Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
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: | \( x^{8} - 2x^{7} - 8x^{6} + 14x^{5} + 18x^{4} - 24x^{3} - 10x^{2} + 10x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.487949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.487949 | −0.345032 | −0.172516 | − | 0.985007i | \(-0.555190\pi\) | ||||
−0.172516 | + | 0.985007i | \(0.555190\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.76191 | −0.880953 | ||||||||
\(5\) | 1.53225 | 0.685241 | 0.342620 | − | 0.939474i | \(-0.388686\pi\) | ||||
0.342620 | + | 0.939474i | \(0.388686\pi\) | |||||||
\(6\) | −0.487949 | −0.199204 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.83562 | 0.648989 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.747657 | −0.236430 | ||||||||
\(11\) | −3.51053 | −1.05846 | −0.529232 | − | 0.848477i | \(-0.677520\pi\) | ||||
−0.529232 | + | 0.848477i | \(0.677520\pi\) | |||||||
\(12\) | −1.76191 | −0.508618 | ||||||||
\(13\) | 2.32735 | 0.645490 | 0.322745 | − | 0.946486i | \(-0.395394\pi\) | ||||
0.322745 | + | 0.946486i | \(0.395394\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.53225 | 0.395624 | ||||||||
\(16\) | 2.62812 | 0.657031 | ||||||||
\(17\) | −4.08881 | −0.991682 | −0.495841 | − | 0.868413i | \(-0.665140\pi\) | ||||
−0.495841 | + | 0.868413i | \(0.665140\pi\) | |||||||
\(18\) | −0.487949 | −0.115011 | ||||||||
\(19\) | 1.32044 | 0.302930 | 0.151465 | − | 0.988463i | \(-0.451601\pi\) | ||||
0.151465 | + | 0.988463i | \(0.451601\pi\) | |||||||
\(20\) | −2.69967 | −0.603665 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.71296 | 0.365204 | ||||||||
\(23\) | 1.38676 | 0.289160 | 0.144580 | − | 0.989493i | \(-0.453817\pi\) | ||||
0.144580 | + | 0.989493i | \(0.453817\pi\) | |||||||
\(24\) | 1.83562 | 0.374694 | ||||||||
\(25\) | −2.65223 | −0.530445 | ||||||||
\(26\) | −1.13563 | −0.222715 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.15628 | −0.957496 | −0.478748 | − | 0.877952i | \(-0.658909\pi\) | ||||
−0.478748 | + | 0.877952i | \(0.658909\pi\) | |||||||
\(30\) | −0.747657 | −0.136503 | ||||||||
\(31\) | 0.813042 | 0.146027 | 0.0730133 | − | 0.997331i | \(-0.476738\pi\) | ||||
0.0730133 | + | 0.997331i | \(0.476738\pi\) | |||||||
\(32\) | −4.95363 | −0.875686 | ||||||||
\(33\) | −3.51053 | −0.611104 | ||||||||
\(34\) | 1.99513 | 0.342162 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.76191 | −0.293651 | ||||||||
\(37\) | 10.0334 | 1.64948 | 0.824739 | − | 0.565514i | \(-0.191322\pi\) | ||||
0.824739 | + | 0.565514i | \(0.191322\pi\) | |||||||
\(38\) | −0.644308 | −0.104521 | ||||||||
\(39\) | 2.32735 | 0.372674 | ||||||||
\(40\) | 2.81262 | 0.444714 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.79727 | −0.426579 | −0.213290 | − | 0.976989i | \(-0.568418\pi\) | ||||
−0.213290 | + | 0.976989i | \(0.568418\pi\) | |||||||
\(44\) | 6.18521 | 0.932456 | ||||||||
\(45\) | 1.53225 | 0.228414 | ||||||||
\(46\) | −0.676670 | −0.0997696 | ||||||||
\(47\) | −10.6010 | −1.54632 | −0.773160 | − | 0.634211i | \(-0.781325\pi\) | ||||
−0.773160 | + | 0.634211i | \(0.781325\pi\) | |||||||
\(48\) | 2.62812 | 0.379337 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.29415 | 0.183021 | ||||||||
\(51\) | −4.08881 | −0.572548 | ||||||||
\(52\) | −4.10057 | −0.568647 | ||||||||
\(53\) | −8.05270 | −1.10612 | −0.553062 | − | 0.833140i | \(-0.686541\pi\) | ||||
−0.553062 | + | 0.833140i | \(0.686541\pi\) | |||||||
\(54\) | −0.487949 | −0.0664015 | ||||||||
\(55\) | −5.37898 | −0.725302 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.32044 | 0.174897 | ||||||||
\(58\) | 2.51600 | 0.330367 | ||||||||
\(59\) | 0.693332 | 0.0902641 | 0.0451321 | − | 0.998981i | \(-0.485629\pi\) | ||||
0.0451321 | + | 0.998981i | \(0.485629\pi\) | |||||||
\(60\) | −2.69967 | −0.348526 | ||||||||
\(61\) | −1.29889 | −0.166306 | −0.0831532 | − | 0.996537i | \(-0.526499\pi\) | ||||
−0.0831532 | + | 0.996537i | \(0.526499\pi\) | |||||||
\(62\) | −0.396723 | −0.0503839 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.83913 | −0.354891 | ||||||||
\(65\) | 3.56607 | 0.442316 | ||||||||
\(66\) | 1.71296 | 0.210850 | ||||||||
\(67\) | 8.82262 | 1.07785 | 0.538927 | − | 0.842352i | \(-0.318830\pi\) | ||||
0.538927 | + | 0.842352i | \(0.318830\pi\) | |||||||
\(68\) | 7.20409 | 0.873625 | ||||||||
\(69\) | 1.38676 | 0.166947 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.16765 | 0.850644 | 0.425322 | − | 0.905042i | \(-0.360161\pi\) | ||||
0.425322 | + | 0.905042i | \(0.360161\pi\) | |||||||
\(72\) | 1.83562 | 0.216330 | ||||||||
\(73\) | −1.53683 | −0.179872 | −0.0899360 | − | 0.995948i | \(-0.528666\pi\) | ||||
−0.0899360 | + | 0.995948i | \(0.528666\pi\) | |||||||
\(74\) | −4.89578 | −0.569123 | ||||||||
\(75\) | −2.65223 | −0.306253 | ||||||||
\(76\) | −2.32649 | −0.266867 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.13563 | −0.128584 | ||||||||
\(79\) | −5.48031 | −0.616583 | −0.308292 | − | 0.951292i | \(-0.599757\pi\) | ||||
−0.308292 | + | 0.951292i | \(0.599757\pi\) | |||||||
\(80\) | 4.02693 | 0.450224 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.487949 | 0.0538850 | ||||||||
\(83\) | −5.90345 | −0.647987 | −0.323994 | − | 0.946059i | \(-0.605026\pi\) | ||||
−0.323994 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.26506 | −0.679541 | ||||||||
\(86\) | 1.36492 | 0.147184 | ||||||||
\(87\) | −5.15628 | −0.552811 | ||||||||
\(88\) | −6.44398 | −0.686931 | ||||||||
\(89\) | −12.6977 | −1.34595 | −0.672977 | − | 0.739664i | \(-0.734985\pi\) | ||||
−0.672977 | + | 0.739664i | \(0.734985\pi\) | |||||||
\(90\) | −0.747657 | −0.0788100 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.44335 | −0.254737 | ||||||||
\(93\) | 0.813042 | 0.0843085 | ||||||||
\(94\) | 5.17277 | 0.533530 | ||||||||
\(95\) | 2.02324 | 0.207580 | ||||||||
\(96\) | −4.95363 | −0.505577 | ||||||||
\(97\) | −14.2954 | −1.45148 | −0.725740 | − | 0.687969i | \(-0.758502\pi\) | ||||
−0.725740 | + | 0.687969i | \(0.758502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.51053 | −0.352821 | ||||||||
\(100\) | 4.67297 | 0.467297 | ||||||||
\(101\) | 9.76287 | 0.971442 | 0.485721 | − | 0.874114i | \(-0.338557\pi\) | ||||
0.485721 | + | 0.874114i | \(0.338557\pi\) | |||||||
\(102\) | 1.99513 | 0.197547 | ||||||||
\(103\) | −6.73133 | −0.663257 | −0.331629 | − | 0.943410i | \(-0.607598\pi\) | ||||
−0.331629 | + | 0.943410i | \(0.607598\pi\) | |||||||
\(104\) | 4.27212 | 0.418916 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.92931 | 0.381648 | ||||||||
\(107\) | 3.40497 | 0.329171 | 0.164585 | − | 0.986363i | \(-0.447371\pi\) | ||||
0.164585 | + | 0.986363i | \(0.447371\pi\) | |||||||
\(108\) | −1.76191 | −0.169539 | ||||||||
\(109\) | 2.90920 | 0.278651 | 0.139326 | − | 0.990247i | \(-0.455507\pi\) | ||||
0.139326 | + | 0.990247i | \(0.455507\pi\) | |||||||
\(110\) | 2.62467 | 0.250253 | ||||||||
\(111\) | 10.0334 | 0.952326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.89937 | 0.366822 | 0.183411 | − | 0.983036i | \(-0.441286\pi\) | ||||
0.183411 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(114\) | −0.644308 | −0.0603449 | ||||||||
\(115\) | 2.12486 | 0.198144 | ||||||||
\(116\) | 9.08487 | 0.843509 | ||||||||
\(117\) | 2.32735 | 0.215163 | ||||||||
\(118\) | −0.338311 | −0.0311440 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.81262 | 0.256756 | ||||||||
\(121\) | 1.32379 | 0.120344 | ||||||||
\(122\) | 0.633794 | 0.0573810 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −1.43250 | −0.128643 | ||||||||
\(125\) | −11.7251 | −1.04872 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.42195 | −0.481120 | −0.240560 | − | 0.970634i | \(-0.577331\pi\) | ||||
−0.240560 | + | 0.970634i | \(0.577331\pi\) | |||||||
\(128\) | 11.2926 | 0.998135 | ||||||||
\(129\) | −2.79727 | −0.246286 | ||||||||
\(130\) | −1.74006 | −0.152613 | ||||||||
\(131\) | −3.23920 | −0.283010 | −0.141505 | − | 0.989938i | \(-0.545194\pi\) | ||||
−0.141505 | + | 0.989938i | \(0.545194\pi\) | |||||||
\(132\) | 6.18521 | 0.538354 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.30499 | −0.371894 | ||||||||
\(135\) | 1.53225 | 0.131875 | ||||||||
\(136\) | −7.50549 | −0.643591 | ||||||||
\(137\) | −7.01858 | −0.599638 | −0.299819 | − | 0.953996i | \(-0.596926\pi\) | ||||
−0.299819 | + | 0.953996i | \(0.596926\pi\) | |||||||
\(138\) | −0.676670 | −0.0576020 | ||||||||
\(139\) | 14.7100 | 1.24769 | 0.623843 | − | 0.781550i | \(-0.285570\pi\) | ||||
0.623843 | + | 0.781550i | \(0.285570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.6010 | −0.892768 | ||||||||
\(142\) | −3.49745 | −0.293499 | ||||||||
\(143\) | −8.17022 | −0.683228 | ||||||||
\(144\) | 2.62812 | 0.219010 | ||||||||
\(145\) | −7.90068 | −0.656116 | ||||||||
\(146\) | 0.749893 | 0.0620616 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.6779 | −1.45311 | ||||||||
\(149\) | 9.98658 | 0.818132 | 0.409066 | − | 0.912505i | \(-0.365855\pi\) | ||||
0.409066 | + | 0.912505i | \(0.365855\pi\) | |||||||
\(150\) | 1.29415 | 0.105667 | ||||||||
\(151\) | −18.2139 | −1.48223 | −0.741114 | − | 0.671380i | \(-0.765702\pi\) | ||||
−0.741114 | + | 0.671380i | \(0.765702\pi\) | |||||||
\(152\) | 2.42382 | 0.196598 | ||||||||
\(153\) | −4.08881 | −0.330561 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.24578 | 0.100063 | ||||||||
\(156\) | −4.10057 | −0.328308 | ||||||||
\(157\) | 4.40579 | 0.351620 | 0.175810 | − | 0.984424i | \(-0.443746\pi\) | ||||
0.175810 | + | 0.984424i | \(0.443746\pi\) | |||||||
\(158\) | 2.67411 | 0.212741 | ||||||||
\(159\) | −8.05270 | −0.638621 | ||||||||
\(160\) | −7.59017 | −0.600056 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.487949 | −0.0383369 | ||||||||
\(163\) | 4.66216 | 0.365169 | 0.182584 | − | 0.983190i | \(-0.441554\pi\) | ||||
0.182584 | + | 0.983190i | \(0.441554\pi\) | |||||||
\(164\) | 1.76191 | 0.137582 | ||||||||
\(165\) | −5.37898 | −0.418753 | ||||||||
\(166\) | 2.88058 | 0.223576 | ||||||||
\(167\) | −7.14687 | −0.553041 | −0.276521 | − | 0.961008i | \(-0.589181\pi\) | ||||
−0.276521 | + | 0.961008i | \(0.589181\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.58345 | −0.583342 | ||||||||
\(170\) | 3.05703 | 0.234463 | ||||||||
\(171\) | 1.32044 | 0.100977 | ||||||||
\(172\) | 4.92852 | 0.375796 | ||||||||
\(173\) | 10.9222 | 0.830397 | 0.415198 | − | 0.909731i | \(-0.363712\pi\) | ||||
0.415198 | + | 0.909731i | \(0.363712\pi\) | |||||||
\(174\) | 2.51600 | 0.190737 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.22609 | −0.695443 | ||||||||
\(177\) | 0.693332 | 0.0521140 | ||||||||
\(178\) | 6.19583 | 0.464397 | ||||||||
\(179\) | −3.51144 | −0.262458 | −0.131229 | − | 0.991352i | \(-0.541892\pi\) | ||||
−0.131229 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(180\) | −2.69967 | −0.201222 | ||||||||
\(181\) | −3.38587 | −0.251669 | −0.125835 | − | 0.992051i | \(-0.540161\pi\) | ||||
−0.125835 | + | 0.992051i | \(0.540161\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.29889 | −0.0960170 | ||||||||
\(184\) | 2.54557 | 0.187662 | ||||||||
\(185\) | 15.3736 | 1.13029 | ||||||||
\(186\) | −0.396723 | −0.0290891 | ||||||||
\(187\) | 14.3539 | 1.04966 | ||||||||
\(188\) | 18.6780 | 1.36224 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.987237 | −0.0716217 | ||||||||
\(191\) | −9.56641 | −0.692201 | −0.346100 | − | 0.938197i | \(-0.612494\pi\) | ||||
−0.346100 | + | 0.938197i | \(0.612494\pi\) | |||||||
\(192\) | −2.83913 | −0.204897 | ||||||||
\(193\) | −3.73602 | −0.268925 | −0.134462 | − | 0.990919i | \(-0.542931\pi\) | ||||
−0.134462 | + | 0.990919i | \(0.542931\pi\) | |||||||
\(194\) | 6.97543 | 0.500807 | ||||||||
\(195\) | 3.56607 | 0.255371 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.86710 | 0.275520 | 0.137760 | − | 0.990466i | \(-0.456010\pi\) | ||||
0.137760 | + | 0.990466i | \(0.456010\pi\) | |||||||
\(198\) | 1.71296 | 0.121735 | ||||||||
\(199\) | −9.78954 | −0.693962 | −0.346981 | − | 0.937872i | \(-0.612793\pi\) | ||||
−0.346981 | + | 0.937872i | \(0.612793\pi\) | |||||||
\(200\) | −4.86847 | −0.344253 | ||||||||
\(201\) | 8.82262 | 0.622300 | ||||||||
\(202\) | −4.76378 | −0.335179 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.20409 | 0.504388 | ||||||||
\(205\) | −1.53225 | −0.107017 | ||||||||
\(206\) | 3.28454 | 0.228845 | ||||||||
\(207\) | 1.38676 | 0.0963868 | ||||||||
\(208\) | 6.11656 | 0.424107 | ||||||||
\(209\) | −4.63544 | −0.320640 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.378702 | 0.0260710 | 0.0130355 | − | 0.999915i | \(-0.495851\pi\) | ||||
0.0130355 | + | 0.999915i | \(0.495851\pi\) | |||||||
\(212\) | 14.1881 | 0.974443 | ||||||||
\(213\) | 7.16765 | 0.491119 | ||||||||
\(214\) | −1.66145 | −0.113574 | ||||||||
\(215\) | −4.28610 | −0.292310 | ||||||||
\(216\) | 1.83562 | 0.124898 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.41954 | −0.0961436 | ||||||||
\(219\) | −1.53683 | −0.103849 | ||||||||
\(220\) | 9.47726 | 0.638957 | ||||||||
\(221\) | −9.51608 | −0.640121 | ||||||||
\(222\) | −4.89578 | −0.328583 | ||||||||
\(223\) | −7.17776 | −0.480659 | −0.240329 | − | 0.970691i | \(-0.577255\pi\) | ||||
−0.240329 | + | 0.970691i | \(0.577255\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.65223 | −0.176815 | ||||||||
\(226\) | −1.90269 | −0.126565 | ||||||||
\(227\) | −16.0821 | −1.06741 | −0.533704 | − | 0.845671i | \(-0.679200\pi\) | ||||
−0.533704 | + | 0.845671i | \(0.679200\pi\) | |||||||
\(228\) | −2.32649 | −0.154076 | ||||||||
\(229\) | 27.5061 | 1.81766 | 0.908828 | − | 0.417172i | \(-0.136979\pi\) | ||||
0.908828 | + | 0.417172i | \(0.136979\pi\) | |||||||
\(230\) | −1.03682 | −0.0683662 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.46495 | −0.621405 | ||||||||
\(233\) | −24.4620 | −1.60256 | −0.801280 | − | 0.598289i | \(-0.795847\pi\) | ||||
−0.801280 | + | 0.598289i | \(0.795847\pi\) | |||||||
\(234\) | −1.13563 | −0.0742383 | ||||||||
\(235\) | −16.2434 | −1.05960 | ||||||||
\(236\) | −1.22159 | −0.0795185 | ||||||||
\(237\) | −5.48031 | −0.355985 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4572 | −1.19390 | −0.596950 | − | 0.802279i | \(-0.703621\pi\) | ||||
−0.596950 | + | 0.802279i | \(0.703621\pi\) | |||||||
\(240\) | 4.02693 | 0.259937 | ||||||||
\(241\) | −26.5183 | −1.70819 | −0.854096 | − | 0.520115i | \(-0.825889\pi\) | ||||
−0.854096 | + | 0.520115i | \(0.825889\pi\) | |||||||
\(242\) | −0.645941 | −0.0415227 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.28853 | 0.146508 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.487949 | 0.0311105 | ||||||||
\(247\) | 3.07313 | 0.195538 | ||||||||
\(248\) | 1.49243 | 0.0947697 | ||||||||
\(249\) | −5.90345 | −0.374116 | ||||||||
\(250\) | 5.72124 | 0.361843 | ||||||||
\(251\) | 6.46587 | 0.408122 | 0.204061 | − | 0.978958i | \(-0.434586\pi\) | ||||
0.204061 | + | 0.978958i | \(0.434586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.86827 | −0.306065 | ||||||||
\(254\) | 2.64563 | 0.166002 | ||||||||
\(255\) | −6.26506 | −0.392333 | ||||||||
\(256\) | 0.168043 | 0.0105027 | ||||||||
\(257\) | −20.8940 | −1.30333 | −0.651666 | − | 0.758506i | \(-0.725929\pi\) | ||||
−0.651666 | + | 0.758506i | \(0.725929\pi\) | |||||||
\(258\) | 1.36492 | 0.0849765 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.28308 | −0.389660 | ||||||||
\(261\) | −5.15628 | −0.319165 | ||||||||
\(262\) | 1.58056 | 0.0976476 | ||||||||
\(263\) | 22.8930 | 1.41164 | 0.705822 | − | 0.708389i | \(-0.250578\pi\) | ||||
0.705822 | + | 0.708389i | \(0.250578\pi\) | |||||||
\(264\) | −6.44398 | −0.396600 | ||||||||
\(265\) | −12.3387 | −0.757961 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6977 | −0.777086 | ||||||||
\(268\) | −15.5446 | −0.949539 | ||||||||
\(269\) | −1.07667 | −0.0656459 | −0.0328229 | − | 0.999461i | \(-0.510450\pi\) | ||||
−0.0328229 | + | 0.999461i | \(0.510450\pi\) | |||||||
\(270\) | −0.747657 | −0.0455010 | ||||||||
\(271\) | 20.4648 | 1.24315 | 0.621574 | − | 0.783355i | \(-0.286493\pi\) | ||||
0.621574 | + | 0.783355i | \(0.286493\pi\) | |||||||
\(272\) | −10.7459 | −0.651565 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.42471 | 0.206894 | ||||||||
\(275\) | 9.31070 | 0.561457 | ||||||||
\(276\) | −2.44335 | −0.147072 | ||||||||
\(277\) | −19.0318 | −1.14351 | −0.571755 | − | 0.820425i | \(-0.693737\pi\) | ||||
−0.571755 | + | 0.820425i | \(0.693737\pi\) | |||||||
\(278\) | −7.17773 | −0.430492 | ||||||||
\(279\) | 0.813042 | 0.0486756 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.92479 | 0.353443 | 0.176722 | − | 0.984261i | \(-0.443451\pi\) | ||||
0.176722 | + | 0.984261i | \(0.443451\pi\) | |||||||
\(282\) | 5.17277 | 0.308034 | ||||||||
\(283\) | 19.1146 | 1.13625 | 0.568123 | − | 0.822944i | \(-0.307670\pi\) | ||||
0.568123 | + | 0.822944i | \(0.307670\pi\) | |||||||
\(284\) | −12.6287 | −0.749377 | ||||||||
\(285\) | 2.02324 | 0.119846 | ||||||||
\(286\) | 3.98665 | 0.235735 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.95363 | −0.291895 | ||||||||
\(289\) | −0.281647 | −0.0165675 | ||||||||
\(290\) | 3.85513 | 0.226381 | ||||||||
\(291\) | −14.2954 | −0.838012 | ||||||||
\(292\) | 2.70774 | 0.158459 | ||||||||
\(293\) | 4.67356 | 0.273032 | 0.136516 | − | 0.990638i | \(-0.456409\pi\) | ||||
0.136516 | + | 0.990638i | \(0.456409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.06235 | 0.0618527 | ||||||||
\(296\) | 18.4175 | 1.07049 | ||||||||
\(297\) | −3.51053 | −0.203701 | ||||||||
\(298\) | −4.87294 | −0.282282 | ||||||||
\(299\) | 3.22748 | 0.186650 | ||||||||
\(300\) | 4.67297 | 0.269794 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.88746 | 0.511416 | ||||||||
\(303\) | 9.76287 | 0.560862 | ||||||||
\(304\) | 3.47028 | 0.199034 | ||||||||
\(305\) | −1.99022 | −0.113960 | ||||||||
\(306\) | 1.99513 | 0.114054 | ||||||||
\(307\) | −32.9595 | −1.88110 | −0.940548 | − | 0.339660i | \(-0.889688\pi\) | ||||
−0.940548 | + | 0.339660i | \(0.889688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.73133 | −0.382932 | ||||||||
\(310\) | −0.607877 | −0.0345251 | ||||||||
\(311\) | 1.39024 | 0.0788331 | 0.0394165 | − | 0.999223i | \(-0.487450\pi\) | ||||
0.0394165 | + | 0.999223i | \(0.487450\pi\) | |||||||
\(312\) | 4.27212 | 0.241861 | ||||||||
\(313\) | 30.8397 | 1.74316 | 0.871580 | − | 0.490252i | \(-0.163095\pi\) | ||||
0.871580 | + | 0.490252i | \(0.163095\pi\) | |||||||
\(314\) | −2.14980 | −0.121320 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.65580 | 0.543181 | ||||||||
\(317\) | −4.30009 | −0.241517 | −0.120758 | − | 0.992682i | \(-0.538533\pi\) | ||||
−0.120758 | + | 0.992682i | \(0.538533\pi\) | |||||||
\(318\) | 3.92931 | 0.220345 | ||||||||
\(319\) | 18.1012 | 1.01347 | ||||||||
\(320\) | −4.35024 | −0.243186 | ||||||||
\(321\) | 3.40497 | 0.190047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.39903 | −0.300410 | ||||||||
\(324\) | −1.76191 | −0.0978837 | ||||||||
\(325\) | −6.17265 | −0.342397 | ||||||||
\(326\) | −2.27490 | −0.125995 | ||||||||
\(327\) | 2.90920 | 0.160879 | ||||||||
\(328\) | −1.83562 | −0.101355 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.62467 | 0.144483 | ||||||||
\(331\) | 12.5388 | 0.689196 | 0.344598 | − | 0.938750i | \(-0.388015\pi\) | ||||
0.344598 | + | 0.938750i | \(0.388015\pi\) | |||||||
\(332\) | 10.4013 | 0.570846 | ||||||||
\(333\) | 10.0334 | 0.549826 | ||||||||
\(334\) | 3.48731 | 0.190817 | ||||||||
\(335\) | 13.5184 | 0.738590 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.90601 | −0.539615 | −0.269807 | − | 0.962914i | \(-0.586960\pi\) | ||||
−0.269807 | + | 0.962914i | \(0.586960\pi\) | |||||||
\(338\) | 3.70034 | 0.201272 | ||||||||
\(339\) | 3.89937 | 0.211785 | ||||||||
\(340\) | 11.0384 | 0.598643 | ||||||||
\(341\) | −2.85420 | −0.154564 | ||||||||
\(342\) | −0.644308 | −0.0348402 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.13472 | −0.276845 | ||||||||
\(345\) | 2.12486 | 0.114399 | ||||||||
\(346\) | −5.32946 | −0.286514 | ||||||||
\(347\) | −14.4682 | −0.776692 | −0.388346 | − | 0.921514i | \(-0.626953\pi\) | ||||
−0.388346 | + | 0.921514i | \(0.626953\pi\) | |||||||
\(348\) | 9.08487 | 0.487000 | ||||||||
\(349\) | 1.75459 | 0.0939213 | 0.0469606 | − | 0.998897i | \(-0.485046\pi\) | ||||
0.0469606 | + | 0.998897i | \(0.485046\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.32735 | 0.124225 | ||||||||
\(352\) | 17.3898 | 0.926881 | ||||||||
\(353\) | 12.1456 | 0.646446 | 0.323223 | − | 0.946323i | \(-0.395234\pi\) | ||||
0.323223 | + | 0.946323i | \(0.395234\pi\) | |||||||
\(354\) | −0.338311 | −0.0179810 | ||||||||
\(355\) | 10.9826 | 0.582896 | ||||||||
\(356\) | 22.3721 | 1.18572 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.71341 | 0.0905563 | ||||||||
\(359\) | 16.5245 | 0.872130 | 0.436065 | − | 0.899915i | \(-0.356372\pi\) | ||||
0.436065 | + | 0.899915i | \(0.356372\pi\) | |||||||
\(360\) | 2.81262 | 0.148238 | ||||||||
\(361\) | −17.2564 | −0.908234 | ||||||||
\(362\) | 1.65213 | 0.0868340 | ||||||||
\(363\) | 1.32379 | 0.0694808 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.35480 | −0.123256 | ||||||||
\(366\) | 0.633794 | 0.0331289 | ||||||||
\(367\) | 8.81154 | 0.459959 | 0.229979 | − | 0.973196i | \(-0.426134\pi\) | ||||
0.229979 | + | 0.973196i | \(0.426134\pi\) | |||||||
\(368\) | 3.64459 | 0.189987 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −7.50153 | −0.389986 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.43250 | −0.0742718 | ||||||||
\(373\) | −1.82834 | −0.0946679 | −0.0473340 | − | 0.998879i | \(-0.515072\pi\) | ||||
−0.0473340 | + | 0.998879i | \(0.515072\pi\) | |||||||
\(374\) | −7.00395 | −0.362166 | ||||||||
\(375\) | −11.7251 | −0.605481 | ||||||||
\(376\) | −19.4595 | −1.00355 | ||||||||
\(377\) | −12.0004 | −0.618055 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.6184 | −1.41866 | −0.709332 | − | 0.704875i | \(-0.751003\pi\) | ||||
−0.709332 | + | 0.704875i | \(0.751003\pi\) | |||||||
\(380\) | −3.56476 | −0.182868 | ||||||||
\(381\) | −5.42195 | −0.277775 | ||||||||
\(382\) | 4.66792 | 0.238832 | ||||||||
\(383\) | −25.2343 | −1.28941 | −0.644705 | − | 0.764431i | \(-0.723020\pi\) | ||||
−0.644705 | + | 0.764431i | \(0.723020\pi\) | |||||||
\(384\) | 11.2926 | 0.576273 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.82299 | 0.0927877 | ||||||||
\(387\) | −2.79727 | −0.142193 | ||||||||
\(388\) | 25.1872 | 1.27868 | ||||||||
\(389\) | −35.0906 | −1.77917 | −0.889583 | − | 0.456774i | \(-0.849005\pi\) | ||||
−0.889583 | + | 0.456774i | \(0.849005\pi\) | |||||||
\(390\) | −1.74006 | −0.0881113 | ||||||||
\(391\) | −5.67021 | −0.286755 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.23920 | −0.163396 | ||||||||
\(394\) | −1.88695 | −0.0950631 | ||||||||
\(395\) | −8.39718 | −0.422508 | ||||||||
\(396\) | 6.18521 | 0.310819 | ||||||||
\(397\) | 25.5787 | 1.28376 | 0.641878 | − | 0.766807i | \(-0.278156\pi\) | ||||
0.641878 | + | 0.766807i | \(0.278156\pi\) | |||||||
\(398\) | 4.77680 | 0.239439 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.97037 | −0.348519 | ||||||||
\(401\) | −15.7251 | −0.785275 | −0.392638 | − | 0.919693i | \(-0.628437\pi\) | ||||
−0.392638 | + | 0.919693i | \(0.628437\pi\) | |||||||
\(402\) | −4.30499 | −0.214713 | ||||||||
\(403\) | 1.89223 | 0.0942588 | ||||||||
\(404\) | −17.2013 | −0.855795 | ||||||||
\(405\) | 1.53225 | 0.0761379 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.2224 | −1.74591 | ||||||||
\(408\) | −7.50549 | −0.371577 | ||||||||
\(409\) | 0.206464 | 0.0102090 | 0.00510448 | − | 0.999987i | \(-0.498375\pi\) | ||||
0.00510448 | + | 0.999987i | \(0.498375\pi\) | |||||||
\(410\) | 0.747657 | 0.0369242 | ||||||||
\(411\) | −7.01858 | −0.346201 | ||||||||
\(412\) | 11.8600 | 0.584298 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.676670 | −0.0332565 | ||||||||
\(415\) | −9.04553 | −0.444027 | ||||||||
\(416\) | −11.5288 | −0.565247 | ||||||||
\(417\) | 14.7100 | 0.720352 | ||||||||
\(418\) | 2.26186 | 0.110631 | ||||||||
\(419\) | 15.2919 | 0.747056 | 0.373528 | − | 0.927619i | \(-0.378148\pi\) | ||||
0.373528 | + | 0.927619i | \(0.378148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0348 | −1.65875 | −0.829377 | − | 0.558690i | \(-0.811304\pi\) | ||||
−0.829377 | + | 0.558690i | \(0.811304\pi\) | |||||||
\(422\) | −0.184787 | −0.00899531 | ||||||||
\(423\) | −10.6010 | −0.515440 | ||||||||
\(424\) | −14.7817 | −0.717862 | ||||||||
\(425\) | 10.8444 | 0.526033 | ||||||||
\(426\) | −3.49745 | −0.169452 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.99923 | −0.289984 | ||||||||
\(429\) | −8.17022 | −0.394462 | ||||||||
\(430\) | 2.09140 | 0.100856 | ||||||||
\(431\) | −16.6176 | −0.800442 | −0.400221 | − | 0.916419i | \(-0.631067\pi\) | ||||
−0.400221 | + | 0.916419i | \(0.631067\pi\) | |||||||
\(432\) | 2.62812 | 0.126446 | ||||||||
\(433\) | −1.16266 | −0.0558738 | −0.0279369 | − | 0.999610i | \(-0.508894\pi\) | ||||
−0.0279369 | + | 0.999610i | \(0.508894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.90068 | −0.378808 | ||||||||
\(436\) | −5.12574 | −0.245479 | ||||||||
\(437\) | 1.83114 | 0.0875953 | ||||||||
\(438\) | 0.749893 | 0.0358313 | ||||||||
\(439\) | −10.6534 | −0.508457 | −0.254228 | − | 0.967144i | \(-0.581822\pi\) | ||||
−0.254228 | + | 0.967144i | \(0.581822\pi\) | |||||||
\(440\) | −9.87376 | −0.470713 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.64336 | 0.220862 | ||||||||
\(443\) | −1.10628 | −0.0525610 | −0.0262805 | − | 0.999655i | \(-0.508366\pi\) | ||||
−0.0262805 | + | 0.999655i | \(0.508366\pi\) | |||||||
\(444\) | −17.6779 | −0.838955 | ||||||||
\(445\) | −19.4560 | −0.922302 | ||||||||
\(446\) | 3.50238 | 0.165843 | ||||||||
\(447\) | 9.98658 | 0.472349 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.3468 | 0.629872 | 0.314936 | − | 0.949113i | \(-0.398017\pi\) | ||||
0.314936 | + | 0.949113i | \(0.398017\pi\) | |||||||
\(450\) | 1.29415 | 0.0610069 | ||||||||
\(451\) | 3.51053 | 0.165304 | ||||||||
\(452\) | −6.87032 | −0.323153 | ||||||||
\(453\) | −18.2139 | −0.855764 | ||||||||
\(454\) | 7.84726 | 0.368290 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.42382 | 0.113506 | ||||||||
\(457\) | −41.0559 | −1.92051 | −0.960256 | − | 0.279120i | \(-0.909957\pi\) | ||||
−0.960256 | + | 0.279120i | \(0.909957\pi\) | |||||||
\(458\) | −13.4216 | −0.627149 | ||||||||
\(459\) | −4.08881 | −0.190849 | ||||||||
\(460\) | −3.74381 | −0.174556 | ||||||||
\(461\) | 30.8859 | 1.43850 | 0.719251 | − | 0.694751i | \(-0.244485\pi\) | ||||
0.719251 | + | 0.694751i | \(0.244485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.4244 | 0.670357 | 0.335178 | − | 0.942155i | \(-0.391203\pi\) | ||||
0.335178 | + | 0.942155i | \(0.391203\pi\) | |||||||
\(464\) | −13.5513 | −0.629105 | ||||||||
\(465\) | 1.24578 | 0.0577716 | ||||||||
\(466\) | 11.9362 | 0.552935 | ||||||||
\(467\) | −26.9128 | −1.24538 | −0.622689 | − | 0.782470i | \(-0.713960\pi\) | ||||
−0.622689 | + | 0.782470i | \(0.713960\pi\) | |||||||
\(468\) | −4.10057 | −0.189549 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.92595 | 0.365597 | ||||||||
\(471\) | 4.40579 | 0.203008 | ||||||||
\(472\) | 1.27269 | 0.0585804 | ||||||||
\(473\) | 9.81988 | 0.451519 | ||||||||
\(474\) | 2.67411 | 0.122826 | ||||||||
\(475\) | −3.50211 | −0.160688 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.05270 | −0.368708 | ||||||||
\(478\) | 9.00619 | 0.411933 | ||||||||
\(479\) | −15.0420 | −0.687288 | −0.343644 | − | 0.939100i | \(-0.611661\pi\) | ||||
−0.343644 | + | 0.939100i | \(0.611661\pi\) | |||||||
\(480\) | −7.59017 | −0.346442 | ||||||||
\(481\) | 23.3512 | 1.06472 | ||||||||
\(482\) | 12.9396 | 0.589381 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.33239 | −0.106018 | ||||||||
\(485\) | −21.9041 | −0.994613 | ||||||||
\(486\) | −0.487949 | −0.0221338 | ||||||||
\(487\) | −10.0306 | −0.454529 | −0.227265 | − | 0.973833i | \(-0.572978\pi\) | ||||
−0.227265 | + | 0.973833i | \(0.572978\pi\) | |||||||
\(488\) | −2.38427 | −0.107931 | ||||||||
\(489\) | 4.66216 | 0.210830 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.0046 | −1.17357 | −0.586786 | − | 0.809742i | \(-0.699607\pi\) | ||||
−0.586786 | + | 0.809742i | \(0.699607\pi\) | |||||||
\(492\) | 1.76191 | 0.0794328 | ||||||||
\(493\) | 21.0830 | 0.949531 | ||||||||
\(494\) | −1.49953 | −0.0674670 | ||||||||
\(495\) | −5.37898 | −0.241767 | ||||||||
\(496\) | 2.13677 | 0.0959440 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.88058 | 0.129082 | ||||||||
\(499\) | −16.9912 | −0.760631 | −0.380315 | − | 0.924857i | \(-0.624185\pi\) | ||||
−0.380315 | + | 0.924857i | \(0.624185\pi\) | |||||||
\(500\) | 20.6585 | 0.923876 | ||||||||
\(501\) | −7.14687 | −0.319298 | ||||||||
\(502\) | −3.15502 | −0.140815 | ||||||||
\(503\) | 13.3920 | 0.597119 | 0.298559 | − | 0.954391i | \(-0.403494\pi\) | ||||
0.298559 | + | 0.954391i | \(0.403494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9591 | 0.665672 | ||||||||
\(506\) | 2.37547 | 0.105602 | ||||||||
\(507\) | −7.58345 | −0.336793 | ||||||||
\(508\) | 9.55296 | 0.423844 | ||||||||
\(509\) | −37.2055 | −1.64910 | −0.824552 | − | 0.565786i | \(-0.808573\pi\) | ||||
−0.824552 | + | 0.565786i | \(0.808573\pi\) | |||||||
\(510\) | 3.05703 | 0.135367 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6672 | −1.00176 | ||||||||
\(513\) | 1.32044 | 0.0582989 | ||||||||
\(514\) | 10.1952 | 0.449691 | ||||||||
\(515\) | −10.3140 | −0.454491 | ||||||||
\(516\) | 4.92852 | 0.216966 | ||||||||
\(517\) | 37.2152 | 1.63672 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9222 | 0.479430 | ||||||||
\(520\) | 6.54594 | 0.287058 | ||||||||
\(521\) | 14.3750 | 0.629778 | 0.314889 | − | 0.949128i | \(-0.398033\pi\) | ||||
0.314889 | + | 0.949128i | \(0.398033\pi\) | |||||||
\(522\) | 2.51600 | 0.110122 | ||||||||
\(523\) | 23.0126 | 1.00627 | 0.503135 | − | 0.864208i | \(-0.332180\pi\) | ||||
0.503135 | + | 0.864208i | \(0.332180\pi\) | |||||||
\(524\) | 5.70717 | 0.249319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.1706 | −0.487063 | ||||||||
\(527\) | −3.32437 | −0.144812 | ||||||||
\(528\) | −9.22609 | −0.401514 | ||||||||
\(529\) | −21.0769 | −0.916386 | ||||||||
\(530\) | 6.02066 | 0.261521 | ||||||||
\(531\) | 0.693332 | 0.0300880 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.32735 | −0.100809 | ||||||||
\(534\) | 6.19583 | 0.268120 | ||||||||
\(535\) | 5.21724 | 0.225561 | ||||||||
\(536\) | 16.1950 | 0.699516 | ||||||||
\(537\) | −3.51144 | −0.151530 | ||||||||
\(538\) | 0.525361 | 0.0226499 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.69967 | −0.116175 | ||||||||
\(541\) | 7.00491 | 0.301165 | 0.150582 | − | 0.988597i | \(-0.451885\pi\) | ||||
0.150582 | + | 0.988597i | \(0.451885\pi\) | |||||||
\(542\) | −9.98578 | −0.428926 | ||||||||
\(543\) | −3.38587 | −0.145301 | ||||||||
\(544\) | 20.2544 | 0.868402 | ||||||||
\(545\) | 4.45761 | 0.190943 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.4358 | 0.788256 | 0.394128 | − | 0.919056i | \(-0.371047\pi\) | ||||
0.394128 | + | 0.919056i | \(0.371047\pi\) | |||||||
\(548\) | 12.3661 | 0.528252 | ||||||||
\(549\) | −1.29889 | −0.0554354 | ||||||||
\(550\) | −4.54315 | −0.193721 | ||||||||
\(551\) | −6.80856 | −0.290054 | ||||||||
\(552\) | 2.54557 | 0.108347 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.28654 | 0.394547 | ||||||||
\(555\) | 15.3736 | 0.652573 | ||||||||
\(556\) | −25.9176 | −1.09915 | ||||||||
\(557\) | 7.62468 | 0.323068 | 0.161534 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161534 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(558\) | −0.396723 | −0.0167946 | ||||||||
\(559\) | −6.51022 | −0.275353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.3539 | 0.606021 | ||||||||
\(562\) | −2.89100 | −0.121949 | ||||||||
\(563\) | −31.2475 | −1.31693 | −0.658464 | − | 0.752613i | \(-0.728793\pi\) | ||||
−0.658464 | + | 0.752613i | \(0.728793\pi\) | |||||||
\(564\) | 18.6780 | 0.786487 | ||||||||
\(565\) | 5.97479 | 0.251361 | ||||||||
\(566\) | −9.32696 | −0.392041 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.1571 | 0.552059 | ||||||||
\(569\) | 15.3290 | 0.642626 | 0.321313 | − | 0.946973i | \(-0.395876\pi\) | ||||
0.321313 | + | 0.946973i | \(0.395876\pi\) | |||||||
\(570\) | −0.987237 | −0.0413508 | ||||||||
\(571\) | −20.7415 | −0.868006 | −0.434003 | − | 0.900911i | \(-0.642899\pi\) | ||||
−0.434003 | + | 0.900911i | \(0.642899\pi\) | |||||||
\(572\) | 14.3952 | 0.601891 | ||||||||
\(573\) | −9.56641 | −0.399642 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.67801 | −0.153384 | ||||||||
\(576\) | −2.83913 | −0.118297 | ||||||||
\(577\) | −29.1178 | −1.21219 | −0.606094 | − | 0.795393i | \(-0.707265\pi\) | ||||
−0.606094 | + | 0.795393i | \(0.707265\pi\) | |||||||
\(578\) | 0.137430 | 0.00571632 | ||||||||
\(579\) | −3.73602 | −0.155264 | ||||||||
\(580\) | 13.9202 | 0.578007 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.97543 | 0.289141 | ||||||||
\(583\) | 28.2692 | 1.17079 | ||||||||
\(584\) | −2.82103 | −0.116735 | ||||||||
\(585\) | 3.56607 | 0.147439 | ||||||||
\(586\) | −2.28046 | −0.0942048 | ||||||||
\(587\) | 8.40584 | 0.346946 | 0.173473 | − | 0.984839i | \(-0.444501\pi\) | ||||
0.173473 | + | 0.984839i | \(0.444501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.07357 | 0.0442358 | ||||||||
\(590\) | −0.518375 | −0.0213412 | ||||||||
\(591\) | 3.86710 | 0.159071 | ||||||||
\(592\) | 26.3690 | 1.08376 | ||||||||
\(593\) | −8.52390 | −0.350035 | −0.175017 | − | 0.984565i | \(-0.555998\pi\) | ||||
−0.175017 | + | 0.984565i | \(0.555998\pi\) | |||||||
\(594\) | 1.71296 | 0.0702835 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.5954 | −0.720736 | ||||||||
\(597\) | −9.78954 | −0.400659 | ||||||||
\(598\) | −1.57485 | −0.0644003 | ||||||||
\(599\) | 1.76430 | 0.0720872 | 0.0360436 | − | 0.999350i | \(-0.488524\pi\) | ||||
0.0360436 | + | 0.999350i | \(0.488524\pi\) | |||||||
\(600\) | −4.86847 | −0.198755 | ||||||||
\(601\) | −43.6074 | −1.77878 | −0.889392 | − | 0.457145i | \(-0.848872\pi\) | ||||
−0.889392 | + | 0.457145i | \(0.848872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.82262 | 0.359285 | ||||||||
\(604\) | 32.0912 | 1.30577 | ||||||||
\(605\) | 2.02837 | 0.0824649 | ||||||||
\(606\) | −4.76378 | −0.193515 | ||||||||
\(607\) | 24.2662 | 0.984936 | 0.492468 | − | 0.870330i | \(-0.336095\pi\) | ||||
0.492468 | + | 0.870330i | \(0.336095\pi\) | |||||||
\(608\) | −6.54097 | −0.265271 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.971128 | 0.0393198 | ||||||||
\(611\) | −24.6723 | −0.998135 | ||||||||
\(612\) | 7.20409 | 0.291208 | ||||||||
\(613\) | 28.8716 | 1.16611 | 0.583056 | − | 0.812432i | \(-0.301857\pi\) | ||||
0.583056 | + | 0.812432i | \(0.301857\pi\) | |||||||
\(614\) | 16.0825 | 0.649039 | ||||||||
\(615\) | −1.53225 | −0.0617861 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0451 | −0.484918 | −0.242459 | − | 0.970162i | \(-0.577954\pi\) | ||||
−0.242459 | + | 0.970162i | \(0.577954\pi\) | |||||||
\(618\) | 3.28454 | 0.132124 | ||||||||
\(619\) | 29.3883 | 1.18121 | 0.590607 | − | 0.806960i | \(-0.298888\pi\) | ||||
0.590607 | + | 0.806960i | \(0.298888\pi\) | |||||||
\(620\) | −2.19495 | −0.0881512 | ||||||||
\(621\) | 1.38676 | 0.0556489 | ||||||||
\(622\) | −0.678364 | −0.0271999 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.11656 | 0.244858 | ||||||||
\(625\) | −4.70458 | −0.188183 | ||||||||
\(626\) | −15.0482 | −0.601446 | ||||||||
\(627\) | −4.63544 | −0.185122 | ||||||||
\(628\) | −7.76259 | −0.309761 | ||||||||
\(629\) | −41.0246 | −1.63576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0954 | 1.59617 | 0.798087 | − | 0.602543i | \(-0.205846\pi\) | ||||
0.798087 | + | 0.602543i | \(0.205846\pi\) | |||||||
\(632\) | −10.0598 | −0.400156 | ||||||||
\(633\) | 0.378702 | 0.0150521 | ||||||||
\(634\) | 2.09822 | 0.0833311 | ||||||||
\(635\) | −8.30775 | −0.329683 | ||||||||
\(636\) | 14.1881 | 0.562595 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.83248 | −0.349681 | ||||||||
\(639\) | 7.16765 | 0.283548 | ||||||||
\(640\) | 17.3030 | 0.683963 | ||||||||
\(641\) | −19.7554 | −0.780293 | −0.390146 | − | 0.920753i | \(-0.627576\pi\) | ||||
−0.390146 | + | 0.920753i | \(0.627576\pi\) | |||||||
\(642\) | −1.66145 | −0.0655722 | ||||||||
\(643\) | 30.7410 | 1.21231 | 0.606154 | − | 0.795347i | \(-0.292711\pi\) | ||||
0.606154 | + | 0.795347i | \(0.292711\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.28610 | −0.168765 | ||||||||
\(646\) | 2.63445 | 0.103651 | ||||||||
\(647\) | −9.16424 | −0.360283 | −0.180142 | − | 0.983641i | \(-0.557656\pi\) | ||||
−0.180142 | + | 0.983641i | \(0.557656\pi\) | |||||||
\(648\) | 1.83562 | 0.0721099 | ||||||||
\(649\) | −2.43396 | −0.0955413 | ||||||||
\(650\) | 3.01194 | 0.118138 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.21429 | −0.321696 | ||||||||
\(653\) | −46.8033 | −1.83155 | −0.915777 | − | 0.401687i | \(-0.868424\pi\) | ||||
−0.915777 | + | 0.401687i | \(0.868424\pi\) | |||||||
\(654\) | −1.41954 | −0.0555085 | ||||||||
\(655\) | −4.96325 | −0.193930 | ||||||||
\(656\) | −2.62812 | −0.102611 | ||||||||
\(657\) | −1.53683 | −0.0599573 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7930 | 0.459389 | 0.229695 | − | 0.973263i | \(-0.426227\pi\) | ||||
0.229695 | + | 0.973263i | \(0.426227\pi\) | |||||||
\(660\) | 9.47726 | 0.368902 | ||||||||
\(661\) | 0.712807 | 0.0277250 | 0.0138625 | − | 0.999904i | \(-0.495587\pi\) | ||||
0.0138625 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(662\) | −6.11830 | −0.237795 | ||||||||
\(663\) | −9.51608 | −0.369574 | ||||||||
\(664\) | −10.8365 | −0.420537 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.89578 | −0.189708 | ||||||||
\(667\) | −7.15054 | −0.276870 | ||||||||
\(668\) | 12.5921 | 0.487203 | ||||||||
\(669\) | −7.17776 | −0.277508 | ||||||||
\(670\) | −6.59630 | −0.254837 | ||||||||
\(671\) | 4.55980 | 0.176029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2796 | 0.588984 | 0.294492 | − | 0.955654i | \(-0.404850\pi\) | ||||
0.294492 | + | 0.955654i | \(0.404850\pi\) | |||||||
\(674\) | 4.83363 | 0.186184 | ||||||||
\(675\) | −2.65223 | −0.102084 | ||||||||
\(676\) | 13.3613 | 0.513897 | ||||||||
\(677\) | 14.7878 | 0.568343 | 0.284172 | − | 0.958773i | \(-0.408281\pi\) | ||||
0.284172 | + | 0.958773i | \(0.408281\pi\) | |||||||
\(678\) | −1.90269 | −0.0730725 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.5003 | −0.441015 | ||||||||
\(681\) | −16.0821 | −0.616269 | ||||||||
\(682\) | 1.39271 | 0.0533295 | ||||||||
\(683\) | 7.33388 | 0.280623 | 0.140312 | − | 0.990107i | \(-0.455190\pi\) | ||||
0.140312 | + | 0.990107i | \(0.455190\pi\) | |||||||
\(684\) | −2.32649 | −0.0889556 | ||||||||
\(685\) | −10.7542 | −0.410896 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.5061 | 1.04942 | ||||||||
\(688\) | −7.35157 | −0.280276 | ||||||||
\(689\) | −18.7414 | −0.713992 | ||||||||
\(690\) | −1.03682 | −0.0394712 | ||||||||
\(691\) | 9.80122 | 0.372856 | 0.186428 | − | 0.982469i | \(-0.440309\pi\) | ||||
0.186428 | + | 0.982469i | \(0.440309\pi\) | |||||||
\(692\) | −19.2438 | −0.731541 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.05973 | 0.267984 | ||||||||
\(695\) | 22.5393 | 0.854965 | ||||||||
\(696\) | −9.46495 | −0.358768 | ||||||||
\(697\) | 4.08881 | 0.154875 | ||||||||
\(698\) | −0.856153 | −0.0324059 | ||||||||
\(699\) | −24.4620 | −0.925239 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.1869 | 1.44230 | 0.721151 | − | 0.692778i | \(-0.243614\pi\) | ||||
0.721151 | + | 0.692778i | \(0.243614\pi\) | |||||||
\(702\) | −1.13563 | −0.0428615 | ||||||||
\(703\) | 13.2485 | 0.499676 | ||||||||
\(704\) | 9.96683 | 0.375639 | ||||||||
\(705\) | −16.2434 | −0.611761 | ||||||||
\(706\) | −5.92645 | −0.223045 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.22159 | −0.0459100 | ||||||||
\(709\) | 49.2240 | 1.84864 | 0.924322 | − | 0.381613i | \(-0.124631\pi\) | ||||
0.924322 | + | 0.381613i | \(0.124631\pi\) | |||||||
\(710\) | −5.35895 | −0.201118 | ||||||||
\(711\) | −5.48031 | −0.205528 | ||||||||
\(712\) | −23.3081 | −0.873509 | ||||||||
\(713\) | 1.12750 | 0.0422251 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.5188 | −0.468176 | ||||||||
\(716\) | 6.18683 | 0.231213 | ||||||||
\(717\) | −18.4572 | −0.689298 | ||||||||
\(718\) | −8.06311 | −0.300913 | ||||||||
\(719\) | 2.98460 | 0.111307 | 0.0556533 | − | 0.998450i | \(-0.482276\pi\) | ||||
0.0556533 | + | 0.998450i | \(0.482276\pi\) | |||||||
\(720\) | 4.02693 | 0.150075 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.42026 | 0.313370 | ||||||||
\(723\) | −26.5183 | −0.986225 | ||||||||
\(724\) | 5.96558 | 0.221709 | ||||||||
\(725\) | 13.6756 | 0.507899 | ||||||||
\(726\) | −0.645941 | −0.0239731 | ||||||||
\(727\) | 32.4202 | 1.20240 | 0.601199 | − | 0.799099i | \(-0.294690\pi\) | ||||
0.601199 | + | 0.799099i | \(0.294690\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.14902 | 0.0425272 | ||||||||
\(731\) | 11.4375 | 0.423031 | ||||||||
\(732\) | 2.28853 | 0.0845865 | ||||||||
\(733\) | 19.5731 | 0.722948 | 0.361474 | − | 0.932382i | \(-0.382274\pi\) | ||||
0.361474 | + | 0.932382i | \(0.382274\pi\) | |||||||
\(734\) | −4.29958 | −0.158701 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.86951 | −0.253214 | ||||||||
\(737\) | −30.9720 | −1.14087 | ||||||||
\(738\) | 0.487949 | 0.0179617 | ||||||||
\(739\) | 20.0765 | 0.738526 | 0.369263 | − | 0.929325i | \(-0.379610\pi\) | ||||
0.369263 | + | 0.929325i | \(0.379610\pi\) | |||||||
\(740\) | −27.0868 | −0.995732 | ||||||||
\(741\) | 3.07313 | 0.112894 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.5791 | 1.45202 | 0.726008 | − | 0.687686i | \(-0.241374\pi\) | ||||
0.726008 | + | 0.687686i | \(0.241374\pi\) | |||||||
\(744\) | 1.49243 | 0.0547153 | ||||||||
\(745\) | 15.3019 | 0.560618 | ||||||||
\(746\) | 0.892137 | 0.0326635 | ||||||||
\(747\) | −5.90345 | −0.215996 | ||||||||
\(748\) | −25.2902 | −0.924700 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.72124 | 0.208910 | ||||||||
\(751\) | −23.0778 | −0.842121 | −0.421061 | − | 0.907033i | \(-0.638342\pi\) | ||||
−0.421061 | + | 0.907033i | \(0.638342\pi\) | |||||||
\(752\) | −27.8608 | −1.01598 | ||||||||
\(753\) | 6.46587 | 0.235629 | ||||||||
\(754\) | 5.85561 | 0.213249 | ||||||||
\(755\) | −27.9082 | −1.01568 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.38807 | −0.123141 | −0.0615707 | − | 0.998103i | \(-0.519611\pi\) | ||||
−0.0615707 | + | 0.998103i | \(0.519611\pi\) | |||||||
\(758\) | 13.4764 | 0.489485 | ||||||||
\(759\) | −4.86827 | −0.176707 | ||||||||
\(760\) | 3.71389 | 0.134717 | ||||||||
\(761\) | −36.0382 | −1.30638 | −0.653191 | − | 0.757193i | \(-0.726570\pi\) | ||||
−0.653191 | + | 0.757193i | \(0.726570\pi\) | |||||||
\(762\) | 2.64563 | 0.0958412 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.8551 | 0.609796 | ||||||||
\(765\) | −6.26506 | −0.226514 | ||||||||
\(766\) | 12.3130 | 0.444888 | ||||||||
\(767\) | 1.61363 | 0.0582646 | ||||||||
\(768\) | 0.168043 | 0.00606374 | ||||||||
\(769\) | 29.7848 | 1.07407 | 0.537034 | − | 0.843561i | \(-0.319545\pi\) | ||||
0.537034 | + | 0.843561i | \(0.319545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.8940 | −0.752479 | ||||||||
\(772\) | 6.58252 | 0.236910 | ||||||||
\(773\) | −27.4004 | −0.985525 | −0.492763 | − | 0.870164i | \(-0.664013\pi\) | ||||
−0.492763 | + | 0.870164i | \(0.664013\pi\) | |||||||
\(774\) | 1.36492 | 0.0490612 | ||||||||
\(775\) | −2.15637 | −0.0774591 | ||||||||
\(776\) | −26.2409 | −0.941994 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1224 | 0.613869 | ||||||||
\(779\) | −1.32044 | −0.0473097 | ||||||||
\(780\) | −6.28308 | −0.224970 | ||||||||
\(781\) | −25.1622 | −0.900375 | ||||||||
\(782\) | 2.76677 | 0.0989396 | ||||||||
\(783\) | −5.15628 | −0.184270 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.75075 | 0.240945 | ||||||||
\(786\) | 1.58056 | 0.0563769 | ||||||||
\(787\) | 16.1782 | 0.576690 | 0.288345 | − | 0.957527i | \(-0.406895\pi\) | ||||
0.288345 | + | 0.957527i | \(0.406895\pi\) | |||||||
\(788\) | −6.81347 | −0.242720 | ||||||||
\(789\) | 22.8930 | 0.815013 | ||||||||
\(790\) | 4.09740 | 0.145779 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.44398 | −0.228977 | ||||||||
\(793\) | −3.02298 | −0.107349 | ||||||||
\(794\) | −12.4811 | −0.442937 | ||||||||
\(795\) | −12.3387 | −0.437609 | ||||||||
\(796\) | 17.2482 | 0.611348 | ||||||||
\(797\) | −38.1592 | −1.35167 | −0.675834 | − | 0.737054i | \(-0.736216\pi\) | ||||
−0.675834 | + | 0.737054i | \(0.736216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.3456 | 1.53346 | ||||||||
\(800\) | 13.1381 | 0.464503 | ||||||||
\(801\) | −12.6977 | −0.448651 | ||||||||
\(802\) | 7.67306 | 0.270945 | ||||||||
\(803\) | 5.39507 | 0.190388 | ||||||||
\(804\) | −15.5446 | −0.548217 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.923313 | −0.0325223 | ||||||||
\(807\) | −1.07667 | −0.0379007 | ||||||||
\(808\) | 17.9209 | 0.630455 | ||||||||
\(809\) | −27.0936 | −0.952561 | −0.476281 | − | 0.879293i | \(-0.658015\pi\) | ||||
−0.476281 | + | 0.879293i | \(0.658015\pi\) | |||||||
\(810\) | −0.747657 | −0.0262700 | ||||||||
\(811\) | 50.5845 | 1.77626 | 0.888131 | − | 0.459591i | \(-0.152004\pi\) | ||||
0.888131 | + | 0.459591i | \(0.152004\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.4648 | 0.717732 | ||||||||
\(814\) | 17.1868 | 0.602396 | ||||||||
\(815\) | 7.14357 | 0.250228 | ||||||||
\(816\) | −10.7459 | −0.376181 | ||||||||
\(817\) | −3.69363 | −0.129224 | ||||||||
\(818\) | −0.100744 | −0.00352242 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.69967 | 0.0942766 | ||||||||
\(821\) | 24.3297 | 0.849114 | 0.424557 | − | 0.905401i | \(-0.360430\pi\) | ||||
0.424557 | + | 0.905401i | \(0.360430\pi\) | |||||||
\(822\) | 3.42471 | 0.119450 | ||||||||
\(823\) | −9.84814 | −0.343285 | −0.171642 | − | 0.985159i | \(-0.554907\pi\) | ||||
−0.171642 | + | 0.985159i | \(0.554907\pi\) | |||||||
\(824\) | −12.3561 | −0.430447 | ||||||||
\(825\) | 9.31070 | 0.324157 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.1328 | 1.43033 | 0.715164 | − | 0.698956i | \(-0.246352\pi\) | ||||
0.715164 | + | 0.698956i | \(0.246352\pi\) | |||||||
\(828\) | −2.44335 | −0.0849122 | ||||||||
\(829\) | 43.7460 | 1.51936 | 0.759681 | − | 0.650296i | \(-0.225355\pi\) | ||||
0.759681 | + | 0.650296i | \(0.225355\pi\) | |||||||
\(830\) | 4.41376 | 0.153204 | ||||||||
\(831\) | −19.0318 | −0.660205 | ||||||||
\(832\) | −6.60764 | −0.229079 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.17773 | −0.248545 | ||||||||
\(835\) | −10.9508 | −0.378966 | ||||||||
\(836\) | 8.16721 | 0.282469 | ||||||||
\(837\) | 0.813042 | 0.0281028 | ||||||||
\(838\) | −7.46165 | −0.257758 | ||||||||
\(839\) | 31.7703 | 1.09683 | 0.548417 | − | 0.836205i | \(-0.315231\pi\) | ||||
0.548417 | + | 0.836205i | \(0.315231\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.41283 | −0.0832009 | ||||||||
\(842\) | 16.6072 | 0.572323 | ||||||||
\(843\) | 5.92479 | 0.204061 | ||||||||
\(844\) | −0.667238 | −0.0229673 | ||||||||
\(845\) | −11.6197 | −0.399730 | ||||||||
\(846\) | 5.17277 | 0.177843 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −21.1635 | −0.726757 | ||||||||
\(849\) | 19.1146 | 0.656012 | ||||||||
\(850\) | −5.29153 | −0.181498 | ||||||||
\(851\) | 13.9139 | 0.476963 | ||||||||
\(852\) | −12.6287 | −0.432653 | ||||||||
\(853\) | −1.20173 | −0.0411463 | −0.0205732 | − | 0.999788i | \(-0.506549\pi\) | ||||
−0.0205732 | + | 0.999788i | \(0.506549\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.02324 | 0.0691933 | ||||||||
\(856\) | 6.25022 | 0.213628 | ||||||||
\(857\) | −11.0723 | −0.378222 | −0.189111 | − | 0.981956i | \(-0.560561\pi\) | ||||
−0.189111 | + | 0.981956i | \(0.560561\pi\) | |||||||
\(858\) | 3.98665 | 0.136102 | ||||||||
\(859\) | 8.79105 | 0.299947 | 0.149973 | − | 0.988690i | \(-0.452081\pi\) | ||||
0.149973 | + | 0.988690i | \(0.452081\pi\) | |||||||
\(860\) | 7.55170 | 0.257511 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.10855 | 0.276178 | ||||||||
\(863\) | 32.4019 | 1.10297 | 0.551487 | − | 0.834183i | \(-0.314060\pi\) | ||||
0.551487 | + | 0.834183i | \(0.314060\pi\) | |||||||
\(864\) | −4.95363 | −0.168526 | ||||||||
\(865\) | 16.7354 | 0.569022 | ||||||||
\(866\) | 0.567318 | 0.0192782 | ||||||||
\(867\) | −0.281647 | −0.00956525 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.2388 | 0.652631 | ||||||||
\(870\) | 3.85513 | 0.130701 | ||||||||
\(871\) | 20.5333 | 0.695745 | ||||||||
\(872\) | 5.34019 | 0.180842 | ||||||||
\(873\) | −14.2954 | −0.483826 | ||||||||
\(874\) | −0.893503 | −0.0302232 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.70774 | 0.0914862 | ||||||||
\(877\) | −38.4772 | −1.29928 | −0.649641 | − | 0.760241i | \(-0.725081\pi\) | ||||
−0.649641 | + | 0.760241i | \(0.725081\pi\) | |||||||
\(878\) | 5.19829 | 0.175434 | ||||||||
\(879\) | 4.67356 | 0.157635 | ||||||||
\(880\) | −14.1366 | −0.476546 | ||||||||
\(881\) | −38.0482 | −1.28188 | −0.640939 | − | 0.767592i | \(-0.721455\pi\) | ||||
−0.640939 | + | 0.767592i | \(0.721455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.84034 | −0.0619323 | −0.0309661 | − | 0.999520i | \(-0.509858\pi\) | ||||
−0.0309661 | + | 0.999520i | \(0.509858\pi\) | |||||||
\(884\) | 16.7664 | 0.563916 | ||||||||
\(885\) | 1.06235 | 0.0357107 | ||||||||
\(886\) | 0.539809 | 0.0181352 | ||||||||
\(887\) | 22.1892 | 0.745040 | 0.372520 | − | 0.928024i | \(-0.378494\pi\) | ||||
0.372520 | + | 0.928024i | \(0.378494\pi\) | |||||||
\(888\) | 18.4175 | 0.618049 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.49353 | 0.318224 | ||||||||
\(891\) | −3.51053 | −0.117607 | ||||||||
\(892\) | 12.6465 | 0.423438 | ||||||||
\(893\) | −13.9980 | −0.468427 | ||||||||
\(894\) | −4.87294 | −0.162976 | ||||||||
\(895\) | −5.38039 | −0.179847 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.22748 | 0.107763 | ||||||||
\(898\) | −6.51254 | −0.217326 | ||||||||
\(899\) | −4.19227 | −0.139820 | ||||||||
\(900\) | 4.67297 | 0.155766 | ||||||||
\(901\) | 32.9259 | 1.09692 | ||||||||
\(902\) | −1.71296 | −0.0570352 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.15775 | 0.238063 | ||||||||
\(905\) | −5.18798 | −0.172454 | ||||||||
\(906\) | 8.88746 | 0.295266 | ||||||||
\(907\) | −12.1000 | −0.401773 | −0.200887 | − | 0.979615i | \(-0.564382\pi\) | ||||
−0.200887 | + | 0.979615i | \(0.564382\pi\) | |||||||
\(908\) | 28.3352 | 0.940336 | ||||||||
\(909\) | 9.76287 | 0.323814 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.33503 | −0.143626 | −0.0718130 | − | 0.997418i | \(-0.522878\pi\) | ||||
−0.0718130 | + | 0.997418i | \(0.522878\pi\) | |||||||
\(912\) | 3.47028 | 0.114912 | ||||||||
\(913\) | 20.7242 | 0.685871 | ||||||||
\(914\) | 20.0332 | 0.662638 | ||||||||
\(915\) | −1.99022 | −0.0657948 | ||||||||
\(916\) | −48.4632 | −1.60127 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.99513 | 0.0658491 | ||||||||
\(919\) | 7.90732 | 0.260838 | 0.130419 | − | 0.991459i | \(-0.458368\pi\) | ||||
0.130419 | + | 0.991459i | \(0.458368\pi\) | |||||||
\(920\) | 3.90044 | 0.128594 | ||||||||
\(921\) | −32.9595 | −1.08605 | ||||||||
\(922\) | −15.0708 | −0.496329 | ||||||||
\(923\) | 16.6816 | 0.549082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.6108 | −0.874957 | ||||||||
\(926\) | −7.03835 | −0.231295 | ||||||||
\(927\) | −6.73133 | −0.221086 | ||||||||
\(928\) | 25.5423 | 0.838466 | ||||||||
\(929\) | −7.05313 | −0.231406 | −0.115703 | − | 0.993284i | \(-0.536912\pi\) | ||||
−0.115703 | + | 0.993284i | \(0.536912\pi\) | |||||||
\(930\) | −0.607877 | −0.0199331 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 43.0998 | 1.41178 | ||||||||
\(933\) | 1.39024 | 0.0455143 | ||||||||
\(934\) | 13.1321 | 0.429695 | ||||||||
\(935\) | 21.9936 | 0.719269 | ||||||||
\(936\) | 4.27212 | 0.139639 | ||||||||
\(937\) | −27.5399 | −0.899689 | −0.449845 | − | 0.893107i | \(-0.648521\pi\) | ||||
−0.449845 | + | 0.893107i | \(0.648521\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.8397 | 1.00641 | ||||||||
\(940\) | 28.6193 | 0.933459 | ||||||||
\(941\) | −24.9906 | −0.814671 | −0.407335 | − | 0.913279i | \(-0.633542\pi\) | ||||
−0.407335 | + | 0.913279i | \(0.633542\pi\) | |||||||
\(942\) | −2.14980 | −0.0700443 | ||||||||
\(943\) | −1.38676 | −0.0451592 | ||||||||
\(944\) | 1.82216 | 0.0593063 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.79160 | −0.155788 | ||||||||
\(947\) | −54.5580 | −1.77290 | −0.886448 | − | 0.462827i | \(-0.846835\pi\) | ||||
−0.886448 | + | 0.462827i | \(0.846835\pi\) | |||||||
\(948\) | 9.65580 | 0.313606 | ||||||||
\(949\) | −3.57673 | −0.116106 | ||||||||
\(950\) | 1.70885 | 0.0554424 | ||||||||
\(951\) | −4.30009 | −0.139440 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.2096 | −0.751832 | −0.375916 | − | 0.926654i | \(-0.622672\pi\) | ||||
−0.375916 | + | 0.926654i | \(0.622672\pi\) | |||||||
\(954\) | 3.92931 | 0.127216 | ||||||||
\(955\) | −14.6581 | −0.474324 | ||||||||
\(956\) | 32.5199 | 1.05177 | ||||||||
\(957\) | 18.1012 | 0.585130 | ||||||||
\(958\) | 7.33975 | 0.237136 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.35024 | −0.140403 | ||||||||
\(961\) | −30.3390 | −0.978676 | ||||||||
\(962\) | −11.3942 | −0.367363 | ||||||||
\(963\) | 3.40497 | 0.109724 | ||||||||
\(964\) | 46.7227 | 1.50484 | ||||||||
\(965\) | −5.72450 | −0.184278 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.5186 | 1.84967 | 0.924837 | − | 0.380364i | \(-0.124201\pi\) | ||||
0.924837 | + | 0.380364i | \(0.124201\pi\) | |||||||
\(968\) | 2.42997 | 0.0781022 | ||||||||
\(969\) | −5.39903 | −0.173442 | ||||||||
\(970\) | 10.6881 | 0.343173 | ||||||||
\(971\) | 1.14481 | 0.0367386 | 0.0183693 | − | 0.999831i | \(-0.494153\pi\) | ||||
0.0183693 | + | 0.999831i | \(0.494153\pi\) | |||||||
\(972\) | −1.76191 | −0.0565132 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.89441 | 0.156827 | ||||||||
\(975\) | −6.17265 | −0.197683 | ||||||||
\(976\) | −3.41365 | −0.109268 | ||||||||
\(977\) | 55.3288 | 1.77013 | 0.885063 | − | 0.465472i | \(-0.154115\pi\) | ||||
0.885063 | + | 0.465472i | \(0.154115\pi\) | |||||||
\(978\) | −2.27490 | −0.0727432 | ||||||||
\(979\) | 44.5756 | 1.42464 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.90920 | 0.0928837 | ||||||||
\(982\) | 12.6889 | 0.404920 | ||||||||
\(983\) | −42.3937 | −1.35215 | −0.676075 | − | 0.736833i | \(-0.736320\pi\) | ||||
−0.676075 | + | 0.736833i | \(0.736320\pi\) | |||||||
\(984\) | −1.83562 | −0.0585174 | ||||||||
\(985\) | 5.92535 | 0.188797 | ||||||||
\(986\) | −10.2874 | −0.327619 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.41456 | −0.172260 | ||||||||
\(989\) | −3.87915 | −0.123350 | ||||||||
\(990\) | 2.62467 | 0.0834175 | ||||||||
\(991\) | −41.8777 | −1.33029 | −0.665144 | − | 0.746715i | \(-0.731630\pi\) | ||||
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(992\) | −4.02751 | −0.127873 | ||||||||
\(993\) | 12.5388 | 0.397907 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.0000 | −0.475531 | ||||||||
\(996\) | 10.4013 | 0.329578 | ||||||||
\(997\) | 23.3614 | 0.739863 | 0.369932 | − | 0.929059i | \(-0.379381\pi\) | ||||
0.369932 | + | 0.929059i | \(0.379381\pi\) | |||||||
\(998\) | 8.29084 | 0.262442 | ||||||||
\(999\) | 10.0334 | 0.317442 |
(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 | 6027.2.a.ba.1.4 | yes | 8 | |
7.6 | odd | 2 | 6027.2.a.z.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.z.1.4 | ✓ | 8 | 7.6 | odd | 2 | ||
6027.2.a.ba.1.4 | yes | 8 | 1.1 | even | 1 | trivial |