Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(0\) |
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: | \( x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + 2776 x^{12} - 83577 x^{11} + 34362 x^{10} + 190617 x^{9} - 150697 x^{8} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Root | \(3.32710\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | 3.32710 | 1.92090 | 0.960451 | − | 0.278450i | \(-0.0898207\pi\) | ||||
0.960451 | + | 0.278450i | \(0.0898207\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.32710 | −1.35828 | ||||||||
\(7\) | −2.87743 | −1.08756 | −0.543782 | − | 0.839226i | \(-0.683008\pi\) | ||||
−0.543782 | + | 0.839226i | \(0.683008\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.06959 | 2.68986 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.79804 | 1.14515 | 0.572576 | − | 0.819852i | \(-0.305944\pi\) | ||||
0.572576 | + | 0.819852i | \(0.305944\pi\) | |||||||
\(12\) | 3.32710 | 0.960451 | ||||||||
\(13\) | −2.47743 | −0.687115 | −0.343557 | − | 0.939132i | \(-0.611632\pi\) | ||||
−0.343557 | + | 0.939132i | \(0.611632\pi\) | |||||||
\(14\) | 2.87743 | 0.769024 | ||||||||
\(15\) | 3.32710 | 0.859053 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.94379 | 0.713973 | 0.356986 | − | 0.934110i | \(-0.383804\pi\) | ||||
0.356986 | + | 0.934110i | \(0.383804\pi\) | |||||||
\(18\) | −8.06959 | −1.90202 | ||||||||
\(19\) | 0.783929 | 0.179846 | 0.0899229 | − | 0.995949i | \(-0.471338\pi\) | ||||
0.0899229 | + | 0.995949i | \(0.471338\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −9.57348 | −2.08910 | ||||||||
\(22\) | −3.79804 | −0.809745 | ||||||||
\(23\) | −0.0265160 | −0.00552897 | −0.00276449 | − | 0.999996i | \(-0.500880\pi\) | ||||
−0.00276449 | + | 0.999996i | \(0.500880\pi\) | |||||||
\(24\) | −3.32710 | −0.679141 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.47743 | 0.485863 | ||||||||
\(27\) | 16.8670 | 3.24606 | ||||||||
\(28\) | −2.87743 | −0.543782 | ||||||||
\(29\) | −8.26058 | −1.53395 | −0.766976 | − | 0.641676i | \(-0.778239\pi\) | ||||
−0.766976 | + | 0.641676i | \(0.778239\pi\) | |||||||
\(30\) | −3.32710 | −0.607442 | ||||||||
\(31\) | 0.619229 | 0.111217 | 0.0556084 | − | 0.998453i | \(-0.482290\pi\) | ||||
0.0556084 | + | 0.998453i | \(0.482290\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 12.6365 | 2.19972 | ||||||||
\(34\) | −2.94379 | −0.504855 | ||||||||
\(35\) | −2.87743 | −0.486374 | ||||||||
\(36\) | 8.06959 | 1.34493 | ||||||||
\(37\) | 1.77151 | 0.291235 | 0.145617 | − | 0.989341i | \(-0.453483\pi\) | ||||
0.145617 | + | 0.989341i | \(0.453483\pi\) | |||||||
\(38\) | −0.783929 | −0.127170 | ||||||||
\(39\) | −8.24264 | −1.31988 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 9.24986 | 1.44458 | 0.722292 | − | 0.691588i | \(-0.243088\pi\) | ||||
0.722292 | + | 0.691588i | \(0.243088\pi\) | |||||||
\(42\) | 9.57348 | 1.47722 | ||||||||
\(43\) | 1.77538 | 0.270742 | 0.135371 | − | 0.990795i | \(-0.456777\pi\) | ||||
0.135371 | + | 0.990795i | \(0.456777\pi\) | |||||||
\(44\) | 3.79804 | 0.572576 | ||||||||
\(45\) | 8.06959 | 1.20294 | ||||||||
\(46\) | 0.0265160 | 0.00390957 | ||||||||
\(47\) | 10.6532 | 1.55392 | 0.776962 | − | 0.629548i | \(-0.216760\pi\) | ||||
0.776962 | + | 0.629548i | \(0.216760\pi\) | |||||||
\(48\) | 3.32710 | 0.480225 | ||||||||
\(49\) | 1.27958 | 0.182797 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 9.79427 | 1.37147 | ||||||||
\(52\) | −2.47743 | −0.343557 | ||||||||
\(53\) | 5.35945 | 0.736177 | 0.368088 | − | 0.929791i | \(-0.380012\pi\) | ||||
0.368088 | + | 0.929791i | \(0.380012\pi\) | |||||||
\(54\) | −16.8670 | −2.29531 | ||||||||
\(55\) | 3.79804 | 0.512128 | ||||||||
\(56\) | 2.87743 | 0.384512 | ||||||||
\(57\) | 2.60821 | 0.345466 | ||||||||
\(58\) | 8.26058 | 1.08467 | ||||||||
\(59\) | 4.82597 | 0.628287 | 0.314144 | − | 0.949375i | \(-0.398283\pi\) | ||||
0.314144 | + | 0.949375i | \(0.398283\pi\) | |||||||
\(60\) | 3.32710 | 0.429527 | ||||||||
\(61\) | 0.650441 | 0.0832805 | 0.0416402 | − | 0.999133i | \(-0.486742\pi\) | ||||
0.0416402 | + | 0.999133i | \(0.486742\pi\) | |||||||
\(62\) | −0.619229 | −0.0786422 | ||||||||
\(63\) | −23.2196 | −2.92540 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.47743 | −0.307287 | ||||||||
\(66\) | −12.6365 | −1.55544 | ||||||||
\(67\) | −10.3791 | −1.26800 | −0.634002 | − | 0.773332i | \(-0.718589\pi\) | ||||
−0.634002 | + | 0.773332i | \(0.718589\pi\) | |||||||
\(68\) | 2.94379 | 0.356986 | ||||||||
\(69\) | −0.0882214 | −0.0106206 | ||||||||
\(70\) | 2.87743 | 0.343918 | ||||||||
\(71\) | 1.13986 | 0.135277 | 0.0676383 | − | 0.997710i | \(-0.478454\pi\) | ||||
0.0676383 | + | 0.997710i | \(0.478454\pi\) | |||||||
\(72\) | −8.06959 | −0.951010 | ||||||||
\(73\) | −3.11153 | −0.364177 | −0.182089 | − | 0.983282i | \(-0.558286\pi\) | ||||
−0.182089 | + | 0.983282i | \(0.558286\pi\) | |||||||
\(74\) | −1.77151 | −0.205934 | ||||||||
\(75\) | 3.32710 | 0.384180 | ||||||||
\(76\) | 0.783929 | 0.0899229 | ||||||||
\(77\) | −10.9286 | −1.24543 | ||||||||
\(78\) | 8.24264 | 0.933296 | ||||||||
\(79\) | 5.43079 | 0.611012 | 0.305506 | − | 0.952190i | \(-0.401174\pi\) | ||||
0.305506 | + | 0.952190i | \(0.401174\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 31.9095 | 3.54550 | ||||||||
\(82\) | −9.24986 | −1.02148 | ||||||||
\(83\) | −7.44281 | −0.816955 | −0.408478 | − | 0.912768i | \(-0.633940\pi\) | ||||
−0.408478 | + | 0.912768i | \(0.633940\pi\) | |||||||
\(84\) | −9.57348 | −1.04455 | ||||||||
\(85\) | 2.94379 | 0.319298 | ||||||||
\(86\) | −1.77538 | −0.191444 | ||||||||
\(87\) | −27.4838 | −2.94657 | ||||||||
\(88\) | −3.79804 | −0.404872 | ||||||||
\(89\) | 4.32672 | 0.458631 | 0.229316 | − | 0.973352i | \(-0.426351\pi\) | ||||
0.229316 | + | 0.973352i | \(0.426351\pi\) | |||||||
\(90\) | −8.06959 | −0.850609 | ||||||||
\(91\) | 7.12861 | 0.747282 | ||||||||
\(92\) | −0.0265160 | −0.00276449 | ||||||||
\(93\) | 2.06024 | 0.213637 | ||||||||
\(94\) | −10.6532 | −1.09879 | ||||||||
\(95\) | 0.783929 | 0.0804295 | ||||||||
\(96\) | −3.32710 | −0.339571 | ||||||||
\(97\) | −6.14854 | −0.624290 | −0.312145 | − | 0.950034i | \(-0.601047\pi\) | ||||
−0.312145 | + | 0.950034i | \(0.601047\pi\) | |||||||
\(98\) | −1.27958 | −0.129257 | ||||||||
\(99\) | 30.6486 | 3.08030 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.2042 | 1.31386 | 0.656931 | − | 0.753950i | \(-0.271854\pi\) | ||||
0.656931 | + | 0.753950i | \(0.271854\pi\) | |||||||
\(102\) | −9.79427 | −0.969777 | ||||||||
\(103\) | −4.04644 | −0.398708 | −0.199354 | − | 0.979928i | \(-0.563884\pi\) | ||||
−0.199354 | + | 0.979928i | \(0.563884\pi\) | |||||||
\(104\) | 2.47743 | 0.242932 | ||||||||
\(105\) | −9.57348 | −0.934276 | ||||||||
\(106\) | −5.35945 | −0.520556 | ||||||||
\(107\) | −13.4285 | −1.29818 | −0.649092 | − | 0.760710i | \(-0.724851\pi\) | ||||
−0.649092 | + | 0.760710i | \(0.724851\pi\) | |||||||
\(108\) | 16.8670 | 1.62303 | ||||||||
\(109\) | −2.02380 | −0.193845 | −0.0969223 | − | 0.995292i | \(-0.530900\pi\) | ||||
−0.0969223 | + | 0.995292i | \(0.530900\pi\) | |||||||
\(110\) | −3.79804 | −0.362129 | ||||||||
\(111\) | 5.89399 | 0.559433 | ||||||||
\(112\) | −2.87743 | −0.271891 | ||||||||
\(113\) | 12.7031 | 1.19501 | 0.597506 | − | 0.801865i | \(-0.296159\pi\) | ||||
0.597506 | + | 0.801865i | \(0.296159\pi\) | |||||||
\(114\) | −2.60821 | −0.244281 | ||||||||
\(115\) | −0.0265160 | −0.00247263 | ||||||||
\(116\) | −8.26058 | −0.766976 | ||||||||
\(117\) | −19.9918 | −1.84824 | ||||||||
\(118\) | −4.82597 | −0.444266 | ||||||||
\(119\) | −8.47053 | −0.776492 | ||||||||
\(120\) | −3.32710 | −0.303721 | ||||||||
\(121\) | 3.42510 | 0.311373 | ||||||||
\(122\) | −0.650441 | −0.0588882 | ||||||||
\(123\) | 30.7752 | 2.77491 | ||||||||
\(124\) | 0.619229 | 0.0556084 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 23.2196 | 2.06857 | ||||||||
\(127\) | 5.11512 | 0.453894 | 0.226947 | − | 0.973907i | \(-0.427126\pi\) | ||||
0.226947 | + | 0.973907i | \(0.427126\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.90686 | 0.520070 | ||||||||
\(130\) | 2.47743 | 0.217285 | ||||||||
\(131\) | 2.82921 | 0.247190 | 0.123595 | − | 0.992333i | \(-0.460558\pi\) | ||||
0.123595 | + | 0.992333i | \(0.460558\pi\) | |||||||
\(132\) | 12.6365 | 1.09986 | ||||||||
\(133\) | −2.25570 | −0.195594 | ||||||||
\(134\) | 10.3791 | 0.896614 | ||||||||
\(135\) | 16.8670 | 1.45168 | ||||||||
\(136\) | −2.94379 | −0.252428 | ||||||||
\(137\) | 8.47126 | 0.723749 | 0.361874 | − | 0.932227i | \(-0.382137\pi\) | ||||
0.361874 | + | 0.932227i | \(0.382137\pi\) | |||||||
\(138\) | 0.0882214 | 0.00750990 | ||||||||
\(139\) | −7.21459 | −0.611934 | −0.305967 | − | 0.952042i | \(-0.598980\pi\) | ||||
−0.305967 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(140\) | −2.87743 | −0.243187 | ||||||||
\(141\) | 35.4441 | 2.98493 | ||||||||
\(142\) | −1.13986 | −0.0956550 | ||||||||
\(143\) | −9.40936 | −0.786851 | ||||||||
\(144\) | 8.06959 | 0.672466 | ||||||||
\(145\) | −8.26058 | −0.686004 | ||||||||
\(146\) | 3.11153 | 0.257512 | ||||||||
\(147\) | 4.25728 | 0.351135 | ||||||||
\(148\) | 1.77151 | 0.145617 | ||||||||
\(149\) | 4.04445 | 0.331334 | 0.165667 | − | 0.986182i | \(-0.447022\pi\) | ||||
0.165667 | + | 0.986182i | \(0.447022\pi\) | |||||||
\(150\) | −3.32710 | −0.271656 | ||||||||
\(151\) | −4.20941 | −0.342557 | −0.171278 | − | 0.985223i | \(-0.554790\pi\) | ||||
−0.171278 | + | 0.985223i | \(0.554790\pi\) | |||||||
\(152\) | −0.783929 | −0.0635851 | ||||||||
\(153\) | 23.7551 | 1.92049 | ||||||||
\(154\) | 10.9286 | 0.880650 | ||||||||
\(155\) | 0.619229 | 0.0497377 | ||||||||
\(156\) | −8.24264 | −0.659940 | ||||||||
\(157\) | −22.1248 | −1.76575 | −0.882876 | − | 0.469606i | \(-0.844396\pi\) | ||||
−0.882876 | + | 0.469606i | \(0.844396\pi\) | |||||||
\(158\) | −5.43079 | −0.432051 | ||||||||
\(159\) | 17.8314 | 1.41412 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.0762979 | 0.00601311 | ||||||||
\(162\) | −31.9095 | −2.50705 | ||||||||
\(163\) | 13.6761 | 1.07120 | 0.535599 | − | 0.844472i | \(-0.320086\pi\) | ||||
0.535599 | + | 0.844472i | \(0.320086\pi\) | |||||||
\(164\) | 9.24986 | 0.722292 | ||||||||
\(165\) | 12.6365 | 0.983747 | ||||||||
\(166\) | 7.44281 | 0.577674 | ||||||||
\(167\) | −22.8840 | −1.77082 | −0.885409 | − | 0.464812i | \(-0.846122\pi\) | ||||
−0.885409 | + | 0.464812i | \(0.846122\pi\) | |||||||
\(168\) | 9.57348 | 0.738610 | ||||||||
\(169\) | −6.86236 | −0.527874 | ||||||||
\(170\) | −2.94379 | −0.225778 | ||||||||
\(171\) | 6.32599 | 0.483760 | ||||||||
\(172\) | 1.77538 | 0.135371 | ||||||||
\(173\) | −14.6738 | −1.11563 | −0.557815 | − | 0.829965i | \(-0.688360\pi\) | ||||
−0.557815 | + | 0.829965i | \(0.688360\pi\) | |||||||
\(174\) | 27.4838 | 2.08354 | ||||||||
\(175\) | −2.87743 | −0.217513 | ||||||||
\(176\) | 3.79804 | 0.286288 | ||||||||
\(177\) | 16.0565 | 1.20688 | ||||||||
\(178\) | −4.32672 | −0.324301 | ||||||||
\(179\) | 9.59560 | 0.717209 | 0.358604 | − | 0.933490i | \(-0.383253\pi\) | ||||
0.358604 | + | 0.933490i | \(0.383253\pi\) | |||||||
\(180\) | 8.06959 | 0.601472 | ||||||||
\(181\) | 10.2207 | 0.759700 | 0.379850 | − | 0.925048i | \(-0.375976\pi\) | ||||
0.379850 | + | 0.925048i | \(0.375976\pi\) | |||||||
\(182\) | −7.12861 | −0.528408 | ||||||||
\(183\) | 2.16408 | 0.159974 | ||||||||
\(184\) | 0.0265160 | 0.00195479 | ||||||||
\(185\) | 1.77151 | 0.130244 | ||||||||
\(186\) | −2.06024 | −0.151064 | ||||||||
\(187\) | 11.1806 | 0.817608 | ||||||||
\(188\) | 10.6532 | 0.776962 | ||||||||
\(189\) | −48.5336 | −3.53030 | ||||||||
\(190\) | −0.783929 | −0.0568722 | ||||||||
\(191\) | −2.14502 | −0.155208 | −0.0776040 | − | 0.996984i | \(-0.524727\pi\) | ||||
−0.0776040 | + | 0.996984i | \(0.524727\pi\) | |||||||
\(192\) | 3.32710 | 0.240113 | ||||||||
\(193\) | 14.3461 | 1.03265 | 0.516326 | − | 0.856392i | \(-0.327299\pi\) | ||||
0.516326 | + | 0.856392i | \(0.327299\pi\) | |||||||
\(194\) | 6.14854 | 0.441440 | ||||||||
\(195\) | −8.24264 | −0.590268 | ||||||||
\(196\) | 1.27958 | 0.0913985 | ||||||||
\(197\) | 12.6963 | 0.904575 | 0.452287 | − | 0.891872i | \(-0.350608\pi\) | ||||
0.452287 | + | 0.891872i | \(0.350608\pi\) | |||||||
\(198\) | −30.6486 | −2.17810 | ||||||||
\(199\) | −12.5782 | −0.891645 | −0.445823 | − | 0.895121i | \(-0.647089\pi\) | ||||
−0.445823 | + | 0.895121i | \(0.647089\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −34.5321 | −2.43571 | ||||||||
\(202\) | −13.2042 | −0.929041 | ||||||||
\(203\) | 23.7692 | 1.66827 | ||||||||
\(204\) | 9.79427 | 0.685736 | ||||||||
\(205\) | 9.24986 | 0.646038 | ||||||||
\(206\) | 4.04644 | 0.281929 | ||||||||
\(207\) | −0.213973 | −0.0148722 | ||||||||
\(208\) | −2.47743 | −0.171779 | ||||||||
\(209\) | 2.97739 | 0.205951 | ||||||||
\(210\) | 9.57348 | 0.660633 | ||||||||
\(211\) | −6.56554 | −0.451991 | −0.225995 | − | 0.974128i | \(-0.572563\pi\) | ||||
−0.225995 | + | 0.974128i | \(0.572563\pi\) | |||||||
\(212\) | 5.35945 | 0.368088 | ||||||||
\(213\) | 3.79243 | 0.259853 | ||||||||
\(214\) | 13.4285 | 0.917954 | ||||||||
\(215\) | 1.77538 | 0.121080 | ||||||||
\(216\) | −16.8670 | −1.14766 | ||||||||
\(217\) | −1.78179 | −0.120956 | ||||||||
\(218\) | 2.02380 | 0.137069 | ||||||||
\(219\) | −10.3524 | −0.699548 | ||||||||
\(220\) | 3.79804 | 0.256064 | ||||||||
\(221\) | −7.29301 | −0.490581 | ||||||||
\(222\) | −5.89399 | −0.395579 | ||||||||
\(223\) | 22.0602 | 1.47726 | 0.738631 | − | 0.674110i | \(-0.235473\pi\) | ||||
0.738631 | + | 0.674110i | \(0.235473\pi\) | |||||||
\(224\) | 2.87743 | 0.192256 | ||||||||
\(225\) | 8.06959 | 0.537972 | ||||||||
\(226\) | −12.7031 | −0.845000 | ||||||||
\(227\) | 12.4121 | 0.823822 | 0.411911 | − | 0.911224i | \(-0.364861\pi\) | ||||
0.411911 | + | 0.911224i | \(0.364861\pi\) | |||||||
\(228\) | 2.60821 | 0.172733 | ||||||||
\(229\) | 8.44156 | 0.557834 | 0.278917 | − | 0.960315i | \(-0.410025\pi\) | ||||
0.278917 | + | 0.960315i | \(0.410025\pi\) | |||||||
\(230\) | 0.0265160 | 0.00174841 | ||||||||
\(231\) | −36.3605 | −2.39234 | ||||||||
\(232\) | 8.26058 | 0.542334 | ||||||||
\(233\) | −21.0833 | −1.38122 | −0.690608 | − | 0.723230i | \(-0.742657\pi\) | ||||
−0.690608 | + | 0.723230i | \(0.742657\pi\) | |||||||
\(234\) | 19.9918 | 1.30691 | ||||||||
\(235\) | 10.6532 | 0.694936 | ||||||||
\(236\) | 4.82597 | 0.314144 | ||||||||
\(237\) | 18.0688 | 1.17369 | ||||||||
\(238\) | 8.47053 | 0.549063 | ||||||||
\(239\) | 23.5046 | 1.52039 | 0.760194 | − | 0.649696i | \(-0.225104\pi\) | ||||
0.760194 | + | 0.649696i | \(0.225104\pi\) | |||||||
\(240\) | 3.32710 | 0.214763 | ||||||||
\(241\) | 27.0218 | 1.74063 | 0.870314 | − | 0.492497i | \(-0.163916\pi\) | ||||
0.870314 | + | 0.492497i | \(0.163916\pi\) | |||||||
\(242\) | −3.42510 | −0.220174 | ||||||||
\(243\) | 55.5649 | 3.56449 | ||||||||
\(244\) | 0.650441 | 0.0416402 | ||||||||
\(245\) | 1.27958 | 0.0817493 | ||||||||
\(246\) | −30.7752 | −1.96215 | ||||||||
\(247\) | −1.94213 | −0.123575 | ||||||||
\(248\) | −0.619229 | −0.0393211 | ||||||||
\(249\) | −24.7630 | −1.56929 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 11.5473 | 0.728858 | 0.364429 | − | 0.931231i | \(-0.381264\pi\) | ||||
0.364429 | + | 0.931231i | \(0.381264\pi\) | |||||||
\(252\) | −23.2196 | −1.46270 | ||||||||
\(253\) | −0.100709 | −0.00633151 | ||||||||
\(254\) | −5.11512 | −0.320951 | ||||||||
\(255\) | 9.79427 | 0.613341 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.9453 | −0.745128 | −0.372564 | − | 0.928006i | \(-0.621521\pi\) | ||||
−0.372564 | + | 0.928006i | \(0.621521\pi\) | |||||||
\(258\) | −5.90686 | −0.367745 | ||||||||
\(259\) | −5.09739 | −0.316736 | ||||||||
\(260\) | −2.47743 | −0.153643 | ||||||||
\(261\) | −66.6595 | −4.12612 | ||||||||
\(262\) | −2.82921 | −0.174789 | ||||||||
\(263\) | −21.0381 | −1.29727 | −0.648633 | − | 0.761102i | \(-0.724659\pi\) | ||||
−0.648633 | + | 0.761102i | \(0.724659\pi\) | |||||||
\(264\) | −12.6365 | −0.777720 | ||||||||
\(265\) | 5.35945 | 0.329228 | ||||||||
\(266\) | 2.25570 | 0.138306 | ||||||||
\(267\) | 14.3954 | 0.880985 | ||||||||
\(268\) | −10.3791 | −0.634002 | ||||||||
\(269\) | −8.55608 | −0.521673 | −0.260837 | − | 0.965383i | \(-0.583998\pi\) | ||||
−0.260837 | + | 0.965383i | \(0.583998\pi\) | |||||||
\(270\) | −16.8670 | −1.02649 | ||||||||
\(271\) | −23.1493 | −1.40622 | −0.703110 | − | 0.711081i | \(-0.748206\pi\) | ||||
−0.703110 | + | 0.711081i | \(0.748206\pi\) | |||||||
\(272\) | 2.94379 | 0.178493 | ||||||||
\(273\) | 23.7176 | 1.43545 | ||||||||
\(274\) | −8.47126 | −0.511768 | ||||||||
\(275\) | 3.79804 | 0.229030 | ||||||||
\(276\) | −0.0882214 | −0.00531030 | ||||||||
\(277\) | −23.3367 | −1.40217 | −0.701083 | − | 0.713079i | \(-0.747300\pi\) | ||||
−0.701083 | + | 0.713079i | \(0.747300\pi\) | |||||||
\(278\) | 7.21459 | 0.432703 | ||||||||
\(279\) | 4.99692 | 0.299158 | ||||||||
\(280\) | 2.87743 | 0.171959 | ||||||||
\(281\) | −20.0167 | −1.19410 | −0.597048 | − | 0.802206i | \(-0.703660\pi\) | ||||
−0.597048 | + | 0.802206i | \(0.703660\pi\) | |||||||
\(282\) | −35.4441 | −2.11067 | ||||||||
\(283\) | 18.7895 | 1.11692 | 0.558460 | − | 0.829531i | \(-0.311392\pi\) | ||||
0.558460 | + | 0.829531i | \(0.311392\pi\) | |||||||
\(284\) | 1.13986 | 0.0676383 | ||||||||
\(285\) | 2.60821 | 0.154497 | ||||||||
\(286\) | 9.40936 | 0.556387 | ||||||||
\(287\) | −26.6158 | −1.57108 | ||||||||
\(288\) | −8.06959 | −0.475505 | ||||||||
\(289\) | −8.33412 | −0.490243 | ||||||||
\(290\) | 8.26058 | 0.485078 | ||||||||
\(291\) | −20.4568 | −1.19920 | ||||||||
\(292\) | −3.11153 | −0.182089 | ||||||||
\(293\) | −15.9251 | −0.930353 | −0.465176 | − | 0.885218i | \(-0.654009\pi\) | ||||
−0.465176 | + | 0.885218i | \(0.654009\pi\) | |||||||
\(294\) | −4.25728 | −0.248290 | ||||||||
\(295\) | 4.82597 | 0.280979 | ||||||||
\(296\) | −1.77151 | −0.102967 | ||||||||
\(297\) | 64.0616 | 3.71723 | ||||||||
\(298\) | −4.04445 | −0.234289 | ||||||||
\(299\) | 0.0656915 | 0.00379904 | ||||||||
\(300\) | 3.32710 | 0.192090 | ||||||||
\(301\) | −5.10852 | −0.294450 | ||||||||
\(302\) | 4.20941 | 0.242224 | ||||||||
\(303\) | 43.9315 | 2.52380 | ||||||||
\(304\) | 0.783929 | 0.0449614 | ||||||||
\(305\) | 0.650441 | 0.0372442 | ||||||||
\(306\) | −23.7551 | −1.35799 | ||||||||
\(307\) | −13.0738 | −0.746159 | −0.373080 | − | 0.927799i | \(-0.621698\pi\) | ||||
−0.373080 | + | 0.927799i | \(0.621698\pi\) | |||||||
\(308\) | −10.9286 | −0.622713 | ||||||||
\(309\) | −13.4629 | −0.765879 | ||||||||
\(310\) | −0.619229 | −0.0351699 | ||||||||
\(311\) | 4.57265 | 0.259291 | 0.129646 | − | 0.991560i | \(-0.458616\pi\) | ||||
0.129646 | + | 0.991560i | \(0.458616\pi\) | |||||||
\(312\) | 8.24264 | 0.466648 | ||||||||
\(313\) | −22.5845 | −1.27655 | −0.638275 | − | 0.769808i | \(-0.720352\pi\) | ||||
−0.638275 | + | 0.769808i | \(0.720352\pi\) | |||||||
\(314\) | 22.1248 | 1.24858 | ||||||||
\(315\) | −23.2196 | −1.30828 | ||||||||
\(316\) | 5.43079 | 0.305506 | ||||||||
\(317\) | −15.0700 | −0.846418 | −0.423209 | − | 0.906032i | \(-0.639096\pi\) | ||||
−0.423209 | + | 0.906032i | \(0.639096\pi\) | |||||||
\(318\) | −17.8314 | −0.999936 | ||||||||
\(319\) | −31.3740 | −1.75661 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −44.6780 | −2.49368 | ||||||||
\(322\) | −0.0762979 | −0.00425191 | ||||||||
\(323\) | 2.30772 | 0.128405 | ||||||||
\(324\) | 31.9095 | 1.77275 | ||||||||
\(325\) | −2.47743 | −0.137423 | ||||||||
\(326\) | −13.6761 | −0.757452 | ||||||||
\(327\) | −6.73337 | −0.372356 | ||||||||
\(328\) | −9.24986 | −0.510738 | ||||||||
\(329\) | −30.6537 | −1.68999 | ||||||||
\(330\) | −12.6365 | −0.695614 | ||||||||
\(331\) | −0.290068 | −0.0159436 | −0.00797178 | − | 0.999968i | \(-0.502538\pi\) | ||||
−0.00797178 | + | 0.999968i | \(0.502538\pi\) | |||||||
\(332\) | −7.44281 | −0.408478 | ||||||||
\(333\) | 14.2954 | 0.783381 | ||||||||
\(334\) | 22.8840 | 1.25216 | ||||||||
\(335\) | −10.3791 | −0.567068 | ||||||||
\(336\) | −9.57348 | −0.522276 | ||||||||
\(337\) | −14.2582 | −0.776696 | −0.388348 | − | 0.921513i | \(-0.626954\pi\) | ||||
−0.388348 | + | 0.921513i | \(0.626954\pi\) | |||||||
\(338\) | 6.86236 | 0.373263 | ||||||||
\(339\) | 42.2646 | 2.29550 | ||||||||
\(340\) | 2.94379 | 0.159649 | ||||||||
\(341\) | 2.35186 | 0.127360 | ||||||||
\(342\) | −6.32599 | −0.342070 | ||||||||
\(343\) | 16.4601 | 0.888761 | ||||||||
\(344\) | −1.77538 | −0.0957219 | ||||||||
\(345\) | −0.0882214 | −0.00474968 | ||||||||
\(346\) | 14.6738 | 0.788870 | ||||||||
\(347\) | −19.9345 | −1.07014 | −0.535069 | − | 0.844808i | \(-0.679714\pi\) | ||||
−0.535069 | + | 0.844808i | \(0.679714\pi\) | |||||||
\(348\) | −27.4838 | −1.47329 | ||||||||
\(349\) | −5.22658 | −0.279773 | −0.139886 | − | 0.990168i | \(-0.544674\pi\) | ||||
−0.139886 | + | 0.990168i | \(0.544674\pi\) | |||||||
\(350\) | 2.87743 | 0.153805 | ||||||||
\(351\) | −41.7868 | −2.23041 | ||||||||
\(352\) | −3.79804 | −0.202436 | ||||||||
\(353\) | −20.6145 | −1.09720 | −0.548599 | − | 0.836085i | \(-0.684839\pi\) | ||||
−0.548599 | + | 0.836085i | \(0.684839\pi\) | |||||||
\(354\) | −16.0565 | −0.853392 | ||||||||
\(355\) | 1.13986 | 0.0604975 | ||||||||
\(356\) | 4.32672 | 0.229316 | ||||||||
\(357\) | −28.1823 | −1.49156 | ||||||||
\(358\) | −9.59560 | −0.507143 | ||||||||
\(359\) | −17.7824 | −0.938517 | −0.469259 | − | 0.883061i | \(-0.655479\pi\) | ||||
−0.469259 | + | 0.883061i | \(0.655479\pi\) | |||||||
\(360\) | −8.06959 | −0.425305 | ||||||||
\(361\) | −18.3855 | −0.967656 | ||||||||
\(362\) | −10.2207 | −0.537189 | ||||||||
\(363\) | 11.3957 | 0.598117 | ||||||||
\(364\) | 7.12861 | 0.373641 | ||||||||
\(365\) | −3.11153 | −0.162865 | ||||||||
\(366\) | −2.16408 | −0.113118 | ||||||||
\(367\) | −3.36265 | −0.175529 | −0.0877643 | − | 0.996141i | \(-0.527972\pi\) | ||||
−0.0877643 | + | 0.996141i | \(0.527972\pi\) | |||||||
\(368\) | −0.0265160 | −0.00138224 | ||||||||
\(369\) | 74.6425 | 3.88573 | ||||||||
\(370\) | −1.77151 | −0.0920965 | ||||||||
\(371\) | −15.4214 | −0.800640 | ||||||||
\(372\) | 2.06024 | 0.106818 | ||||||||
\(373\) | 6.13110 | 0.317457 | 0.158728 | − | 0.987322i | \(-0.449261\pi\) | ||||
0.158728 | + | 0.987322i | \(0.449261\pi\) | |||||||
\(374\) | −11.1806 | −0.578136 | ||||||||
\(375\) | 3.32710 | 0.171811 | ||||||||
\(376\) | −10.6532 | −0.549395 | ||||||||
\(377\) | 20.4650 | 1.05400 | ||||||||
\(378\) | 48.5336 | 2.49630 | ||||||||
\(379\) | 29.4156 | 1.51098 | 0.755488 | − | 0.655163i | \(-0.227400\pi\) | ||||
0.755488 | + | 0.655163i | \(0.227400\pi\) | |||||||
\(380\) | 0.783929 | 0.0402147 | ||||||||
\(381\) | 17.0185 | 0.871885 | ||||||||
\(382\) | 2.14502 | 0.109749 | ||||||||
\(383\) | −15.2014 | −0.776756 | −0.388378 | − | 0.921500i | \(-0.626964\pi\) | ||||
−0.388378 | + | 0.921500i | \(0.626964\pi\) | |||||||
\(384\) | −3.32710 | −0.169785 | ||||||||
\(385\) | −10.9286 | −0.556972 | ||||||||
\(386\) | −14.3461 | −0.730195 | ||||||||
\(387\) | 14.3266 | 0.728260 | ||||||||
\(388\) | −6.14854 | −0.312145 | ||||||||
\(389\) | 13.5439 | 0.686704 | 0.343352 | − | 0.939207i | \(-0.388438\pi\) | ||||
0.343352 | + | 0.939207i | \(0.388438\pi\) | |||||||
\(390\) | 8.24264 | 0.417382 | ||||||||
\(391\) | −0.0780575 | −0.00394754 | ||||||||
\(392\) | −1.27958 | −0.0646285 | ||||||||
\(393\) | 9.41307 | 0.474827 | ||||||||
\(394\) | −12.6963 | −0.639631 | ||||||||
\(395\) | 5.43079 | 0.273253 | ||||||||
\(396\) | 30.6486 | 1.54015 | ||||||||
\(397\) | −20.7482 | −1.04132 | −0.520661 | − | 0.853763i | \(-0.674314\pi\) | ||||
−0.520661 | + | 0.853763i | \(0.674314\pi\) | |||||||
\(398\) | 12.5782 | 0.630488 | ||||||||
\(399\) | −7.50493 | −0.375717 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 34.5321 | 1.72231 | ||||||||
\(403\) | −1.53410 | −0.0764187 | ||||||||
\(404\) | 13.2042 | 0.656931 | ||||||||
\(405\) | 31.9095 | 1.58559 | ||||||||
\(406\) | −23.7692 | −1.17965 | ||||||||
\(407\) | 6.72827 | 0.333508 | ||||||||
\(408\) | −9.79427 | −0.484888 | ||||||||
\(409\) | 32.3855 | 1.60136 | 0.800679 | − | 0.599093i | \(-0.204472\pi\) | ||||
0.800679 | + | 0.599093i | \(0.204472\pi\) | |||||||
\(410\) | −9.24986 | −0.456818 | ||||||||
\(411\) | 28.1847 | 1.39025 | ||||||||
\(412\) | −4.04644 | −0.199354 | ||||||||
\(413\) | −13.8864 | −0.683303 | ||||||||
\(414\) | 0.213973 | 0.0105162 | ||||||||
\(415\) | −7.44281 | −0.365353 | ||||||||
\(416\) | 2.47743 | 0.121466 | ||||||||
\(417\) | −24.0037 | −1.17546 | ||||||||
\(418\) | −2.97739 | −0.145629 | ||||||||
\(419\) | −18.4374 | −0.900725 | −0.450362 | − | 0.892846i | \(-0.648705\pi\) | ||||
−0.450362 | + | 0.892846i | \(0.648705\pi\) | |||||||
\(420\) | −9.57348 | −0.467138 | ||||||||
\(421\) | 15.3683 | 0.749007 | 0.374503 | − | 0.927226i | \(-0.377813\pi\) | ||||
0.374503 | + | 0.927226i | \(0.377813\pi\) | |||||||
\(422\) | 6.56554 | 0.319606 | ||||||||
\(423\) | 85.9666 | 4.17984 | ||||||||
\(424\) | −5.35945 | −0.260278 | ||||||||
\(425\) | 2.94379 | 0.142795 | ||||||||
\(426\) | −3.79243 | −0.183744 | ||||||||
\(427\) | −1.87160 | −0.0905729 | ||||||||
\(428\) | −13.4285 | −0.649092 | ||||||||
\(429\) | −31.3059 | −1.51146 | ||||||||
\(430\) | −1.77538 | −0.0856163 | ||||||||
\(431\) | 37.0475 | 1.78452 | 0.892258 | − | 0.451525i | \(-0.149120\pi\) | ||||
0.892258 | + | 0.451525i | \(0.149120\pi\) | |||||||
\(432\) | 16.8670 | 0.811515 | ||||||||
\(433\) | 30.8682 | 1.48343 | 0.741716 | − | 0.670714i | \(-0.234012\pi\) | ||||
0.741716 | + | 0.670714i | \(0.234012\pi\) | |||||||
\(434\) | 1.78179 | 0.0855285 | ||||||||
\(435\) | −27.4838 | −1.31775 | ||||||||
\(436\) | −2.02380 | −0.0969223 | ||||||||
\(437\) | −0.0207867 | −0.000994362 0 | ||||||||
\(438\) | 10.3524 | 0.494655 | ||||||||
\(439\) | −38.2997 | −1.82795 | −0.913973 | − | 0.405774i | \(-0.867002\pi\) | ||||
−0.913973 | + | 0.405774i | \(0.867002\pi\) | |||||||
\(440\) | −3.79804 | −0.181064 | ||||||||
\(441\) | 10.3257 | 0.491699 | ||||||||
\(442\) | 7.29301 | 0.346893 | ||||||||
\(443\) | −9.53641 | −0.453089 | −0.226544 | − | 0.974001i | \(-0.572743\pi\) | ||||
−0.226544 | + | 0.974001i | \(0.572743\pi\) | |||||||
\(444\) | 5.89399 | 0.279716 | ||||||||
\(445\) | 4.32672 | 0.205106 | ||||||||
\(446\) | −22.0602 | −1.04458 | ||||||||
\(447\) | 13.4563 | 0.636460 | ||||||||
\(448\) | −2.87743 | −0.135946 | ||||||||
\(449\) | −36.7230 | −1.73306 | −0.866532 | − | 0.499121i | \(-0.833656\pi\) | ||||
−0.866532 | + | 0.499121i | \(0.833656\pi\) | |||||||
\(450\) | −8.06959 | −0.380404 | ||||||||
\(451\) | 35.1313 | 1.65427 | ||||||||
\(452\) | 12.7031 | 0.597506 | ||||||||
\(453\) | −14.0051 | −0.658018 | ||||||||
\(454\) | −12.4121 | −0.582530 | ||||||||
\(455\) | 7.12861 | 0.334194 | ||||||||
\(456\) | −2.60821 | −0.122141 | ||||||||
\(457\) | 34.4625 | 1.61209 | 0.806044 | − | 0.591856i | \(-0.201604\pi\) | ||||
0.806044 | + | 0.591856i | \(0.201604\pi\) | |||||||
\(458\) | −8.44156 | −0.394448 | ||||||||
\(459\) | 49.6529 | 2.31760 | ||||||||
\(460\) | −0.0265160 | −0.00123632 | ||||||||
\(461\) | 32.8634 | 1.53060 | 0.765300 | − | 0.643674i | \(-0.222591\pi\) | ||||
0.765300 | + | 0.643674i | \(0.222591\pi\) | |||||||
\(462\) | 36.3605 | 1.69164 | ||||||||
\(463\) | −3.98341 | −0.185125 | −0.0925624 | − | 0.995707i | \(-0.529506\pi\) | ||||
−0.0925624 | + | 0.995707i | \(0.529506\pi\) | |||||||
\(464\) | −8.26058 | −0.383488 | ||||||||
\(465\) | 2.06024 | 0.0955412 | ||||||||
\(466\) | 21.0833 | 0.976667 | ||||||||
\(467\) | 1.64490 | 0.0761171 | 0.0380586 | − | 0.999276i | \(-0.487883\pi\) | ||||
0.0380586 | + | 0.999276i | \(0.487883\pi\) | |||||||
\(468\) | −19.9918 | −0.924122 | ||||||||
\(469\) | 29.8650 | 1.37904 | ||||||||
\(470\) | −10.6532 | −0.491394 | ||||||||
\(471\) | −73.6114 | −3.39184 | ||||||||
\(472\) | −4.82597 | −0.222133 | ||||||||
\(473\) | 6.74295 | 0.310041 | ||||||||
\(474\) | −18.0688 | −0.829927 | ||||||||
\(475\) | 0.783929 | 0.0359691 | ||||||||
\(476\) | −8.47053 | −0.388246 | ||||||||
\(477\) | 43.2485 | 1.98021 | ||||||||
\(478\) | −23.5046 | −1.07508 | ||||||||
\(479\) | 0.132786 | 0.00606715 | 0.00303357 | − | 0.999995i | \(-0.499034\pi\) | ||||
0.00303357 | + | 0.999995i | \(0.499034\pi\) | |||||||
\(480\) | −3.32710 | −0.151861 | ||||||||
\(481\) | −4.38879 | −0.200112 | ||||||||
\(482\) | −27.0218 | −1.23081 | ||||||||
\(483\) | 0.253851 | 0.0115506 | ||||||||
\(484\) | 3.42510 | 0.155687 | ||||||||
\(485\) | −6.14854 | −0.279191 | ||||||||
\(486\) | −55.5649 | −2.52048 | ||||||||
\(487\) | −14.6785 | −0.665148 | −0.332574 | − | 0.943077i | \(-0.607917\pi\) | ||||
−0.332574 | + | 0.943077i | \(0.607917\pi\) | |||||||
\(488\) | −0.650441 | −0.0294441 | ||||||||
\(489\) | 45.5019 | 2.05767 | ||||||||
\(490\) | −1.27958 | −0.0578055 | ||||||||
\(491\) | 6.99801 | 0.315816 | 0.157908 | − | 0.987454i | \(-0.449525\pi\) | ||||
0.157908 | + | 0.987454i | \(0.449525\pi\) | |||||||
\(492\) | 30.7752 | 1.38745 | ||||||||
\(493\) | −24.3174 | −1.09520 | ||||||||
\(494\) | 1.94213 | 0.0873805 | ||||||||
\(495\) | 30.6486 | 1.37755 | ||||||||
\(496\) | 0.619229 | 0.0278042 | ||||||||
\(497\) | −3.27986 | −0.147122 | ||||||||
\(498\) | 24.7630 | 1.10966 | ||||||||
\(499\) | −0.837087 | −0.0374732 | −0.0187366 | − | 0.999824i | \(-0.505964\pi\) | ||||
−0.0187366 | + | 0.999824i | \(0.505964\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −76.1374 | −3.40157 | ||||||||
\(502\) | −11.5473 | −0.515380 | ||||||||
\(503\) | 22.7655 | 1.01507 | 0.507533 | − | 0.861633i | \(-0.330558\pi\) | ||||
0.507533 | + | 0.861633i | \(0.330558\pi\) | |||||||
\(504\) | 23.2196 | 1.03428 | ||||||||
\(505\) | 13.2042 | 0.587577 | ||||||||
\(506\) | 0.100709 | 0.00447706 | ||||||||
\(507\) | −22.8317 | −1.01399 | ||||||||
\(508\) | 5.11512 | 0.226947 | ||||||||
\(509\) | 5.32735 | 0.236131 | 0.118065 | − | 0.993006i | \(-0.462331\pi\) | ||||
0.118065 | + | 0.993006i | \(0.462331\pi\) | |||||||
\(510\) | −9.79427 | −0.433697 | ||||||||
\(511\) | 8.95320 | 0.396066 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 13.2226 | 0.583790 | ||||||||
\(514\) | 11.9453 | 0.526885 | ||||||||
\(515\) | −4.04644 | −0.178308 | ||||||||
\(516\) | 5.90686 | 0.260035 | ||||||||
\(517\) | 40.4611 | 1.77948 | ||||||||
\(518\) | 5.09739 | 0.223966 | ||||||||
\(519\) | −48.8213 | −2.14302 | ||||||||
\(520\) | 2.47743 | 0.108642 | ||||||||
\(521\) | −0.814586 | −0.0356877 | −0.0178438 | − | 0.999841i | \(-0.505680\pi\) | ||||
−0.0178438 | + | 0.999841i | \(0.505680\pi\) | |||||||
\(522\) | 66.6595 | 2.91761 | ||||||||
\(523\) | 34.2010 | 1.49551 | 0.747753 | − | 0.663977i | \(-0.231133\pi\) | ||||
0.747753 | + | 0.663977i | \(0.231133\pi\) | |||||||
\(524\) | 2.82921 | 0.123595 | ||||||||
\(525\) | −9.57348 | −0.417821 | ||||||||
\(526\) | 21.0381 | 0.917305 | ||||||||
\(527\) | 1.82288 | 0.0794058 | ||||||||
\(528\) | 12.6365 | 0.549931 | ||||||||
\(529\) | −22.9993 | −0.999969 | ||||||||
\(530\) | −5.35945 | −0.232800 | ||||||||
\(531\) | 38.9436 | 1.69001 | ||||||||
\(532\) | −2.25570 | −0.0977969 | ||||||||
\(533\) | −22.9158 | −0.992595 | ||||||||
\(534\) | −14.3954 | −0.622951 | ||||||||
\(535\) | −13.4285 | −0.580565 | ||||||||
\(536\) | 10.3791 | 0.448307 | ||||||||
\(537\) | 31.9255 | 1.37769 | ||||||||
\(538\) | 8.55608 | 0.368879 | ||||||||
\(539\) | 4.85989 | 0.209330 | ||||||||
\(540\) | 16.8670 | 0.725841 | ||||||||
\(541\) | 40.9278 | 1.75962 | 0.879812 | − | 0.475321i | \(-0.157668\pi\) | ||||
0.879812 | + | 0.475321i | \(0.157668\pi\) | |||||||
\(542\) | 23.1493 | 0.994348 | ||||||||
\(543\) | 34.0053 | 1.45931 | ||||||||
\(544\) | −2.94379 | −0.126214 | ||||||||
\(545\) | −2.02380 | −0.0866899 | ||||||||
\(546\) | −23.7176 | −1.01502 | ||||||||
\(547\) | 25.3583 | 1.08424 | 0.542121 | − | 0.840301i | \(-0.317622\pi\) | ||||
0.542121 | + | 0.840301i | \(0.317622\pi\) | |||||||
\(548\) | 8.47126 | 0.361874 | ||||||||
\(549\) | 5.24879 | 0.224013 | ||||||||
\(550\) | −3.79804 | −0.161949 | ||||||||
\(551\) | −6.47571 | −0.275875 | ||||||||
\(552\) | 0.0882214 | 0.00375495 | ||||||||
\(553\) | −15.6267 | −0.664515 | ||||||||
\(554\) | 23.3367 | 0.991481 | ||||||||
\(555\) | 5.89399 | 0.250186 | ||||||||
\(556\) | −7.21459 | −0.305967 | ||||||||
\(557\) | −34.5302 | −1.46309 | −0.731546 | − | 0.681792i | \(-0.761201\pi\) | ||||
−0.731546 | + | 0.681792i | \(0.761201\pi\) | |||||||
\(558\) | −4.99692 | −0.211537 | ||||||||
\(559\) | −4.39837 | −0.186031 | ||||||||
\(560\) | −2.87743 | −0.121593 | ||||||||
\(561\) | 37.1990 | 1.57054 | ||||||||
\(562\) | 20.0167 | 0.844353 | ||||||||
\(563\) | −8.33455 | −0.351259 | −0.175630 | − | 0.984456i | \(-0.556196\pi\) | ||||
−0.175630 | + | 0.984456i | \(0.556196\pi\) | |||||||
\(564\) | 35.4441 | 1.49247 | ||||||||
\(565\) | 12.7031 | 0.534425 | ||||||||
\(566\) | −18.7895 | −0.789782 | ||||||||
\(567\) | −91.8171 | −3.85596 | ||||||||
\(568\) | −1.13986 | −0.0478275 | ||||||||
\(569\) | −27.0660 | −1.13467 | −0.567333 | − | 0.823489i | \(-0.692025\pi\) | ||||
−0.567333 | + | 0.823489i | \(0.692025\pi\) | |||||||
\(570\) | −2.60821 | −0.109246 | ||||||||
\(571\) | −19.9083 | −0.833137 | −0.416569 | − | 0.909104i | \(-0.636767\pi\) | ||||
−0.416569 | + | 0.909104i | \(0.636767\pi\) | |||||||
\(572\) | −9.40936 | −0.393425 | ||||||||
\(573\) | −7.13668 | −0.298139 | ||||||||
\(574\) | 26.6158 | 1.11092 | ||||||||
\(575\) | −0.0265160 | −0.00110579 | ||||||||
\(576\) | 8.06959 | 0.336233 | ||||||||
\(577\) | −30.6239 | −1.27489 | −0.637444 | − | 0.770496i | \(-0.720008\pi\) | ||||
−0.637444 | + | 0.770496i | \(0.720008\pi\) | |||||||
\(578\) | 8.33412 | 0.346654 | ||||||||
\(579\) | 47.7307 | 1.98362 | ||||||||
\(580\) | −8.26058 | −0.343002 | ||||||||
\(581\) | 21.4161 | 0.888491 | ||||||||
\(582\) | 20.4568 | 0.847962 | ||||||||
\(583\) | 20.3554 | 0.843035 | ||||||||
\(584\) | 3.11153 | 0.128756 | ||||||||
\(585\) | −19.9918 | −0.826560 | ||||||||
\(586\) | 15.9251 | 0.657859 | ||||||||
\(587\) | 7.03383 | 0.290317 | 0.145159 | − | 0.989408i | \(-0.453631\pi\) | ||||
0.145159 | + | 0.989408i | \(0.453631\pi\) | |||||||
\(588\) | 4.25728 | 0.175567 | ||||||||
\(589\) | 0.485432 | 0.0200019 | ||||||||
\(590\) | −4.82597 | −0.198682 | ||||||||
\(591\) | 42.2419 | 1.73760 | ||||||||
\(592\) | 1.77151 | 0.0728086 | ||||||||
\(593\) | −38.6111 | −1.58557 | −0.792784 | − | 0.609503i | \(-0.791369\pi\) | ||||
−0.792784 | + | 0.609503i | \(0.791369\pi\) | |||||||
\(594\) | −64.0616 | −2.62848 | ||||||||
\(595\) | −8.47053 | −0.347258 | ||||||||
\(596\) | 4.04445 | 0.165667 | ||||||||
\(597\) | −41.8489 | −1.71276 | ||||||||
\(598\) | −0.0656915 | −0.00268632 | ||||||||
\(599\) | −13.7963 | −0.563703 | −0.281852 | − | 0.959458i | \(-0.590949\pi\) | ||||
−0.281852 | + | 0.959458i | \(0.590949\pi\) | |||||||
\(600\) | −3.32710 | −0.135828 | ||||||||
\(601\) | 37.2149 | 1.51803 | 0.759014 | − | 0.651075i | \(-0.225682\pi\) | ||||
0.759014 | + | 0.651075i | \(0.225682\pi\) | |||||||
\(602\) | 5.10852 | 0.208208 | ||||||||
\(603\) | −83.7547 | −3.41075 | ||||||||
\(604\) | −4.20941 | −0.171278 | ||||||||
\(605\) | 3.42510 | 0.139250 | ||||||||
\(606\) | −43.9315 | −1.78460 | ||||||||
\(607\) | −31.3955 | −1.27430 | −0.637152 | − | 0.770738i | \(-0.719888\pi\) | ||||
−0.637152 | + | 0.770738i | \(0.719888\pi\) | |||||||
\(608\) | −0.783929 | −0.0317925 | ||||||||
\(609\) | 79.0825 | 3.20459 | ||||||||
\(610\) | −0.650441 | −0.0263356 | ||||||||
\(611\) | −26.3924 | −1.06772 | ||||||||
\(612\) | 23.7551 | 0.960245 | ||||||||
\(613\) | 44.8344 | 1.81084 | 0.905422 | − | 0.424513i | \(-0.139555\pi\) | ||||
0.905422 | + | 0.424513i | \(0.139555\pi\) | |||||||
\(614\) | 13.0738 | 0.527614 | ||||||||
\(615\) | 30.7752 | 1.24098 | ||||||||
\(616\) | 10.9286 | 0.440325 | ||||||||
\(617\) | −35.8872 | −1.44476 | −0.722382 | − | 0.691494i | \(-0.756953\pi\) | ||||
−0.722382 | + | 0.691494i | \(0.756953\pi\) | |||||||
\(618\) | 13.4629 | 0.541558 | ||||||||
\(619\) | 5.64832 | 0.227025 | 0.113513 | − | 0.993537i | \(-0.463790\pi\) | ||||
0.113513 | + | 0.993537i | \(0.463790\pi\) | |||||||
\(620\) | 0.619229 | 0.0248688 | ||||||||
\(621\) | −0.447246 | −0.0179474 | ||||||||
\(622\) | −4.57265 | −0.183347 | ||||||||
\(623\) | −12.4498 | −0.498791 | ||||||||
\(624\) | −8.24264 | −0.329970 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.5845 | 0.902657 | ||||||||
\(627\) | 9.90609 | 0.395611 | ||||||||
\(628\) | −22.1248 | −0.882876 | ||||||||
\(629\) | 5.21495 | 0.207934 | ||||||||
\(630\) | 23.2196 | 0.925092 | ||||||||
\(631\) | −35.7341 | −1.42255 | −0.711277 | − | 0.702912i | \(-0.751883\pi\) | ||||
−0.711277 | + | 0.702912i | \(0.751883\pi\) | |||||||
\(632\) | −5.43079 | −0.216025 | ||||||||
\(633\) | −21.8442 | −0.868230 | ||||||||
\(634\) | 15.0700 | 0.598508 | ||||||||
\(635\) | 5.11512 | 0.202987 | ||||||||
\(636\) | 17.8314 | 0.707062 | ||||||||
\(637\) | −3.17006 | −0.125602 | ||||||||
\(638\) | 31.3740 | 1.24211 | ||||||||
\(639\) | 9.19820 | 0.363875 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −11.8594 | −0.468418 | −0.234209 | − | 0.972186i | \(-0.575250\pi\) | ||||
−0.234209 | + | 0.972186i | \(0.575250\pi\) | |||||||
\(642\) | 44.6780 | 1.76330 | ||||||||
\(643\) | −13.4394 | −0.530000 | −0.265000 | − | 0.964248i | \(-0.585372\pi\) | ||||
−0.265000 | + | 0.964248i | \(0.585372\pi\) | |||||||
\(644\) | 0.0762979 | 0.00300656 | ||||||||
\(645\) | 5.90686 | 0.232582 | ||||||||
\(646\) | −2.30772 | −0.0907960 | ||||||||
\(647\) | −11.8536 | −0.466013 | −0.233007 | − | 0.972475i | \(-0.574856\pi\) | ||||
−0.233007 | + | 0.972475i | \(0.574856\pi\) | |||||||
\(648\) | −31.9095 | −1.25352 | ||||||||
\(649\) | 18.3292 | 0.719485 | ||||||||
\(650\) | 2.47743 | 0.0971727 | ||||||||
\(651\) | −5.92818 | −0.232344 | ||||||||
\(652\) | 13.6761 | 0.535599 | ||||||||
\(653\) | −25.5777 | −1.00093 | −0.500466 | − | 0.865756i | \(-0.666838\pi\) | ||||
−0.500466 | + | 0.865756i | \(0.666838\pi\) | |||||||
\(654\) | 6.73337 | 0.263296 | ||||||||
\(655\) | 2.82921 | 0.110547 | ||||||||
\(656\) | 9.24986 | 0.361146 | ||||||||
\(657\) | −25.1088 | −0.979586 | ||||||||
\(658\) | 30.6537 | 1.19501 | ||||||||
\(659\) | −25.7646 | −1.00365 | −0.501823 | − | 0.864970i | \(-0.667337\pi\) | ||||
−0.501823 | + | 0.864970i | \(0.667337\pi\) | |||||||
\(660\) | 12.6365 | 0.491873 | ||||||||
\(661\) | −32.9276 | −1.28074 | −0.640368 | − | 0.768068i | \(-0.721218\pi\) | ||||
−0.640368 | + | 0.768068i | \(0.721218\pi\) | |||||||
\(662\) | 0.290068 | 0.0112738 | ||||||||
\(663\) | −24.2646 | −0.942358 | ||||||||
\(664\) | 7.44281 | 0.288837 | ||||||||
\(665\) | −2.25570 | −0.0874722 | ||||||||
\(666\) | −14.2954 | −0.553934 | ||||||||
\(667\) | 0.219038 | 0.00848118 | ||||||||
\(668\) | −22.8840 | −0.885409 | ||||||||
\(669\) | 73.3965 | 2.83767 | ||||||||
\(670\) | 10.3791 | 0.400978 | ||||||||
\(671\) | 2.47040 | 0.0953688 | ||||||||
\(672\) | 9.57348 | 0.369305 | ||||||||
\(673\) | 21.7958 | 0.840166 | 0.420083 | − | 0.907486i | \(-0.362001\pi\) | ||||
0.420083 | + | 0.907486i | \(0.362001\pi\) | |||||||
\(674\) | 14.2582 | 0.549207 | ||||||||
\(675\) | 16.8670 | 0.649212 | ||||||||
\(676\) | −6.86236 | −0.263937 | ||||||||
\(677\) | 5.89169 | 0.226436 | 0.113218 | − | 0.993570i | \(-0.463884\pi\) | ||||
0.113218 | + | 0.993570i | \(0.463884\pi\) | |||||||
\(678\) | −42.2646 | −1.62316 | ||||||||
\(679\) | 17.6920 | 0.678956 | ||||||||
\(680\) | −2.94379 | −0.112889 | ||||||||
\(681\) | 41.2964 | 1.58248 | ||||||||
\(682\) | −2.35186 | −0.0900573 | ||||||||
\(683\) | 16.0949 | 0.615854 | 0.307927 | − | 0.951410i | \(-0.400365\pi\) | ||||
0.307927 | + | 0.951410i | \(0.400365\pi\) | |||||||
\(684\) | 6.32599 | 0.241880 | ||||||||
\(685\) | 8.47126 | 0.323670 | ||||||||
\(686\) | −16.4601 | −0.628449 | ||||||||
\(687\) | 28.0859 | 1.07154 | ||||||||
\(688\) | 1.77538 | 0.0676856 | ||||||||
\(689\) | −13.2776 | −0.505838 | ||||||||
\(690\) | 0.0882214 | 0.00335853 | ||||||||
\(691\) | 30.5236 | 1.16117 | 0.580586 | − | 0.814199i | \(-0.302823\pi\) | ||||
0.580586 | + | 0.814199i | \(0.302823\pi\) | |||||||
\(692\) | −14.6738 | −0.557815 | ||||||||
\(693\) | −88.1891 | −3.35003 | ||||||||
\(694\) | 19.9345 | 0.756702 | ||||||||
\(695\) | −7.21459 | −0.273665 | ||||||||
\(696\) | 27.4838 | 1.04177 | ||||||||
\(697\) | 27.2296 | 1.03139 | ||||||||
\(698\) | 5.22658 | 0.197829 | ||||||||
\(699\) | −70.1463 | −2.65318 | ||||||||
\(700\) | −2.87743 | −0.108756 | ||||||||
\(701\) | −34.5197 | −1.30379 | −0.651895 | − | 0.758309i | \(-0.726026\pi\) | ||||
−0.651895 | + | 0.758309i | \(0.726026\pi\) | |||||||
\(702\) | 41.7868 | 1.57714 | ||||||||
\(703\) | 1.38874 | 0.0523773 | ||||||||
\(704\) | 3.79804 | 0.143144 | ||||||||
\(705\) | 35.4441 | 1.33490 | ||||||||
\(706\) | 20.6145 | 0.775837 | ||||||||
\(707\) | −37.9940 | −1.42891 | ||||||||
\(708\) | 16.0565 | 0.603439 | ||||||||
\(709\) | 6.79341 | 0.255132 | 0.127566 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127566 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(710\) | −1.13986 | −0.0427782 | ||||||||
\(711\) | 43.8242 | 1.64354 | ||||||||
\(712\) | −4.32672 | −0.162151 | ||||||||
\(713\) | −0.0164195 | −0.000614915 0 | ||||||||
\(714\) | 28.1823 | 1.05470 | ||||||||
\(715\) | −9.40936 | −0.351890 | ||||||||
\(716\) | 9.59560 | 0.358604 | ||||||||
\(717\) | 78.2022 | 2.92052 | ||||||||
\(718\) | 17.7824 | 0.663632 | ||||||||
\(719\) | −1.31472 | −0.0490307 | −0.0245153 | − | 0.999699i | \(-0.507804\pi\) | ||||
−0.0245153 | + | 0.999699i | \(0.507804\pi\) | |||||||
\(720\) | 8.06959 | 0.300736 | ||||||||
\(721\) | 11.6433 | 0.433621 | ||||||||
\(722\) | 18.3855 | 0.684236 | ||||||||
\(723\) | 89.9043 | 3.34358 | ||||||||
\(724\) | 10.2207 | 0.379850 | ||||||||
\(725\) | −8.26058 | −0.306790 | ||||||||
\(726\) | −11.3957 | −0.422933 | ||||||||
\(727\) | 27.9140 | 1.03527 | 0.517636 | − | 0.855601i | \(-0.326812\pi\) | ||||
0.517636 | + | 0.855601i | \(0.326812\pi\) | |||||||
\(728\) | −7.12861 | −0.264204 | ||||||||
\(729\) | 89.1416 | 3.30154 | ||||||||
\(730\) | 3.11153 | 0.115163 | ||||||||
\(731\) | 5.22633 | 0.193303 | ||||||||
\(732\) | 2.16408 | 0.0799868 | ||||||||
\(733\) | −46.0733 | −1.70176 | −0.850878 | − | 0.525363i | \(-0.823930\pi\) | ||||
−0.850878 | + | 0.525363i | \(0.823930\pi\) | |||||||
\(734\) | 3.36265 | 0.124117 | ||||||||
\(735\) | 4.25728 | 0.157032 | ||||||||
\(736\) | 0.0265160 | 0.000977393 0 | ||||||||
\(737\) | −39.4201 | −1.45206 | ||||||||
\(738\) | −74.6425 | −2.74763 | ||||||||
\(739\) | 7.96261 | 0.292909 | 0.146455 | − | 0.989217i | \(-0.453214\pi\) | ||||
0.146455 | + | 0.989217i | \(0.453214\pi\) | |||||||
\(740\) | 1.77151 | 0.0651220 | ||||||||
\(741\) | −6.46165 | −0.237375 | ||||||||
\(742\) | 15.4214 | 0.566138 | ||||||||
\(743\) | −2.89731 | −0.106292 | −0.0531461 | − | 0.998587i | \(-0.516925\pi\) | ||||
−0.0531461 | + | 0.998587i | \(0.516925\pi\) | |||||||
\(744\) | −2.06024 | −0.0755320 | ||||||||
\(745\) | 4.04445 | 0.148177 | ||||||||
\(746\) | −6.13110 | −0.224476 | ||||||||
\(747\) | −60.0604 | −2.19750 | ||||||||
\(748\) | 11.1806 | 0.408804 | ||||||||
\(749\) | 38.6395 | 1.41186 | ||||||||
\(750\) | −3.32710 | −0.121488 | ||||||||
\(751\) | −24.0517 | −0.877658 | −0.438829 | − | 0.898570i | \(-0.644607\pi\) | ||||
−0.438829 | + | 0.898570i | \(0.644607\pi\) | |||||||
\(752\) | 10.6532 | 0.388481 | ||||||||
\(753\) | 38.4189 | 1.40006 | ||||||||
\(754\) | −20.4650 | −0.745291 | ||||||||
\(755\) | −4.20941 | −0.153196 | ||||||||
\(756\) | −48.5336 | −1.76515 | ||||||||
\(757\) | 50.6602 | 1.84128 | 0.920638 | − | 0.390418i | \(-0.127670\pi\) | ||||
0.920638 | + | 0.390418i | \(0.127670\pi\) | |||||||
\(758\) | −29.4156 | −1.06842 | ||||||||
\(759\) | −0.335068 | −0.0121622 | ||||||||
\(760\) | −0.783929 | −0.0284361 | ||||||||
\(761\) | 9.81709 | 0.355869 | 0.177935 | − | 0.984042i | \(-0.443058\pi\) | ||||
0.177935 | + | 0.984042i | \(0.443058\pi\) | |||||||
\(762\) | −17.0185 | −0.616516 | ||||||||
\(763\) | 5.82332 | 0.210819 | ||||||||
\(764\) | −2.14502 | −0.0776040 | ||||||||
\(765\) | 23.7551 | 0.858869 | ||||||||
\(766\) | 15.2014 | 0.549249 | ||||||||
\(767\) | −11.9560 | −0.431705 | ||||||||
\(768\) | 3.32710 | 0.120056 | ||||||||
\(769\) | 41.6658 | 1.50251 | 0.751254 | − | 0.660014i | \(-0.229450\pi\) | ||||
0.751254 | + | 0.660014i | \(0.229450\pi\) | |||||||
\(770\) | 10.9286 | 0.393839 | ||||||||
\(771\) | −39.7432 | −1.43132 | ||||||||
\(772\) | 14.3461 | 0.516326 | ||||||||
\(773\) | −0.937508 | −0.0337198 | −0.0168599 | − | 0.999858i | \(-0.505367\pi\) | ||||
−0.0168599 | + | 0.999858i | \(0.505367\pi\) | |||||||
\(774\) | −14.3266 | −0.514958 | ||||||||
\(775\) | 0.619229 | 0.0222434 | ||||||||
\(776\) | 6.14854 | 0.220720 | ||||||||
\(777\) | −16.9595 | −0.608419 | ||||||||
\(778\) | −13.5439 | −0.485573 | ||||||||
\(779\) | 7.25123 | 0.259802 | ||||||||
\(780\) | −8.24264 | −0.295134 | ||||||||
\(781\) | 4.32924 | 0.154912 | ||||||||
\(782\) | 0.0780575 | 0.00279133 | ||||||||
\(783\) | −139.331 | −4.97930 | ||||||||
\(784\) | 1.27958 | 0.0456992 | ||||||||
\(785\) | −22.1248 | −0.789668 | ||||||||
\(786\) | −9.41307 | −0.335753 | ||||||||
\(787\) | 9.10469 | 0.324547 | 0.162274 | − | 0.986746i | \(-0.448117\pi\) | ||||
0.162274 | + | 0.986746i | \(0.448117\pi\) | |||||||
\(788\) | 12.6963 | 0.452287 | ||||||||
\(789\) | −69.9959 | −2.49192 | ||||||||
\(790\) | −5.43079 | −0.193219 | ||||||||
\(791\) | −36.5523 | −1.29965 | ||||||||
\(792\) | −30.6486 | −1.08905 | ||||||||
\(793\) | −1.61142 | −0.0572232 | ||||||||
\(794\) | 20.7482 | 0.736326 | ||||||||
\(795\) | 17.8314 | 0.632415 | ||||||||
\(796\) | −12.5782 | −0.445823 | ||||||||
\(797\) | 13.9593 | 0.494464 | 0.247232 | − | 0.968956i | \(-0.420479\pi\) | ||||
0.247232 | + | 0.968956i | \(0.420479\pi\) | |||||||
\(798\) | 7.50493 | 0.265672 | ||||||||
\(799\) | 31.3606 | 1.10946 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 34.9148 | 1.23365 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −11.8177 | −0.417038 | ||||||||
\(804\) | −34.5321 | −1.21785 | ||||||||
\(805\) | 0.0762979 | 0.00268915 | ||||||||
\(806\) | 1.53410 | 0.0540362 | ||||||||
\(807\) | −28.4669 | −1.00208 | ||||||||
\(808\) | −13.2042 | −0.464521 | ||||||||
\(809\) | 29.2557 | 1.02857 | 0.514287 | − | 0.857618i | \(-0.328057\pi\) | ||||
0.514287 | + | 0.857618i | \(0.328057\pi\) | |||||||
\(810\) | −31.9095 | −1.12118 | ||||||||
\(811\) | −23.9151 | −0.839772 | −0.419886 | − | 0.907577i | \(-0.637930\pi\) | ||||
−0.419886 | + | 0.907577i | \(0.637930\pi\) | |||||||
\(812\) | 23.7692 | 0.834136 | ||||||||
\(813\) | −77.0200 | −2.70121 | ||||||||
\(814\) | −6.72827 | −0.235826 | ||||||||
\(815\) | 13.6761 | 0.479055 | ||||||||
\(816\) | 9.79427 | 0.342868 | ||||||||
\(817\) | 1.39177 | 0.0486919 | ||||||||
\(818\) | −32.3855 | −1.13233 | ||||||||
\(819\) | 57.5249 | 2.01008 | ||||||||
\(820\) | 9.24986 | 0.323019 | ||||||||
\(821\) | −47.7783 | −1.66747 | −0.833737 | − | 0.552161i | \(-0.813803\pi\) | ||||
−0.833737 | + | 0.552161i | \(0.813803\pi\) | |||||||
\(822\) | −28.1847 | −0.983056 | ||||||||
\(823\) | −7.84950 | −0.273616 | −0.136808 | − | 0.990598i | \(-0.543684\pi\) | ||||
−0.136808 | + | 0.990598i | \(0.543684\pi\) | |||||||
\(824\) | 4.04644 | 0.140965 | ||||||||
\(825\) | 12.6365 | 0.439945 | ||||||||
\(826\) | 13.8864 | 0.483168 | ||||||||
\(827\) | −31.7419 | −1.10378 | −0.551888 | − | 0.833918i | \(-0.686092\pi\) | ||||
−0.551888 | + | 0.833918i | \(0.686092\pi\) | |||||||
\(828\) | −0.213973 | −0.00743609 | ||||||||
\(829\) | 0.0702186 | 0.00243879 | 0.00121940 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00121940 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(830\) | 7.44281 | 0.258344 | ||||||||
\(831\) | −77.6435 | −2.69342 | ||||||||
\(832\) | −2.47743 | −0.0858893 | ||||||||
\(833\) | 3.76681 | 0.130512 | ||||||||
\(834\) | 24.0037 | 0.831179 | ||||||||
\(835\) | −22.8840 | −0.791934 | ||||||||
\(836\) | 2.97739 | 0.102975 | ||||||||
\(837\) | 10.4446 | 0.361017 | ||||||||
\(838\) | 18.4374 | 0.636909 | ||||||||
\(839\) | −41.0691 | −1.41786 | −0.708932 | − | 0.705277i | \(-0.750823\pi\) | ||||
−0.708932 | + | 0.705277i | \(0.750823\pi\) | |||||||
\(840\) | 9.57348 | 0.330316 | ||||||||
\(841\) | 39.2372 | 1.35301 | ||||||||
\(842\) | −15.3683 | −0.529628 | ||||||||
\(843\) | −66.5975 | −2.29374 | ||||||||
\(844\) | −6.56554 | −0.225995 | ||||||||
\(845\) | −6.86236 | −0.236072 | ||||||||
\(846\) | −85.9666 | −2.95559 | ||||||||
\(847\) | −9.85548 | −0.338638 | ||||||||
\(848\) | 5.35945 | 0.184044 | ||||||||
\(849\) | 62.5145 | 2.14549 | ||||||||
\(850\) | −2.94379 | −0.100971 | ||||||||
\(851\) | −0.0469734 | −0.00161023 | ||||||||
\(852\) | 3.79243 | 0.129926 | ||||||||
\(853\) | 37.9699 | 1.30006 | 0.650032 | − | 0.759907i | \(-0.274755\pi\) | ||||
0.650032 | + | 0.759907i | \(0.274755\pi\) | |||||||
\(854\) | 1.87160 | 0.0640447 | ||||||||
\(855\) | 6.32599 | 0.216344 | ||||||||
\(856\) | 13.4285 | 0.458977 | ||||||||
\(857\) | 23.2158 | 0.793038 | 0.396519 | − | 0.918026i | \(-0.370218\pi\) | ||||
0.396519 | + | 0.918026i | \(0.370218\pi\) | |||||||
\(858\) | 31.3059 | 1.06877 | ||||||||
\(859\) | −4.72303 | −0.161148 | −0.0805739 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805739 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(860\) | 1.77538 | 0.0605399 | ||||||||
\(861\) | −88.5533 | −3.01789 | ||||||||
\(862\) | −37.0475 | −1.26184 | ||||||||
\(863\) | 24.1263 | 0.821270 | 0.410635 | − | 0.911800i | \(-0.365307\pi\) | ||||
0.410635 | + | 0.911800i | \(0.365307\pi\) | |||||||
\(864\) | −16.8670 | −0.573828 | ||||||||
\(865\) | −14.6738 | −0.498925 | ||||||||
\(866\) | −30.8682 | −1.04895 | ||||||||
\(867\) | −27.7285 | −0.941708 | ||||||||
\(868\) | −1.78179 | −0.0604778 | ||||||||
\(869\) | 20.6264 | 0.699701 | ||||||||
\(870\) | 27.4838 | 0.931787 | ||||||||
\(871\) | 25.7133 | 0.871263 | ||||||||
\(872\) | 2.02380 | 0.0685344 | ||||||||
\(873\) | −49.6162 | −1.67925 | ||||||||
\(874\) | 0.0207867 | 0.000703120 0 | ||||||||
\(875\) | −2.87743 | −0.0972747 | ||||||||
\(876\) | −10.3524 | −0.349774 | ||||||||
\(877\) | 1.52197 | 0.0513933 | 0.0256966 | − | 0.999670i | \(-0.491820\pi\) | ||||
0.0256966 | + | 0.999670i | \(0.491820\pi\) | |||||||
\(878\) | 38.2997 | 1.29255 | ||||||||
\(879\) | −52.9843 | −1.78712 | ||||||||
\(880\) | 3.79804 | 0.128032 | ||||||||
\(881\) | 8.08799 | 0.272491 | 0.136246 | − | 0.990675i | \(-0.456496\pi\) | ||||
0.136246 | + | 0.990675i | \(0.456496\pi\) | |||||||
\(882\) | −10.3257 | −0.347683 | ||||||||
\(883\) | −11.8485 | −0.398735 | −0.199367 | − | 0.979925i | \(-0.563889\pi\) | ||||
−0.199367 | + | 0.979925i | \(0.563889\pi\) | |||||||
\(884\) | −7.29301 | −0.245291 | ||||||||
\(885\) | 16.0565 | 0.539732 | ||||||||
\(886\) | 9.53641 | 0.320382 | ||||||||
\(887\) | −9.32235 | −0.313014 | −0.156507 | − | 0.987677i | \(-0.550023\pi\) | ||||
−0.156507 | + | 0.987677i | \(0.550023\pi\) | |||||||
\(888\) | −5.89399 | −0.197789 | ||||||||
\(889\) | −14.7184 | −0.493639 | ||||||||
\(890\) | −4.32672 | −0.145032 | ||||||||
\(891\) | 121.193 | 4.06013 | ||||||||
\(892\) | 22.0602 | 0.738631 | ||||||||
\(893\) | 8.35133 | 0.279467 | ||||||||
\(894\) | −13.4563 | −0.450045 | ||||||||
\(895\) | 9.59560 | 0.320745 | ||||||||
\(896\) | 2.87743 | 0.0961280 | ||||||||
\(897\) | 0.218562 | 0.00729757 | ||||||||
\(898\) | 36.7230 | 1.22546 | ||||||||
\(899\) | −5.11520 | −0.170601 | ||||||||
\(900\) | 8.06959 | 0.268986 | ||||||||
\(901\) | 15.7771 | 0.525610 | ||||||||
\(902\) | −35.1313 | −1.16975 | ||||||||
\(903\) | −16.9965 | −0.565609 | ||||||||
\(904\) | −12.7031 | −0.422500 | ||||||||
\(905\) | 10.2207 | 0.339748 | ||||||||
\(906\) | 14.0051 | 0.465289 | ||||||||
\(907\) | −55.2371 | −1.83412 | −0.917058 | − | 0.398753i | \(-0.869443\pi\) | ||||
−0.917058 | + | 0.398753i | \(0.869443\pi\) | |||||||
\(908\) | 12.4121 | 0.411911 | ||||||||
\(909\) | 106.552 | 3.53411 | ||||||||
\(910\) | −7.12861 | −0.236311 | ||||||||
\(911\) | 39.1120 | 1.29584 | 0.647919 | − | 0.761709i | \(-0.275639\pi\) | ||||
0.647919 | + | 0.761709i | \(0.275639\pi\) | |||||||
\(912\) | 2.60821 | 0.0863665 | ||||||||
\(913\) | −28.2681 | −0.935538 | ||||||||
\(914\) | −34.4625 | −1.13992 | ||||||||
\(915\) | 2.16408 | 0.0715424 | ||||||||
\(916\) | 8.44156 | 0.278917 | ||||||||
\(917\) | −8.14085 | −0.268835 | ||||||||
\(918\) | −49.6529 | −1.63879 | ||||||||
\(919\) | −54.4431 | −1.79591 | −0.897957 | − | 0.440084i | \(-0.854949\pi\) | ||||
−0.897957 | + | 0.440084i | \(0.854949\pi\) | |||||||
\(920\) | 0.0265160 | 0.000874207 0 | ||||||||
\(921\) | −43.4977 | −1.43330 | ||||||||
\(922\) | −32.8634 | −1.08230 | ||||||||
\(923\) | −2.82392 | −0.0929505 | ||||||||
\(924\) | −36.3605 | −1.19617 | ||||||||
\(925\) | 1.77151 | 0.0582469 | ||||||||
\(926\) | 3.98341 | 0.130903 | ||||||||
\(927\) | −32.6531 | −1.07247 | ||||||||
\(928\) | 8.26058 | 0.271167 | ||||||||
\(929\) | −1.74749 | −0.0573334 | −0.0286667 | − | 0.999589i | \(-0.509126\pi\) | ||||
−0.0286667 | + | 0.999589i | \(0.509126\pi\) | |||||||
\(930\) | −2.06024 | −0.0675578 | ||||||||
\(931\) | 1.00310 | 0.0328752 | ||||||||
\(932\) | −21.0833 | −0.690608 | ||||||||
\(933\) | 15.2137 | 0.498073 | ||||||||
\(934\) | −1.64490 | −0.0538229 | ||||||||
\(935\) | 11.1806 | 0.365645 | ||||||||
\(936\) | 19.9918 | 0.653453 | ||||||||
\(937\) | −51.7617 | −1.69098 | −0.845491 | − | 0.533989i | \(-0.820692\pi\) | ||||
−0.845491 | + | 0.533989i | \(0.820692\pi\) | |||||||
\(938\) | −29.8650 | −0.975125 | ||||||||
\(939\) | −75.1408 | −2.45213 | ||||||||
\(940\) | 10.6532 | 0.347468 | ||||||||
\(941\) | −15.7490 | −0.513404 | −0.256702 | − | 0.966491i | \(-0.582636\pi\) | ||||
−0.256702 | + | 0.966491i | \(0.582636\pi\) | |||||||
\(942\) | 73.6114 | 2.39839 | ||||||||
\(943\) | −0.245269 | −0.00798707 | ||||||||
\(944\) | 4.82597 | 0.157072 | ||||||||
\(945\) | −48.5336 | −1.57880 | ||||||||
\(946\) | −6.74295 | −0.219232 | ||||||||
\(947\) | −30.5208 | −0.991793 | −0.495896 | − | 0.868382i | \(-0.665160\pi\) | ||||
−0.495896 | + | 0.868382i | \(0.665160\pi\) | |||||||
\(948\) | 18.0688 | 0.586847 | ||||||||
\(949\) | 7.70859 | 0.250231 | ||||||||
\(950\) | −0.783929 | −0.0254340 | ||||||||
\(951\) | −50.1395 | −1.62589 | ||||||||
\(952\) | 8.47053 | 0.274531 | ||||||||
\(953\) | −50.3980 | −1.63255 | −0.816275 | − | 0.577663i | \(-0.803965\pi\) | ||||
−0.816275 | + | 0.577663i | \(0.803965\pi\) | |||||||
\(954\) | −43.2485 | −1.40022 | ||||||||
\(955\) | −2.14502 | −0.0694111 | ||||||||
\(956\) | 23.5046 | 0.760194 | ||||||||
\(957\) | −104.384 | −3.37427 | ||||||||
\(958\) | −0.132786 | −0.00429012 | ||||||||
\(959\) | −24.3754 | −0.787124 | ||||||||
\(960\) | 3.32710 | 0.107382 | ||||||||
\(961\) | −30.6166 | −0.987631 | ||||||||
\(962\) | 4.38879 | 0.141500 | ||||||||
\(963\) | −108.363 | −3.49193 | ||||||||
\(964\) | 27.0218 | 0.870314 | ||||||||
\(965\) | 14.3461 | 0.461816 | ||||||||
\(966\) | −0.253851 | −0.00816751 | ||||||||
\(967\) | 8.83722 | 0.284186 | 0.142093 | − | 0.989853i | \(-0.454617\pi\) | ||||
0.142093 | + | 0.989853i | \(0.454617\pi\) | |||||||
\(968\) | −3.42510 | −0.110087 | ||||||||
\(969\) | 7.67801 | 0.246653 | ||||||||
\(970\) | 6.14854 | 0.197418 | ||||||||
\(971\) | 44.5253 | 1.42889 | 0.714443 | − | 0.699693i | \(-0.246680\pi\) | ||||
0.714443 | + | 0.699693i | \(0.246680\pi\) | |||||||
\(972\) | 55.5649 | 1.78225 | ||||||||
\(973\) | 20.7595 | 0.665518 | ||||||||
\(974\) | 14.6785 | 0.470331 | ||||||||
\(975\) | −8.24264 | −0.263976 | ||||||||
\(976\) | 0.650441 | 0.0208201 | ||||||||
\(977\) | −33.0350 | −1.05688 | −0.528441 | − | 0.848970i | \(-0.677223\pi\) | ||||
−0.528441 | + | 0.848970i | \(0.677223\pi\) | |||||||
\(978\) | −45.5019 | −1.45499 | ||||||||
\(979\) | 16.4330 | 0.525202 | ||||||||
\(980\) | 1.27958 | 0.0408746 | ||||||||
\(981\) | −16.3312 | −0.521415 | ||||||||
\(982\) | −6.99801 | −0.223315 | ||||||||
\(983\) | 39.3209 | 1.25414 | 0.627071 | − | 0.778962i | \(-0.284254\pi\) | ||||
0.627071 | + | 0.778962i | \(0.284254\pi\) | |||||||
\(984\) | −30.7752 | −0.981077 | ||||||||
\(985\) | 12.6963 | 0.404538 | ||||||||
\(986\) | 24.3174 | 0.774424 | ||||||||
\(987\) | −101.988 | −3.24631 | ||||||||
\(988\) | −1.94213 | −0.0617873 | ||||||||
\(989\) | −0.0470759 | −0.00149693 | ||||||||
\(990\) | −30.6486 | −0.974077 | ||||||||
\(991\) | 29.9847 | 0.952496 | 0.476248 | − | 0.879311i | \(-0.341996\pi\) | ||||
0.476248 | + | 0.879311i | \(0.341996\pi\) | |||||||
\(992\) | −0.619229 | −0.0196606 | ||||||||
\(993\) | −0.965084 | −0.0306260 | ||||||||
\(994\) | 3.27986 | 0.104031 | ||||||||
\(995\) | −12.5782 | −0.398756 | ||||||||
\(996\) | −24.7630 | −0.784645 | ||||||||
\(997\) | 23.5075 | 0.744490 | 0.372245 | − | 0.928135i | \(-0.378588\pi\) | ||||
0.372245 | + | 0.928135i | \(0.378588\pi\) | |||||||
\(998\) | 0.837087 | 0.0264975 | ||||||||
\(999\) | 29.8801 | 0.945365 |
(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 | 4010.2.a.m.1.20 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.m.1.20 | ✓ | 20 | 1.1 | even | 1 | trivial |