Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.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: | \(32.1557568940\) |
Analytic rank: | \(1\) |
Dimension: | \(159\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54982 | −1.80299 | −0.901497 | − | 0.432785i | \(-0.857531\pi\) | ||||
−0.901497 | + | 0.432785i | \(0.857531\pi\) | |||||||
\(3\) | 3.26459 | 1.88481 | 0.942405 | − | 0.334474i | \(-0.108559\pi\) | ||||
0.942405 | + | 0.334474i | \(0.108559\pi\) | |||||||
\(4\) | 4.50158 | 2.25079 | ||||||||
\(5\) | −1.30834 | −0.585107 | −0.292554 | − | 0.956249i | \(-0.594505\pi\) | ||||
−0.292554 | + | 0.956249i | \(0.594505\pi\) | |||||||
\(6\) | −8.32411 | −3.39830 | ||||||||
\(7\) | 3.58480 | 1.35493 | 0.677463 | − | 0.735557i | \(-0.263080\pi\) | ||||
0.677463 | + | 0.735557i | \(0.263080\pi\) | |||||||
\(8\) | −6.37858 | −2.25517 | ||||||||
\(9\) | 7.65753 | 2.55251 | ||||||||
\(10\) | 3.33603 | 1.05494 | ||||||||
\(11\) | 0.411280 | 0.124006 | 0.0620028 | − | 0.998076i | \(-0.480251\pi\) | ||||
0.0620028 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(12\) | 14.6958 | 4.24231 | ||||||||
\(13\) | −6.00076 | −1.66431 | −0.832155 | − | 0.554543i | \(-0.812893\pi\) | ||||
−0.832155 | + | 0.554543i | \(0.812893\pi\) | |||||||
\(14\) | −9.14058 | −2.44292 | ||||||||
\(15\) | −4.27119 | −1.10282 | ||||||||
\(16\) | 7.26106 | 1.81527 | ||||||||
\(17\) | −6.43986 | −1.56190 | −0.780948 | − | 0.624596i | \(-0.785264\pi\) | ||||
−0.780948 | + | 0.624596i | \(0.785264\pi\) | |||||||
\(18\) | −19.5253 | −4.60216 | ||||||||
\(19\) | −6.79506 | −1.55889 | −0.779447 | − | 0.626468i | \(-0.784500\pi\) | ||||
−0.779447 | + | 0.626468i | \(0.784500\pi\) | |||||||
\(20\) | −5.88959 | −1.31695 | ||||||||
\(21\) | 11.7029 | 2.55378 | ||||||||
\(22\) | −1.04869 | −0.223581 | ||||||||
\(23\) | 2.21132 | 0.461091 | 0.230546 | − | 0.973062i | \(-0.425949\pi\) | ||||
0.230546 | + | 0.973062i | \(0.425949\pi\) | |||||||
\(24\) | −20.8234 | −4.25056 | ||||||||
\(25\) | −3.28825 | −0.657650 | ||||||||
\(26\) | 15.3008 | 3.00074 | ||||||||
\(27\) | 15.2049 | 2.92619 | ||||||||
\(28\) | 16.1372 | 3.04965 | ||||||||
\(29\) | −9.83730 | −1.82674 | −0.913370 | − | 0.407131i | \(-0.866529\pi\) | ||||
−0.913370 | + | 0.407131i | \(0.866529\pi\) | |||||||
\(30\) | 10.8908 | 1.98837 | ||||||||
\(31\) | −0.964118 | −0.173161 | −0.0865804 | − | 0.996245i | \(-0.527594\pi\) | ||||
−0.0865804 | + | 0.996245i | \(0.527594\pi\) | |||||||
\(32\) | −5.75724 | −1.01775 | ||||||||
\(33\) | 1.34266 | 0.233727 | ||||||||
\(34\) | 16.4205 | 2.81609 | ||||||||
\(35\) | −4.69013 | −0.792776 | ||||||||
\(36\) | 34.4710 | 5.74516 | ||||||||
\(37\) | 4.83938 | 0.795589 | 0.397794 | − | 0.917475i | \(-0.369776\pi\) | ||||
0.397794 | + | 0.917475i | \(0.369776\pi\) | |||||||
\(38\) | 17.3262 | 2.81068 | ||||||||
\(39\) | −19.5900 | −3.13691 | ||||||||
\(40\) | 8.34534 | 1.31951 | ||||||||
\(41\) | −8.99880 | −1.40538 | −0.702688 | − | 0.711498i | \(-0.748017\pi\) | ||||
−0.702688 | + | 0.711498i | \(0.748017\pi\) | |||||||
\(42\) | −29.8402 | −4.60445 | ||||||||
\(43\) | 9.23238 | 1.40792 | 0.703962 | − | 0.710237i | \(-0.251412\pi\) | ||||
0.703962 | + | 0.710237i | \(0.251412\pi\) | |||||||
\(44\) | 1.85141 | 0.279111 | ||||||||
\(45\) | −10.0186 | −1.49349 | ||||||||
\(46\) | −5.63846 | −0.831345 | ||||||||
\(47\) | −1.06569 | −0.155447 | −0.0777236 | − | 0.996975i | \(-0.524765\pi\) | ||||
−0.0777236 | + | 0.996975i | \(0.524765\pi\) | |||||||
\(48\) | 23.7044 | 3.42143 | ||||||||
\(49\) | 5.85076 | 0.835823 | ||||||||
\(50\) | 8.38444 | 1.18574 | ||||||||
\(51\) | −21.0235 | −2.94388 | ||||||||
\(52\) | −27.0129 | −3.74601 | ||||||||
\(53\) | −10.5409 | −1.44791 | −0.723954 | − | 0.689848i | \(-0.757677\pi\) | ||||
−0.723954 | + | 0.689848i | \(0.757677\pi\) | |||||||
\(54\) | −38.7698 | −5.27590 | ||||||||
\(55\) | −0.538094 | −0.0725565 | ||||||||
\(56\) | −22.8659 | −3.05558 | ||||||||
\(57\) | −22.1831 | −2.93822 | ||||||||
\(58\) | 25.0833 | 3.29360 | ||||||||
\(59\) | −11.4102 | −1.48549 | −0.742743 | − | 0.669577i | \(-0.766476\pi\) | ||||
−0.742743 | + | 0.669577i | \(0.766476\pi\) | |||||||
\(60\) | −19.2271 | −2.48221 | ||||||||
\(61\) | −11.8226 | −1.51373 | −0.756867 | − | 0.653569i | \(-0.773271\pi\) | ||||
−0.756867 | + | 0.653569i | \(0.773271\pi\) | |||||||
\(62\) | 2.45833 | 0.312208 | ||||||||
\(63\) | 27.4507 | 3.45846 | ||||||||
\(64\) | 0.157808 | 0.0197259 | ||||||||
\(65\) | 7.85102 | 0.973800 | ||||||||
\(66\) | −3.42354 | −0.421409 | ||||||||
\(67\) | 4.27373 | 0.522119 | 0.261059 | − | 0.965323i | \(-0.415928\pi\) | ||||
0.261059 | + | 0.965323i | \(0.415928\pi\) | |||||||
\(68\) | −28.9896 | −3.51550 | ||||||||
\(69\) | 7.21903 | 0.869070 | ||||||||
\(70\) | 11.9590 | 1.42937 | ||||||||
\(71\) | −1.28532 | −0.152539 | −0.0762695 | − | 0.997087i | \(-0.524301\pi\) | ||||
−0.0762695 | + | 0.997087i | \(0.524301\pi\) | |||||||
\(72\) | −48.8441 | −5.75634 | ||||||||
\(73\) | −2.34435 | −0.274386 | −0.137193 | − | 0.990544i | \(-0.543808\pi\) | ||||
−0.137193 | + | 0.990544i | \(0.543808\pi\) | |||||||
\(74\) | −12.3395 | −1.43444 | ||||||||
\(75\) | −10.7348 | −1.23954 | ||||||||
\(76\) | −30.5885 | −3.50874 | ||||||||
\(77\) | 1.47435 | 0.168018 | ||||||||
\(78\) | 49.9509 | 5.65583 | ||||||||
\(79\) | −0.336788 | −0.0378916 | −0.0189458 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189458 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(80\) | −9.49993 | −1.06212 | ||||||||
\(81\) | 26.6652 | 2.96280 | ||||||||
\(82\) | 22.9453 | 2.53389 | ||||||||
\(83\) | −1.65711 | −0.181892 | −0.0909460 | − | 0.995856i | \(-0.528989\pi\) | ||||
−0.0909460 | + | 0.995856i | \(0.528989\pi\) | |||||||
\(84\) | 52.6814 | 5.74802 | ||||||||
\(85\) | 8.42553 | 0.913877 | ||||||||
\(86\) | −23.5409 | −2.53848 | ||||||||
\(87\) | −32.1147 | −3.44306 | ||||||||
\(88\) | −2.62338 | −0.279653 | ||||||||
\(89\) | 10.6011 | 1.12371 | 0.561855 | − | 0.827236i | \(-0.310088\pi\) | ||||
0.561855 | + | 0.827236i | \(0.310088\pi\) | |||||||
\(90\) | 25.5457 | 2.69276 | ||||||||
\(91\) | −21.5115 | −2.25502 | ||||||||
\(92\) | 9.95442 | 1.03782 | ||||||||
\(93\) | −3.14745 | −0.326375 | ||||||||
\(94\) | 2.71732 | 0.280271 | ||||||||
\(95\) | 8.89024 | 0.912120 | ||||||||
\(96\) | −18.7950 | −1.91826 | ||||||||
\(97\) | 5.44847 | 0.553209 | 0.276604 | − | 0.960984i | \(-0.410791\pi\) | ||||
0.276604 | + | 0.960984i | \(0.410791\pi\) | |||||||
\(98\) | −14.9184 | −1.50698 | ||||||||
\(99\) | 3.14939 | 0.316525 | ||||||||
\(100\) | −14.8023 | −1.48023 | ||||||||
\(101\) | −11.1996 | −1.11440 | −0.557199 | − | 0.830379i | \(-0.688124\pi\) | ||||
−0.557199 | + | 0.830379i | \(0.688124\pi\) | |||||||
\(102\) | 53.6061 | 5.30780 | ||||||||
\(103\) | 4.75386 | 0.468412 | 0.234206 | − | 0.972187i | \(-0.424751\pi\) | ||||
0.234206 | + | 0.972187i | \(0.424751\pi\) | |||||||
\(104\) | 38.2763 | 3.75330 | ||||||||
\(105\) | −15.3113 | −1.49423 | ||||||||
\(106\) | 26.8775 | 2.61057 | ||||||||
\(107\) | −3.17007 | −0.306462 | −0.153231 | − | 0.988190i | \(-0.548968\pi\) | ||||
−0.153231 | + | 0.988190i | \(0.548968\pi\) | |||||||
\(108\) | 68.4461 | 6.58623 | ||||||||
\(109\) | 5.44427 | 0.521466 | 0.260733 | − | 0.965411i | \(-0.416036\pi\) | ||||
0.260733 | + | 0.965411i | \(0.416036\pi\) | |||||||
\(110\) | 1.37204 | 0.130819 | ||||||||
\(111\) | 15.7986 | 1.49953 | ||||||||
\(112\) | 26.0294 | 2.45955 | ||||||||
\(113\) | −2.45297 | −0.230756 | −0.115378 | − | 0.993322i | \(-0.536808\pi\) | ||||
−0.115378 | + | 0.993322i | \(0.536808\pi\) | |||||||
\(114\) | 56.5628 | 5.29759 | ||||||||
\(115\) | −2.89315 | −0.269788 | ||||||||
\(116\) | −44.2834 | −4.11161 | ||||||||
\(117\) | −45.9510 | −4.24817 | ||||||||
\(118\) | 29.0940 | 2.67832 | ||||||||
\(119\) | −23.0856 | −2.11625 | ||||||||
\(120\) | 27.2441 | 2.48703 | ||||||||
\(121\) | −10.8308 | −0.984623 | ||||||||
\(122\) | 30.1456 | 2.72925 | ||||||||
\(123\) | −29.3774 | −2.64887 | ||||||||
\(124\) | −4.34006 | −0.389749 | ||||||||
\(125\) | 10.8438 | 0.969903 | ||||||||
\(126\) | −69.9943 | −6.23559 | ||||||||
\(127\) | 6.94291 | 0.616084 | 0.308042 | − | 0.951373i | \(-0.400326\pi\) | ||||
0.308042 | + | 0.951373i | \(0.400326\pi\) | |||||||
\(128\) | 11.1121 | 0.982181 | ||||||||
\(129\) | 30.1399 | 2.65367 | ||||||||
\(130\) | −20.0187 | −1.75576 | ||||||||
\(131\) | −6.65546 | −0.581490 | −0.290745 | − | 0.956801i | \(-0.593903\pi\) | ||||
−0.290745 | + | 0.956801i | \(0.593903\pi\) | |||||||
\(132\) | 6.04409 | 0.526070 | ||||||||
\(133\) | −24.3589 | −2.11218 | ||||||||
\(134\) | −10.8972 | −0.941378 | ||||||||
\(135\) | −19.8932 | −1.71213 | ||||||||
\(136\) | 41.0772 | 3.52234 | ||||||||
\(137\) | 17.1113 | 1.46192 | 0.730958 | − | 0.682422i | \(-0.239073\pi\) | ||||
0.730958 | + | 0.682422i | \(0.239073\pi\) | |||||||
\(138\) | −18.4072 | −1.56693 | ||||||||
\(139\) | 9.05478 | 0.768016 | 0.384008 | − | 0.923330i | \(-0.374543\pi\) | ||||
0.384008 | + | 0.923330i | \(0.374543\pi\) | |||||||
\(140\) | −21.1130 | −1.78437 | ||||||||
\(141\) | −3.47905 | −0.292989 | ||||||||
\(142\) | 3.27732 | 0.275027 | ||||||||
\(143\) | −2.46799 | −0.206384 | ||||||||
\(144\) | 55.6018 | 4.63348 | ||||||||
\(145\) | 12.8705 | 1.06884 | ||||||||
\(146\) | 5.97768 | 0.494716 | ||||||||
\(147\) | 19.1003 | 1.57537 | ||||||||
\(148\) | 21.7848 | 1.79070 | ||||||||
\(149\) | 10.1611 | 0.832429 | 0.416215 | − | 0.909266i | \(-0.363356\pi\) | ||||
0.416215 | + | 0.909266i | \(0.363356\pi\) | |||||||
\(150\) | 27.3717 | 2.23489 | ||||||||
\(151\) | 10.9212 | 0.888759 | 0.444379 | − | 0.895839i | \(-0.353424\pi\) | ||||
0.444379 | + | 0.895839i | \(0.353424\pi\) | |||||||
\(152\) | 43.3428 | 3.51557 | ||||||||
\(153\) | −49.3134 | −3.98676 | ||||||||
\(154\) | −3.75934 | −0.302936 | ||||||||
\(155\) | 1.26139 | 0.101318 | ||||||||
\(156\) | −88.1859 | −7.06052 | ||||||||
\(157\) | −15.8883 | −1.26802 | −0.634011 | − | 0.773324i | \(-0.718593\pi\) | ||||
−0.634011 | + | 0.773324i | \(0.718593\pi\) | |||||||
\(158\) | 0.858748 | 0.0683183 | ||||||||
\(159\) | −34.4118 | −2.72903 | ||||||||
\(160\) | 7.53243 | 0.595491 | ||||||||
\(161\) | 7.92712 | 0.624744 | ||||||||
\(162\) | −67.9913 | −5.34190 | ||||||||
\(163\) | −13.7364 | −1.07592 | −0.537958 | − | 0.842971i | \(-0.680804\pi\) | ||||
−0.537958 | + | 0.842971i | \(0.680804\pi\) | |||||||
\(164\) | −40.5088 | −3.16321 | ||||||||
\(165\) | −1.75665 | −0.136755 | ||||||||
\(166\) | 4.22534 | 0.327950 | ||||||||
\(167\) | −1.80503 | −0.139677 | −0.0698386 | − | 0.997558i | \(-0.522248\pi\) | ||||
−0.0698386 | + | 0.997558i | \(0.522248\pi\) | |||||||
\(168\) | −74.6477 | −5.75920 | ||||||||
\(169\) | 23.0091 | 1.76993 | ||||||||
\(170\) | −21.4836 | −1.64771 | ||||||||
\(171\) | −52.0334 | −3.97909 | ||||||||
\(172\) | 41.5603 | 3.16894 | ||||||||
\(173\) | −3.27531 | −0.249017 | −0.124509 | − | 0.992219i | \(-0.539735\pi\) | ||||
−0.124509 | + | 0.992219i | \(0.539735\pi\) | |||||||
\(174\) | 81.8867 | 6.20782 | ||||||||
\(175\) | −11.7877 | −0.891066 | ||||||||
\(176\) | 2.98633 | 0.225103 | ||||||||
\(177\) | −37.2497 | −2.79986 | ||||||||
\(178\) | −27.0308 | −2.02604 | ||||||||
\(179\) | 13.0586 | 0.976045 | 0.488022 | − | 0.872831i | \(-0.337718\pi\) | ||||
0.488022 | + | 0.872831i | \(0.337718\pi\) | |||||||
\(180\) | −45.0997 | −3.36154 | ||||||||
\(181\) | −11.8647 | −0.881893 | −0.440947 | − | 0.897533i | \(-0.645357\pi\) | ||||
−0.440947 | + | 0.897533i | \(0.645357\pi\) | |||||||
\(182\) | 54.8504 | 4.06578 | ||||||||
\(183\) | −38.5960 | −2.85310 | ||||||||
\(184\) | −14.1051 | −1.03984 | ||||||||
\(185\) | −6.33155 | −0.465505 | ||||||||
\(186\) | 8.02543 | 0.588453 | ||||||||
\(187\) | −2.64859 | −0.193684 | ||||||||
\(188\) | −4.79730 | −0.349879 | ||||||||
\(189\) | 54.5065 | 3.96476 | ||||||||
\(190\) | −22.6685 | −1.64455 | ||||||||
\(191\) | 11.9273 | 0.863029 | 0.431514 | − | 0.902106i | \(-0.357979\pi\) | ||||
0.431514 | + | 0.902106i | \(0.357979\pi\) | |||||||
\(192\) | 0.515177 | 0.0371797 | ||||||||
\(193\) | 17.4408 | 1.25542 | 0.627710 | − | 0.778447i | \(-0.283992\pi\) | ||||
0.627710 | + | 0.778447i | \(0.283992\pi\) | |||||||
\(194\) | −13.8926 | −0.997432 | ||||||||
\(195\) | 25.6303 | 1.83543 | ||||||||
\(196\) | 26.3377 | 1.88126 | ||||||||
\(197\) | −22.5623 | −1.60749 | −0.803747 | − | 0.594971i | \(-0.797163\pi\) | ||||
−0.803747 | + | 0.594971i | \(0.797163\pi\) | |||||||
\(198\) | −8.03037 | −0.570694 | ||||||||
\(199\) | 19.7135 | 1.39745 | 0.698726 | − | 0.715389i | \(-0.253751\pi\) | ||||
0.698726 | + | 0.715389i | \(0.253751\pi\) | |||||||
\(200\) | 20.9743 | 1.48311 | ||||||||
\(201\) | 13.9520 | 0.984095 | ||||||||
\(202\) | 28.5569 | 2.00925 | ||||||||
\(203\) | −35.2647 | −2.47510 | ||||||||
\(204\) | −94.6390 | −6.62605 | ||||||||
\(205\) | 11.7735 | 0.822296 | ||||||||
\(206\) | −12.1215 | −0.844544 | ||||||||
\(207\) | 16.9332 | 1.17694 | ||||||||
\(208\) | −43.5719 | −3.02116 | ||||||||
\(209\) | −2.79467 | −0.193312 | ||||||||
\(210\) | 39.0411 | 2.69409 | ||||||||
\(211\) | 1.48029 | 0.101907 | 0.0509536 | − | 0.998701i | \(-0.483774\pi\) | ||||
0.0509536 | + | 0.998701i | \(0.483774\pi\) | |||||||
\(212\) | −47.4508 | −3.25894 | ||||||||
\(213\) | −4.19603 | −0.287507 | ||||||||
\(214\) | 8.08310 | 0.552549 | ||||||||
\(215\) | −12.0791 | −0.823787 | ||||||||
\(216\) | −96.9857 | −6.59904 | ||||||||
\(217\) | −3.45617 | −0.234620 | ||||||||
\(218\) | −13.8819 | −0.940201 | ||||||||
\(219\) | −7.65335 | −0.517165 | ||||||||
\(220\) | −2.42227 | −0.163310 | ||||||||
\(221\) | 38.6441 | 2.59948 | ||||||||
\(222\) | −40.2835 | −2.70365 | ||||||||
\(223\) | 26.7924 | 1.79415 | 0.897076 | − | 0.441876i | \(-0.145687\pi\) | ||||
0.897076 | + | 0.441876i | \(0.145687\pi\) | |||||||
\(224\) | −20.6385 | −1.37897 | ||||||||
\(225\) | −25.1799 | −1.67866 | ||||||||
\(226\) | 6.25463 | 0.416052 | ||||||||
\(227\) | −4.25407 | −0.282353 | −0.141176 | − | 0.989984i | \(-0.545088\pi\) | ||||
−0.141176 | + | 0.989984i | \(0.545088\pi\) | |||||||
\(228\) | −99.8588 | −6.61331 | ||||||||
\(229\) | 18.4264 | 1.21765 | 0.608824 | − | 0.793305i | \(-0.291641\pi\) | ||||
0.608824 | + | 0.793305i | \(0.291641\pi\) | |||||||
\(230\) | 7.37701 | 0.486426 | ||||||||
\(231\) | 4.81316 | 0.316683 | ||||||||
\(232\) | 62.7480 | 4.11960 | ||||||||
\(233\) | 17.6588 | 1.15687 | 0.578433 | − | 0.815730i | \(-0.303664\pi\) | ||||
0.578433 | + | 0.815730i | \(0.303664\pi\) | |||||||
\(234\) | 117.167 | 7.65942 | ||||||||
\(235\) | 1.39429 | 0.0909533 | ||||||||
\(236\) | −51.3641 | −3.34352 | ||||||||
\(237\) | −1.09947 | −0.0714184 | ||||||||
\(238\) | 58.8641 | 3.81559 | ||||||||
\(239\) | 19.5435 | 1.26416 | 0.632081 | − | 0.774903i | \(-0.282201\pi\) | ||||
0.632081 | + | 0.774903i | \(0.282201\pi\) | |||||||
\(240\) | −31.0134 | −2.00190 | ||||||||
\(241\) | 21.1757 | 1.36405 | 0.682024 | − | 0.731330i | \(-0.261100\pi\) | ||||
0.682024 | + | 0.731330i | \(0.261100\pi\) | |||||||
\(242\) | 27.6167 | 1.77527 | ||||||||
\(243\) | 41.4360 | 2.65812 | ||||||||
\(244\) | −53.2205 | −3.40710 | ||||||||
\(245\) | −7.65478 | −0.489046 | ||||||||
\(246\) | 74.9070 | 4.77589 | ||||||||
\(247\) | 40.7755 | 2.59448 | ||||||||
\(248\) | 6.14970 | 0.390507 | ||||||||
\(249\) | −5.40980 | −0.342832 | ||||||||
\(250\) | −27.6498 | −1.74873 | ||||||||
\(251\) | −1.43428 | −0.0905311 | −0.0452656 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452656 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(252\) | 123.571 | 7.78427 | ||||||||
\(253\) | 0.909470 | 0.0571779 | ||||||||
\(254\) | −17.7032 | −1.11080 | ||||||||
\(255\) | 27.5059 | 1.72248 | ||||||||
\(256\) | −28.6495 | −1.79059 | ||||||||
\(257\) | −23.2274 | −1.44888 | −0.724442 | − | 0.689336i | \(-0.757903\pi\) | ||||
−0.724442 | + | 0.689336i | \(0.757903\pi\) | |||||||
\(258\) | −76.8513 | −4.78456 | ||||||||
\(259\) | 17.3482 | 1.07796 | ||||||||
\(260\) | 35.3420 | 2.19182 | ||||||||
\(261\) | −75.3294 | −4.66277 | ||||||||
\(262\) | 16.9702 | 1.04842 | ||||||||
\(263\) | 18.5577 | 1.14432 | 0.572158 | − | 0.820144i | \(-0.306107\pi\) | ||||
0.572158 | + | 0.820144i | \(0.306107\pi\) | |||||||
\(264\) | −8.56426 | −0.527094 | ||||||||
\(265\) | 13.7911 | 0.847181 | ||||||||
\(266\) | 62.1108 | 3.80826 | ||||||||
\(267\) | 34.6081 | 2.11798 | ||||||||
\(268\) | 19.2385 | 1.17518 | ||||||||
\(269\) | −8.08164 | −0.492746 | −0.246373 | − | 0.969175i | \(-0.579239\pi\) | ||||
−0.246373 | + | 0.969175i | \(0.579239\pi\) | |||||||
\(270\) | 50.7240 | 3.08696 | ||||||||
\(271\) | −4.84411 | −0.294258 | −0.147129 | − | 0.989117i | \(-0.547003\pi\) | ||||
−0.147129 | + | 0.989117i | \(0.547003\pi\) | |||||||
\(272\) | −46.7603 | −2.83526 | ||||||||
\(273\) | −70.2261 | −4.25028 | ||||||||
\(274\) | −43.6307 | −2.63583 | ||||||||
\(275\) | −1.35239 | −0.0815522 | ||||||||
\(276\) | 32.4971 | 1.95609 | ||||||||
\(277\) | −17.6155 | −1.05841 | −0.529207 | − | 0.848493i | \(-0.677511\pi\) | ||||
−0.529207 | + | 0.848493i | \(0.677511\pi\) | |||||||
\(278\) | −23.0880 | −1.38473 | ||||||||
\(279\) | −7.38276 | −0.441995 | ||||||||
\(280\) | 29.9163 | 1.78784 | ||||||||
\(281\) | 31.7310 | 1.89291 | 0.946456 | − | 0.322833i | \(-0.104635\pi\) | ||||
0.946456 | + | 0.322833i | \(0.104635\pi\) | |||||||
\(282\) | 8.87094 | 0.528257 | ||||||||
\(283\) | 8.20055 | 0.487472 | 0.243736 | − | 0.969842i | \(-0.421627\pi\) | ||||
0.243736 | + | 0.969842i | \(0.421627\pi\) | |||||||
\(284\) | −5.78595 | −0.343333 | ||||||||
\(285\) | 29.0230 | 1.71917 | ||||||||
\(286\) | 6.29293 | 0.372109 | ||||||||
\(287\) | −32.2589 | −1.90418 | ||||||||
\(288\) | −44.0863 | −2.59781 | ||||||||
\(289\) | 24.4719 | 1.43952 | ||||||||
\(290\) | −32.8175 | −1.92711 | ||||||||
\(291\) | 17.7870 | 1.04269 | ||||||||
\(292\) | −10.5533 | −0.617585 | ||||||||
\(293\) | −19.9298 | −1.16431 | −0.582157 | − | 0.813077i | \(-0.697791\pi\) | ||||
−0.582157 | + | 0.813077i | \(0.697791\pi\) | |||||||
\(294\) | −48.7024 | −2.84038 | ||||||||
\(295\) | 14.9285 | 0.869168 | ||||||||
\(296\) | −30.8683 | −1.79419 | ||||||||
\(297\) | 6.25347 | 0.362863 | ||||||||
\(298\) | −25.9090 | −1.50087 | ||||||||
\(299\) | −13.2696 | −0.767399 | ||||||||
\(300\) | −48.3234 | −2.78996 | ||||||||
\(301\) | 33.0962 | 1.90763 | ||||||||
\(302\) | −27.8472 | −1.60243 | ||||||||
\(303\) | −36.5620 | −2.10043 | ||||||||
\(304\) | −49.3394 | −2.82981 | ||||||||
\(305\) | 15.4680 | 0.885696 | ||||||||
\(306\) | 125.740 | 7.18810 | ||||||||
\(307\) | −14.2019 | −0.810545 | −0.405272 | − | 0.914196i | \(-0.632823\pi\) | ||||
−0.405272 | + | 0.914196i | \(0.632823\pi\) | |||||||
\(308\) | 6.63693 | 0.378174 | ||||||||
\(309\) | 15.5194 | 0.882867 | ||||||||
\(310\) | −3.21633 | −0.182675 | ||||||||
\(311\) | −21.6827 | −1.22952 | −0.614758 | − | 0.788716i | \(-0.710746\pi\) | ||||
−0.614758 | + | 0.788716i | \(0.710746\pi\) | |||||||
\(312\) | 124.956 | 7.07425 | ||||||||
\(313\) | −13.8563 | −0.783205 | −0.391603 | − | 0.920134i | \(-0.628079\pi\) | ||||
−0.391603 | + | 0.920134i | \(0.628079\pi\) | |||||||
\(314\) | 40.5122 | 2.28624 | ||||||||
\(315\) | −35.9148 | −2.02357 | ||||||||
\(316\) | −1.51608 | −0.0852860 | ||||||||
\(317\) | 9.68610 | 0.544025 | 0.272013 | − | 0.962294i | \(-0.412311\pi\) | ||||
0.272013 | + | 0.962294i | \(0.412311\pi\) | |||||||
\(318\) | 87.7438 | 4.92043 | ||||||||
\(319\) | −4.04588 | −0.226526 | ||||||||
\(320\) | −0.206466 | −0.0115418 | ||||||||
\(321\) | −10.3490 | −0.577623 | ||||||||
\(322\) | −20.2127 | −1.12641 | ||||||||
\(323\) | 43.7593 | 2.43483 | ||||||||
\(324\) | 120.035 | 6.66863 | ||||||||
\(325\) | 19.7320 | 1.09453 | ||||||||
\(326\) | 35.0253 | 1.93987 | ||||||||
\(327\) | 17.7733 | 0.982865 | ||||||||
\(328\) | 57.3995 | 3.16936 | ||||||||
\(329\) | −3.82029 | −0.210619 | ||||||||
\(330\) | 4.47915 | 0.246569 | ||||||||
\(331\) | 11.6817 | 0.642085 | 0.321042 | − | 0.947065i | \(-0.395967\pi\) | ||||
0.321042 | + | 0.947065i | \(0.395967\pi\) | |||||||
\(332\) | −7.45964 | −0.409401 | ||||||||
\(333\) | 37.0577 | 2.03075 | ||||||||
\(334\) | 4.60249 | 0.251837 | ||||||||
\(335\) | −5.59148 | −0.305495 | ||||||||
\(336\) | 84.9753 | 4.63578 | ||||||||
\(337\) | 35.1362 | 1.91399 | 0.956996 | − | 0.290101i | \(-0.0936888\pi\) | ||||
0.956996 | + | 0.290101i | \(0.0936888\pi\) | |||||||
\(338\) | −58.6690 | −3.19117 | ||||||||
\(339\) | −8.00793 | −0.434931 | ||||||||
\(340\) | 37.9282 | 2.05694 | ||||||||
\(341\) | −0.396523 | −0.0214729 | ||||||||
\(342\) | 132.676 | 7.17428 | ||||||||
\(343\) | −4.11979 | −0.222448 | ||||||||
\(344\) | −58.8895 | −3.17511 | ||||||||
\(345\) | −9.44495 | −0.508499 | ||||||||
\(346\) | 8.35145 | 0.448977 | ||||||||
\(347\) | 6.39188 | 0.343134 | 0.171567 | − | 0.985172i | \(-0.445117\pi\) | ||||
0.171567 | + | 0.985172i | \(0.445117\pi\) | |||||||
\(348\) | −144.567 | −7.74960 | ||||||||
\(349\) | −19.9636 | −1.06863 | −0.534313 | − | 0.845286i | \(-0.679430\pi\) | ||||
−0.534313 | + | 0.845286i | \(0.679430\pi\) | |||||||
\(350\) | 30.0565 | 1.60659 | ||||||||
\(351\) | −91.2409 | −4.87008 | ||||||||
\(352\) | −2.36784 | −0.126206 | ||||||||
\(353\) | −2.29044 | −0.121908 | −0.0609538 | − | 0.998141i | \(-0.519414\pi\) | ||||
−0.0609538 | + | 0.998141i | \(0.519414\pi\) | |||||||
\(354\) | 94.9800 | 5.04813 | ||||||||
\(355\) | 1.68163 | 0.0892516 | ||||||||
\(356\) | 47.7215 | 2.52924 | ||||||||
\(357\) | −75.3650 | −3.98874 | ||||||||
\(358\) | −33.2971 | −1.75980 | ||||||||
\(359\) | −10.0595 | −0.530920 | −0.265460 | − | 0.964122i | \(-0.585524\pi\) | ||||
−0.265460 | + | 0.964122i | \(0.585524\pi\) | |||||||
\(360\) | 63.9047 | 3.36807 | ||||||||
\(361\) | 27.1728 | 1.43015 | ||||||||
\(362\) | 30.2528 | 1.59005 | ||||||||
\(363\) | −35.3582 | −1.85583 | ||||||||
\(364\) | −96.8357 | −5.07557 | ||||||||
\(365\) | 3.06721 | 0.160545 | ||||||||
\(366\) | 98.4129 | 5.14412 | ||||||||
\(367\) | −28.6183 | −1.49386 | −0.746931 | − | 0.664902i | \(-0.768473\pi\) | ||||
−0.746931 | + | 0.664902i | \(0.768473\pi\) | |||||||
\(368\) | 16.0565 | 0.837003 | ||||||||
\(369\) | −68.9086 | −3.58724 | ||||||||
\(370\) | 16.1443 | 0.839302 | ||||||||
\(371\) | −37.7871 | −1.96181 | ||||||||
\(372\) | −14.1685 | −0.734602 | ||||||||
\(373\) | 0.0767872 | 0.00397589 | 0.00198795 | − | 0.999998i | \(-0.499367\pi\) | ||||
0.00198795 | + | 0.999998i | \(0.499367\pi\) | |||||||
\(374\) | 6.75342 | 0.349211 | ||||||||
\(375\) | 35.4007 | 1.82808 | ||||||||
\(376\) | 6.79760 | 0.350560 | ||||||||
\(377\) | 59.0312 | 3.04026 | ||||||||
\(378\) | −138.982 | −7.14845 | ||||||||
\(379\) | −16.5756 | −0.851431 | −0.425715 | − | 0.904857i | \(-0.639978\pi\) | ||||
−0.425715 | + | 0.904857i | \(0.639978\pi\) | |||||||
\(380\) | 40.0201 | 2.05299 | ||||||||
\(381\) | 22.6657 | 1.16120 | ||||||||
\(382\) | −30.4124 | −1.55604 | ||||||||
\(383\) | −9.53902 | −0.487421 | −0.243711 | − | 0.969848i | \(-0.578365\pi\) | ||||
−0.243711 | + | 0.969848i | \(0.578365\pi\) | |||||||
\(384\) | 36.2764 | 1.85122 | ||||||||
\(385\) | −1.92896 | −0.0983087 | ||||||||
\(386\) | −44.4710 | −2.26351 | ||||||||
\(387\) | 70.6972 | 3.59374 | ||||||||
\(388\) | 24.5267 | 1.24516 | ||||||||
\(389\) | −12.1337 | −0.615203 | −0.307601 | − | 0.951515i | \(-0.599526\pi\) | ||||
−0.307601 | + | 0.951515i | \(0.599526\pi\) | |||||||
\(390\) | −65.3528 | −3.30927 | ||||||||
\(391\) | −14.2406 | −0.720177 | ||||||||
\(392\) | −37.3195 | −1.88492 | ||||||||
\(393\) | −21.7273 | −1.09600 | ||||||||
\(394\) | 57.5297 | 2.89830 | ||||||||
\(395\) | 0.440632 | 0.0221706 | ||||||||
\(396\) | 14.1772 | 0.712432 | ||||||||
\(397\) | −8.36633 | −0.419894 | −0.209947 | − | 0.977713i | \(-0.567329\pi\) | ||||
−0.209947 | + | 0.977713i | \(0.567329\pi\) | |||||||
\(398\) | −50.2658 | −2.51960 | ||||||||
\(399\) | −79.5218 | −3.98107 | ||||||||
\(400\) | −23.8762 | −1.19381 | ||||||||
\(401\) | −22.0525 | −1.10125 | −0.550625 | − | 0.834752i | \(-0.685611\pi\) | ||||
−0.550625 | + | 0.834752i | \(0.685611\pi\) | |||||||
\(402\) | −35.5750 | −1.77432 | ||||||||
\(403\) | 5.78544 | 0.288193 | ||||||||
\(404\) | −50.4157 | −2.50828 | ||||||||
\(405\) | −34.8871 | −1.73355 | ||||||||
\(406\) | 89.9186 | 4.46259 | ||||||||
\(407\) | 1.99034 | 0.0986575 | ||||||||
\(408\) | 134.100 | 6.63894 | ||||||||
\(409\) | −14.6263 | −0.723222 | −0.361611 | − | 0.932329i | \(-0.617773\pi\) | ||||
−0.361611 | + | 0.932329i | \(0.617773\pi\) | |||||||
\(410\) | −30.0203 | −1.48259 | ||||||||
\(411\) | 55.8613 | 2.75544 | ||||||||
\(412\) | 21.3999 | 1.05430 | ||||||||
\(413\) | −40.9034 | −2.01272 | ||||||||
\(414\) | −43.1766 | −2.12202 | ||||||||
\(415\) | 2.16807 | 0.106426 | ||||||||
\(416\) | 34.5478 | 1.69385 | ||||||||
\(417\) | 29.5601 | 1.44756 | ||||||||
\(418\) | 7.12591 | 0.348540 | ||||||||
\(419\) | −19.6119 | −0.958104 | −0.479052 | − | 0.877787i | \(-0.659019\pi\) | ||||
−0.479052 | + | 0.877787i | \(0.659019\pi\) | |||||||
\(420\) | −68.9252 | −3.36320 | ||||||||
\(421\) | 20.4536 | 0.996849 | 0.498424 | − | 0.866933i | \(-0.333912\pi\) | ||||
0.498424 | + | 0.866933i | \(0.333912\pi\) | |||||||
\(422\) | −3.77447 | −0.183738 | ||||||||
\(423\) | −8.16057 | −0.396781 | ||||||||
\(424\) | 67.2361 | 3.26527 | ||||||||
\(425\) | 21.1759 | 1.02718 | ||||||||
\(426\) | 10.6991 | 0.518373 | ||||||||
\(427\) | −42.3817 | −2.05100 | ||||||||
\(428\) | −14.2703 | −0.689781 | ||||||||
\(429\) | −8.05697 | −0.388994 | ||||||||
\(430\) | 30.7995 | 1.48528 | ||||||||
\(431\) | 26.9400 | 1.29765 | 0.648827 | − | 0.760936i | \(-0.275260\pi\) | ||||
0.648827 | + | 0.760936i | \(0.275260\pi\) | |||||||
\(432\) | 110.404 | 5.31180 | ||||||||
\(433\) | 11.3900 | 0.547370 | 0.273685 | − | 0.961819i | \(-0.411757\pi\) | ||||
0.273685 | + | 0.961819i | \(0.411757\pi\) | |||||||
\(434\) | 8.81260 | 0.423019 | ||||||||
\(435\) | 42.0169 | 2.01456 | ||||||||
\(436\) | 24.5078 | 1.17371 | ||||||||
\(437\) | −15.0260 | −0.718792 | ||||||||
\(438\) | 19.5147 | 0.932446 | ||||||||
\(439\) | 31.2537 | 1.49166 | 0.745829 | − | 0.666138i | \(-0.232054\pi\) | ||||
0.745829 | + | 0.666138i | \(0.232054\pi\) | |||||||
\(440\) | 3.43227 | 0.163627 | ||||||||
\(441\) | 44.8024 | 2.13345 | ||||||||
\(442\) | −98.5354 | −4.68685 | ||||||||
\(443\) | −9.11996 | −0.433302 | −0.216651 | − | 0.976249i | \(-0.569513\pi\) | ||||
−0.216651 | + | 0.976249i | \(0.569513\pi\) | |||||||
\(444\) | 71.1185 | 3.37514 | ||||||||
\(445\) | −13.8698 | −0.657491 | ||||||||
\(446\) | −68.3158 | −3.23485 | ||||||||
\(447\) | 33.1718 | 1.56897 | ||||||||
\(448\) | 0.565708 | 0.0267272 | ||||||||
\(449\) | −0.313559 | −0.0147978 | −0.00739888 | − | 0.999973i | \(-0.502355\pi\) | ||||
−0.00739888 | + | 0.999973i | \(0.502355\pi\) | |||||||
\(450\) | 64.2041 | 3.02661 | ||||||||
\(451\) | −3.70103 | −0.174275 | ||||||||
\(452\) | −11.0422 | −0.519383 | ||||||||
\(453\) | 35.6534 | 1.67514 | ||||||||
\(454\) | 10.8471 | 0.509080 | ||||||||
\(455\) | 28.1443 | 1.31943 | ||||||||
\(456\) | 141.496 | 6.62618 | ||||||||
\(457\) | −32.1299 | −1.50297 | −0.751487 | − | 0.659748i | \(-0.770663\pi\) | ||||
−0.751487 | + | 0.659748i | \(0.770663\pi\) | |||||||
\(458\) | −46.9839 | −2.19541 | ||||||||
\(459\) | −97.9175 | −4.57040 | ||||||||
\(460\) | −13.0238 | −0.607236 | ||||||||
\(461\) | 32.3718 | 1.50771 | 0.753853 | − | 0.657043i | \(-0.228193\pi\) | ||||
0.753853 | + | 0.657043i | \(0.228193\pi\) | |||||||
\(462\) | −12.2727 | −0.570977 | ||||||||
\(463\) | −31.9572 | −1.48517 | −0.742587 | − | 0.669749i | \(-0.766402\pi\) | ||||
−0.742587 | + | 0.669749i | \(0.766402\pi\) | |||||||
\(464\) | −71.4292 | −3.31602 | ||||||||
\(465\) | 4.11793 | 0.190964 | ||||||||
\(466\) | −45.0268 | −2.08582 | ||||||||
\(467\) | 6.17443 | 0.285719 | 0.142859 | − | 0.989743i | \(-0.454370\pi\) | ||||
0.142859 | + | 0.989743i | \(0.454370\pi\) | |||||||
\(468\) | −206.852 | −9.56173 | ||||||||
\(469\) | 15.3204 | 0.707432 | ||||||||
\(470\) | −3.55518 | −0.163988 | ||||||||
\(471\) | −51.8687 | −2.38998 | ||||||||
\(472\) | 72.7811 | 3.35002 | ||||||||
\(473\) | 3.79709 | 0.174591 | ||||||||
\(474\) | 2.80346 | 0.128767 | ||||||||
\(475\) | 22.3438 | 1.02521 | ||||||||
\(476\) | −103.922 | −4.76324 | ||||||||
\(477\) | −80.7174 | −3.69580 | ||||||||
\(478\) | −49.8323 | −2.27928 | ||||||||
\(479\) | 5.68226 | 0.259629 | 0.129815 | − | 0.991538i | \(-0.458562\pi\) | ||||
0.129815 | + | 0.991538i | \(0.458562\pi\) | |||||||
\(480\) | 24.5903 | 1.12239 | ||||||||
\(481\) | −29.0399 | −1.32411 | ||||||||
\(482\) | −53.9942 | −2.45937 | ||||||||
\(483\) | 25.8788 | 1.17752 | ||||||||
\(484\) | −48.7559 | −2.21618 | ||||||||
\(485\) | −7.12845 | −0.323686 | ||||||||
\(486\) | −105.654 | −4.79258 | ||||||||
\(487\) | −21.8856 | −0.991731 | −0.495866 | − | 0.868399i | \(-0.665149\pi\) | ||||
−0.495866 | + | 0.868399i | \(0.665149\pi\) | |||||||
\(488\) | 75.4116 | 3.41372 | ||||||||
\(489\) | −44.8436 | −2.02790 | ||||||||
\(490\) | 19.5183 | 0.881747 | ||||||||
\(491\) | 35.9607 | 1.62289 | 0.811443 | − | 0.584432i | \(-0.198683\pi\) | ||||
0.811443 | + | 0.584432i | \(0.198683\pi\) | |||||||
\(492\) | −132.245 | −5.96205 | ||||||||
\(493\) | 63.3509 | 2.85318 | ||||||||
\(494\) | −103.970 | −4.67784 | ||||||||
\(495\) | −4.12047 | −0.185201 | ||||||||
\(496\) | −7.00052 | −0.314333 | ||||||||
\(497\) | −4.60759 | −0.206679 | ||||||||
\(498\) | 13.7940 | 0.618124 | ||||||||
\(499\) | −13.9074 | −0.622581 | −0.311291 | − | 0.950315i | \(-0.600761\pi\) | ||||
−0.311291 | + | 0.950315i | \(0.600761\pi\) | |||||||
\(500\) | 48.8144 | 2.18305 | ||||||||
\(501\) | −5.89267 | −0.263265 | ||||||||
\(502\) | 3.65716 | 0.163227 | ||||||||
\(503\) | −7.28881 | −0.324992 | −0.162496 | − | 0.986709i | \(-0.551954\pi\) | ||||
−0.162496 | + | 0.986709i | \(0.551954\pi\) | |||||||
\(504\) | −175.096 | −7.79941 | ||||||||
\(505\) | 14.6528 | 0.652042 | ||||||||
\(506\) | −2.31898 | −0.103091 | ||||||||
\(507\) | 75.1151 | 3.33598 | ||||||||
\(508\) | 31.2541 | 1.38668 | ||||||||
\(509\) | 3.05791 | 0.135540 | 0.0677698 | − | 0.997701i | \(-0.478412\pi\) | ||||
0.0677698 | + | 0.997701i | \(0.478412\pi\) | |||||||
\(510\) | −70.1350 | −3.10563 | ||||||||
\(511\) | −8.40403 | −0.371772 | ||||||||
\(512\) | 50.8268 | 2.24625 | ||||||||
\(513\) | −103.318 | −4.56161 | ||||||||
\(514\) | 59.2256 | 2.61233 | ||||||||
\(515\) | −6.21966 | −0.274071 | ||||||||
\(516\) | 135.677 | 5.97286 | ||||||||
\(517\) | −0.438298 | −0.0192763 | ||||||||
\(518\) | −44.2347 | −1.94356 | ||||||||
\(519\) | −10.6925 | −0.469350 | ||||||||
\(520\) | −50.0784 | −2.19608 | ||||||||
\(521\) | 22.3066 | 0.977272 | 0.488636 | − | 0.872488i | \(-0.337495\pi\) | ||||
0.488636 | + | 0.872488i | \(0.337495\pi\) | |||||||
\(522\) | 192.076 | 8.40695 | ||||||||
\(523\) | 16.8476 | 0.736693 | 0.368346 | − | 0.929689i | \(-0.379924\pi\) | ||||
0.368346 | + | 0.929689i | \(0.379924\pi\) | |||||||
\(524\) | −29.9601 | −1.30881 | ||||||||
\(525\) | −38.4820 | −1.67949 | ||||||||
\(526\) | −47.3187 | −2.06319 | ||||||||
\(527\) | 6.20879 | 0.270459 | ||||||||
\(528\) | 9.74913 | 0.424277 | ||||||||
\(529\) | −18.1101 | −0.787395 | ||||||||
\(530\) | −35.1648 | −1.52746 | ||||||||
\(531\) | −87.3742 | −3.79172 | ||||||||
\(532\) | −109.654 | −4.75408 | ||||||||
\(533\) | 53.9996 | 2.33898 | ||||||||
\(534\) | −88.2444 | −3.81871 | ||||||||
\(535\) | 4.14752 | 0.179313 | ||||||||
\(536\) | −27.2603 | −1.17747 | ||||||||
\(537\) | 42.6309 | 1.83966 | ||||||||
\(538\) | 20.6067 | 0.888419 | ||||||||
\(539\) | 2.40630 | 0.103647 | ||||||||
\(540\) | −89.5507 | −3.85365 | ||||||||
\(541\) | 4.11699 | 0.177003 | 0.0885016 | − | 0.996076i | \(-0.471792\pi\) | ||||
0.0885016 | + | 0.996076i | \(0.471792\pi\) | |||||||
\(542\) | 12.3516 | 0.530546 | ||||||||
\(543\) | −38.7332 | −1.66220 | ||||||||
\(544\) | 37.0759 | 1.58961 | ||||||||
\(545\) | −7.12295 | −0.305114 | ||||||||
\(546\) | 179.064 | 7.66323 | ||||||||
\(547\) | −22.7473 | −0.972606 | −0.486303 | − | 0.873790i | \(-0.661655\pi\) | ||||
−0.486303 | + | 0.873790i | \(0.661655\pi\) | |||||||
\(548\) | 77.0279 | 3.29047 | ||||||||
\(549\) | −90.5322 | −3.86382 | ||||||||
\(550\) | 3.44835 | 0.147038 | ||||||||
\(551\) | 66.8450 | 2.84769 | ||||||||
\(552\) | −46.0472 | −1.95990 | ||||||||
\(553\) | −1.20732 | −0.0513403 | ||||||||
\(554\) | 44.9164 | 1.90832 | ||||||||
\(555\) | −20.6699 | −0.877388 | ||||||||
\(556\) | 40.7608 | 1.72864 | ||||||||
\(557\) | −3.26824 | −0.138480 | −0.0692399 | − | 0.997600i | \(-0.522057\pi\) | ||||
−0.0692399 | + | 0.997600i | \(0.522057\pi\) | |||||||
\(558\) | 18.8247 | 0.796914 | ||||||||
\(559\) | −55.4013 | −2.34322 | ||||||||
\(560\) | −34.0553 | −1.43910 | ||||||||
\(561\) | −8.64655 | −0.365057 | ||||||||
\(562\) | −80.9083 | −3.41291 | ||||||||
\(563\) | −3.33565 | −0.140581 | −0.0702905 | − | 0.997527i | \(-0.522393\pi\) | ||||
−0.0702905 | + | 0.997527i | \(0.522393\pi\) | |||||||
\(564\) | −15.6612 | −0.659456 | ||||||||
\(565\) | 3.20931 | 0.135017 | ||||||||
\(566\) | −20.9099 | −0.878910 | ||||||||
\(567\) | 95.5891 | 4.01437 | ||||||||
\(568\) | 8.19849 | 0.344001 | ||||||||
\(569\) | −36.7685 | −1.54142 | −0.770709 | − | 0.637187i | \(-0.780098\pi\) | ||||
−0.770709 | + | 0.637187i | \(0.780098\pi\) | |||||||
\(570\) | −74.0033 | −3.09966 | ||||||||
\(571\) | −37.8739 | −1.58497 | −0.792487 | − | 0.609888i | \(-0.791214\pi\) | ||||
−0.792487 | + | 0.609888i | \(0.791214\pi\) | |||||||
\(572\) | −11.1099 | −0.464526 | ||||||||
\(573\) | 38.9377 | 1.62665 | ||||||||
\(574\) | 82.2543 | 3.43323 | ||||||||
\(575\) | −7.27136 | −0.303237 | ||||||||
\(576\) | 1.20842 | 0.0503507 | ||||||||
\(577\) | 3.73009 | 0.155286 | 0.0776429 | − | 0.996981i | \(-0.475261\pi\) | ||||
0.0776429 | + | 0.996981i | \(0.475261\pi\) | |||||||
\(578\) | −62.3988 | −2.59545 | ||||||||
\(579\) | 56.9372 | 2.36623 | ||||||||
\(580\) | 57.9377 | 2.40573 | ||||||||
\(581\) | −5.94042 | −0.246450 | ||||||||
\(582\) | −45.3537 | −1.87997 | ||||||||
\(583\) | −4.33527 | −0.179549 | ||||||||
\(584\) | 14.9536 | 0.618786 | ||||||||
\(585\) | 60.1194 | 2.48563 | ||||||||
\(586\) | 50.8175 | 2.09925 | ||||||||
\(587\) | −18.2255 | −0.752249 | −0.376124 | − | 0.926569i | \(-0.622743\pi\) | ||||
−0.376124 | + | 0.926569i | \(0.622743\pi\) | |||||||
\(588\) | 85.9816 | 3.54582 | ||||||||
\(589\) | 6.55124 | 0.269939 | ||||||||
\(590\) | −38.0649 | −1.56711 | ||||||||
\(591\) | −73.6564 | −3.02982 | ||||||||
\(592\) | 35.1390 | 1.44421 | ||||||||
\(593\) | −48.2860 | −1.98287 | −0.991435 | − | 0.130603i | \(-0.958309\pi\) | ||||
−0.991435 | + | 0.130603i | \(0.958309\pi\) | |||||||
\(594\) | −15.9452 | −0.654241 | ||||||||
\(595\) | 30.2038 | 1.23823 | ||||||||
\(596\) | 45.7410 | 1.87362 | ||||||||
\(597\) | 64.3564 | 2.63393 | ||||||||
\(598\) | 33.8350 | 1.38362 | ||||||||
\(599\) | −28.7434 | −1.17442 | −0.587211 | − | 0.809434i | \(-0.699774\pi\) | ||||
−0.587211 | + | 0.809434i | \(0.699774\pi\) | |||||||
\(600\) | 68.4726 | 2.79538 | ||||||||
\(601\) | −21.4289 | −0.874104 | −0.437052 | − | 0.899436i | \(-0.643977\pi\) | ||||
−0.437052 | + | 0.899436i | \(0.643977\pi\) | |||||||
\(602\) | −84.3893 | −3.43945 | ||||||||
\(603\) | 32.7262 | 1.33271 | ||||||||
\(604\) | 49.1629 | 2.00041 | ||||||||
\(605\) | 14.1704 | 0.576110 | ||||||||
\(606\) | 93.2264 | 3.78706 | ||||||||
\(607\) | −26.6178 | −1.08038 | −0.540192 | − | 0.841542i | \(-0.681648\pi\) | ||||
−0.540192 | + | 0.841542i | \(0.681648\pi\) | |||||||
\(608\) | 39.1208 | 1.58656 | ||||||||
\(609\) | −115.125 | −4.66509 | ||||||||
\(610\) | −39.4407 | −1.59691 | ||||||||
\(611\) | 6.39496 | 0.258712 | ||||||||
\(612\) | −221.988 | −8.97335 | ||||||||
\(613\) | −3.50119 | −0.141412 | −0.0707058 | − | 0.997497i | \(-0.522525\pi\) | ||||
−0.0707058 | + | 0.997497i | \(0.522525\pi\) | |||||||
\(614\) | 36.2123 | 1.46141 | ||||||||
\(615\) | 38.4356 | 1.54987 | ||||||||
\(616\) | −9.40429 | −0.378910 | ||||||||
\(617\) | −14.3979 | −0.579638 | −0.289819 | − | 0.957082i | \(-0.593595\pi\) | ||||
−0.289819 | + | 0.957082i | \(0.593595\pi\) | |||||||
\(618\) | −39.5716 | −1.59180 | ||||||||
\(619\) | 26.5743 | 1.06811 | 0.534055 | − | 0.845450i | \(-0.320668\pi\) | ||||
0.534055 | + | 0.845450i | \(0.320668\pi\) | |||||||
\(620\) | 5.67827 | 0.228045 | ||||||||
\(621\) | 33.6229 | 1.34924 | ||||||||
\(622\) | 55.2871 | 2.21681 | ||||||||
\(623\) | 38.0026 | 1.52254 | ||||||||
\(624\) | −142.244 | −5.69432 | ||||||||
\(625\) | 2.25382 | 0.0901529 | ||||||||
\(626\) | 35.3311 | 1.41212 | ||||||||
\(627\) | −9.12345 | −0.364356 | ||||||||
\(628\) | −71.5224 | −2.85405 | ||||||||
\(629\) | −31.1649 | −1.24263 | ||||||||
\(630\) | 91.5762 | 3.64849 | ||||||||
\(631\) | −44.2818 | −1.76283 | −0.881415 | − | 0.472342i | \(-0.843409\pi\) | ||||
−0.881415 | + | 0.472342i | \(0.843409\pi\) | |||||||
\(632\) | 2.14823 | 0.0854519 | ||||||||
\(633\) | 4.83253 | 0.192076 | ||||||||
\(634\) | −24.6978 | −0.980875 | ||||||||
\(635\) | −9.08368 | −0.360475 | ||||||||
\(636\) | −154.907 | −6.14248 | ||||||||
\(637\) | −35.1090 | −1.39107 | ||||||||
\(638\) | 10.3163 | 0.408425 | ||||||||
\(639\) | −9.84234 | −0.389357 | ||||||||
\(640\) | −14.5384 | −0.574681 | ||||||||
\(641\) | 39.5854 | 1.56353 | 0.781764 | − | 0.623575i | \(-0.214320\pi\) | ||||
0.781764 | + | 0.623575i | \(0.214320\pi\) | |||||||
\(642\) | 26.3880 | 1.04145 | ||||||||
\(643\) | −8.67869 | −0.342254 | −0.171127 | − | 0.985249i | \(-0.554741\pi\) | ||||
−0.171127 | + | 0.985249i | \(0.554741\pi\) | |||||||
\(644\) | 35.6846 | 1.40617 | ||||||||
\(645\) | −39.4332 | −1.55268 | ||||||||
\(646\) | −111.578 | −4.38999 | ||||||||
\(647\) | −14.4066 | −0.566382 | −0.283191 | − | 0.959064i | \(-0.591393\pi\) | ||||
−0.283191 | + | 0.959064i | \(0.591393\pi\) | |||||||
\(648\) | −170.086 | −6.68160 | ||||||||
\(649\) | −4.69280 | −0.184209 | ||||||||
\(650\) | −50.3130 | −1.97344 | ||||||||
\(651\) | −11.2830 | −0.442214 | ||||||||
\(652\) | −61.8355 | −2.42166 | ||||||||
\(653\) | 46.4250 | 1.81675 | 0.908374 | − | 0.418158i | \(-0.137324\pi\) | ||||
0.908374 | + | 0.418158i | \(0.137324\pi\) | |||||||
\(654\) | −45.3187 | −1.77210 | ||||||||
\(655\) | 8.70760 | 0.340234 | ||||||||
\(656\) | −65.3408 | −2.55113 | ||||||||
\(657\) | −17.9520 | −0.700372 | ||||||||
\(658\) | 9.74105 | 0.379746 | ||||||||
\(659\) | 5.30176 | 0.206527 | 0.103264 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103264 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(660\) | −7.90772 | −0.307808 | ||||||||
\(661\) | 47.3720 | 1.84256 | 0.921278 | − | 0.388904i | \(-0.127146\pi\) | ||||
0.921278 | + | 0.388904i | \(0.127146\pi\) | |||||||
\(662\) | −29.7862 | −1.15768 | ||||||||
\(663\) | 126.157 | 4.89953 | ||||||||
\(664\) | 10.5700 | 0.410197 | ||||||||
\(665\) | 31.8697 | 1.23585 | ||||||||
\(666\) | −94.4904 | −3.66143 | ||||||||
\(667\) | −21.7534 | −0.842294 | ||||||||
\(668\) | −8.12547 | −0.314384 | ||||||||
\(669\) | 87.4661 | 3.38164 | ||||||||
\(670\) | 14.2573 | 0.550807 | ||||||||
\(671\) | −4.86241 | −0.187711 | ||||||||
\(672\) | −67.3763 | −2.59910 | ||||||||
\(673\) | 10.4408 | 0.402464 | 0.201232 | − | 0.979544i | \(-0.435506\pi\) | ||||
0.201232 | + | 0.979544i | \(0.435506\pi\) | |||||||
\(674\) | −89.5910 | −3.45092 | ||||||||
\(675\) | −49.9975 | −1.92441 | ||||||||
\(676\) | 103.577 | 3.98374 | ||||||||
\(677\) | 1.68708 | 0.0648396 | 0.0324198 | − | 0.999474i | \(-0.489679\pi\) | ||||
0.0324198 | + | 0.999474i | \(0.489679\pi\) | |||||||
\(678\) | 20.4188 | 0.784178 | ||||||||
\(679\) | 19.5317 | 0.749557 | ||||||||
\(680\) | −53.7429 | −2.06095 | ||||||||
\(681\) | −13.8878 | −0.532181 | ||||||||
\(682\) | 1.01106 | 0.0387155 | ||||||||
\(683\) | −34.2998 | −1.31245 | −0.656223 | − | 0.754567i | \(-0.727847\pi\) | ||||
−0.656223 | + | 0.754567i | \(0.727847\pi\) | |||||||
\(684\) | −234.232 | −8.95610 | ||||||||
\(685\) | −22.3874 | −0.855378 | ||||||||
\(686\) | 10.5047 | 0.401072 | ||||||||
\(687\) | 60.1545 | 2.29504 | ||||||||
\(688\) | 67.0369 | 2.55576 | ||||||||
\(689\) | 63.2535 | 2.40977 | ||||||||
\(690\) | 24.0829 | 0.916821 | ||||||||
\(691\) | −11.7251 | −0.446046 | −0.223023 | − | 0.974813i | \(-0.571592\pi\) | ||||
−0.223023 | + | 0.974813i | \(0.571592\pi\) | |||||||
\(692\) | −14.7441 | −0.560485 | ||||||||
\(693\) | 11.2899 | 0.428868 | ||||||||
\(694\) | −16.2981 | −0.618669 | ||||||||
\(695\) | −11.8467 | −0.449372 | ||||||||
\(696\) | 204.846 | 7.76467 | ||||||||
\(697\) | 57.9511 | 2.19505 | ||||||||
\(698\) | 50.9036 | 1.92673 | ||||||||
\(699\) | 57.6487 | 2.18047 | ||||||||
\(700\) | −53.0633 | −2.00560 | ||||||||
\(701\) | −8.25435 | −0.311762 | −0.155881 | − | 0.987776i | \(-0.549822\pi\) | ||||
−0.155881 | + | 0.987776i | \(0.549822\pi\) | |||||||
\(702\) | 232.648 | 8.78073 | ||||||||
\(703\) | −32.8839 | −1.24024 | ||||||||
\(704\) | 0.0649031 | 0.00244613 | ||||||||
\(705\) | 4.55177 | 0.171430 | ||||||||
\(706\) | 5.84020 | 0.219799 | ||||||||
\(707\) | −40.1481 | −1.50993 | ||||||||
\(708\) | −167.683 | −6.30190 | ||||||||
\(709\) | −19.3772 | −0.727725 | −0.363863 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363863 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(710\) | −4.28785 | −0.160920 | ||||||||
\(711\) | −2.57896 | −0.0967186 | ||||||||
\(712\) | −67.6197 | −2.53415 | ||||||||
\(713\) | −2.13197 | −0.0798429 | ||||||||
\(714\) | 192.167 | 7.19167 | ||||||||
\(715\) | 3.22897 | 0.120757 | ||||||||
\(716\) | 58.7843 | 2.19687 | ||||||||
\(717\) | 63.8013 | 2.38270 | ||||||||
\(718\) | 25.6499 | 0.957247 | ||||||||
\(719\) | −37.2591 | −1.38953 | −0.694766 | − | 0.719236i | \(-0.744492\pi\) | ||||
−0.694766 | + | 0.719236i | \(0.744492\pi\) | |||||||
\(720\) | −72.7460 | −2.71108 | ||||||||
\(721\) | 17.0416 | 0.634663 | ||||||||
\(722\) | −69.2859 | −2.57855 | ||||||||
\(723\) | 69.1299 | 2.57097 | ||||||||
\(724\) | −53.4097 | −1.98496 | ||||||||
\(725\) | 32.3475 | 1.20136 | ||||||||
\(726\) | 90.1572 | 3.34605 | ||||||||
\(727\) | 11.1107 | 0.412073 | 0.206036 | − | 0.978544i | \(-0.433943\pi\) | ||||
0.206036 | + | 0.978544i | \(0.433943\pi\) | |||||||
\(728\) | 137.213 | 5.08544 | ||||||||
\(729\) | 55.2760 | 2.04726 | ||||||||
\(730\) | −7.82083 | −0.289462 | ||||||||
\(731\) | −59.4553 | −2.19903 | ||||||||
\(732\) | −173.743 | −6.42173 | ||||||||
\(733\) | −8.17948 | −0.302116 | −0.151058 | − | 0.988525i | \(-0.548268\pi\) | ||||
−0.151058 | + | 0.988525i | \(0.548268\pi\) | |||||||
\(734\) | 72.9714 | 2.69342 | ||||||||
\(735\) | −24.9897 | −0.921759 | ||||||||
\(736\) | −12.7311 | −0.469274 | ||||||||
\(737\) | 1.75770 | 0.0647457 | ||||||||
\(738\) | 175.704 | 6.46777 | ||||||||
\(739\) | 18.9959 | 0.698777 | 0.349389 | − | 0.936978i | \(-0.386389\pi\) | ||||
0.349389 | + | 0.936978i | \(0.386389\pi\) | |||||||
\(740\) | −28.5020 | −1.04775 | ||||||||
\(741\) | 133.115 | 4.89011 | ||||||||
\(742\) | 96.3502 | 3.53713 | ||||||||
\(743\) | 5.81776 | 0.213433 | 0.106716 | − | 0.994289i | \(-0.465966\pi\) | ||||
0.106716 | + | 0.994289i | \(0.465966\pi\) | |||||||
\(744\) | 20.0762 | 0.736031 | ||||||||
\(745\) | −13.2942 | −0.487060 | ||||||||
\(746\) | −0.195794 | −0.00716851 | ||||||||
\(747\) | −12.6894 | −0.464281 | ||||||||
\(748\) | −11.9228 | −0.435942 | ||||||||
\(749\) | −11.3640 | −0.415233 | ||||||||
\(750\) | −90.2653 | −3.29602 | ||||||||
\(751\) | −53.5728 | −1.95490 | −0.977450 | − | 0.211167i | \(-0.932273\pi\) | ||||
−0.977450 | + | 0.211167i | \(0.932273\pi\) | |||||||
\(752\) | −7.73806 | −0.282178 | ||||||||
\(753\) | −4.68234 | −0.170634 | ||||||||
\(754\) | −150.519 | −5.48158 | ||||||||
\(755\) | −14.2887 | −0.520019 | ||||||||
\(756\) | 245.365 | 8.92385 | ||||||||
\(757\) | −23.3108 | −0.847244 | −0.423622 | − | 0.905839i | \(-0.639242\pi\) | ||||
−0.423622 | + | 0.905839i | \(0.639242\pi\) | |||||||
\(758\) | 42.2648 | 1.53513 | ||||||||
\(759\) | 2.96904 | 0.107769 | ||||||||
\(760\) | −56.7071 | −2.05698 | ||||||||
\(761\) | 22.9700 | 0.832662 | 0.416331 | − | 0.909213i | \(-0.363316\pi\) | ||||
0.416331 | + | 0.909213i | \(0.363316\pi\) | |||||||
\(762\) | −57.7935 | −2.09364 | ||||||||
\(763\) | 19.5166 | 0.706548 | ||||||||
\(764\) | 53.6917 | 1.94250 | ||||||||
\(765\) | 64.5187 | 2.33268 | ||||||||
\(766\) | 24.3228 | 0.878818 | ||||||||
\(767\) | 68.4700 | 2.47231 | ||||||||
\(768\) | −93.5287 | −3.37493 | ||||||||
\(769\) | −1.93400 | −0.0697418 | −0.0348709 | − | 0.999392i | \(-0.511102\pi\) | ||||
−0.0348709 | + | 0.999392i | \(0.511102\pi\) | |||||||
\(770\) | 4.91849 | 0.177250 | ||||||||
\(771\) | −75.8278 | −2.73087 | ||||||||
\(772\) | 78.5114 | 2.82569 | ||||||||
\(773\) | 14.9331 | 0.537107 | 0.268553 | − | 0.963265i | \(-0.413454\pi\) | ||||
0.268553 | + | 0.963265i | \(0.413454\pi\) | |||||||
\(774\) | −180.265 | −6.47950 | ||||||||
\(775\) | 3.17026 | 0.113879 | ||||||||
\(776\) | −34.7535 | −1.24758 | ||||||||
\(777\) | 56.6347 | 2.03176 | ||||||||
\(778\) | 30.9387 | 1.10921 | ||||||||
\(779\) | 61.1474 | 2.19083 | ||||||||
\(780\) | 115.377 | 4.13116 | ||||||||
\(781\) | −0.528625 | −0.0189157 | ||||||||
\(782\) | 36.3109 | 1.29848 | ||||||||
\(783\) | −149.575 | −5.34538 | ||||||||
\(784\) | 42.4827 | 1.51724 | ||||||||
\(785\) | 20.7873 | 0.741929 | ||||||||
\(786\) | 55.4008 | 1.97608 | ||||||||
\(787\) | 10.8527 | 0.386858 | 0.193429 | − | 0.981114i | \(-0.438039\pi\) | ||||
0.193429 | + | 0.981114i | \(0.438039\pi\) | |||||||
\(788\) | −101.566 | −3.61813 | ||||||||
\(789\) | 60.5831 | 2.15682 | ||||||||
\(790\) | −1.12353 | −0.0399735 | ||||||||
\(791\) | −8.79339 | −0.312657 | ||||||||
\(792\) | −20.0886 | −0.713818 | ||||||||
\(793\) | 70.9447 | 2.51932 | ||||||||
\(794\) | 21.3326 | 0.757067 | ||||||||
\(795\) | 45.0223 | 1.59678 | ||||||||
\(796\) | 88.7418 | 3.14537 | ||||||||
\(797\) | −47.8515 | −1.69499 | −0.847494 | − | 0.530805i | \(-0.821890\pi\) | ||||
−0.847494 | + | 0.530805i | \(0.821890\pi\) | |||||||
\(798\) | 202.766 | 7.17784 | ||||||||
\(799\) | 6.86292 | 0.242793 | ||||||||
\(800\) | 18.9312 | 0.669321 | ||||||||
\(801\) | 81.1779 | 2.86828 | ||||||||
\(802\) | 56.2300 | 1.98555 | ||||||||
\(803\) | −0.964186 | −0.0340254 | ||||||||
\(804\) | 62.8058 | 2.21499 | ||||||||
\(805\) | −10.3714 | −0.365542 | ||||||||
\(806\) | −14.7518 | −0.519611 | ||||||||
\(807\) | −26.3832 | −0.928733 | ||||||||
\(808\) | 71.4373 | 2.51315 | ||||||||
\(809\) | 19.3790 | 0.681328 | 0.340664 | − | 0.940185i | \(-0.389348\pi\) | ||||
0.340664 | + | 0.940185i | \(0.389348\pi\) | |||||||
\(810\) | 88.9557 | 3.12559 | ||||||||
\(811\) | 25.9855 | 0.912476 | 0.456238 | − | 0.889858i | \(-0.349197\pi\) | ||||
0.456238 | + | 0.889858i | \(0.349197\pi\) | |||||||
\(812\) | −158.747 | −5.57092 | ||||||||
\(813\) | −15.8140 | −0.554621 | ||||||||
\(814\) | −5.07501 | −0.177879 | ||||||||
\(815\) | 17.9719 | 0.629527 | ||||||||
\(816\) | −152.653 | −5.34392 | ||||||||
\(817\) | −62.7346 | −2.19481 | ||||||||
\(818\) | 37.2943 | 1.30397 | ||||||||
\(819\) | −164.725 | −5.75595 | ||||||||
\(820\) | 52.9993 | 1.85081 | ||||||||
\(821\) | 20.6028 | 0.719041 | 0.359521 | − | 0.933137i | \(-0.382940\pi\) | ||||
0.359521 | + | 0.933137i | \(0.382940\pi\) | |||||||
\(822\) | −142.436 | −4.96803 | ||||||||
\(823\) | −30.9010 | −1.07714 | −0.538570 | − | 0.842581i | \(-0.681035\pi\) | ||||
−0.538570 | + | 0.842581i | \(0.681035\pi\) | |||||||
\(824\) | −30.3229 | −1.05635 | ||||||||
\(825\) | −4.41500 | −0.153711 | ||||||||
\(826\) | 104.296 | 3.62893 | ||||||||
\(827\) | 45.7225 | 1.58993 | 0.794964 | − | 0.606657i | \(-0.207490\pi\) | ||||
0.794964 | + | 0.606657i | \(0.207490\pi\) | |||||||
\(828\) | 76.2262 | 2.64904 | ||||||||
\(829\) | −38.8858 | −1.35056 | −0.675279 | − | 0.737562i | \(-0.735977\pi\) | ||||
−0.675279 | + | 0.737562i | \(0.735977\pi\) | |||||||
\(830\) | −5.52818 | −0.191886 | ||||||||
\(831\) | −57.5074 | −1.99491 | ||||||||
\(832\) | −0.946965 | −0.0328301 | ||||||||
\(833\) | −37.6781 | −1.30547 | ||||||||
\(834\) | −75.3729 | −2.60995 | ||||||||
\(835\) | 2.36159 | 0.0817261 | ||||||||
\(836\) | −12.5804 | −0.435104 | ||||||||
\(837\) | −14.6593 | −0.506701 | ||||||||
\(838\) | 50.0068 | 1.72746 | ||||||||
\(839\) | −9.34091 | −0.322484 | −0.161242 | − | 0.986915i | \(-0.551550\pi\) | ||||
−0.161242 | + | 0.986915i | \(0.551550\pi\) | |||||||
\(840\) | 97.6645 | 3.36975 | ||||||||
\(841\) | 67.7724 | 2.33698 | ||||||||
\(842\) | −52.1531 | −1.79731 | ||||||||
\(843\) | 103.589 | 3.56778 | ||||||||
\(844\) | 6.66363 | 0.229372 | ||||||||
\(845\) | −30.1037 | −1.03560 | ||||||||
\(846\) | 20.8080 | 0.715393 | ||||||||
\(847\) | −38.8264 | −1.33409 | ||||||||
\(848\) | −76.5383 | −2.62834 | ||||||||
\(849\) | 26.7714 | 0.918793 | ||||||||
\(850\) | −53.9947 | −1.85200 | ||||||||
\(851\) | 10.7014 | 0.366839 | ||||||||
\(852\) | −18.8887 | −0.647118 | ||||||||
\(853\) | −4.43051 | −0.151698 | −0.0758490 | − | 0.997119i | \(-0.524167\pi\) | ||||
−0.0758490 | + | 0.997119i | \(0.524167\pi\) | |||||||
\(854\) | 108.066 | 3.69794 | ||||||||
\(855\) | 68.0773 | 2.32819 | ||||||||
\(856\) | 20.2205 | 0.691123 | ||||||||
\(857\) | −39.5153 | −1.34982 | −0.674909 | − | 0.737901i | \(-0.735817\pi\) | ||||
−0.674909 | + | 0.737901i | \(0.735817\pi\) | |||||||
\(858\) | 20.5438 | 0.701355 | ||||||||
\(859\) | −41.9086 | −1.42990 | −0.714951 | − | 0.699174i | \(-0.753551\pi\) | ||||
−0.714951 | + | 0.699174i | \(0.753551\pi\) | |||||||
\(860\) | −54.3750 | −1.85417 | ||||||||
\(861\) | −105.312 | −3.58902 | ||||||||
\(862\) | −68.6921 | −2.33966 | ||||||||
\(863\) | −7.80570 | −0.265709 | −0.132855 | − | 0.991136i | \(-0.542414\pi\) | ||||
−0.132855 | + | 0.991136i | \(0.542414\pi\) | |||||||
\(864\) | −87.5384 | −2.97812 | ||||||||
\(865\) | 4.28522 | 0.145702 | ||||||||
\(866\) | −29.0425 | −0.986906 | ||||||||
\(867\) | 79.8905 | 2.71322 | ||||||||
\(868\) | −15.5582 | −0.528080 | ||||||||
\(869\) | −0.138514 | −0.00469877 | ||||||||
\(870\) | −107.136 | −3.63224 | ||||||||
\(871\) | −25.6456 | −0.868968 | ||||||||
\(872\) | −34.7267 | −1.17599 | ||||||||
\(873\) | 41.7218 | 1.41207 | ||||||||
\(874\) | 38.3137 | 1.29598 | ||||||||
\(875\) | 38.8730 | 1.31415 | ||||||||
\(876\) | −34.4522 | −1.16403 | ||||||||
\(877\) | −21.8789 | −0.738796 | −0.369398 | − | 0.929271i | \(-0.620436\pi\) | ||||
−0.369398 | + | 0.929271i | \(0.620436\pi\) | |||||||
\(878\) | −79.6913 | −2.68945 | ||||||||
\(879\) | −65.0627 | −2.19451 | ||||||||
\(880\) | −3.90713 | −0.131709 | ||||||||
\(881\) | −30.4737 | −1.02669 | −0.513343 | − | 0.858183i | \(-0.671593\pi\) | ||||
−0.513343 | + | 0.858183i | \(0.671593\pi\) | |||||||
\(882\) | −114.238 | −3.84659 | ||||||||
\(883\) | −15.5433 | −0.523075 | −0.261537 | − | 0.965193i | \(-0.584229\pi\) | ||||
−0.261537 | + | 0.965193i | \(0.584229\pi\) | |||||||
\(884\) | 173.959 | 5.85088 | ||||||||
\(885\) | 48.7352 | 1.63822 | ||||||||
\(886\) | 23.2542 | 0.781242 | ||||||||
\(887\) | 14.7229 | 0.494347 | 0.247174 | − | 0.968971i | \(-0.420498\pi\) | ||||
0.247174 | + | 0.968971i | \(0.420498\pi\) | |||||||
\(888\) | −100.772 | −3.38170 | ||||||||
\(889\) | 24.8889 | 0.834748 | ||||||||
\(890\) | 35.3654 | 1.18545 | ||||||||
\(891\) | 10.9668 | 0.367403 | ||||||||
\(892\) | 120.608 | 4.03826 | ||||||||
\(893\) | 7.24145 | 0.242326 | ||||||||
\(894\) | −84.5821 | −2.82885 | ||||||||
\(895\) | −17.0851 | −0.571091 | ||||||||
\(896\) | 39.8346 | 1.33078 | ||||||||
\(897\) | −43.3197 | −1.44640 | ||||||||
\(898\) | 0.799518 | 0.0266803 | ||||||||
\(899\) | 9.48432 | 0.316320 | ||||||||
\(900\) | −113.349 | −3.77830 | ||||||||
\(901\) | 67.8821 | 2.26148 | ||||||||
\(902\) | 9.43695 | 0.314216 | ||||||||
\(903\) | 108.045 | 3.59553 | ||||||||
\(904\) | 15.6465 | 0.520393 | ||||||||
\(905\) | 15.5230 | 0.516002 | ||||||||
\(906\) | −90.9096 | −3.02027 | ||||||||
\(907\) | 6.99966 | 0.232420 | 0.116210 | − | 0.993225i | \(-0.462925\pi\) | ||||
0.116210 | + | 0.993225i | \(0.462925\pi\) | |||||||
\(908\) | −19.1500 | −0.635516 | ||||||||
\(909\) | −85.7610 | −2.84451 | ||||||||
\(910\) | −71.7629 | −2.37892 | ||||||||
\(911\) | −31.3243 | −1.03782 | −0.518910 | − | 0.854829i | \(-0.673662\pi\) | ||||
−0.518910 | + | 0.854829i | \(0.673662\pi\) | |||||||
\(912\) | −161.073 | −5.33365 | ||||||||
\(913\) | −0.681538 | −0.0225556 | ||||||||
\(914\) | 81.9255 | 2.70985 | ||||||||
\(915\) | 50.4967 | 1.66937 | ||||||||
\(916\) | 82.9477 | 2.74067 | ||||||||
\(917\) | −23.8585 | −0.787876 | ||||||||
\(918\) | 249.672 | 8.24041 | ||||||||
\(919\) | −14.8413 | −0.489568 | −0.244784 | − | 0.969578i | \(-0.578717\pi\) | ||||
−0.244784 | + | 0.969578i | \(0.578717\pi\) | |||||||
\(920\) | 18.4542 | 0.608417 | ||||||||
\(921\) | −46.3633 | −1.52772 | ||||||||
\(922\) | −82.5423 | −2.71839 | ||||||||
\(923\) | 7.71287 | 0.253872 | ||||||||
\(924\) | 21.6668 | 0.712786 | ||||||||
\(925\) | −15.9131 | −0.523219 | ||||||||
\(926\) | 81.4850 | 2.67776 | ||||||||
\(927\) | 36.4028 | 1.19563 | ||||||||
\(928\) | 56.6357 | 1.85916 | ||||||||
\(929\) | 23.7271 | 0.778461 | 0.389230 | − | 0.921140i | \(-0.372741\pi\) | ||||
0.389230 | + | 0.921140i | \(0.372741\pi\) | |||||||
\(930\) | −10.5000 | −0.344308 | ||||||||
\(931\) | −39.7563 | −1.30296 | ||||||||
\(932\) | 79.4925 | 2.60386 | ||||||||
\(933\) | −70.7852 | −2.31740 | ||||||||
\(934\) | −15.7437 | −0.515149 | ||||||||
\(935\) | 3.46525 | 0.113326 | ||||||||
\(936\) | 293.102 | 9.58033 | ||||||||
\(937\) | −17.9739 | −0.587182 | −0.293591 | − | 0.955931i | \(-0.594850\pi\) | ||||
−0.293591 | + | 0.955931i | \(0.594850\pi\) | |||||||
\(938\) | −39.0644 | −1.27550 | ||||||||
\(939\) | −45.2352 | −1.47619 | ||||||||
\(940\) | 6.27650 | 0.204717 | ||||||||
\(941\) | −20.0900 | −0.654916 | −0.327458 | − | 0.944866i | \(-0.606192\pi\) | ||||
−0.327458 | + | 0.944866i | \(0.606192\pi\) | |||||||
\(942\) | 132.256 | 4.30913 | ||||||||
\(943\) | −19.8992 | −0.648007 | ||||||||
\(944\) | −82.8504 | −2.69655 | ||||||||
\(945\) | −71.3130 | −2.31981 | ||||||||
\(946\) | −9.68190 | −0.314786 | ||||||||
\(947\) | 19.3138 | 0.627613 | 0.313807 | − | 0.949487i | \(-0.398396\pi\) | ||||
0.313807 | + | 0.949487i | \(0.398396\pi\) | |||||||
\(948\) | −4.94936 | −0.160748 | ||||||||
\(949\) | 14.0679 | 0.456663 | ||||||||
\(950\) | −56.9728 | −1.84844 | ||||||||
\(951\) | 31.6211 | 1.02538 | ||||||||
\(952\) | 147.253 | 4.77251 | ||||||||
\(953\) | −31.4249 | −1.01795 | −0.508977 | − | 0.860780i | \(-0.669976\pi\) | ||||
−0.508977 | + | 0.860780i | \(0.669976\pi\) | |||||||
\(954\) | 205.815 | 6.66350 | ||||||||
\(955\) | −15.6049 | −0.504964 | ||||||||
\(956\) | 87.9764 | 2.84536 | ||||||||
\(957\) | −13.2081 | −0.426958 | ||||||||
\(958\) | −14.4887 | −0.468110 | ||||||||
\(959\) | 61.3405 | 1.98079 | ||||||||
\(960\) | −0.674026 | −0.0217541 | ||||||||
\(961\) | −30.0705 | −0.970015 | ||||||||
\(962\) | 74.0466 | 2.38736 | ||||||||
\(963\) | −24.2749 | −0.782247 | ||||||||
\(964\) | 95.3241 | 3.07018 | ||||||||
\(965\) | −22.8185 | −0.734555 | ||||||||
\(966\) | −65.9862 | −2.12307 | ||||||||
\(967\) | −38.1062 | −1.22541 | −0.612707 | − | 0.790310i | \(-0.709919\pi\) | ||||
−0.612707 | + | 0.790310i | \(0.709919\pi\) | |||||||
\(968\) | 69.0854 | 2.22049 | ||||||||
\(969\) | 142.856 | 4.58919 | ||||||||
\(970\) | 18.1763 | 0.583605 | ||||||||
\(971\) | 47.7544 | 1.53251 | 0.766256 | − | 0.642536i | \(-0.222118\pi\) | ||||
0.766256 | + | 0.642536i | \(0.222118\pi\) | |||||||
\(972\) | 186.527 | 5.98287 | ||||||||
\(973\) | 32.4595 | 1.04060 | ||||||||
\(974\) | 55.8043 | 1.78809 | ||||||||
\(975\) | 64.4167 | 2.06299 | ||||||||
\(976\) | −85.8449 | −2.74783 | ||||||||
\(977\) | 40.5852 | 1.29843 | 0.649217 | − | 0.760603i | \(-0.275097\pi\) | ||||
0.649217 | + | 0.760603i | \(0.275097\pi\) | |||||||
\(978\) | 114.343 | 3.65629 | ||||||||
\(979\) | 4.36000 | 0.139346 | ||||||||
\(980\) | −34.4586 | −1.10074 | ||||||||
\(981\) | 41.6896 | 1.33105 | ||||||||
\(982\) | −91.6934 | −2.92605 | ||||||||
\(983\) | 5.83521 | 0.186114 | 0.0930571 | − | 0.995661i | \(-0.470336\pi\) | ||||
0.0930571 | + | 0.995661i | \(0.470336\pi\) | |||||||
\(984\) | 187.386 | 5.97364 | ||||||||
\(985\) | 29.5191 | 0.940556 | ||||||||
\(986\) | −161.533 | −5.14427 | ||||||||
\(987\) | −12.4717 | −0.396978 | ||||||||
\(988\) | 183.554 | 5.83964 | ||||||||
\(989\) | 20.4157 | 0.649182 | ||||||||
\(990\) | 10.5065 | 0.333917 | ||||||||
\(991\) | −25.4460 | −0.808320 | −0.404160 | − | 0.914688i | \(-0.632436\pi\) | ||||
−0.404160 | + | 0.914688i | \(0.632436\pi\) | |||||||
\(992\) | 5.55066 | 0.176234 | ||||||||
\(993\) | 38.1359 | 1.21021 | ||||||||
\(994\) | 11.7485 | 0.372641 | ||||||||
\(995\) | −25.7919 | −0.817659 | ||||||||
\(996\) | −24.3526 | −0.771643 | ||||||||
\(997\) | −45.2344 | −1.43259 | −0.716294 | − | 0.697798i | \(-0.754163\pi\) | ||||
−0.716294 | + | 0.697798i | \(0.754163\pi\) | |||||||
\(998\) | 35.4614 | 1.12251 | ||||||||
\(999\) | 73.5823 | 2.32804 |
(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 | 4027.2.a.b.1.14 | ✓ | 159 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.b.1.14 | ✓ | 159 | 1.1 | even | 1 | trivial |