Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
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 | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381966 | 0.270091 | 0.135045 | − | 0.990839i | \(-0.456882\pi\) | ||||
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0.381966 | 0.120788 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.00000 | 0.866025 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | −0.381966 | −0.102085 | ||||||||
\(15\) | −1.61803 | −0.417775 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −3.09017 | −0.749476 | −0.374738 | − | 0.927131i | \(-0.622267\pi\) | ||||
−0.374738 | + | 0.927131i | \(0.622267\pi\) | |||||||
\(18\) | −0.145898 | −0.0343885 | ||||||||
\(19\) | 1.76393 | 0.404674 | 0.202337 | − | 0.979316i | \(-0.435146\pi\) | ||||
0.202337 | + | 0.979316i | \(0.435146\pi\) | |||||||
\(20\) | −1.85410 | −0.414590 | ||||||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.09017 | 1.06137 | 0.530687 | − | 0.847568i | \(-0.321934\pi\) | ||||
0.530687 | + | 0.847568i | \(0.321934\pi\) | |||||||
\(24\) | 2.38197 | 0.486217 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0.472136 | 0.0925935 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 1.85410 | 0.350392 | ||||||||
\(29\) | 4.61803 | 0.857547 | 0.428774 | − | 0.903412i | \(-0.358946\pi\) | ||||
0.428774 | + | 0.903412i | \(0.358946\pi\) | |||||||
\(30\) | −0.618034 | −0.112837 | ||||||||
\(31\) | −4.23607 | −0.760820 | −0.380410 | − | 0.924818i | \(-0.624217\pi\) | ||||
−0.380410 | + | 0.924818i | \(0.624217\pi\) | |||||||
\(32\) | 4.14590 | 0.732898 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.18034 | −0.202427 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0.708204 | 0.118034 | ||||||||
\(37\) | 6.47214 | 1.06401 | 0.532006 | − | 0.846740i | \(-0.321438\pi\) | ||||
0.532006 | + | 0.846740i | \(0.321438\pi\) | |||||||
\(38\) | 0.673762 | 0.109299 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | −1.47214 | −0.232765 | ||||||||
\(41\) | 11.1803 | 1.74608 | 0.873038 | − | 0.487652i | \(-0.162147\pi\) | ||||
0.873038 | + | 0.487652i | \(0.162147\pi\) | |||||||
\(42\) | 0.618034 | 0.0953647 | ||||||||
\(43\) | 12.5623 | 1.91573 | 0.957867 | − | 0.287213i | \(-0.0927286\pi\) | ||||
0.957867 | + | 0.287213i | \(0.0927286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | 1.94427 | 0.286667 | ||||||||
\(47\) | −6.61803 | −0.965339 | −0.482670 | − | 0.875802i | \(-0.660333\pi\) | ||||
−0.482670 | + | 0.875802i | \(0.660333\pi\) | |||||||
\(48\) | −5.09017 | −0.734703 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.52786 | −0.216073 | ||||||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | −2.29180 | −0.317815 | ||||||||
\(53\) | −2.38197 | −0.327188 | −0.163594 | − | 0.986528i | \(-0.552309\pi\) | ||||
−0.163594 | + | 0.986528i | \(0.552309\pi\) | |||||||
\(54\) | 2.09017 | 0.284436 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.47214 | 0.196722 | ||||||||
\(57\) | −2.85410 | −0.378035 | ||||||||
\(58\) | 1.76393 | 0.231616 | ||||||||
\(59\) | 11.0902 | 1.44382 | 0.721909 | − | 0.691988i | \(-0.243265\pi\) | ||||
0.721909 | + | 0.691988i | \(0.243265\pi\) | |||||||
\(60\) | 3.00000 | 0.387298 | ||||||||
\(61\) | 7.61803 | 0.975389 | 0.487695 | − | 0.873014i | \(-0.337838\pi\) | ||||
0.487695 | + | 0.873014i | \(0.337838\pi\) | |||||||
\(62\) | −1.61803 | −0.205491 | ||||||||
\(63\) | 0.381966 | 0.0481232 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 1.23607 | 0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.32624 | −1.01721 | −0.508606 | − | 0.860999i | \(-0.669839\pi\) | ||||
−0.508606 | + | 0.860999i | \(0.669839\pi\) | |||||||
\(68\) | 5.72949 | 0.694803 | ||||||||
\(69\) | −8.23607 | −0.991506 | ||||||||
\(70\) | −0.381966 | −0.0456537 | ||||||||
\(71\) | −16.0902 | −1.90955 | −0.954776 | − | 0.297326i | \(-0.903905\pi\) | ||||
−0.954776 | + | 0.297326i | \(0.903905\pi\) | |||||||
\(72\) | 0.562306 | 0.0662684 | ||||||||
\(73\) | 14.2361 | 1.66621 | 0.833103 | − | 0.553118i | \(-0.186562\pi\) | ||||
0.833103 | + | 0.553118i | \(0.186562\pi\) | |||||||
\(74\) | 2.47214 | 0.287380 | ||||||||
\(75\) | 6.47214 | 0.747338 | ||||||||
\(76\) | −3.27051 | −0.375153 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.763932 | −0.0864983 | ||||||||
\(79\) | −6.38197 | −0.718027 | −0.359014 | − | 0.933332i | \(-0.616887\pi\) | ||||
−0.359014 | + | 0.933332i | \(0.616887\pi\) | |||||||
\(80\) | 3.14590 | 0.351722 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 4.27051 | 0.471599 | ||||||||
\(83\) | −2.70820 | −0.297264 | −0.148632 | − | 0.988893i | \(-0.547487\pi\) | ||||
−0.148632 | + | 0.988893i | \(0.547487\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | −3.09017 | −0.335176 | ||||||||
\(86\) | 4.79837 | 0.517422 | ||||||||
\(87\) | −7.47214 | −0.801097 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.85410 | 0.726533 | 0.363267 | − | 0.931685i | \(-0.381661\pi\) | ||||
0.363267 | + | 0.931685i | \(0.381661\pi\) | |||||||
\(90\) | −0.145898 | −0.0153790 | ||||||||
\(91\) | −1.23607 | −0.129575 | ||||||||
\(92\) | −9.43769 | −0.983948 | ||||||||
\(93\) | 6.85410 | 0.710737 | ||||||||
\(94\) | −2.52786 | −0.260729 | ||||||||
\(95\) | 1.76393 | 0.180976 | ||||||||
\(96\) | −6.70820 | −0.684653 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 0.381966 | 0.0385844 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.41641 | 0.741641 | ||||||||
\(101\) | 14.7984 | 1.47249 | 0.736247 | − | 0.676713i | \(-0.236596\pi\) | ||||
0.736247 | + | 0.676713i | \(0.236596\pi\) | |||||||
\(102\) | 1.90983 | 0.189101 | ||||||||
\(103\) | 8.85410 | 0.872421 | 0.436210 | − | 0.899845i | \(-0.356320\pi\) | ||||
0.436210 | + | 0.899845i | \(0.356320\pi\) | |||||||
\(104\) | −1.81966 | −0.178432 | ||||||||
\(105\) | 1.61803 | 0.157904 | ||||||||
\(106\) | −0.909830 | −0.0883705 | ||||||||
\(107\) | −2.70820 | −0.261812 | −0.130906 | − | 0.991395i | \(-0.541789\pi\) | ||||
−0.130906 | + | 0.991395i | \(0.541789\pi\) | |||||||
\(108\) | −10.1459 | −0.976289 | ||||||||
\(109\) | 1.52786 | 0.146343 | 0.0731714 | − | 0.997319i | \(-0.476688\pi\) | ||||
0.0731714 | + | 0.997319i | \(0.476688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | −3.14590 | −0.297259 | ||||||||
\(113\) | 0.145898 | 0.0137249 | 0.00686247 | − | 0.999976i | \(-0.497816\pi\) | ||||
0.00686247 | + | 0.999976i | \(0.497816\pi\) | |||||||
\(114\) | −1.09017 | −0.102104 | ||||||||
\(115\) | 5.09017 | 0.474661 | ||||||||
\(116\) | −8.56231 | −0.794990 | ||||||||
\(117\) | −0.472136 | −0.0436490 | ||||||||
\(118\) | 4.23607 | 0.389962 | ||||||||
\(119\) | 3.09017 | 0.283275 | ||||||||
\(120\) | 2.38197 | 0.217443 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.90983 | 0.263444 | ||||||||
\(123\) | −18.0902 | −1.63114 | ||||||||
\(124\) | 7.85410 | 0.705319 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0.145898 | 0.0129976 | ||||||||
\(127\) | −2.94427 | −0.261262 | −0.130631 | − | 0.991431i | \(-0.541700\pi\) | ||||
−0.130631 | + | 0.991431i | \(0.541700\pi\) | |||||||
\(128\) | −10.0902 | −0.891853 | ||||||||
\(129\) | −20.3262 | −1.78963 | ||||||||
\(130\) | 0.472136 | 0.0414091 | ||||||||
\(131\) | −18.9443 | −1.65517 | −0.827584 | − | 0.561341i | \(-0.810285\pi\) | ||||
−0.827584 | + | 0.561341i | \(0.810285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.76393 | −0.152952 | ||||||||
\(134\) | −3.18034 | −0.274740 | ||||||||
\(135\) | 5.47214 | 0.470966 | ||||||||
\(136\) | 4.54915 | 0.390086 | ||||||||
\(137\) | −15.3262 | −1.30941 | −0.654704 | − | 0.755885i | \(-0.727207\pi\) | ||||
−0.654704 | + | 0.755885i | \(0.727207\pi\) | |||||||
\(138\) | −3.14590 | −0.267797 | ||||||||
\(139\) | −11.9443 | −1.01310 | −0.506550 | − | 0.862211i | \(-0.669079\pi\) | ||||
−0.506550 | + | 0.862211i | \(0.669079\pi\) | |||||||
\(140\) | 1.85410 | 0.156700 | ||||||||
\(141\) | 10.7082 | 0.901793 | ||||||||
\(142\) | −6.14590 | −0.515752 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.20163 | −0.100136 | ||||||||
\(145\) | 4.61803 | 0.383507 | ||||||||
\(146\) | 5.43769 | 0.450027 | ||||||||
\(147\) | −1.61803 | −0.133453 | ||||||||
\(148\) | −12.0000 | −0.986394 | ||||||||
\(149\) | 8.85410 | 0.725356 | 0.362678 | − | 0.931914i | \(-0.381862\pi\) | ||||
0.362678 | + | 0.931914i | \(0.381862\pi\) | |||||||
\(150\) | 2.47214 | 0.201849 | ||||||||
\(151\) | −0.0557281 | −0.00453509 | −0.00226754 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226754 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(152\) | −2.59675 | −0.210624 | ||||||||
\(153\) | 1.18034 | 0.0954248 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.23607 | −0.340249 | ||||||||
\(156\) | 3.70820 | 0.296894 | ||||||||
\(157\) | 19.8885 | 1.58728 | 0.793639 | − | 0.608389i | \(-0.208184\pi\) | ||||
0.793639 | + | 0.608389i | \(0.208184\pi\) | |||||||
\(158\) | −2.43769 | −0.193933 | ||||||||
\(159\) | 3.85410 | 0.305650 | ||||||||
\(160\) | 4.14590 | 0.327762 | ||||||||
\(161\) | −5.09017 | −0.401162 | ||||||||
\(162\) | −2.94427 | −0.231324 | ||||||||
\(163\) | −8.70820 | −0.682079 | −0.341040 | − | 0.940049i | \(-0.610779\pi\) | ||||
−0.341040 | + | 0.940049i | \(0.610779\pi\) | |||||||
\(164\) | −20.7295 | −1.61870 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.03444 | −0.0802883 | ||||||||
\(167\) | −6.47214 | −0.500829 | −0.250414 | − | 0.968139i | \(-0.580567\pi\) | ||||
−0.250414 | + | 0.968139i | \(0.580567\pi\) | |||||||
\(168\) | −2.38197 | −0.183773 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | −1.18034 | −0.0905279 | ||||||||
\(171\) | −0.673762 | −0.0515239 | ||||||||
\(172\) | −23.2918 | −1.77598 | ||||||||
\(173\) | 15.3820 | 1.16947 | 0.584735 | − | 0.811225i | \(-0.301199\pi\) | ||||
0.584735 | + | 0.811225i | \(0.301199\pi\) | |||||||
\(174\) | −2.85410 | −0.216369 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.9443 | −1.34877 | ||||||||
\(178\) | 2.61803 | 0.196230 | ||||||||
\(179\) | −3.76393 | −0.281329 | −0.140665 | − | 0.990057i | \(-0.544924\pi\) | ||||
−0.140665 | + | 0.990057i | \(0.544924\pi\) | |||||||
\(180\) | 0.708204 | 0.0527864 | ||||||||
\(181\) | −7.41641 | −0.551257 | −0.275629 | − | 0.961264i | \(-0.588886\pi\) | ||||
−0.275629 | + | 0.961264i | \(0.588886\pi\) | |||||||
\(182\) | −0.472136 | −0.0349970 | ||||||||
\(183\) | −12.3262 | −0.911182 | ||||||||
\(184\) | −7.49342 | −0.552422 | ||||||||
\(185\) | 6.47214 | 0.475841 | ||||||||
\(186\) | 2.61803 | 0.191964 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.2705 | 0.894919 | ||||||||
\(189\) | −5.47214 | −0.398039 | ||||||||
\(190\) | 0.673762 | 0.0488798 | ||||||||
\(191\) | 15.7639 | 1.14064 | 0.570319 | − | 0.821423i | \(-0.306820\pi\) | ||||
0.570319 | + | 0.821423i | \(0.306820\pi\) | |||||||
\(192\) | 7.61803 | 0.549784 | ||||||||
\(193\) | 15.3262 | 1.10321 | 0.551603 | − | 0.834107i | \(-0.314016\pi\) | ||||
0.551603 | + | 0.834107i | \(0.314016\pi\) | |||||||
\(194\) | 2.67376 | 0.191965 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | −1.85410 | −0.132436 | ||||||||
\(197\) | 4.29180 | 0.305778 | 0.152889 | − | 0.988243i | \(-0.451142\pi\) | ||||
0.152889 | + | 0.988243i | \(0.451142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.23607 | −0.583839 | −0.291920 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291920 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(200\) | 5.88854 | 0.416383 | ||||||||
\(201\) | 13.4721 | 0.950251 | ||||||||
\(202\) | 5.65248 | 0.397707 | ||||||||
\(203\) | −4.61803 | −0.324122 | ||||||||
\(204\) | −9.27051 | −0.649066 | ||||||||
\(205\) | 11.1803 | 0.780869 | ||||||||
\(206\) | 3.38197 | 0.235633 | ||||||||
\(207\) | −1.94427 | −0.135136 | ||||||||
\(208\) | 3.88854 | 0.269622 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.618034 | 0.0426484 | ||||||||
\(211\) | −15.6180 | −1.07519 | −0.537595 | − | 0.843203i | \(-0.680667\pi\) | ||||
−0.537595 | + | 0.843203i | \(0.680667\pi\) | |||||||
\(212\) | 4.41641 | 0.303320 | ||||||||
\(213\) | 26.0344 | 1.78385 | ||||||||
\(214\) | −1.03444 | −0.0707130 | ||||||||
\(215\) | 12.5623 | 0.856742 | ||||||||
\(216\) | −8.05573 | −0.548123 | ||||||||
\(217\) | 4.23607 | 0.287563 | ||||||||
\(218\) | 0.583592 | 0.0395258 | ||||||||
\(219\) | −23.0344 | −1.55652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.81966 | −0.256938 | ||||||||
\(222\) | −4.00000 | −0.268462 | ||||||||
\(223\) | 2.03444 | 0.136236 | 0.0681182 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681182 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(224\) | −4.14590 | −0.277009 | ||||||||
\(225\) | 1.52786 | 0.101858 | ||||||||
\(226\) | 0.0557281 | 0.00370698 | ||||||||
\(227\) | 16.0344 | 1.06424 | 0.532122 | − | 0.846668i | \(-0.321395\pi\) | ||||
0.532122 | + | 0.846668i | \(0.321395\pi\) | |||||||
\(228\) | 5.29180 | 0.350458 | ||||||||
\(229\) | 6.76393 | 0.446973 | 0.223487 | − | 0.974707i | \(-0.428256\pi\) | ||||
0.223487 | + | 0.974707i | \(0.428256\pi\) | |||||||
\(230\) | 1.94427 | 0.128201 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.79837 | −0.446335 | ||||||||
\(233\) | 29.4164 | 1.92713 | 0.963566 | − | 0.267469i | \(-0.0861873\pi\) | ||||
0.963566 | + | 0.267469i | \(0.0861873\pi\) | |||||||
\(234\) | −0.180340 | −0.0117892 | ||||||||
\(235\) | −6.61803 | −0.431713 | ||||||||
\(236\) | −20.5623 | −1.33849 | ||||||||
\(237\) | 10.3262 | 0.670761 | ||||||||
\(238\) | 1.18034 | 0.0765101 | ||||||||
\(239\) | 17.0902 | 1.10547 | 0.552736 | − | 0.833357i | \(-0.313584\pi\) | ||||
0.552736 | + | 0.833357i | \(0.313584\pi\) | |||||||
\(240\) | −5.09017 | −0.328569 | ||||||||
\(241\) | −16.2705 | −1.04808 | −0.524038 | − | 0.851695i | \(-0.675575\pi\) | ||||
−0.524038 | + | 0.851695i | \(0.675575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | −14.1246 | −0.904236 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −6.90983 | −0.440555 | ||||||||
\(247\) | 2.18034 | 0.138732 | ||||||||
\(248\) | 6.23607 | 0.395991 | ||||||||
\(249\) | 4.38197 | 0.277696 | ||||||||
\(250\) | −3.43769 | −0.217419 | ||||||||
\(251\) | 23.0000 | 1.45175 | 0.725874 | − | 0.687828i | \(-0.241436\pi\) | ||||
0.725874 | + | 0.687828i | \(0.241436\pi\) | |||||||
\(252\) | −0.708204 | −0.0446127 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.12461 | −0.0705644 | ||||||||
\(255\) | 5.00000 | 0.313112 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | −8.56231 | −0.534102 | −0.267051 | − | 0.963682i | \(-0.586049\pi\) | ||||
−0.267051 | + | 0.963682i | \(0.586049\pi\) | |||||||
\(258\) | −7.76393 | −0.483361 | ||||||||
\(259\) | −6.47214 | −0.402159 | ||||||||
\(260\) | −2.29180 | −0.142131 | ||||||||
\(261\) | −1.76393 | −0.109185 | ||||||||
\(262\) | −7.23607 | −0.447046 | ||||||||
\(263\) | 17.1246 | 1.05595 | 0.527974 | − | 0.849260i | \(-0.322952\pi\) | ||||
0.527974 | + | 0.849260i | \(0.322952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38197 | −0.146323 | ||||||||
\(266\) | −0.673762 | −0.0413110 | ||||||||
\(267\) | −11.0902 | −0.678707 | ||||||||
\(268\) | 15.4377 | 0.943007 | ||||||||
\(269\) | 16.8541 | 1.02761 | 0.513806 | − | 0.857906i | \(-0.328235\pi\) | ||||
0.513806 | + | 0.857906i | \(0.328235\pi\) | |||||||
\(270\) | 2.09017 | 0.127204 | ||||||||
\(271\) | 4.79837 | 0.291480 | 0.145740 | − | 0.989323i | \(-0.453444\pi\) | ||||
0.145740 | + | 0.989323i | \(0.453444\pi\) | |||||||
\(272\) | −9.72136 | −0.589444 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | −5.85410 | −0.353659 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.2705 | 0.919177 | ||||||||
\(277\) | −23.0344 | −1.38401 | −0.692003 | − | 0.721895i | \(-0.743271\pi\) | ||||
−0.692003 | + | 0.721895i | \(0.743271\pi\) | |||||||
\(278\) | −4.56231 | −0.273629 | ||||||||
\(279\) | 1.61803 | 0.0968692 | ||||||||
\(280\) | 1.47214 | 0.0879770 | ||||||||
\(281\) | 25.1803 | 1.50213 | 0.751067 | − | 0.660226i | \(-0.229540\pi\) | ||||
0.751067 | + | 0.660226i | \(0.229540\pi\) | |||||||
\(282\) | 4.09017 | 0.243566 | ||||||||
\(283\) | −11.9443 | −0.710013 | −0.355007 | − | 0.934864i | \(-0.615521\pi\) | ||||
−0.355007 | + | 0.934864i | \(0.615521\pi\) | |||||||
\(284\) | 29.8328 | 1.77025 | ||||||||
\(285\) | −2.85410 | −0.169062 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.1803 | −0.659955 | ||||||||
\(288\) | −1.58359 | −0.0933141 | ||||||||
\(289\) | −7.45085 | −0.438285 | ||||||||
\(290\) | 1.76393 | 0.103582 | ||||||||
\(291\) | −11.3262 | −0.663956 | ||||||||
\(292\) | −26.3951 | −1.54466 | ||||||||
\(293\) | 11.0000 | 0.642627 | 0.321313 | − | 0.946973i | \(-0.395876\pi\) | ||||
0.321313 | + | 0.946973i | \(0.395876\pi\) | |||||||
\(294\) | −0.618034 | −0.0360445 | ||||||||
\(295\) | 11.0902 | 0.645695 | ||||||||
\(296\) | −9.52786 | −0.553796 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.38197 | 0.195912 | ||||||||
\(299\) | 6.29180 | 0.363864 | ||||||||
\(300\) | −12.0000 | −0.692820 | ||||||||
\(301\) | −12.5623 | −0.724079 | ||||||||
\(302\) | −0.0212862 | −0.00122489 | ||||||||
\(303\) | −23.9443 | −1.37556 | ||||||||
\(304\) | 5.54915 | 0.318266 | ||||||||
\(305\) | 7.61803 | 0.436207 | ||||||||
\(306\) | 0.450850 | 0.0257734 | ||||||||
\(307\) | 23.1803 | 1.32297 | 0.661486 | − | 0.749958i | \(-0.269926\pi\) | ||||
0.661486 | + | 0.749958i | \(0.269926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.3262 | −0.814991 | ||||||||
\(310\) | −1.61803 | −0.0918982 | ||||||||
\(311\) | 9.00000 | 0.510343 | 0.255172 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255172 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(312\) | 2.94427 | 0.166687 | ||||||||
\(313\) | 18.3262 | 1.03586 | 0.517930 | − | 0.855423i | \(-0.326703\pi\) | ||||
0.517930 | + | 0.855423i | \(0.326703\pi\) | |||||||
\(314\) | 7.59675 | 0.428709 | ||||||||
\(315\) | 0.381966 | 0.0215213 | ||||||||
\(316\) | 11.8328 | 0.665648 | ||||||||
\(317\) | −4.43769 | −0.249246 | −0.124623 | − | 0.992204i | \(-0.539772\pi\) | ||||
−0.124623 | + | 0.992204i | \(0.539772\pi\) | |||||||
\(318\) | 1.47214 | 0.0825533 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.70820 | −0.263197 | ||||||||
\(321\) | 4.38197 | 0.244577 | ||||||||
\(322\) | −1.94427 | −0.108350 | ||||||||
\(323\) | −5.45085 | −0.303293 | ||||||||
\(324\) | 14.2918 | 0.793989 | ||||||||
\(325\) | −4.94427 | −0.274259 | ||||||||
\(326\) | −3.32624 | −0.184223 | ||||||||
\(327\) | −2.47214 | −0.136709 | ||||||||
\(328\) | −16.4590 | −0.908795 | ||||||||
\(329\) | 6.61803 | 0.364864 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.18034 | 0.339702 | 0.169851 | − | 0.985470i | \(-0.445671\pi\) | ||||
0.169851 | + | 0.985470i | \(0.445671\pi\) | |||||||
\(332\) | 5.02129 | 0.275579 | ||||||||
\(333\) | −2.47214 | −0.135472 | ||||||||
\(334\) | −2.47214 | −0.135269 | ||||||||
\(335\) | −8.32624 | −0.454911 | ||||||||
\(336\) | 5.09017 | 0.277692 | ||||||||
\(337\) | −25.9443 | −1.41327 | −0.706637 | − | 0.707576i | \(-0.749789\pi\) | ||||
−0.706637 | + | 0.707576i | \(0.749789\pi\) | |||||||
\(338\) | −4.38197 | −0.238348 | ||||||||
\(339\) | −0.236068 | −0.0128215 | ||||||||
\(340\) | 5.72949 | 0.310725 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.257354 | −0.0139161 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −18.4934 | −0.997099 | ||||||||
\(345\) | −8.23607 | −0.443415 | ||||||||
\(346\) | 5.87539 | 0.315863 | ||||||||
\(347\) | −2.34752 | −0.126022 | −0.0630108 | − | 0.998013i | \(-0.520070\pi\) | ||||
−0.0630108 | + | 0.998013i | \(0.520070\pi\) | |||||||
\(348\) | 13.8541 | 0.742658 | ||||||||
\(349\) | −32.7984 | −1.75566 | −0.877828 | − | 0.478975i | \(-0.841008\pi\) | ||||
−0.877828 | + | 0.478975i | \(0.841008\pi\) | |||||||
\(350\) | 1.52786 | 0.0816678 | ||||||||
\(351\) | 6.76393 | 0.361032 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0902 | 1.28219 | 0.641095 | − | 0.767461i | \(-0.278480\pi\) | ||||
0.641095 | + | 0.767461i | \(0.278480\pi\) | |||||||
\(354\) | −6.85410 | −0.364291 | ||||||||
\(355\) | −16.0902 | −0.853978 | ||||||||
\(356\) | −12.7082 | −0.673533 | ||||||||
\(357\) | −5.00000 | −0.264628 | ||||||||
\(358\) | −1.43769 | −0.0759845 | ||||||||
\(359\) | 15.6180 | 0.824288 | 0.412144 | − | 0.911119i | \(-0.364780\pi\) | ||||
0.412144 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(360\) | 0.562306 | 0.0296361 | ||||||||
\(361\) | −15.8885 | −0.836239 | ||||||||
\(362\) | −2.83282 | −0.148889 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.29180 | 0.120123 | ||||||||
\(365\) | 14.2361 | 0.745150 | ||||||||
\(366\) | −4.70820 | −0.246102 | ||||||||
\(367\) | 32.8328 | 1.71386 | 0.856930 | − | 0.515434i | \(-0.172369\pi\) | ||||
0.856930 | + | 0.515434i | \(0.172369\pi\) | |||||||
\(368\) | 16.0132 | 0.834743 | ||||||||
\(369\) | −4.27051 | −0.222314 | ||||||||
\(370\) | 2.47214 | 0.128520 | ||||||||
\(371\) | 2.38197 | 0.123666 | ||||||||
\(372\) | −12.7082 | −0.658890 | ||||||||
\(373\) | 15.4377 | 0.799334 | 0.399667 | − | 0.916661i | \(-0.369126\pi\) | ||||
0.399667 | + | 0.916661i | \(0.369126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.5623 | 0.751994 | ||||||||
\(376\) | 9.74265 | 0.502439 | ||||||||
\(377\) | 5.70820 | 0.293987 | ||||||||
\(378\) | −2.09017 | −0.107507 | ||||||||
\(379\) | 32.0689 | 1.64727 | 0.823634 | − | 0.567122i | \(-0.191943\pi\) | ||||
0.823634 | + | 0.567122i | \(0.191943\pi\) | |||||||
\(380\) | −3.27051 | −0.167774 | ||||||||
\(381\) | 4.76393 | 0.244064 | ||||||||
\(382\) | 6.02129 | 0.308076 | ||||||||
\(383\) | −34.5967 | −1.76781 | −0.883906 | − | 0.467665i | \(-0.845095\pi\) | ||||
−0.883906 | + | 0.467665i | \(0.845095\pi\) | |||||||
\(384\) | 16.3262 | 0.833145 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.85410 | 0.297966 | ||||||||
\(387\) | −4.79837 | −0.243915 | ||||||||
\(388\) | −12.9787 | −0.658894 | ||||||||
\(389\) | −34.1803 | −1.73301 | −0.866506 | − | 0.499167i | \(-0.833640\pi\) | ||||
−0.866506 | + | 0.499167i | \(0.833640\pi\) | |||||||
\(390\) | −0.763932 | −0.0386832 | ||||||||
\(391\) | −15.7295 | −0.795475 | ||||||||
\(392\) | −1.47214 | −0.0743541 | ||||||||
\(393\) | 30.6525 | 1.54621 | ||||||||
\(394\) | 1.63932 | 0.0825878 | ||||||||
\(395\) | −6.38197 | −0.321112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.819660 | −0.0411376 | −0.0205688 | − | 0.999788i | \(-0.506548\pi\) | ||||
−0.0205688 | + | 0.999788i | \(0.506548\pi\) | |||||||
\(398\) | −3.14590 | −0.157690 | ||||||||
\(399\) | 2.85410 | 0.142884 | ||||||||
\(400\) | −12.5836 | −0.629180 | ||||||||
\(401\) | −17.5279 | −0.875300 | −0.437650 | − | 0.899145i | \(-0.644189\pi\) | ||||
−0.437650 | + | 0.899145i | \(0.644189\pi\) | |||||||
\(402\) | 5.14590 | 0.256654 | ||||||||
\(403\) | −5.23607 | −0.260827 | ||||||||
\(404\) | −27.4377 | −1.36508 | ||||||||
\(405\) | −7.70820 | −0.383024 | ||||||||
\(406\) | −1.76393 | −0.0875425 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.36068 | −0.364408 | ||||||||
\(409\) | 17.7082 | 0.875614 | 0.437807 | − | 0.899069i | \(-0.355755\pi\) | ||||
0.437807 | + | 0.899069i | \(0.355755\pi\) | |||||||
\(410\) | 4.27051 | 0.210905 | ||||||||
\(411\) | 24.7984 | 1.22321 | ||||||||
\(412\) | −16.4164 | −0.808778 | ||||||||
\(413\) | −11.0902 | −0.545712 | ||||||||
\(414\) | −0.742646 | −0.0364990 | ||||||||
\(415\) | −2.70820 | −0.132941 | ||||||||
\(416\) | 5.12461 | 0.251255 | ||||||||
\(417\) | 19.3262 | 0.946410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.8885 | 1.46015 | 0.730075 | − | 0.683367i | \(-0.239485\pi\) | ||||
0.730075 | + | 0.683367i | \(0.239485\pi\) | |||||||
\(420\) | −3.00000 | −0.146385 | ||||||||
\(421\) | 0.763932 | 0.0372318 | 0.0186159 | − | 0.999827i | \(-0.494074\pi\) | ||||
0.0186159 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(422\) | −5.96556 | −0.290399 | ||||||||
\(423\) | 2.52786 | 0.122909 | ||||||||
\(424\) | 3.50658 | 0.170294 | ||||||||
\(425\) | 12.3607 | 0.599581 | ||||||||
\(426\) | 9.94427 | 0.481802 | ||||||||
\(427\) | −7.61803 | −0.368663 | ||||||||
\(428\) | 5.02129 | 0.242713 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.79837 | 0.231398 | ||||||||
\(431\) | 13.8541 | 0.667329 | 0.333664 | − | 0.942692i | \(-0.391715\pi\) | ||||
0.333664 | + | 0.942692i | \(0.391715\pi\) | |||||||
\(432\) | 17.2148 | 0.828247 | ||||||||
\(433\) | −8.96556 | −0.430857 | −0.215429 | − | 0.976520i | \(-0.569115\pi\) | ||||
−0.215429 | + | 0.976520i | \(0.569115\pi\) | |||||||
\(434\) | 1.61803 | 0.0776681 | ||||||||
\(435\) | −7.47214 | −0.358261 | ||||||||
\(436\) | −2.83282 | −0.135667 | ||||||||
\(437\) | 8.97871 | 0.429510 | ||||||||
\(438\) | −8.79837 | −0.420403 | ||||||||
\(439\) | −3.38197 | −0.161412 | −0.0807062 | − | 0.996738i | \(-0.525718\pi\) | ||||
−0.0807062 | + | 0.996738i | \(0.525718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | −1.45898 | −0.0693966 | ||||||||
\(443\) | 3.09017 | 0.146818 | 0.0734092 | − | 0.997302i | \(-0.476612\pi\) | ||||
0.0734092 | + | 0.997302i | \(0.476612\pi\) | |||||||
\(444\) | 19.4164 | 0.921462 | ||||||||
\(445\) | 6.85410 | 0.324916 | ||||||||
\(446\) | 0.777088 | 0.0367962 | ||||||||
\(447\) | −14.3262 | −0.677608 | ||||||||
\(448\) | 4.70820 | 0.222442 | ||||||||
\(449\) | 12.3262 | 0.581711 | 0.290856 | − | 0.956767i | \(-0.406060\pi\) | ||||
0.290856 | + | 0.956767i | \(0.406060\pi\) | |||||||
\(450\) | 0.583592 | 0.0275108 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.270510 | −0.0127237 | ||||||||
\(453\) | 0.0901699 | 0.00423655 | ||||||||
\(454\) | 6.12461 | 0.287442 | ||||||||
\(455\) | −1.23607 | −0.0579478 | ||||||||
\(456\) | 4.20163 | 0.196759 | ||||||||
\(457\) | 0.145898 | 0.00682482 | 0.00341241 | − | 0.999994i | \(-0.498914\pi\) | ||||
0.00341241 | + | 0.999994i | \(0.498914\pi\) | |||||||
\(458\) | 2.58359 | 0.120723 | ||||||||
\(459\) | −16.9098 | −0.789283 | ||||||||
\(460\) | −9.43769 | −0.440035 | ||||||||
\(461\) | 18.5066 | 0.861937 | 0.430969 | − | 0.902367i | \(-0.358172\pi\) | ||||
0.430969 | + | 0.902367i | \(0.358172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2361 | 1.03340 | 0.516699 | − | 0.856167i | \(-0.327161\pi\) | ||||
0.516699 | + | 0.856167i | \(0.327161\pi\) | |||||||
\(464\) | 14.5279 | 0.674439 | ||||||||
\(465\) | 6.85410 | 0.317851 | ||||||||
\(466\) | 11.2361 | 0.520501 | ||||||||
\(467\) | −4.50658 | −0.208540 | −0.104270 | − | 0.994549i | \(-0.533251\pi\) | ||||
−0.104270 | + | 0.994549i | \(0.533251\pi\) | |||||||
\(468\) | 0.875388 | 0.0404648 | ||||||||
\(469\) | 8.32624 | 0.384470 | ||||||||
\(470\) | −2.52786 | −0.116602 | ||||||||
\(471\) | −32.1803 | −1.48279 | ||||||||
\(472\) | −16.3262 | −0.751476 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.94427 | 0.181166 | ||||||||
\(475\) | −7.05573 | −0.323739 | ||||||||
\(476\) | −5.72949 | −0.262611 | ||||||||
\(477\) | 0.909830 | 0.0416583 | ||||||||
\(478\) | 6.52786 | 0.298578 | ||||||||
\(479\) | −21.7639 | −0.994419 | −0.497210 | − | 0.867630i | \(-0.665642\pi\) | ||||
−0.497210 | + | 0.867630i | \(0.665642\pi\) | |||||||
\(480\) | −6.70820 | −0.306186 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | −6.21478 | −0.283076 | ||||||||
\(483\) | 8.23607 | 0.374754 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00000 | 0.317854 | ||||||||
\(486\) | −1.50658 | −0.0683398 | ||||||||
\(487\) | −32.5967 | −1.47710 | −0.738550 | − | 0.674199i | \(-0.764489\pi\) | ||||
−0.738550 | + | 0.674199i | \(0.764489\pi\) | |||||||
\(488\) | −11.2148 | −0.507669 | ||||||||
\(489\) | 14.0902 | 0.637180 | ||||||||
\(490\) | 0.381966 | 0.0172555 | ||||||||
\(491\) | −22.1459 | −0.999430 | −0.499715 | − | 0.866190i | \(-0.666562\pi\) | ||||
−0.499715 | + | 0.866190i | \(0.666562\pi\) | |||||||
\(492\) | 33.5410 | 1.51215 | ||||||||
\(493\) | −14.2705 | −0.642711 | ||||||||
\(494\) | 0.832816 | 0.0374702 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.3262 | −0.598366 | ||||||||
\(497\) | 16.0902 | 0.721743 | ||||||||
\(498\) | 1.67376 | 0.0750031 | ||||||||
\(499\) | −10.0902 | −0.451698 | −0.225849 | − | 0.974162i | \(-0.572516\pi\) | ||||
−0.225849 | + | 0.974162i | \(0.572516\pi\) | |||||||
\(500\) | 16.6869 | 0.746262 | ||||||||
\(501\) | 10.4721 | 0.467861 | ||||||||
\(502\) | 8.78522 | 0.392103 | ||||||||
\(503\) | 34.8328 | 1.55312 | 0.776559 | − | 0.630044i | \(-0.216963\pi\) | ||||
0.776559 | + | 0.630044i | \(0.216963\pi\) | |||||||
\(504\) | −0.562306 | −0.0250471 | ||||||||
\(505\) | 14.7984 | 0.658519 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.5623 | 0.824381 | ||||||||
\(508\) | 5.45898 | 0.242203 | ||||||||
\(509\) | −10.7426 | −0.476159 | −0.238080 | − | 0.971246i | \(-0.576518\pi\) | ||||
−0.238080 | + | 0.971246i | \(0.576518\pi\) | |||||||
\(510\) | 1.90983 | 0.0845687 | ||||||||
\(511\) | −14.2361 | −0.629767 | ||||||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | 9.65248 | 0.426167 | ||||||||
\(514\) | −3.27051 | −0.144256 | ||||||||
\(515\) | 8.85410 | 0.390158 | ||||||||
\(516\) | 37.6869 | 1.65907 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.47214 | −0.108619 | ||||||||
\(519\) | −24.8885 | −1.09249 | ||||||||
\(520\) | −1.81966 | −0.0797974 | ||||||||
\(521\) | −12.2361 | −0.536072 | −0.268036 | − | 0.963409i | \(-0.586375\pi\) | ||||
−0.268036 | + | 0.963409i | \(0.586375\pi\) | |||||||
\(522\) | −0.673762 | −0.0294898 | ||||||||
\(523\) | −16.5623 | −0.724219 | −0.362110 | − | 0.932136i | \(-0.617943\pi\) | ||||
−0.362110 | + | 0.932136i | \(0.617943\pi\) | |||||||
\(524\) | 35.1246 | 1.53443 | ||||||||
\(525\) | −6.47214 | −0.282467 | ||||||||
\(526\) | 6.54102 | 0.285202 | ||||||||
\(527\) | 13.0902 | 0.570217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.90983 | 0.126514 | ||||||||
\(530\) | −0.909830 | −0.0395205 | ||||||||
\(531\) | −4.23607 | −0.183830 | ||||||||
\(532\) | 3.27051 | 0.141795 | ||||||||
\(533\) | 13.8197 | 0.598596 | ||||||||
\(534\) | −4.23607 | −0.183313 | ||||||||
\(535\) | −2.70820 | −0.117086 | ||||||||
\(536\) | 12.2574 | 0.529437 | ||||||||
\(537\) | 6.09017 | 0.262810 | ||||||||
\(538\) | 6.43769 | 0.277549 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.1459 | −0.436610 | ||||||||
\(541\) | −0.708204 | −0.0304481 | −0.0152240 | − | 0.999884i | \(-0.504846\pi\) | ||||
−0.0152240 | + | 0.999884i | \(0.504846\pi\) | |||||||
\(542\) | 1.83282 | 0.0787262 | ||||||||
\(543\) | 12.0000 | 0.514969 | ||||||||
\(544\) | −12.8115 | −0.549290 | ||||||||
\(545\) | 1.52786 | 0.0654465 | ||||||||
\(546\) | 0.763932 | 0.0326933 | ||||||||
\(547\) | 1.72949 | 0.0739477 | 0.0369738 | − | 0.999316i | \(-0.488228\pi\) | ||||
0.0369738 | + | 0.999316i | \(0.488228\pi\) | |||||||
\(548\) | 28.4164 | 1.21389 | ||||||||
\(549\) | −2.90983 | −0.124189 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.14590 | 0.347027 | ||||||||
\(552\) | 12.1246 | 0.516058 | ||||||||
\(553\) | 6.38197 | 0.271389 | ||||||||
\(554\) | −8.79837 | −0.373807 | ||||||||
\(555\) | −10.4721 | −0.444517 | ||||||||
\(556\) | 22.1459 | 0.939195 | ||||||||
\(557\) | 9.76393 | 0.413711 | 0.206856 | − | 0.978371i | \(-0.433677\pi\) | ||||
0.206856 | + | 0.978371i | \(0.433677\pi\) | |||||||
\(558\) | 0.618034 | 0.0261635 | ||||||||
\(559\) | 15.5279 | 0.656759 | ||||||||
\(560\) | −3.14590 | −0.132938 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.61803 | 0.405712 | ||||||||
\(563\) | 31.9787 | 1.34774 | 0.673871 | − | 0.738849i | \(-0.264630\pi\) | ||||
0.673871 | + | 0.738849i | \(0.264630\pi\) | |||||||
\(564\) | −19.8541 | −0.836009 | ||||||||
\(565\) | 0.145898 | 0.00613798 | ||||||||
\(566\) | −4.56231 | −0.191768 | ||||||||
\(567\) | 7.70820 | 0.323714 | ||||||||
\(568\) | 23.6869 | 0.993881 | ||||||||
\(569\) | −37.3050 | −1.56390 | −0.781952 | − | 0.623338i | \(-0.785776\pi\) | ||||
−0.781952 | + | 0.623338i | \(0.785776\pi\) | |||||||
\(570\) | −1.09017 | −0.0456622 | ||||||||
\(571\) | −34.3050 | −1.43562 | −0.717809 | − | 0.696240i | \(-0.754855\pi\) | ||||
−0.717809 | + | 0.696240i | \(0.754855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.5066 | −1.06555 | ||||||||
\(574\) | −4.27051 | −0.178248 | ||||||||
\(575\) | −20.3607 | −0.849099 | ||||||||
\(576\) | 1.79837 | 0.0749322 | ||||||||
\(577\) | 9.65248 | 0.401838 | 0.200919 | − | 0.979608i | \(-0.435607\pi\) | ||||
0.200919 | + | 0.979608i | \(0.435607\pi\) | |||||||
\(578\) | −2.84597 | −0.118377 | ||||||||
\(579\) | −24.7984 | −1.03059 | ||||||||
\(580\) | −8.56231 | −0.355530 | ||||||||
\(581\) | 2.70820 | 0.112355 | ||||||||
\(582\) | −4.32624 | −0.179328 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −20.9574 | −0.867225 | ||||||||
\(585\) | −0.472136 | −0.0195204 | ||||||||
\(586\) | 4.20163 | 0.173568 | ||||||||
\(587\) | 1.00000 | 0.0412744 | 0.0206372 | − | 0.999787i | \(-0.493431\pi\) | ||||
0.0206372 | + | 0.999787i | \(0.493431\pi\) | |||||||
\(588\) | 3.00000 | 0.123718 | ||||||||
\(589\) | −7.47214 | −0.307884 | ||||||||
\(590\) | 4.23607 | 0.174396 | ||||||||
\(591\) | −6.94427 | −0.285649 | ||||||||
\(592\) | 20.3607 | 0.836819 | ||||||||
\(593\) | −11.1246 | −0.456833 | −0.228417 | − | 0.973564i | \(-0.573355\pi\) | ||||
−0.228417 | + | 0.973564i | \(0.573355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.09017 | 0.126685 | ||||||||
\(596\) | −16.4164 | −0.672442 | ||||||||
\(597\) | 13.3262 | 0.545407 | ||||||||
\(598\) | 2.40325 | 0.0982763 | ||||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | −9.52786 | −0.388973 | ||||||||
\(601\) | −13.7082 | −0.559169 | −0.279585 | − | 0.960121i | \(-0.590197\pi\) | ||||
−0.279585 | + | 0.960121i | \(0.590197\pi\) | |||||||
\(602\) | −4.79837 | −0.195567 | ||||||||
\(603\) | 3.18034 | 0.129513 | ||||||||
\(604\) | 0.103326 | 0.00420426 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.14590 | −0.371527 | ||||||||
\(607\) | −20.2016 | −0.819959 | −0.409979 | − | 0.912095i | \(-0.634464\pi\) | ||||
−0.409979 | + | 0.912095i | \(0.634464\pi\) | |||||||
\(608\) | 7.31308 | 0.296585 | ||||||||
\(609\) | 7.47214 | 0.302786 | ||||||||
\(610\) | 2.90983 | 0.117816 | ||||||||
\(611\) | −8.18034 | −0.330941 | ||||||||
\(612\) | −2.18847 | −0.0884637 | ||||||||
\(613\) | 0.888544 | 0.0358879 | 0.0179440 | − | 0.999839i | \(-0.494288\pi\) | ||||
0.0179440 | + | 0.999839i | \(0.494288\pi\) | |||||||
\(614\) | 8.85410 | 0.357322 | ||||||||
\(615\) | −18.0902 | −0.729466 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.41641 | 0.379090 | 0.189545 | − | 0.981872i | \(-0.439299\pi\) | ||||
0.189545 | + | 0.981872i | \(0.439299\pi\) | |||||||
\(618\) | −5.47214 | −0.220122 | ||||||||
\(619\) | −39.7082 | −1.59601 | −0.798004 | − | 0.602653i | \(-0.794111\pi\) | ||||
−0.798004 | + | 0.602653i | \(0.794111\pi\) | |||||||
\(620\) | 7.85410 | 0.315428 | ||||||||
\(621\) | 27.8541 | 1.11775 | ||||||||
\(622\) | 3.43769 | 0.137839 | ||||||||
\(623\) | −6.85410 | −0.274604 | ||||||||
\(624\) | −6.29180 | −0.251873 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 7.00000 | 0.279776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.8754 | −1.47149 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0.145898 | 0.00581272 | ||||||||
\(631\) | 17.8328 | 0.709913 | 0.354957 | − | 0.934883i | \(-0.384496\pi\) | ||||
0.354957 | + | 0.934883i | \(0.384496\pi\) | |||||||
\(632\) | 9.39512 | 0.373718 | ||||||||
\(633\) | 25.2705 | 1.00441 | ||||||||
\(634\) | −1.69505 | −0.0673190 | ||||||||
\(635\) | −2.94427 | −0.116840 | ||||||||
\(636\) | −7.14590 | −0.283353 | ||||||||
\(637\) | 1.23607 | 0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.14590 | 0.243128 | ||||||||
\(640\) | −10.0902 | −0.398849 | ||||||||
\(641\) | 31.6525 | 1.25020 | 0.625099 | − | 0.780546i | \(-0.285059\pi\) | ||||
0.625099 | + | 0.780546i | \(0.285059\pi\) | |||||||
\(642\) | 1.67376 | 0.0660581 | ||||||||
\(643\) | 1.58359 | 0.0624508 | 0.0312254 | − | 0.999512i | \(-0.490059\pi\) | ||||
0.0312254 | + | 0.999512i | \(0.490059\pi\) | |||||||
\(644\) | 9.43769 | 0.371897 | ||||||||
\(645\) | −20.3262 | −0.800345 | ||||||||
\(646\) | −2.08204 | −0.0819167 | ||||||||
\(647\) | 6.18034 | 0.242974 | 0.121487 | − | 0.992593i | \(-0.461234\pi\) | ||||
0.121487 | + | 0.992593i | \(0.461234\pi\) | |||||||
\(648\) | 11.3475 | 0.445773 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.88854 | −0.0740748 | ||||||||
\(651\) | −6.85410 | −0.268633 | ||||||||
\(652\) | 16.1459 | 0.632322 | ||||||||
\(653\) | 18.2361 | 0.713632 | 0.356816 | − | 0.934175i | \(-0.383862\pi\) | ||||
0.356816 | + | 0.934175i | \(0.383862\pi\) | |||||||
\(654\) | −0.944272 | −0.0369240 | ||||||||
\(655\) | −18.9443 | −0.740214 | ||||||||
\(656\) | 35.1722 | 1.37324 | ||||||||
\(657\) | −5.43769 | −0.212145 | ||||||||
\(658\) | 2.52786 | 0.0985464 | ||||||||
\(659\) | −31.4721 | −1.22598 | −0.612990 | − | 0.790091i | \(-0.710033\pi\) | ||||
−0.612990 | + | 0.790091i | \(0.710033\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.5623 | −1.34432 | −0.672159 | − | 0.740407i | \(-0.734633\pi\) | ||||
−0.672159 | + | 0.740407i | \(0.734633\pi\) | |||||||
\(662\) | 2.36068 | 0.0917504 | ||||||||
\(663\) | 6.18034 | 0.240025 | ||||||||
\(664\) | 3.98684 | 0.154720 | ||||||||
\(665\) | −1.76393 | −0.0684023 | ||||||||
\(666\) | −0.944272 | −0.0365898 | ||||||||
\(667\) | 23.5066 | 0.910178 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | −3.29180 | −0.127268 | ||||||||
\(670\) | −3.18034 | −0.122867 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.70820 | 0.258775 | ||||||||
\(673\) | 6.58359 | 0.253779 | 0.126889 | − | 0.991917i | \(-0.459501\pi\) | ||||
0.126889 | + | 0.991917i | \(0.459501\pi\) | |||||||
\(674\) | −9.90983 | −0.381712 | ||||||||
\(675\) | −21.8885 | −0.842490 | ||||||||
\(676\) | 21.2705 | 0.818097 | ||||||||
\(677\) | 36.2705 | 1.39399 | 0.696994 | − | 0.717077i | \(-0.254520\pi\) | ||||
0.696994 | + | 0.717077i | \(0.254520\pi\) | |||||||
\(678\) | −0.0901699 | −0.00346296 | ||||||||
\(679\) | −7.00000 | −0.268635 | ||||||||
\(680\) | 4.54915 | 0.174452 | ||||||||
\(681\) | −25.9443 | −0.994187 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.493422 | 0.0188803 | 0.00944014 | − | 0.999955i | \(-0.496995\pi\) | ||||
0.00944014 | + | 0.999955i | \(0.496995\pi\) | |||||||
\(684\) | 1.24922 | 0.0477653 | ||||||||
\(685\) | −15.3262 | −0.585585 | ||||||||
\(686\) | −0.381966 | −0.0145835 | ||||||||
\(687\) | −10.9443 | −0.417550 | ||||||||
\(688\) | 39.5197 | 1.50668 | ||||||||
\(689\) | −2.94427 | −0.112168 | ||||||||
\(690\) | −3.14590 | −0.119762 | ||||||||
\(691\) | 18.5410 | 0.705334 | 0.352667 | − | 0.935749i | \(-0.385275\pi\) | ||||
0.352667 | + | 0.935749i | \(0.385275\pi\) | |||||||
\(692\) | −28.5197 | −1.08416 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.896674 | −0.0340373 | ||||||||
\(695\) | −11.9443 | −0.453072 | ||||||||
\(696\) | 11.0000 | 0.416954 | ||||||||
\(697\) | −34.5492 | −1.30864 | ||||||||
\(698\) | −12.5279 | −0.474187 | ||||||||
\(699\) | −47.5967 | −1.80027 | ||||||||
\(700\) | −7.41641 | −0.280314 | ||||||||
\(701\) | −18.5066 | −0.698984 | −0.349492 | − | 0.936939i | \(-0.613646\pi\) | ||||
−0.349492 | + | 0.936939i | \(0.613646\pi\) | |||||||
\(702\) | 2.58359 | 0.0975114 | ||||||||
\(703\) | 11.4164 | 0.430578 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.7082 | 0.403294 | ||||||||
\(706\) | 9.20163 | 0.346308 | ||||||||
\(707\) | −14.7984 | −0.556550 | ||||||||
\(708\) | 33.2705 | 1.25038 | ||||||||
\(709\) | −7.03444 | −0.264184 | −0.132092 | − | 0.991237i | \(-0.542169\pi\) | ||||
−0.132092 | + | 0.991237i | \(0.542169\pi\) | |||||||
\(710\) | −6.14590 | −0.230651 | ||||||||
\(711\) | 2.43769 | 0.0914207 | ||||||||
\(712\) | −10.0902 | −0.378145 | ||||||||
\(713\) | −21.5623 | −0.807515 | ||||||||
\(714\) | −1.90983 | −0.0714736 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.97871 | 0.260807 | ||||||||
\(717\) | −27.6525 | −1.03270 | ||||||||
\(718\) | 5.96556 | 0.222633 | ||||||||
\(719\) | −2.88854 | −0.107725 | −0.0538623 | − | 0.998548i | \(-0.517153\pi\) | ||||
−0.0538623 | + | 0.998548i | \(0.517153\pi\) | |||||||
\(720\) | −1.20163 | −0.0447820 | ||||||||
\(721\) | −8.85410 | −0.329744 | ||||||||
\(722\) | −6.06888 | −0.225860 | ||||||||
\(723\) | 26.3262 | 0.979083 | ||||||||
\(724\) | 13.7508 | 0.511044 | ||||||||
\(725\) | −18.4721 | −0.686038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4508 | −0.461776 | −0.230888 | − | 0.972980i | \(-0.574163\pi\) | ||||
−0.230888 | + | 0.972980i | \(0.574163\pi\) | |||||||
\(728\) | 1.81966 | 0.0674411 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 5.43769 | 0.201258 | ||||||||
\(731\) | −38.8197 | −1.43580 | ||||||||
\(732\) | 22.8541 | 0.844712 | ||||||||
\(733\) | −52.9443 | −1.95554 | −0.977771 | − | 0.209677i | \(-0.932759\pi\) | ||||
−0.977771 | + | 0.209677i | \(0.932759\pi\) | |||||||
\(734\) | 12.5410 | 0.462897 | ||||||||
\(735\) | −1.61803 | −0.0596821 | ||||||||
\(736\) | 21.1033 | 0.777879 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.63119 | −0.0600449 | ||||||||
\(739\) | 11.3820 | 0.418692 | 0.209346 | − | 0.977842i | \(-0.432866\pi\) | ||||
0.209346 | + | 0.977842i | \(0.432866\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | −3.52786 | −0.129599 | ||||||||
\(742\) | 0.909830 | 0.0334009 | ||||||||
\(743\) | 14.9098 | 0.546989 | 0.273494 | − | 0.961874i | \(-0.411821\pi\) | ||||
0.273494 | + | 0.961874i | \(0.411821\pi\) | |||||||
\(744\) | −10.0902 | −0.369924 | ||||||||
\(745\) | 8.85410 | 0.324389 | ||||||||
\(746\) | 5.89667 | 0.215893 | ||||||||
\(747\) | 1.03444 | 0.0378482 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.70820 | 0.0989556 | ||||||||
\(750\) | 5.56231 | 0.203107 | ||||||||
\(751\) | 41.3050 | 1.50724 | 0.753620 | − | 0.657311i | \(-0.228306\pi\) | ||||
0.753620 | + | 0.657311i | \(0.228306\pi\) | |||||||
\(752\) | −20.8197 | −0.759215 | ||||||||
\(753\) | −37.2148 | −1.35618 | ||||||||
\(754\) | 2.18034 | 0.0794033 | ||||||||
\(755\) | −0.0557281 | −0.00202815 | ||||||||
\(756\) | 10.1459 | 0.369003 | ||||||||
\(757\) | −14.7639 | −0.536604 | −0.268302 | − | 0.963335i | \(-0.586463\pi\) | ||||
−0.268302 | + | 0.963335i | \(0.586463\pi\) | |||||||
\(758\) | 12.2492 | 0.444912 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.59675 | −0.0941939 | ||||||||
\(761\) | −15.3050 | −0.554804 | −0.277402 | − | 0.960754i | \(-0.589473\pi\) | ||||
−0.277402 | + | 0.960754i | \(0.589473\pi\) | |||||||
\(762\) | 1.81966 | 0.0659193 | ||||||||
\(763\) | −1.52786 | −0.0553124 | ||||||||
\(764\) | −29.2279 | −1.05743 | ||||||||
\(765\) | 1.18034 | 0.0426753 | ||||||||
\(766\) | −13.2148 | −0.477469 | ||||||||
\(767\) | 13.7082 | 0.494975 | ||||||||
\(768\) | −9.00000 | −0.324760 | ||||||||
\(769\) | −48.5623 | −1.75120 | −0.875601 | − | 0.483035i | \(-0.839534\pi\) | ||||
−0.875601 | + | 0.483035i | \(0.839534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.8541 | 0.498943 | ||||||||
\(772\) | −28.4164 | −1.02273 | ||||||||
\(773\) | 40.2361 | 1.44719 | 0.723595 | − | 0.690224i | \(-0.242488\pi\) | ||||
0.723595 | + | 0.690224i | \(0.242488\pi\) | |||||||
\(774\) | −1.83282 | −0.0658792 | ||||||||
\(775\) | 16.9443 | 0.608656 | ||||||||
\(776\) | −10.3050 | −0.369926 | ||||||||
\(777\) | 10.4721 | 0.375686 | ||||||||
\(778\) | −13.0557 | −0.468071 | ||||||||
\(779\) | 19.7214 | 0.706591 | ||||||||
\(780\) | 3.70820 | 0.132775 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.00813 | −0.214850 | ||||||||
\(783\) | 25.2705 | 0.903094 | ||||||||
\(784\) | 3.14590 | 0.112354 | ||||||||
\(785\) | 19.8885 | 0.709853 | ||||||||
\(786\) | 11.7082 | 0.417618 | ||||||||
\(787\) | −20.5623 | −0.732967 | −0.366484 | − | 0.930425i | \(-0.619438\pi\) | ||||
−0.366484 | + | 0.930425i | \(0.619438\pi\) | |||||||
\(788\) | −7.95743 | −0.283472 | ||||||||
\(789\) | −27.7082 | −0.986438 | ||||||||
\(790\) | −2.43769 | −0.0867293 | ||||||||
\(791\) | −0.145898 | −0.00518754 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.41641 | 0.334386 | ||||||||
\(794\) | −0.313082 | −0.0111109 | ||||||||
\(795\) | 3.85410 | 0.136691 | ||||||||
\(796\) | 15.2705 | 0.541249 | ||||||||
\(797\) | 32.2361 | 1.14186 | 0.570930 | − | 0.820999i | \(-0.306583\pi\) | ||||
0.570930 | + | 0.820999i | \(0.306583\pi\) | |||||||
\(798\) | 1.09017 | 0.0385916 | ||||||||
\(799\) | 20.4508 | 0.723499 | ||||||||
\(800\) | −16.5836 | −0.586319 | ||||||||
\(801\) | −2.61803 | −0.0925037 | ||||||||
\(802\) | −6.69505 | −0.236410 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −24.9787 | −0.880931 | ||||||||
\(805\) | −5.09017 | −0.179405 | ||||||||
\(806\) | −2.00000 | −0.0704470 | ||||||||
\(807\) | −27.2705 | −0.959967 | ||||||||
\(808\) | −21.7852 | −0.766401 | ||||||||
\(809\) | −32.5066 | −1.14287 | −0.571435 | − | 0.820647i | \(-0.693613\pi\) | ||||
−0.571435 | + | 0.820647i | \(0.693613\pi\) | |||||||
\(810\) | −2.94427 | −0.103451 | ||||||||
\(811\) | −1.16718 | −0.0409854 | −0.0204927 | − | 0.999790i | \(-0.506523\pi\) | ||||
−0.0204927 | + | 0.999790i | \(0.506523\pi\) | |||||||
\(812\) | 8.56231 | 0.300478 | ||||||||
\(813\) | −7.76393 | −0.272293 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.70820 | −0.305035 | ||||||||
\(816\) | 15.7295 | 0.550642 | ||||||||
\(817\) | 22.1591 | 0.775247 | ||||||||
\(818\) | 6.76393 | 0.236495 | ||||||||
\(819\) | 0.472136 | 0.0164978 | ||||||||
\(820\) | −20.7295 | −0.723905 | ||||||||
\(821\) | −56.6656 | −1.97764 | −0.988822 | − | 0.149100i | \(-0.952362\pi\) | ||||
−0.988822 | + | 0.149100i | \(0.952362\pi\) | |||||||
\(822\) | 9.47214 | 0.330379 | ||||||||
\(823\) | −31.8885 | −1.11156 | −0.555782 | − | 0.831328i | \(-0.687581\pi\) | ||||
−0.555782 | + | 0.831328i | \(0.687581\pi\) | |||||||
\(824\) | −13.0344 | −0.454076 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.23607 | −0.147392 | ||||||||
\(827\) | 19.5967 | 0.681446 | 0.340723 | − | 0.940164i | \(-0.389328\pi\) | ||||
0.340723 | + | 0.940164i | \(0.389328\pi\) | |||||||
\(828\) | 3.60488 | 0.125278 | ||||||||
\(829\) | −47.9787 | −1.66637 | −0.833185 | − | 0.552995i | \(-0.813485\pi\) | ||||
−0.833185 | + | 0.552995i | \(0.813485\pi\) | |||||||
\(830\) | −1.03444 | −0.0359060 | ||||||||
\(831\) | 37.2705 | 1.29290 | ||||||||
\(832\) | −5.81966 | −0.201760 | ||||||||
\(833\) | −3.09017 | −0.107068 | ||||||||
\(834\) | 7.38197 | 0.255617 | ||||||||
\(835\) | −6.47214 | −0.223978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.1803 | −0.801230 | ||||||||
\(838\) | 11.4164 | 0.394373 | ||||||||
\(839\) | 30.5967 | 1.05632 | 0.528159 | − | 0.849146i | \(-0.322883\pi\) | ||||
0.528159 | + | 0.849146i | \(0.322883\pi\) | |||||||
\(840\) | −2.38197 | −0.0821856 | ||||||||
\(841\) | −7.67376 | −0.264612 | ||||||||
\(842\) | 0.291796 | 0.0100560 | ||||||||
\(843\) | −40.7426 | −1.40325 | ||||||||
\(844\) | 28.9574 | 0.996756 | ||||||||
\(845\) | −11.4721 | −0.394653 | ||||||||
\(846\) | 0.965558 | 0.0331966 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.49342 | −0.257325 | ||||||||
\(849\) | 19.3262 | 0.663275 | ||||||||
\(850\) | 4.72136 | 0.161941 | ||||||||
\(851\) | 32.9443 | 1.12932 | ||||||||
\(852\) | −48.2705 | −1.65372 | ||||||||
\(853\) | 34.9098 | 1.19529 | 0.597645 | − | 0.801761i | \(-0.296103\pi\) | ||||
0.597645 | + | 0.801761i | \(0.296103\pi\) | |||||||
\(854\) | −2.90983 | −0.0995723 | ||||||||
\(855\) | −0.673762 | −0.0230422 | ||||||||
\(856\) | 3.98684 | 0.136268 | ||||||||
\(857\) | 15.0902 | 0.515470 | 0.257735 | − | 0.966216i | \(-0.417024\pi\) | ||||
0.257735 | + | 0.966216i | \(0.417024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.5623 | 0.735696 | 0.367848 | − | 0.929886i | \(-0.380095\pi\) | ||||
0.367848 | + | 0.929886i | \(0.380095\pi\) | |||||||
\(860\) | −23.2918 | −0.794244 | ||||||||
\(861\) | 18.0902 | 0.616511 | ||||||||
\(862\) | 5.29180 | 0.180239 | ||||||||
\(863\) | −47.9443 | −1.63204 | −0.816021 | − | 0.578022i | \(-0.803825\pi\) | ||||
−0.816021 | + | 0.578022i | \(0.803825\pi\) | |||||||
\(864\) | 22.6869 | 0.771825 | ||||||||
\(865\) | 15.3820 | 0.523003 | ||||||||
\(866\) | −3.42454 | −0.116371 | ||||||||
\(867\) | 12.0557 | 0.409434 | ||||||||
\(868\) | −7.85410 | −0.266586 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.85410 | −0.0967631 | ||||||||
\(871\) | −10.2918 | −0.348724 | ||||||||
\(872\) | −2.24922 | −0.0761683 | ||||||||
\(873\) | −2.67376 | −0.0904931 | ||||||||
\(874\) | 3.42956 | 0.116007 | ||||||||
\(875\) | 9.00000 | 0.304256 | ||||||||
\(876\) | 42.7082 | 1.44298 | ||||||||
\(877\) | −13.0000 | −0.438979 | −0.219489 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219489 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(878\) | −1.29180 | −0.0435960 | ||||||||
\(879\) | −17.7984 | −0.600324 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1459 | 0.476587 | 0.238294 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238294 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(882\) | −0.145898 | −0.00491264 | ||||||||
\(883\) | 31.6312 | 1.06447 | 0.532237 | − | 0.846595i | \(-0.321351\pi\) | ||||
0.532237 | + | 0.846595i | \(0.321351\pi\) | |||||||
\(884\) | 7.08204 | 0.238195 | ||||||||
\(885\) | −17.9443 | −0.603190 | ||||||||
\(886\) | 1.18034 | 0.0396543 | ||||||||
\(887\) | −57.2148 | −1.92108 | −0.960542 | − | 0.278134i | \(-0.910284\pi\) | ||||
−0.960542 | + | 0.278134i | \(0.910284\pi\) | |||||||
\(888\) | 15.4164 | 0.517341 | ||||||||
\(889\) | 2.94427 | 0.0987477 | ||||||||
\(890\) | 2.61803 | 0.0877567 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.77206 | −0.126298 | ||||||||
\(893\) | −11.6738 | −0.390648 | ||||||||
\(894\) | −5.47214 | −0.183016 | ||||||||
\(895\) | −3.76393 | −0.125814 | ||||||||
\(896\) | 10.0902 | 0.337089 | ||||||||
\(897\) | −10.1803 | −0.339912 | ||||||||
\(898\) | 4.70820 | 0.157115 | ||||||||
\(899\) | −19.5623 | −0.652439 | ||||||||
\(900\) | −2.83282 | −0.0944272 | ||||||||
\(901\) | 7.36068 | 0.245220 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.3262 | 0.676415 | ||||||||
\(904\) | −0.214782 | −0.00714353 | ||||||||
\(905\) | −7.41641 | −0.246530 | ||||||||
\(906\) | 0.0344419 | 0.00114425 | ||||||||
\(907\) | −15.7639 | −0.523433 | −0.261716 | − | 0.965145i | \(-0.584289\pi\) | ||||
−0.261716 | + | 0.965145i | \(0.584289\pi\) | |||||||
\(908\) | −29.7295 | −0.986608 | ||||||||
\(909\) | −5.65248 | −0.187481 | ||||||||
\(910\) | −0.472136 | −0.0156512 | ||||||||
\(911\) | −45.1803 | −1.49689 | −0.748446 | − | 0.663196i | \(-0.769200\pi\) | ||||
−0.748446 | + | 0.663196i | \(0.769200\pi\) | |||||||
\(912\) | −8.97871 | −0.297315 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.0557281 | 0.00184332 | ||||||||
\(915\) | −12.3262 | −0.407493 | ||||||||
\(916\) | −12.5410 | −0.414367 | ||||||||
\(917\) | 18.9443 | 0.625595 | ||||||||
\(918\) | −6.45898 | −0.213178 | ||||||||
\(919\) | 14.8885 | 0.491128 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(920\) | −7.49342 | −0.247051 | ||||||||
\(921\) | −37.5066 | −1.23588 | ||||||||
\(922\) | 7.06888 | 0.232801 | ||||||||
\(923\) | −19.8885 | −0.654639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.8885 | −0.851210 | ||||||||
\(926\) | 8.49342 | 0.279111 | ||||||||
\(927\) | −3.38197 | −0.111078 | ||||||||
\(928\) | 19.1459 | 0.628495 | ||||||||
\(929\) | 24.0000 | 0.787414 | 0.393707 | − | 0.919236i | \(-0.371192\pi\) | ||||
0.393707 | + | 0.919236i | \(0.371192\pi\) | |||||||
\(930\) | 2.61803 | 0.0858487 | ||||||||
\(931\) | 1.76393 | 0.0578105 | ||||||||
\(932\) | −54.5410 | −1.78655 | ||||||||
\(933\) | −14.5623 | −0.476748 | ||||||||
\(934\) | −1.72136 | −0.0563246 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.695048 | 0.0227184 | ||||||||
\(937\) | 51.7214 | 1.68966 | 0.844832 | − | 0.535032i | \(-0.179701\pi\) | ||||
0.844832 | + | 0.535032i | \(0.179701\pi\) | |||||||
\(938\) | 3.18034 | 0.103842 | ||||||||
\(939\) | −29.6525 | −0.967672 | ||||||||
\(940\) | 12.2705 | 0.400220 | ||||||||
\(941\) | −27.0689 | −0.882420 | −0.441210 | − | 0.897404i | \(-0.645451\pi\) | ||||
−0.441210 | + | 0.897404i | \(0.645451\pi\) | |||||||
\(942\) | −12.2918 | −0.400488 | ||||||||
\(943\) | 56.9098 | 1.85324 | ||||||||
\(944\) | 34.8885 | 1.13553 | ||||||||
\(945\) | −5.47214 | −0.178009 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.29180 | 0.204456 | 0.102228 | − | 0.994761i | \(-0.467403\pi\) | ||||
0.102228 | + | 0.994761i | \(0.467403\pi\) | |||||||
\(948\) | −19.1459 | −0.621830 | ||||||||
\(949\) | 17.5967 | 0.571215 | ||||||||
\(950\) | −2.69505 | −0.0874389 | ||||||||
\(951\) | 7.18034 | 0.232838 | ||||||||
\(952\) | −4.54915 | −0.147439 | ||||||||
\(953\) | 6.23607 | 0.202006 | 0.101003 | − | 0.994886i | \(-0.467795\pi\) | ||||
0.101003 | + | 0.994886i | \(0.467795\pi\) | |||||||
\(954\) | 0.347524 | 0.0112515 | ||||||||
\(955\) | 15.7639 | 0.510109 | ||||||||
\(956\) | −31.6869 | −1.02483 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.31308 | −0.268583 | ||||||||
\(959\) | 15.3262 | 0.494910 | ||||||||
\(960\) | 7.61803 | 0.245871 | ||||||||
\(961\) | −13.0557 | −0.421153 | ||||||||
\(962\) | 3.05573 | 0.0985206 | ||||||||
\(963\) | 1.03444 | 0.0333344 | ||||||||
\(964\) | 30.1672 | 0.971620 | ||||||||
\(965\) | 15.3262 | 0.493369 | ||||||||
\(966\) | 3.14590 | 0.101218 | ||||||||
\(967\) | −27.4508 | −0.882760 | −0.441380 | − | 0.897320i | \(-0.645511\pi\) | ||||
−0.441380 | + | 0.897320i | \(0.645511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.81966 | 0.283328 | ||||||||
\(970\) | 2.67376 | 0.0858493 | ||||||||
\(971\) | −28.2492 | −0.906561 | −0.453280 | − | 0.891368i | \(-0.649746\pi\) | ||||
−0.453280 | + | 0.891368i | \(0.649746\pi\) | |||||||
\(972\) | 7.31308 | 0.234567 | ||||||||
\(973\) | 11.9443 | 0.382916 | ||||||||
\(974\) | −12.4508 | −0.398951 | ||||||||
\(975\) | 8.00000 | 0.256205 | ||||||||
\(976\) | 23.9656 | 0.767119 | ||||||||
\(977\) | −10.8197 | −0.346152 | −0.173076 | − | 0.984909i | \(-0.555371\pi\) | ||||
−0.173076 | + | 0.984909i | \(0.555371\pi\) | |||||||
\(978\) | 5.38197 | 0.172096 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.85410 | −0.0592271 | ||||||||
\(981\) | −0.583592 | −0.0186327 | ||||||||
\(982\) | −8.45898 | −0.269937 | ||||||||
\(983\) | −12.3820 | −0.394923 | −0.197462 | − | 0.980311i | \(-0.563270\pi\) | ||||
−0.197462 | + | 0.980311i | \(0.563270\pi\) | |||||||
\(984\) | 26.6312 | 0.848971 | ||||||||
\(985\) | 4.29180 | 0.136748 | ||||||||
\(986\) | −5.45085 | −0.173590 | ||||||||
\(987\) | −10.7082 | −0.340846 | ||||||||
\(988\) | −4.04257 | −0.128611 | ||||||||
\(989\) | 63.9443 | 2.03331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.729490 | −0.0231730 | −0.0115865 | − | 0.999933i | \(-0.503688\pi\) | ||||
−0.0115865 | + | 0.999933i | \(0.503688\pi\) | |||||||
\(992\) | −17.5623 | −0.557604 | ||||||||
\(993\) | −10.0000 | −0.317340 | ||||||||
\(994\) | 6.14590 | 0.194936 | ||||||||
\(995\) | −8.23607 | −0.261101 | ||||||||
\(996\) | −8.12461 | −0.257438 | ||||||||
\(997\) | 55.8673 | 1.76933 | 0.884667 | − | 0.466224i | \(-0.154386\pi\) | ||||
0.884667 | + | 0.466224i | \(0.154386\pi\) | |||||||
\(998\) | −3.85410 | −0.121999 | ||||||||
\(999\) | 35.4164 | 1.12053 |
(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 | 847.2.a.h.1.1 | yes | 2 | |
3.2 | odd | 2 | 7623.2.a.t.1.2 | 2 | |||
7.6 | odd | 2 | 5929.2.a.s.1.1 | 2 | |||
11.2 | odd | 10 | 847.2.f.d.323.1 | 4 | |||
11.3 | even | 5 | 847.2.f.c.372.1 | 4 | |||
11.4 | even | 5 | 847.2.f.c.148.1 | 4 | |||
11.5 | even | 5 | 847.2.f.j.729.1 | 4 | |||
11.6 | odd | 10 | 847.2.f.d.729.1 | 4 | |||
11.7 | odd | 10 | 847.2.f.l.148.1 | 4 | |||
11.8 | odd | 10 | 847.2.f.l.372.1 | 4 | |||
11.9 | even | 5 | 847.2.f.j.323.1 | 4 | |||
11.10 | odd | 2 | 847.2.a.d.1.2 | ✓ | 2 | ||
33.32 | even | 2 | 7623.2.a.bx.1.1 | 2 | |||
77.76 | even | 2 | 5929.2.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.d.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
847.2.a.h.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
847.2.f.c.148.1 | 4 | 11.4 | even | 5 | |||
847.2.f.c.372.1 | 4 | 11.3 | even | 5 | |||
847.2.f.d.323.1 | 4 | 11.2 | odd | 10 | |||
847.2.f.d.729.1 | 4 | 11.6 | odd | 10 | |||
847.2.f.j.323.1 | 4 | 11.9 | even | 5 | |||
847.2.f.j.729.1 | 4 | 11.5 | even | 5 | |||
847.2.f.l.148.1 | 4 | 11.7 | odd | 10 | |||
847.2.f.l.372.1 | 4 | 11.8 | odd | 10 | |||
5929.2.a.i.1.2 | 2 | 77.76 | even | 2 | |||
5929.2.a.s.1.1 | 2 | 7.6 | odd | 2 | |||
7623.2.a.t.1.2 | 2 | 3.2 | odd | 2 | |||
7623.2.a.bx.1.1 | 2 | 33.32 | even | 2 |