Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + 2170 x^{12} - 42069 x^{11} + 19553 x^{10} + 84697 x^{9} - 82713 x^{8} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(1.69438\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | 1.69438 | 0.978252 | 0.489126 | − | 0.872213i | \(-0.337316\pi\) | ||||
0.489126 | + | 0.872213i | \(0.337316\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.04996 | −1.81120 | −0.905598 | − | 0.424137i | \(-0.860577\pi\) | ||||
−0.905598 | + | 0.424137i | \(0.860577\pi\) | |||||||
\(6\) | −1.69438 | −0.691728 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.129071 | −0.0430236 | ||||||||
\(10\) | 4.04996 | 1.28071 | ||||||||
\(11\) | −1.22767 | −0.370155 | −0.185078 | − | 0.982724i | \(-0.559254\pi\) | ||||
−0.185078 | + | 0.982724i | \(0.559254\pi\) | |||||||
\(12\) | 1.69438 | 0.489126 | ||||||||
\(13\) | −1.01270 | −0.280872 | −0.140436 | − | 0.990090i | \(-0.544850\pi\) | ||||
−0.140436 | + | 0.990090i | \(0.544850\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −6.86217 | −1.77181 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.455224 | 0.110408 | 0.0552040 | − | 0.998475i | \(-0.482419\pi\) | ||||
0.0552040 | + | 0.998475i | \(0.482419\pi\) | |||||||
\(18\) | 0.129071 | 0.0304223 | ||||||||
\(19\) | 3.36763 | 0.772588 | 0.386294 | − | 0.922376i | \(-0.373755\pi\) | ||||
0.386294 | + | 0.922376i | \(0.373755\pi\) | |||||||
\(20\) | −4.04996 | −0.905598 | ||||||||
\(21\) | 1.69438 | 0.369744 | ||||||||
\(22\) | 1.22767 | 0.261739 | ||||||||
\(23\) | −0.370189 | −0.0771897 | −0.0385948 | − | 0.999255i | \(-0.512288\pi\) | ||||
−0.0385948 | + | 0.999255i | \(0.512288\pi\) | |||||||
\(24\) | −1.69438 | −0.345864 | ||||||||
\(25\) | 11.4022 | 2.28043 | ||||||||
\(26\) | 1.01270 | 0.198606 | ||||||||
\(27\) | −5.30184 | −1.02034 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.63036 | 0.674140 | 0.337070 | − | 0.941480i | \(-0.390564\pi\) | ||||
0.337070 | + | 0.941480i | \(0.390564\pi\) | |||||||
\(30\) | 6.86217 | 1.25286 | ||||||||
\(31\) | 4.99252 | 0.896684 | 0.448342 | − | 0.893862i | \(-0.352015\pi\) | ||||
0.448342 | + | 0.893862i | \(0.352015\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.08013 | −0.362105 | ||||||||
\(34\) | −0.455224 | −0.0780702 | ||||||||
\(35\) | −4.04996 | −0.684568 | ||||||||
\(36\) | −0.129071 | −0.0215118 | ||||||||
\(37\) | −3.73589 | −0.614176 | −0.307088 | − | 0.951681i | \(-0.599355\pi\) | ||||
−0.307088 | + | 0.951681i | \(0.599355\pi\) | |||||||
\(38\) | −3.36763 | −0.546302 | ||||||||
\(39\) | −1.71590 | −0.274763 | ||||||||
\(40\) | 4.04996 | 0.640355 | ||||||||
\(41\) | 3.64381 | 0.569068 | 0.284534 | − | 0.958666i | \(-0.408161\pi\) | ||||
0.284534 | + | 0.958666i | \(0.408161\pi\) | |||||||
\(42\) | −1.69438 | −0.261449 | ||||||||
\(43\) | 7.02184 | 1.07082 | 0.535410 | − | 0.844592i | \(-0.320157\pi\) | ||||
0.535410 | + | 0.844592i | \(0.320157\pi\) | |||||||
\(44\) | −1.22767 | −0.185078 | ||||||||
\(45\) | 0.522731 | 0.0779242 | ||||||||
\(46\) | 0.370189 | 0.0545813 | ||||||||
\(47\) | −9.70825 | −1.41609 | −0.708047 | − | 0.706166i | \(-0.750423\pi\) | ||||
−0.708047 | + | 0.706166i | \(0.750423\pi\) | |||||||
\(48\) | 1.69438 | 0.244563 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −11.4022 | −1.61251 | ||||||||
\(51\) | 0.771323 | 0.108007 | ||||||||
\(52\) | −1.01270 | −0.140436 | ||||||||
\(53\) | 5.61269 | 0.770962 | 0.385481 | − | 0.922716i | \(-0.374036\pi\) | ||||
0.385481 | + | 0.922716i | \(0.374036\pi\) | |||||||
\(54\) | 5.30184 | 0.721489 | ||||||||
\(55\) | 4.97199 | 0.670424 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 5.70605 | 0.755785 | ||||||||
\(58\) | −3.63036 | −0.476689 | ||||||||
\(59\) | −3.93901 | −0.512816 | −0.256408 | − | 0.966569i | \(-0.582539\pi\) | ||||
−0.256408 | + | 0.966569i | \(0.582539\pi\) | |||||||
\(60\) | −6.86217 | −0.885903 | ||||||||
\(61\) | 5.28219 | 0.676316 | 0.338158 | − | 0.941089i | \(-0.390196\pi\) | ||||
0.338158 | + | 0.941089i | \(0.390196\pi\) | |||||||
\(62\) | −4.99252 | −0.634051 | ||||||||
\(63\) | −0.129071 | −0.0162614 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.10138 | 0.508714 | ||||||||
\(66\) | 2.08013 | 0.256047 | ||||||||
\(67\) | 11.6016 | 1.41736 | 0.708678 | − | 0.705532i | \(-0.249292\pi\) | ||||
0.708678 | + | 0.705532i | \(0.249292\pi\) | |||||||
\(68\) | 0.455224 | 0.0552040 | ||||||||
\(69\) | −0.627241 | −0.0755109 | ||||||||
\(70\) | 4.04996 | 0.484063 | ||||||||
\(71\) | −16.0530 | −1.90514 | −0.952572 | − | 0.304313i | \(-0.901573\pi\) | ||||
−0.952572 | + | 0.304313i | \(0.901573\pi\) | |||||||
\(72\) | 0.129071 | 0.0152111 | ||||||||
\(73\) | 3.51325 | 0.411195 | 0.205597 | − | 0.978637i | \(-0.434086\pi\) | ||||
0.205597 | + | 0.978637i | \(0.434086\pi\) | |||||||
\(74\) | 3.73589 | 0.434288 | ||||||||
\(75\) | 19.3196 | 2.23084 | ||||||||
\(76\) | 3.36763 | 0.386294 | ||||||||
\(77\) | −1.22767 | −0.139905 | ||||||||
\(78\) | 1.71590 | 0.194287 | ||||||||
\(79\) | −13.8367 | −1.55675 | −0.778377 | − | 0.627797i | \(-0.783957\pi\) | ||||
−0.778377 | + | 0.627797i | \(0.783957\pi\) | |||||||
\(80\) | −4.04996 | −0.452799 | ||||||||
\(81\) | −8.59613 | −0.955125 | ||||||||
\(82\) | −3.64381 | −0.402392 | ||||||||
\(83\) | −12.9247 | −1.41867 | −0.709333 | − | 0.704874i | \(-0.751004\pi\) | ||||
−0.709333 | + | 0.704874i | \(0.751004\pi\) | |||||||
\(84\) | 1.69438 | 0.184872 | ||||||||
\(85\) | −1.84364 | −0.199971 | ||||||||
\(86\) | −7.02184 | −0.757185 | ||||||||
\(87\) | 6.15121 | 0.659479 | ||||||||
\(88\) | 1.22767 | 0.130870 | ||||||||
\(89\) | 2.53987 | 0.269226 | 0.134613 | − | 0.990898i | \(-0.457021\pi\) | ||||
0.134613 | + | 0.990898i | \(0.457021\pi\) | |||||||
\(90\) | −0.522731 | −0.0551007 | ||||||||
\(91\) | −1.01270 | −0.106160 | ||||||||
\(92\) | −0.370189 | −0.0385948 | ||||||||
\(93\) | 8.45924 | 0.877182 | ||||||||
\(94\) | 9.70825 | 1.00133 | ||||||||
\(95\) | −13.6388 | −1.39931 | ||||||||
\(96\) | −1.69438 | −0.172932 | ||||||||
\(97\) | 10.8779 | 1.10448 | 0.552242 | − | 0.833684i | \(-0.313772\pi\) | ||||
0.552242 | + | 0.833684i | \(0.313772\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0.158456 | 0.0159254 | ||||||||
\(100\) | 11.4022 | 1.14022 | ||||||||
\(101\) | 9.17481 | 0.912928 | 0.456464 | − | 0.889742i | \(-0.349116\pi\) | ||||
0.456464 | + | 0.889742i | \(0.349116\pi\) | |||||||
\(102\) | −0.771323 | −0.0763723 | ||||||||
\(103\) | −13.6620 | −1.34616 | −0.673079 | − | 0.739571i | \(-0.735029\pi\) | ||||
−0.673079 | + | 0.739571i | \(0.735029\pi\) | |||||||
\(104\) | 1.01270 | 0.0993031 | ||||||||
\(105\) | −6.86217 | −0.669680 | ||||||||
\(106\) | −5.61269 | −0.545152 | ||||||||
\(107\) | −1.17574 | −0.113663 | −0.0568316 | − | 0.998384i | \(-0.518100\pi\) | ||||
−0.0568316 | + | 0.998384i | \(0.518100\pi\) | |||||||
\(108\) | −5.30184 | −0.510170 | ||||||||
\(109\) | −15.0842 | −1.44480 | −0.722401 | − | 0.691474i | \(-0.756961\pi\) | ||||
−0.722401 | + | 0.691474i | \(0.756961\pi\) | |||||||
\(110\) | −4.97199 | −0.474061 | ||||||||
\(111\) | −6.33002 | −0.600819 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −18.0915 | −1.70190 | −0.850951 | − | 0.525244i | \(-0.823974\pi\) | ||||
−0.850951 | + | 0.525244i | \(0.823974\pi\) | |||||||
\(114\) | −5.70605 | −0.534421 | ||||||||
\(115\) | 1.49925 | 0.139806 | ||||||||
\(116\) | 3.63036 | 0.337070 | ||||||||
\(117\) | 0.130710 | 0.0120841 | ||||||||
\(118\) | 3.93901 | 0.362615 | ||||||||
\(119\) | 0.455224 | 0.0417303 | ||||||||
\(120\) | 6.86217 | 0.626428 | ||||||||
\(121\) | −9.49284 | −0.862985 | ||||||||
\(122\) | −5.28219 | −0.478227 | ||||||||
\(123\) | 6.17401 | 0.556692 | ||||||||
\(124\) | 4.99252 | 0.448342 | ||||||||
\(125\) | −25.9285 | −2.31911 | ||||||||
\(126\) | 0.129071 | 0.0114985 | ||||||||
\(127\) | 9.26295 | 0.821954 | 0.410977 | − | 0.911646i | \(-0.365188\pi\) | ||||
0.410977 | + | 0.911646i | \(0.365188\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.8977 | 1.04753 | ||||||||
\(130\) | −4.10138 | −0.359715 | ||||||||
\(131\) | 12.8101 | 1.11923 | 0.559613 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559613 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(132\) | −2.08013 | −0.181052 | ||||||||
\(133\) | 3.36763 | 0.292011 | ||||||||
\(134\) | −11.6016 | −1.00222 | ||||||||
\(135\) | 21.4722 | 1.84804 | ||||||||
\(136\) | −0.455224 | −0.0390351 | ||||||||
\(137\) | 14.6909 | 1.25513 | 0.627564 | − | 0.778565i | \(-0.284052\pi\) | ||||
0.627564 | + | 0.778565i | \(0.284052\pi\) | |||||||
\(138\) | 0.627241 | 0.0533943 | ||||||||
\(139\) | −17.0680 | −1.44769 | −0.723845 | − | 0.689962i | \(-0.757627\pi\) | ||||
−0.723845 | + | 0.689962i | \(0.757627\pi\) | |||||||
\(140\) | −4.04996 | −0.342284 | ||||||||
\(141\) | −16.4495 | −1.38530 | ||||||||
\(142\) | 16.0530 | 1.34714 | ||||||||
\(143\) | 1.24325 | 0.103966 | ||||||||
\(144\) | −0.129071 | −0.0107559 | ||||||||
\(145\) | −14.7028 | −1.22100 | ||||||||
\(146\) | −3.51325 | −0.290759 | ||||||||
\(147\) | 1.69438 | 0.139750 | ||||||||
\(148\) | −3.73589 | −0.307088 | ||||||||
\(149\) | −14.4653 | −1.18505 | −0.592523 | − | 0.805554i | \(-0.701868\pi\) | ||||
−0.592523 | + | 0.805554i | \(0.701868\pi\) | |||||||
\(150\) | −19.3196 | −1.57744 | ||||||||
\(151\) | 0.765320 | 0.0622809 | 0.0311404 | − | 0.999515i | \(-0.490086\pi\) | ||||
0.0311404 | + | 0.999515i | \(0.490086\pi\) | |||||||
\(152\) | −3.36763 | −0.273151 | ||||||||
\(153\) | −0.0587561 | −0.00475015 | ||||||||
\(154\) | 1.22767 | 0.0989281 | ||||||||
\(155\) | −20.2195 | −1.62407 | ||||||||
\(156\) | −1.71590 | −0.137382 | ||||||||
\(157\) | −20.2064 | −1.61264 | −0.806321 | − | 0.591478i | \(-0.798545\pi\) | ||||
−0.806321 | + | 0.591478i | \(0.798545\pi\) | |||||||
\(158\) | 13.8367 | 1.10079 | ||||||||
\(159\) | 9.51003 | 0.754195 | ||||||||
\(160\) | 4.04996 | 0.320177 | ||||||||
\(161\) | −0.370189 | −0.0291749 | ||||||||
\(162\) | 8.59613 | 0.675376 | ||||||||
\(163\) | −19.0857 | −1.49491 | −0.747454 | − | 0.664314i | \(-0.768724\pi\) | ||||
−0.747454 | + | 0.664314i | \(0.768724\pi\) | |||||||
\(164\) | 3.64381 | 0.284534 | ||||||||
\(165\) | 8.42446 | 0.655843 | ||||||||
\(166\) | 12.9247 | 1.00315 | ||||||||
\(167\) | −1.80685 | −0.139818 | −0.0699090 | − | 0.997553i | \(-0.522271\pi\) | ||||
−0.0699090 | + | 0.997553i | \(0.522271\pi\) | |||||||
\(168\) | −1.69438 | −0.130724 | ||||||||
\(169\) | −11.9744 | −0.921111 | ||||||||
\(170\) | 1.84364 | 0.141400 | ||||||||
\(171\) | −0.434663 | −0.0332395 | ||||||||
\(172\) | 7.02184 | 0.535410 | ||||||||
\(173\) | 13.1842 | 1.00238 | 0.501189 | − | 0.865338i | \(-0.332896\pi\) | ||||
0.501189 | + | 0.865338i | \(0.332896\pi\) | |||||||
\(174\) | −6.15121 | −0.466322 | ||||||||
\(175\) | 11.4022 | 0.861922 | ||||||||
\(176\) | −1.22767 | −0.0925388 | ||||||||
\(177\) | −6.67419 | −0.501663 | ||||||||
\(178\) | −2.53987 | −0.190371 | ||||||||
\(179\) | 21.9446 | 1.64022 | 0.820109 | − | 0.572208i | \(-0.193913\pi\) | ||||
0.820109 | + | 0.572208i | \(0.193913\pi\) | |||||||
\(180\) | 0.522731 | 0.0389621 | ||||||||
\(181\) | 17.2828 | 1.28462 | 0.642311 | − | 0.766444i | \(-0.277976\pi\) | ||||
0.642311 | + | 0.766444i | \(0.277976\pi\) | |||||||
\(182\) | 1.01270 | 0.0750661 | ||||||||
\(183\) | 8.95005 | 0.661607 | ||||||||
\(184\) | 0.370189 | 0.0272907 | ||||||||
\(185\) | 15.1302 | 1.11239 | ||||||||
\(186\) | −8.45924 | −0.620261 | ||||||||
\(187\) | −0.558863 | −0.0408681 | ||||||||
\(188\) | −9.70825 | −0.708047 | ||||||||
\(189\) | −5.30184 | −0.385652 | ||||||||
\(190\) | 13.6388 | 0.989460 | ||||||||
\(191\) | −20.5812 | −1.48921 | −0.744603 | − | 0.667507i | \(-0.767361\pi\) | ||||
−0.744603 | + | 0.667507i | \(0.767361\pi\) | |||||||
\(192\) | 1.69438 | 0.122281 | ||||||||
\(193\) | 7.07694 | 0.509409 | 0.254705 | − | 0.967019i | \(-0.418022\pi\) | ||||
0.254705 | + | 0.967019i | \(0.418022\pi\) | |||||||
\(194\) | −10.8779 | −0.780988 | ||||||||
\(195\) | 6.94930 | 0.497650 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −24.8708 | −1.77197 | −0.885987 | − | 0.463710i | \(-0.846518\pi\) | ||||
−0.885987 | + | 0.463710i | \(0.846518\pi\) | |||||||
\(198\) | −0.158456 | −0.0112610 | ||||||||
\(199\) | 10.9476 | 0.776058 | 0.388029 | − | 0.921647i | \(-0.373156\pi\) | ||||
0.388029 | + | 0.921647i | \(0.373156\pi\) | |||||||
\(200\) | −11.4022 | −0.806254 | ||||||||
\(201\) | 19.6575 | 1.38653 | ||||||||
\(202\) | −9.17481 | −0.645538 | ||||||||
\(203\) | 3.63036 | 0.254801 | ||||||||
\(204\) | 0.771323 | 0.0540034 | ||||||||
\(205\) | −14.7573 | −1.03069 | ||||||||
\(206\) | 13.6620 | 0.951877 | ||||||||
\(207\) | 0.0477805 | 0.00332098 | ||||||||
\(208\) | −1.01270 | −0.0702179 | ||||||||
\(209\) | −4.13433 | −0.285977 | ||||||||
\(210\) | 6.86217 | 0.473535 | ||||||||
\(211\) | −21.3568 | −1.47026 | −0.735130 | − | 0.677926i | \(-0.762879\pi\) | ||||
−0.735130 | + | 0.677926i | \(0.762879\pi\) | |||||||
\(212\) | 5.61269 | 0.385481 | ||||||||
\(213\) | −27.2000 | −1.86371 | ||||||||
\(214\) | 1.17574 | 0.0803721 | ||||||||
\(215\) | −28.4382 | −1.93947 | ||||||||
\(216\) | 5.30184 | 0.360745 | ||||||||
\(217\) | 4.99252 | 0.338915 | ||||||||
\(218\) | 15.0842 | 1.02163 | ||||||||
\(219\) | 5.95279 | 0.402252 | ||||||||
\(220\) | 4.97199 | 0.335212 | ||||||||
\(221\) | −0.461004 | −0.0310105 | ||||||||
\(222\) | 6.33002 | 0.424843 | ||||||||
\(223\) | 19.2587 | 1.28966 | 0.644830 | − | 0.764326i | \(-0.276928\pi\) | ||||
0.644830 | + | 0.764326i | \(0.276928\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −1.47169 | −0.0981123 | ||||||||
\(226\) | 18.0915 | 1.20343 | ||||||||
\(227\) | −27.8002 | −1.84516 | −0.922581 | − | 0.385803i | \(-0.873924\pi\) | ||||
−0.922581 | + | 0.385803i | \(0.873924\pi\) | |||||||
\(228\) | 5.70605 | 0.377893 | ||||||||
\(229\) | 11.0885 | 0.732747 | 0.366373 | − | 0.930468i | \(-0.380599\pi\) | ||||
0.366373 | + | 0.930468i | \(0.380599\pi\) | |||||||
\(230\) | −1.49925 | −0.0988575 | ||||||||
\(231\) | −2.08013 | −0.136863 | ||||||||
\(232\) | −3.63036 | −0.238345 | ||||||||
\(233\) | 26.3989 | 1.72945 | 0.864724 | − | 0.502248i | \(-0.167494\pi\) | ||||
0.864724 | + | 0.502248i | \(0.167494\pi\) | |||||||
\(234\) | −0.130710 | −0.00854476 | ||||||||
\(235\) | 39.3180 | 2.56482 | ||||||||
\(236\) | −3.93901 | −0.256408 | ||||||||
\(237\) | −23.4447 | −1.52290 | ||||||||
\(238\) | −0.455224 | −0.0295078 | ||||||||
\(239\) | −1.44825 | −0.0936793 | −0.0468397 | − | 0.998902i | \(-0.514915\pi\) | ||||
−0.0468397 | + | 0.998902i | \(0.514915\pi\) | |||||||
\(240\) | −6.86217 | −0.442951 | ||||||||
\(241\) | −18.0067 | −1.15992 | −0.579958 | − | 0.814647i | \(-0.696931\pi\) | ||||
−0.579958 | + | 0.814647i | \(0.696931\pi\) | |||||||
\(242\) | 9.49284 | 0.610223 | ||||||||
\(243\) | 1.34040 | 0.0859866 | ||||||||
\(244\) | 5.28219 | 0.338158 | ||||||||
\(245\) | −4.04996 | −0.258742 | ||||||||
\(246\) | −6.17401 | −0.393641 | ||||||||
\(247\) | −3.41039 | −0.216998 | ||||||||
\(248\) | −4.99252 | −0.317026 | ||||||||
\(249\) | −21.8993 | −1.38781 | ||||||||
\(250\) | 25.9285 | 1.63986 | ||||||||
\(251\) | 3.57879 | 0.225891 | 0.112946 | − | 0.993601i | \(-0.463971\pi\) | ||||
0.112946 | + | 0.993601i | \(0.463971\pi\) | |||||||
\(252\) | −0.129071 | −0.00813070 | ||||||||
\(253\) | 0.454468 | 0.0285721 | ||||||||
\(254\) | −9.26295 | −0.581209 | ||||||||
\(255\) | −3.12382 | −0.195621 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.128614 | 0.00802275 | 0.00401138 | − | 0.999992i | \(-0.498723\pi\) | ||||
0.00401138 | + | 0.999992i | \(0.498723\pi\) | |||||||
\(258\) | −11.8977 | −0.740717 | ||||||||
\(259\) | −3.73589 | −0.232137 | ||||||||
\(260\) | 4.10138 | 0.254357 | ||||||||
\(261\) | −0.468573 | −0.0290039 | ||||||||
\(262\) | −12.8101 | −0.791412 | ||||||||
\(263\) | 6.36157 | 0.392271 | 0.196136 | − | 0.980577i | \(-0.437161\pi\) | ||||
0.196136 | + | 0.980577i | \(0.437161\pi\) | |||||||
\(264\) | 2.08013 | 0.128023 | ||||||||
\(265\) | −22.7311 | −1.39636 | ||||||||
\(266\) | −3.36763 | −0.206483 | ||||||||
\(267\) | 4.30351 | 0.263370 | ||||||||
\(268\) | 11.6016 | 0.708678 | ||||||||
\(269\) | −10.9848 | −0.669756 | −0.334878 | − | 0.942261i | \(-0.608695\pi\) | ||||
−0.334878 | + | 0.942261i | \(0.608695\pi\) | |||||||
\(270\) | −21.4722 | −1.30676 | ||||||||
\(271\) | −27.0448 | −1.64285 | −0.821427 | − | 0.570314i | \(-0.806822\pi\) | ||||
−0.821427 | + | 0.570314i | \(0.806822\pi\) | |||||||
\(272\) | 0.455224 | 0.0276020 | ||||||||
\(273\) | −1.71590 | −0.103851 | ||||||||
\(274\) | −14.6909 | −0.887509 | ||||||||
\(275\) | −13.9980 | −0.844113 | ||||||||
\(276\) | −0.627241 | −0.0377555 | ||||||||
\(277\) | −8.73221 | −0.524667 | −0.262334 | − | 0.964977i | \(-0.584492\pi\) | ||||
−0.262334 | + | 0.964977i | \(0.584492\pi\) | |||||||
\(278\) | 17.0680 | 1.02367 | ||||||||
\(279\) | −0.644389 | −0.0385786 | ||||||||
\(280\) | 4.04996 | 0.242031 | ||||||||
\(281\) | 11.2372 | 0.670357 | 0.335179 | − | 0.942155i | \(-0.391203\pi\) | ||||
0.335179 | + | 0.942155i | \(0.391203\pi\) | |||||||
\(282\) | 16.4495 | 0.979552 | ||||||||
\(283\) | −21.5351 | −1.28013 | −0.640065 | − | 0.768321i | \(-0.721093\pi\) | ||||
−0.640065 | + | 0.768321i | \(0.721093\pi\) | |||||||
\(284\) | −16.0530 | −0.952572 | ||||||||
\(285\) | −23.1093 | −1.36888 | ||||||||
\(286\) | −1.24325 | −0.0735151 | ||||||||
\(287\) | 3.64381 | 0.215088 | ||||||||
\(288\) | 0.129071 | 0.00760557 | ||||||||
\(289\) | −16.7928 | −0.987810 | ||||||||
\(290\) | 14.7028 | 0.863377 | ||||||||
\(291\) | 18.4313 | 1.08046 | ||||||||
\(292\) | 3.51325 | 0.205597 | ||||||||
\(293\) | −17.9971 | −1.05140 | −0.525700 | − | 0.850670i | \(-0.676197\pi\) | ||||
−0.525700 | + | 0.850670i | \(0.676197\pi\) | |||||||
\(294\) | −1.69438 | −0.0988183 | ||||||||
\(295\) | 15.9528 | 0.928810 | ||||||||
\(296\) | 3.73589 | 0.217144 | ||||||||
\(297\) | 6.50889 | 0.377684 | ||||||||
\(298\) | 14.4653 | 0.837954 | ||||||||
\(299\) | 0.374889 | 0.0216804 | ||||||||
\(300\) | 19.3196 | 1.11542 | ||||||||
\(301\) | 7.02184 | 0.404732 | ||||||||
\(302\) | −0.765320 | −0.0440392 | ||||||||
\(303\) | 15.5456 | 0.893073 | ||||||||
\(304\) | 3.36763 | 0.193147 | ||||||||
\(305\) | −21.3927 | −1.22494 | ||||||||
\(306\) | 0.0587561 | 0.00335886 | ||||||||
\(307\) | −6.09863 | −0.348067 | −0.174034 | − | 0.984740i | \(-0.555680\pi\) | ||||
−0.174034 | + | 0.984740i | \(0.555680\pi\) | |||||||
\(308\) | −1.22767 | −0.0699527 | ||||||||
\(309\) | −23.1487 | −1.31688 | ||||||||
\(310\) | 20.2195 | 1.14839 | ||||||||
\(311\) | 0.136369 | 0.00773276 | 0.00386638 | − | 0.999993i | \(-0.498769\pi\) | ||||
0.00386638 | + | 0.999993i | \(0.498769\pi\) | |||||||
\(312\) | 1.71590 | 0.0971435 | ||||||||
\(313\) | 14.6617 | 0.828728 | 0.414364 | − | 0.910111i | \(-0.364004\pi\) | ||||
0.414364 | + | 0.910111i | \(0.364004\pi\) | |||||||
\(314\) | 20.2064 | 1.14031 | ||||||||
\(315\) | 0.522731 | 0.0294526 | ||||||||
\(316\) | −13.8367 | −0.778377 | ||||||||
\(317\) | 17.8736 | 1.00388 | 0.501940 | − | 0.864902i | \(-0.332620\pi\) | ||||
0.501940 | + | 0.864902i | \(0.332620\pi\) | |||||||
\(318\) | −9.51003 | −0.533296 | ||||||||
\(319\) | −4.45686 | −0.249536 | ||||||||
\(320\) | −4.04996 | −0.226400 | ||||||||
\(321\) | −1.99216 | −0.111191 | ||||||||
\(322\) | 0.370189 | 0.0206298 | ||||||||
\(323\) | 1.53303 | 0.0852998 | ||||||||
\(324\) | −8.59613 | −0.477563 | ||||||||
\(325\) | −11.5469 | −0.640509 | ||||||||
\(326\) | 19.0857 | 1.05706 | ||||||||
\(327\) | −25.5583 | −1.41338 | ||||||||
\(328\) | −3.64381 | −0.201196 | ||||||||
\(329\) | −9.70825 | −0.535233 | ||||||||
\(330\) | −8.42446 | −0.463751 | ||||||||
\(331\) | −34.9839 | −1.92289 | −0.961443 | − | 0.275003i | \(-0.911321\pi\) | ||||
−0.961443 | + | 0.275003i | \(0.911321\pi\) | |||||||
\(332\) | −12.9247 | −0.709333 | ||||||||
\(333\) | 0.482194 | 0.0264241 | ||||||||
\(334\) | 1.80685 | 0.0988663 | ||||||||
\(335\) | −46.9858 | −2.56711 | ||||||||
\(336\) | 1.69438 | 0.0924361 | ||||||||
\(337\) | 8.29791 | 0.452016 | 0.226008 | − | 0.974125i | \(-0.427432\pi\) | ||||
0.226008 | + | 0.974125i | \(0.427432\pi\) | |||||||
\(338\) | 11.9744 | 0.651324 | ||||||||
\(339\) | −30.6539 | −1.66489 | ||||||||
\(340\) | −1.84364 | −0.0999853 | ||||||||
\(341\) | −6.12915 | −0.331912 | ||||||||
\(342\) | 0.434663 | 0.0235039 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.02184 | −0.378592 | ||||||||
\(345\) | 2.54030 | 0.136765 | ||||||||
\(346\) | −13.1842 | −0.708789 | ||||||||
\(347\) | −9.70924 | −0.521219 | −0.260610 | − | 0.965444i | \(-0.583924\pi\) | ||||
−0.260610 | + | 0.965444i | \(0.583924\pi\) | |||||||
\(348\) | 6.15121 | 0.329739 | ||||||||
\(349\) | −6.21256 | −0.332551 | −0.166275 | − | 0.986079i | \(-0.553174\pi\) | ||||
−0.166275 | + | 0.986079i | \(0.553174\pi\) | |||||||
\(350\) | −11.4022 | −0.609471 | ||||||||
\(351\) | 5.36916 | 0.286585 | ||||||||
\(352\) | 1.22767 | 0.0654348 | ||||||||
\(353\) | −24.0250 | −1.27872 | −0.639362 | − | 0.768906i | \(-0.720801\pi\) | ||||
−0.639362 | + | 0.768906i | \(0.720801\pi\) | |||||||
\(354\) | 6.67419 | 0.354729 | ||||||||
\(355\) | 65.0141 | 3.45059 | ||||||||
\(356\) | 2.53987 | 0.134613 | ||||||||
\(357\) | 0.771323 | 0.0408227 | ||||||||
\(358\) | −21.9446 | −1.15981 | ||||||||
\(359\) | −10.2462 | −0.540774 | −0.270387 | − | 0.962752i | \(-0.587152\pi\) | ||||
−0.270387 | + | 0.962752i | \(0.587152\pi\) | |||||||
\(360\) | −0.522731 | −0.0275504 | ||||||||
\(361\) | −7.65906 | −0.403108 | ||||||||
\(362\) | −17.2828 | −0.908365 | ||||||||
\(363\) | −16.0845 | −0.844217 | ||||||||
\(364\) | −1.01270 | −0.0530798 | ||||||||
\(365\) | −14.2285 | −0.744754 | ||||||||
\(366\) | −8.95005 | −0.467827 | ||||||||
\(367\) | 14.8716 | 0.776290 | 0.388145 | − | 0.921598i | \(-0.373116\pi\) | ||||
0.388145 | + | 0.921598i | \(0.373116\pi\) | |||||||
\(368\) | −0.370189 | −0.0192974 | ||||||||
\(369\) | −0.470310 | −0.0244834 | ||||||||
\(370\) | −15.1302 | −0.786580 | ||||||||
\(371\) | 5.61269 | 0.291396 | ||||||||
\(372\) | 8.45924 | 0.438591 | ||||||||
\(373\) | 17.1193 | 0.886403 | 0.443202 | − | 0.896422i | \(-0.353843\pi\) | ||||
0.443202 | + | 0.896422i | \(0.353843\pi\) | |||||||
\(374\) | 0.558863 | 0.0288981 | ||||||||
\(375\) | −43.9327 | −2.26868 | ||||||||
\(376\) | 9.70825 | 0.500665 | ||||||||
\(377\) | −3.67645 | −0.189347 | ||||||||
\(378\) | 5.30184 | 0.272697 | ||||||||
\(379\) | 26.1615 | 1.34383 | 0.671914 | − | 0.740629i | \(-0.265473\pi\) | ||||
0.671914 | + | 0.740629i | \(0.265473\pi\) | |||||||
\(380\) | −13.6388 | −0.699654 | ||||||||
\(381\) | 15.6950 | 0.804078 | ||||||||
\(382\) | 20.5812 | 1.05303 | ||||||||
\(383\) | −25.4018 | −1.29797 | −0.648986 | − | 0.760801i | \(-0.724807\pi\) | ||||
−0.648986 | + | 0.760801i | \(0.724807\pi\) | |||||||
\(384\) | −1.69438 | −0.0864661 | ||||||||
\(385\) | 4.97199 | 0.253396 | ||||||||
\(386\) | −7.07694 | −0.360207 | ||||||||
\(387\) | −0.906315 | −0.0460706 | ||||||||
\(388\) | 10.8779 | 0.552242 | ||||||||
\(389\) | −26.6661 | −1.35202 | −0.676011 | − | 0.736891i | \(-0.736293\pi\) | ||||
−0.676011 | + | 0.736891i | \(0.736293\pi\) | |||||||
\(390\) | −6.94930 | −0.351892 | ||||||||
\(391\) | −0.168519 | −0.00852235 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 21.7052 | 1.09488 | ||||||||
\(394\) | 24.8708 | 1.25298 | ||||||||
\(395\) | 56.0382 | 2.81959 | ||||||||
\(396\) | 0.158456 | 0.00796270 | ||||||||
\(397\) | 18.6176 | 0.934391 | 0.467196 | − | 0.884154i | \(-0.345264\pi\) | ||||
0.467196 | + | 0.884154i | \(0.345264\pi\) | |||||||
\(398\) | −10.9476 | −0.548756 | ||||||||
\(399\) | 5.70605 | 0.285660 | ||||||||
\(400\) | 11.4022 | 0.570108 | ||||||||
\(401\) | 11.3576 | 0.567170 | 0.283585 | − | 0.958947i | \(-0.408476\pi\) | ||||
0.283585 | + | 0.958947i | \(0.408476\pi\) | |||||||
\(402\) | −19.6575 | −0.980425 | ||||||||
\(403\) | −5.05591 | −0.251853 | ||||||||
\(404\) | 9.17481 | 0.456464 | ||||||||
\(405\) | 34.8140 | 1.72992 | ||||||||
\(406\) | −3.63036 | −0.180172 | ||||||||
\(407\) | 4.58642 | 0.227340 | ||||||||
\(408\) | −0.771323 | −0.0381862 | ||||||||
\(409\) | −14.6733 | −0.725550 | −0.362775 | − | 0.931877i | \(-0.618171\pi\) | ||||
−0.362775 | + | 0.931877i | \(0.618171\pi\) | |||||||
\(410\) | 14.7573 | 0.728811 | ||||||||
\(411\) | 24.8920 | 1.22783 | ||||||||
\(412\) | −13.6620 | −0.673079 | ||||||||
\(413\) | −3.93901 | −0.193826 | ||||||||
\(414\) | −0.0477805 | −0.00234828 | ||||||||
\(415\) | 52.3443 | 2.56948 | ||||||||
\(416\) | 1.01270 | 0.0496516 | ||||||||
\(417\) | −28.9197 | −1.41621 | ||||||||
\(418\) | 4.13433 | 0.202216 | ||||||||
\(419\) | −25.1561 | −1.22896 | −0.614478 | − | 0.788934i | \(-0.710633\pi\) | ||||
−0.614478 | + | 0.788934i | \(0.710633\pi\) | |||||||
\(420\) | −6.86217 | −0.334840 | ||||||||
\(421\) | 7.60205 | 0.370501 | 0.185251 | − | 0.982691i | \(-0.440690\pi\) | ||||
0.185251 | + | 0.982691i | \(0.440690\pi\) | |||||||
\(422\) | 21.3568 | 1.03963 | ||||||||
\(423\) | 1.25305 | 0.0609254 | ||||||||
\(424\) | −5.61269 | −0.272576 | ||||||||
\(425\) | 5.19053 | 0.251778 | ||||||||
\(426\) | 27.2000 | 1.31784 | ||||||||
\(427\) | 5.28219 | 0.255623 | ||||||||
\(428\) | −1.17574 | −0.0568316 | ||||||||
\(429\) | 2.10655 | 0.101705 | ||||||||
\(430\) | 28.4382 | 1.37141 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −5.30184 | −0.255085 | ||||||||
\(433\) | 5.77007 | 0.277292 | 0.138646 | − | 0.990342i | \(-0.455725\pi\) | ||||
0.138646 | + | 0.990342i | \(0.455725\pi\) | |||||||
\(434\) | −4.99252 | −0.239649 | ||||||||
\(435\) | −24.9121 | −1.19445 | ||||||||
\(436\) | −15.0842 | −0.722401 | ||||||||
\(437\) | −1.24666 | −0.0596358 | ||||||||
\(438\) | −5.95279 | −0.284435 | ||||||||
\(439\) | −21.9324 | −1.04677 | −0.523387 | − | 0.852095i | \(-0.675332\pi\) | ||||
−0.523387 | + | 0.852095i | \(0.675332\pi\) | |||||||
\(440\) | −4.97199 | −0.237031 | ||||||||
\(441\) | −0.129071 | −0.00614623 | ||||||||
\(442\) | 0.461004 | 0.0219277 | ||||||||
\(443\) | 11.3476 | 0.539143 | 0.269571 | − | 0.962980i | \(-0.413118\pi\) | ||||
0.269571 | + | 0.962980i | \(0.413118\pi\) | |||||||
\(444\) | −6.33002 | −0.300409 | ||||||||
\(445\) | −10.2864 | −0.487621 | ||||||||
\(446\) | −19.2587 | −0.911928 | ||||||||
\(447\) | −24.5098 | −1.15927 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −9.13298 | −0.431012 | −0.215506 | − | 0.976503i | \(-0.569140\pi\) | ||||
−0.215506 | + | 0.976503i | \(0.569140\pi\) | |||||||
\(450\) | 1.47169 | 0.0693759 | ||||||||
\(451\) | −4.47339 | −0.210644 | ||||||||
\(452\) | −18.0915 | −0.850951 | ||||||||
\(453\) | 1.29674 | 0.0609264 | ||||||||
\(454\) | 27.8002 | 1.30473 | ||||||||
\(455\) | 4.10138 | 0.192276 | ||||||||
\(456\) | −5.70605 | −0.267210 | ||||||||
\(457\) | −11.0013 | −0.514621 | −0.257311 | − | 0.966329i | \(-0.582836\pi\) | ||||
−0.257311 | + | 0.966329i | \(0.582836\pi\) | |||||||
\(458\) | −11.0885 | −0.518130 | ||||||||
\(459\) | −2.41352 | −0.112654 | ||||||||
\(460\) | 1.49925 | 0.0699028 | ||||||||
\(461\) | 22.9284 | 1.06788 | 0.533941 | − | 0.845522i | \(-0.320710\pi\) | ||||
0.533941 | + | 0.845522i | \(0.320710\pi\) | |||||||
\(462\) | 2.08013 | 0.0967766 | ||||||||
\(463\) | −20.1512 | −0.936507 | −0.468254 | − | 0.883594i | \(-0.655117\pi\) | ||||
−0.468254 | + | 0.883594i | \(0.655117\pi\) | |||||||
\(464\) | 3.63036 | 0.168535 | ||||||||
\(465\) | −34.2596 | −1.58875 | ||||||||
\(466\) | −26.3989 | −1.22290 | ||||||||
\(467\) | 33.3189 | 1.54181 | 0.770907 | − | 0.636948i | \(-0.219804\pi\) | ||||
0.770907 | + | 0.636948i | \(0.219804\pi\) | |||||||
\(468\) | 0.130710 | 0.00604205 | ||||||||
\(469\) | 11.6016 | 0.535710 | ||||||||
\(470\) | −39.3180 | −1.81360 | ||||||||
\(471\) | −34.2373 | −1.57757 | ||||||||
\(472\) | 3.93901 | 0.181308 | ||||||||
\(473\) | −8.62047 | −0.396370 | ||||||||
\(474\) | 23.4447 | 1.07685 | ||||||||
\(475\) | 38.3983 | 1.76183 | ||||||||
\(476\) | 0.455224 | 0.0208651 | ||||||||
\(477\) | −0.724434 | −0.0331695 | ||||||||
\(478\) | 1.44825 | 0.0662413 | ||||||||
\(479\) | −2.45506 | −0.112175 | −0.0560873 | − | 0.998426i | \(-0.517863\pi\) | ||||
−0.0560873 | + | 0.998426i | \(0.517863\pi\) | |||||||
\(480\) | 6.86217 | 0.313214 | ||||||||
\(481\) | 3.78332 | 0.172505 | ||||||||
\(482\) | 18.0067 | 0.820184 | ||||||||
\(483\) | −0.627241 | −0.0285404 | ||||||||
\(484\) | −9.49284 | −0.431493 | ||||||||
\(485\) | −44.0551 | −2.00044 | ||||||||
\(486\) | −1.34040 | −0.0608017 | ||||||||
\(487\) | 37.8017 | 1.71296 | 0.856478 | − | 0.516183i | \(-0.172648\pi\) | ||||
0.856478 | + | 0.516183i | \(0.172648\pi\) | |||||||
\(488\) | −5.28219 | −0.239114 | ||||||||
\(489\) | −32.3385 | −1.46240 | ||||||||
\(490\) | 4.04996 | 0.182958 | ||||||||
\(491\) | 26.4129 | 1.19200 | 0.596000 | − | 0.802985i | \(-0.296756\pi\) | ||||
0.596000 | + | 0.802985i | \(0.296756\pi\) | |||||||
\(492\) | 6.17401 | 0.278346 | ||||||||
\(493\) | 1.65262 | 0.0744305 | ||||||||
\(494\) | 3.41039 | 0.153441 | ||||||||
\(495\) | −0.641739 | −0.0288440 | ||||||||
\(496\) | 4.99252 | 0.224171 | ||||||||
\(497\) | −16.0530 | −0.720077 | ||||||||
\(498\) | 21.8993 | 0.981332 | ||||||||
\(499\) | 31.6075 | 1.41495 | 0.707473 | − | 0.706740i | \(-0.249835\pi\) | ||||
0.707473 | + | 0.706740i | \(0.249835\pi\) | |||||||
\(500\) | −25.9285 | −1.15956 | ||||||||
\(501\) | −3.06149 | −0.136777 | ||||||||
\(502\) | −3.57879 | −0.159729 | ||||||||
\(503\) | 35.8375 | 1.59792 | 0.798958 | − | 0.601387i | \(-0.205385\pi\) | ||||
0.798958 | + | 0.601387i | \(0.205385\pi\) | |||||||
\(504\) | 0.129071 | 0.00574927 | ||||||||
\(505\) | −37.1576 | −1.65349 | ||||||||
\(506\) | −0.454468 | −0.0202036 | ||||||||
\(507\) | −20.2893 | −0.901079 | ||||||||
\(508\) | 9.26295 | 0.410977 | ||||||||
\(509\) | 28.4515 | 1.26109 | 0.630546 | − | 0.776152i | \(-0.282831\pi\) | ||||
0.630546 | + | 0.776152i | \(0.282831\pi\) | |||||||
\(510\) | 3.12382 | 0.138325 | ||||||||
\(511\) | 3.51325 | 0.155417 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.8546 | −0.788302 | ||||||||
\(514\) | −0.128614 | −0.00567294 | ||||||||
\(515\) | 55.3306 | 2.43816 | ||||||||
\(516\) | 11.8977 | 0.523766 | ||||||||
\(517\) | 11.9185 | 0.524174 | ||||||||
\(518\) | 3.73589 | 0.164145 | ||||||||
\(519\) | 22.3391 | 0.980578 | ||||||||
\(520\) | −4.10138 | −0.179857 | ||||||||
\(521\) | −5.09817 | −0.223355 | −0.111678 | − | 0.993744i | \(-0.535622\pi\) | ||||
−0.111678 | + | 0.993744i | \(0.535622\pi\) | |||||||
\(522\) | 0.468573 | 0.0205089 | ||||||||
\(523\) | 33.2179 | 1.45252 | 0.726259 | − | 0.687421i | \(-0.241257\pi\) | ||||
0.726259 | + | 0.687421i | \(0.241257\pi\) | |||||||
\(524\) | 12.8101 | 0.559613 | ||||||||
\(525\) | 19.3196 | 0.843177 | ||||||||
\(526\) | −6.36157 | −0.277378 | ||||||||
\(527\) | 2.27272 | 0.0990010 | ||||||||
\(528\) | −2.08013 | −0.0905262 | ||||||||
\(529\) | −22.8630 | −0.994042 | ||||||||
\(530\) | 22.7311 | 0.987378 | ||||||||
\(531\) | 0.508411 | 0.0220632 | ||||||||
\(532\) | 3.36763 | 0.146005 | ||||||||
\(533\) | −3.69008 | −0.159835 | ||||||||
\(534\) | −4.30351 | −0.186231 | ||||||||
\(535\) | 4.76171 | 0.205866 | ||||||||
\(536\) | −11.6016 | −0.501111 | ||||||||
\(537\) | 37.1825 | 1.60455 | ||||||||
\(538\) | 10.9848 | 0.473589 | ||||||||
\(539\) | −1.22767 | −0.0528793 | ||||||||
\(540\) | 21.4722 | 0.924018 | ||||||||
\(541\) | −25.4103 | −1.09248 | −0.546238 | − | 0.837630i | \(-0.683940\pi\) | ||||
−0.546238 | + | 0.837630i | \(0.683940\pi\) | |||||||
\(542\) | 27.0448 | 1.16167 | ||||||||
\(543\) | 29.2837 | 1.25668 | ||||||||
\(544\) | −0.455224 | −0.0195176 | ||||||||
\(545\) | 61.0903 | 2.61682 | ||||||||
\(546\) | 1.71590 | 0.0734336 | ||||||||
\(547\) | −4.47439 | −0.191311 | −0.0956555 | − | 0.995414i | \(-0.530495\pi\) | ||||
−0.0956555 | + | 0.995414i | \(0.530495\pi\) | |||||||
\(548\) | 14.6909 | 0.627564 | ||||||||
\(549\) | −0.681777 | −0.0290975 | ||||||||
\(550\) | 13.9980 | 0.596878 | ||||||||
\(551\) | 12.2257 | 0.520832 | ||||||||
\(552\) | 0.627241 | 0.0266971 | ||||||||
\(553\) | −13.8367 | −0.588398 | ||||||||
\(554\) | 8.73221 | 0.370996 | ||||||||
\(555\) | 25.6363 | 1.08820 | ||||||||
\(556\) | −17.0680 | −0.723845 | ||||||||
\(557\) | −39.9598 | −1.69315 | −0.846576 | − | 0.532268i | \(-0.821340\pi\) | ||||
−0.846576 | + | 0.532268i | \(0.821340\pi\) | |||||||
\(558\) | 0.644389 | 0.0272792 | ||||||||
\(559\) | −7.11100 | −0.300763 | ||||||||
\(560\) | −4.04996 | −0.171142 | ||||||||
\(561\) | −0.946927 | −0.0399793 | ||||||||
\(562\) | −11.2372 | −0.474014 | ||||||||
\(563\) | −16.8827 | −0.711520 | −0.355760 | − | 0.934577i | \(-0.615778\pi\) | ||||
−0.355760 | + | 0.934577i | \(0.615778\pi\) | |||||||
\(564\) | −16.4495 | −0.692648 | ||||||||
\(565\) | 73.2697 | 3.08248 | ||||||||
\(566\) | 21.5351 | 0.905189 | ||||||||
\(567\) | −8.59613 | −0.361003 | ||||||||
\(568\) | 16.0530 | 0.673570 | ||||||||
\(569\) | 25.8643 | 1.08429 | 0.542145 | − | 0.840285i | \(-0.317612\pi\) | ||||
0.542145 | + | 0.840285i | \(0.317612\pi\) | |||||||
\(570\) | 23.1093 | 0.967941 | ||||||||
\(571\) | 23.5807 | 0.986823 | 0.493412 | − | 0.869796i | \(-0.335750\pi\) | ||||
0.493412 | + | 0.869796i | \(0.335750\pi\) | |||||||
\(572\) | 1.24325 | 0.0519830 | ||||||||
\(573\) | −34.8725 | −1.45682 | ||||||||
\(574\) | −3.64381 | −0.152090 | ||||||||
\(575\) | −4.22095 | −0.176026 | ||||||||
\(576\) | −0.129071 | −0.00537795 | ||||||||
\(577\) | −10.5502 | −0.439211 | −0.219605 | − | 0.975589i | \(-0.570477\pi\) | ||||
−0.219605 | + | 0.975589i | \(0.570477\pi\) | |||||||
\(578\) | 16.7928 | 0.698487 | ||||||||
\(579\) | 11.9910 | 0.498331 | ||||||||
\(580\) | −14.7028 | −0.610500 | ||||||||
\(581\) | −12.9247 | −0.536205 | ||||||||
\(582\) | −18.4313 | −0.764003 | ||||||||
\(583\) | −6.89050 | −0.285375 | ||||||||
\(584\) | −3.51325 | −0.145379 | ||||||||
\(585\) | −0.529368 | −0.0218867 | ||||||||
\(586\) | 17.9971 | 0.743453 | ||||||||
\(587\) | 28.6982 | 1.18450 | 0.592251 | − | 0.805753i | \(-0.298239\pi\) | ||||
0.592251 | + | 0.805753i | \(0.298239\pi\) | |||||||
\(588\) | 1.69438 | 0.0698751 | ||||||||
\(589\) | 16.8130 | 0.692767 | ||||||||
\(590\) | −15.9528 | −0.656768 | ||||||||
\(591\) | −42.1407 | −1.73344 | ||||||||
\(592\) | −3.73589 | −0.153544 | ||||||||
\(593\) | −19.5840 | −0.804217 | −0.402108 | − | 0.915592i | \(-0.631723\pi\) | ||||
−0.402108 | + | 0.915592i | \(0.631723\pi\) | |||||||
\(594\) | −6.50889 | −0.267063 | ||||||||
\(595\) | −1.84364 | −0.0755817 | ||||||||
\(596\) | −14.4653 | −0.592523 | ||||||||
\(597\) | 18.5495 | 0.759180 | ||||||||
\(598\) | −0.374889 | −0.0153303 | ||||||||
\(599\) | 17.1604 | 0.701157 | 0.350578 | − | 0.936533i | \(-0.385985\pi\) | ||||
0.350578 | + | 0.936533i | \(0.385985\pi\) | |||||||
\(600\) | −19.3196 | −0.788720 | ||||||||
\(601\) | −16.2600 | −0.663260 | −0.331630 | − | 0.943410i | \(-0.607598\pi\) | ||||
−0.331630 | + | 0.943410i | \(0.607598\pi\) | |||||||
\(602\) | −7.02184 | −0.286189 | ||||||||
\(603\) | −1.49742 | −0.0609797 | ||||||||
\(604\) | 0.765320 | 0.0311404 | ||||||||
\(605\) | 38.4456 | 1.56304 | ||||||||
\(606\) | −15.5456 | −0.631498 | ||||||||
\(607\) | 33.8465 | 1.37379 | 0.686894 | − | 0.726757i | \(-0.258973\pi\) | ||||
0.686894 | + | 0.726757i | \(0.258973\pi\) | |||||||
\(608\) | −3.36763 | −0.136575 | ||||||||
\(609\) | 6.15121 | 0.249260 | ||||||||
\(610\) | 21.3927 | 0.866164 | ||||||||
\(611\) | 9.83151 | 0.397740 | ||||||||
\(612\) | −0.0587561 | −0.00237507 | ||||||||
\(613\) | −15.9246 | −0.643189 | −0.321594 | − | 0.946878i | \(-0.604219\pi\) | ||||
−0.321594 | + | 0.946878i | \(0.604219\pi\) | |||||||
\(614\) | 6.09863 | 0.246121 | ||||||||
\(615\) | −25.0045 | −1.00828 | ||||||||
\(616\) | 1.22767 | 0.0494641 | ||||||||
\(617\) | −1.27042 | −0.0511452 | −0.0255726 | − | 0.999673i | \(-0.508141\pi\) | ||||
−0.0255726 | + | 0.999673i | \(0.508141\pi\) | |||||||
\(618\) | 23.1487 | 0.931176 | ||||||||
\(619\) | 11.6977 | 0.470169 | 0.235085 | − | 0.971975i | \(-0.424463\pi\) | ||||
0.235085 | + | 0.971975i | \(0.424463\pi\) | |||||||
\(620\) | −20.2195 | −0.812035 | ||||||||
\(621\) | 1.96268 | 0.0787597 | ||||||||
\(622\) | −0.136369 | −0.00546789 | ||||||||
\(623\) | 2.53987 | 0.101758 | ||||||||
\(624\) | −1.71590 | −0.0686908 | ||||||||
\(625\) | 47.9984 | 1.91994 | ||||||||
\(626\) | −14.6617 | −0.585999 | ||||||||
\(627\) | −7.00513 | −0.279758 | ||||||||
\(628\) | −20.2064 | −0.806321 | ||||||||
\(629\) | −1.70066 | −0.0678099 | ||||||||
\(630\) | −0.522731 | −0.0208261 | ||||||||
\(631\) | 35.6124 | 1.41771 | 0.708854 | − | 0.705355i | \(-0.249212\pi\) | ||||
0.708854 | + | 0.705355i | \(0.249212\pi\) | |||||||
\(632\) | 13.8367 | 0.550396 | ||||||||
\(633\) | −36.1865 | −1.43829 | ||||||||
\(634\) | −17.8736 | −0.709851 | ||||||||
\(635\) | −37.5145 | −1.48872 | ||||||||
\(636\) | 9.51003 | 0.377097 | ||||||||
\(637\) | −1.01270 | −0.0401245 | ||||||||
\(638\) | 4.45686 | 0.176449 | ||||||||
\(639\) | 2.07198 | 0.0819661 | ||||||||
\(640\) | 4.04996 | 0.160089 | ||||||||
\(641\) | −42.5386 | −1.68018 | −0.840088 | − | 0.542451i | \(-0.817496\pi\) | ||||
−0.840088 | + | 0.542451i | \(0.817496\pi\) | |||||||
\(642\) | 1.99216 | 0.0786241 | ||||||||
\(643\) | −33.9921 | −1.34052 | −0.670259 | − | 0.742127i | \(-0.733817\pi\) | ||||
−0.670259 | + | 0.742127i | \(0.733817\pi\) | |||||||
\(644\) | −0.370189 | −0.0145875 | ||||||||
\(645\) | −48.1851 | −1.89729 | ||||||||
\(646\) | −1.53303 | −0.0603161 | ||||||||
\(647\) | −37.3199 | −1.46720 | −0.733598 | − | 0.679584i | \(-0.762160\pi\) | ||||
−0.733598 | + | 0.679584i | \(0.762160\pi\) | |||||||
\(648\) | 8.59613 | 0.337688 | ||||||||
\(649\) | 4.83579 | 0.189821 | ||||||||
\(650\) | 11.5469 | 0.452908 | ||||||||
\(651\) | 8.45924 | 0.331544 | ||||||||
\(652\) | −19.0857 | −0.747454 | ||||||||
\(653\) | −43.1135 | −1.68716 | −0.843581 | − | 0.537002i | \(-0.819557\pi\) | ||||
−0.843581 | + | 0.537002i | \(0.819557\pi\) | |||||||
\(654\) | 25.5583 | 0.999410 | ||||||||
\(655\) | −51.8805 | −2.02714 | ||||||||
\(656\) | 3.64381 | 0.142267 | ||||||||
\(657\) | −0.453458 | −0.0176911 | ||||||||
\(658\) | 9.70825 | 0.378467 | ||||||||
\(659\) | −13.1760 | −0.513264 | −0.256632 | − | 0.966509i | \(-0.582613\pi\) | ||||
−0.256632 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(660\) | 8.42446 | 0.327921 | ||||||||
\(661\) | −15.9695 | −0.621141 | −0.310570 | − | 0.950550i | \(-0.600520\pi\) | ||||
−0.310570 | + | 0.950550i | \(0.600520\pi\) | |||||||
\(662\) | 34.9839 | 1.35969 | ||||||||
\(663\) | −0.781116 | −0.0303361 | ||||||||
\(664\) | 12.9247 | 0.501574 | ||||||||
\(665\) | −13.6388 | −0.528889 | ||||||||
\(666\) | −0.482194 | −0.0186846 | ||||||||
\(667\) | −1.34392 | −0.0520366 | ||||||||
\(668\) | −1.80685 | −0.0699090 | ||||||||
\(669\) | 32.6317 | 1.26161 | ||||||||
\(670\) | 46.9858 | 1.81522 | ||||||||
\(671\) | −6.48477 | −0.250342 | ||||||||
\(672\) | −1.69438 | −0.0653622 | ||||||||
\(673\) | −24.6479 | −0.950106 | −0.475053 | − | 0.879957i | \(-0.657571\pi\) | ||||
−0.475053 | + | 0.879957i | \(0.657571\pi\) | |||||||
\(674\) | −8.29791 | −0.319624 | ||||||||
\(675\) | −60.4524 | −2.32681 | ||||||||
\(676\) | −11.9744 | −0.460556 | ||||||||
\(677\) | 6.98276 | 0.268369 | 0.134185 | − | 0.990956i | \(-0.457158\pi\) | ||||
0.134185 | + | 0.990956i | \(0.457158\pi\) | |||||||
\(678\) | 30.6539 | 1.17725 | ||||||||
\(679\) | 10.8779 | 0.417456 | ||||||||
\(680\) | 1.84364 | 0.0707002 | ||||||||
\(681\) | −47.1041 | −1.80503 | ||||||||
\(682\) | 6.12915 | 0.234697 | ||||||||
\(683\) | −46.3513 | −1.77358 | −0.886792 | − | 0.462169i | \(-0.847071\pi\) | ||||
−0.886792 | + | 0.462169i | \(0.847071\pi\) | |||||||
\(684\) | −0.434663 | −0.0166197 | ||||||||
\(685\) | −59.4975 | −2.27328 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 18.7881 | 0.716811 | ||||||||
\(688\) | 7.02184 | 0.267705 | ||||||||
\(689\) | −5.68395 | −0.216541 | ||||||||
\(690\) | −2.54030 | −0.0967075 | ||||||||
\(691\) | 39.4119 | 1.49930 | 0.749650 | − | 0.661835i | \(-0.230222\pi\) | ||||
0.749650 | + | 0.661835i | \(0.230222\pi\) | |||||||
\(692\) | 13.1842 | 0.501189 | ||||||||
\(693\) | 0.158456 | 0.00601924 | ||||||||
\(694\) | 9.70924 | 0.368558 | ||||||||
\(695\) | 69.1248 | 2.62205 | ||||||||
\(696\) | −6.15121 | −0.233161 | ||||||||
\(697\) | 1.65875 | 0.0628297 | ||||||||
\(698\) | 6.21256 | 0.235149 | ||||||||
\(699\) | 44.7298 | 1.69183 | ||||||||
\(700\) | 11.4022 | 0.430961 | ||||||||
\(701\) | 9.42552 | 0.355997 | 0.177998 | − | 0.984031i | \(-0.443038\pi\) | ||||
0.177998 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(702\) | −5.36916 | −0.202646 | ||||||||
\(703\) | −12.5811 | −0.474505 | ||||||||
\(704\) | −1.22767 | −0.0462694 | ||||||||
\(705\) | 66.6197 | 2.50904 | ||||||||
\(706\) | 24.0250 | 0.904194 | ||||||||
\(707\) | 9.17481 | 0.345054 | ||||||||
\(708\) | −6.67419 | −0.250831 | ||||||||
\(709\) | 19.7652 | 0.742299 | 0.371149 | − | 0.928573i | \(-0.378964\pi\) | ||||
0.371149 | + | 0.928573i | \(0.378964\pi\) | |||||||
\(710\) | −65.0141 | −2.43993 | ||||||||
\(711\) | 1.78592 | 0.0669772 | ||||||||
\(712\) | −2.53987 | −0.0951857 | ||||||||
\(713\) | −1.84817 | −0.0692147 | ||||||||
\(714\) | −0.771323 | −0.0288660 | ||||||||
\(715\) | −5.03512 | −0.188303 | ||||||||
\(716\) | 21.9446 | 0.820109 | ||||||||
\(717\) | −2.45388 | −0.0916420 | ||||||||
\(718\) | 10.2462 | 0.382385 | ||||||||
\(719\) | −31.6490 | −1.18031 | −0.590154 | − | 0.807291i | \(-0.700933\pi\) | ||||
−0.590154 | + | 0.807291i | \(0.700933\pi\) | |||||||
\(720\) | 0.522731 | 0.0194810 | ||||||||
\(721\) | −13.6620 | −0.508800 | ||||||||
\(722\) | 7.65906 | 0.285041 | ||||||||
\(723\) | −30.5103 | −1.13469 | ||||||||
\(724\) | 17.2828 | 0.642311 | ||||||||
\(725\) | 41.3939 | 1.53733 | ||||||||
\(726\) | 16.0845 | 0.596951 | ||||||||
\(727\) | −14.9907 | −0.555973 | −0.277986 | − | 0.960585i | \(-0.589667\pi\) | ||||
−0.277986 | + | 0.960585i | \(0.589667\pi\) | |||||||
\(728\) | 1.01270 | 0.0375331 | ||||||||
\(729\) | 28.0595 | 1.03924 | ||||||||
\(730\) | 14.2285 | 0.526621 | ||||||||
\(731\) | 3.19651 | 0.118227 | ||||||||
\(732\) | 8.95005 | 0.330803 | ||||||||
\(733\) | 3.95892 | 0.146226 | 0.0731130 | − | 0.997324i | \(-0.476707\pi\) | ||||
0.0731130 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(734\) | −14.8716 | −0.548920 | ||||||||
\(735\) | −6.86217 | −0.253115 | ||||||||
\(736\) | 0.370189 | 0.0136453 | ||||||||
\(737\) | −14.2428 | −0.524641 | ||||||||
\(738\) | 0.470310 | 0.0173124 | ||||||||
\(739\) | 25.9678 | 0.955239 | 0.477620 | − | 0.878567i | \(-0.341500\pi\) | ||||
0.477620 | + | 0.878567i | \(0.341500\pi\) | |||||||
\(740\) | 15.1302 | 0.556196 | ||||||||
\(741\) | −5.77850 | −0.212279 | ||||||||
\(742\) | −5.61269 | −0.206048 | ||||||||
\(743\) | −40.6421 | −1.49101 | −0.745507 | − | 0.666498i | \(-0.767793\pi\) | ||||
−0.745507 | + | 0.666498i | \(0.767793\pi\) | |||||||
\(744\) | −8.45924 | −0.310131 | ||||||||
\(745\) | 58.5839 | 2.14635 | ||||||||
\(746\) | −17.1193 | −0.626782 | ||||||||
\(747\) | 1.66820 | 0.0610361 | ||||||||
\(748\) | −0.558863 | −0.0204340 | ||||||||
\(749\) | −1.17574 | −0.0429607 | ||||||||
\(750\) | 43.9327 | 1.60420 | ||||||||
\(751\) | −35.0716 | −1.27978 | −0.639890 | − | 0.768466i | \(-0.721020\pi\) | ||||
−0.639890 | + | 0.768466i | \(0.721020\pi\) | |||||||
\(752\) | −9.70825 | −0.354023 | ||||||||
\(753\) | 6.06383 | 0.220978 | ||||||||
\(754\) | 3.67645 | 0.133888 | ||||||||
\(755\) | −3.09951 | −0.112803 | ||||||||
\(756\) | −5.30184 | −0.192826 | ||||||||
\(757\) | −29.5195 | −1.07290 | −0.536452 | − | 0.843931i | \(-0.680236\pi\) | ||||
−0.536452 | + | 0.843931i | \(0.680236\pi\) | |||||||
\(758\) | −26.1615 | −0.950230 | ||||||||
\(759\) | 0.770042 | 0.0279508 | ||||||||
\(760\) | 13.6388 | 0.494730 | ||||||||
\(761\) | −35.0810 | −1.27168 | −0.635842 | − | 0.771819i | \(-0.719347\pi\) | ||||
−0.635842 | + | 0.771819i | \(0.719347\pi\) | |||||||
\(762\) | −15.6950 | −0.568569 | ||||||||
\(763\) | −15.0842 | −0.546084 | ||||||||
\(764\) | −20.5812 | −0.744603 | ||||||||
\(765\) | 0.237960 | 0.00860345 | ||||||||
\(766\) | 25.4018 | 0.917804 | ||||||||
\(767\) | 3.98903 | 0.144035 | ||||||||
\(768\) | 1.69438 | 0.0611407 | ||||||||
\(769\) | −8.63816 | −0.311500 | −0.155750 | − | 0.987796i | \(-0.549779\pi\) | ||||
−0.155750 | + | 0.987796i | \(0.549779\pi\) | |||||||
\(770\) | −4.97199 | −0.179178 | ||||||||
\(771\) | 0.217922 | 0.00784827 | ||||||||
\(772\) | 7.07694 | 0.254705 | ||||||||
\(773\) | −6.80172 | −0.244641 | −0.122320 | − | 0.992491i | \(-0.539034\pi\) | ||||
−0.122320 | + | 0.992491i | \(0.539034\pi\) | |||||||
\(774\) | 0.906315 | 0.0325768 | ||||||||
\(775\) | 56.9255 | 2.04483 | ||||||||
\(776\) | −10.8779 | −0.390494 | ||||||||
\(777\) | −6.33002 | −0.227088 | ||||||||
\(778\) | 26.6661 | 0.956024 | ||||||||
\(779\) | 12.2710 | 0.439655 | ||||||||
\(780\) | 6.94930 | 0.248825 | ||||||||
\(781\) | 19.7078 | 0.705199 | ||||||||
\(782\) | 0.168519 | 0.00602621 | ||||||||
\(783\) | −19.2476 | −0.687852 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 81.8349 | 2.92081 | ||||||||
\(786\) | −21.7052 | −0.774201 | ||||||||
\(787\) | 30.6448 | 1.09237 | 0.546184 | − | 0.837665i | \(-0.316080\pi\) | ||||
0.546184 | + | 0.837665i | \(0.316080\pi\) | |||||||
\(788\) | −24.8708 | −0.885987 | ||||||||
\(789\) | 10.7789 | 0.383740 | ||||||||
\(790\) | −56.0382 | −1.99375 | ||||||||
\(791\) | −18.0915 | −0.643259 | ||||||||
\(792\) | −0.158456 | −0.00563048 | ||||||||
\(793\) | −5.34926 | −0.189958 | ||||||||
\(794\) | −18.6176 | −0.660714 | ||||||||
\(795\) | −38.5152 | −1.36599 | ||||||||
\(796\) | 10.9476 | 0.388029 | ||||||||
\(797\) | 6.16844 | 0.218497 | 0.109249 | − | 0.994014i | \(-0.465156\pi\) | ||||
0.109249 | + | 0.994014i | \(0.465156\pi\) | |||||||
\(798\) | −5.70605 | −0.201992 | ||||||||
\(799\) | −4.41942 | −0.156348 | ||||||||
\(800\) | −11.4022 | −0.403127 | ||||||||
\(801\) | −0.327823 | −0.0115831 | ||||||||
\(802\) | −11.3576 | −0.401050 | ||||||||
\(803\) | −4.31310 | −0.152206 | ||||||||
\(804\) | 19.6575 | 0.693265 | ||||||||
\(805\) | 1.49925 | 0.0528415 | ||||||||
\(806\) | 5.05591 | 0.178087 | ||||||||
\(807\) | −18.6125 | −0.655190 | ||||||||
\(808\) | −9.17481 | −0.322769 | ||||||||
\(809\) | −19.2956 | −0.678396 | −0.339198 | − | 0.940715i | \(-0.610156\pi\) | ||||
−0.339198 | + | 0.940715i | \(0.610156\pi\) | |||||||
\(810\) | −34.8140 | −1.22324 | ||||||||
\(811\) | 28.1345 | 0.987934 | 0.493967 | − | 0.869481i | \(-0.335546\pi\) | ||||
0.493967 | + | 0.869481i | \(0.335546\pi\) | |||||||
\(812\) | 3.63036 | 0.127401 | ||||||||
\(813\) | −45.8242 | −1.60712 | ||||||||
\(814\) | −4.58642 | −0.160754 | ||||||||
\(815\) | 77.2963 | 2.70757 | ||||||||
\(816\) | 0.771323 | 0.0270017 | ||||||||
\(817\) | 23.6470 | 0.827303 | ||||||||
\(818\) | 14.6733 | 0.513041 | ||||||||
\(819\) | 0.130710 | 0.00456736 | ||||||||
\(820\) | −14.7573 | −0.515347 | ||||||||
\(821\) | 21.3065 | 0.743601 | 0.371800 | − | 0.928313i | \(-0.378741\pi\) | ||||
0.371800 | + | 0.928313i | \(0.378741\pi\) | |||||||
\(822\) | −24.8920 | −0.868207 | ||||||||
\(823\) | 0.638428 | 0.0222542 | 0.0111271 | − | 0.999938i | \(-0.496458\pi\) | ||||
0.0111271 | + | 0.999938i | \(0.496458\pi\) | |||||||
\(824\) | 13.6620 | 0.475939 | ||||||||
\(825\) | −23.7180 | −0.825755 | ||||||||
\(826\) | 3.93901 | 0.137056 | ||||||||
\(827\) | −20.2058 | −0.702624 | −0.351312 | − | 0.936258i | \(-0.614264\pi\) | ||||
−0.351312 | + | 0.936258i | \(0.614264\pi\) | |||||||
\(828\) | 0.0477805 | 0.00166049 | ||||||||
\(829\) | 35.8559 | 1.24533 | 0.622663 | − | 0.782490i | \(-0.286051\pi\) | ||||
0.622663 | + | 0.782490i | \(0.286051\pi\) | |||||||
\(830\) | −52.3443 | −1.81690 | ||||||||
\(831\) | −14.7957 | −0.513257 | ||||||||
\(832\) | −1.01270 | −0.0351090 | ||||||||
\(833\) | 0.455224 | 0.0157726 | ||||||||
\(834\) | 28.9197 | 1.00141 | ||||||||
\(835\) | 7.31765 | 0.253238 | ||||||||
\(836\) | −4.13433 | −0.142989 | ||||||||
\(837\) | −26.4696 | −0.914922 | ||||||||
\(838\) | 25.1561 | 0.869003 | ||||||||
\(839\) | −30.0836 | −1.03860 | −0.519300 | − | 0.854592i | \(-0.673807\pi\) | ||||
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(840\) | 6.86217 | 0.236767 | ||||||||
\(841\) | −15.8205 | −0.545535 | ||||||||
\(842\) | −7.60205 | −0.261984 | ||||||||
\(843\) | 19.0402 | 0.655778 | ||||||||
\(844\) | −21.3568 | −0.735130 | ||||||||
\(845\) | 48.4960 | 1.66831 | ||||||||
\(846\) | −1.25305 | −0.0430808 | ||||||||
\(847\) | −9.49284 | −0.326178 | ||||||||
\(848\) | 5.61269 | 0.192740 | ||||||||
\(849\) | −36.4887 | −1.25229 | ||||||||
\(850\) | −5.19053 | −0.178034 | ||||||||
\(851\) | 1.38298 | 0.0474080 | ||||||||
\(852\) | −27.2000 | −0.931855 | ||||||||
\(853\) | 7.66644 | 0.262494 | 0.131247 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131247 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(854\) | −5.28219 | −0.180753 | ||||||||
\(855\) | 1.76037 | 0.0602033 | ||||||||
\(856\) | 1.17574 | 0.0401860 | ||||||||
\(857\) | 42.9555 | 1.46733 | 0.733666 | − | 0.679510i | \(-0.237808\pi\) | ||||
0.733666 | + | 0.679510i | \(0.237808\pi\) | |||||||
\(858\) | −2.10655 | −0.0719163 | ||||||||
\(859\) | −32.0705 | −1.09423 | −0.547115 | − | 0.837058i | \(-0.684274\pi\) | ||||
−0.547115 | + | 0.837058i | \(0.684274\pi\) | |||||||
\(860\) | −28.4382 | −0.969733 | ||||||||
\(861\) | 6.17401 | 0.210410 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −40.8641 | −1.39103 | −0.695516 | − | 0.718511i | \(-0.744824\pi\) | ||||
−0.695516 | + | 0.718511i | \(0.744824\pi\) | |||||||
\(864\) | 5.30184 | 0.180372 | ||||||||
\(865\) | −53.3956 | −1.81550 | ||||||||
\(866\) | −5.77007 | −0.196075 | ||||||||
\(867\) | −28.4534 | −0.966327 | ||||||||
\(868\) | 4.99252 | 0.169457 | ||||||||
\(869\) | 16.9869 | 0.576241 | ||||||||
\(870\) | 24.9121 | 0.844600 | ||||||||
\(871\) | −11.7489 | −0.398095 | ||||||||
\(872\) | 15.0842 | 0.510815 | ||||||||
\(873\) | −1.40402 | −0.0475189 | ||||||||
\(874\) | 1.24666 | 0.0421689 | ||||||||
\(875\) | −25.9285 | −0.876542 | ||||||||
\(876\) | 5.95279 | 0.201126 | ||||||||
\(877\) | −33.7627 | −1.14009 | −0.570043 | − | 0.821615i | \(-0.693074\pi\) | ||||
−0.570043 | + | 0.821615i | \(0.693074\pi\) | |||||||
\(878\) | 21.9324 | 0.740181 | ||||||||
\(879\) | −30.4939 | −1.02853 | ||||||||
\(880\) | 4.97199 | 0.167606 | ||||||||
\(881\) | 18.6504 | 0.628346 | 0.314173 | − | 0.949366i | \(-0.398273\pi\) | ||||
0.314173 | + | 0.949366i | \(0.398273\pi\) | |||||||
\(882\) | 0.129071 | 0.00434604 | ||||||||
\(883\) | −18.4592 | −0.621203 | −0.310602 | − | 0.950540i | \(-0.600530\pi\) | ||||
−0.310602 | + | 0.950540i | \(0.600530\pi\) | |||||||
\(884\) | −0.461004 | −0.0155052 | ||||||||
\(885\) | 27.0302 | 0.908610 | ||||||||
\(886\) | −11.3476 | −0.381231 | ||||||||
\(887\) | −38.6016 | −1.29611 | −0.648057 | − | 0.761592i | \(-0.724418\pi\) | ||||
−0.648057 | + | 0.761592i | \(0.724418\pi\) | |||||||
\(888\) | 6.33002 | 0.212421 | ||||||||
\(889\) | 9.26295 | 0.310669 | ||||||||
\(890\) | 10.2864 | 0.344800 | ||||||||
\(891\) | 10.5532 | 0.353545 | ||||||||
\(892\) | 19.2587 | 0.644830 | ||||||||
\(893\) | −32.6938 | −1.09406 | ||||||||
\(894\) | 24.5098 | 0.819729 | ||||||||
\(895\) | −88.8747 | −2.97075 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0.635205 | 0.0212089 | ||||||||
\(898\) | 9.13298 | 0.304771 | ||||||||
\(899\) | 18.1246 | 0.604490 | ||||||||
\(900\) | −1.47169 | −0.0490562 | ||||||||
\(901\) | 2.55503 | 0.0851203 | ||||||||
\(902\) | 4.47339 | 0.148947 | ||||||||
\(903\) | 11.8977 | 0.395930 | ||||||||
\(904\) | 18.0915 | 0.601713 | ||||||||
\(905\) | −69.9947 | −2.32670 | ||||||||
\(906\) | −1.29674 | −0.0430814 | ||||||||
\(907\) | 10.2804 | 0.341355 | 0.170677 | − | 0.985327i | \(-0.445404\pi\) | ||||
0.170677 | + | 0.985327i | \(0.445404\pi\) | |||||||
\(908\) | −27.8002 | −0.922581 | ||||||||
\(909\) | −1.18420 | −0.0392774 | ||||||||
\(910\) | −4.10138 | −0.135959 | ||||||||
\(911\) | 27.4015 | 0.907852 | 0.453926 | − | 0.891039i | \(-0.350023\pi\) | ||||
0.453926 | + | 0.891039i | \(0.350023\pi\) | |||||||
\(912\) | 5.70605 | 0.188946 | ||||||||
\(913\) | 15.8672 | 0.525127 | ||||||||
\(914\) | 11.0013 | 0.363892 | ||||||||
\(915\) | −36.2473 | −1.19830 | ||||||||
\(916\) | 11.0885 | 0.366373 | ||||||||
\(917\) | 12.8101 | 0.423028 | ||||||||
\(918\) | 2.41352 | 0.0796582 | ||||||||
\(919\) | −53.2178 | −1.75549 | −0.877747 | − | 0.479125i | \(-0.840954\pi\) | ||||
−0.877747 | + | 0.479125i | \(0.840954\pi\) | |||||||
\(920\) | −1.49925 | −0.0494287 | ||||||||
\(921\) | −10.3334 | −0.340497 | ||||||||
\(922\) | −22.9284 | −0.755107 | ||||||||
\(923\) | 16.2569 | 0.535101 | ||||||||
\(924\) | −2.08013 | −0.0684314 | ||||||||
\(925\) | −42.5971 | −1.40059 | ||||||||
\(926\) | 20.1512 | 0.662211 | ||||||||
\(927\) | 1.76337 | 0.0579165 | ||||||||
\(928\) | −3.63036 | −0.119172 | ||||||||
\(929\) | −24.6008 | −0.807127 | −0.403563 | − | 0.914952i | \(-0.632229\pi\) | ||||
−0.403563 | + | 0.914952i | \(0.632229\pi\) | |||||||
\(930\) | 34.2596 | 1.12342 | ||||||||
\(931\) | 3.36763 | 0.110370 | ||||||||
\(932\) | 26.3989 | 0.864724 | ||||||||
\(933\) | 0.231061 | 0.00756458 | ||||||||
\(934\) | −33.3189 | −1.09023 | ||||||||
\(935\) | 2.26337 | 0.0740201 | ||||||||
\(936\) | −0.130710 | −0.00427238 | ||||||||
\(937\) | −32.7632 | −1.07033 | −0.535164 | − | 0.844748i | \(-0.679750\pi\) | ||||
−0.535164 | + | 0.844748i | \(0.679750\pi\) | |||||||
\(938\) | −11.6016 | −0.378804 | ||||||||
\(939\) | 24.8425 | 0.810705 | ||||||||
\(940\) | 39.3180 | 1.28241 | ||||||||
\(941\) | 19.4389 | 0.633690 | 0.316845 | − | 0.948477i | \(-0.397376\pi\) | ||||
0.316845 | + | 0.948477i | \(0.397376\pi\) | |||||||
\(942\) | 34.2373 | 1.11551 | ||||||||
\(943\) | −1.34890 | −0.0439262 | ||||||||
\(944\) | −3.93901 | −0.128204 | ||||||||
\(945\) | 21.4722 | 0.698492 | ||||||||
\(946\) | 8.62047 | 0.280276 | ||||||||
\(947\) | 15.7947 | 0.513258 | 0.256629 | − | 0.966510i | \(-0.417388\pi\) | ||||
0.256629 | + | 0.966510i | \(0.417388\pi\) | |||||||
\(948\) | −23.4447 | −0.761449 | ||||||||
\(949\) | −3.55786 | −0.115493 | ||||||||
\(950\) | −38.3983 | −1.24580 | ||||||||
\(951\) | 30.2847 | 0.982048 | ||||||||
\(952\) | −0.455224 | −0.0147539 | ||||||||
\(953\) | −44.7353 | −1.44912 | −0.724559 | − | 0.689213i | \(-0.757957\pi\) | ||||
−0.724559 | + | 0.689213i | \(0.757957\pi\) | |||||||
\(954\) | 0.724434 | 0.0234544 | ||||||||
\(955\) | 83.3532 | 2.69724 | ||||||||
\(956\) | −1.44825 | −0.0468397 | ||||||||
\(957\) | −7.55163 | −0.244109 | ||||||||
\(958\) | 2.45506 | 0.0793194 | ||||||||
\(959\) | 14.6909 | 0.474393 | ||||||||
\(960\) | −6.86217 | −0.221476 | ||||||||
\(961\) | −6.07472 | −0.195959 | ||||||||
\(962\) | −3.78332 | −0.121979 | ||||||||
\(963\) | 0.151754 | 0.00489020 | ||||||||
\(964\) | −18.0067 | −0.579958 | ||||||||
\(965\) | −28.6613 | −0.922640 | ||||||||
\(966\) | 0.627241 | 0.0201811 | ||||||||
\(967\) | −28.1299 | −0.904597 | −0.452299 | − | 0.891867i | \(-0.649396\pi\) | ||||
−0.452299 | + | 0.891867i | \(0.649396\pi\) | |||||||
\(968\) | 9.49284 | 0.305111 | ||||||||
\(969\) | 2.59753 | 0.0834447 | ||||||||
\(970\) | 44.0551 | 1.41452 | ||||||||
\(971\) | 37.4754 | 1.20264 | 0.601322 | − | 0.799007i | \(-0.294641\pi\) | ||||
0.601322 | + | 0.799007i | \(0.294641\pi\) | |||||||
\(972\) | 1.34040 | 0.0429933 | ||||||||
\(973\) | −17.0680 | −0.547176 | ||||||||
\(974\) | −37.8017 | −1.21124 | ||||||||
\(975\) | −19.5649 | −0.626579 | ||||||||
\(976\) | 5.28219 | 0.169079 | ||||||||
\(977\) | 24.9367 | 0.797795 | 0.398898 | − | 0.916995i | \(-0.369393\pi\) | ||||
0.398898 | + | 0.916995i | \(0.369393\pi\) | |||||||
\(978\) | 32.3385 | 1.03407 | ||||||||
\(979\) | −3.11811 | −0.0996553 | ||||||||
\(980\) | −4.04996 | −0.129371 | ||||||||
\(981\) | 1.94693 | 0.0621606 | ||||||||
\(982\) | −26.4129 | −0.842871 | ||||||||
\(983\) | 16.4300 | 0.524035 | 0.262018 | − | 0.965063i | \(-0.415612\pi\) | ||||
0.262018 | + | 0.965063i | \(0.415612\pi\) | |||||||
\(984\) | −6.17401 | −0.196820 | ||||||||
\(985\) | 100.726 | 3.20939 | ||||||||
\(986\) | −1.65262 | −0.0526303 | ||||||||
\(987\) | −16.4495 | −0.523593 | ||||||||
\(988\) | −3.41039 | −0.108499 | ||||||||
\(989\) | −2.59941 | −0.0826563 | ||||||||
\(990\) | 0.641739 | 0.0203958 | ||||||||
\(991\) | 11.3800 | 0.361496 | 0.180748 | − | 0.983529i | \(-0.442148\pi\) | ||||
0.180748 | + | 0.983529i | \(0.442148\pi\) | |||||||
\(992\) | −4.99252 | −0.158513 | ||||||||
\(993\) | −59.2760 | −1.88107 | ||||||||
\(994\) | 16.0530 | 0.509171 | ||||||||
\(995\) | −44.3375 | −1.40559 | ||||||||
\(996\) | −21.8993 | −0.693906 | ||||||||
\(997\) | 21.4949 | 0.680751 | 0.340376 | − | 0.940290i | \(-0.389446\pi\) | ||||
0.340376 | + | 0.940290i | \(0.389446\pi\) | |||||||
\(998\) | −31.6075 | −1.00052 | ||||||||
\(999\) | 19.8071 | 0.626668 |
(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 | 6034.2.a.k.1.16 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.k.1.16 | ✓ | 20 | 1.1 | even | 1 | trivial |