Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
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: | no (minimal twist has level 847) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 | \(0.456882\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.381966 | −0.120788 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23607 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | 0 | ||||||||
\(19\) | −1.76393 | −0.404674 | −0.202337 | − | 0.979316i | \(-0.564854\pi\) | ||||
−0.202337 | + | 0.979316i | \(0.564854\pi\) | |||||||
\(20\) | 1.85410 | 0.414590 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.09017 | −1.06137 | −0.530687 | − | 0.847568i | \(-0.678066\pi\) | ||||
−0.530687 | + | 0.847568i | \(0.678066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −0.472136 | −0.0925935 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −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 | 0 | ||||||||
\(31\) | −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 | 0 | ||||||||
\(37\) | 6.47214 | 1.06401 | 0.532006 | − | 0.846740i | \(-0.321438\pi\) | ||||
0.532006 | + | 0.846740i | \(0.321438\pi\) | |||||||
\(38\) | −0.673762 | −0.109299 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | 0 | ||||||||
\(43\) | −12.5623 | −1.91573 | −0.957867 | − | 0.287213i | \(-0.907271\pi\) | ||||
−0.957867 | + | 0.287213i | \(0.907271\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.94427 | −0.286667 | ||||||||
\(47\) | 6.61803 | 0.965339 | 0.482670 | − | 0.875802i | \(-0.339667\pi\) | ||||
0.482670 | + | 0.875802i | \(0.339667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.52786 | −0.216073 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.29180 | 0.317815 | ||||||||
\(53\) | 2.38197 | 0.327188 | 0.163594 | − | 0.986528i | \(-0.447691\pi\) | ||||
0.163594 | + | 0.986528i | \(0.447691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.47214 | −0.196722 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.76393 | 0.231616 | ||||||||
\(59\) | −11.0902 | −1.44382 | −0.721909 | − | 0.691988i | \(-0.756735\pi\) | ||||
−0.721909 | + | 0.691988i | \(0.756735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.61803 | −0.975389 | −0.487695 | − | 0.873014i | \(-0.662162\pi\) | ||||
−0.487695 | + | 0.873014i | \(0.662162\pi\) | |||||||
\(62\) | −1.61803 | −0.205491 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.381966 | −0.0456537 | ||||||||
\(71\) | 16.0902 | 1.90955 | 0.954776 | − | 0.297326i | \(-0.0960949\pi\) | ||||
0.954776 | + | 0.297326i | \(0.0960949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.2361 | −1.66621 | −0.833103 | − | 0.553118i | \(-0.813438\pi\) | ||||
−0.833103 | + | 0.553118i | \(0.813438\pi\) | |||||||
\(74\) | 2.47214 | 0.287380 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.27051 | 0.375153 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.38197 | 0.718027 | 0.359014 | − | 0.933332i | \(-0.383113\pi\) | ||||
0.359014 | + | 0.933332i | \(0.383113\pi\) | |||||||
\(80\) | −3.14590 | −0.351722 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.27051 | 0.471599 | ||||||||
\(83\) | −2.70820 | −0.297264 | −0.148632 | − | 0.988893i | \(-0.547487\pi\) | ||||
−0.148632 | + | 0.988893i | \(0.547487\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.09017 | 0.335176 | ||||||||
\(86\) | −4.79837 | −0.517422 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.85410 | −0.726533 | −0.363267 | − | 0.931685i | \(-0.618339\pi\) | ||||
−0.363267 | + | 0.931685i | \(0.618339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23607 | −0.129575 | ||||||||
\(92\) | 9.43769 | 0.983948 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.52786 | 0.260729 | ||||||||
\(95\) | 1.76393 | 0.180976 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 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 | \(0.236596\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.85410 | 0.872421 | 0.436210 | − | 0.899845i | \(-0.356320\pi\) | ||||
0.436210 | + | 0.899845i | \(0.356320\pi\) | |||||||
\(104\) | 1.81966 | 0.178432 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.909830 | 0.0883705 | ||||||||
\(107\) | −2.70820 | −0.261812 | −0.130906 | − | 0.991395i | \(-0.541789\pi\) | ||||
−0.130906 | + | 0.991395i | \(0.541789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.52786 | −0.146343 | −0.0731714 | − | 0.997319i | \(-0.523312\pi\) | ||||
−0.0731714 | + | 0.997319i | \(0.523312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.14590 | 0.297259 | ||||||||
\(113\) | −0.145898 | −0.0137249 | −0.00686247 | − | 0.999976i | \(-0.502184\pi\) | ||||
−0.00686247 | + | 0.999976i | \(0.502184\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.09017 | 0.474661 | ||||||||
\(116\) | −8.56231 | −0.794990 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.23607 | −0.389962 | ||||||||
\(119\) | −3.09017 | −0.283275 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.90983 | −0.263444 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.85410 | 0.705319 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.94427 | 0.261262 | 0.130631 | − | 0.991431i | \(-0.458300\pi\) | ||||
0.130631 | + | 0.991431i | \(0.458300\pi\) | |||||||
\(128\) | −10.0902 | −0.891853 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.54915 | 0.390086 | ||||||||
\(137\) | 15.3262 | 1.30941 | 0.654704 | − | 0.755885i | \(-0.272793\pi\) | ||||
0.654704 | + | 0.755885i | \(0.272793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9443 | 1.01310 | 0.506550 | − | 0.862211i | \(-0.330921\pi\) | ||||
0.506550 | + | 0.862211i | \(0.330921\pi\) | |||||||
\(140\) | 1.85410 | 0.156700 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.14590 | 0.515752 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.61803 | −0.383507 | ||||||||
\(146\) | −5.43769 | −0.450027 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.0000 | −0.986394 | ||||||||
\(149\) | 8.85410 | 0.725356 | 0.362678 | − | 0.931914i | \(-0.381862\pi\) | ||||
0.362678 | + | 0.931914i | \(0.381862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0557281 | 0.00453509 | 0.00226754 | − | 0.999997i | \(-0.499278\pi\) | ||||
0.00226754 | + | 0.999997i | \(0.499278\pi\) | |||||||
\(152\) | 2.59675 | 0.210624 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.23607 | 0.340249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.8885 | 1.58728 | 0.793639 | − | 0.608389i | \(-0.208184\pi\) | ||||
0.793639 | + | 0.608389i | \(0.208184\pi\) | |||||||
\(158\) | 2.43769 | 0.193933 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.14590 | −0.327762 | ||||||||
\(161\) | −5.09017 | −0.401162 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −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 | \(0.580567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 1.18034 | 0.0905279 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 23.2918 | 1.77598 | ||||||||
\(173\) | 15.3820 | 1.16947 | 0.584735 | − | 0.811225i | \(-0.301199\pi\) | ||||
0.584735 | + | 0.811225i | \(0.301199\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.61803 | −0.196230 | ||||||||
\(179\) | 3.76393 | 0.281329 | 0.140665 | − | 0.990057i | \(-0.455076\pi\) | ||||
0.140665 | + | 0.990057i | \(0.455076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.41641 | −0.551257 | −0.275629 | − | 0.961264i | \(-0.588886\pi\) | ||||
−0.275629 | + | 0.961264i | \(0.588886\pi\) | |||||||
\(182\) | −0.472136 | −0.0349970 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.49342 | 0.552422 | ||||||||
\(185\) | −6.47214 | −0.475841 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.2705 | −0.894919 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.673762 | 0.0488798 | ||||||||
\(191\) | −15.7639 | −1.14064 | −0.570319 | − | 0.821423i | \(-0.693180\pi\) | ||||
−0.570319 | + | 0.821423i | \(0.693180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.3262 | −1.10321 | −0.551603 | − | 0.834107i | \(-0.685984\pi\) | ||||
−0.551603 | + | 0.834107i | \(0.685984\pi\) | |||||||
\(194\) | 2.67376 | 0.191965 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −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 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.65248 | 0.397707 | ||||||||
\(203\) | 4.61803 | 0.324122 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1803 | −0.780869 | ||||||||
\(206\) | 3.38197 | 0.235633 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.88854 | −0.269622 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6180 | 1.07519 | 0.537595 | − | 0.843203i | \(-0.319333\pi\) | ||||
0.537595 | + | 0.843203i | \(0.319333\pi\) | |||||||
\(212\) | −4.41641 | −0.303320 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.03444 | −0.0707130 | ||||||||
\(215\) | 12.5623 | 0.856742 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.23607 | −0.287563 | ||||||||
\(218\) | −0.583592 | −0.0395258 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.81966 | 0.256938 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.03444 | 0.136236 | 0.0681182 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681182 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(224\) | 4.14590 | 0.277009 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.0557281 | −0.00370698 | ||||||||
\(227\) | 16.0344 | 1.06424 | 0.532122 | − | 0.846668i | \(-0.321395\pi\) | ||||
0.532122 | + | 0.846668i | \(0.321395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | 0 | ||||||||
\(235\) | −6.61803 | −0.431713 | ||||||||
\(236\) | 20.5623 | 1.33849 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.18034 | −0.0765101 | ||||||||
\(239\) | 17.0902 | 1.10547 | 0.552736 | − | 0.833357i | \(-0.313584\pi\) | ||||
0.552736 | + | 0.833357i | \(0.313584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2705 | 1.04808 | 0.524038 | − | 0.851695i | \(-0.324425\pi\) | ||||
0.524038 | + | 0.851695i | \(0.324425\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.1246 | 0.904236 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.18034 | 0.138732 | ||||||||
\(248\) | 6.23607 | 0.395991 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.43769 | 0.217419 | ||||||||
\(251\) | −23.0000 | −1.45175 | −0.725874 | − | 0.687828i | \(-0.758564\pi\) | ||||
−0.725874 | + | 0.687828i | \(0.758564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.12461 | 0.0705644 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | 8.56231 | 0.534102 | 0.267051 | − | 0.963682i | \(-0.413951\pi\) | ||||
0.267051 | + | 0.963682i | \(0.413951\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.47214 | 0.402159 | ||||||||
\(260\) | −2.29180 | −0.142131 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.4377 | 0.943007 | ||||||||
\(269\) | −16.8541 | −1.02761 | −0.513806 | − | 0.857906i | \(-0.671765\pi\) | ||||
−0.513806 | + | 0.857906i | \(0.671765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.79837 | −0.291480 | −0.145740 | − | 0.989323i | \(-0.546556\pi\) | ||||
−0.145740 | + | 0.989323i | \(0.546556\pi\) | |||||||
\(272\) | −9.72136 | −0.589444 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.85410 | 0.353659 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0344 | 1.38401 | 0.692003 | − | 0.721895i | \(-0.256729\pi\) | ||||
0.692003 | + | 0.721895i | \(0.256729\pi\) | |||||||
\(278\) | 4.56231 | 0.273629 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.47214 | 0.0879770 | ||||||||
\(281\) | 25.1803 | 1.50213 | 0.751067 | − | 0.660226i | \(-0.229540\pi\) | ||||
0.751067 | + | 0.660226i | \(0.229540\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9443 | 0.710013 | 0.355007 | − | 0.934864i | \(-0.384479\pi\) | ||||
0.355007 | + | 0.934864i | \(0.384479\pi\) | |||||||
\(284\) | −29.8328 | −1.77025 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.1803 | 0.659955 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.45085 | −0.438285 | ||||||||
\(290\) | −1.76393 | −0.103582 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | 0 | ||||||||
\(295\) | 11.0902 | 0.645695 | ||||||||
\(296\) | −9.52786 | −0.553796 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.38197 | 0.195912 | ||||||||
\(299\) | 6.29180 | 0.363864 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5623 | −0.724079 | ||||||||
\(302\) | 0.0212862 | 0.00122489 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.54915 | −0.318266 | ||||||||
\(305\) | 7.61803 | 0.436207 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.1803 | −1.32297 | −0.661486 | − | 0.749958i | \(-0.730074\pi\) | ||||
−0.661486 | + | 0.749958i | \(0.730074\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.61803 | 0.0918982 | ||||||||
\(311\) | −9.00000 | −0.510343 | −0.255172 | − | 0.966896i | \(-0.582132\pi\) | ||||
−0.255172 | + | 0.966896i | \(0.582132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 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 | 0 | ||||||||
\(316\) | −11.8328 | −0.665648 | ||||||||
\(317\) | 4.43769 | 0.249246 | 0.124623 | − | 0.992204i | \(-0.460228\pi\) | ||||
0.124623 | + | 0.992204i | \(0.460228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.70820 | 0.263197 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.94427 | −0.108350 | ||||||||
\(323\) | 5.45085 | 0.303293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.94427 | 0.274259 | ||||||||
\(326\) | −3.32624 | −0.184223 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.47214 | −0.135269 | ||||||||
\(335\) | 8.32624 | 0.454911 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.9443 | 1.41327 | 0.706637 | − | 0.707576i | \(-0.250211\pi\) | ||||
0.706637 | + | 0.707576i | \(0.250211\pi\) | |||||||
\(338\) | −4.38197 | −0.238348 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.72949 | −0.310725 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 18.4934 | 0.997099 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.87539 | 0.315863 | ||||||||
\(347\) | −2.34752 | −0.126022 | −0.0630108 | − | 0.998013i | \(-0.520070\pi\) | ||||
−0.0630108 | + | 0.998013i | \(0.520070\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.7984 | 1.75566 | 0.877828 | − | 0.478975i | \(-0.158992\pi\) | ||||
0.877828 | + | 0.478975i | \(0.158992\pi\) | |||||||
\(350\) | −1.52786 | −0.0816678 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.0902 | −1.28219 | −0.641095 | − | 0.767461i | \(-0.721520\pi\) | ||||
−0.641095 | + | 0.767461i | \(0.721520\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0902 | −0.853978 | ||||||||
\(356\) | 12.7082 | 0.673533 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | 0 | ||||||||
\(361\) | −15.8885 | −0.836239 | ||||||||
\(362\) | −2.83282 | −0.148889 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.29180 | 0.120123 | ||||||||
\(365\) | 14.2361 | 0.745150 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.8328 | 1.71386 | 0.856930 | − | 0.515434i | \(-0.172369\pi\) | ||||
0.856930 | + | 0.515434i | \(0.172369\pi\) | |||||||
\(368\) | −16.0132 | −0.834743 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.47214 | −0.128520 | ||||||||
\(371\) | 2.38197 | 0.123666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.4377 | −0.799334 | −0.399667 | − | 0.916661i | \(-0.630874\pi\) | ||||
−0.399667 | + | 0.916661i | \(0.630874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.74265 | −0.502439 | ||||||||
\(377\) | −5.70820 | −0.293987 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0689 | 1.64727 | 0.823634 | − | 0.567122i | \(-0.191943\pi\) | ||||
0.823634 | + | 0.567122i | \(0.191943\pi\) | |||||||
\(380\) | −3.27051 | −0.167774 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.02129 | −0.308076 | ||||||||
\(383\) | 34.5967 | 1.76781 | 0.883906 | − | 0.467665i | \(-0.154905\pi\) | ||||
0.883906 | + | 0.467665i | \(0.154905\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.85410 | −0.297966 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.9787 | −0.658894 | ||||||||
\(389\) | 34.1803 | 1.73301 | 0.866506 | − | 0.499167i | \(-0.166360\pi\) | ||||
0.866506 | + | 0.499167i | \(0.166360\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.7295 | 0.795475 | ||||||||
\(392\) | −1.47214 | −0.0743541 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.5836 | −0.629180 | ||||||||
\(401\) | 17.5279 | 0.875300 | 0.437650 | − | 0.899145i | \(-0.355811\pi\) | ||||
0.437650 | + | 0.899145i | \(0.355811\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.23607 | 0.260827 | ||||||||
\(404\) | −27.4377 | −1.36508 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.76393 | 0.0875425 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.7082 | −0.875614 | −0.437807 | − | 0.899069i | \(-0.644245\pi\) | ||||
−0.437807 | + | 0.899069i | \(0.644245\pi\) | |||||||
\(410\) | −4.27051 | −0.210905 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.4164 | −0.808778 | ||||||||
\(413\) | −11.0902 | −0.545712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.70820 | 0.132941 | ||||||||
\(416\) | −5.12461 | −0.251255 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.8885 | −1.46015 | −0.730075 | − | 0.683367i | \(-0.760515\pi\) | ||||
−0.730075 | + | 0.683367i | \(0.760515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.763932 | 0.0372318 | 0.0186159 | − | 0.999827i | \(-0.494074\pi\) | ||||
0.0186159 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(422\) | 5.96556 | 0.290399 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.50658 | −0.170294 | ||||||||
\(425\) | 12.3607 | 0.599581 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −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 | \(0.391715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.96556 | −0.430857 | −0.215429 | − | 0.976520i | \(-0.569115\pi\) | ||||
−0.215429 | + | 0.976520i | \(0.569115\pi\) | |||||||
\(434\) | −1.61803 | −0.0776681 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.83282 | 0.135667 | ||||||||
\(437\) | 8.97871 | 0.429510 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.38197 | 0.161412 | 0.0807062 | − | 0.996738i | \(-0.474282\pi\) | ||||
0.0807062 | + | 0.996738i | \(0.474282\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.45898 | 0.0693966 | ||||||||
\(443\) | −3.09017 | −0.146818 | −0.0734092 | − | 0.997302i | \(-0.523388\pi\) | ||||
−0.0734092 | + | 0.997302i | \(0.523388\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.85410 | 0.324916 | ||||||||
\(446\) | 0.777088 | 0.0367962 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.70820 | −0.222442 | ||||||||
\(449\) | −12.3262 | −0.581711 | −0.290856 | − | 0.956767i | \(-0.593940\pi\) | ||||
−0.290856 | + | 0.956767i | \(0.593940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.270510 | 0.0127237 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.12461 | 0.287442 | ||||||||
\(455\) | 1.23607 | 0.0579478 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.145898 | −0.00682482 | −0.00341241 | − | 0.999994i | \(-0.501086\pi\) | ||||
−0.00341241 | + | 0.999994i | \(0.501086\pi\) | |||||||
\(458\) | 2.58359 | 0.120723 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.2361 | 0.520501 | ||||||||
\(467\) | 4.50658 | 0.208540 | 0.104270 | − | 0.994549i | \(-0.466749\pi\) | ||||
0.104270 | + | 0.994549i | \(0.466749\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.32624 | −0.384470 | ||||||||
\(470\) | −2.52786 | −0.116602 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.3262 | 0.751476 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.05573 | 0.323739 | ||||||||
\(476\) | 5.72949 | 0.262611 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.52786 | 0.298578 | ||||||||
\(479\) | −21.7639 | −0.994419 | −0.497210 | − | 0.867630i | \(-0.665642\pi\) | ||||
−0.497210 | + | 0.867630i | \(0.665642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 6.21478 | 0.283076 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.00000 | −0.317854 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.5967 | −1.47710 | −0.738550 | − | 0.674199i | \(-0.764489\pi\) | ||||
−0.738550 | + | 0.674199i | \(0.764489\pi\) | |||||||
\(488\) | 11.2148 | 0.507669 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.381966 | −0.0172555 | ||||||||
\(491\) | −22.1459 | −0.999430 | −0.499715 | − | 0.866190i | \(-0.666562\pi\) | ||||
−0.499715 | + | 0.866190i | \(0.666562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2705 | −0.642711 | ||||||||
\(494\) | 0.832816 | 0.0374702 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.3262 | −0.598366 | ||||||||
\(497\) | 16.0902 | 0.721743 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0902 | −0.451698 | −0.225849 | − | 0.974162i | \(-0.572516\pi\) | ||||
−0.225849 | + | 0.974162i | \(0.572516\pi\) | |||||||
\(500\) | −16.6869 | −0.746262 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −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 | 0 | ||||||||
\(505\) | −14.7984 | −0.658519 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.45898 | −0.242203 | ||||||||
\(509\) | 10.7426 | 0.476159 | 0.238080 | − | 0.971246i | \(-0.423482\pi\) | ||||
0.238080 | + | 0.971246i | \(0.423482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.2361 | −0.629767 | ||||||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.27051 | 0.144256 | ||||||||
\(515\) | −8.85410 | −0.390158 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.47214 | 0.108619 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.81966 | −0.0797974 | ||||||||
\(521\) | 12.2361 | 0.536072 | 0.268036 | − | 0.963409i | \(-0.413625\pi\) | ||||
0.268036 | + | 0.963409i | \(0.413625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5623 | 0.724219 | 0.362110 | − | 0.932136i | \(-0.382057\pi\) | ||||
0.362110 | + | 0.932136i | \(0.382057\pi\) | |||||||
\(524\) | 35.1246 | 1.53443 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.54102 | 0.285202 | ||||||||
\(527\) | 13.0902 | 0.570217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.90983 | 0.126514 | ||||||||
\(530\) | −0.909830 | −0.0395205 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.27051 | 0.141795 | ||||||||
\(533\) | −13.8197 | −0.598596 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.70820 | 0.117086 | ||||||||
\(536\) | 12.2574 | 0.529437 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.43769 | −0.277549 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.708204 | 0.0304481 | 0.0152240 | − | 0.999884i | \(-0.495154\pi\) | ||||
0.0152240 | + | 0.999884i | \(0.495154\pi\) | |||||||
\(542\) | −1.83282 | −0.0787262 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.8115 | −0.549290 | ||||||||
\(545\) | 1.52786 | 0.0654465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.72949 | −0.0739477 | −0.0369738 | − | 0.999316i | \(-0.511772\pi\) | ||||
−0.0369738 | + | 0.999316i | \(0.511772\pi\) | |||||||
\(548\) | −28.4164 | −1.21389 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.14590 | −0.347027 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.38197 | 0.271389 | ||||||||
\(554\) | 8.79837 | 0.373807 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −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 | 0 | ||||||||
\(559\) | 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 | \(0.264630\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.145898 | 0.00613798 | ||||||||
\(566\) | 4.56231 | 0.191768 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23.6869 | −0.993881 | ||||||||
\(569\) | −37.3050 | −1.56390 | −0.781952 | − | 0.623338i | \(-0.785776\pi\) | ||||
−0.781952 | + | 0.623338i | \(0.785776\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.3050 | 1.43562 | 0.717809 | − | 0.696240i | \(-0.245145\pi\) | ||||
0.717809 | + | 0.696240i | \(0.245145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.27051 | 0.178248 | ||||||||
\(575\) | 20.3607 | 0.849099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.65248 | 0.401838 | 0.200919 | − | 0.979608i | \(-0.435607\pi\) | ||||
0.200919 | + | 0.979608i | \(0.435607\pi\) | |||||||
\(578\) | −2.84597 | −0.118377 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.56231 | 0.355530 | ||||||||
\(581\) | −2.70820 | −0.112355 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 20.9574 | 0.867225 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.20163 | 0.173568 | ||||||||
\(587\) | −1.00000 | −0.0412744 | −0.0206372 | − | 0.999787i | \(-0.506569\pi\) | ||||
−0.0206372 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.47214 | 0.307884 | ||||||||
\(590\) | 4.23607 | 0.174396 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.40325 | 0.0982763 | ||||||||
\(599\) | 16.0000 | 0.653742 | 0.326871 | − | 0.945069i | \(-0.394006\pi\) | ||||
0.326871 | + | 0.945069i | \(0.394006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.7082 | 0.559169 | 0.279585 | − | 0.960121i | \(-0.409803\pi\) | ||||
0.279585 | + | 0.960121i | \(0.409803\pi\) | |||||||
\(602\) | −4.79837 | −0.195567 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.103326 | −0.00420426 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.2016 | 0.819959 | 0.409979 | − | 0.912095i | \(-0.365536\pi\) | ||||
0.409979 | + | 0.912095i | \(0.365536\pi\) | |||||||
\(608\) | −7.31308 | −0.296585 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.90983 | 0.117816 | ||||||||
\(611\) | −8.18034 | −0.330941 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.888544 | −0.0358879 | −0.0179440 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179440 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(614\) | −8.85410 | −0.357322 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.41641 | −0.379090 | −0.189545 | − | 0.981872i | \(-0.560701\pi\) | ||||
−0.189545 | + | 0.981872i | \(0.560701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.7082 | −1.59601 | −0.798004 | − | 0.602653i | \(-0.794111\pi\) | ||||
−0.798004 | + | 0.602653i | \(0.794111\pi\) | |||||||
\(620\) | −7.85410 | −0.315428 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.43769 | −0.137839 | ||||||||
\(623\) | −6.85410 | −0.274604 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 7.00000 | 0.279776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.8754 | −1.47149 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8328 | 0.709913 | 0.354957 | − | 0.934883i | \(-0.384496\pi\) | ||||
0.354957 | + | 0.934883i | \(0.384496\pi\) | |||||||
\(632\) | −9.39512 | −0.373718 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.69505 | 0.0673190 | ||||||||
\(635\) | −2.94427 | −0.116840 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.23607 | −0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.0902 | 0.398849 | ||||||||
\(641\) | −31.6525 | −1.25020 | −0.625099 | − | 0.780546i | \(-0.714941\pi\) | ||||
−0.625099 | + | 0.780546i | \(0.714941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.58359 | 0.0624508 | 0.0312254 | − | 0.999512i | \(-0.490059\pi\) | ||||
0.0312254 | + | 0.999512i | \(0.490059\pi\) | |||||||
\(644\) | 9.43769 | 0.371897 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.08204 | 0.0819167 | ||||||||
\(647\) | −6.18034 | −0.242974 | −0.121487 | − | 0.992593i | \(-0.538766\pi\) | ||||
−0.121487 | + | 0.992593i | \(0.538766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.88854 | 0.0740748 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.1459 | 0.632322 | ||||||||
\(653\) | −18.2361 | −0.713632 | −0.356816 | − | 0.934175i | \(-0.616138\pi\) | ||||
−0.356816 | + | 0.934175i | \(0.616138\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.9443 | 0.740214 | ||||||||
\(656\) | 35.1722 | 1.37324 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.98684 | 0.154720 | ||||||||
\(665\) | 1.76393 | 0.0684023 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.5066 | −0.910178 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.18034 | 0.122867 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.58359 | −0.253779 | −0.126889 | − | 0.991917i | \(-0.540499\pi\) | ||||
−0.126889 | + | 0.991917i | \(0.540499\pi\) | |||||||
\(674\) | 9.90983 | 0.381712 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | 0 | ||||||||
\(679\) | 7.00000 | 0.268635 | ||||||||
\(680\) | −4.54915 | −0.174452 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.493422 | −0.0188803 | −0.00944014 | − | 0.999955i | \(-0.503005\pi\) | ||||
−0.00944014 | + | 0.999955i | \(0.503005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.3262 | −0.585585 | ||||||||
\(686\) | 0.381966 | 0.0145835 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −39.5197 | −1.50668 | ||||||||
\(689\) | −2.94427 | −0.112168 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 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 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.5492 | −1.30864 | ||||||||
\(698\) | 12.5279 | 0.474187 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.41641 | 0.280314 | ||||||||
\(701\) | −18.5066 | −0.698984 | −0.349492 | − | 0.936939i | \(-0.613646\pi\) | ||||
−0.349492 | + | 0.936939i | \(0.613646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4164 | −0.430578 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.20163 | −0.346308 | ||||||||
\(707\) | 14.7984 | 0.556550 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.03444 | −0.264184 | −0.132092 | − | 0.991237i | \(-0.542169\pi\) | ||||
−0.132092 | + | 0.991237i | \(0.542169\pi\) | |||||||
\(710\) | −6.14590 | −0.230651 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0902 | 0.378145 | ||||||||
\(713\) | 21.5623 | 0.807515 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.97871 | −0.260807 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.96556 | 0.222633 | ||||||||
\(719\) | 2.88854 | 0.107725 | 0.0538623 | − | 0.998548i | \(-0.482847\pi\) | ||||
0.0538623 | + | 0.998548i | \(0.482847\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.85410 | 0.329744 | ||||||||
\(722\) | −6.06888 | −0.225860 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.43769 | 0.201258 | ||||||||
\(731\) | 38.8197 | 1.43580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.9443 | 1.95554 | 0.977771 | − | 0.209677i | \(-0.0672413\pi\) | ||||
0.977771 | + | 0.209677i | \(0.0672413\pi\) | |||||||
\(734\) | 12.5410 | 0.462897 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.1033 | −0.777879 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.3820 | −0.418692 | −0.209346 | − | 0.977842i | \(-0.567134\pi\) | ||||
−0.209346 | + | 0.977842i | \(0.567134\pi\) | |||||||
\(740\) | 12.0000 | 0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.909830 | 0.0334009 | ||||||||
\(743\) | 14.9098 | 0.546989 | 0.273494 | − | 0.961874i | \(-0.411821\pi\) | ||||
0.273494 | + | 0.961874i | \(0.411821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.85410 | −0.324389 | ||||||||
\(746\) | −5.89667 | −0.215893 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.70820 | −0.0989556 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.3050 | 1.50724 | 0.753620 | − | 0.657311i | \(-0.228306\pi\) | ||||
0.753620 | + | 0.657311i | \(0.228306\pi\) | |||||||
\(752\) | 20.8197 | 0.759215 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.18034 | −0.0794033 | ||||||||
\(755\) | −0.0557281 | −0.00202815 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −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 | \(0.589473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.52786 | −0.0553124 | ||||||||
\(764\) | 29.2279 | 1.05743 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.2148 | 0.477469 | ||||||||
\(767\) | 13.7082 | 0.494975 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.5623 | 1.75120 | 0.875601 | − | 0.483035i | \(-0.160466\pi\) | ||||
0.875601 | + | 0.483035i | \(0.160466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.4164 | 1.02273 | ||||||||
\(773\) | −40.2361 | −1.44719 | −0.723595 | − | 0.690224i | \(-0.757512\pi\) | ||||
−0.723595 | + | 0.690224i | \(0.757512\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.9443 | 0.608656 | ||||||||
\(776\) | −10.3050 | −0.369926 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.0557 | 0.468071 | ||||||||
\(779\) | −19.7214 | −0.706591 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.00813 | 0.214850 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.14590 | 0.112354 | ||||||||
\(785\) | −19.8885 | −0.709853 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5623 | 0.732967 | 0.366484 | − | 0.930425i | \(-0.380562\pi\) | ||||
0.366484 | + | 0.930425i | \(0.380562\pi\) | |||||||
\(788\) | −7.95743 | −0.283472 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.43769 | −0.0867293 | ||||||||
\(791\) | −0.145898 | −0.00518754 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.41641 | 0.334386 | ||||||||
\(794\) | −0.313082 | −0.0111109 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.2705 | 0.541249 | ||||||||
\(797\) | −32.2361 | −1.14186 | −0.570930 | − | 0.820999i | \(-0.693417\pi\) | ||||
−0.570930 | + | 0.820999i | \(0.693417\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.4508 | −0.723499 | ||||||||
\(800\) | −16.5836 | −0.586319 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.69505 | 0.236410 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.09017 | 0.179405 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.7852 | −0.766401 | ||||||||
\(809\) | −32.5066 | −1.14287 | −0.571435 | − | 0.820647i | \(-0.693613\pi\) | ||||
−0.571435 | + | 0.820647i | \(0.693613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.16718 | 0.0409854 | 0.0204927 | − | 0.999790i | \(-0.493477\pi\) | ||||
0.0204927 | + | 0.999790i | \(0.493477\pi\) | |||||||
\(812\) | −8.56231 | −0.300478 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.70820 | 0.305035 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.1591 | 0.775247 | ||||||||
\(818\) | −6.76393 | −0.236495 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.7295 | 0.723905 | ||||||||
\(821\) | −56.6656 | −1.97764 | −0.988822 | − | 0.149100i | \(-0.952362\pi\) | ||||
−0.988822 | + | 0.149100i | \(0.952362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −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 | \(0.389328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.9787 | −1.66637 | −0.833185 | − | 0.552995i | \(-0.813485\pi\) | ||||
−0.833185 | + | 0.552995i | \(0.813485\pi\) | |||||||
\(830\) | 1.03444 | 0.0359060 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.81966 | 0.201760 | ||||||||
\(833\) | −3.09017 | −0.107068 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.47214 | 0.223978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.4164 | −0.394373 | ||||||||
\(839\) | −30.5967 | −1.05632 | −0.528159 | − | 0.849146i | \(-0.677117\pi\) | ||||
−0.528159 | + | 0.849146i | \(0.677117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.67376 | −0.264612 | ||||||||
\(842\) | 0.291796 | 0.0100560 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.9574 | −0.996756 | ||||||||
\(845\) | 11.4721 | 0.394653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.49342 | 0.257325 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.72136 | 0.161941 | ||||||||
\(851\) | −32.9443 | −1.12932 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.9098 | −1.19529 | −0.597645 | − | 0.801761i | \(-0.703897\pi\) | ||||
−0.597645 | + | 0.801761i | \(0.703897\pi\) | |||||||
\(854\) | −2.90983 | −0.0995723 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.29180 | 0.180239 | ||||||||
\(863\) | 47.9443 | 1.63204 | 0.816021 | − | 0.578022i | \(-0.196175\pi\) | ||||
0.816021 | + | 0.578022i | \(0.196175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.3820 | −0.523003 | ||||||||
\(866\) | −3.42454 | −0.116371 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.85410 | 0.266586 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.2918 | 0.348724 | ||||||||
\(872\) | 2.24922 | 0.0761683 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.42956 | 0.116007 | ||||||||
\(875\) | 9.00000 | 0.304256 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.0000 | 0.438979 | 0.219489 | − | 0.975615i | \(-0.429561\pi\) | ||||
0.219489 | + | 0.975615i | \(0.429561\pi\) | |||||||
\(878\) | 1.29180 | 0.0435960 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.1459 | −0.476587 | −0.238294 | − | 0.971193i | \(-0.576588\pi\) | ||||
−0.238294 | + | 0.971193i | \(0.576588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.6312 | 1.06447 | 0.532237 | − | 0.846595i | \(-0.321351\pi\) | ||||
0.532237 | + | 0.846595i | \(0.321351\pi\) | |||||||
\(884\) | −7.08204 | −0.238195 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.18034 | −0.0396543 | ||||||||
\(887\) | −57.2148 | −1.92108 | −0.960542 | − | 0.278134i | \(-0.910284\pi\) | ||||
−0.960542 | + | 0.278134i | \(0.910284\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.94427 | 0.0987477 | ||||||||
\(890\) | 2.61803 | 0.0877567 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.77206 | −0.126298 | ||||||||
\(893\) | −11.6738 | −0.390648 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.76393 | −0.125814 | ||||||||
\(896\) | −10.0902 | −0.337089 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.70820 | −0.157115 | ||||||||
\(899\) | −19.5623 | −0.652439 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.36068 | −0.245220 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.214782 | 0.00714353 | ||||||||
\(905\) | 7.41641 | 0.246530 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7639 | −0.523433 | −0.261716 | − | 0.965145i | \(-0.584289\pi\) | ||||
−0.261716 | + | 0.965145i | \(0.584289\pi\) | |||||||
\(908\) | −29.7295 | −0.986608 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.472136 | 0.0156512 | ||||||||
\(911\) | 45.1803 | 1.49689 | 0.748446 | − | 0.663196i | \(-0.230800\pi\) | ||||
0.748446 | + | 0.663196i | \(0.230800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.0557281 | −0.00184332 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.5410 | −0.414367 | ||||||||
\(917\) | −18.9443 | −0.625595 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.8885 | −0.491128 | −0.245564 | − | 0.969380i | \(-0.578973\pi\) | ||||
−0.245564 | + | 0.969380i | \(0.578973\pi\) | |||||||
\(920\) | −7.49342 | −0.247051 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.06888 | 0.232801 | ||||||||
\(923\) | −19.8885 | −0.654639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.8885 | −0.851210 | ||||||||
\(926\) | 8.49342 | 0.279111 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.1459 | 0.628495 | ||||||||
\(929\) | −24.0000 | −0.787414 | −0.393707 | − | 0.919236i | \(-0.628808\pi\) | ||||
−0.393707 | + | 0.919236i | \(0.628808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.76393 | −0.0578105 | ||||||||
\(932\) | −54.5410 | −1.78655 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.72136 | 0.0563246 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.7214 | −1.68966 | −0.844832 | − | 0.535032i | \(-0.820299\pi\) | ||||
−0.844832 | + | 0.535032i | \(0.820299\pi\) | |||||||
\(938\) | −3.18034 | −0.103842 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.2705 | 0.400220 | ||||||||
\(941\) | −27.0689 | −0.882420 | −0.441210 | − | 0.897404i | \(-0.645451\pi\) | ||||
−0.441210 | + | 0.897404i | \(0.645451\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.9098 | −1.85324 | ||||||||
\(944\) | −34.8885 | −1.13553 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.29180 | −0.204456 | −0.102228 | − | 0.994761i | \(-0.532597\pi\) | ||||
−0.102228 | + | 0.994761i | \(0.532597\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.5967 | 0.571215 | ||||||||
\(950\) | 2.69505 | 0.0874389 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | 0 | ||||||||
\(955\) | 15.7639 | 0.510109 | ||||||||
\(956\) | −31.6869 | −1.02483 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.31308 | −0.268583 | ||||||||
\(959\) | 15.3262 | 0.494910 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0557 | −0.421153 | ||||||||
\(962\) | −3.05573 | −0.0985206 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −30.1672 | −0.971620 | ||||||||
\(965\) | 15.3262 | 0.493369 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.4508 | 0.882760 | 0.441380 | − | 0.897320i | \(-0.354489\pi\) | ||||
0.441380 | + | 0.897320i | \(0.354489\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.67376 | −0.0858493 | ||||||||
\(971\) | 28.2492 | 0.906561 | 0.453280 | − | 0.891368i | \(-0.350254\pi\) | ||||
0.453280 | + | 0.891368i | \(0.350254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.9443 | 0.382916 | ||||||||
\(974\) | −12.4508 | −0.398951 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.9656 | −0.767119 | ||||||||
\(977\) | 10.8197 | 0.346152 | 0.173076 | − | 0.984909i | \(-0.444629\pi\) | ||||
0.173076 | + | 0.984909i | \(0.444629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.85410 | 0.0592271 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.45898 | −0.269937 | ||||||||
\(983\) | 12.3820 | 0.394923 | 0.197462 | − | 0.980311i | \(-0.436730\pi\) | ||||
0.197462 | + | 0.980311i | \(0.436730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.29180 | −0.136748 | ||||||||
\(986\) | −5.45085 | −0.173590 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.14590 | 0.194936 | ||||||||
\(995\) | 8.23607 | 0.261101 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.8673 | −1.76933 | −0.884667 | − | 0.466224i | \(-0.845614\pi\) | ||||
−0.884667 | + | 0.466224i | \(0.845614\pi\) | |||||||
\(998\) | −3.85410 | −0.121999 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.bx.1.1 | 2 | ||
3.2 | odd | 2 | 847.2.a.d.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 7623.2.a.t.1.2 | 2 | |||
21.20 | even | 2 | 5929.2.a.i.1.2 | 2 | |||
33.2 | even | 10 | 847.2.f.j.323.1 | 4 | |||
33.5 | odd | 10 | 847.2.f.d.729.1 | 4 | |||
33.8 | even | 10 | 847.2.f.c.372.1 | 4 | |||
33.14 | odd | 10 | 847.2.f.l.372.1 | 4 | |||
33.17 | even | 10 | 847.2.f.j.729.1 | 4 | |||
33.20 | odd | 10 | 847.2.f.d.323.1 | 4 | |||
33.26 | odd | 10 | 847.2.f.l.148.1 | 4 | |||
33.29 | even | 10 | 847.2.f.c.148.1 | 4 | |||
33.32 | even | 2 | 847.2.a.h.1.1 | yes | 2 | ||
231.230 | odd | 2 | 5929.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.d.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
847.2.a.h.1.1 | yes | 2 | 33.32 | even | 2 | ||
847.2.f.c.148.1 | 4 | 33.29 | even | 10 | |||
847.2.f.c.372.1 | 4 | 33.8 | even | 10 | |||
847.2.f.d.323.1 | 4 | 33.20 | odd | 10 | |||
847.2.f.d.729.1 | 4 | 33.5 | odd | 10 | |||
847.2.f.j.323.1 | 4 | 33.2 | even | 10 | |||
847.2.f.j.729.1 | 4 | 33.17 | even | 10 | |||
847.2.f.l.148.1 | 4 | 33.26 | odd | 10 | |||
847.2.f.l.372.1 | 4 | 33.14 | odd | 10 | |||
5929.2.a.i.1.2 | 2 | 21.20 | even | 2 | |||
5929.2.a.s.1.1 | 2 | 231.230 | odd | 2 | |||
7623.2.a.t.1.2 | 2 | 11.10 | odd | 2 | |||
7623.2.a.bx.1.1 | 2 | 1.1 | even | 1 | trivial |