Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7674048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.82356\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.823556 | 0.582342 | 0.291171 | − | 0.956671i | \(-0.405955\pi\) | ||||
0.291171 | + | 0.956671i | \(0.405955\pi\) | |||||||
\(3\) | 2.66029 | 1.53592 | 0.767960 | − | 0.640498i | \(-0.221272\pi\) | ||||
0.767960 | + | 0.640498i | \(0.221272\pi\) | |||||||
\(4\) | −1.32176 | −0.660878 | ||||||||
\(5\) | −3.16209 | −1.41413 | −0.707065 | − | 0.707148i | \(-0.749981\pi\) | ||||
−0.707065 | + | 0.707148i | \(0.749981\pi\) | |||||||
\(6\) | 2.19090 | 0.894431 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.73565 | −0.967199 | ||||||||
\(9\) | 4.07715 | 1.35905 | ||||||||
\(10\) | −2.60416 | −0.823508 | ||||||||
\(11\) | −5.94270 | −1.79179 | −0.895895 | − | 0.444265i | \(-0.853465\pi\) | ||||
−0.895895 | + | 0.444265i | \(0.853465\pi\) | |||||||
\(12\) | −3.51626 | −1.01506 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.823556 | 0.220105 | ||||||||
\(15\) | −8.41209 | −2.17199 | ||||||||
\(16\) | 0.390549 | 0.0976372 | ||||||||
\(17\) | −2.69964 | −0.654760 | −0.327380 | − | 0.944893i | \(-0.606166\pi\) | ||||
−0.327380 | + | 0.944893i | \(0.606166\pi\) | |||||||
\(18\) | 3.35776 | 0.791433 | ||||||||
\(19\) | −1.95705 | −0.448978 | −0.224489 | − | 0.974477i | \(-0.572071\pi\) | ||||
−0.224489 | + | 0.974477i | \(0.572071\pi\) | |||||||
\(20\) | 4.17951 | 0.934568 | ||||||||
\(21\) | 2.66029 | 0.580523 | ||||||||
\(22\) | −4.89414 | −1.04343 | ||||||||
\(23\) | −2.72941 | −0.569122 | −0.284561 | − | 0.958658i | \(-0.591848\pi\) | ||||
−0.284561 | + | 0.958658i | \(0.591848\pi\) | |||||||
\(24\) | −7.27763 | −1.48554 | ||||||||
\(25\) | 4.99883 | 0.999766 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.86554 | 0.551474 | ||||||||
\(28\) | −1.32176 | −0.249788 | ||||||||
\(29\) | −5.99845 | −1.11388 | −0.556942 | − | 0.830551i | \(-0.688026\pi\) | ||||
−0.556942 | + | 0.830551i | \(0.688026\pi\) | |||||||
\(30\) | −6.92783 | −1.26484 | ||||||||
\(31\) | −1.15155 | −0.206824 | −0.103412 | − | 0.994639i | \(-0.532976\pi\) | ||||
−0.103412 | + | 0.994639i | \(0.532976\pi\) | |||||||
\(32\) | 5.79294 | 1.02406 | ||||||||
\(33\) | −15.8093 | −2.75205 | ||||||||
\(34\) | −2.22331 | −0.381294 | ||||||||
\(35\) | −3.16209 | −0.534491 | ||||||||
\(36\) | −5.38900 | −0.898167 | ||||||||
\(37\) | 6.50454 | 1.06934 | 0.534670 | − | 0.845061i | \(-0.320436\pi\) | ||||
0.534670 | + | 0.845061i | \(0.320436\pi\) | |||||||
\(38\) | −1.61174 | −0.261459 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.65038 | 1.36775 | ||||||||
\(41\) | −3.73374 | −0.583112 | −0.291556 | − | 0.956554i | \(-0.594173\pi\) | ||||
−0.291556 | + | 0.956554i | \(0.594173\pi\) | |||||||
\(42\) | 2.19090 | 0.338063 | ||||||||
\(43\) | 6.99125 | 1.06616 | 0.533078 | − | 0.846066i | \(-0.321035\pi\) | ||||
0.533078 | + | 0.846066i | \(0.321035\pi\) | |||||||
\(44\) | 7.85479 | 1.18415 | ||||||||
\(45\) | −12.8923 | −1.92188 | ||||||||
\(46\) | −2.24783 | −0.331424 | ||||||||
\(47\) | −0.456071 | −0.0665248 | −0.0332624 | − | 0.999447i | \(-0.510590\pi\) | ||||
−0.0332624 | + | 0.999447i | \(0.510590\pi\) | |||||||
\(48\) | 1.03897 | 0.149963 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.11682 | 0.582206 | ||||||||
\(51\) | −7.18184 | −1.00566 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.399286 | 0.0548462 | 0.0274231 | − | 0.999624i | \(-0.491270\pi\) | ||||
0.0274231 | + | 0.999624i | \(0.491270\pi\) | |||||||
\(54\) | 2.35994 | 0.321146 | ||||||||
\(55\) | 18.7914 | 2.53383 | ||||||||
\(56\) | −2.73565 | −0.365567 | ||||||||
\(57\) | −5.20632 | −0.689594 | ||||||||
\(58\) | −4.94006 | −0.648662 | ||||||||
\(59\) | 4.80586 | 0.625670 | 0.312835 | − | 0.949807i | \(-0.398721\pi\) | ||||
0.312835 | + | 0.949807i | \(0.398721\pi\) | |||||||
\(60\) | 11.1187 | 1.43542 | ||||||||
\(61\) | −1.15703 | −0.148142 | −0.0740711 | − | 0.997253i | \(-0.523599\pi\) | ||||
−0.0740711 | + | 0.997253i | \(0.523599\pi\) | |||||||
\(62\) | −0.948365 | −0.120442 | ||||||||
\(63\) | 4.07715 | 0.513673 | ||||||||
\(64\) | 3.98971 | 0.498714 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.0199 | −1.60263 | ||||||||
\(67\) | −6.27918 | −0.767124 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(68\) | 3.56827 | 0.432716 | ||||||||
\(69\) | −7.26104 | −0.874127 | ||||||||
\(70\) | −2.60416 | −0.311257 | ||||||||
\(71\) | −4.50720 | −0.534906 | −0.267453 | − | 0.963571i | \(-0.586182\pi\) | ||||
−0.267453 | + | 0.963571i | \(0.586182\pi\) | |||||||
\(72\) | −11.1537 | −1.31447 | ||||||||
\(73\) | −8.30575 | −0.972115 | −0.486057 | − | 0.873927i | \(-0.661565\pi\) | ||||
−0.486057 | + | 0.873927i | \(0.661565\pi\) | |||||||
\(74\) | 5.35685 | 0.622721 | ||||||||
\(75\) | 13.2983 | 1.53556 | ||||||||
\(76\) | 2.58674 | 0.296719 | ||||||||
\(77\) | −5.94270 | −0.677233 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.91410 | −0.890405 | −0.445203 | − | 0.895430i | \(-0.646868\pi\) | ||||
−0.445203 | + | 0.895430i | \(0.646868\pi\) | |||||||
\(80\) | −1.23495 | −0.138072 | ||||||||
\(81\) | −4.60828 | −0.512031 | ||||||||
\(82\) | −3.07494 | −0.339571 | ||||||||
\(83\) | 6.19795 | 0.680313 | 0.340156 | − | 0.940369i | \(-0.389520\pi\) | ||||
0.340156 | + | 0.940369i | \(0.389520\pi\) | |||||||
\(84\) | −3.51626 | −0.383655 | ||||||||
\(85\) | 8.53652 | 0.925916 | ||||||||
\(86\) | 5.75769 | 0.620867 | ||||||||
\(87\) | −15.9576 | −1.71084 | ||||||||
\(88\) | 16.2571 | 1.73302 | ||||||||
\(89\) | −3.56136 | −0.377504 | −0.188752 | − | 0.982025i | \(-0.560444\pi\) | ||||
−0.188752 | + | 0.982025i | \(0.560444\pi\) | |||||||
\(90\) | −10.6176 | −1.11919 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.60762 | 0.376120 | ||||||||
\(93\) | −3.06345 | −0.317665 | ||||||||
\(94\) | −0.375600 | −0.0387402 | ||||||||
\(95\) | 6.18837 | 0.634913 | ||||||||
\(96\) | 15.4109 | 1.57287 | ||||||||
\(97\) | 3.42751 | 0.348011 | 0.174005 | − | 0.984745i | \(-0.444329\pi\) | ||||
0.174005 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(98\) | 0.823556 | 0.0831917 | ||||||||
\(99\) | −24.2293 | −2.43513 | ||||||||
\(100\) | −6.60723 | −0.660723 | ||||||||
\(101\) | −13.3295 | −1.32633 | −0.663167 | − | 0.748472i | \(-0.730788\pi\) | ||||
−0.663167 | + | 0.748472i | \(0.730788\pi\) | |||||||
\(102\) | −5.91465 | −0.585637 | ||||||||
\(103\) | 11.6450 | 1.14741 | 0.573706 | − | 0.819061i | \(-0.305505\pi\) | ||||
0.573706 | + | 0.819061i | \(0.305505\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.41209 | −0.820936 | ||||||||
\(106\) | 0.328834 | 0.0319392 | ||||||||
\(107\) | 3.92966 | 0.379894 | 0.189947 | − | 0.981794i | \(-0.439168\pi\) | ||||
0.189947 | + | 0.981794i | \(0.439168\pi\) | |||||||
\(108\) | −3.78755 | −0.364457 | ||||||||
\(109\) | 11.2533 | 1.07787 | 0.538936 | − | 0.842346i | \(-0.318826\pi\) | ||||
0.538936 | + | 0.842346i | \(0.318826\pi\) | |||||||
\(110\) | 15.4757 | 1.47555 | ||||||||
\(111\) | 17.3040 | 1.64242 | ||||||||
\(112\) | 0.390549 | 0.0369034 | ||||||||
\(113\) | −5.77418 | −0.543189 | −0.271595 | − | 0.962412i | \(-0.587551\pi\) | ||||
−0.271595 | + | 0.962412i | \(0.587551\pi\) | |||||||
\(114\) | −4.28770 | −0.401579 | ||||||||
\(115\) | 8.63066 | 0.804813 | ||||||||
\(116\) | 7.92849 | 0.736142 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.95790 | 0.364354 | ||||||||
\(119\) | −2.69964 | −0.247476 | ||||||||
\(120\) | 23.0125 | 2.10075 | ||||||||
\(121\) | 24.3156 | 2.21051 | ||||||||
\(122\) | −0.952877 | −0.0862694 | ||||||||
\(123\) | −9.93284 | −0.895614 | ||||||||
\(124\) | 1.52207 | 0.136686 | ||||||||
\(125\) | 0.00370455 | 0.000331345 0 | ||||||||
\(126\) | 3.35776 | 0.299133 | ||||||||
\(127\) | 6.13117 | 0.544053 | 0.272027 | − | 0.962290i | \(-0.412306\pi\) | ||||
0.272027 | + | 0.962290i | \(0.412306\pi\) | |||||||
\(128\) | −8.30013 | −0.733635 | ||||||||
\(129\) | 18.5988 | 1.63753 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2217 | 0.893073 | 0.446537 | − | 0.894765i | \(-0.352657\pi\) | ||||
0.446537 | + | 0.894765i | \(0.352657\pi\) | |||||||
\(132\) | 20.8960 | 1.81877 | ||||||||
\(133\) | −1.95705 | −0.169698 | ||||||||
\(134\) | −5.17126 | −0.446729 | ||||||||
\(135\) | −9.06111 | −0.779856 | ||||||||
\(136\) | 7.38528 | 0.633283 | ||||||||
\(137\) | −19.9475 | −1.70423 | −0.852116 | − | 0.523353i | \(-0.824681\pi\) | ||||
−0.852116 | + | 0.523353i | \(0.824681\pi\) | |||||||
\(138\) | −5.97987 | −0.509041 | ||||||||
\(139\) | −20.3275 | −1.72415 | −0.862077 | − | 0.506777i | \(-0.830837\pi\) | ||||
−0.862077 | + | 0.506777i | \(0.830837\pi\) | |||||||
\(140\) | 4.17951 | 0.353233 | ||||||||
\(141\) | −1.21328 | −0.102177 | ||||||||
\(142\) | −3.71193 | −0.311498 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.59233 | 0.132694 | ||||||||
\(145\) | 18.9677 | 1.57518 | ||||||||
\(146\) | −6.84025 | −0.566103 | ||||||||
\(147\) | 2.66029 | 0.219417 | ||||||||
\(148\) | −8.59741 | −0.706703 | ||||||||
\(149\) | 10.7162 | 0.877901 | 0.438951 | − | 0.898511i | \(-0.355350\pi\) | ||||
0.438951 | + | 0.898511i | \(0.355350\pi\) | |||||||
\(150\) | 10.9519 | 0.894221 | ||||||||
\(151\) | 8.74416 | 0.711590 | 0.355795 | − | 0.934564i | \(-0.384210\pi\) | ||||
0.355795 | + | 0.934564i | \(0.384210\pi\) | |||||||
\(152\) | 5.35380 | 0.434251 | ||||||||
\(153\) | −11.0069 | −0.889852 | ||||||||
\(154\) | −4.89414 | −0.394381 | ||||||||
\(155\) | 3.64130 | 0.292476 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.50734 | 0.519342 | 0.259671 | − | 0.965697i | \(-0.416386\pi\) | ||||
0.259671 | + | 0.965697i | \(0.416386\pi\) | |||||||
\(158\) | −6.51770 | −0.518520 | ||||||||
\(159\) | 1.06222 | 0.0842393 | ||||||||
\(160\) | −18.3178 | −1.44815 | ||||||||
\(161\) | −2.72941 | −0.215108 | ||||||||
\(162\) | −3.79518 | −0.298177 | ||||||||
\(163\) | 2.61267 | 0.204640 | 0.102320 | − | 0.994752i | \(-0.467373\pi\) | ||||
0.102320 | + | 0.994752i | \(0.467373\pi\) | |||||||
\(164\) | 4.93509 | 0.385366 | ||||||||
\(165\) | 49.9905 | 3.89175 | ||||||||
\(166\) | 5.10436 | 0.396175 | ||||||||
\(167\) | 3.88624 | 0.300726 | 0.150363 | − | 0.988631i | \(-0.451956\pi\) | ||||
0.150363 | + | 0.988631i | \(0.451956\pi\) | |||||||
\(168\) | −7.27763 | −0.561482 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.03030 | 0.539200 | ||||||||
\(171\) | −7.97919 | −0.610184 | ||||||||
\(172\) | −9.24072 | −0.704599 | ||||||||
\(173\) | 13.9768 | 1.06263 | 0.531317 | − | 0.847173i | \(-0.321697\pi\) | ||||
0.531317 | + | 0.847173i | \(0.321697\pi\) | |||||||
\(174\) | −13.1420 | −0.996293 | ||||||||
\(175\) | 4.99883 | 0.377876 | ||||||||
\(176\) | −2.32091 | −0.174945 | ||||||||
\(177\) | 12.7850 | 0.960979 | ||||||||
\(178\) | −2.93298 | −0.219836 | ||||||||
\(179\) | −25.2843 | −1.88984 | −0.944919 | − | 0.327305i | \(-0.893860\pi\) | ||||
−0.944919 | + | 0.327305i | \(0.893860\pi\) | |||||||
\(180\) | 17.0405 | 1.27013 | ||||||||
\(181\) | 0.864474 | 0.0642559 | 0.0321279 | − | 0.999484i | \(-0.489772\pi\) | ||||
0.0321279 | + | 0.999484i | \(0.489772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.07803 | −0.227535 | ||||||||
\(184\) | 7.46673 | 0.550454 | ||||||||
\(185\) | −20.5680 | −1.51219 | ||||||||
\(186\) | −2.52293 | −0.184990 | ||||||||
\(187\) | 16.0432 | 1.17319 | ||||||||
\(188\) | 0.602814 | 0.0439647 | ||||||||
\(189\) | 2.86554 | 0.208438 | ||||||||
\(190\) | 5.09647 | 0.369737 | ||||||||
\(191\) | 14.6676 | 1.06131 | 0.530657 | − | 0.847587i | \(-0.321945\pi\) | ||||
0.530657 | + | 0.847587i | \(0.321945\pi\) | |||||||
\(192\) | 10.6138 | 0.765985 | ||||||||
\(193\) | −16.4959 | −1.18740 | −0.593700 | − | 0.804686i | \(-0.702333\pi\) | ||||
−0.593700 | + | 0.804686i | \(0.702333\pi\) | |||||||
\(194\) | 2.82275 | 0.202661 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.32176 | −0.0944111 | ||||||||
\(197\) | 11.0102 | 0.784443 | 0.392222 | − | 0.919871i | \(-0.371707\pi\) | ||||
0.392222 | + | 0.919871i | \(0.371707\pi\) | |||||||
\(198\) | −19.9542 | −1.41808 | ||||||||
\(199\) | −21.2117 | −1.50366 | −0.751829 | − | 0.659358i | \(-0.770828\pi\) | ||||
−0.751829 | + | 0.659358i | \(0.770828\pi\) | |||||||
\(200\) | −13.6751 | −0.966972 | ||||||||
\(201\) | −16.7045 | −1.17824 | ||||||||
\(202\) | −10.9776 | −0.772380 | ||||||||
\(203\) | −5.99845 | −0.421009 | ||||||||
\(204\) | 9.49264 | 0.664617 | ||||||||
\(205\) | 11.8064 | 0.824597 | ||||||||
\(206\) | 9.59027 | 0.668186 | ||||||||
\(207\) | −11.1282 | −0.773466 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.6301 | 0.804474 | ||||||||
\(210\) | −6.92783 | −0.478065 | ||||||||
\(211\) | −17.9358 | −1.23475 | −0.617375 | − | 0.786669i | \(-0.711804\pi\) | ||||
−0.617375 | + | 0.786669i | \(0.711804\pi\) | |||||||
\(212\) | −0.527759 | −0.0362466 | ||||||||
\(213\) | −11.9905 | −0.821572 | ||||||||
\(214\) | 3.23629 | 0.221228 | ||||||||
\(215\) | −22.1070 | −1.50768 | ||||||||
\(216\) | −7.83913 | −0.533385 | ||||||||
\(217\) | −1.15155 | −0.0781722 | ||||||||
\(218\) | 9.26774 | 0.627691 | ||||||||
\(219\) | −22.0957 | −1.49309 | ||||||||
\(220\) | −24.8376 | −1.67455 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 14.2508 | 0.956451 | ||||||||
\(223\) | −16.0312 | −1.07353 | −0.536763 | − | 0.843733i | \(-0.680353\pi\) | ||||
−0.536763 | + | 0.843733i | \(0.680353\pi\) | |||||||
\(224\) | 5.79294 | 0.387057 | ||||||||
\(225\) | 20.3810 | 1.35873 | ||||||||
\(226\) | −4.75536 | −0.316322 | ||||||||
\(227\) | 16.3750 | 1.08685 | 0.543424 | − | 0.839458i | \(-0.317127\pi\) | ||||
0.543424 | + | 0.839458i | \(0.317127\pi\) | |||||||
\(228\) | 6.88148 | 0.455737 | ||||||||
\(229\) | −27.0104 | −1.78490 | −0.892449 | − | 0.451148i | \(-0.851015\pi\) | ||||
−0.892449 | + | 0.451148i | \(0.851015\pi\) | |||||||
\(230\) | 7.10783 | 0.468677 | ||||||||
\(231\) | −15.8093 | −1.04018 | ||||||||
\(232\) | 16.4097 | 1.07735 | ||||||||
\(233\) | 11.5681 | 0.757853 | 0.378926 | − | 0.925427i | \(-0.376293\pi\) | ||||
0.378926 | + | 0.925427i | \(0.376293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.44214 | 0.0940747 | ||||||||
\(236\) | −6.35217 | −0.413491 | ||||||||
\(237\) | −21.0538 | −1.36759 | ||||||||
\(238\) | −2.22331 | −0.144116 | ||||||||
\(239\) | −14.6731 | −0.949122 | −0.474561 | − | 0.880223i | \(-0.657393\pi\) | ||||
−0.474561 | + | 0.880223i | \(0.657393\pi\) | |||||||
\(240\) | −3.28533 | −0.212067 | ||||||||
\(241\) | 14.3467 | 0.924151 | 0.462076 | − | 0.886841i | \(-0.347105\pi\) | ||||
0.462076 | + | 0.886841i | \(0.347105\pi\) | |||||||
\(242\) | 20.0253 | 1.28727 | ||||||||
\(243\) | −20.8560 | −1.33791 | ||||||||
\(244\) | 1.52931 | 0.0979039 | ||||||||
\(245\) | −3.16209 | −0.202019 | ||||||||
\(246\) | −8.18025 | −0.521554 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.15024 | 0.200040 | ||||||||
\(249\) | 16.4883 | 1.04491 | ||||||||
\(250\) | 0.00305091 | 0.000192956 0 | ||||||||
\(251\) | 8.61452 | 0.543744 | 0.271872 | − | 0.962333i | \(-0.412357\pi\) | ||||
0.271872 | + | 0.962333i | \(0.412357\pi\) | |||||||
\(252\) | −5.38900 | −0.339475 | ||||||||
\(253\) | 16.2201 | 1.01975 | ||||||||
\(254\) | 5.04936 | 0.316825 | ||||||||
\(255\) | 22.7096 | 1.42213 | ||||||||
\(256\) | −14.8151 | −0.925941 | ||||||||
\(257\) | 10.3639 | 0.646485 | 0.323243 | − | 0.946316i | \(-0.395227\pi\) | ||||
0.323243 | + | 0.946316i | \(0.395227\pi\) | |||||||
\(258\) | 15.3171 | 0.953603 | ||||||||
\(259\) | 6.50454 | 0.404172 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.4566 | −1.51383 | ||||||||
\(262\) | 8.41813 | 0.520074 | ||||||||
\(263\) | −22.0826 | −1.36167 | −0.680835 | − | 0.732436i | \(-0.738383\pi\) | ||||
−0.680835 | + | 0.732436i | \(0.738383\pi\) | |||||||
\(264\) | 43.2488 | 2.66178 | ||||||||
\(265\) | −1.26258 | −0.0775596 | ||||||||
\(266\) | −1.61174 | −0.0988220 | ||||||||
\(267\) | −9.47427 | −0.579816 | ||||||||
\(268\) | 8.29954 | 0.506975 | ||||||||
\(269\) | 12.9399 | 0.788960 | 0.394480 | − | 0.918905i | \(-0.370925\pi\) | ||||
0.394480 | + | 0.918905i | \(0.370925\pi\) | |||||||
\(270\) | −7.46233 | −0.454143 | ||||||||
\(271\) | 17.6749 | 1.07367 | 0.536837 | − | 0.843686i | \(-0.319619\pi\) | ||||
0.536837 | + | 0.843686i | \(0.319619\pi\) | |||||||
\(272\) | −1.05434 | −0.0639289 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4279 | −0.992446 | ||||||||
\(275\) | −29.7065 | −1.79137 | ||||||||
\(276\) | 9.59732 | 0.577691 | ||||||||
\(277\) | −18.0150 | −1.08242 | −0.541209 | − | 0.840888i | \(-0.682033\pi\) | ||||
−0.541209 | + | 0.840888i | \(0.682033\pi\) | |||||||
\(278\) | −16.7408 | −1.00405 | ||||||||
\(279\) | −4.69504 | −0.281085 | ||||||||
\(280\) | 8.65038 | 0.516959 | ||||||||
\(281\) | −2.44178 | −0.145665 | −0.0728323 | − | 0.997344i | \(-0.523204\pi\) | ||||
−0.0728323 | + | 0.997344i | \(0.523204\pi\) | |||||||
\(282\) | −0.999205 | −0.0595018 | ||||||||
\(283\) | −28.7240 | −1.70746 | −0.853732 | − | 0.520713i | \(-0.825666\pi\) | ||||
−0.853732 | + | 0.520713i | \(0.825666\pi\) | |||||||
\(284\) | 5.95741 | 0.353507 | ||||||||
\(285\) | 16.4629 | 0.975176 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.73374 | −0.220396 | ||||||||
\(288\) | 23.6187 | 1.39175 | ||||||||
\(289\) | −9.71193 | −0.571290 | ||||||||
\(290\) | 15.6209 | 0.917292 | ||||||||
\(291\) | 9.11818 | 0.534517 | ||||||||
\(292\) | 10.9782 | 0.642449 | ||||||||
\(293\) | 29.3309 | 1.71353 | 0.856763 | − | 0.515710i | \(-0.172472\pi\) | ||||
0.856763 | + | 0.515710i | \(0.172472\pi\) | |||||||
\(294\) | 2.19090 | 0.127776 | ||||||||
\(295\) | −15.1966 | −0.884779 | ||||||||
\(296\) | −17.7942 | −1.03426 | ||||||||
\(297\) | −17.0291 | −0.988126 | ||||||||
\(298\) | 8.82535 | 0.511239 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −17.5772 | −1.01482 | ||||||||
\(301\) | 6.99125 | 0.402969 | ||||||||
\(302\) | 7.20131 | 0.414389 | ||||||||
\(303\) | −35.4603 | −2.03714 | ||||||||
\(304\) | −0.764323 | −0.0438369 | ||||||||
\(305\) | 3.65863 | 0.209492 | ||||||||
\(306\) | −9.06476 | −0.518198 | ||||||||
\(307\) | 7.06910 | 0.403455 | 0.201728 | − | 0.979442i | \(-0.435344\pi\) | ||||
0.201728 | + | 0.979442i | \(0.435344\pi\) | |||||||
\(308\) | 7.85479 | 0.447568 | ||||||||
\(309\) | 30.9790 | 1.76233 | ||||||||
\(310\) | 2.99882 | 0.170321 | ||||||||
\(311\) | −22.2686 | −1.26274 | −0.631368 | − | 0.775483i | \(-0.717506\pi\) | ||||
−0.631368 | + | 0.775483i | \(0.717506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.0840 | −1.58740 | −0.793700 | − | 0.608309i | \(-0.791848\pi\) | ||||
−0.793700 | + | 0.608309i | \(0.791848\pi\) | |||||||
\(314\) | 5.35916 | 0.302435 | ||||||||
\(315\) | −12.8923 | −0.726401 | ||||||||
\(316\) | 10.4605 | 0.588449 | ||||||||
\(317\) | −19.5155 | −1.09610 | −0.548049 | − | 0.836446i | \(-0.684629\pi\) | ||||
−0.548049 | + | 0.836446i | \(0.684629\pi\) | |||||||
\(318\) | 0.874796 | 0.0490561 | ||||||||
\(319\) | 35.6470 | 1.99585 | ||||||||
\(320\) | −12.6158 | −0.705247 | ||||||||
\(321\) | 10.4540 | 0.583488 | ||||||||
\(322\) | −2.24783 | −0.125266 | ||||||||
\(323\) | 5.28333 | 0.293972 | ||||||||
\(324\) | 6.09102 | 0.338390 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.15168 | 0.119171 | ||||||||
\(327\) | 29.9371 | 1.65553 | ||||||||
\(328\) | 10.2142 | 0.563986 | ||||||||
\(329\) | −0.456071 | −0.0251440 | ||||||||
\(330\) | 41.1700 | 2.26633 | ||||||||
\(331\) | −15.6308 | −0.859145 | −0.429573 | − | 0.903032i | \(-0.641336\pi\) | ||||
−0.429573 | + | 0.903032i | \(0.641336\pi\) | |||||||
\(332\) | −8.19217 | −0.449604 | ||||||||
\(333\) | 26.5200 | 1.45329 | ||||||||
\(334\) | 3.20053 | 0.175125 | ||||||||
\(335\) | 19.8553 | 1.08481 | ||||||||
\(336\) | 1.03897 | 0.0566807 | ||||||||
\(337\) | −21.7501 | −1.18480 | −0.592401 | − | 0.805643i | \(-0.701820\pi\) | ||||
−0.592401 | + | 0.805643i | \(0.701820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.3610 | −0.834295 | ||||||||
\(340\) | −11.2832 | −0.611917 | ||||||||
\(341\) | 6.84330 | 0.370586 | ||||||||
\(342\) | −6.57131 | −0.355336 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −19.1256 | −1.03118 | ||||||||
\(345\) | 22.9601 | 1.23613 | ||||||||
\(346\) | 11.5106 | 0.618816 | ||||||||
\(347\) | −15.9590 | −0.856726 | −0.428363 | − | 0.903607i | \(-0.640909\pi\) | ||||
−0.428363 | + | 0.903607i | \(0.640909\pi\) | |||||||
\(348\) | 21.0921 | 1.13065 | ||||||||
\(349\) | −6.81706 | −0.364909 | −0.182455 | − | 0.983214i | \(-0.558404\pi\) | ||||
−0.182455 | + | 0.983214i | \(0.558404\pi\) | |||||||
\(350\) | 4.11682 | 0.220053 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −34.4257 | −1.83490 | ||||||||
\(353\) | 14.0033 | 0.745318 | 0.372659 | − | 0.927968i | \(-0.378446\pi\) | ||||
0.372659 | + | 0.927968i | \(0.378446\pi\) | |||||||
\(354\) | 10.5292 | 0.559619 | ||||||||
\(355\) | 14.2522 | 0.756427 | ||||||||
\(356\) | 4.70725 | 0.249484 | ||||||||
\(357\) | −7.18184 | −0.380103 | ||||||||
\(358\) | −20.8230 | −1.10053 | ||||||||
\(359\) | −5.41494 | −0.285789 | −0.142895 | − | 0.989738i | \(-0.545641\pi\) | ||||
−0.142895 | + | 0.989738i | \(0.545641\pi\) | |||||||
\(360\) | 35.2689 | 1.85884 | ||||||||
\(361\) | −15.1700 | −0.798419 | ||||||||
\(362\) | 0.711943 | 0.0374189 | ||||||||
\(363\) | 64.6867 | 3.39517 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.2636 | 1.37470 | ||||||||
\(366\) | −2.53493 | −0.132503 | ||||||||
\(367\) | 30.0317 | 1.56764 | 0.783822 | − | 0.620985i | \(-0.213267\pi\) | ||||
0.783822 | + | 0.620985i | \(0.213267\pi\) | |||||||
\(368\) | −1.06597 | −0.0555675 | ||||||||
\(369\) | −15.2230 | −0.792480 | ||||||||
\(370\) | −16.9389 | −0.880610 | ||||||||
\(371\) | 0.399286 | 0.0207299 | ||||||||
\(372\) | 4.04914 | 0.209938 | ||||||||
\(373\) | 21.4098 | 1.10856 | 0.554278 | − | 0.832332i | \(-0.312995\pi\) | ||||
0.554278 | + | 0.832332i | \(0.312995\pi\) | |||||||
\(374\) | 13.2124 | 0.683199 | ||||||||
\(375\) | 0.00985519 | 0.000508920 0 | ||||||||
\(376\) | 1.24765 | 0.0643427 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.35994 | 0.121382 | ||||||||
\(379\) | −9.47655 | −0.486778 | −0.243389 | − | 0.969929i | \(-0.578259\pi\) | ||||
−0.243389 | + | 0.969929i | \(0.578259\pi\) | |||||||
\(380\) | −8.17951 | −0.419600 | ||||||||
\(381\) | 16.3107 | 0.835622 | ||||||||
\(382\) | 12.0796 | 0.618048 | ||||||||
\(383\) | 5.43061 | 0.277491 | 0.138746 | − | 0.990328i | \(-0.455693\pi\) | ||||
0.138746 | + | 0.990328i | \(0.455693\pi\) | |||||||
\(384\) | −22.0808 | −1.12680 | ||||||||
\(385\) | 18.7914 | 0.957696 | ||||||||
\(386\) | −13.5853 | −0.691473 | ||||||||
\(387\) | 28.5044 | 1.44896 | ||||||||
\(388\) | −4.53033 | −0.229993 | ||||||||
\(389\) | −10.6422 | −0.539580 | −0.269790 | − | 0.962919i | \(-0.586954\pi\) | ||||
−0.269790 | + | 0.962919i | \(0.586954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.36845 | 0.372638 | ||||||||
\(392\) | −2.73565 | −0.138171 | ||||||||
\(393\) | 27.1927 | 1.37169 | ||||||||
\(394\) | 9.06750 | 0.456814 | ||||||||
\(395\) | 25.0251 | 1.25915 | ||||||||
\(396\) | 32.0252 | 1.60933 | ||||||||
\(397\) | 37.1854 | 1.86628 | 0.933140 | − | 0.359512i | \(-0.117057\pi\) | ||||
0.933140 | + | 0.359512i | \(0.117057\pi\) | |||||||
\(398\) | −17.4690 | −0.875644 | ||||||||
\(399\) | −5.20632 | −0.260642 | ||||||||
\(400\) | 1.95229 | 0.0976143 | ||||||||
\(401\) | 0.896610 | 0.0447746 | 0.0223873 | − | 0.999749i | \(-0.492873\pi\) | ||||
0.0223873 | + | 0.999749i | \(0.492873\pi\) | |||||||
\(402\) | −13.7571 | −0.686139 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 17.6183 | 0.876545 | ||||||||
\(405\) | 14.5718 | 0.724079 | ||||||||
\(406\) | −4.94006 | −0.245171 | ||||||||
\(407\) | −38.6545 | −1.91603 | ||||||||
\(408\) | 19.6470 | 0.972672 | ||||||||
\(409\) | −24.5773 | −1.21527 | −0.607635 | − | 0.794217i | \(-0.707881\pi\) | ||||
−0.607635 | + | 0.794217i | \(0.707881\pi\) | |||||||
\(410\) | 9.72326 | 0.480198 | ||||||||
\(411\) | −53.0662 | −2.61756 | ||||||||
\(412\) | −15.3918 | −0.758299 | ||||||||
\(413\) | 4.80586 | 0.236481 | ||||||||
\(414\) | −9.16473 | −0.450422 | ||||||||
\(415\) | −19.5985 | −0.962052 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −54.0770 | −2.64816 | ||||||||
\(418\) | 9.57807 | 0.468479 | ||||||||
\(419\) | −7.64558 | −0.373511 | −0.186755 | − | 0.982406i | \(-0.559797\pi\) | ||||
−0.186755 | + | 0.982406i | \(0.559797\pi\) | |||||||
\(420\) | 11.1187 | 0.542538 | ||||||||
\(421\) | 25.0780 | 1.22223 | 0.611113 | − | 0.791544i | \(-0.290722\pi\) | ||||
0.611113 | + | 0.791544i | \(0.290722\pi\) | |||||||
\(422\) | −14.7711 | −0.719046 | ||||||||
\(423\) | −1.85947 | −0.0904106 | ||||||||
\(424\) | −1.09231 | −0.0530471 | ||||||||
\(425\) | −13.4951 | −0.654606 | ||||||||
\(426\) | −9.87481 | −0.478436 | ||||||||
\(427\) | −1.15703 | −0.0559925 | ||||||||
\(428\) | −5.19405 | −0.251064 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.2063 | −0.877987 | ||||||||
\(431\) | 7.75404 | 0.373499 | 0.186750 | − | 0.982408i | \(-0.440205\pi\) | ||||
0.186750 | + | 0.982408i | \(0.440205\pi\) | |||||||
\(432\) | 1.11913 | 0.0538444 | ||||||||
\(433\) | 35.9760 | 1.72890 | 0.864448 | − | 0.502722i | \(-0.167668\pi\) | ||||
0.864448 | + | 0.502722i | \(0.167668\pi\) | |||||||
\(434\) | −0.948365 | −0.0455230 | ||||||||
\(435\) | 50.4595 | 2.41935 | ||||||||
\(436\) | −14.8741 | −0.712342 | ||||||||
\(437\) | 5.34160 | 0.255523 | ||||||||
\(438\) | −18.1971 | −0.869489 | ||||||||
\(439\) | −28.2350 | −1.34758 | −0.673792 | − | 0.738921i | \(-0.735336\pi\) | ||||
−0.673792 | + | 0.738921i | \(0.735336\pi\) | |||||||
\(440\) | −51.4066 | −2.45071 | ||||||||
\(441\) | 4.07715 | 0.194150 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.7918 | 1.36794 | 0.683970 | − | 0.729511i | \(-0.260252\pi\) | ||||
0.683970 | + | 0.729511i | \(0.260252\pi\) | |||||||
\(444\) | −22.8716 | −1.08544 | ||||||||
\(445\) | 11.2614 | 0.533840 | ||||||||
\(446\) | −13.2026 | −0.625159 | ||||||||
\(447\) | 28.5081 | 1.34839 | ||||||||
\(448\) | 3.98971 | 0.188496 | ||||||||
\(449\) | −29.1902 | −1.37757 | −0.688785 | − | 0.724965i | \(-0.741856\pi\) | ||||
−0.688785 | + | 0.724965i | \(0.741856\pi\) | |||||||
\(450\) | 16.7849 | 0.791247 | ||||||||
\(451\) | 22.1885 | 1.04482 | ||||||||
\(452\) | 7.63205 | 0.358982 | ||||||||
\(453\) | 23.2620 | 1.09295 | ||||||||
\(454\) | 13.4858 | 0.632918 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.2427 | 0.666974 | ||||||||
\(457\) | −31.6848 | −1.48215 | −0.741077 | − | 0.671420i | \(-0.765684\pi\) | ||||
−0.741077 | + | 0.671420i | \(0.765684\pi\) | |||||||
\(458\) | −22.2446 | −1.03942 | ||||||||
\(459\) | −7.73594 | −0.361083 | ||||||||
\(460\) | −11.4076 | −0.531883 | ||||||||
\(461\) | 22.1018 | 1.02938 | 0.514691 | − | 0.857376i | \(-0.327907\pi\) | ||||
0.514691 | + | 0.857376i | \(0.327907\pi\) | |||||||
\(462\) | −13.0199 | −0.605738 | ||||||||
\(463\) | 38.8811 | 1.80696 | 0.903479 | − | 0.428632i | \(-0.141004\pi\) | ||||
0.903479 | + | 0.428632i | \(0.141004\pi\) | |||||||
\(464\) | −2.34269 | −0.108757 | ||||||||
\(465\) | 9.68693 | 0.449220 | ||||||||
\(466\) | 9.52699 | 0.441329 | ||||||||
\(467\) | 13.2823 | 0.614632 | 0.307316 | − | 0.951607i | \(-0.400569\pi\) | ||||
0.307316 | + | 0.951607i | \(0.400569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.27918 | −0.289946 | ||||||||
\(470\) | 1.18768 | 0.0547837 | ||||||||
\(471\) | 17.3114 | 0.797668 | ||||||||
\(472\) | −13.1472 | −0.605147 | ||||||||
\(473\) | −41.5469 | −1.91033 | ||||||||
\(474\) | −17.3390 | −0.796406 | ||||||||
\(475\) | −9.78295 | −0.448872 | ||||||||
\(476\) | 3.56827 | 0.163551 | ||||||||
\(477\) | 1.62795 | 0.0745387 | ||||||||
\(478\) | −12.0841 | −0.552714 | ||||||||
\(479\) | −6.63512 | −0.303166 | −0.151583 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151583 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(480\) | −48.7307 | −2.22424 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.8153 | 0.538172 | ||||||||
\(483\) | −7.26104 | −0.330389 | ||||||||
\(484\) | −32.1393 | −1.46088 | ||||||||
\(485\) | −10.8381 | −0.492133 | ||||||||
\(486\) | −17.1761 | −0.779123 | ||||||||
\(487\) | −33.4701 | −1.51668 | −0.758338 | − | 0.651861i | \(-0.773988\pi\) | ||||
−0.758338 | + | 0.651861i | \(0.773988\pi\) | |||||||
\(488\) | 3.16522 | 0.143283 | ||||||||
\(489\) | 6.95047 | 0.314311 | ||||||||
\(490\) | −2.60416 | −0.117644 | ||||||||
\(491\) | −37.3287 | −1.68462 | −0.842310 | − | 0.538993i | \(-0.818805\pi\) | ||||
−0.842310 | + | 0.538993i | \(0.818805\pi\) | |||||||
\(492\) | 13.1288 | 0.591891 | ||||||||
\(493\) | 16.1937 | 0.729327 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 76.6152 | 3.44360 | ||||||||
\(496\) | −0.449736 | −0.0201937 | ||||||||
\(497\) | −4.50720 | −0.202175 | ||||||||
\(498\) | 13.5791 | 0.608493 | ||||||||
\(499\) | −34.1327 | −1.52799 | −0.763994 | − | 0.645223i | \(-0.776764\pi\) | ||||
−0.763994 | + | 0.645223i | \(0.776764\pi\) | |||||||
\(500\) | −0.00489651 | −0.000218979 0 | ||||||||
\(501\) | 10.3385 | 0.461891 | ||||||||
\(502\) | 7.09454 | 0.316645 | ||||||||
\(503\) | 15.3089 | 0.682592 | 0.341296 | − | 0.939956i | \(-0.389134\pi\) | ||||
0.341296 | + | 0.939956i | \(0.389134\pi\) | |||||||
\(504\) | −11.1537 | −0.496824 | ||||||||
\(505\) | 42.1491 | 1.87561 | ||||||||
\(506\) | 13.3581 | 0.593842 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.10390 | −0.359553 | ||||||||
\(509\) | −18.4970 | −0.819866 | −0.409933 | − | 0.912116i | \(-0.634448\pi\) | ||||
−0.409933 | + | 0.912116i | \(0.634448\pi\) | |||||||
\(510\) | 18.7027 | 0.828168 | ||||||||
\(511\) | −8.30575 | −0.367425 | ||||||||
\(512\) | 4.39924 | 0.194421 | ||||||||
\(513\) | −5.60801 | −0.247599 | ||||||||
\(514\) | 8.53529 | 0.376476 | ||||||||
\(515\) | −36.8224 | −1.62259 | ||||||||
\(516\) | −24.5830 | −1.08221 | ||||||||
\(517\) | 2.71029 | 0.119198 | ||||||||
\(518\) | 5.35685 | 0.235367 | ||||||||
\(519\) | 37.1823 | 1.63212 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.5865 | 1.03334 | 0.516671 | − | 0.856184i | \(-0.327171\pi\) | ||||
0.516671 | + | 0.856184i | \(0.327171\pi\) | |||||||
\(522\) | −20.1414 | −0.881564 | ||||||||
\(523\) | 12.3059 | 0.538099 | 0.269049 | − | 0.963126i | \(-0.413291\pi\) | ||||
0.269049 | + | 0.963126i | \(0.413291\pi\) | |||||||
\(524\) | −13.5106 | −0.590212 | ||||||||
\(525\) | 13.2983 | 0.580387 | ||||||||
\(526\) | −18.1862 | −0.792958 | ||||||||
\(527\) | 3.10877 | 0.135420 | ||||||||
\(528\) | −6.17431 | −0.268702 | ||||||||
\(529\) | −15.5503 | −0.676100 | ||||||||
\(530\) | −1.03980 | −0.0451662 | ||||||||
\(531\) | 19.5942 | 0.850317 | ||||||||
\(532\) | 2.58674 | 0.112149 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7.80259 | −0.337651 | ||||||||
\(535\) | −12.4259 | −0.537220 | ||||||||
\(536\) | 17.1777 | 0.741962 | ||||||||
\(537\) | −67.2636 | −2.90264 | ||||||||
\(538\) | 10.6567 | 0.459444 | ||||||||
\(539\) | −5.94270 | −0.255970 | ||||||||
\(540\) | 11.9766 | 0.515390 | ||||||||
\(541\) | −19.4411 | −0.835838 | −0.417919 | − | 0.908484i | \(-0.637240\pi\) | ||||
−0.417919 | + | 0.908484i | \(0.637240\pi\) | |||||||
\(542\) | 14.5563 | 0.625245 | ||||||||
\(543\) | 2.29975 | 0.0986919 | ||||||||
\(544\) | −15.6389 | −0.670511 | ||||||||
\(545\) | −35.5841 | −1.52425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.2163 | 1.71953 | 0.859763 | − | 0.510693i | \(-0.170611\pi\) | ||||
0.859763 | + | 0.510693i | \(0.170611\pi\) | |||||||
\(548\) | 26.3658 | 1.12629 | ||||||||
\(549\) | −4.71738 | −0.201333 | ||||||||
\(550\) | −24.4650 | −1.04319 | ||||||||
\(551\) | 11.7393 | 0.500109 | ||||||||
\(552\) | 19.8637 | 0.845454 | ||||||||
\(553\) | −7.91410 | −0.336542 | ||||||||
\(554\) | −14.8364 | −0.630337 | ||||||||
\(555\) | −54.7168 | −2.32260 | ||||||||
\(556\) | 26.8680 | 1.13945 | ||||||||
\(557\) | −7.96399 | −0.337445 | −0.168722 | − | 0.985664i | \(-0.553964\pi\) | ||||
−0.168722 | + | 0.985664i | \(0.553964\pi\) | |||||||
\(558\) | −3.86663 | −0.163687 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.23495 | −0.0521862 | ||||||||
\(561\) | 42.6795 | 1.80193 | ||||||||
\(562\) | −2.01095 | −0.0848266 | ||||||||
\(563\) | −1.42396 | −0.0600128 | −0.0300064 | − | 0.999550i | \(-0.509553\pi\) | ||||
−0.0300064 | + | 0.999550i | \(0.509553\pi\) | |||||||
\(564\) | 1.60366 | 0.0675263 | ||||||||
\(565\) | 18.2585 | 0.768140 | ||||||||
\(566\) | −23.6558 | −0.994327 | ||||||||
\(567\) | −4.60828 | −0.193530 | ||||||||
\(568\) | 12.3301 | 0.517360 | ||||||||
\(569\) | −18.5189 | −0.776353 | −0.388177 | − | 0.921585i | \(-0.626895\pi\) | ||||
−0.388177 | + | 0.921585i | \(0.626895\pi\) | |||||||
\(570\) | 13.5581 | 0.567886 | ||||||||
\(571\) | 4.35766 | 0.182362 | 0.0911812 | − | 0.995834i | \(-0.470936\pi\) | ||||
0.0911812 | + | 0.995834i | \(0.470936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.0202 | 1.63009 | ||||||||
\(574\) | −3.07494 | −0.128346 | ||||||||
\(575\) | −13.6439 | −0.568989 | ||||||||
\(576\) | 16.2667 | 0.677778 | ||||||||
\(577\) | 9.56416 | 0.398161 | 0.199081 | − | 0.979983i | \(-0.436204\pi\) | ||||
0.199081 | + | 0.979983i | \(0.436204\pi\) | |||||||
\(578\) | −7.99832 | −0.332686 | ||||||||
\(579\) | −43.8839 | −1.82375 | ||||||||
\(580\) | −25.0706 | −1.04100 | ||||||||
\(581\) | 6.19795 | 0.257134 | ||||||||
\(582\) | 7.50933 | 0.311272 | ||||||||
\(583\) | −2.37284 | −0.0982728 | ||||||||
\(584\) | 22.7216 | 0.940228 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.1556 | 0.997859 | ||||||||
\(587\) | −2.36053 | −0.0974296 | −0.0487148 | − | 0.998813i | \(-0.515513\pi\) | ||||
−0.0487148 | + | 0.998813i | \(0.515513\pi\) | |||||||
\(588\) | −3.51626 | −0.145008 | ||||||||
\(589\) | 2.25364 | 0.0928594 | ||||||||
\(590\) | −12.5152 | −0.515244 | ||||||||
\(591\) | 29.2903 | 1.20484 | ||||||||
\(592\) | 2.54034 | 0.104407 | ||||||||
\(593\) | −40.4292 | −1.66023 | −0.830114 | − | 0.557594i | \(-0.811725\pi\) | ||||
−0.830114 | + | 0.557594i | \(0.811725\pi\) | |||||||
\(594\) | −14.0244 | −0.575427 | ||||||||
\(595\) | 8.53652 | 0.349963 | ||||||||
\(596\) | −14.1641 | −0.580185 | ||||||||
\(597\) | −56.4294 | −2.30950 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.5873 | −1.57663 | −0.788316 | − | 0.615270i | \(-0.789047\pi\) | ||||
−0.788316 | + | 0.615270i | \(0.789047\pi\) | |||||||
\(600\) | −36.3796 | −1.48519 | ||||||||
\(601\) | 8.16231 | 0.332948 | 0.166474 | − | 0.986046i | \(-0.446762\pi\) | ||||
0.166474 | + | 0.986046i | \(0.446762\pi\) | |||||||
\(602\) | 5.75769 | 0.234666 | ||||||||
\(603\) | −25.6012 | −1.04256 | ||||||||
\(604\) | −11.5576 | −0.470274 | ||||||||
\(605\) | −76.8883 | −3.12595 | ||||||||
\(606\) | −29.2036 | −1.18631 | ||||||||
\(607\) | 7.58525 | 0.307876 | 0.153938 | − | 0.988081i | \(-0.450804\pi\) | ||||
0.153938 | + | 0.988081i | \(0.450804\pi\) | |||||||
\(608\) | −11.3371 | −0.459779 | ||||||||
\(609\) | −15.9576 | −0.646636 | ||||||||
\(610\) | 3.01308 | 0.121996 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 14.5484 | 0.588083 | ||||||||
\(613\) | −15.5778 | −0.629183 | −0.314592 | − | 0.949227i | \(-0.601868\pi\) | ||||
−0.314592 | + | 0.949227i | \(0.601868\pi\) | |||||||
\(614\) | 5.82180 | 0.234949 | ||||||||
\(615\) | 31.4086 | 1.26652 | ||||||||
\(616\) | 16.2571 | 0.655019 | ||||||||
\(617\) | −23.8687 | −0.960916 | −0.480458 | − | 0.877018i | \(-0.659529\pi\) | ||||
−0.480458 | + | 0.877018i | \(0.659529\pi\) | |||||||
\(618\) | 25.5129 | 1.02628 | ||||||||
\(619\) | 19.4963 | 0.783622 | 0.391811 | − | 0.920046i | \(-0.371849\pi\) | ||||
0.391811 | + | 0.920046i | \(0.371849\pi\) | |||||||
\(620\) | −4.81291 | −0.193291 | ||||||||
\(621\) | −7.82126 | −0.313856 | ||||||||
\(622\) | −18.3394 | −0.735344 | ||||||||
\(623\) | −3.56136 | −0.142683 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0059 | −1.00023 | ||||||||
\(626\) | −23.1287 | −0.924410 | ||||||||
\(627\) | 30.9396 | 1.23561 | ||||||||
\(628\) | −8.60111 | −0.343222 | ||||||||
\(629\) | −17.5599 | −0.700161 | ||||||||
\(630\) | −10.6176 | −0.423014 | ||||||||
\(631\) | −25.6619 | −1.02158 | −0.510792 | − | 0.859704i | \(-0.670648\pi\) | ||||
−0.510792 | + | 0.859704i | \(0.670648\pi\) | |||||||
\(632\) | 21.6502 | 0.861199 | ||||||||
\(633\) | −47.7144 | −1.89648 | ||||||||
\(634\) | −16.0721 | −0.638304 | ||||||||
\(635\) | −19.3873 | −0.769362 | ||||||||
\(636\) | −1.40399 | −0.0556719 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29.3573 | 1.16227 | ||||||||
\(639\) | −18.3765 | −0.726964 | ||||||||
\(640\) | 26.2458 | 1.03746 | ||||||||
\(641\) | −1.10604 | −0.0436860 | −0.0218430 | − | 0.999761i | \(-0.506953\pi\) | ||||
−0.0218430 | + | 0.999761i | \(0.506953\pi\) | |||||||
\(642\) | 8.60949 | 0.339789 | ||||||||
\(643\) | −12.6367 | −0.498341 | −0.249171 | − | 0.968460i | \(-0.580158\pi\) | ||||
−0.249171 | + | 0.968460i | \(0.580158\pi\) | |||||||
\(644\) | 3.60762 | 0.142160 | ||||||||
\(645\) | −58.8110 | −2.31568 | ||||||||
\(646\) | 4.35112 | 0.171192 | ||||||||
\(647\) | 25.7148 | 1.01095 | 0.505477 | − | 0.862840i | \(-0.331317\pi\) | ||||
0.505477 | + | 0.862840i | \(0.331317\pi\) | |||||||
\(648\) | 12.6066 | 0.495236 | ||||||||
\(649\) | −28.5598 | −1.12107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.06345 | −0.120066 | ||||||||
\(652\) | −3.45331 | −0.135242 | ||||||||
\(653\) | 25.2607 | 0.988527 | 0.494263 | − | 0.869312i | \(-0.335438\pi\) | ||||
0.494263 | + | 0.869312i | \(0.335438\pi\) | |||||||
\(654\) | 24.6549 | 0.964083 | ||||||||
\(655\) | −32.3219 | −1.26292 | ||||||||
\(656\) | −1.45821 | −0.0569335 | ||||||||
\(657\) | −33.8638 | −1.32115 | ||||||||
\(658\) | −0.375600 | −0.0146424 | ||||||||
\(659\) | 22.9764 | 0.895034 | 0.447517 | − | 0.894275i | \(-0.352308\pi\) | ||||
0.447517 | + | 0.894275i | \(0.352308\pi\) | |||||||
\(660\) | −66.0752 | −2.57197 | ||||||||
\(661\) | −30.4326 | −1.18369 | −0.591845 | − | 0.806051i | \(-0.701600\pi\) | ||||
−0.591845 | + | 0.806051i | \(0.701600\pi\) | |||||||
\(662\) | −12.8728 | −0.500316 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.9554 | −0.657998 | ||||||||
\(665\) | 6.18837 | 0.239975 | ||||||||
\(666\) | 21.8407 | 0.846310 | ||||||||
\(667\) | 16.3723 | 0.633937 | ||||||||
\(668\) | −5.13665 | −0.198743 | ||||||||
\(669\) | −42.6475 | −1.64885 | ||||||||
\(670\) | 16.3520 | 0.631733 | ||||||||
\(671\) | 6.87586 | 0.265440 | ||||||||
\(672\) | 15.4109 | 0.594489 | ||||||||
\(673\) | 10.8387 | 0.417800 | 0.208900 | − | 0.977937i | \(-0.433012\pi\) | ||||
0.208900 | + | 0.977937i | \(0.433012\pi\) | |||||||
\(674\) | −17.9124 | −0.689960 | ||||||||
\(675\) | 14.3244 | 0.551345 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.1209 | −0.696442 | −0.348221 | − | 0.937412i | \(-0.613214\pi\) | ||||
−0.348221 | + | 0.937412i | \(0.613214\pi\) | |||||||
\(678\) | −12.6506 | −0.485845 | ||||||||
\(679\) | 3.42751 | 0.131536 | ||||||||
\(680\) | −23.3529 | −0.895545 | ||||||||
\(681\) | 43.5624 | 1.66931 | ||||||||
\(682\) | 5.63584 | 0.215808 | ||||||||
\(683\) | 37.8352 | 1.44772 | 0.723861 | − | 0.689946i | \(-0.242366\pi\) | ||||
0.723861 | + | 0.689946i | \(0.242366\pi\) | |||||||
\(684\) | 10.5465 | 0.403257 | ||||||||
\(685\) | 63.0759 | 2.41001 | ||||||||
\(686\) | 0.823556 | 0.0314435 | ||||||||
\(687\) | −71.8556 | −2.74146 | ||||||||
\(688\) | 2.73042 | 0.104096 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.9089 | 0.719850 | ||||||||
\(691\) | 30.0261 | 1.14225 | 0.571124 | − | 0.820864i | \(-0.306508\pi\) | ||||
0.571124 | + | 0.820864i | \(0.306508\pi\) | |||||||
\(692\) | −18.4739 | −0.702271 | ||||||||
\(693\) | −24.2293 | −0.920394 | ||||||||
\(694\) | −13.1432 | −0.498907 | ||||||||
\(695\) | 64.2774 | 2.43818 | ||||||||
\(696\) | 43.6545 | 1.65472 | ||||||||
\(697\) | 10.0798 | 0.381798 | ||||||||
\(698\) | −5.61423 | −0.212502 | ||||||||
\(699\) | 30.7746 | 1.16400 | ||||||||
\(700\) | −6.60723 | −0.249730 | ||||||||
\(701\) | −0.116177 | −0.00438796 | −0.00219398 | − | 0.999998i | \(-0.500698\pi\) | ||||
−0.00219398 | + | 0.999998i | \(0.500698\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.7297 | −0.480110 | ||||||||
\(704\) | −23.7097 | −0.893591 | ||||||||
\(705\) | 3.83651 | 0.144491 | ||||||||
\(706\) | 11.5325 | 0.434030 | ||||||||
\(707\) | −13.3295 | −0.501307 | ||||||||
\(708\) | −16.8986 | −0.635090 | ||||||||
\(709\) | 6.72993 | 0.252748 | 0.126374 | − | 0.991983i | \(-0.459666\pi\) | ||||
0.126374 | + | 0.991983i | \(0.459666\pi\) | |||||||
\(710\) | 11.7375 | 0.440499 | ||||||||
\(711\) | −32.2670 | −1.21011 | ||||||||
\(712\) | 9.74265 | 0.365121 | ||||||||
\(713\) | 3.14305 | 0.117708 | ||||||||
\(714\) | −5.91465 | −0.221350 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33.4197 | 1.24895 | ||||||||
\(717\) | −39.0347 | −1.45778 | ||||||||
\(718\) | −4.45950 | −0.166427 | ||||||||
\(719\) | 46.8078 | 1.74564 | 0.872818 | − | 0.488046i | \(-0.162290\pi\) | ||||
0.872818 | + | 0.488046i | \(0.162290\pi\) | |||||||
\(720\) | −5.03509 | −0.187647 | ||||||||
\(721\) | 11.6450 | 0.433681 | ||||||||
\(722\) | −12.4933 | −0.464953 | ||||||||
\(723\) | 38.1664 | 1.41942 | ||||||||
\(724\) | −1.14262 | −0.0424653 | ||||||||
\(725\) | −29.9852 | −1.11362 | ||||||||
\(726\) | 53.2731 | 1.97715 | ||||||||
\(727\) | −13.3362 | −0.494611 | −0.247305 | − | 0.968938i | \(-0.579545\pi\) | ||||
−0.247305 | + | 0.968938i | \(0.579545\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.6582 | −1.54290 | ||||||||
\(730\) | 21.6295 | 0.800544 | ||||||||
\(731\) | −18.8739 | −0.698076 | ||||||||
\(732\) | 4.06840 | 0.150373 | ||||||||
\(733\) | 29.4612 | 1.08817 | 0.544087 | − | 0.839029i | \(-0.316876\pi\) | ||||
0.544087 | + | 0.839029i | \(0.316876\pi\) | |||||||
\(734\) | 24.7328 | 0.912905 | ||||||||
\(735\) | −8.41209 | −0.310285 | ||||||||
\(736\) | −15.8113 | −0.582814 | ||||||||
\(737\) | 37.3153 | 1.37453 | ||||||||
\(738\) | −12.5370 | −0.461494 | ||||||||
\(739\) | 12.0302 | 0.442537 | 0.221269 | − | 0.975213i | \(-0.428980\pi\) | ||||
0.221269 | + | 0.975213i | \(0.428980\pi\) | |||||||
\(740\) | 27.1858 | 0.999370 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.328834 | 0.0120719 | ||||||||
\(743\) | −21.8826 | −0.802796 | −0.401398 | − | 0.915904i | \(-0.631476\pi\) | ||||
−0.401398 | + | 0.915904i | \(0.631476\pi\) | |||||||
\(744\) | 8.38055 | 0.307246 | ||||||||
\(745\) | −33.8855 | −1.24147 | ||||||||
\(746\) | 17.6321 | 0.645558 | ||||||||
\(747\) | 25.2700 | 0.924580 | ||||||||
\(748\) | −21.2051 | −0.775337 | ||||||||
\(749\) | 3.92966 | 0.143587 | ||||||||
\(750\) | 0.00811630 | 0.000296365 0 | ||||||||
\(751\) | 34.7492 | 1.26802 | 0.634008 | − | 0.773327i | \(-0.281409\pi\) | ||||
0.634008 | + | 0.773327i | \(0.281409\pi\) | |||||||
\(752\) | −0.178118 | −0.00649529 | ||||||||
\(753\) | 22.9172 | 0.835147 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.6498 | −1.00628 | ||||||||
\(756\) | −3.78755 | −0.137752 | ||||||||
\(757\) | 43.9263 | 1.59653 | 0.798265 | − | 0.602307i | \(-0.205752\pi\) | ||||
0.798265 | + | 0.602307i | \(0.205752\pi\) | |||||||
\(758\) | −7.80447 | −0.283471 | ||||||||
\(759\) | 43.1502 | 1.56625 | ||||||||
\(760\) | −16.9292 | −0.614087 | ||||||||
\(761\) | 0.141391 | 0.00512543 | 0.00256272 | − | 0.999997i | \(-0.499184\pi\) | ||||
0.00256272 | + | 0.999997i | \(0.499184\pi\) | |||||||
\(762\) | 13.4328 | 0.486618 | ||||||||
\(763\) | 11.2533 | 0.407398 | ||||||||
\(764\) | −19.3870 | −0.701399 | ||||||||
\(765\) | 34.8047 | 1.25837 | ||||||||
\(766\) | 4.47241 | 0.161595 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −39.4124 | −1.42217 | ||||||||
\(769\) | 13.6486 | 0.492180 | 0.246090 | − | 0.969247i | \(-0.420854\pi\) | ||||
0.246090 | + | 0.969247i | \(0.420854\pi\) | |||||||
\(770\) | 15.4757 | 0.557707 | ||||||||
\(771\) | 27.5711 | 0.992950 | ||||||||
\(772\) | 21.8035 | 0.784726 | ||||||||
\(773\) | −17.5894 | −0.632646 | −0.316323 | − | 0.948652i | \(-0.602448\pi\) | ||||
−0.316323 | + | 0.948652i | \(0.602448\pi\) | |||||||
\(774\) | 23.4750 | 0.843790 | ||||||||
\(775\) | −5.75639 | −0.206776 | ||||||||
\(776\) | −9.37647 | −0.336596 | ||||||||
\(777\) | 17.3040 | 0.620777 | ||||||||
\(778\) | −8.76443 | −0.314220 | ||||||||
\(779\) | 7.30711 | 0.261804 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.7849 | 0.958439 | ||||||||
\(782\) | 6.06833 | 0.217003 | ||||||||
\(783\) | −17.1888 | −0.614278 | ||||||||
\(784\) | 0.390549 | 0.0139482 | ||||||||
\(785\) | −20.5768 | −0.734418 | ||||||||
\(786\) | 22.3947 | 0.798792 | ||||||||
\(787\) | 2.96845 | 0.105814 | 0.0529069 | − | 0.998599i | \(-0.483151\pi\) | ||||
0.0529069 | + | 0.998599i | \(0.483151\pi\) | |||||||
\(788\) | −14.5528 | −0.518421 | ||||||||
\(789\) | −58.7461 | −2.09142 | ||||||||
\(790\) | 20.6096 | 0.733256 | ||||||||
\(791\) | −5.77418 | −0.205306 | ||||||||
\(792\) | 66.2829 | 2.35526 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 30.6242 | 1.08681 | ||||||||
\(795\) | −3.35883 | −0.119125 | ||||||||
\(796\) | 28.0367 | 0.993735 | ||||||||
\(797\) | 9.45221 | 0.334815 | 0.167407 | − | 0.985888i | \(-0.446461\pi\) | ||||
0.167407 | + | 0.985888i | \(0.446461\pi\) | |||||||
\(798\) | −4.28770 | −0.151783 | ||||||||
\(799\) | 1.23123 | 0.0435577 | ||||||||
\(800\) | 28.9579 | 1.02382 | ||||||||
\(801\) | −14.5202 | −0.513047 | ||||||||
\(802\) | 0.738409 | 0.0260741 | ||||||||
\(803\) | 49.3586 | 1.74183 | ||||||||
\(804\) | 22.0792 | 0.778674 | ||||||||
\(805\) | 8.63066 | 0.304191 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.4239 | 1.21178 | ||||||||
\(808\) | 36.4648 | 1.28283 | ||||||||
\(809\) | −1.16255 | −0.0408729 | −0.0204365 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204365 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(810\) | 12.0007 | 0.421662 | ||||||||
\(811\) | 19.5561 | 0.686706 | 0.343353 | − | 0.939206i | \(-0.388437\pi\) | ||||
0.343353 | + | 0.939206i | \(0.388437\pi\) | |||||||
\(812\) | 7.92849 | 0.278235 | ||||||||
\(813\) | 47.0204 | 1.64908 | ||||||||
\(814\) | −31.8342 | −1.11579 | ||||||||
\(815\) | −8.26151 | −0.289388 | ||||||||
\(816\) | −2.80486 | −0.0981897 | ||||||||
\(817\) | −13.6822 | −0.478680 | ||||||||
\(818\) | −20.2408 | −0.707702 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.6052 | −0.544958 | ||||||||
\(821\) | 12.6189 | 0.440403 | 0.220201 | − | 0.975454i | \(-0.429329\pi\) | ||||
0.220201 | + | 0.975454i | \(0.429329\pi\) | |||||||
\(822\) | −43.7030 | −1.52432 | ||||||||
\(823\) | −6.56808 | −0.228949 | −0.114474 | − | 0.993426i | \(-0.536518\pi\) | ||||
−0.114474 | + | 0.993426i | \(0.536518\pi\) | |||||||
\(824\) | −31.8565 | −1.10978 | ||||||||
\(825\) | −79.0280 | −2.75140 | ||||||||
\(826\) | 3.95790 | 0.137713 | ||||||||
\(827\) | 17.3050 | 0.601754 | 0.300877 | − | 0.953663i | \(-0.402721\pi\) | ||||
0.300877 | + | 0.953663i | \(0.402721\pi\) | |||||||
\(828\) | 14.7088 | 0.511167 | ||||||||
\(829\) | −3.75674 | −0.130477 | −0.0652385 | − | 0.997870i | \(-0.520781\pi\) | ||||
−0.0652385 | + | 0.997870i | \(0.520781\pi\) | |||||||
\(830\) | −16.1404 | −0.560243 | ||||||||
\(831\) | −47.9252 | −1.66251 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.69964 | −0.0935371 | ||||||||
\(834\) | −44.5355 | −1.54214 | ||||||||
\(835\) | −12.2886 | −0.425266 | ||||||||
\(836\) | −15.3722 | −0.531659 | ||||||||
\(837\) | −3.29981 | −0.114058 | ||||||||
\(838\) | −6.29656 | −0.217511 | ||||||||
\(839\) | −46.3427 | −1.59993 | −0.799965 | − | 0.600047i | \(-0.795148\pi\) | ||||
−0.799965 | + | 0.600047i | \(0.795148\pi\) | |||||||
\(840\) | 23.0125 | 0.794008 | ||||||||
\(841\) | 6.98142 | 0.240739 | ||||||||
\(842\) | 20.6531 | 0.711753 | ||||||||
\(843\) | −6.49586 | −0.223729 | ||||||||
\(844\) | 23.7067 | 0.816018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.53138 | −0.0526499 | ||||||||
\(847\) | 24.3156 | 0.835495 | ||||||||
\(848\) | 0.155941 | 0.00535503 | ||||||||
\(849\) | −76.4142 | −2.62253 | ||||||||
\(850\) | −11.1139 | −0.381205 | ||||||||
\(851\) | −17.7536 | −0.608585 | ||||||||
\(852\) | 15.8485 | 0.542959 | ||||||||
\(853\) | 15.3103 | 0.524215 | 0.262107 | − | 0.965039i | \(-0.415583\pi\) | ||||
0.262107 | + | 0.965039i | \(0.415583\pi\) | |||||||
\(854\) | −0.952877 | −0.0326068 | ||||||||
\(855\) | 25.2309 | 0.862879 | ||||||||
\(856\) | −10.7502 | −0.367433 | ||||||||
\(857\) | 2.59248 | 0.0885574 | 0.0442787 | − | 0.999019i | \(-0.485901\pi\) | ||||
0.0442787 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.7738 | −0.469955 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(860\) | 29.2200 | 0.996394 | ||||||||
\(861\) | −9.93284 | −0.338510 | ||||||||
\(862\) | 6.38589 | 0.217504 | ||||||||
\(863\) | 29.7592 | 1.01302 | 0.506508 | − | 0.862235i | \(-0.330936\pi\) | ||||
0.506508 | + | 0.862235i | \(0.330936\pi\) | |||||||
\(864\) | 16.5999 | 0.564741 | ||||||||
\(865\) | −44.1958 | −1.50270 | ||||||||
\(866\) | 29.6282 | 1.00681 | ||||||||
\(867\) | −25.8366 | −0.877456 | ||||||||
\(868\) | 1.52207 | 0.0516623 | ||||||||
\(869\) | 47.0311 | 1.59542 | ||||||||
\(870\) | 41.5562 | 1.40889 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −30.7852 | −1.04252 | ||||||||
\(873\) | 13.9745 | 0.472965 | ||||||||
\(874\) | 4.39910 | 0.148802 | ||||||||
\(875\) | 0.00370455 | 0.000125237 0 | ||||||||
\(876\) | 29.2051 | 0.986750 | ||||||||
\(877\) | 1.44332 | 0.0487374 | 0.0243687 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243687 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(878\) | −23.2531 | −0.784755 | ||||||||
\(879\) | 78.0286 | 2.63184 | ||||||||
\(880\) | 7.33894 | 0.247396 | ||||||||
\(881\) | −35.8804 | −1.20884 | −0.604420 | − | 0.796666i | \(-0.706595\pi\) | ||||
−0.604420 | + | 0.796666i | \(0.706595\pi\) | |||||||
\(882\) | 3.35776 | 0.113062 | ||||||||
\(883\) | −10.5626 | −0.355458 | −0.177729 | − | 0.984079i | \(-0.556875\pi\) | ||||
−0.177729 | + | 0.984079i | \(0.556875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −40.4273 | −1.35895 | ||||||||
\(886\) | 23.7116 | 0.796608 | ||||||||
\(887\) | 12.2280 | 0.410577 | 0.205288 | − | 0.978702i | \(-0.434187\pi\) | ||||
0.205288 | + | 0.978702i | \(0.434187\pi\) | |||||||
\(888\) | −47.3377 | −1.58855 | ||||||||
\(889\) | 6.13117 | 0.205633 | ||||||||
\(890\) | 9.27436 | 0.310877 | ||||||||
\(891\) | 27.3856 | 0.917452 | ||||||||
\(892\) | 21.1893 | 0.709469 | ||||||||
\(893\) | 0.892553 | 0.0298681 | ||||||||
\(894\) | 23.4780 | 0.785222 | ||||||||
\(895\) | 79.9513 | 2.67248 | ||||||||
\(896\) | −8.30013 | −0.277288 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.0398 | −0.802217 | ||||||||
\(899\) | 6.90751 | 0.230378 | ||||||||
\(900\) | −26.9387 | −0.897956 | ||||||||
\(901\) | −1.07793 | −0.0359110 | ||||||||
\(902\) | 18.2735 | 0.608440 | ||||||||
\(903\) | 18.5988 | 0.618928 | ||||||||
\(904\) | 15.7961 | 0.525372 | ||||||||
\(905\) | −2.73355 | −0.0908662 | ||||||||
\(906\) | 19.1576 | 0.636468 | ||||||||
\(907\) | 4.52555 | 0.150269 | 0.0751343 | − | 0.997173i | \(-0.476061\pi\) | ||||
0.0751343 | + | 0.997173i | \(0.476061\pi\) | |||||||
\(908\) | −21.6438 | −0.718274 | ||||||||
\(909\) | −54.3464 | −1.80256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.2723 | −1.89751 | −0.948757 | − | 0.316006i | \(-0.897658\pi\) | ||||
−0.948757 | + | 0.316006i | \(0.897658\pi\) | |||||||
\(912\) | −2.03332 | −0.0673300 | ||||||||
\(913\) | −36.8325 | −1.21898 | ||||||||
\(914\) | −26.0942 | −0.863120 | ||||||||
\(915\) | 9.73302 | 0.321764 | ||||||||
\(916\) | 35.7012 | 1.17960 | ||||||||
\(917\) | 10.2217 | 0.337550 | ||||||||
\(918\) | −6.37098 | −0.210274 | ||||||||
\(919\) | −40.7551 | −1.34439 | −0.672193 | − | 0.740376i | \(-0.734648\pi\) | ||||
−0.672193 | + | 0.740376i | \(0.734648\pi\) | |||||||
\(920\) | −23.6105 | −0.778415 | ||||||||
\(921\) | 18.8059 | 0.619675 | ||||||||
\(922\) | 18.2021 | 0.599453 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 20.8960 | 0.687429 | ||||||||
\(925\) | 32.5151 | 1.06909 | ||||||||
\(926\) | 32.0208 | 1.05227 | ||||||||
\(927\) | 47.4783 | 1.55939 | ||||||||
\(928\) | −34.7487 | −1.14068 | ||||||||
\(929\) | −52.2791 | −1.71522 | −0.857611 | − | 0.514298i | \(-0.828052\pi\) | ||||
−0.857611 | + | 0.514298i | \(0.828052\pi\) | |||||||
\(930\) | 7.97773 | 0.261600 | ||||||||
\(931\) | −1.95705 | −0.0641397 | ||||||||
\(932\) | −15.2902 | −0.500848 | ||||||||
\(933\) | −59.2410 | −1.93946 | ||||||||
\(934\) | 10.9387 | 0.357926 | ||||||||
\(935\) | −50.7300 | −1.65905 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.38634 | −0.208633 | −0.104316 | − | 0.994544i | \(-0.533265\pi\) | ||||
−0.104316 | + | 0.994544i | \(0.533265\pi\) | |||||||
\(938\) | −5.17126 | −0.168848 | ||||||||
\(939\) | −74.7116 | −2.43812 | ||||||||
\(940\) | −1.90615 | −0.0621719 | ||||||||
\(941\) | −25.3711 | −0.827073 | −0.413536 | − | 0.910488i | \(-0.635707\pi\) | ||||
−0.413536 | + | 0.910488i | \(0.635707\pi\) | |||||||
\(942\) | 14.2569 | 0.464516 | ||||||||
\(943\) | 10.1909 | 0.331862 | ||||||||
\(944\) | 1.87692 | 0.0610887 | ||||||||
\(945\) | −9.06111 | −0.294758 | ||||||||
\(946\) | −34.2162 | −1.11246 | ||||||||
\(947\) | −27.2061 | −0.884080 | −0.442040 | − | 0.896995i | \(-0.645745\pi\) | ||||
−0.442040 | + | 0.896995i | \(0.645745\pi\) | |||||||
\(948\) | 27.8280 | 0.903811 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.05681 | −0.261397 | ||||||||
\(951\) | −51.9169 | −1.68352 | ||||||||
\(952\) | 7.38528 | 0.239358 | ||||||||
\(953\) | 26.5879 | 0.861265 | 0.430633 | − | 0.902527i | \(-0.358290\pi\) | ||||
0.430633 | + | 0.902527i | \(0.358290\pi\) | |||||||
\(954\) | 1.34071 | 0.0434070 | ||||||||
\(955\) | −46.3805 | −1.50084 | ||||||||
\(956\) | 19.3942 | 0.627254 | ||||||||
\(957\) | 94.8314 | 3.06546 | ||||||||
\(958\) | −5.46439 | −0.176546 | ||||||||
\(959\) | −19.9475 | −0.644139 | ||||||||
\(960\) | −33.5618 | −1.08320 | ||||||||
\(961\) | −29.6739 | −0.957224 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0218 | 0.516296 | ||||||||
\(964\) | −18.9628 | −0.610751 | ||||||||
\(965\) | 52.1615 | 1.67914 | ||||||||
\(966\) | −5.97987 | −0.192399 | ||||||||
\(967\) | 35.2467 | 1.13346 | 0.566729 | − | 0.823904i | \(-0.308209\pi\) | ||||
0.566729 | + | 0.823904i | \(0.308209\pi\) | |||||||
\(968\) | −66.5191 | −2.13801 | ||||||||
\(969\) | 14.0552 | 0.451518 | ||||||||
\(970\) | −8.92578 | −0.286590 | ||||||||
\(971\) | 36.9783 | 1.18669 | 0.593344 | − | 0.804949i | \(-0.297807\pi\) | ||||
0.593344 | + | 0.804949i | \(0.297807\pi\) | |||||||
\(972\) | 27.5665 | 0.884197 | ||||||||
\(973\) | −20.3275 | −0.651669 | ||||||||
\(974\) | −27.5645 | −0.883224 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.451876 | −0.0144642 | ||||||||
\(977\) | −24.7525 | −0.791902 | −0.395951 | − | 0.918272i | \(-0.629585\pi\) | ||||
−0.395951 | + | 0.918272i | \(0.629585\pi\) | |||||||
\(978\) | 5.72410 | 0.183036 | ||||||||
\(979\) | 21.1641 | 0.676408 | ||||||||
\(980\) | 4.17951 | 0.133510 | ||||||||
\(981\) | 45.8815 | 1.46488 | ||||||||
\(982\) | −30.7423 | −0.981025 | ||||||||
\(983\) | −4.55736 | −0.145357 | −0.0726786 | − | 0.997355i | \(-0.523155\pi\) | ||||
−0.0726786 | + | 0.997355i | \(0.523155\pi\) | |||||||
\(984\) | 27.1728 | 0.866237 | ||||||||
\(985\) | −34.8152 | −1.10930 | ||||||||
\(986\) | 13.3364 | 0.424718 | ||||||||
\(987\) | −1.21328 | −0.0386192 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.0820 | −0.606773 | ||||||||
\(990\) | 63.0969 | 2.00535 | ||||||||
\(991\) | −27.1963 | −0.863919 | −0.431960 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431960 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(992\) | −6.67085 | −0.211800 | ||||||||
\(993\) | −41.5824 | −1.31958 | ||||||||
\(994\) | −3.71193 | −0.117735 | ||||||||
\(995\) | 67.0734 | 2.12637 | ||||||||
\(996\) | −21.7936 | −0.690556 | ||||||||
\(997\) | −30.2274 | −0.957312 | −0.478656 | − | 0.878002i | \(-0.658876\pi\) | ||||
−0.478656 | + | 0.878002i | \(0.658876\pi\) | |||||||
\(998\) | −28.1102 | −0.889812 | ||||||||
\(999\) | 18.6390 | 0.589713 |
(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 | 1183.2.a.m.1.5 | 6 | ||
7.6 | odd | 2 | 8281.2.a.by.1.5 | 6 | |||
13.2 | odd | 12 | 91.2.q.a.43.4 | yes | 12 | ||
13.5 | odd | 4 | 1183.2.c.i.337.5 | 12 | |||
13.7 | odd | 12 | 91.2.q.a.36.4 | ✓ | 12 | ||
13.8 | odd | 4 | 1183.2.c.i.337.8 | 12 | |||
13.12 | even | 2 | 1183.2.a.p.1.2 | 6 | |||
39.2 | even | 12 | 819.2.ct.a.316.3 | 12 | |||
39.20 | even | 12 | 819.2.ct.a.127.3 | 12 | |||
52.7 | even | 12 | 1456.2.cc.c.673.6 | 12 | |||
52.15 | even | 12 | 1456.2.cc.c.225.6 | 12 | |||
91.2 | odd | 12 | 637.2.k.h.459.3 | 12 | |||
91.20 | even | 12 | 637.2.q.h.491.4 | 12 | |||
91.33 | even | 12 | 637.2.u.i.361.3 | 12 | |||
91.41 | even | 12 | 637.2.q.h.589.4 | 12 | |||
91.46 | odd | 12 | 637.2.k.h.569.4 | 12 | |||
91.54 | even | 12 | 637.2.k.g.459.3 | 12 | |||
91.59 | even | 12 | 637.2.k.g.569.4 | 12 | |||
91.67 | odd | 12 | 637.2.u.h.30.3 | 12 | |||
91.72 | odd | 12 | 637.2.u.h.361.3 | 12 | |||
91.80 | even | 12 | 637.2.u.i.30.3 | 12 | |||
91.90 | odd | 2 | 8281.2.a.ch.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.4 | ✓ | 12 | 13.7 | odd | 12 | ||
91.2.q.a.43.4 | yes | 12 | 13.2 | odd | 12 | ||
637.2.k.g.459.3 | 12 | 91.54 | even | 12 | |||
637.2.k.g.569.4 | 12 | 91.59 | even | 12 | |||
637.2.k.h.459.3 | 12 | 91.2 | odd | 12 | |||
637.2.k.h.569.4 | 12 | 91.46 | odd | 12 | |||
637.2.q.h.491.4 | 12 | 91.20 | even | 12 | |||
637.2.q.h.589.4 | 12 | 91.41 | even | 12 | |||
637.2.u.h.30.3 | 12 | 91.67 | odd | 12 | |||
637.2.u.h.361.3 | 12 | 91.72 | odd | 12 | |||
637.2.u.i.30.3 | 12 | 91.80 | even | 12 | |||
637.2.u.i.361.3 | 12 | 91.33 | even | 12 | |||
819.2.ct.a.127.3 | 12 | 39.20 | even | 12 | |||
819.2.ct.a.316.3 | 12 | 39.2 | even | 12 | |||
1183.2.a.m.1.5 | 6 | 1.1 | even | 1 | trivial | ||
1183.2.a.p.1.2 | 6 | 13.12 | even | 2 | |||
1183.2.c.i.337.5 | 12 | 13.5 | odd | 4 | |||
1183.2.c.i.337.8 | 12 | 13.8 | odd | 4 | |||
1456.2.cc.c.225.6 | 12 | 52.15 | even | 12 | |||
1456.2.cc.c.673.6 | 12 | 52.7 | even | 12 | |||
8281.2.a.by.1.5 | 6 | 7.6 | odd | 2 | |||
8281.2.a.ch.1.2 | 6 | 91.90 | odd | 2 |