Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6038,2,Mod(1,6038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6038 = 2 \cdot 3019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6038.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2136727404\) |
Analytic rank: | \(2\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6038.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(6\) | −0.381966 | −0.155937 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | −3.61803 | −1.14412 | ||||||||
\(11\) | −4.61803 | −1.39239 | −0.696195 | − | 0.717853i | \(-0.745125\pi\) | ||||
−0.696195 | + | 0.717853i | \(0.745125\pi\) | |||||||
\(12\) | −0.381966 | −0.110264 | ||||||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 1.38197 | 0.356822 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.47214 | 0.357045 | 0.178523 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178523 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(18\) | −2.85410 | −0.672718 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | −3.61803 | −0.809017 | ||||||||
\(21\) | 1.14590 | 0.250055 | ||||||||
\(22\) | −4.61803 | −0.984568 | ||||||||
\(23\) | −7.47214 | −1.55805 | −0.779024 | − | 0.626994i | \(-0.784285\pi\) | ||||
−0.779024 | + | 0.626994i | \(0.784285\pi\) | |||||||
\(24\) | −0.381966 | −0.0779685 | ||||||||
\(25\) | 8.09017 | 1.61803 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | −3.00000 | −0.566947 | ||||||||
\(29\) | −4.76393 | −0.884640 | −0.442320 | − | 0.896857i | \(-0.645844\pi\) | ||||
−0.442320 | + | 0.896857i | \(0.645844\pi\) | |||||||
\(30\) | 1.38197 | 0.252311 | ||||||||
\(31\) | 5.09017 | 0.914222 | 0.457111 | − | 0.889410i | \(-0.348884\pi\) | ||||
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.76393 | 0.307061 | ||||||||
\(34\) | 1.47214 | 0.252469 | ||||||||
\(35\) | 10.8541 | 1.83468 | ||||||||
\(36\) | −2.85410 | −0.475684 | ||||||||
\(37\) | 4.85410 | 0.798009 | 0.399005 | − | 0.916949i | \(-0.369356\pi\) | ||||
0.399005 | + | 0.916949i | \(0.369356\pi\) | |||||||
\(38\) | −3.00000 | −0.486664 | ||||||||
\(39\) | 1.14590 | 0.183491 | ||||||||
\(40\) | −3.61803 | −0.572061 | ||||||||
\(41\) | −11.1803 | −1.74608 | −0.873038 | − | 0.487652i | \(-0.837853\pi\) | ||||
−0.873038 | + | 0.487652i | \(0.837853\pi\) | |||||||
\(42\) | 1.14590 | 0.176816 | ||||||||
\(43\) | −4.76393 | −0.726493 | −0.363246 | − | 0.931693i | \(-0.618332\pi\) | ||||
−0.363246 | + | 0.931693i | \(0.618332\pi\) | |||||||
\(44\) | −4.61803 | −0.696195 | ||||||||
\(45\) | 10.3262 | 1.53934 | ||||||||
\(46\) | −7.47214 | −1.10171 | ||||||||
\(47\) | −8.56231 | −1.24894 | −0.624470 | − | 0.781049i | \(-0.714685\pi\) | ||||
−0.624470 | + | 0.781049i | \(0.714685\pi\) | |||||||
\(48\) | −0.381966 | −0.0551320 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 8.09017 | 1.14412 | ||||||||
\(51\) | −0.562306 | −0.0787386 | ||||||||
\(52\) | −3.00000 | −0.416025 | ||||||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | 16.7082 | 2.25293 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 1.14590 | 0.151778 | ||||||||
\(58\) | −4.76393 | −0.625535 | ||||||||
\(59\) | −14.2361 | −1.85338 | −0.926689 | − | 0.375829i | \(-0.877358\pi\) | ||||
−0.926689 | + | 0.375829i | \(0.877358\pi\) | |||||||
\(60\) | 1.38197 | 0.178411 | ||||||||
\(61\) | −4.61803 | −0.591279 | −0.295639 | − | 0.955300i | \(-0.595533\pi\) | ||||
−0.295639 | + | 0.955300i | \(0.595533\pi\) | |||||||
\(62\) | 5.09017 | 0.646452 | ||||||||
\(63\) | 8.56231 | 1.07875 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.8541 | 1.34629 | ||||||||
\(66\) | 1.76393 | 0.217125 | ||||||||
\(67\) | −4.85410 | −0.593023 | −0.296511 | − | 0.955029i | \(-0.595823\pi\) | ||||
−0.296511 | + | 0.955029i | \(0.595823\pi\) | |||||||
\(68\) | 1.47214 | 0.178523 | ||||||||
\(69\) | 2.85410 | 0.343594 | ||||||||
\(70\) | 10.8541 | 1.29731 | ||||||||
\(71\) | 5.94427 | 0.705455 | 0.352728 | − | 0.935726i | \(-0.385254\pi\) | ||||
0.352728 | + | 0.935726i | \(0.385254\pi\) | |||||||
\(72\) | −2.85410 | −0.336359 | ||||||||
\(73\) | −12.7082 | −1.48738 | −0.743691 | − | 0.668523i | \(-0.766927\pi\) | ||||
−0.743691 | + | 0.668523i | \(0.766927\pi\) | |||||||
\(74\) | 4.85410 | 0.564278 | ||||||||
\(75\) | −3.09017 | −0.356822 | ||||||||
\(76\) | −3.00000 | −0.344124 | ||||||||
\(77\) | 13.8541 | 1.57882 | ||||||||
\(78\) | 1.14590 | 0.129747 | ||||||||
\(79\) | 4.85410 | 0.546129 | 0.273065 | − | 0.961996i | \(-0.411963\pi\) | ||||
0.273065 | + | 0.961996i | \(0.411963\pi\) | |||||||
\(80\) | −3.61803 | −0.404508 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | −11.1803 | −1.23466 | ||||||||
\(83\) | 15.9443 | 1.75011 | 0.875056 | − | 0.484022i | \(-0.160825\pi\) | ||||
0.875056 | + | 0.484022i | \(0.160825\pi\) | |||||||
\(84\) | 1.14590 | 0.125028 | ||||||||
\(85\) | −5.32624 | −0.577712 | ||||||||
\(86\) | −4.76393 | −0.513708 | ||||||||
\(87\) | 1.81966 | 0.195088 | ||||||||
\(88\) | −4.61803 | −0.492284 | ||||||||
\(89\) | 7.79837 | 0.826626 | 0.413313 | − | 0.910589i | \(-0.364372\pi\) | ||||
0.413313 | + | 0.910589i | \(0.364372\pi\) | |||||||
\(90\) | 10.3262 | 1.08848 | ||||||||
\(91\) | 9.00000 | 0.943456 | ||||||||
\(92\) | −7.47214 | −0.779024 | ||||||||
\(93\) | −1.94427 | −0.201612 | ||||||||
\(94\) | −8.56231 | −0.883134 | ||||||||
\(95\) | 10.8541 | 1.11361 | ||||||||
\(96\) | −0.381966 | −0.0389842 | ||||||||
\(97\) | 18.2361 | 1.85159 | 0.925796 | − | 0.378023i | \(-0.123396\pi\) | ||||
0.925796 | + | 0.378023i | \(0.123396\pi\) | |||||||
\(98\) | 2.00000 | 0.202031 | ||||||||
\(99\) | 13.1803 | 1.32467 | ||||||||
\(100\) | 8.09017 | 0.809017 | ||||||||
\(101\) | 0.763932 | 0.0760141 | 0.0380070 | − | 0.999277i | \(-0.487899\pi\) | ||||
0.0380070 | + | 0.999277i | \(0.487899\pi\) | |||||||
\(102\) | −0.562306 | −0.0556766 | ||||||||
\(103\) | 11.8541 | 1.16802 | 0.584010 | − | 0.811747i | \(-0.301483\pi\) | ||||
0.584010 | + | 0.811747i | \(0.301483\pi\) | |||||||
\(104\) | −3.00000 | −0.294174 | ||||||||
\(105\) | −4.14590 | −0.404598 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | −8.23607 | −0.796211 | −0.398105 | − | 0.917340i | \(-0.630332\pi\) | ||||
−0.398105 | + | 0.917340i | \(0.630332\pi\) | |||||||
\(108\) | 2.23607 | 0.215166 | ||||||||
\(109\) | −0.527864 | −0.0505602 | −0.0252801 | − | 0.999680i | \(-0.508048\pi\) | ||||
−0.0252801 | + | 0.999680i | \(0.508048\pi\) | |||||||
\(110\) | 16.7082 | 1.59306 | ||||||||
\(111\) | −1.85410 | −0.175984 | ||||||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | −6.61803 | −0.622572 | −0.311286 | − | 0.950316i | \(-0.600760\pi\) | ||||
−0.311286 | + | 0.950316i | \(0.600760\pi\) | |||||||
\(114\) | 1.14590 | 0.107323 | ||||||||
\(115\) | 27.0344 | 2.52097 | ||||||||
\(116\) | −4.76393 | −0.442320 | ||||||||
\(117\) | 8.56231 | 0.791585 | ||||||||
\(118\) | −14.2361 | −1.31054 | ||||||||
\(119\) | −4.41641 | −0.404851 | ||||||||
\(120\) | 1.38197 | 0.126156 | ||||||||
\(121\) | 10.3262 | 0.938749 | ||||||||
\(122\) | −4.61803 | −0.418097 | ||||||||
\(123\) | 4.27051 | 0.385059 | ||||||||
\(124\) | 5.09017 | 0.457111 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 8.56231 | 0.762791 | ||||||||
\(127\) | 14.4164 | 1.27925 | 0.639625 | − | 0.768687i | \(-0.279090\pi\) | ||||
0.639625 | + | 0.768687i | \(0.279090\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.81966 | 0.160212 | ||||||||
\(130\) | 10.8541 | 0.951968 | ||||||||
\(131\) | 19.3820 | 1.69341 | 0.846705 | − | 0.532062i | \(-0.178583\pi\) | ||||
0.846705 | + | 0.532062i | \(0.178583\pi\) | |||||||
\(132\) | 1.76393 | 0.153531 | ||||||||
\(133\) | 9.00000 | 0.780399 | ||||||||
\(134\) | −4.85410 | −0.419331 | ||||||||
\(135\) | −8.09017 | −0.696291 | ||||||||
\(136\) | 1.47214 | 0.126235 | ||||||||
\(137\) | −11.5623 | −0.987834 | −0.493917 | − | 0.869509i | \(-0.664435\pi\) | ||||
−0.493917 | + | 0.869509i | \(0.664435\pi\) | |||||||
\(138\) | 2.85410 | 0.242957 | ||||||||
\(139\) | −6.52786 | −0.553686 | −0.276843 | − | 0.960915i | \(-0.589288\pi\) | ||||
−0.276843 | + | 0.960915i | \(0.589288\pi\) | |||||||
\(140\) | 10.8541 | 0.917339 | ||||||||
\(141\) | 3.27051 | 0.275427 | ||||||||
\(142\) | 5.94427 | 0.498832 | ||||||||
\(143\) | 13.8541 | 1.15854 | ||||||||
\(144\) | −2.85410 | −0.237842 | ||||||||
\(145\) | 17.2361 | 1.43138 | ||||||||
\(146\) | −12.7082 | −1.05174 | ||||||||
\(147\) | −0.763932 | −0.0630081 | ||||||||
\(148\) | 4.85410 | 0.399005 | ||||||||
\(149\) | 2.23607 | 0.183186 | 0.0915929 | − | 0.995797i | \(-0.470804\pi\) | ||||
0.0915929 | + | 0.995797i | \(0.470804\pi\) | |||||||
\(150\) | −3.09017 | −0.252311 | ||||||||
\(151\) | 14.7984 | 1.20427 | 0.602137 | − | 0.798393i | \(-0.294316\pi\) | ||||
0.602137 | + | 0.798393i | \(0.294316\pi\) | |||||||
\(152\) | −3.00000 | −0.243332 | ||||||||
\(153\) | −4.20163 | −0.339681 | ||||||||
\(154\) | 13.8541 | 1.11640 | ||||||||
\(155\) | −18.4164 | −1.47924 | ||||||||
\(156\) | 1.14590 | 0.0917453 | ||||||||
\(157\) | −3.09017 | −0.246622 | −0.123311 | − | 0.992368i | \(-0.539351\pi\) | ||||
−0.123311 | + | 0.992368i | \(0.539351\pi\) | |||||||
\(158\) | 4.85410 | 0.386172 | ||||||||
\(159\) | 3.43769 | 0.272627 | ||||||||
\(160\) | −3.61803 | −0.286031 | ||||||||
\(161\) | 22.4164 | 1.76666 | ||||||||
\(162\) | 7.70820 | 0.605614 | ||||||||
\(163\) | −5.85410 | −0.458529 | −0.229264 | − | 0.973364i | \(-0.573632\pi\) | ||||
−0.229264 | + | 0.973364i | \(0.573632\pi\) | |||||||
\(164\) | −11.1803 | −0.873038 | ||||||||
\(165\) | −6.38197 | −0.496835 | ||||||||
\(166\) | 15.9443 | 1.23752 | ||||||||
\(167\) | −0.763932 | −0.0591148 | −0.0295574 | − | 0.999563i | \(-0.509410\pi\) | ||||
−0.0295574 | + | 0.999563i | \(0.509410\pi\) | |||||||
\(168\) | 1.14590 | 0.0884080 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | −5.32624 | −0.408504 | ||||||||
\(171\) | 8.56231 | 0.654776 | ||||||||
\(172\) | −4.76393 | −0.363246 | ||||||||
\(173\) | −23.3262 | −1.77346 | −0.886731 | − | 0.462287i | \(-0.847029\pi\) | ||||
−0.886731 | + | 0.462287i | \(0.847029\pi\) | |||||||
\(174\) | 1.81966 | 0.137948 | ||||||||
\(175\) | −24.2705 | −1.83468 | ||||||||
\(176\) | −4.61803 | −0.348097 | ||||||||
\(177\) | 5.43769 | 0.408722 | ||||||||
\(178\) | 7.79837 | 0.584513 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 10.3262 | 0.769672 | ||||||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 9.00000 | 0.667124 | ||||||||
\(183\) | 1.76393 | 0.130394 | ||||||||
\(184\) | −7.47214 | −0.550853 | ||||||||
\(185\) | −17.5623 | −1.29121 | ||||||||
\(186\) | −1.94427 | −0.142561 | ||||||||
\(187\) | −6.79837 | −0.497146 | ||||||||
\(188\) | −8.56231 | −0.624470 | ||||||||
\(189\) | −6.70820 | −0.487950 | ||||||||
\(190\) | 10.8541 | 0.787439 | ||||||||
\(191\) | −22.3607 | −1.61796 | −0.808981 | − | 0.587835i | \(-0.799981\pi\) | ||||
−0.808981 | + | 0.587835i | \(0.799981\pi\) | |||||||
\(192\) | −0.381966 | −0.0275660 | ||||||||
\(193\) | 9.85410 | 0.709314 | 0.354657 | − | 0.934997i | \(-0.384598\pi\) | ||||
0.354657 | + | 0.934997i | \(0.384598\pi\) | |||||||
\(194\) | 18.2361 | 1.30927 | ||||||||
\(195\) | −4.14590 | −0.296894 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 21.7984 | 1.55307 | 0.776535 | − | 0.630074i | \(-0.216976\pi\) | ||||
0.776535 | + | 0.630074i | \(0.216976\pi\) | |||||||
\(198\) | 13.1803 | 0.936686 | ||||||||
\(199\) | −12.2705 | −0.869833 | −0.434917 | − | 0.900471i | \(-0.643222\pi\) | ||||
−0.434917 | + | 0.900471i | \(0.643222\pi\) | |||||||
\(200\) | 8.09017 | 0.572061 | ||||||||
\(201\) | 1.85410 | 0.130778 | ||||||||
\(202\) | 0.763932 | 0.0537501 | ||||||||
\(203\) | 14.2918 | 1.00309 | ||||||||
\(204\) | −0.562306 | −0.0393693 | ||||||||
\(205\) | 40.4508 | 2.82521 | ||||||||
\(206\) | 11.8541 | 0.825914 | ||||||||
\(207\) | 21.3262 | 1.48228 | ||||||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | 13.8541 | 0.958308 | ||||||||
\(210\) | −4.14590 | −0.286094 | ||||||||
\(211\) | 11.1459 | 0.767315 | 0.383658 | − | 0.923475i | \(-0.374664\pi\) | ||||
0.383658 | + | 0.923475i | \(0.374664\pi\) | |||||||
\(212\) | −9.00000 | −0.618123 | ||||||||
\(213\) | −2.27051 | −0.155573 | ||||||||
\(214\) | −8.23607 | −0.563006 | ||||||||
\(215\) | 17.2361 | 1.17549 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −15.2705 | −1.03663 | ||||||||
\(218\) | −0.527864 | −0.0357515 | ||||||||
\(219\) | 4.85410 | 0.328010 | ||||||||
\(220\) | 16.7082 | 1.12647 | ||||||||
\(221\) | −4.41641 | −0.297080 | ||||||||
\(222\) | −1.85410 | −0.124439 | ||||||||
\(223\) | −28.4164 | −1.90290 | −0.951452 | − | 0.307798i | \(-0.900408\pi\) | ||||
−0.951452 | + | 0.307798i | \(0.900408\pi\) | |||||||
\(224\) | −3.00000 | −0.200446 | ||||||||
\(225\) | −23.0902 | −1.53934 | ||||||||
\(226\) | −6.61803 | −0.440225 | ||||||||
\(227\) | 7.14590 | 0.474290 | 0.237145 | − | 0.971474i | \(-0.423788\pi\) | ||||
0.237145 | + | 0.971474i | \(0.423788\pi\) | |||||||
\(228\) | 1.14590 | 0.0758890 | ||||||||
\(229\) | −22.5967 | −1.49324 | −0.746618 | − | 0.665253i | \(-0.768323\pi\) | ||||
−0.746618 | + | 0.665253i | \(0.768323\pi\) | |||||||
\(230\) | 27.0344 | 1.78260 | ||||||||
\(231\) | −5.29180 | −0.348175 | ||||||||
\(232\) | −4.76393 | −0.312767 | ||||||||
\(233\) | 10.8541 | 0.711076 | 0.355538 | − | 0.934662i | \(-0.384298\pi\) | ||||
0.355538 | + | 0.934662i | \(0.384298\pi\) | |||||||
\(234\) | 8.56231 | 0.559735 | ||||||||
\(235\) | 30.9787 | 2.02083 | ||||||||
\(236\) | −14.2361 | −0.926689 | ||||||||
\(237\) | −1.85410 | −0.120437 | ||||||||
\(238\) | −4.41641 | −0.286273 | ||||||||
\(239\) | −9.70820 | −0.627972 | −0.313986 | − | 0.949428i | \(-0.601664\pi\) | ||||
−0.313986 | + | 0.949428i | \(0.601664\pi\) | |||||||
\(240\) | 1.38197 | 0.0892055 | ||||||||
\(241\) | 16.4164 | 1.05747 | 0.528737 | − | 0.848786i | \(-0.322666\pi\) | ||||
0.528737 | + | 0.848786i | \(0.322666\pi\) | |||||||
\(242\) | 10.3262 | 0.663796 | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | −4.61803 | −0.295639 | ||||||||
\(245\) | −7.23607 | −0.462295 | ||||||||
\(246\) | 4.27051 | 0.272278 | ||||||||
\(247\) | 9.00000 | 0.572656 | ||||||||
\(248\) | 5.09017 | 0.323226 | ||||||||
\(249\) | −6.09017 | −0.385949 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | −16.9443 | −1.06951 | −0.534756 | − | 0.845006i | \(-0.679597\pi\) | ||||
−0.534756 | + | 0.845006i | \(0.679597\pi\) | |||||||
\(252\) | 8.56231 | 0.539375 | ||||||||
\(253\) | 34.5066 | 2.16941 | ||||||||
\(254\) | 14.4164 | 0.904566 | ||||||||
\(255\) | 2.03444 | 0.127402 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.4164 | −1.77257 | −0.886283 | − | 0.463143i | \(-0.846722\pi\) | ||||
−0.886283 | + | 0.463143i | \(0.846722\pi\) | |||||||
\(258\) | 1.81966 | 0.113287 | ||||||||
\(259\) | −14.5623 | −0.904858 | ||||||||
\(260\) | 10.8541 | 0.673143 | ||||||||
\(261\) | 13.5967 | 0.841618 | ||||||||
\(262\) | 19.3820 | 1.19742 | ||||||||
\(263\) | −26.3607 | −1.62547 | −0.812735 | − | 0.582634i | \(-0.802022\pi\) | ||||
−0.812735 | + | 0.582634i | \(0.802022\pi\) | |||||||
\(264\) | 1.76393 | 0.108563 | ||||||||
\(265\) | 32.5623 | 2.00029 | ||||||||
\(266\) | 9.00000 | 0.551825 | ||||||||
\(267\) | −2.97871 | −0.182294 | ||||||||
\(268\) | −4.85410 | −0.296511 | ||||||||
\(269\) | 14.5623 | 0.887879 | 0.443940 | − | 0.896057i | \(-0.353580\pi\) | ||||
0.443940 | + | 0.896057i | \(0.353580\pi\) | |||||||
\(270\) | −8.09017 | −0.492352 | ||||||||
\(271\) | −4.38197 | −0.266185 | −0.133093 | − | 0.991104i | \(-0.542491\pi\) | ||||
−0.133093 | + | 0.991104i | \(0.542491\pi\) | |||||||
\(272\) | 1.47214 | 0.0892614 | ||||||||
\(273\) | −3.43769 | −0.208059 | ||||||||
\(274\) | −11.5623 | −0.698504 | ||||||||
\(275\) | −37.3607 | −2.25293 | ||||||||
\(276\) | 2.85410 | 0.171797 | ||||||||
\(277\) | −0.437694 | −0.0262985 | −0.0131492 | − | 0.999914i | \(-0.504186\pi\) | ||||
−0.0131492 | + | 0.999914i | \(0.504186\pi\) | |||||||
\(278\) | −6.52786 | −0.391515 | ||||||||
\(279\) | −14.5279 | −0.869760 | ||||||||
\(280\) | 10.8541 | 0.648657 | ||||||||
\(281\) | 19.3607 | 1.15496 | 0.577481 | − | 0.816404i | \(-0.304036\pi\) | ||||
0.577481 | + | 0.816404i | \(0.304036\pi\) | |||||||
\(282\) | 3.27051 | 0.194756 | ||||||||
\(283\) | −2.70820 | −0.160986 | −0.0804930 | − | 0.996755i | \(-0.525649\pi\) | ||||
−0.0804930 | + | 0.996755i | \(0.525649\pi\) | |||||||
\(284\) | 5.94427 | 0.352728 | ||||||||
\(285\) | −4.14590 | −0.245582 | ||||||||
\(286\) | 13.8541 | 0.819210 | ||||||||
\(287\) | 33.5410 | 1.97986 | ||||||||
\(288\) | −2.85410 | −0.168180 | ||||||||
\(289\) | −14.8328 | −0.872519 | ||||||||
\(290\) | 17.2361 | 1.01214 | ||||||||
\(291\) | −6.96556 | −0.408328 | ||||||||
\(292\) | −12.7082 | −0.743691 | ||||||||
\(293\) | −20.9098 | −1.22157 | −0.610783 | − | 0.791798i | \(-0.709145\pi\) | ||||
−0.610783 | + | 0.791798i | \(0.709145\pi\) | |||||||
\(294\) | −0.763932 | −0.0445534 | ||||||||
\(295\) | 51.5066 | 2.99883 | ||||||||
\(296\) | 4.85410 | 0.282139 | ||||||||
\(297\) | −10.3262 | −0.599189 | ||||||||
\(298\) | 2.23607 | 0.129532 | ||||||||
\(299\) | 22.4164 | 1.29637 | ||||||||
\(300\) | −3.09017 | −0.178411 | ||||||||
\(301\) | 14.2918 | 0.823765 | ||||||||
\(302\) | 14.7984 | 0.851551 | ||||||||
\(303\) | −0.291796 | −0.0167632 | ||||||||
\(304\) | −3.00000 | −0.172062 | ||||||||
\(305\) | 16.7082 | 0.956709 | ||||||||
\(306\) | −4.20163 | −0.240191 | ||||||||
\(307\) | 15.0902 | 0.861241 | 0.430621 | − | 0.902533i | \(-0.358295\pi\) | ||||
0.430621 | + | 0.902533i | \(0.358295\pi\) | |||||||
\(308\) | 13.8541 | 0.789411 | ||||||||
\(309\) | −4.52786 | −0.257581 | ||||||||
\(310\) | −18.4164 | −1.04598 | ||||||||
\(311\) | 29.2361 | 1.65783 | 0.828913 | − | 0.559378i | \(-0.188960\pi\) | ||||
0.828913 | + | 0.559378i | \(0.188960\pi\) | |||||||
\(312\) | 1.14590 | 0.0648737 | ||||||||
\(313\) | −9.74265 | −0.550687 | −0.275343 | − | 0.961346i | \(-0.588792\pi\) | ||||
−0.275343 | + | 0.961346i | \(0.588792\pi\) | |||||||
\(314\) | −3.09017 | −0.174388 | ||||||||
\(315\) | −30.9787 | −1.74545 | ||||||||
\(316\) | 4.85410 | 0.273065 | ||||||||
\(317\) | −8.38197 | −0.470778 | −0.235389 | − | 0.971901i | \(-0.575636\pi\) | ||||
−0.235389 | + | 0.971901i | \(0.575636\pi\) | |||||||
\(318\) | 3.43769 | 0.192776 | ||||||||
\(319\) | 22.0000 | 1.23176 | ||||||||
\(320\) | −3.61803 | −0.202254 | ||||||||
\(321\) | 3.14590 | 0.175587 | ||||||||
\(322\) | 22.4164 | 1.24922 | ||||||||
\(323\) | −4.41641 | −0.245736 | ||||||||
\(324\) | 7.70820 | 0.428234 | ||||||||
\(325\) | −24.2705 | −1.34629 | ||||||||
\(326\) | −5.85410 | −0.324229 | ||||||||
\(327\) | 0.201626 | 0.0111500 | ||||||||
\(328\) | −11.1803 | −0.617331 | ||||||||
\(329\) | 25.6869 | 1.41617 | ||||||||
\(330\) | −6.38197 | −0.351316 | ||||||||
\(331\) | −25.5623 | −1.40503 | −0.702516 | − | 0.711668i | \(-0.747940\pi\) | ||||
−0.702516 | + | 0.711668i | \(0.747940\pi\) | |||||||
\(332\) | 15.9443 | 0.875056 | ||||||||
\(333\) | −13.8541 | −0.759200 | ||||||||
\(334\) | −0.763932 | −0.0418005 | ||||||||
\(335\) | 17.5623 | 0.959531 | ||||||||
\(336\) | 1.14590 | 0.0625139 | ||||||||
\(337\) | 2.38197 | 0.129754 | 0.0648770 | − | 0.997893i | \(-0.479335\pi\) | ||||
0.0648770 | + | 0.997893i | \(0.479335\pi\) | |||||||
\(338\) | −4.00000 | −0.217571 | ||||||||
\(339\) | 2.52786 | 0.137295 | ||||||||
\(340\) | −5.32624 | −0.288856 | ||||||||
\(341\) | −23.5066 | −1.27295 | ||||||||
\(342\) | 8.56231 | 0.462996 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −4.76393 | −0.256854 | ||||||||
\(345\) | −10.3262 | −0.555946 | ||||||||
\(346\) | −23.3262 | −1.25403 | ||||||||
\(347\) | −24.3262 | −1.30590 | −0.652950 | − | 0.757401i | \(-0.726469\pi\) | ||||
−0.652950 | + | 0.757401i | \(0.726469\pi\) | |||||||
\(348\) | 1.81966 | 0.0975440 | ||||||||
\(349\) | −9.29180 | −0.497378 | −0.248689 | − | 0.968583i | \(-0.580000\pi\) | ||||
−0.248689 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(350\) | −24.2705 | −1.29731 | ||||||||
\(351\) | −6.70820 | −0.358057 | ||||||||
\(352\) | −4.61803 | −0.246142 | ||||||||
\(353\) | −29.1803 | −1.55311 | −0.776556 | − | 0.630048i | \(-0.783035\pi\) | ||||
−0.776556 | + | 0.630048i | \(0.783035\pi\) | |||||||
\(354\) | 5.43769 | 0.289010 | ||||||||
\(355\) | −21.5066 | −1.14145 | ||||||||
\(356\) | 7.79837 | 0.413313 | ||||||||
\(357\) | 1.68692 | 0.0892812 | ||||||||
\(358\) | −9.00000 | −0.475665 | ||||||||
\(359\) | 34.5967 | 1.82595 | 0.912973 | − | 0.408019i | \(-0.133780\pi\) | ||||
0.912973 | + | 0.408019i | \(0.133780\pi\) | |||||||
\(360\) | 10.3262 | 0.544241 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | −18.0000 | −0.946059 | ||||||||
\(363\) | −3.94427 | −0.207021 | ||||||||
\(364\) | 9.00000 | 0.471728 | ||||||||
\(365\) | 45.9787 | 2.40664 | ||||||||
\(366\) | 1.76393 | 0.0922022 | ||||||||
\(367\) | −30.8885 | −1.61237 | −0.806184 | − | 0.591664i | \(-0.798471\pi\) | ||||
−0.806184 | + | 0.591664i | \(0.798471\pi\) | |||||||
\(368\) | −7.47214 | −0.389512 | ||||||||
\(369\) | 31.9098 | 1.66116 | ||||||||
\(370\) | −17.5623 | −0.913021 | ||||||||
\(371\) | 27.0000 | 1.40177 | ||||||||
\(372\) | −1.94427 | −0.100806 | ||||||||
\(373\) | −12.0000 | −0.621336 | −0.310668 | − | 0.950518i | \(-0.600553\pi\) | ||||
−0.310668 | + | 0.950518i | \(0.600553\pi\) | |||||||
\(374\) | −6.79837 | −0.351536 | ||||||||
\(375\) | 4.27051 | 0.220528 | ||||||||
\(376\) | −8.56231 | −0.441567 | ||||||||
\(377\) | 14.2918 | 0.736065 | ||||||||
\(378\) | −6.70820 | −0.345033 | ||||||||
\(379\) | −30.8328 | −1.58378 | −0.791888 | − | 0.610667i | \(-0.790901\pi\) | ||||
−0.791888 | + | 0.610667i | \(0.790901\pi\) | |||||||
\(380\) | 10.8541 | 0.556804 | ||||||||
\(381\) | −5.50658 | −0.282111 | ||||||||
\(382\) | −22.3607 | −1.14407 | ||||||||
\(383\) | −15.7082 | −0.802652 | −0.401326 | − | 0.915935i | \(-0.631451\pi\) | ||||
−0.401326 | + | 0.915935i | \(0.631451\pi\) | |||||||
\(384\) | −0.381966 | −0.0194921 | ||||||||
\(385\) | −50.1246 | −2.55459 | ||||||||
\(386\) | 9.85410 | 0.501561 | ||||||||
\(387\) | 13.5967 | 0.691162 | ||||||||
\(388\) | 18.2361 | 0.925796 | ||||||||
\(389\) | −22.7639 | −1.15418 | −0.577089 | − | 0.816682i | \(-0.695811\pi\) | ||||
−0.577089 | + | 0.816682i | \(0.695811\pi\) | |||||||
\(390\) | −4.14590 | −0.209936 | ||||||||
\(391\) | −11.0000 | −0.556294 | ||||||||
\(392\) | 2.00000 | 0.101015 | ||||||||
\(393\) | −7.40325 | −0.373445 | ||||||||
\(394\) | 21.7984 | 1.09819 | ||||||||
\(395\) | −17.5623 | −0.883656 | ||||||||
\(396\) | 13.1803 | 0.662337 | ||||||||
\(397\) | 11.5623 | 0.580295 | 0.290148 | − | 0.956982i | \(-0.406296\pi\) | ||||
0.290148 | + | 0.956982i | \(0.406296\pi\) | |||||||
\(398\) | −12.2705 | −0.615065 | ||||||||
\(399\) | −3.43769 | −0.172100 | ||||||||
\(400\) | 8.09017 | 0.404508 | ||||||||
\(401\) | −31.9443 | −1.59522 | −0.797610 | − | 0.603173i | \(-0.793903\pi\) | ||||
−0.797610 | + | 0.603173i | \(0.793903\pi\) | |||||||
\(402\) | 1.85410 | 0.0924742 | ||||||||
\(403\) | −15.2705 | −0.760678 | ||||||||
\(404\) | 0.763932 | 0.0380070 | ||||||||
\(405\) | −27.8885 | −1.38579 | ||||||||
\(406\) | 14.2918 | 0.709290 | ||||||||
\(407\) | −22.4164 | −1.11114 | ||||||||
\(408\) | −0.562306 | −0.0278383 | ||||||||
\(409\) | −6.58359 | −0.325538 | −0.162769 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162769 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(410\) | 40.4508 | 1.99773 | ||||||||
\(411\) | 4.41641 | 0.217845 | ||||||||
\(412\) | 11.8541 | 0.584010 | ||||||||
\(413\) | 42.7082 | 2.10153 | ||||||||
\(414\) | 21.3262 | 1.04813 | ||||||||
\(415\) | −57.6869 | −2.83174 | ||||||||
\(416\) | −3.00000 | −0.147087 | ||||||||
\(417\) | 2.49342 | 0.122103 | ||||||||
\(418\) | 13.8541 | 0.677626 | ||||||||
\(419\) | 16.3262 | 0.797589 | 0.398794 | − | 0.917040i | \(-0.369429\pi\) | ||||
0.398794 | + | 0.917040i | \(0.369429\pi\) | |||||||
\(420\) | −4.14590 | −0.202299 | ||||||||
\(421\) | −40.3951 | −1.96874 | −0.984369 | − | 0.176119i | \(-0.943646\pi\) | ||||
−0.984369 | + | 0.176119i | \(0.943646\pi\) | |||||||
\(422\) | 11.1459 | 0.542574 | ||||||||
\(423\) | 24.4377 | 1.18820 | ||||||||
\(424\) | −9.00000 | −0.437079 | ||||||||
\(425\) | 11.9098 | 0.577712 | ||||||||
\(426\) | −2.27051 | −0.110007 | ||||||||
\(427\) | 13.8541 | 0.670447 | ||||||||
\(428\) | −8.23607 | −0.398105 | ||||||||
\(429\) | −5.29180 | −0.255490 | ||||||||
\(430\) | 17.2361 | 0.831197 | ||||||||
\(431\) | −29.2361 | −1.40825 | −0.704126 | − | 0.710075i | \(-0.748661\pi\) | ||||
−0.704126 | + | 0.710075i | \(0.748661\pi\) | |||||||
\(432\) | 2.23607 | 0.107583 | ||||||||
\(433\) | 32.4164 | 1.55783 | 0.778917 | − | 0.627128i | \(-0.215770\pi\) | ||||
0.778917 | + | 0.627128i | \(0.215770\pi\) | |||||||
\(434\) | −15.2705 | −0.733008 | ||||||||
\(435\) | −6.58359 | −0.315659 | ||||||||
\(436\) | −0.527864 | −0.0252801 | ||||||||
\(437\) | 22.4164 | 1.07232 | ||||||||
\(438\) | 4.85410 | 0.231938 | ||||||||
\(439\) | −13.0000 | −0.620456 | −0.310228 | − | 0.950662i | \(-0.600405\pi\) | ||||
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 16.7082 | 0.796532 | ||||||||
\(441\) | −5.70820 | −0.271819 | ||||||||
\(442\) | −4.41641 | −0.210067 | ||||||||
\(443\) | 13.4721 | 0.640080 | 0.320040 | − | 0.947404i | \(-0.396304\pi\) | ||||
0.320040 | + | 0.947404i | \(0.396304\pi\) | |||||||
\(444\) | −1.85410 | −0.0879918 | ||||||||
\(445\) | −28.2148 | −1.33751 | ||||||||
\(446\) | −28.4164 | −1.34556 | ||||||||
\(447\) | −0.854102 | −0.0403976 | ||||||||
\(448\) | −3.00000 | −0.141737 | ||||||||
\(449\) | 27.3607 | 1.29123 | 0.645615 | − | 0.763663i | \(-0.276601\pi\) | ||||
0.645615 | + | 0.763663i | \(0.276601\pi\) | |||||||
\(450\) | −23.0902 | −1.08848 | ||||||||
\(451\) | 51.6312 | 2.43122 | ||||||||
\(452\) | −6.61803 | −0.311286 | ||||||||
\(453\) | −5.65248 | −0.265576 | ||||||||
\(454\) | 7.14590 | 0.335374 | ||||||||
\(455\) | −32.5623 | −1.52654 | ||||||||
\(456\) | 1.14590 | 0.0536616 | ||||||||
\(457\) | −11.9656 | −0.559725 | −0.279863 | − | 0.960040i | \(-0.590289\pi\) | ||||
−0.279863 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(458\) | −22.5967 | −1.05588 | ||||||||
\(459\) | 3.29180 | 0.153648 | ||||||||
\(460\) | 27.0344 | 1.26049 | ||||||||
\(461\) | −4.61803 | −0.215083 | −0.107542 | − | 0.994201i | \(-0.534298\pi\) | ||||
−0.107542 | + | 0.994201i | \(0.534298\pi\) | |||||||
\(462\) | −5.29180 | −0.246197 | ||||||||
\(463\) | −18.3607 | −0.853293 | −0.426647 | − | 0.904418i | \(-0.640305\pi\) | ||||
−0.426647 | + | 0.904418i | \(0.640305\pi\) | |||||||
\(464\) | −4.76393 | −0.221160 | ||||||||
\(465\) | 7.03444 | 0.326214 | ||||||||
\(466\) | 10.8541 | 0.502807 | ||||||||
\(467\) | 7.20163 | 0.333252 | 0.166626 | − | 0.986020i | \(-0.446713\pi\) | ||||
0.166626 | + | 0.986020i | \(0.446713\pi\) | |||||||
\(468\) | 8.56231 | 0.395793 | ||||||||
\(469\) | 14.5623 | 0.672425 | ||||||||
\(470\) | 30.9787 | 1.42894 | ||||||||
\(471\) | 1.18034 | 0.0543872 | ||||||||
\(472\) | −14.2361 | −0.655268 | ||||||||
\(473\) | 22.0000 | 1.01156 | ||||||||
\(474\) | −1.85410 | −0.0851617 | ||||||||
\(475\) | −24.2705 | −1.11361 | ||||||||
\(476\) | −4.41641 | −0.202426 | ||||||||
\(477\) | 25.6869 | 1.17612 | ||||||||
\(478\) | −9.70820 | −0.444043 | ||||||||
\(479\) | −7.14590 | −0.326504 | −0.163252 | − | 0.986584i | \(-0.552198\pi\) | ||||
−0.163252 | + | 0.986584i | \(0.552198\pi\) | |||||||
\(480\) | 1.38197 | 0.0630778 | ||||||||
\(481\) | −14.5623 | −0.663984 | ||||||||
\(482\) | 16.4164 | 0.747747 | ||||||||
\(483\) | −8.56231 | −0.389598 | ||||||||
\(484\) | 10.3262 | 0.469374 | ||||||||
\(485\) | −65.9787 | −2.99594 | ||||||||
\(486\) | −9.65248 | −0.437845 | ||||||||
\(487\) | −19.8885 | −0.901236 | −0.450618 | − | 0.892717i | \(-0.648796\pi\) | ||||
−0.450618 | + | 0.892717i | \(0.648796\pi\) | |||||||
\(488\) | −4.61803 | −0.209049 | ||||||||
\(489\) | 2.23607 | 0.101118 | ||||||||
\(490\) | −7.23607 | −0.326892 | ||||||||
\(491\) | 27.2705 | 1.23070 | 0.615350 | − | 0.788254i | \(-0.289015\pi\) | ||||
0.615350 | + | 0.788254i | \(0.289015\pi\) | |||||||
\(492\) | 4.27051 | 0.192529 | ||||||||
\(493\) | −7.01316 | −0.315857 | ||||||||
\(494\) | 9.00000 | 0.404929 | ||||||||
\(495\) | −47.6869 | −2.14337 | ||||||||
\(496\) | 5.09017 | 0.228555 | ||||||||
\(497\) | −17.8328 | −0.799911 | ||||||||
\(498\) | −6.09017 | −0.272907 | ||||||||
\(499\) | 25.6525 | 1.14836 | 0.574181 | − | 0.818728i | \(-0.305320\pi\) | ||||
0.574181 | + | 0.818728i | \(0.305320\pi\) | |||||||
\(500\) | −11.1803 | −0.500000 | ||||||||
\(501\) | 0.291796 | 0.0130365 | ||||||||
\(502\) | −16.9443 | −0.756260 | ||||||||
\(503\) | 18.7082 | 0.834158 | 0.417079 | − | 0.908870i | \(-0.363054\pi\) | ||||
0.417079 | + | 0.908870i | \(0.363054\pi\) | |||||||
\(504\) | 8.56231 | 0.381395 | ||||||||
\(505\) | −2.76393 | −0.122993 | ||||||||
\(506\) | 34.5066 | 1.53400 | ||||||||
\(507\) | 1.52786 | 0.0678548 | ||||||||
\(508\) | 14.4164 | 0.639625 | ||||||||
\(509\) | −1.58359 | −0.0701915 | −0.0350957 | − | 0.999384i | \(-0.511174\pi\) | ||||
−0.0350957 | + | 0.999384i | \(0.511174\pi\) | |||||||
\(510\) | 2.03444 | 0.0900866 | ||||||||
\(511\) | 38.1246 | 1.68653 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.70820 | −0.296174 | ||||||||
\(514\) | −28.4164 | −1.25339 | ||||||||
\(515\) | −42.8885 | −1.88990 | ||||||||
\(516\) | 1.81966 | 0.0801061 | ||||||||
\(517\) | 39.5410 | 1.73901 | ||||||||
\(518\) | −14.5623 | −0.639831 | ||||||||
\(519\) | 8.90983 | 0.391098 | ||||||||
\(520\) | 10.8541 | 0.475984 | ||||||||
\(521\) | 18.6525 | 0.817180 | 0.408590 | − | 0.912718i | \(-0.366021\pi\) | ||||
0.408590 | + | 0.912718i | \(0.366021\pi\) | |||||||
\(522\) | 13.5967 | 0.595113 | ||||||||
\(523\) | 23.0344 | 1.00723 | 0.503613 | − | 0.863929i | \(-0.332004\pi\) | ||||
0.503613 | + | 0.863929i | \(0.332004\pi\) | |||||||
\(524\) | 19.3820 | 0.846705 | ||||||||
\(525\) | 9.27051 | 0.404598 | ||||||||
\(526\) | −26.3607 | −1.14938 | ||||||||
\(527\) | 7.49342 | 0.326419 | ||||||||
\(528\) | 1.76393 | 0.0767653 | ||||||||
\(529\) | 32.8328 | 1.42751 | ||||||||
\(530\) | 32.5623 | 1.41442 | ||||||||
\(531\) | 40.6312 | 1.76324 | ||||||||
\(532\) | 9.00000 | 0.390199 | ||||||||
\(533\) | 33.5410 | 1.45282 | ||||||||
\(534\) | −2.97871 | −0.128902 | ||||||||
\(535\) | 29.7984 | 1.28830 | ||||||||
\(536\) | −4.85410 | −0.209665 | ||||||||
\(537\) | 3.43769 | 0.148347 | ||||||||
\(538\) | 14.5623 | 0.627826 | ||||||||
\(539\) | −9.23607 | −0.397826 | ||||||||
\(540\) | −8.09017 | −0.348145 | ||||||||
\(541\) | −18.2918 | −0.786426 | −0.393213 | − | 0.919447i | \(-0.628636\pi\) | ||||
−0.393213 | + | 0.919447i | \(0.628636\pi\) | |||||||
\(542\) | −4.38197 | −0.188222 | ||||||||
\(543\) | 6.87539 | 0.295051 | ||||||||
\(544\) | 1.47214 | 0.0631173 | ||||||||
\(545\) | 1.90983 | 0.0818081 | ||||||||
\(546\) | −3.43769 | −0.147120 | ||||||||
\(547\) | −7.94427 | −0.339673 | −0.169836 | − | 0.985472i | \(-0.554324\pi\) | ||||
−0.169836 | + | 0.985472i | \(0.554324\pi\) | |||||||
\(548\) | −11.5623 | −0.493917 | ||||||||
\(549\) | 13.1803 | 0.562523 | ||||||||
\(550\) | −37.3607 | −1.59306 | ||||||||
\(551\) | 14.2918 | 0.608851 | ||||||||
\(552\) | 2.85410 | 0.121479 | ||||||||
\(553\) | −14.5623 | −0.619252 | ||||||||
\(554\) | −0.437694 | −0.0185958 | ||||||||
\(555\) | 6.70820 | 0.284747 | ||||||||
\(556\) | −6.52786 | −0.276843 | ||||||||
\(557\) | −12.2361 | −0.518459 | −0.259229 | − | 0.965816i | \(-0.583469\pi\) | ||||
−0.259229 | + | 0.965816i | \(0.583469\pi\) | |||||||
\(558\) | −14.5279 | −0.615014 | ||||||||
\(559\) | 14.2918 | 0.604479 | ||||||||
\(560\) | 10.8541 | 0.458670 | ||||||||
\(561\) | 2.59675 | 0.109635 | ||||||||
\(562\) | 19.3607 | 0.816681 | ||||||||
\(563\) | 0.270510 | 0.0114006 | 0.00570032 | − | 0.999984i | \(-0.498186\pi\) | ||||
0.00570032 | + | 0.999984i | \(0.498186\pi\) | |||||||
\(564\) | 3.27051 | 0.137713 | ||||||||
\(565\) | 23.9443 | 1.00734 | ||||||||
\(566\) | −2.70820 | −0.113834 | ||||||||
\(567\) | −23.1246 | −0.971142 | ||||||||
\(568\) | 5.94427 | 0.249416 | ||||||||
\(569\) | −43.0344 | −1.80410 | −0.902049 | − | 0.431634i | \(-0.857937\pi\) | ||||
−0.902049 | + | 0.431634i | \(0.857937\pi\) | |||||||
\(570\) | −4.14590 | −0.173653 | ||||||||
\(571\) | −25.0000 | −1.04622 | −0.523109 | − | 0.852266i | \(-0.675228\pi\) | ||||
−0.523109 | + | 0.852266i | \(0.675228\pi\) | |||||||
\(572\) | 13.8541 | 0.579269 | ||||||||
\(573\) | 8.54102 | 0.356806 | ||||||||
\(574\) | 33.5410 | 1.39998 | ||||||||
\(575\) | −60.4508 | −2.52097 | ||||||||
\(576\) | −2.85410 | −0.118921 | ||||||||
\(577\) | 22.4164 | 0.933207 | 0.466604 | − | 0.884467i | \(-0.345477\pi\) | ||||
0.466604 | + | 0.884467i | \(0.345477\pi\) | |||||||
\(578\) | −14.8328 | −0.616964 | ||||||||
\(579\) | −3.76393 | −0.156424 | ||||||||
\(580\) | 17.2361 | 0.715689 | ||||||||
\(581\) | −47.8328 | −1.98444 | ||||||||
\(582\) | −6.96556 | −0.288732 | ||||||||
\(583\) | 41.5623 | 1.72133 | ||||||||
\(584\) | −12.7082 | −0.525869 | ||||||||
\(585\) | −30.9787 | −1.28081 | ||||||||
\(586\) | −20.9098 | −0.863777 | ||||||||
\(587\) | −23.0557 | −0.951612 | −0.475806 | − | 0.879550i | \(-0.657844\pi\) | ||||
−0.475806 | + | 0.879550i | \(0.657844\pi\) | |||||||
\(588\) | −0.763932 | −0.0315040 | ||||||||
\(589\) | −15.2705 | −0.629210 | ||||||||
\(590\) | 51.5066 | 2.12049 | ||||||||
\(591\) | −8.32624 | −0.342496 | ||||||||
\(592\) | 4.85410 | 0.199502 | ||||||||
\(593\) | −21.2148 | −0.871187 | −0.435593 | − | 0.900144i | \(-0.643461\pi\) | ||||
−0.435593 | + | 0.900144i | \(0.643461\pi\) | |||||||
\(594\) | −10.3262 | −0.423691 | ||||||||
\(595\) | 15.9787 | 0.655063 | ||||||||
\(596\) | 2.23607 | 0.0915929 | ||||||||
\(597\) | 4.68692 | 0.191823 | ||||||||
\(598\) | 22.4164 | 0.916675 | ||||||||
\(599\) | −22.8541 | −0.933793 | −0.466897 | − | 0.884312i | \(-0.654628\pi\) | ||||
−0.466897 | + | 0.884312i | \(0.654628\pi\) | |||||||
\(600\) | −3.09017 | −0.126156 | ||||||||
\(601\) | 16.2705 | 0.663688 | 0.331844 | − | 0.943334i | \(-0.392329\pi\) | ||||
0.331844 | + | 0.943334i | \(0.392329\pi\) | |||||||
\(602\) | 14.2918 | 0.582490 | ||||||||
\(603\) | 13.8541 | 0.564183 | ||||||||
\(604\) | 14.7984 | 0.602137 | ||||||||
\(605\) | −37.3607 | −1.51893 | ||||||||
\(606\) | −0.291796 | −0.0118534 | ||||||||
\(607\) | −20.4164 | −0.828676 | −0.414338 | − | 0.910123i | \(-0.635987\pi\) | ||||
−0.414338 | + | 0.910123i | \(0.635987\pi\) | |||||||
\(608\) | −3.00000 | −0.121666 | ||||||||
\(609\) | −5.45898 | −0.221209 | ||||||||
\(610\) | 16.7082 | 0.676495 | ||||||||
\(611\) | 25.6869 | 1.03918 | ||||||||
\(612\) | −4.20163 | −0.169841 | ||||||||
\(613\) | −3.41641 | −0.137987 | −0.0689937 | − | 0.997617i | \(-0.521979\pi\) | ||||
−0.0689937 | + | 0.997617i | \(0.521979\pi\) | |||||||
\(614\) | 15.0902 | 0.608990 | ||||||||
\(615\) | −15.4508 | −0.623038 | ||||||||
\(616\) | 13.8541 | 0.558198 | ||||||||
\(617\) | 5.67376 | 0.228417 | 0.114209 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114209 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(618\) | −4.52786 | −0.182137 | ||||||||
\(619\) | 38.1459 | 1.53321 | 0.766607 | − | 0.642117i | \(-0.221944\pi\) | ||||
0.766607 | + | 0.642117i | \(0.221944\pi\) | |||||||
\(620\) | −18.4164 | −0.739621 | ||||||||
\(621\) | −16.7082 | −0.670477 | ||||||||
\(622\) | 29.2361 | 1.17226 | ||||||||
\(623\) | −23.3951 | −0.937306 | ||||||||
\(624\) | 1.14590 | 0.0458726 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.74265 | −0.389394 | ||||||||
\(627\) | −5.29180 | −0.211334 | ||||||||
\(628\) | −3.09017 | −0.123311 | ||||||||
\(629\) | 7.14590 | 0.284926 | ||||||||
\(630\) | −30.9787 | −1.23422 | ||||||||
\(631\) | −18.2705 | −0.727338 | −0.363669 | − | 0.931528i | \(-0.618476\pi\) | ||||
−0.363669 | + | 0.931528i | \(0.618476\pi\) | |||||||
\(632\) | 4.85410 | 0.193086 | ||||||||
\(633\) | −4.25735 | −0.169215 | ||||||||
\(634\) | −8.38197 | −0.332890 | ||||||||
\(635\) | −52.1591 | −2.06987 | ||||||||
\(636\) | 3.43769 | 0.136313 | ||||||||
\(637\) | −6.00000 | −0.237729 | ||||||||
\(638\) | 22.0000 | 0.870988 | ||||||||
\(639\) | −16.9656 | −0.671147 | ||||||||
\(640\) | −3.61803 | −0.143015 | ||||||||
\(641\) | 41.1803 | 1.62653 | 0.813263 | − | 0.581897i | \(-0.197689\pi\) | ||||
0.813263 | + | 0.581897i | \(0.197689\pi\) | |||||||
\(642\) | 3.14590 | 0.124159 | ||||||||
\(643\) | 32.3050 | 1.27398 | 0.636991 | − | 0.770871i | \(-0.280179\pi\) | ||||
0.636991 | + | 0.770871i | \(0.280179\pi\) | |||||||
\(644\) | 22.4164 | 0.883330 | ||||||||
\(645\) | −6.58359 | −0.259229 | ||||||||
\(646\) | −4.41641 | −0.173761 | ||||||||
\(647\) | 18.3262 | 0.720479 | 0.360239 | − | 0.932860i | \(-0.382695\pi\) | ||||
0.360239 | + | 0.932860i | \(0.382695\pi\) | |||||||
\(648\) | 7.70820 | 0.302807 | ||||||||
\(649\) | 65.7426 | 2.58062 | ||||||||
\(650\) | −24.2705 | −0.951968 | ||||||||
\(651\) | 5.83282 | 0.228606 | ||||||||
\(652\) | −5.85410 | −0.229264 | ||||||||
\(653\) | 6.90983 | 0.270403 | 0.135201 | − | 0.990818i | \(-0.456832\pi\) | ||||
0.135201 | + | 0.990818i | \(0.456832\pi\) | |||||||
\(654\) | 0.201626 | 0.00788421 | ||||||||
\(655\) | −70.1246 | −2.74000 | ||||||||
\(656\) | −11.1803 | −0.436519 | ||||||||
\(657\) | 36.2705 | 1.41505 | ||||||||
\(658\) | 25.6869 | 1.00138 | ||||||||
\(659\) | −6.47214 | −0.252119 | −0.126059 | − | 0.992023i | \(-0.540233\pi\) | ||||
−0.126059 | + | 0.992023i | \(0.540233\pi\) | |||||||
\(660\) | −6.38197 | −0.248418 | ||||||||
\(661\) | 32.2918 | 1.25601 | 0.628003 | − | 0.778211i | \(-0.283873\pi\) | ||||
0.628003 | + | 0.778211i | \(0.283873\pi\) | |||||||
\(662\) | −25.5623 | −0.993507 | ||||||||
\(663\) | 1.68692 | 0.0655145 | ||||||||
\(664\) | 15.9443 | 0.618758 | ||||||||
\(665\) | −32.5623 | −1.26271 | ||||||||
\(666\) | −13.8541 | −0.536836 | ||||||||
\(667\) | 35.5967 | 1.37831 | ||||||||
\(668\) | −0.763932 | −0.0295574 | ||||||||
\(669\) | 10.8541 | 0.419644 | ||||||||
\(670\) | 17.5623 | 0.678491 | ||||||||
\(671\) | 21.3262 | 0.823290 | ||||||||
\(672\) | 1.14590 | 0.0442040 | ||||||||
\(673\) | 48.5410 | 1.87112 | 0.935559 | − | 0.353169i | \(-0.114896\pi\) | ||||
0.935559 | + | 0.353169i | \(0.114896\pi\) | |||||||
\(674\) | 2.38197 | 0.0917499 | ||||||||
\(675\) | 18.0902 | 0.696291 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 12.8885 | 0.495347 | 0.247673 | − | 0.968844i | \(-0.420334\pi\) | ||||
0.247673 | + | 0.968844i | \(0.420334\pi\) | |||||||
\(678\) | 2.52786 | 0.0970820 | ||||||||
\(679\) | −54.7082 | −2.09951 | ||||||||
\(680\) | −5.32624 | −0.204252 | ||||||||
\(681\) | −2.72949 | −0.104594 | ||||||||
\(682\) | −23.5066 | −0.900113 | ||||||||
\(683\) | 11.6180 | 0.444552 | 0.222276 | − | 0.974984i | \(-0.428651\pi\) | ||||
0.222276 | + | 0.974984i | \(0.428651\pi\) | |||||||
\(684\) | 8.56231 | 0.327388 | ||||||||
\(685\) | 41.8328 | 1.59835 | ||||||||
\(686\) | 15.0000 | 0.572703 | ||||||||
\(687\) | 8.63119 | 0.329300 | ||||||||
\(688\) | −4.76393 | −0.181623 | ||||||||
\(689\) | 27.0000 | 1.02862 | ||||||||
\(690\) | −10.3262 | −0.393113 | ||||||||
\(691\) | −3.90983 | −0.148737 | −0.0743685 | − | 0.997231i | \(-0.523694\pi\) | ||||
−0.0743685 | + | 0.997231i | \(0.523694\pi\) | |||||||
\(692\) | −23.3262 | −0.886731 | ||||||||
\(693\) | −39.5410 | −1.50204 | ||||||||
\(694\) | −24.3262 | −0.923411 | ||||||||
\(695\) | 23.6180 | 0.895883 | ||||||||
\(696\) | 1.81966 | 0.0689740 | ||||||||
\(697\) | −16.4590 | −0.623428 | ||||||||
\(698\) | −9.29180 | −0.351700 | ||||||||
\(699\) | −4.14590 | −0.156812 | ||||||||
\(700\) | −24.2705 | −0.917339 | ||||||||
\(701\) | 2.21478 | 0.0836512 | 0.0418256 | − | 0.999125i | \(-0.486683\pi\) | ||||
0.0418256 | + | 0.999125i | \(0.486683\pi\) | |||||||
\(702\) | −6.70820 | −0.253185 | ||||||||
\(703\) | −14.5623 | −0.549228 | ||||||||
\(704\) | −4.61803 | −0.174049 | ||||||||
\(705\) | −11.8328 | −0.445650 | ||||||||
\(706\) | −29.1803 | −1.09822 | ||||||||
\(707\) | −2.29180 | −0.0861919 | ||||||||
\(708\) | 5.43769 | 0.204361 | ||||||||
\(709\) | −34.9443 | −1.31236 | −0.656180 | − | 0.754605i | \(-0.727829\pi\) | ||||
−0.656180 | + | 0.754605i | \(0.727829\pi\) | |||||||
\(710\) | −21.5066 | −0.807127 | ||||||||
\(711\) | −13.8541 | −0.519569 | ||||||||
\(712\) | 7.79837 | 0.292256 | ||||||||
\(713\) | −38.0344 | −1.42440 | ||||||||
\(714\) | 1.68692 | 0.0631313 | ||||||||
\(715\) | −50.1246 | −1.87455 | ||||||||
\(716\) | −9.00000 | −0.336346 | ||||||||
\(717\) | 3.70820 | 0.138485 | ||||||||
\(718\) | 34.5967 | 1.29114 | ||||||||
\(719\) | −32.9443 | −1.22861 | −0.614307 | − | 0.789067i | \(-0.710564\pi\) | ||||
−0.614307 | + | 0.789067i | \(0.710564\pi\) | |||||||
\(720\) | 10.3262 | 0.384836 | ||||||||
\(721\) | −35.5623 | −1.32441 | ||||||||
\(722\) | −10.0000 | −0.372161 | ||||||||
\(723\) | −6.27051 | −0.233203 | ||||||||
\(724\) | −18.0000 | −0.668965 | ||||||||
\(725\) | −38.5410 | −1.43138 | ||||||||
\(726\) | −3.94427 | −0.146386 | ||||||||
\(727\) | 6.47214 | 0.240038 | 0.120019 | − | 0.992772i | \(-0.461704\pi\) | ||||
0.120019 | + | 0.992772i | \(0.461704\pi\) | |||||||
\(728\) | 9.00000 | 0.333562 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 45.9787 | 1.70175 | ||||||||
\(731\) | −7.01316 | −0.259391 | ||||||||
\(732\) | 1.76393 | 0.0651968 | ||||||||
\(733\) | −36.8885 | −1.36251 | −0.681255 | − | 0.732046i | \(-0.738565\pi\) | ||||
−0.681255 | + | 0.732046i | \(0.738565\pi\) | |||||||
\(734\) | −30.8885 | −1.14012 | ||||||||
\(735\) | 2.76393 | 0.101949 | ||||||||
\(736\) | −7.47214 | −0.275427 | ||||||||
\(737\) | 22.4164 | 0.825719 | ||||||||
\(738\) | 31.9098 | 1.17462 | ||||||||
\(739\) | −29.5279 | −1.08620 | −0.543100 | − | 0.839668i | \(-0.682750\pi\) | ||||
−0.543100 | + | 0.839668i | \(0.682750\pi\) | |||||||
\(740\) | −17.5623 | −0.645603 | ||||||||
\(741\) | −3.43769 | −0.126287 | ||||||||
\(742\) | 27.0000 | 0.991201 | ||||||||
\(743\) | −17.2361 | −0.632330 | −0.316165 | − | 0.948704i | \(-0.602395\pi\) | ||||
−0.316165 | + | 0.948704i | \(0.602395\pi\) | |||||||
\(744\) | −1.94427 | −0.0712805 | ||||||||
\(745\) | −8.09017 | −0.296401 | ||||||||
\(746\) | −12.0000 | −0.439351 | ||||||||
\(747\) | −45.5066 | −1.66500 | ||||||||
\(748\) | −6.79837 | −0.248573 | ||||||||
\(749\) | 24.7082 | 0.902818 | ||||||||
\(750\) | 4.27051 | 0.155937 | ||||||||
\(751\) | −3.43769 | −0.125443 | −0.0627216 | − | 0.998031i | \(-0.519978\pi\) | ||||
−0.0627216 | + | 0.998031i | \(0.519978\pi\) | |||||||
\(752\) | −8.56231 | −0.312235 | ||||||||
\(753\) | 6.47214 | 0.235858 | ||||||||
\(754\) | 14.2918 | 0.520477 | ||||||||
\(755\) | −53.5410 | −1.94856 | ||||||||
\(756\) | −6.70820 | −0.243975 | ||||||||
\(757\) | −1.70820 | −0.0620857 | −0.0310429 | − | 0.999518i | \(-0.509883\pi\) | ||||
−0.0310429 | + | 0.999518i | \(0.509883\pi\) | |||||||
\(758\) | −30.8328 | −1.11990 | ||||||||
\(759\) | −13.1803 | −0.478416 | ||||||||
\(760\) | 10.8541 | 0.393720 | ||||||||
\(761\) | 26.0344 | 0.943748 | 0.471874 | − | 0.881666i | \(-0.343578\pi\) | ||||
0.471874 | + | 0.881666i | \(0.343578\pi\) | |||||||
\(762\) | −5.50658 | −0.199482 | ||||||||
\(763\) | 1.58359 | 0.0573299 | ||||||||
\(764\) | −22.3607 | −0.808981 | ||||||||
\(765\) | 15.2016 | 0.549616 | ||||||||
\(766\) | −15.7082 | −0.567560 | ||||||||
\(767\) | 42.7082 | 1.54210 | ||||||||
\(768\) | −0.381966 | −0.0137830 | ||||||||
\(769\) | 13.4164 | 0.483808 | 0.241904 | − | 0.970300i | \(-0.422228\pi\) | ||||
0.241904 | + | 0.970300i | \(0.422228\pi\) | |||||||
\(770\) | −50.1246 | −1.80637 | ||||||||
\(771\) | 10.8541 | 0.390901 | ||||||||
\(772\) | 9.85410 | 0.354657 | ||||||||
\(773\) | −36.7639 | −1.32231 | −0.661153 | − | 0.750251i | \(-0.729933\pi\) | ||||
−0.661153 | + | 0.750251i | \(0.729933\pi\) | |||||||
\(774\) | 13.5967 | 0.488725 | ||||||||
\(775\) | 41.1803 | 1.47924 | ||||||||
\(776\) | 18.2361 | 0.654637 | ||||||||
\(777\) | 5.56231 | 0.199547 | ||||||||
\(778\) | −22.7639 | −0.816127 | ||||||||
\(779\) | 33.5410 | 1.20173 | ||||||||
\(780\) | −4.14590 | −0.148447 | ||||||||
\(781\) | −27.4508 | −0.982269 | ||||||||
\(782\) | −11.0000 | −0.393359 | ||||||||
\(783\) | −10.6525 | −0.380688 | ||||||||
\(784\) | 2.00000 | 0.0714286 | ||||||||
\(785\) | 11.1803 | 0.399043 | ||||||||
\(786\) | −7.40325 | −0.264065 | ||||||||
\(787\) | 9.94427 | 0.354475 | 0.177238 | − | 0.984168i | \(-0.443284\pi\) | ||||
0.177238 | + | 0.984168i | \(0.443284\pi\) | |||||||
\(788\) | 21.7984 | 0.776535 | ||||||||
\(789\) | 10.0689 | 0.358462 | ||||||||
\(790\) | −17.5623 | −0.624839 | ||||||||
\(791\) | 19.8541 | 0.705931 | ||||||||
\(792\) | 13.1803 | 0.468343 | ||||||||
\(793\) | 13.8541 | 0.491974 | ||||||||
\(794\) | 11.5623 | 0.410331 | ||||||||
\(795\) | −12.4377 | −0.441120 | ||||||||
\(796\) | −12.2705 | −0.434917 | ||||||||
\(797\) | −13.0557 | −0.462458 | −0.231229 | − | 0.972899i | \(-0.574275\pi\) | ||||
−0.231229 | + | 0.972899i | \(0.574275\pi\) | |||||||
\(798\) | −3.43769 | −0.121693 | ||||||||
\(799\) | −12.6049 | −0.445929 | ||||||||
\(800\) | 8.09017 | 0.286031 | ||||||||
\(801\) | −22.2574 | −0.786425 | ||||||||
\(802\) | −31.9443 | −1.12799 | ||||||||
\(803\) | 58.6869 | 2.07102 | ||||||||
\(804\) | 1.85410 | 0.0653891 | ||||||||
\(805\) | −81.1033 | −2.85852 | ||||||||
\(806\) | −15.2705 | −0.537881 | ||||||||
\(807\) | −5.56231 | −0.195802 | ||||||||
\(808\) | 0.763932 | 0.0268750 | ||||||||
\(809\) | 37.8541 | 1.33088 | 0.665440 | − | 0.746452i | \(-0.268244\pi\) | ||||
0.665440 | + | 0.746452i | \(0.268244\pi\) | |||||||
\(810\) | −27.8885 | −0.979904 | ||||||||
\(811\) | −5.05573 | −0.177531 | −0.0887653 | − | 0.996053i | \(-0.528292\pi\) | ||||
−0.0887653 | + | 0.996053i | \(0.528292\pi\) | |||||||
\(812\) | 14.2918 | 0.501544 | ||||||||
\(813\) | 1.67376 | 0.0587014 | ||||||||
\(814\) | −22.4164 | −0.785695 | ||||||||
\(815\) | 21.1803 | 0.741915 | ||||||||
\(816\) | −0.562306 | −0.0196846 | ||||||||
\(817\) | 14.2918 | 0.500007 | ||||||||
\(818\) | −6.58359 | −0.230190 | ||||||||
\(819\) | −25.6869 | −0.897574 | ||||||||
\(820\) | 40.4508 | 1.41260 | ||||||||
\(821\) | −39.5066 | −1.37879 | −0.689395 | − | 0.724386i | \(-0.742123\pi\) | ||||
−0.689395 | + | 0.724386i | \(0.742123\pi\) | |||||||
\(822\) | 4.41641 | 0.154040 | ||||||||
\(823\) | −7.41641 | −0.258520 | −0.129260 | − | 0.991611i | \(-0.541260\pi\) | ||||
−0.129260 | + | 0.991611i | \(0.541260\pi\) | |||||||
\(824\) | 11.8541 | 0.412957 | ||||||||
\(825\) | 14.2705 | 0.496835 | ||||||||
\(826\) | 42.7082 | 1.48601 | ||||||||
\(827\) | 23.0557 | 0.801726 | 0.400863 | − | 0.916138i | \(-0.368710\pi\) | ||||
0.400863 | + | 0.916138i | \(0.368710\pi\) | |||||||
\(828\) | 21.3262 | 0.741138 | ||||||||
\(829\) | −20.7082 | −0.719226 | −0.359613 | − | 0.933102i | \(-0.617091\pi\) | ||||
−0.359613 | + | 0.933102i | \(0.617091\pi\) | |||||||
\(830\) | −57.6869 | −2.00234 | ||||||||
\(831\) | 0.167184 | 0.00579956 | ||||||||
\(832\) | −3.00000 | −0.104006 | ||||||||
\(833\) | 2.94427 | 0.102013 | ||||||||
\(834\) | 2.49342 | 0.0863401 | ||||||||
\(835\) | 2.76393 | 0.0956498 | ||||||||
\(836\) | 13.8541 | 0.479154 | ||||||||
\(837\) | 11.3820 | 0.393418 | ||||||||
\(838\) | 16.3262 | 0.563981 | ||||||||
\(839\) | 46.6525 | 1.61062 | 0.805311 | − | 0.592852i | \(-0.201998\pi\) | ||||
0.805311 | + | 0.592852i | \(0.201998\pi\) | |||||||
\(840\) | −4.14590 | −0.143047 | ||||||||
\(841\) | −6.30495 | −0.217412 | ||||||||
\(842\) | −40.3951 | −1.39211 | ||||||||
\(843\) | −7.39512 | −0.254702 | ||||||||
\(844\) | 11.1459 | 0.383658 | ||||||||
\(845\) | 14.4721 | 0.497857 | ||||||||
\(846\) | 24.4377 | 0.840185 | ||||||||
\(847\) | −30.9787 | −1.06444 | ||||||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | 1.03444 | 0.0355020 | ||||||||
\(850\) | 11.9098 | 0.408504 | ||||||||
\(851\) | −36.2705 | −1.24334 | ||||||||
\(852\) | −2.27051 | −0.0777864 | ||||||||
\(853\) | 33.5623 | 1.14915 | 0.574576 | − | 0.818451i | \(-0.305167\pi\) | ||||
0.574576 | + | 0.818451i | \(0.305167\pi\) | |||||||
\(854\) | 13.8541 | 0.474078 | ||||||||
\(855\) | −30.9787 | −1.05945 | ||||||||
\(856\) | −8.23607 | −0.281503 | ||||||||
\(857\) | −20.9098 | −0.714266 | −0.357133 | − | 0.934054i | \(-0.616246\pi\) | ||||
−0.357133 | + | 0.934054i | \(0.616246\pi\) | |||||||
\(858\) | −5.29180 | −0.180659 | ||||||||
\(859\) | 33.9443 | 1.15816 | 0.579082 | − | 0.815269i | \(-0.303411\pi\) | ||||
0.579082 | + | 0.815269i | \(0.303411\pi\) | |||||||
\(860\) | 17.2361 | 0.587745 | ||||||||
\(861\) | −12.8115 | −0.436616 | ||||||||
\(862\) | −29.2361 | −0.995784 | ||||||||
\(863\) | 32.0132 | 1.08974 | 0.544870 | − | 0.838520i | \(-0.316579\pi\) | ||||
0.544870 | + | 0.838520i | \(0.316579\pi\) | |||||||
\(864\) | 2.23607 | 0.0760726 | ||||||||
\(865\) | 84.3951 | 2.86952 | ||||||||
\(866\) | 32.4164 | 1.10155 | ||||||||
\(867\) | 5.66563 | 0.192415 | ||||||||
\(868\) | −15.2705 | −0.518315 | ||||||||
\(869\) | −22.4164 | −0.760425 | ||||||||
\(870\) | −6.58359 | −0.223205 | ||||||||
\(871\) | 14.5623 | 0.493425 | ||||||||
\(872\) | −0.527864 | −0.0178757 | ||||||||
\(873\) | −52.0476 | −1.76154 | ||||||||
\(874\) | 22.4164 | 0.758246 | ||||||||
\(875\) | 33.5410 | 1.13389 | ||||||||
\(876\) | 4.85410 | 0.164005 | ||||||||
\(877\) | 5.12461 | 0.173046 | 0.0865229 | − | 0.996250i | \(-0.472424\pi\) | ||||
0.0865229 | + | 0.996250i | \(0.472424\pi\) | |||||||
\(878\) | −13.0000 | −0.438729 | ||||||||
\(879\) | 7.98684 | 0.269390 | ||||||||
\(880\) | 16.7082 | 0.563233 | ||||||||
\(881\) | 31.7214 | 1.06872 | 0.534360 | − | 0.845257i | \(-0.320553\pi\) | ||||
0.534360 | + | 0.845257i | \(0.320553\pi\) | |||||||
\(882\) | −5.70820 | −0.192205 | ||||||||
\(883\) | −21.9656 | −0.739200 | −0.369600 | − | 0.929191i | \(-0.620505\pi\) | ||||
−0.369600 | + | 0.929191i | \(0.620505\pi\) | |||||||
\(884\) | −4.41641 | −0.148540 | ||||||||
\(885\) | −19.6738 | −0.661326 | ||||||||
\(886\) | 13.4721 | 0.452605 | ||||||||
\(887\) | 9.70820 | 0.325970 | 0.162985 | − | 0.986629i | \(-0.447888\pi\) | ||||
0.162985 | + | 0.986629i | \(0.447888\pi\) | |||||||
\(888\) | −1.85410 | −0.0622196 | ||||||||
\(889\) | −43.2492 | −1.45053 | ||||||||
\(890\) | −28.2148 | −0.945762 | ||||||||
\(891\) | −35.5967 | −1.19254 | ||||||||
\(892\) | −28.4164 | −0.951452 | ||||||||
\(893\) | 25.6869 | 0.859580 | ||||||||
\(894\) | −0.854102 | −0.0285654 | ||||||||
\(895\) | 32.5623 | 1.08844 | ||||||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | −8.56231 | −0.285887 | ||||||||
\(898\) | 27.3607 | 0.913038 | ||||||||
\(899\) | −24.2492 | −0.808757 | ||||||||
\(900\) | −23.0902 | −0.769672 | ||||||||
\(901\) | −13.2492 | −0.441396 | ||||||||
\(902\) | 51.6312 | 1.71913 | ||||||||
\(903\) | −5.45898 | −0.181663 | ||||||||
\(904\) | −6.61803 | −0.220113 | ||||||||
\(905\) | 65.1246 | 2.16482 | ||||||||
\(906\) | −5.65248 | −0.187791 | ||||||||
\(907\) | 5.41641 | 0.179849 | 0.0899244 | − | 0.995949i | \(-0.471337\pi\) | ||||
0.0899244 | + | 0.995949i | \(0.471337\pi\) | |||||||
\(908\) | 7.14590 | 0.237145 | ||||||||
\(909\) | −2.18034 | −0.0723173 | ||||||||
\(910\) | −32.5623 | −1.07943 | ||||||||
\(911\) | −11.5623 | −0.383076 | −0.191538 | − | 0.981485i | \(-0.561348\pi\) | ||||
−0.191538 | + | 0.981485i | \(0.561348\pi\) | |||||||
\(912\) | 1.14590 | 0.0379445 | ||||||||
\(913\) | −73.6312 | −2.43684 | ||||||||
\(914\) | −11.9656 | −0.395785 | ||||||||
\(915\) | −6.38197 | −0.210981 | ||||||||
\(916\) | −22.5967 | −0.746618 | ||||||||
\(917\) | −58.1459 | −1.92015 | ||||||||
\(918\) | 3.29180 | 0.108645 | ||||||||
\(919\) | −45.7214 | −1.50821 | −0.754104 | − | 0.656755i | \(-0.771929\pi\) | ||||
−0.754104 | + | 0.656755i | \(0.771929\pi\) | |||||||
\(920\) | 27.0344 | 0.891299 | ||||||||
\(921\) | −5.76393 | −0.189928 | ||||||||
\(922\) | −4.61803 | −0.152087 | ||||||||
\(923\) | −17.8328 | −0.586974 | ||||||||
\(924\) | −5.29180 | −0.174087 | ||||||||
\(925\) | 39.2705 | 1.29121 | ||||||||
\(926\) | −18.3607 | −0.603369 | ||||||||
\(927\) | −33.8328 | −1.11122 | ||||||||
\(928\) | −4.76393 | −0.156384 | ||||||||
\(929\) | −11.8328 | −0.388222 | −0.194111 | − | 0.980980i | \(-0.562182\pi\) | ||||
−0.194111 | + | 0.980980i | \(0.562182\pi\) | |||||||
\(930\) | 7.03444 | 0.230668 | ||||||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | 10.8541 | 0.355538 | ||||||||
\(933\) | −11.1672 | −0.365597 | ||||||||
\(934\) | 7.20163 | 0.235644 | ||||||||
\(935\) | 24.5967 | 0.804400 | ||||||||
\(936\) | 8.56231 | 0.279868 | ||||||||
\(937\) | 44.8328 | 1.46462 | 0.732312 | − | 0.680969i | \(-0.238441\pi\) | ||||
0.732312 | + | 0.680969i | \(0.238441\pi\) | |||||||
\(938\) | 14.5623 | 0.475476 | ||||||||
\(939\) | 3.72136 | 0.121442 | ||||||||
\(940\) | 30.9787 | 1.01041 | ||||||||
\(941\) | −22.7984 | −0.743206 | −0.371603 | − | 0.928392i | \(-0.621192\pi\) | ||||
−0.371603 | + | 0.928392i | \(0.621192\pi\) | |||||||
\(942\) | 1.18034 | 0.0384576 | ||||||||
\(943\) | 83.5410 | 2.72047 | ||||||||
\(944\) | −14.2361 | −0.463345 | ||||||||
\(945\) | 24.2705 | 0.789520 | ||||||||
\(946\) | 22.0000 | 0.715282 | ||||||||
\(947\) | −40.7984 | −1.32577 | −0.662885 | − | 0.748722i | \(-0.730668\pi\) | ||||
−0.662885 | + | 0.748722i | \(0.730668\pi\) | |||||||
\(948\) | −1.85410 | −0.0602184 | ||||||||
\(949\) | 38.1246 | 1.23758 | ||||||||
\(950\) | −24.2705 | −0.787439 | ||||||||
\(951\) | 3.20163 | 0.103820 | ||||||||
\(952\) | −4.41641 | −0.143137 | ||||||||
\(953\) | −57.6525 | −1.86755 | −0.933773 | − | 0.357865i | \(-0.883505\pi\) | ||||
−0.933773 | + | 0.357865i | \(0.883505\pi\) | |||||||
\(954\) | 25.6869 | 0.831645 | ||||||||
\(955\) | 80.9017 | 2.61792 | ||||||||
\(956\) | −9.70820 | −0.313986 | ||||||||
\(957\) | −8.40325 | −0.271639 | ||||||||
\(958\) | −7.14590 | −0.230873 | ||||||||
\(959\) | 34.6869 | 1.12010 | ||||||||
\(960\) | 1.38197 | 0.0446028 | ||||||||
\(961\) | −5.09017 | −0.164199 | ||||||||
\(962\) | −14.5623 | −0.469508 | ||||||||
\(963\) | 23.5066 | 0.757489 | ||||||||
\(964\) | 16.4164 | 0.528737 | ||||||||
\(965\) | −35.6525 | −1.14769 | ||||||||
\(966\) | −8.56231 | −0.275488 | ||||||||
\(967\) | 5.16718 | 0.166165 | 0.0830827 | − | 0.996543i | \(-0.473523\pi\) | ||||
0.0830827 | + | 0.996543i | \(0.473523\pi\) | |||||||
\(968\) | 10.3262 | 0.331898 | ||||||||
\(969\) | 1.68692 | 0.0541916 | ||||||||
\(970\) | −65.9787 | −2.11845 | ||||||||
\(971\) | 49.2492 | 1.58048 | 0.790241 | − | 0.612796i | \(-0.209955\pi\) | ||||
0.790241 | + | 0.612796i | \(0.209955\pi\) | |||||||
\(972\) | −9.65248 | −0.309603 | ||||||||
\(973\) | 19.5836 | 0.627821 | ||||||||
\(974\) | −19.8885 | −0.637270 | ||||||||
\(975\) | 9.27051 | 0.296894 | ||||||||
\(976\) | −4.61803 | −0.147820 | ||||||||
\(977\) | −18.2361 | −0.583424 | −0.291712 | − | 0.956506i | \(-0.594225\pi\) | ||||
−0.291712 | + | 0.956506i | \(0.594225\pi\) | |||||||
\(978\) | 2.23607 | 0.0715016 | ||||||||
\(979\) | −36.0132 | −1.15099 | ||||||||
\(980\) | −7.23607 | −0.231148 | ||||||||
\(981\) | 1.50658 | 0.0481013 | ||||||||
\(982\) | 27.2705 | 0.870237 | ||||||||
\(983\) | 31.7426 | 1.01243 | 0.506217 | − | 0.862406i | \(-0.331044\pi\) | ||||
0.506217 | + | 0.862406i | \(0.331044\pi\) | |||||||
\(984\) | 4.27051 | 0.136139 | ||||||||
\(985\) | −78.8673 | −2.51292 | ||||||||
\(986\) | −7.01316 | −0.223344 | ||||||||
\(987\) | −9.81153 | −0.312304 | ||||||||
\(988\) | 9.00000 | 0.286328 | ||||||||
\(989\) | 35.5967 | 1.13191 | ||||||||
\(990\) | −47.6869 | −1.51559 | ||||||||
\(991\) | 53.3050 | 1.69329 | 0.846644 | − | 0.532160i | \(-0.178620\pi\) | ||||
0.846644 | + | 0.532160i | \(0.178620\pi\) | |||||||
\(992\) | 5.09017 | 0.161613 | ||||||||
\(993\) | 9.76393 | 0.309849 | ||||||||
\(994\) | −17.8328 | −0.565623 | ||||||||
\(995\) | 44.3951 | 1.40742 | ||||||||
\(996\) | −6.09017 | −0.192974 | ||||||||
\(997\) | 35.0000 | 1.10846 | 0.554231 | − | 0.832363i | \(-0.313013\pi\) | ||||
0.554231 | + | 0.832363i | \(0.313013\pi\) | |||||||
\(998\) | 25.6525 | 0.812015 | ||||||||
\(999\) | 10.8541 | 0.343409 |
(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 | 6038.2.a.a.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6038.2.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |