||||||
\(402\) | 3.12773 | 0.155997 | ||||||||
\(403\) | −7.41763 | −0.369499 | ||||||||
\(404\) | −15.5977 | −0.776014 | ||||||||
\(405\) | −2.55242 | −0.126831 | ||||||||
\(406\) | 0.453994 | 0.0225313 | ||||||||
\(407\) | −28.2659 | −1.40109 | ||||||||
\(408\) | 3.57390 | 0.176934 | ||||||||
\(409\) | 5.38841 | 0.266440 | 0.133220 | − | 0.991086i | \(-0.457468\pi\) | ||||
0.133220 | + | 0.991086i | \(0.457468\pi\) | |||||||
\(410\) | −20.0551 | −0.990450 | ||||||||
\(411\) | −17.1905 | −0.847944 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 11.4966 | 0.565711 | ||||||||
\(414\) | −3.65040 | −0.179407 | ||||||||
\(415\) | 2.85846 | 0.140316 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −18.1741 | −0.889988 | ||||||||
\(418\) | −1.55295 | −0.0759573 | ||||||||
\(419\) | −17.1706 | −0.838840 | −0.419420 | − | 0.907792i | \(-0.637767\pi\) | ||||
−0.419420 | + | 0.907792i | \(0.637767\pi\) | |||||||
\(420\) | 3.51779 | 0.171651 | ||||||||
\(421\) | −27.6057 | −1.34542 | −0.672710 | − | 0.739906i | \(-0.734870\pi\) | ||||
−0.672710 | + | 0.739906i | \(0.734870\pi\) | |||||||
\(422\) | 21.1987 | 1.03194 | ||||||||
\(423\) | −2.13101 | −0.103613 | ||||||||
\(424\) | 10.1230 | 0.491616 | ||||||||
\(425\) | 5.41395 | 0.262615 | ||||||||
\(426\) | 8.40081 | 0.407020 | ||||||||
\(427\) | −0.437072 | −0.0211514 | ||||||||
\(428\) | 10.0618 | 0.486357 | ||||||||
\(429\) | −4.10597 | −0.198238 | ||||||||
\(430\) | −6.99442 | −0.337301 | ||||||||
\(431\) | −6.25335 | −0.301213 | −0.150607 | − | 0.988594i | \(-0.548123\pi\) | ||||
−0.150607 | + | 0.988594i | \(0.548123\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.4271 | −0.741380 | −0.370690 | − | 0.928757i | \(-0.620879\pi\) | ||||
−0.370690 | + | 0.928757i | \(0.620879\pi\) | |||||||
\(434\) | 10.2231 | 0.490725 | ||||||||
\(435\) | −0.840784 | −0.0403125 | ||||||||
\(436\) | 11.4816 | 0.549869 | ||||||||
\(437\) | 1.38065 | 0.0660453 | ||||||||
\(438\) | 2.15179 | 0.102817 | ||||||||
\(439\) | 10.2796 | 0.490617 | 0.245309 | − | 0.969445i | \(-0.421111\pi\) | ||||
0.245309 | + | 0.969445i | \(0.421111\pi\) | |||||||
\(440\) | 10.4802 | 0.499622 | ||||||||
\(441\) | −5.10052 | −0.242882 | ||||||||
\(442\) | −3.57390 | −0.169993 | ||||||||
\(443\) | 29.9234 | 1.42170 | 0.710852 | − | 0.703342i | \(-0.248310\pi\) | ||||
0.710852 | + | 0.703342i | \(0.248310\pi\) | |||||||
\(444\) | 6.88409 | 0.326704 | ||||||||
\(445\) | −0.662023 | −0.0313829 | ||||||||
\(446\) | −9.75733 | −0.462023 | ||||||||
\(447\) | 7.54334 | 0.356788 | ||||||||
\(448\) | 1.37822 | 0.0651147 | ||||||||
\(449\) | −6.67530 | −0.315027 | −0.157513 | − | 0.987517i | \(-0.550348\pi\) | ||||
−0.157513 | + | 0.987517i | \(0.550348\pi\) | |||||||
\(450\) | −1.51486 | −0.0714112 | ||||||||
\(451\) | −32.2617 | −1.51915 | ||||||||
\(452\) | 4.69080 | 0.220637 | ||||||||
\(453\) | 22.2535 | 1.04556 | ||||||||
\(454\) | −26.6880 | −1.25253 | ||||||||
\(455\) | −3.51779 | −0.164917 | ||||||||
\(456\) | 0.378218 | 0.0177117 | ||||||||
\(457\) | −5.76757 | −0.269796 | −0.134898 | − | 0.990860i | \(-0.543071\pi\) | ||||
−0.134898 | + | 0.990860i | \(0.543071\pi\) | |||||||
\(458\) | 21.0379 | 0.983036 | ||||||||
\(459\) | −3.57390 | −0.166815 | ||||||||
\(460\) | −9.31736 | −0.434424 | ||||||||
\(461\) | 10.8327 | 0.504528 | 0.252264 | − | 0.967658i | \(-0.418825\pi\) | ||||
0.252264 | + | 0.967658i | \(0.418825\pi\) | |||||||
\(462\) | 5.65892 | 0.263277 | ||||||||
\(463\) | −11.7791 | −0.547420 | −0.273710 | − | 0.961812i | \(-0.588251\pi\) | ||||
−0.273710 | + | 0.961812i | \(0.588251\pi\) | |||||||
\(464\) | −0.329406 | −0.0152923 | ||||||||
\(465\) | −18.9329 | −0.877994 | ||||||||
\(466\) | 8.73734 | 0.404749 | ||||||||
\(467\) | 33.0283 | 1.52837 | 0.764184 | − | 0.644998i | \(-0.223142\pi\) | ||||
0.764184 | + | 0.644998i | \(0.223142\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 4.31069 | 0.199049 | ||||||||
\(470\) | −5.43923 | −0.250893 | ||||||||
\(471\) | 11.8126 | 0.544295 | ||||||||
\(472\) | −8.34165 | −0.383955 | ||||||||
\(473\) | −11.2516 | −0.517350 | ||||||||
\(474\) | −5.79457 | −0.266154 | ||||||||
\(475\) | 0.572947 | 0.0262886 | ||||||||
\(476\) | 4.92561 | 0.225765 | ||||||||
\(477\) | −10.1230 | −0.463500 | ||||||||
\(478\) | 17.3130 | 0.791877 | ||||||||
\(479\) | −19.4169 | −0.887179 | −0.443589 | − | 0.896230i | \(-0.646295\pi\) | ||||
−0.443589 | + | 0.896230i | \(0.646295\pi\) | |||||||
\(480\) | −2.55242 | −0.116502 | ||||||||
\(481\) | −6.88409 | −0.313887 | ||||||||
\(482\) | −19.3299 | −0.880453 | ||||||||
\(483\) | −5.03104 | −0.228920 | ||||||||
\(484\) | 5.85898 | 0.266317 | ||||||||
\(485\) | −11.8352 | −0.537410 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 12.6915 | 0.575107 | 0.287554 | − | 0.957765i | \(-0.407158\pi\) | ||||
0.287554 | + | 0.957765i | \(0.407158\pi\) | |||||||
\(488\) | 0.317128 | 0.0143557 | ||||||||
\(489\) | 5.81167 | 0.262813 | ||||||||
\(490\) | −13.0187 | −0.588124 | ||||||||
\(491\) | −14.4170 | −0.650629 | −0.325315 | − | 0.945606i | \(-0.605470\pi\) | ||||
−0.325315 | + | 0.945606i | \(0.605470\pi\) | |||||||
\(492\) | 7.85728 | 0.354233 | ||||||||
\(493\) | −1.17726 | −0.0530213 | ||||||||
\(494\) | −0.378218 | −0.0170168 | ||||||||
\(495\) | −10.4802 | −0.471048 | ||||||||
\(496\) | −7.41763 | −0.333062 | ||||||||
\(497\) | 11.5781 | 0.519351 | ||||||||
\(498\) | −1.11990 | −0.0501839 | ||||||||
\(499\) | 13.4253 | 0.600998 | 0.300499 | − | 0.953782i | \(-0.402847\pi\) | ||||
0.300499 | + | 0.953782i | \(0.402847\pi\) | |||||||
\(500\) | 8.89555 | 0.397821 | ||||||||
\(501\) | 8.49879 | 0.379698 | ||||||||
\(502\) | −11.1871 | −0.499306 | ||||||||
\(503\) | 22.0217 | 0.981900 | 0.490950 | − | 0.871188i | \(-0.336650\pi\) | ||||
0.490950 | + | 0.871188i | \(0.336650\pi\) | |||||||
\(504\) | −1.37822 | −0.0613907 | ||||||||
\(505\) | 39.8119 | 1.77161 | ||||||||
\(506\) | −14.9884 | −0.666317 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −18.9176 | −0.839335 | ||||||||
\(509\) | −1.19058 | −0.0527714 | −0.0263857 | − | 0.999652i | \(-0.508400\pi\) | ||||
−0.0263857 | + | 0.999652i | \(0.508400\pi\) | |||||||
\(510\) | −9.12209 | −0.403933 | ||||||||
\(511\) | 2.96564 | 0.131192 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.378218 | −0.0166987 | ||||||||
\(514\) | 25.3163 | 1.11666 | ||||||||
\(515\) | −2.55242 | −0.112473 | ||||||||
\(516\) | 2.74031 | 0.120635 | ||||||||
\(517\) | −8.74985 | −0.384818 | ||||||||
\(518\) | 9.48777 | 0.416869 | ||||||||
\(519\) | 16.5832 | 0.727921 | ||||||||
\(520\) | 2.55242 | 0.111931 | ||||||||
\(521\) | −14.7616 | −0.646718 | −0.323359 | − | 0.946276i | \(-0.604812\pi\) | ||||
−0.323359 | + | 0.946276i | \(0.604812\pi\) | |||||||
\(522\) | 0.329406 | 0.0144177 | ||||||||
\(523\) | 34.5063 | 1.50885 | 0.754427 | − | 0.656384i | \(-0.227915\pi\) | ||||
0.754427 | + | 0.656384i | \(0.227915\pi\) | |||||||
\(524\) | 14.9131 | 0.651483 | ||||||||
\(525\) | −2.08781 | −0.0911194 | ||||||||
\(526\) | 22.2746 | 0.971217 | ||||||||
\(527\) | −26.5098 | −1.15479 | ||||||||
\(528\) | −4.10597 | −0.178689 | ||||||||
\(529\) | −9.67459 | −0.420634 | ||||||||
\(530\) | −25.8382 | −1.12234 | ||||||||
\(531\) | 8.34165 | 0.361997 | ||||||||
\(532\) | 0.521267 | 0.0225998 | ||||||||
\(533\) | −7.85728 | −0.340336 | ||||||||
\(534\) | 0.259370 | 0.0112241 | ||||||||
\(535\) | −25.6820 | −1.11033 | ||||||||
\(536\) | −3.12773 | −0.135097 | ||||||||
\(537\) | 14.9667 | 0.645859 | ||||||||
\(538\) | −23.4427 | −1.01069 | ||||||||
\(539\) | −20.9426 | −0.902060 | ||||||||
\(540\) | 2.55242 | 0.109839 | ||||||||
\(541\) | −17.0031 | −0.731020 | −0.365510 | − | 0.930807i | \(-0.619105\pi\) | ||||
−0.365510 | + | 0.930807i | \(0.619105\pi\) | |||||||
\(542\) | −14.7770 | −0.634726 | ||||||||
\(543\) | 15.9377 | 0.683951 | ||||||||
\(544\) | −3.57390 | −0.153230 | ||||||||
\(545\) | −29.3059 | −1.25533 | ||||||||
\(546\) | 1.37822 | 0.0589823 | ||||||||
\(547\) | 36.4996 | 1.56061 | 0.780306 | − | 0.625398i | \(-0.215063\pi\) | ||||
0.780306 | + | 0.625398i | \(0.215063\pi\) | |||||||
\(548\) | 17.1905 | 0.734341 | ||||||||
\(549\) | −0.317128 | −0.0135347 | ||||||||
\(550\) | −6.21997 | −0.265220 | ||||||||
\(551\) | −0.124587 | −0.00530760 | ||||||||
\(552\) | 3.65040 | 0.155371 | ||||||||
\(553\) | −7.98618 | −0.339607 | ||||||||
\(554\) | −0.941275 | −0.0399909 | ||||||||
\(555\) | −17.5711 | −0.745852 | ||||||||
\(556\) | 18.1741 | 0.770752 | ||||||||
\(557\) | −43.3356 | −1.83619 | −0.918094 | − | 0.396363i | \(-0.870272\pi\) | ||||
−0.918094 | + | 0.396363i | \(0.870272\pi\) | |||||||
\(558\) | 7.41763 | 0.314013 | ||||||||
\(559\) | −2.74031 | −0.115903 | ||||||||
\(560\) | −3.51779 | −0.148654 | ||||||||
\(561\) | −14.6743 | −0.619550 | ||||||||
\(562\) | 8.44093 | 0.356059 | ||||||||
\(563\) | −37.0062 | −1.55962 | −0.779812 | − | 0.626014i | \(-0.784685\pi\) | ||||
−0.779812 | + | 0.626014i | \(0.784685\pi\) | |||||||
\(564\) | 2.13101 | 0.0897316 | ||||||||
\(565\) | −11.9729 | −0.503704 | ||||||||
\(566\) | −0.458757 | −0.0192830 | ||||||||
\(567\) | 1.37822 | 0.0578797 | ||||||||
\(568\) | −8.40081 | −0.352490 | ||||||||
\(569\) | −20.9891 | −0.879910 | −0.439955 | − | 0.898020i | \(-0.645006\pi\) | ||||
−0.439955 | + | 0.898020i | \(0.645006\pi\) | |||||||
\(570\) | −0.965372 | −0.0404350 | ||||||||
\(571\) | −13.1783 | −0.551495 | −0.275748 | − | 0.961230i | \(-0.588925\pi\) | ||||
−0.275748 | + | 0.961230i | \(0.588925\pi\) | |||||||
\(572\) | 4.10597 | 0.171679 | ||||||||
\(573\) | −14.0461 | −0.586784 | ||||||||
\(574\) | 10.8290 | 0.451995 | ||||||||
\(575\) | 5.52984 | 0.230610 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −31.5512 | −1.31349 | −0.656746 | − | 0.754112i | \(-0.728068\pi\) | ||||
−0.656746 | + | 0.754112i | \(0.728068\pi\) | |||||||
\(578\) | 4.22727 | 0.175831 | ||||||||
\(579\) | 9.70946 | 0.403512 | ||||||||
\(580\) | 0.840784 | 0.0349117 | ||||||||
\(581\) | −1.54347 | −0.0640338 | ||||||||
\(582\) | 4.63686 | 0.192204 | ||||||||
\(583\) | −41.5647 | −1.72144 | ||||||||
\(584\) | −2.15179 | −0.0890417 | ||||||||
\(585\) | −2.55242 | −0.105530 | ||||||||
\(586\) | 5.81927 | 0.240392 | ||||||||
\(587\) | −28.2823 | −1.16734 | −0.583668 | − | 0.811992i | \(-0.698383\pi\) | ||||
−0.583668 | + | 0.811992i | \(0.698383\pi\) | |||||||
\(588\) | 5.10052 | 0.210342 | ||||||||
\(589\) | −2.80548 | −0.115598 | ||||||||
\(590\) | 21.2914 | 0.876553 | ||||||||
\(591\) | −10.6953 | −0.439945 | ||||||||
\(592\) | −6.88409 | −0.282934 | ||||||||
\(593\) | 3.23446 | 0.132823 | 0.0664117 | − | 0.997792i | \(-0.478845\pi\) | ||||
0.0664117 | + | 0.997792i | \(0.478845\pi\) | |||||||
\(594\) | 4.10597 | 0.168470 | ||||||||
\(595\) | −12.5722 | −0.515411 | ||||||||
\(596\) | −7.54334 | −0.308987 | ||||||||
\(597\) | 4.21109 | 0.172348 | ||||||||
\(598\) | −3.65040 | −0.149276 | ||||||||
\(599\) | −16.7633 | −0.684930 | −0.342465 | − | 0.939531i | \(-0.611262\pi\) | ||||
−0.342465 | + | 0.939531i | \(0.611262\pi\) | |||||||
\(600\) | 1.51486 | 0.0618439 | ||||||||
\(601\) | 28.5348 | 1.16396 | 0.581980 | − | 0.813203i | \(-0.302278\pi\) | ||||
0.581980 | + | 0.813203i | \(0.302278\pi\) | |||||||
\(602\) | 3.77674 | 0.153929 | ||||||||
\(603\) | 3.12773 | 0.127371 | ||||||||
\(604\) | −22.2535 | −0.905481 | ||||||||
\(605\) | −14.9546 | −0.607991 | ||||||||
\(606\) | −15.5977 | −0.633613 | ||||||||
\(607\) | 38.5489 | 1.56465 | 0.782327 | − | 0.622868i | \(-0.214033\pi\) | ||||
0.782327 | + | 0.622868i | \(0.214033\pi\) | |||||||
\(608\) | −0.378218 | −0.0153388 | ||||||||
\(609\) | 0.453994 | 0.0183968 | ||||||||
\(610\) | −0.809445 | −0.0327735 | ||||||||
\(611\) | −2.13101 | −0.0862114 | ||||||||
\(612\) | 3.57390 | 0.144466 | ||||||||
\(613\) | 23.7566 | 0.959522 | 0.479761 | − | 0.877399i | \(-0.340723\pi\) | ||||
0.479761 | + | 0.877399i | \(0.340723\pi\) | |||||||
\(614\) | 15.4051 | 0.621698 | ||||||||
\(615\) | −20.0551 | −0.808699 | ||||||||
\(616\) | −5.65892 | −0.228004 | ||||||||
\(617\) | −2.88539 | −0.116161 | −0.0580807 | − | 0.998312i | \(-0.518498\pi\) | ||||
−0.0580807 | + | 0.998312i | \(0.518498\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −25.6125 | −1.02945 | −0.514727 | − | 0.857354i | \(-0.672107\pi\) | ||||
−0.514727 | + | 0.857354i | \(0.672107\pi\) | |||||||
\(620\) | 18.9329 | 0.760365 | ||||||||
\(621\) | −3.65040 | −0.146485 | ||||||||
\(622\) | −21.3489 | −0.856012 | ||||||||
\(623\) | 0.357469 | 0.0143217 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −30.2795 | −1.21118 | ||||||||
\(626\) | 0.467785 | 0.0186964 | ||||||||
\(627\) | −1.55295 | −0.0620189 | ||||||||
\(628\) | −11.8126 | −0.471373 | ||||||||
\(629\) | −24.6030 | −0.980987 | ||||||||
\(630\) | 3.51779 | 0.140152 | ||||||||
\(631\) | −2.46911 | −0.0982939 | −0.0491469 | − | 0.998792i | \(-0.515650\pi\) | ||||
−0.0491469 | + | 0.998792i | \(0.515650\pi\) | |||||||
\(632\) | 5.79457 | 0.230496 | ||||||||
\(633\) | 21.1987 | 0.842574 | ||||||||
\(634\) | −17.6599 | −0.701366 | ||||||||
\(635\) | 48.2858 | 1.91616 | ||||||||
\(636\) | 10.1230 | 0.401403 | ||||||||
\(637\) | −5.10052 | −0.202090 | ||||||||
\(638\) | 1.35253 | 0.0535473 | ||||||||
\(639\) | 8.40081 | 0.332331 | ||||||||
\(640\) | 2.55242 | 0.100893 | ||||||||
\(641\) | 41.5397 | 1.64072 | 0.820360 | − | 0.571847i | \(-0.193773\pi\) | ||||
0.820360 | + | 0.571847i | \(0.193773\pi\) | |||||||
\(642\) | 10.0618 | 0.397109 | ||||||||
\(643\) | −6.01921 | −0.237374 | −0.118687 | − | 0.992932i | \(-0.537869\pi\) | ||||
−0.118687 | + | 0.992932i | \(0.537869\pi\) | |||||||
\(644\) | 5.03104 | 0.198251 | ||||||||
\(645\) | −6.99442 | −0.275405 | ||||||||
\(646\) | −1.35171 | −0.0531824 | ||||||||
\(647\) | −6.66297 | −0.261949 | −0.130974 | − | 0.991386i | \(-0.541811\pi\) | ||||
−0.130974 | + | 0.991386i | \(0.541811\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 34.2505 | 1.34445 | ||||||||
\(650\) | −1.51486 | −0.0594177 | ||||||||
\(651\) | 10.2231 | 0.400675 | ||||||||
\(652\) | −5.81167 | −0.227603 | ||||||||
\(653\) | 44.0181 | 1.72256 | 0.861282 | − | 0.508128i | \(-0.169662\pi\) | ||||
0.861282 | + | 0.508128i | \(0.169662\pi\) | |||||||
\(654\) | 11.4816 | 0.448966 | ||||||||
\(655\) | −38.0646 | −1.48731 | ||||||||
\(656\) | −7.85728 | −0.306775 | ||||||||
\(657\) | 2.15179 | 0.0839494 | ||||||||
\(658\) | 2.93699 | 0.114496 | ||||||||
\(659\) | 36.7419 | 1.43126 | 0.715631 | − | 0.698479i | \(-0.246139\pi\) | ||||
0.715631 | + | 0.698479i | \(0.246139\pi\) | |||||||
\(660\) | 10.4802 | 0.407940 | ||||||||
\(661\) | −19.5472 | −0.760298 | −0.380149 | − | 0.924925i | \(-0.624127\pi\) | ||||
−0.380149 | + | 0.924925i | \(0.624127\pi\) | |||||||
\(662\) | 14.5394 | 0.565088 | ||||||||
\(663\) | −3.57390 | −0.138799 | ||||||||
\(664\) | 1.11990 | 0.0434605 | ||||||||
\(665\) | −1.33049 | −0.0515943 | ||||||||
\(666\) | 6.88409 | 0.266753 | ||||||||
\(667\) | −1.20246 | −0.0465596 | ||||||||
\(668\) | −8.49879 | −0.328828 | ||||||||
\(669\) | −9.75733 | −0.377240 | ||||||||
\(670\) | 7.98328 | 0.308421 | ||||||||
\(671\) | −1.30212 | −0.0502677 | ||||||||
\(672\) | 1.37822 | 0.0531659 | ||||||||
\(673\) | 14.6908 | 0.566289 | 0.283144 | − | 0.959077i | \(-0.408622\pi\) | ||||
0.283144 | + | 0.959077i | \(0.408622\pi\) | |||||||
\(674\) | 27.2491 | 1.04960 | ||||||||
\(675\) | −1.51486 | −0.0583070 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 26.6253 | 1.02329 | 0.511646 | − | 0.859196i | \(-0.329036\pi\) | ||||
0.511646 | + | 0.859196i | \(0.329036\pi\) | |||||||
\(678\) | 4.69080 | 0.180149 | ||||||||
\(679\) | 6.39061 | 0.245249 | ||||||||
\(680\) | 9.12209 | 0.349816 | ||||||||
\(681\) | −26.6880 | −1.02269 | ||||||||
\(682\) | 30.4566 | 1.16624 | ||||||||
\(683\) | 15.9055 | 0.608607 | 0.304303 | − | 0.952575i | \(-0.401576\pi\) | ||||
0.304303 | + | 0.952575i | \(0.401576\pi\) | |||||||
\(684\) | 0.378218 | 0.0144615 | ||||||||
\(685\) | −43.8774 | −1.67647 | ||||||||
\(686\) | 16.6771 | 0.636736 | ||||||||
\(687\) | 21.0379 | 0.802646 | ||||||||
\(688\) | −2.74031 | −0.104473 | ||||||||
\(689\) | −10.1230 | −0.385656 | ||||||||
\(690\) | −9.31736 | −0.354706 | ||||||||
\(691\) | 48.6228 | 1.84970 | 0.924849 | − | 0.380335i | \(-0.124191\pi\) | ||||
0.924849 | + | 0.380335i | \(0.124191\pi\) | |||||||
\(692\) | −16.5832 | −0.630398 | ||||||||
\(693\) | 5.65892 | 0.214965 | ||||||||
\(694\) | 6.74311 | 0.255965 | ||||||||
\(695\) | −46.3879 | −1.75959 | ||||||||
\(696\) | −0.329406 | −0.0124861 | ||||||||
\(697\) | −28.0811 | −1.06365 | ||||||||
\(698\) | 9.28940 | 0.351609 | ||||||||
\(699\) | 8.73734 | 0.330477 | ||||||||
\(700\) | 2.08781 | 0.0789117 | ||||||||
\(701\) | −15.0542 | −0.568588 | −0.284294 | − | 0.958737i | \(-0.591759\pi\) | ||||
−0.284294 | + | 0.958737i | \(0.591759\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −2.60369 | −0.0981999 | ||||||||
\(704\) | 4.10597 | 0.154750 | ||||||||
\(705\) | −5.43923 | −0.204853 | ||||||||
\(706\) | −9.67070 | −0.363962 | ||||||||
\(707\) | −21.4970 | −0.808479 | ||||||||
\(708\) | −8.34165 | −0.313498 | ||||||||
\(709\) | 31.3168 | 1.17613 | 0.588063 | − | 0.808815i | \(-0.299891\pi\) | ||||
0.588063 | + | 0.808815i | \(0.299891\pi\) | |||||||
\(710\) | 21.4424 | 0.804719 | ||||||||
\(711\) | −5.79457 | −0.217313 | ||||||||
\(712\) | −0.259370 | −0.00972032 | ||||||||
\(713\) | −27.0773 | −1.01405 | ||||||||
\(714\) | 4.92561 | 0.184336 | ||||||||
\(715\) | −10.4802 | −0.391936 | ||||||||
\(716\) | −14.9667 | −0.559331 | ||||||||
\(717\) | 17.3130 | 0.646565 | ||||||||
\(718\) | 3.21503 | 0.119984 | ||||||||
\(719\) | −52.9418 | −1.97440 | −0.987198 | − | 0.159500i | \(-0.949012\pi\) | ||||
−0.987198 | + | 0.159500i | \(0.949012\pi\) | |||||||
\(720\) | −2.55242 | −0.0951232 | ||||||||
\(721\) | 1.37822 | 0.0513275 | ||||||||
\(722\) | 18.8570 | 0.701783 | ||||||||
\(723\) | −19.3299 | −0.718886 | ||||||||
\(724\) | −15.9377 | −0.592319 | ||||||||
\(725\) | −0.499005 | −0.0185326 | ||||||||
\(726\) | 5.85898 | 0.217447 | ||||||||
\(727\) | 5.87787 | 0.217998 | 0.108999 | − | 0.994042i | \(-0.465235\pi\) | ||||
0.108999 | + | 0.994042i | \(0.465235\pi\) | |||||||
\(728\) | −1.37822 | −0.0510802 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.49228 | 0.203278 | ||||||||
\(731\) | −9.79358 | −0.362229 | ||||||||
\(732\) | 0.317128 | 0.0117214 | ||||||||
\(733\) | 35.8254 | 1.32324 | 0.661622 | − | 0.749838i | \(-0.269869\pi\) | ||||
0.661622 | + | 0.749838i | \(0.269869\pi\) | |||||||
\(734\) | −13.5101 | −0.498668 | ||||||||
\(735\) | −13.0187 | −0.480201 | ||||||||
\(736\) | −3.65040 | −0.134555 | ||||||||
\(737\) | 12.8423 | 0.473054 | ||||||||
\(738\) | 7.85728 | 0.289230 | ||||||||
\(739\) | −10.0672 | −0.370327 | −0.185164 | − | 0.982708i | \(-0.559281\pi\) | ||||
−0.185164 | + | 0.982708i | \(0.559281\pi\) | |||||||
\(740\) | 17.5711 | 0.645927 | ||||||||
\(741\) | −0.378218 | −0.0138942 | ||||||||
\(742\) | 13.9517 | 0.512183 | ||||||||
\(743\) | 24.4390 | 0.896580 | 0.448290 | − | 0.893888i | \(-0.352033\pi\) | ||||
0.448290 | + | 0.893888i | \(0.352033\pi\) | |||||||
\(744\) | −7.41763 | −0.271944 | ||||||||
\(745\) | 19.2538 | 0.705405 | ||||||||
\(746\) | 8.16869 | 0.299077 | ||||||||
\(747\) | −1.11990 | −0.0409750 | ||||||||
\(748\) | 14.6743 | 0.536546 | ||||||||
\(749\) | 13.8674 | 0.506704 | ||||||||
\(750\) | 8.89555 | 0.324820 | ||||||||
\(751\) | −11.2872 | −0.411874 | −0.205937 | − | 0.978565i | \(-0.566024\pi\) | ||||
−0.205937 | + | 0.978565i | \(0.566024\pi\) | |||||||
\(752\) | −2.13101 | −0.0777099 | ||||||||
\(753\) | −11.1871 | −0.407682 | ||||||||
\(754\) | 0.329406 | 0.0119963 | ||||||||
\(755\) | 56.8003 | 2.06717 | ||||||||
\(756\) | −1.37822 | −0.0501253 | ||||||||
\(757\) | −31.1159 | −1.13093 | −0.565464 | − | 0.824773i | \(-0.691303\pi\) | ||||
−0.565464 | + | 0.824773i | \(0.691303\pi\) | |||||||
\(758\) | 5.83245 | 0.211844 | ||||||||
\(759\) | −14.9884 | −0.544045 | ||||||||
\(760\) | 0.965372 | 0.0350177 | ||||||||
\(761\) | 43.0335 | 1.55996 | 0.779982 | − | 0.625802i | \(-0.215228\pi\) | ||||
0.779982 | + | 0.625802i | \(0.215228\pi\) | |||||||
\(762\) | −18.9176 | −0.685314 | ||||||||
\(763\) | 15.8241 | 0.572873 | ||||||||
\(764\) | 14.0461 | 0.508170 | ||||||||
\(765\) | −9.12209 | −0.329810 | ||||||||
\(766\) | −10.4854 | −0.378853 | ||||||||
\(767\) | 8.34165 | 0.301199 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 6.89994 | 0.248818 | 0.124409 | − | 0.992231i | \(-0.460296\pi\) | ||||
0.124409 | + | 0.992231i | \(0.460296\pi\) | |||||||
\(770\) | 14.4440 | 0.520524 | ||||||||
\(771\) | 25.3163 | 0.911745 | ||||||||
\(772\) | −9.70946 | −0.349451 | ||||||||
\(773\) | 13.3315 | 0.479499 | 0.239750 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239750 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(774\) | 2.74031 | 0.0984984 | ||||||||
\(775\) | −11.2367 | −0.403633 | ||||||||
\(776\) | −4.63686 | −0.166454 | ||||||||
\(777\) | 9.48777 | 0.340372 | ||||||||
\(778\) | 1.54358 | 0.0553402 | ||||||||
\(779\) | −2.97176 | −0.106474 | ||||||||
\(780\) | 2.55242 | 0.0913914 | ||||||||
\(781\) | 34.4935 | 1.23427 | ||||||||
\(782\) | −13.0461 | −0.466529 | ||||||||
\(783\) | 0.329406 | 0.0117720 | ||||||||
\(784\) | −5.10052 | −0.182161 | ||||||||
\(785\) | 30.1507 | 1.07612 | ||||||||
\(786\) | 14.9131 | 0.531934 | ||||||||
\(787\) | −22.2913 | −0.794597 | −0.397299 | − | 0.917689i | \(-0.630052\pi\) | ||||
−0.397299 | + | 0.917689i | \(0.630052\pi\) | |||||||
\(788\) | 10.6953 | 0.381003 | ||||||||
\(789\) | 22.2746 | 0.792995 | ||||||||
\(790\) | −14.7902 | −0.526212 | ||||||||
\(791\) | 6.46495 | 0.229867 | ||||||||
\(792\) | −4.10597 | −0.145899 | ||||||||
\(793\) | −0.317128 | −0.0112615 | ||||||||
\(794\) | −25.3759 | −0.900556 | ||||||||
\(795\) | −25.8382 | −0.916386 | ||||||||
\(796\) | −4.21109 | −0.149258 | ||||||||
\(797\) | −50.1769 | −1.77736 | −0.888678 | − | 0.458532i | \(-0.848375\pi\) | ||||
−0.888678 | + | 0.458532i | \(0.848375\pi\) | |||||||
\(798\) | 0.521267 | 0.0184526 | ||||||||
\(799\) | −7.61600 | −0.269435 | ||||||||
\(800\) | −1.51486 | −0.0535584 | ||||||||
\(801\) | 0.259370 | 0.00916441 | ||||||||
\(802\) | 18.4808 | 0.652580 | ||||||||
\(803\) | 8.83519 | 0.311787 | ||||||||
\(804\) | −3.12773 | −0.110306 | ||||||||
\(805\) | −12.8414 | −0.452598 | ||||||||
\(806\) | 7.41763 | 0.261275 | ||||||||
\(807\) | −23.4427 | −0.825221 | ||||||||
\(808\) | 15.5977 | 0.548725 | ||||||||
\(809\) | −47.5700 | −1.67247 | −0.836235 | − | 0.548371i | \(-0.815248\pi\) | ||||
−0.836235 | + | 0.548371i | \(0.815248\pi\) | |||||||
\(810\) | 2.55242 | 0.0896830 | ||||||||
\(811\) | −31.1647 | −1.09434 | −0.547171 | − | 0.837021i | \(-0.684295\pi\) | ||||
−0.547171 | + | 0.837021i | \(0.684295\pi\) | |||||||
\(812\) | −0.453994 | −0.0159321 | ||||||||
\(813\) | −14.7770 | −0.518251 | ||||||||
\(814\) | 28.2659 | 0.990718 | ||||||||
\(815\) | 14.8338 | 0.519607 | ||||||||
\(816\) | −3.57390 | −0.125111 | ||||||||
\(817\) | −1.03643 | −0.0362602 | ||||||||
\(818\) | −5.38841 | −0.188401 | ||||||||
\(819\) | 1.37822 | 0.0481588 | ||||||||
\(820\) | 20.0551 | 0.700354 | ||||||||
\(821\) | −7.31853 | −0.255418 | −0.127709 | − | 0.991812i | \(-0.540762\pi\) | ||||
−0.127709 | + | 0.991812i | \(0.540762\pi\) | |||||||
\(822\) | 17.1905 | 0.599587 | ||||||||
\(823\) | −14.1340 | −0.492682 | −0.246341 | − | 0.969183i | \(-0.579228\pi\) | ||||
−0.246341 | + | 0.969183i | \(0.579228\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −6.21997 | −0.216552 | ||||||||
\(826\) | −11.4966 | −0.400018 | ||||||||
\(827\) | −32.4299 | −1.12770 | −0.563850 | − | 0.825877i | \(-0.690680\pi\) | ||||
−0.563850 | + | 0.825877i | \(0.690680\pi\) | |||||||
\(828\) | 3.65040 | 0.126860 | ||||||||
\(829\) | 20.4679 | 0.710881 | 0.355440 | − | 0.934699i | \(-0.384331\pi\) | ||||
0.355440 | + | 0.934699i | \(0.384331\pi\) | |||||||
\(830\) | −2.85846 | −0.0992185 | ||||||||
\(831\) | −0.941275 | −0.0326525 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −18.2287 | −0.631587 | ||||||||
\(834\) | 18.1741 | 0.629316 | ||||||||
\(835\) | 21.6925 | 0.750700 | ||||||||
\(836\) | 1.55295 | 0.0537099 | ||||||||
\(837\) | 7.41763 | 0.256391 | ||||||||
\(838\) | 17.1706 | 0.593150 | ||||||||
\(839\) | −13.3546 | −0.461052 | −0.230526 | − | 0.973066i | \(-0.574045\pi\) | ||||
−0.230526 | + | 0.973066i | \(0.574045\pi\) | |||||||
\(840\) | −3.51779 | −0.121375 | ||||||||
\(841\) | −28.8915 | −0.996258 | ||||||||
\(842\) | 27.6057 | 0.951356 | ||||||||
\(843\) | 8.44093 | 0.290721 | ||||||||
\(844\) | −21.1987 | −0.729690 | ||||||||
\(845\) | −2.55242 | −0.0878060 | ||||||||
\(846\) | 2.13101 | 0.0732656 | ||||||||
\(847\) | 8.07495 | 0.277459 | ||||||||
\(848\) | −10.1230 | −0.347625 | ||||||||
\(849\) | −0.458757 | −0.0157445 | ||||||||
\(850\) | −5.41395 | −0.185697 | ||||||||
\(851\) | −25.1297 | −0.861434 | ||||||||
\(852\) | −8.40081 | −0.287807 | ||||||||
\(853\) | 26.5489 | 0.909017 | 0.454508 | − | 0.890742i | \(-0.349815\pi\) | ||||
0.454508 | + | 0.890742i | \(0.349815\pi\) | |||||||
\(854\) | 0.437072 | 0.0149563 | ||||||||
\(855\) | −0.965372 | −0.0330150 | ||||||||
\(856\) | −10.0618 | −0.343906 | ||||||||
\(857\) | −31.4250 | −1.07346 | −0.536728 | − | 0.843755i | \(-0.680340\pi\) | ||||
−0.536728 | + | 0.843755i | \(0.680340\pi\) | |||||||
\(858\) | 4.10597 | 0.140175 | ||||||||
\(859\) | −34.3335 | −1.17144 | −0.585721 | − | 0.810513i | \(-0.699189\pi\) | ||||
−0.585721 | + | 0.810513i | \(0.699189\pi\) | |||||||
\(860\) | 6.99442 | 0.238508 | ||||||||
\(861\) | 10.8290 | 0.369053 | ||||||||
\(862\) | 6.25335 | 0.212990 | ||||||||
\(863\) | −13.8241 | −0.470577 | −0.235289 | − | 0.971926i | \(-0.575604\pi\) | ||||
−0.235289 | + | 0.971926i | \(0.575604\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 42.3273 | 1.43917 | ||||||||
\(866\) | 15.4271 | 0.524235 | ||||||||
\(867\) | 4.22727 | 0.143566 | ||||||||
\(868\) | −10.2231 | −0.346995 | ||||||||
\(869\) | −23.7923 | −0.807100 | ||||||||
\(870\) | 0.840784 | 0.0285053 | ||||||||
\(871\) | 3.12773 | 0.105979 | ||||||||
\(872\) | −11.4816 | −0.388816 | ||||||||
\(873\) | 4.63686 | 0.156934 | ||||||||
\(874\) | −1.38065 | −0.0467010 | ||||||||
\(875\) | 12.2600 | 0.414464 | ||||||||
\(876\) | −2.15179 | −0.0727023 | ||||||||
\(877\) | 0.0399391 | 0.00134865 | 0.000674324 | − | 1.00000i | \(-0.499785\pi\) | ||||
0.000674324 | 1.00000i | \(0.499785\pi\) | ||||||||
\(878\) | −10.2796 | −0.346919 | ||||||||
\(879\) | 5.81927 | 0.196279 | ||||||||
\(880\) | −10.4802 | −0.353286 | ||||||||
\(881\) | −22.9628 | −0.773638 | −0.386819 | − | 0.922156i | \(-0.626426\pi\) | ||||
−0.386819 | + | 0.922156i | \(0.626426\pi\) | |||||||
\(882\) | 5.10052 | 0.171743 | ||||||||
\(883\) | 2.20731 | 0.0742821 | 0.0371410 | − | 0.999310i | \(-0.488175\pi\) | ||||
0.0371410 | + | 0.999310i | \(0.488175\pi\) | |||||||
\(884\) | 3.57390 | 0.120203 | ||||||||
\(885\) | 21.2914 | 0.715703 | ||||||||
\(886\) | −29.9234 | −1.00530 | ||||||||
\(887\) | −24.6791 | −0.828644 | −0.414322 | − | 0.910130i | \(-0.635981\pi\) | ||||
−0.414322 | + | 0.910130i | \(0.635981\pi\) | |||||||
\(888\) | −6.88409 | −0.231015 | ||||||||
\(889\) | −26.0726 | −0.874448 | ||||||||
\(890\) | 0.662023 | 0.0221911 | ||||||||
\(891\) | 4.10597 | 0.137555 | ||||||||
\(892\) | 9.75733 | 0.326700 | ||||||||
\(893\) | −0.805985 | −0.0269713 | ||||||||
\(894\) | −7.54334 | −0.252287 | ||||||||
\(895\) | 38.2013 | 1.27693 | ||||||||
\(896\) | −1.37822 | −0.0460430 | ||||||||
\(897\) | −3.65040 | −0.121883 | ||||||||
\(898\) | 6.67530 | 0.222758 | ||||||||
\(899\) | 2.44342 | 0.0814925 | ||||||||
\(900\) | 1.51486 | 0.0504953 | ||||||||
\(901\) | −36.1786 | −1.20528 | ||||||||
\(902\) | 32.2617 | 1.07420 | ||||||||
\(903\) | 3.77674 | 0.125682 | ||||||||
\(904\) | −4.69080 | −0.156014 | ||||||||
\(905\) | 40.6797 | 1.35224 | ||||||||
\(906\) | −22.2535 | −0.739322 | ||||||||
\(907\) | −23.5663 | −0.782508 | −0.391254 | − | 0.920283i | \(-0.627959\pi\) | ||||
−0.391254 | + | 0.920283i | \(0.627959\pi\) | |||||||
\(908\) | 26.6880 | 0.885673 | ||||||||
\(909\) | −15.5977 | −0.517343 | ||||||||
\(910\) | 3.51779 | 0.116614 | ||||||||
\(911\) | −28.0145 | −0.928163 | −0.464082 | − | 0.885792i | \(-0.653616\pi\) | ||||
−0.464082 | + | 0.885792i | \(0.653616\pi\) | |||||||
\(912\) | −0.378218 | −0.0125240 | ||||||||
\(913\) | −4.59827 | −0.152181 | ||||||||
\(914\) | 5.76757 | 0.190774 | ||||||||
\(915\) | −0.809445 | −0.0267594 | ||||||||
\(916\) | −21.0379 | −0.695112 | ||||||||
\(917\) | 20.5535 | 0.678738 | ||||||||
\(918\) | 3.57390 | 0.117956 | ||||||||
\(919\) | −13.9310 | −0.459542 | −0.229771 | − | 0.973245i | \(-0.573798\pi\) | ||||
−0.229771 | + | 0.973245i | \(0.573798\pi\) | |||||||
\(920\) | 9.31736 | 0.307184 | ||||||||
\(921\) | 15.4051 | 0.507614 | ||||||||
\(922\) | −10.8327 | −0.356755 | ||||||||
\(923\) | 8.40081 | 0.276516 | ||||||||
\(924\) | −5.65892 | −0.186165 | ||||||||
\(925\) | −10.4284 | −0.342885 | ||||||||
\(926\) | 11.7791 | 0.387084 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 0.329406 | 0.0108133 | ||||||||
\(929\) | −55.5699 | −1.82319 | −0.911594 | − | 0.411091i | \(-0.865148\pi\) | ||||
−0.911594 | + | 0.411091i | \(0.865148\pi\) | |||||||
\(930\) | 18.9329 | 0.620835 | ||||||||
\(931\) | −1.92911 | −0.0632239 | ||||||||
\(932\) | −8.73734 | −0.286201 | ||||||||
\(933\) | −21.3489 | −0.698931 | ||||||||
\(934\) | −33.0283 | −1.08072 | ||||||||
\(935\) | −37.4550 | −1.22491 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 16.7160 | 0.546088 | 0.273044 | − | 0.962002i | \(-0.411969\pi\) | ||||
0.273044 | + | 0.962002i | \(0.411969\pi\) | |||||||
\(938\) | −4.31069 | −0.140749 | ||||||||
\(939\) | 0.467785 | 0.0152656 | ||||||||
\(940\) | 5.43923 | 0.177408 | ||||||||
\(941\) | −2.93553 | −0.0956957 | −0.0478478 | − | 0.998855i | \(-0.515236\pi\) | ||||
−0.0478478 | + | 0.998855i | \(0.515236\pi\) | |||||||
\(942\) | −11.8126 | −0.384875 | ||||||||
\(943\) | −28.6822 | −0.934021 | ||||||||
\(944\) | 8.34165 | 0.271497 | ||||||||
\(945\) | 3.51779 | 0.114434 | ||||||||
\(946\) | 11.2516 | 0.365822 | ||||||||
\(947\) | 30.9142 | 1.00458 | 0.502288 | − | 0.864700i | \(-0.332492\pi\) | ||||
0.502288 | + | 0.864700i | \(0.332492\pi\) | |||||||
\(948\) | 5.79457 | 0.188199 | ||||||||
\(949\) | 2.15179 | 0.0698501 | ||||||||
\(950\) | −0.572947 | −0.0185889 | ||||||||
\(951\) | −17.6599 | −0.572663 | ||||||||
\(952\) | −4.92561 | −0.159640 | ||||||||
\(953\) | −39.3113 | −1.27342 | −0.636709 | − | 0.771104i | \(-0.719705\pi\) | ||||
−0.636709 | + | 0.771104i | \(0.719705\pi\) | |||||||
\(954\) | 10.1230 | 0.327744 | ||||||||
\(955\) | −35.8516 | −1.16013 | ||||||||
\(956\) | −17.3130 | −0.559942 | ||||||||
\(957\) | 1.35253 | 0.0437212 | ||||||||
\(958\) | 19.4169 | 0.627330 | ||||||||
\(959\) | 23.6922 | 0.765062 | ||||||||
\(960\) | 2.55242 | 0.0823791 | ||||||||
\(961\) | 24.0213 | 0.774880 | ||||||||
\(962\) | 6.88409 | 0.221952 | ||||||||
\(963\) | 10.0618 | 0.324238 | ||||||||
\(964\) | 19.3299 | 0.622574 | ||||||||
\(965\) | 24.7827 | 0.797782 | ||||||||
\(966\) | 5.03104 | 0.161871 | ||||||||
\(967\) | 33.4298 | 1.07503 | 0.537515 | − | 0.843254i | \(-0.319363\pi\) | ||||
0.537515 | + | 0.843254i | \(0.319363\pi\) | |||||||
\(968\) | −5.85898 | −0.188315 | ||||||||
\(969\) | −1.35171 | −0.0434232 | ||||||||
\(970\) | 11.8352 | 0.380006 | ||||||||
\(971\) | −1.90635 | −0.0611778 | −0.0305889 | − | 0.999532i | \(-0.509738\pi\) | ||||
−0.0305889 | + | 0.999532i | \(0.509738\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 25.0478 | 0.802996 | ||||||||
\(974\) | −12.6915 | −0.406662 | ||||||||
\(975\) | −1.51486 | −0.0485144 | ||||||||
\(976\) | −0.317128 | −0.0101510 | ||||||||
\(977\) | 22.6232 | 0.723781 | 0.361891 | − | 0.932221i | \(-0.382131\pi\) | ||||
0.361891 | + | 0.932221i | \(0.382131\pi\) | |||||||
\(978\) | −5.81167 | −0.185837 | ||||||||
\(979\) | 1.06497 | 0.0340365 | ||||||||
\(980\) | 13.0187 | 0.415866 | ||||||||
\(981\) | 11.4816 | 0.366579 | ||||||||
\(982\) | 14.4170 | 0.460064 | ||||||||
\(983\) | −35.9535 | −1.14674 | −0.573369 | − | 0.819297i | \(-0.694364\pi\) | ||||
−0.573369 | + | 0.819297i | \(0.694364\pi\) | |||||||
\(984\) | −7.85728 | −0.250481 | ||||||||
\(985\) | −27.2988 | −0.869814 | ||||||||
\(986\) | 1.17726 | 0.0374917 | ||||||||
\(987\) | 2.93699 | 0.0934855 | ||||||||
\(988\) | 0.378218 | 0.0120327 | ||||||||
\(989\) | −10.0032 | −0.318084 | ||||||||
\(990\) | 10.4802 | 0.333082 | ||||||||
\(991\) | −47.8301 | −1.51937 | −0.759686 | − | 0.650290i | \(-0.774647\pi\) | ||||
−0.759686 | + | 0.650290i | \(0.774647\pi\) | |||||||
\(992\) | 7.41763 | 0.235510 | ||||||||
\(993\) | 14.5394 | 0.461392 | ||||||||
\(994\) | −11.5781 | −0.367236 | ||||||||
\(995\) | 10.7485 | 0.340750 | ||||||||
\(996\) | 1.11990 | 0.0354854 | ||||||||
\(997\) | −44.1437 | −1.39805 | −0.699023 | − | 0.715099i | \(-0.746381\pi\) | ||||
−0.699023 | + | 0.715099i | \(0.746381\pi\) | |||||||
\(998\) | −13.4253 | −0.424970 | ||||||||
\(999\) | 6.88409 | 0.217803 |
(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 | 8034.2.a.o.1.3 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.o.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial |