Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2523,2,Mod(1,2523)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2523, 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("2523.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2523 = 3 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2523.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: | \(20.1462564300\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 6x^{7} + 33x^{6} + 6x^{5} - 90x^{4} + 21x^{3} + 84x^{2} - 36x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 87) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.822927\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2523.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.177073 | 0.125209 | 0.0626046 | − | 0.998038i | \(-0.480059\pi\) | ||||
0.0626046 | + | 0.998038i | \(0.480059\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.96865 | −0.984323 | ||||||||
\(5\) | −3.45143 | −1.54353 | −0.771763 | − | 0.635910i | \(-0.780625\pi\) | ||||
−0.771763 | + | 0.635910i | \(0.780625\pi\) | |||||||
\(6\) | 0.177073 | 0.0722896 | ||||||||
\(7\) | −3.79521 | −1.43445 | −0.717227 | − | 0.696839i | \(-0.754589\pi\) | ||||
−0.717227 | + | 0.696839i | \(0.754589\pi\) | |||||||
\(8\) | −0.702739 | −0.248456 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.611154 | −0.193264 | ||||||||
\(11\) | −4.26673 | −1.28647 | −0.643234 | − | 0.765670i | \(-0.722408\pi\) | ||||
−0.643234 | + | 0.765670i | \(0.722408\pi\) | |||||||
\(12\) | −1.96865 | −0.568299 | ||||||||
\(13\) | −4.64311 | −1.28777 | −0.643883 | − | 0.765124i | \(-0.722678\pi\) | ||||
−0.643883 | + | 0.765124i | \(0.722678\pi\) | |||||||
\(14\) | −0.672028 | −0.179607 | ||||||||
\(15\) | −3.45143 | −0.891156 | ||||||||
\(16\) | 3.81285 | 0.953214 | ||||||||
\(17\) | −3.07208 | −0.745088 | −0.372544 | − | 0.928014i | \(-0.621514\pi\) | ||||
−0.372544 | + | 0.928014i | \(0.621514\pi\) | |||||||
\(18\) | 0.177073 | 0.0417364 | ||||||||
\(19\) | −3.59269 | −0.824219 | −0.412109 | − | 0.911134i | \(-0.635208\pi\) | ||||
−0.412109 | + | 0.911134i | \(0.635208\pi\) | |||||||
\(20\) | 6.79464 | 1.51933 | ||||||||
\(21\) | −3.79521 | −0.828183 | ||||||||
\(22\) | −0.755521 | −0.161078 | ||||||||
\(23\) | −0.433603 | −0.0904125 | −0.0452063 | − | 0.998978i | \(-0.514395\pi\) | ||||
−0.0452063 | + | 0.998978i | \(0.514395\pi\) | |||||||
\(24\) | −0.702739 | −0.143446 | ||||||||
\(25\) | 6.91237 | 1.38247 | ||||||||
\(26\) | −0.822167 | −0.161240 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 7.47142 | 1.41197 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | −0.611154 | −0.111581 | ||||||||
\(31\) | −4.52230 | −0.812230 | −0.406115 | − | 0.913822i | \(-0.633117\pi\) | ||||
−0.406115 | + | 0.913822i | \(0.633117\pi\) | |||||||
\(32\) | 2.08063 | 0.367807 | ||||||||
\(33\) | −4.26673 | −0.742742 | ||||||||
\(34\) | −0.543981 | −0.0932920 | ||||||||
\(35\) | 13.0989 | 2.21412 | ||||||||
\(36\) | −1.96865 | −0.328108 | ||||||||
\(37\) | 6.32794 | 1.04031 | 0.520153 | − | 0.854073i | \(-0.325875\pi\) | ||||
0.520153 | + | 0.854073i | \(0.325875\pi\) | |||||||
\(38\) | −0.636166 | −0.103200 | ||||||||
\(39\) | −4.64311 | −0.743492 | ||||||||
\(40\) | 2.42545 | 0.383498 | ||||||||
\(41\) | −1.97128 | −0.307862 | −0.153931 | − | 0.988082i | \(-0.549193\pi\) | ||||
−0.153931 | + | 0.988082i | \(0.549193\pi\) | |||||||
\(42\) | −0.672028 | −0.103696 | ||||||||
\(43\) | −0.251178 | −0.0383043 | −0.0191522 | − | 0.999817i | \(-0.506097\pi\) | ||||
−0.0191522 | + | 0.999817i | \(0.506097\pi\) | |||||||
\(44\) | 8.39968 | 1.26630 | ||||||||
\(45\) | −3.45143 | −0.514509 | ||||||||
\(46\) | −0.0767793 | −0.0113205 | ||||||||
\(47\) | −4.81629 | −0.702529 | −0.351264 | − | 0.936276i | \(-0.614248\pi\) | ||||
−0.351264 | + | 0.936276i | \(0.614248\pi\) | |||||||
\(48\) | 3.81285 | 0.550338 | ||||||||
\(49\) | 7.40363 | 1.05766 | ||||||||
\(50\) | 1.22399 | 0.173099 | ||||||||
\(51\) | −3.07208 | −0.430177 | ||||||||
\(52\) | 9.14063 | 1.26758 | ||||||||
\(53\) | 10.9694 | 1.50676 | 0.753382 | − | 0.657583i | \(-0.228421\pi\) | ||||
0.753382 | + | 0.657583i | \(0.228421\pi\) | |||||||
\(54\) | 0.177073 | 0.0240965 | ||||||||
\(55\) | 14.7263 | 1.98570 | ||||||||
\(56\) | 2.66704 | 0.356398 | ||||||||
\(57\) | −3.59269 | −0.475863 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.06991 | −0.790234 | −0.395117 | − | 0.918631i | \(-0.629296\pi\) | ||||
−0.395117 | + | 0.918631i | \(0.629296\pi\) | |||||||
\(60\) | 6.79464 | 0.877185 | ||||||||
\(61\) | 3.79174 | 0.485483 | 0.242741 | − | 0.970091i | \(-0.421953\pi\) | ||||
0.242741 | + | 0.970091i | \(0.421953\pi\) | |||||||
\(62\) | −0.800776 | −0.101699 | ||||||||
\(63\) | −3.79521 | −0.478152 | ||||||||
\(64\) | −7.25729 | −0.907161 | ||||||||
\(65\) | 16.0254 | 1.98770 | ||||||||
\(66\) | −0.755521 | −0.0929982 | ||||||||
\(67\) | −5.26714 | −0.643484 | −0.321742 | − | 0.946827i | \(-0.604268\pi\) | ||||
−0.321742 | + | 0.946827i | \(0.604268\pi\) | |||||||
\(68\) | 6.04783 | 0.733407 | ||||||||
\(69\) | −0.433603 | −0.0521997 | ||||||||
\(70\) | 2.31946 | 0.277228 | ||||||||
\(71\) | −5.83609 | −0.692616 | −0.346308 | − | 0.938121i | \(-0.612565\pi\) | ||||
−0.346308 | + | 0.938121i | \(0.612565\pi\) | |||||||
\(72\) | −0.702739 | −0.0828185 | ||||||||
\(73\) | −10.5495 | −1.23473 | −0.617365 | − | 0.786677i | \(-0.711800\pi\) | ||||
−0.617365 | + | 0.786677i | \(0.711800\pi\) | |||||||
\(74\) | 1.12051 | 0.130256 | ||||||||
\(75\) | 6.91237 | 0.798172 | ||||||||
\(76\) | 7.07272 | 0.811297 | ||||||||
\(77\) | 16.1931 | 1.84538 | ||||||||
\(78\) | −0.822167 | −0.0930921 | ||||||||
\(79\) | 10.0367 | 1.12921 | 0.564607 | − | 0.825360i | \(-0.309028\pi\) | ||||
0.564607 | + | 0.825360i | \(0.309028\pi\) | |||||||
\(80\) | −13.1598 | −1.47131 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.349059 | −0.0385471 | ||||||||
\(83\) | −7.09816 | −0.779124 | −0.389562 | − | 0.921000i | \(-0.627374\pi\) | ||||
−0.389562 | + | 0.921000i | \(0.627374\pi\) | |||||||
\(84\) | 7.47142 | 0.815199 | ||||||||
\(85\) | 10.6031 | 1.15006 | ||||||||
\(86\) | −0.0444768 | −0.00479606 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.99840 | 0.319630 | ||||||||
\(89\) | −13.9762 | −1.48147 | −0.740737 | − | 0.671795i | \(-0.765524\pi\) | ||||
−0.740737 | + | 0.671795i | \(0.765524\pi\) | |||||||
\(90\) | −0.611154 | −0.0644213 | ||||||||
\(91\) | 17.6216 | 1.84724 | ||||||||
\(92\) | 0.853611 | 0.0889951 | ||||||||
\(93\) | −4.52230 | −0.468941 | ||||||||
\(94\) | −0.852834 | −0.0879631 | ||||||||
\(95\) | 12.3999 | 1.27220 | ||||||||
\(96\) | 2.08063 | 0.212353 | ||||||||
\(97\) | −14.3224 | −1.45422 | −0.727111 | − | 0.686520i | \(-0.759137\pi\) | ||||
−0.727111 | + | 0.686520i | \(0.759137\pi\) | |||||||
\(98\) | 1.31098 | 0.132429 | ||||||||
\(99\) | −4.26673 | −0.428822 | ||||||||
\(100\) | −13.6080 | −1.36080 | ||||||||
\(101\) | 0.816445 | 0.0812393 | 0.0406196 | − | 0.999175i | \(-0.487067\pi\) | ||||
0.0406196 | + | 0.999175i | \(0.487067\pi\) | |||||||
\(102\) | −0.543981 | −0.0538622 | ||||||||
\(103\) | −4.95795 | −0.488521 | −0.244260 | − | 0.969710i | \(-0.578545\pi\) | ||||
−0.244260 | + | 0.969710i | \(0.578545\pi\) | |||||||
\(104\) | 3.26289 | 0.319953 | ||||||||
\(105\) | 13.0989 | 1.27832 | ||||||||
\(106\) | 1.94238 | 0.188661 | ||||||||
\(107\) | −11.5359 | −1.11521 | −0.557607 | − | 0.830105i | \(-0.688280\pi\) | ||||
−0.557607 | + | 0.830105i | \(0.688280\pi\) | |||||||
\(108\) | −1.96865 | −0.189433 | ||||||||
\(109\) | 8.64718 | 0.828250 | 0.414125 | − | 0.910220i | \(-0.364088\pi\) | ||||
0.414125 | + | 0.910220i | \(0.364088\pi\) | |||||||
\(110\) | 2.60763 | 0.248628 | ||||||||
\(111\) | 6.32794 | 0.600621 | ||||||||
\(112\) | −14.4706 | −1.36734 | ||||||||
\(113\) | 7.58551 | 0.713584 | 0.356792 | − | 0.934184i | \(-0.383870\pi\) | ||||
0.356792 | + | 0.934184i | \(0.383870\pi\) | |||||||
\(114\) | −0.636166 | −0.0595824 | ||||||||
\(115\) | 1.49655 | 0.139554 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.64311 | −0.429255 | ||||||||
\(118\) | −1.07481 | −0.0989447 | ||||||||
\(119\) | 11.6592 | 1.06880 | ||||||||
\(120\) | 2.42545 | 0.221413 | ||||||||
\(121\) | 7.20498 | 0.654998 | ||||||||
\(122\) | 0.671414 | 0.0607869 | ||||||||
\(123\) | −1.97128 | −0.177744 | ||||||||
\(124\) | 8.90281 | 0.799496 | ||||||||
\(125\) | −6.60043 | −0.590360 | ||||||||
\(126\) | −0.672028 | −0.0598690 | ||||||||
\(127\) | 1.23469 | 0.109561 | 0.0547807 | − | 0.998498i | \(-0.482554\pi\) | ||||
0.0547807 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(128\) | −5.44633 | −0.481392 | ||||||||
\(129\) | −0.251178 | −0.0221150 | ||||||||
\(130\) | 2.83765 | 0.248879 | ||||||||
\(131\) | −3.99564 | −0.349101 | −0.174550 | − | 0.984648i | \(-0.555847\pi\) | ||||
−0.174550 | + | 0.984648i | \(0.555847\pi\) | |||||||
\(132\) | 8.39968 | 0.731098 | ||||||||
\(133\) | 13.6350 | 1.18230 | ||||||||
\(134\) | −0.932667 | −0.0805702 | ||||||||
\(135\) | −3.45143 | −0.297052 | ||||||||
\(136\) | 2.15887 | 0.185121 | ||||||||
\(137\) | 16.6539 | 1.42284 | 0.711418 | − | 0.702769i | \(-0.248053\pi\) | ||||
0.711418 | + | 0.702769i | \(0.248053\pi\) | |||||||
\(138\) | −0.0767793 | −0.00653589 | ||||||||
\(139\) | 8.27106 | 0.701543 | 0.350771 | − | 0.936461i | \(-0.385919\pi\) | ||||
0.350771 | + | 0.936461i | \(0.385919\pi\) | |||||||
\(140\) | −25.7871 | −2.17941 | ||||||||
\(141\) | −4.81629 | −0.405605 | ||||||||
\(142\) | −1.03341 | −0.0867219 | ||||||||
\(143\) | 19.8109 | 1.65667 | ||||||||
\(144\) | 3.81285 | 0.317738 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.86803 | −0.154600 | ||||||||
\(147\) | 7.40363 | 0.610641 | ||||||||
\(148\) | −12.4575 | −1.02400 | ||||||||
\(149\) | −9.38848 | −0.769135 | −0.384567 | − | 0.923097i | \(-0.625649\pi\) | ||||
−0.384567 | + | 0.923097i | \(0.625649\pi\) | |||||||
\(150\) | 1.22399 | 0.0999386 | ||||||||
\(151\) | 19.6633 | 1.60018 | 0.800088 | − | 0.599883i | \(-0.204786\pi\) | ||||
0.800088 | + | 0.599883i | \(0.204786\pi\) | |||||||
\(152\) | 2.52472 | 0.204782 | ||||||||
\(153\) | −3.07208 | −0.248363 | ||||||||
\(154\) | 2.86736 | 0.231059 | ||||||||
\(155\) | 15.6084 | 1.25370 | ||||||||
\(156\) | 9.14063 | 0.731836 | ||||||||
\(157\) | −2.61457 | −0.208665 | −0.104333 | − | 0.994542i | \(-0.533271\pi\) | ||||
−0.104333 | + | 0.994542i | \(0.533271\pi\) | |||||||
\(158\) | 1.77722 | 0.141388 | ||||||||
\(159\) | 10.9694 | 0.869931 | ||||||||
\(160\) | −7.18115 | −0.567720 | ||||||||
\(161\) | 1.64562 | 0.129693 | ||||||||
\(162\) | 0.177073 | 0.0139121 | ||||||||
\(163\) | −0.527800 | −0.0413405 | −0.0206702 | − | 0.999786i | \(-0.506580\pi\) | ||||
−0.0206702 | + | 0.999786i | \(0.506580\pi\) | |||||||
\(164\) | 3.88074 | 0.303035 | ||||||||
\(165\) | 14.7263 | 1.14644 | ||||||||
\(166\) | −1.25689 | −0.0975536 | ||||||||
\(167\) | −15.0489 | −1.16452 | −0.582261 | − | 0.813002i | \(-0.697832\pi\) | ||||
−0.582261 | + | 0.813002i | \(0.697832\pi\) | |||||||
\(168\) | 2.66704 | 0.205767 | ||||||||
\(169\) | 8.55844 | 0.658342 | ||||||||
\(170\) | 1.87751 | 0.143999 | ||||||||
\(171\) | −3.59269 | −0.274740 | ||||||||
\(172\) | 0.494481 | 0.0377038 | ||||||||
\(173\) | 0.103233 | 0.00784865 | 0.00392433 | − | 0.999992i | \(-0.498751\pi\) | ||||
0.00392433 | + | 0.999992i | \(0.498751\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.2339 | −1.98310 | ||||||||
\(176\) | −16.2684 | −1.22628 | ||||||||
\(177\) | −6.06991 | −0.456242 | ||||||||
\(178\) | −2.47480 | −0.185494 | ||||||||
\(179\) | −4.04916 | −0.302649 | −0.151324 | − | 0.988484i | \(-0.548354\pi\) | ||||
−0.151324 | + | 0.988484i | \(0.548354\pi\) | |||||||
\(180\) | 6.79464 | 0.506443 | ||||||||
\(181\) | −11.5222 | −0.856442 | −0.428221 | − | 0.903674i | \(-0.640860\pi\) | ||||
−0.428221 | + | 0.903674i | \(0.640860\pi\) | |||||||
\(182\) | 3.12030 | 0.231292 | ||||||||
\(183\) | 3.79174 | 0.280293 | ||||||||
\(184\) | 0.304710 | 0.0224635 | ||||||||
\(185\) | −21.8404 | −1.60574 | ||||||||
\(186\) | −0.800776 | −0.0587158 | ||||||||
\(187\) | 13.1077 | 0.958532 | ||||||||
\(188\) | 9.48157 | 0.691515 | ||||||||
\(189\) | −3.79521 | −0.276061 | ||||||||
\(190\) | 2.19568 | 0.159292 | ||||||||
\(191\) | 1.55942 | 0.112836 | 0.0564179 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564179 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(192\) | −7.25729 | −0.523750 | ||||||||
\(193\) | 13.3775 | 0.962932 | 0.481466 | − | 0.876465i | \(-0.340104\pi\) | ||||
0.481466 | + | 0.876465i | \(0.340104\pi\) | |||||||
\(194\) | −2.53611 | −0.182082 | ||||||||
\(195\) | 16.0254 | 1.14760 | ||||||||
\(196\) | −14.5751 | −1.04108 | ||||||||
\(197\) | −12.7756 | −0.910226 | −0.455113 | − | 0.890434i | \(-0.650401\pi\) | ||||
−0.455113 | + | 0.890434i | \(0.650401\pi\) | |||||||
\(198\) | −0.755521 | −0.0536926 | ||||||||
\(199\) | 8.82206 | 0.625379 | 0.312690 | − | 0.949855i | \(-0.398770\pi\) | ||||
0.312690 | + | 0.949855i | \(0.398770\pi\) | |||||||
\(200\) | −4.85759 | −0.343484 | ||||||||
\(201\) | −5.26714 | −0.371516 | ||||||||
\(202\) | 0.144570 | 0.0101719 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.04783 | 0.423433 | ||||||||
\(205\) | 6.80372 | 0.475193 | ||||||||
\(206\) | −0.877917 | −0.0611674 | ||||||||
\(207\) | −0.433603 | −0.0301375 | ||||||||
\(208\) | −17.7035 | −1.22752 | ||||||||
\(209\) | 15.3290 | 1.06033 | ||||||||
\(210\) | 2.31946 | 0.160058 | ||||||||
\(211\) | −15.0234 | −1.03425 | −0.517127 | − | 0.855909i | \(-0.672998\pi\) | ||||
−0.517127 | + | 0.855909i | \(0.672998\pi\) | |||||||
\(212\) | −21.5949 | −1.48314 | ||||||||
\(213\) | −5.83609 | −0.399882 | ||||||||
\(214\) | −2.04269 | −0.139635 | ||||||||
\(215\) | 0.866924 | 0.0591237 | ||||||||
\(216\) | −0.702739 | −0.0478153 | ||||||||
\(217\) | 17.1631 | 1.16511 | ||||||||
\(218\) | 1.53118 | 0.103705 | ||||||||
\(219\) | −10.5495 | −0.712871 | ||||||||
\(220\) | −28.9909 | −1.95457 | ||||||||
\(221\) | 14.2640 | 0.959500 | ||||||||
\(222\) | 1.12051 | 0.0752034 | ||||||||
\(223\) | 23.9456 | 1.60352 | 0.801759 | − | 0.597648i | \(-0.203898\pi\) | ||||
0.801759 | + | 0.597648i | \(0.203898\pi\) | |||||||
\(224\) | −7.89643 | −0.527602 | ||||||||
\(225\) | 6.91237 | 0.460825 | ||||||||
\(226\) | 1.34319 | 0.0893474 | ||||||||
\(227\) | −5.15851 | −0.342382 | −0.171191 | − | 0.985238i | \(-0.554762\pi\) | ||||
−0.171191 | + | 0.985238i | \(0.554762\pi\) | |||||||
\(228\) | 7.07272 | 0.468403 | ||||||||
\(229\) | −8.10170 | −0.535375 | −0.267688 | − | 0.963506i | \(-0.586260\pi\) | ||||
−0.267688 | + | 0.963506i | \(0.586260\pi\) | |||||||
\(230\) | 0.264998 | 0.0174735 | ||||||||
\(231\) | 16.1931 | 1.06543 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.5153 | 1.60605 | 0.803027 | − | 0.595943i | \(-0.203222\pi\) | ||||
0.803027 | + | 0.595943i | \(0.203222\pi\) | |||||||
\(234\) | −0.822167 | −0.0537468 | ||||||||
\(235\) | 16.6231 | 1.08437 | ||||||||
\(236\) | 11.9495 | 0.777846 | ||||||||
\(237\) | 10.0367 | 0.651952 | ||||||||
\(238\) | 2.06452 | 0.133823 | ||||||||
\(239\) | −27.9408 | −1.80734 | −0.903669 | − | 0.428232i | \(-0.859137\pi\) | ||||
−0.903669 | + | 0.428232i | \(0.859137\pi\) | |||||||
\(240\) | −13.1598 | −0.849462 | ||||||||
\(241\) | 3.96836 | 0.255625 | 0.127812 | − | 0.991798i | \(-0.459204\pi\) | ||||
0.127812 | + | 0.991798i | \(0.459204\pi\) | |||||||
\(242\) | 1.27581 | 0.0820119 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.46459 | −0.477871 | ||||||||
\(245\) | −25.5531 | −1.63253 | ||||||||
\(246\) | −0.349059 | −0.0222552 | ||||||||
\(247\) | 16.6812 | 1.06140 | ||||||||
\(248\) | 3.17800 | 0.201803 | ||||||||
\(249\) | −7.09816 | −0.449828 | ||||||||
\(250\) | −1.16876 | −0.0739186 | ||||||||
\(251\) | −31.6093 | −1.99516 | −0.997581 | − | 0.0695077i | \(-0.977857\pi\) | ||||
−0.997581 | + | 0.0695077i | \(0.977857\pi\) | |||||||
\(252\) | 7.47142 | 0.470655 | ||||||||
\(253\) | 1.85007 | 0.116313 | ||||||||
\(254\) | 0.218631 | 0.0137181 | ||||||||
\(255\) | 10.6031 | 0.663990 | ||||||||
\(256\) | 13.5502 | 0.846886 | ||||||||
\(257\) | −4.05027 | −0.252649 | −0.126324 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126324 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(258\) | −0.0444768 | −0.00276900 | ||||||||
\(259\) | −24.0159 | −1.49227 | ||||||||
\(260\) | −31.5483 | −1.95654 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.707518 | −0.0437106 | ||||||||
\(263\) | −14.3001 | −0.881782 | −0.440891 | − | 0.897561i | \(-0.645338\pi\) | ||||
−0.440891 | + | 0.897561i | \(0.645338\pi\) | |||||||
\(264\) | 2.99840 | 0.184539 | ||||||||
\(265\) | −37.8602 | −2.32573 | ||||||||
\(266\) | 2.41439 | 0.148035 | ||||||||
\(267\) | −13.9762 | −0.855329 | ||||||||
\(268\) | 10.3691 | 0.633396 | ||||||||
\(269\) | 21.5174 | 1.31194 | 0.655970 | − | 0.754787i | \(-0.272260\pi\) | ||||
0.655970 | + | 0.754787i | \(0.272260\pi\) | |||||||
\(270\) | −0.611154 | −0.0371937 | ||||||||
\(271\) | −19.7901 | −1.20216 | −0.601080 | − | 0.799189i | \(-0.705263\pi\) | ||||
−0.601080 | + | 0.799189i | \(0.705263\pi\) | |||||||
\(272\) | −11.7134 | −0.710228 | ||||||||
\(273\) | 17.6216 | 1.06651 | ||||||||
\(274\) | 2.94895 | 0.178152 | ||||||||
\(275\) | −29.4932 | −1.77851 | ||||||||
\(276\) | 0.853611 | 0.0513813 | ||||||||
\(277\) | 5.60355 | 0.336685 | 0.168342 | − | 0.985729i | \(-0.446159\pi\) | ||||
0.168342 | + | 0.985729i | \(0.446159\pi\) | |||||||
\(278\) | 1.46458 | 0.0878397 | ||||||||
\(279\) | −4.52230 | −0.270743 | ||||||||
\(280\) | −9.20511 | −0.550110 | ||||||||
\(281\) | −10.8186 | −0.645382 | −0.322691 | − | 0.946504i | \(-0.604587\pi\) | ||||
−0.322691 | + | 0.946504i | \(0.604587\pi\) | |||||||
\(282\) | −0.852834 | −0.0507855 | ||||||||
\(283\) | −7.43490 | −0.441959 | −0.220980 | − | 0.975278i | \(-0.570925\pi\) | ||||
−0.220980 | + | 0.975278i | \(0.570925\pi\) | |||||||
\(284\) | 11.4892 | 0.681757 | ||||||||
\(285\) | 12.3999 | 0.734507 | ||||||||
\(286\) | 3.50797 | 0.207430 | ||||||||
\(287\) | 7.48141 | 0.441614 | ||||||||
\(288\) | 2.08063 | 0.122602 | ||||||||
\(289\) | −7.56234 | −0.444843 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.3224 | −0.839595 | ||||||||
\(292\) | 20.7683 | 1.21537 | ||||||||
\(293\) | 12.4164 | 0.725373 | 0.362686 | − | 0.931911i | \(-0.381860\pi\) | ||||
0.362686 | + | 0.931911i | \(0.381860\pi\) | |||||||
\(294\) | 1.31098 | 0.0764579 | ||||||||
\(295\) | 20.9499 | 1.21975 | ||||||||
\(296\) | −4.44689 | −0.258470 | ||||||||
\(297\) | −4.26673 | −0.247581 | ||||||||
\(298\) | −1.66244 | −0.0963028 | ||||||||
\(299\) | 2.01327 | 0.116430 | ||||||||
\(300\) | −13.6080 | −0.785659 | ||||||||
\(301\) | 0.953274 | 0.0549458 | ||||||||
\(302\) | 3.48183 | 0.200357 | ||||||||
\(303\) | 0.816445 | 0.0469035 | ||||||||
\(304\) | −13.6984 | −0.785656 | ||||||||
\(305\) | −13.0869 | −0.749355 | ||||||||
\(306\) | −0.543981 | −0.0310973 | ||||||||
\(307\) | 24.0387 | 1.37196 | 0.685981 | − | 0.727620i | \(-0.259373\pi\) | ||||
0.685981 | + | 0.727620i | \(0.259373\pi\) | |||||||
\(308\) | −31.8785 | −1.81645 | ||||||||
\(309\) | −4.95795 | −0.282048 | ||||||||
\(310\) | 2.76382 | 0.156975 | ||||||||
\(311\) | −31.2545 | −1.77228 | −0.886140 | − | 0.463418i | \(-0.846623\pi\) | ||||
−0.886140 | + | 0.463418i | \(0.846623\pi\) | |||||||
\(312\) | 3.26289 | 0.184725 | ||||||||
\(313\) | −21.0508 | −1.18986 | −0.594931 | − | 0.803777i | \(-0.702821\pi\) | ||||
−0.594931 | + | 0.803777i | \(0.702821\pi\) | |||||||
\(314\) | −0.462969 | −0.0261268 | ||||||||
\(315\) | 13.0989 | 0.738040 | ||||||||
\(316\) | −19.7586 | −1.11151 | ||||||||
\(317\) | −15.6515 | −0.879073 | −0.439537 | − | 0.898225i | \(-0.644857\pi\) | ||||
−0.439537 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(318\) | 1.94238 | 0.108923 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 25.0480 | 1.40023 | ||||||||
\(321\) | −11.5359 | −0.643869 | ||||||||
\(322\) | 0.291394 | 0.0162387 | ||||||||
\(323\) | 11.0370 | 0.614116 | ||||||||
\(324\) | −1.96865 | −0.109369 | ||||||||
\(325\) | −32.0949 | −1.78030 | ||||||||
\(326\) | −0.0934589 | −0.00517621 | ||||||||
\(327\) | 8.64718 | 0.478190 | ||||||||
\(328\) | 1.38529 | 0.0764900 | ||||||||
\(329\) | 18.2788 | 1.00775 | ||||||||
\(330\) | 2.60763 | 0.143545 | ||||||||
\(331\) | −19.4595 | −1.06959 | −0.534796 | − | 0.844981i | \(-0.679612\pi\) | ||||
−0.534796 | + | 0.844981i | \(0.679612\pi\) | |||||||
\(332\) | 13.9738 | 0.766910 | ||||||||
\(333\) | 6.32794 | 0.346769 | ||||||||
\(334\) | −2.66476 | −0.145809 | ||||||||
\(335\) | 18.1792 | 0.993235 | ||||||||
\(336\) | −14.4706 | −0.789435 | ||||||||
\(337\) | 20.1780 | 1.09916 | 0.549582 | − | 0.835440i | \(-0.314787\pi\) | ||||
0.549582 | + | 0.835440i | \(0.314787\pi\) | |||||||
\(338\) | 1.51547 | 0.0824305 | ||||||||
\(339\) | 7.58551 | 0.411988 | ||||||||
\(340\) | −20.8737 | −1.13203 | ||||||||
\(341\) | 19.2954 | 1.04491 | ||||||||
\(342\) | −0.636166 | −0.0343999 | ||||||||
\(343\) | −1.53184 | −0.0827119 | ||||||||
\(344\) | 0.176513 | 0.00951692 | ||||||||
\(345\) | 1.49655 | 0.0805716 | ||||||||
\(346\) | 0.0182797 | 0.000982724 0 | ||||||||
\(347\) | 0.788354 | 0.0423211 | 0.0211605 | − | 0.999776i | \(-0.493264\pi\) | ||||
0.0211605 | + | 0.999776i | \(0.493264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9417 | 1.12098 | 0.560491 | − | 0.828161i | \(-0.310613\pi\) | ||||
0.560491 | + | 0.828161i | \(0.310613\pi\) | |||||||
\(350\) | −4.64531 | −0.248302 | ||||||||
\(351\) | −4.64311 | −0.247831 | ||||||||
\(352\) | −8.87748 | −0.473172 | ||||||||
\(353\) | −36.0882 | −1.92078 | −0.960390 | − | 0.278659i | \(-0.910110\pi\) | ||||
−0.960390 | + | 0.278659i | \(0.910110\pi\) | |||||||
\(354\) | −1.07481 | −0.0571258 | ||||||||
\(355\) | 20.1428 | 1.06907 | ||||||||
\(356\) | 27.5142 | 1.45825 | ||||||||
\(357\) | 11.6592 | 0.617069 | ||||||||
\(358\) | −0.716996 | −0.0378944 | ||||||||
\(359\) | 18.6229 | 0.982881 | 0.491441 | − | 0.870911i | \(-0.336471\pi\) | ||||
0.491441 | + | 0.870911i | \(0.336471\pi\) | |||||||
\(360\) | 2.42545 | 0.127833 | ||||||||
\(361\) | −6.09261 | −0.320664 | ||||||||
\(362\) | −2.04028 | −0.107235 | ||||||||
\(363\) | 7.20498 | 0.378163 | ||||||||
\(364\) | −34.6906 | −1.81828 | ||||||||
\(365\) | 36.4110 | 1.90584 | ||||||||
\(366\) | 0.671414 | 0.0350953 | ||||||||
\(367\) | 16.1322 | 0.842094 | 0.421047 | − | 0.907039i | \(-0.361663\pi\) | ||||
0.421047 | + | 0.907039i | \(0.361663\pi\) | |||||||
\(368\) | −1.65327 | −0.0861824 | ||||||||
\(369\) | −1.97128 | −0.102621 | ||||||||
\(370\) | −3.86735 | −0.201054 | ||||||||
\(371\) | −41.6312 | −2.16139 | ||||||||
\(372\) | 8.90281 | 0.461589 | ||||||||
\(373\) | 1.13592 | 0.0588156 | 0.0294078 | − | 0.999567i | \(-0.490638\pi\) | ||||
0.0294078 | + | 0.999567i | \(0.490638\pi\) | |||||||
\(374\) | 2.32102 | 0.120017 | ||||||||
\(375\) | −6.60043 | −0.340845 | ||||||||
\(376\) | 3.38460 | 0.174547 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.672028 | −0.0345654 | ||||||||
\(379\) | 30.2475 | 1.55371 | 0.776856 | − | 0.629679i | \(-0.216813\pi\) | ||||
0.776856 | + | 0.629679i | \(0.216813\pi\) | |||||||
\(380\) | −24.4110 | −1.25226 | ||||||||
\(381\) | 1.23469 | 0.0632553 | ||||||||
\(382\) | 0.276131 | 0.0141281 | ||||||||
\(383\) | −17.5797 | −0.898280 | −0.449140 | − | 0.893461i | \(-0.648270\pi\) | ||||
−0.449140 | + | 0.893461i | \(0.648270\pi\) | |||||||
\(384\) | −5.44633 | −0.277932 | ||||||||
\(385\) | −55.8895 | −2.84839 | ||||||||
\(386\) | 2.36879 | 0.120568 | ||||||||
\(387\) | −0.251178 | −0.0127681 | ||||||||
\(388\) | 28.1958 | 1.43142 | ||||||||
\(389\) | 38.5442 | 1.95427 | 0.977134 | − | 0.212625i | \(-0.0682014\pi\) | ||||
0.977134 | + | 0.212625i | \(0.0682014\pi\) | |||||||
\(390\) | 2.83765 | 0.143690 | ||||||||
\(391\) | 1.33206 | 0.0673653 | ||||||||
\(392\) | −5.20281 | −0.262782 | ||||||||
\(393\) | −3.99564 | −0.201553 | ||||||||
\(394\) | −2.26222 | −0.113969 | ||||||||
\(395\) | −34.6409 | −1.74297 | ||||||||
\(396\) | 8.39968 | 0.422100 | ||||||||
\(397\) | −21.0742 | −1.05768 | −0.528841 | − | 0.848721i | \(-0.677373\pi\) | ||||
−0.528841 | + | 0.848721i | \(0.677373\pi\) | |||||||
\(398\) | 1.56215 | 0.0783033 | ||||||||
\(399\) | 13.6350 | 0.682604 | ||||||||
\(400\) | 26.3559 | 1.31779 | ||||||||
\(401\) | −34.7249 | −1.73408 | −0.867039 | − | 0.498240i | \(-0.833980\pi\) | ||||
−0.867039 | + | 0.498240i | \(0.833980\pi\) | |||||||
\(402\) | −0.932667 | −0.0465172 | ||||||||
\(403\) | 20.9975 | 1.04596 | ||||||||
\(404\) | −1.60729 | −0.0799657 | ||||||||
\(405\) | −3.45143 | −0.171503 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.9996 | −1.33832 | ||||||||
\(408\) | 2.15887 | 0.106880 | ||||||||
\(409\) | −3.13466 | −0.154999 | −0.0774995 | − | 0.996992i | \(-0.524694\pi\) | ||||
−0.0774995 | + | 0.996992i | \(0.524694\pi\) | |||||||
\(410\) | 1.20475 | 0.0594985 | ||||||||
\(411\) | 16.6539 | 0.821475 | ||||||||
\(412\) | 9.76044 | 0.480862 | ||||||||
\(413\) | 23.0366 | 1.13356 | ||||||||
\(414\) | −0.0767793 | −0.00377350 | ||||||||
\(415\) | 24.4988 | 1.20260 | ||||||||
\(416\) | −9.66059 | −0.473649 | ||||||||
\(417\) | 8.27106 | 0.405036 | ||||||||
\(418\) | 2.71435 | 0.132763 | ||||||||
\(419\) | −8.68305 | −0.424195 | −0.212097 | − | 0.977249i | \(-0.568029\pi\) | ||||
−0.212097 | + | 0.977249i | \(0.568029\pi\) | |||||||
\(420\) | −25.7871 | −1.25828 | ||||||||
\(421\) | 28.3830 | 1.38330 | 0.691651 | − | 0.722232i | \(-0.256884\pi\) | ||||
0.691651 | + | 0.722232i | \(0.256884\pi\) | |||||||
\(422\) | −2.66023 | −0.129498 | ||||||||
\(423\) | −4.81629 | −0.234176 | ||||||||
\(424\) | −7.70863 | −0.374364 | ||||||||
\(425\) | −21.2354 | −1.03007 | ||||||||
\(426\) | −1.03341 | −0.0500689 | ||||||||
\(427\) | −14.3905 | −0.696403 | ||||||||
\(428\) | 22.7100 | 1.09773 | ||||||||
\(429\) | 19.8109 | 0.956478 | ||||||||
\(430\) | 0.153509 | 0.00740284 | ||||||||
\(431\) | 0.0823506 | 0.00396669 | 0.00198334 | − | 0.999998i | \(-0.499369\pi\) | ||||
0.00198334 | + | 0.999998i | \(0.499369\pi\) | |||||||
\(432\) | 3.81285 | 0.183446 | ||||||||
\(433\) | 1.26450 | 0.0607678 | 0.0303839 | − | 0.999538i | \(-0.490327\pi\) | ||||
0.0303839 | + | 0.999538i | \(0.490327\pi\) | |||||||
\(434\) | 3.03912 | 0.145882 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.0232 | −0.815265 | ||||||||
\(437\) | 1.55780 | 0.0745197 | ||||||||
\(438\) | −1.86803 | −0.0892581 | ||||||||
\(439\) | 29.1767 | 1.39253 | 0.696263 | − | 0.717787i | \(-0.254845\pi\) | ||||
0.696263 | + | 0.717787i | \(0.254845\pi\) | |||||||
\(440\) | −10.3488 | −0.493358 | ||||||||
\(441\) | 7.40363 | 0.352554 | ||||||||
\(442\) | 2.52576 | 0.120138 | ||||||||
\(443\) | −18.2966 | −0.869298 | −0.434649 | − | 0.900600i | \(-0.643128\pi\) | ||||
−0.434649 | + | 0.900600i | \(0.643128\pi\) | |||||||
\(444\) | −12.4575 | −0.591205 | ||||||||
\(445\) | 48.2379 | 2.28669 | ||||||||
\(446\) | 4.24012 | 0.200775 | ||||||||
\(447\) | −9.38848 | −0.444060 | ||||||||
\(448\) | 27.5429 | 1.30128 | ||||||||
\(449\) | −10.6432 | −0.502283 | −0.251142 | − | 0.967950i | \(-0.580806\pi\) | ||||
−0.251142 | + | 0.967950i | \(0.580806\pi\) | |||||||
\(450\) | 1.22399 | 0.0576996 | ||||||||
\(451\) | 8.41090 | 0.396054 | ||||||||
\(452\) | −14.9332 | −0.702397 | ||||||||
\(453\) | 19.6633 | 0.923861 | ||||||||
\(454\) | −0.913431 | −0.0428694 | ||||||||
\(455\) | −60.8196 | −2.85127 | ||||||||
\(456\) | 2.52472 | 0.118231 | ||||||||
\(457\) | 30.2026 | 1.41282 | 0.706408 | − | 0.707804i | \(-0.250314\pi\) | ||||
0.706408 | + | 0.707804i | \(0.250314\pi\) | |||||||
\(458\) | −1.43459 | −0.0670340 | ||||||||
\(459\) | −3.07208 | −0.143392 | ||||||||
\(460\) | −2.94618 | −0.137366 | ||||||||
\(461\) | −36.4593 | −1.69808 | −0.849041 | − | 0.528328i | \(-0.822819\pi\) | ||||
−0.849041 | + | 0.528328i | \(0.822819\pi\) | |||||||
\(462\) | 2.86736 | 0.133402 | ||||||||
\(463\) | 18.1919 | 0.845450 | 0.422725 | − | 0.906258i | \(-0.361074\pi\) | ||||
0.422725 | + | 0.906258i | \(0.361074\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.6084 | 0.723823 | ||||||||
\(466\) | 4.34100 | 0.201093 | ||||||||
\(467\) | 9.91290 | 0.458714 | 0.229357 | − | 0.973342i | \(-0.426338\pi\) | ||||
0.229357 | + | 0.973342i | \(0.426338\pi\) | |||||||
\(468\) | 9.14063 | 0.422526 | ||||||||
\(469\) | 19.9899 | 0.923049 | ||||||||
\(470\) | 2.94350 | 0.135773 | ||||||||
\(471\) | −2.61457 | −0.120473 | ||||||||
\(472\) | 4.26556 | 0.196338 | ||||||||
\(473\) | 1.07171 | 0.0492772 | ||||||||
\(474\) | 1.77722 | 0.0816304 | ||||||||
\(475\) | −24.8340 | −1.13946 | ||||||||
\(476\) | −22.9528 | −1.05204 | ||||||||
\(477\) | 10.9694 | 0.502255 | ||||||||
\(478\) | −4.94755 | −0.226296 | ||||||||
\(479\) | 42.7297 | 1.95237 | 0.976184 | − | 0.216945i | \(-0.0696091\pi\) | ||||
0.976184 | + | 0.216945i | \(0.0696091\pi\) | |||||||
\(480\) | −7.18115 | −0.327773 | ||||||||
\(481\) | −29.3813 | −1.33967 | ||||||||
\(482\) | 0.702689 | 0.0320066 | ||||||||
\(483\) | 1.64562 | 0.0748781 | ||||||||
\(484\) | −14.1841 | −0.644730 | ||||||||
\(485\) | 49.4328 | 2.24463 | ||||||||
\(486\) | 0.177073 | 0.00803218 | ||||||||
\(487\) | −25.4364 | −1.15263 | −0.576316 | − | 0.817227i | \(-0.695510\pi\) | ||||
−0.576316 | + | 0.817227i | \(0.695510\pi\) | |||||||
\(488\) | −2.66460 | −0.120621 | ||||||||
\(489\) | −0.527800 | −0.0238679 | ||||||||
\(490\) | −4.52476 | −0.204408 | ||||||||
\(491\) | 31.4216 | 1.41804 | 0.709018 | − | 0.705190i | \(-0.249138\pi\) | ||||
0.709018 | + | 0.705190i | \(0.249138\pi\) | |||||||
\(492\) | 3.88074 | 0.174957 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.95379 | 0.132897 | ||||||||
\(495\) | 14.7263 | 0.661899 | ||||||||
\(496\) | −17.2429 | −0.774228 | ||||||||
\(497\) | 22.1492 | 0.993526 | ||||||||
\(498\) | −1.25689 | −0.0563226 | ||||||||
\(499\) | −6.94660 | −0.310973 | −0.155486 | − | 0.987838i | \(-0.549694\pi\) | ||||
−0.155486 | + | 0.987838i | \(0.549694\pi\) | |||||||
\(500\) | 12.9939 | 0.581105 | ||||||||
\(501\) | −15.0489 | −0.672337 | ||||||||
\(502\) | −5.59715 | −0.249813 | ||||||||
\(503\) | 26.5513 | 1.18386 | 0.591932 | − | 0.805988i | \(-0.298365\pi\) | ||||
0.591932 | + | 0.805988i | \(0.298365\pi\) | |||||||
\(504\) | 2.66704 | 0.118799 | ||||||||
\(505\) | −2.81790 | −0.125395 | ||||||||
\(506\) | 0.327596 | 0.0145634 | ||||||||
\(507\) | 8.55844 | 0.380094 | ||||||||
\(508\) | −2.43067 | −0.107844 | ||||||||
\(509\) | −1.38050 | −0.0611896 | −0.0305948 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305948 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(510\) | 1.87751 | 0.0831377 | ||||||||
\(511\) | 40.0377 | 1.77116 | ||||||||
\(512\) | 13.2920 | 0.587430 | ||||||||
\(513\) | −3.59269 | −0.158621 | ||||||||
\(514\) | −0.717192 | −0.0316340 | ||||||||
\(515\) | 17.1120 | 0.754045 | ||||||||
\(516\) | 0.494481 | 0.0217683 | ||||||||
\(517\) | 20.5498 | 0.903780 | ||||||||
\(518\) | −4.25255 | −0.186846 | ||||||||
\(519\) | 0.103233 | 0.00453142 | ||||||||
\(520\) | −11.2616 | −0.493856 | ||||||||
\(521\) | 8.46722 | 0.370956 | 0.185478 | − | 0.982648i | \(-0.440617\pi\) | ||||
0.185478 | + | 0.982648i | \(0.440617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.74716 | 0.207579 | 0.103789 | − | 0.994599i | \(-0.466903\pi\) | ||||
0.103789 | + | 0.994599i | \(0.466903\pi\) | |||||||
\(524\) | 7.86599 | 0.343628 | ||||||||
\(525\) | −26.2339 | −1.14494 | ||||||||
\(526\) | −2.53216 | −0.110407 | ||||||||
\(527\) | 13.8929 | 0.605183 | ||||||||
\(528\) | −16.2684 | −0.707992 | ||||||||
\(529\) | −22.8120 | −0.991826 | ||||||||
\(530\) | −6.70400 | −0.291203 | ||||||||
\(531\) | −6.06991 | −0.263411 | ||||||||
\(532\) | −26.8425 | −1.16377 | ||||||||
\(533\) | 9.15285 | 0.396454 | ||||||||
\(534\) | −2.47480 | −0.107095 | ||||||||
\(535\) | 39.8152 | 1.72136 | ||||||||
\(536\) | 3.70143 | 0.159877 | ||||||||
\(537\) | −4.04916 | −0.174734 | ||||||||
\(538\) | 3.81015 | 0.164267 | ||||||||
\(539\) | −31.5893 | −1.36065 | ||||||||
\(540\) | 6.79464 | 0.292395 | ||||||||
\(541\) | 2.44407 | 0.105079 | 0.0525394 | − | 0.998619i | \(-0.483268\pi\) | ||||
0.0525394 | + | 0.998619i | \(0.483268\pi\) | |||||||
\(542\) | −3.50428 | −0.150522 | ||||||||
\(543\) | −11.5222 | −0.494467 | ||||||||
\(544\) | −6.39186 | −0.274049 | ||||||||
\(545\) | −29.8451 | −1.27843 | ||||||||
\(546\) | 3.12030 | 0.133536 | ||||||||
\(547\) | 6.17333 | 0.263952 | 0.131976 | − | 0.991253i | \(-0.457868\pi\) | ||||
0.131976 | + | 0.991253i | \(0.457868\pi\) | |||||||
\(548\) | −32.7856 | −1.40053 | ||||||||
\(549\) | 3.79174 | 0.161828 | ||||||||
\(550\) | −5.22245 | −0.222686 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.304710 | 0.0129693 | ||||||||
\(553\) | −38.0913 | −1.61981 | ||||||||
\(554\) | 0.992235 | 0.0421560 | ||||||||
\(555\) | −21.8404 | −0.927075 | ||||||||
\(556\) | −16.2828 | −0.690544 | ||||||||
\(557\) | −12.4564 | −0.527794 | −0.263897 | − | 0.964551i | \(-0.585008\pi\) | ||||
−0.263897 | + | 0.964551i | \(0.585008\pi\) | |||||||
\(558\) | −0.800776 | −0.0338996 | ||||||||
\(559\) | 1.16625 | 0.0493270 | ||||||||
\(560\) | 49.9442 | 2.11053 | ||||||||
\(561\) | 13.1077 | 0.553409 | ||||||||
\(562\) | −1.91567 | −0.0808078 | ||||||||
\(563\) | −3.58213 | −0.150969 | −0.0754843 | − | 0.997147i | \(-0.524050\pi\) | ||||
−0.0754843 | + | 0.997147i | \(0.524050\pi\) | |||||||
\(564\) | 9.48157 | 0.399246 | ||||||||
\(565\) | −26.1809 | −1.10144 | ||||||||
\(566\) | −1.31652 | −0.0553374 | ||||||||
\(567\) | −3.79521 | −0.159384 | ||||||||
\(568\) | 4.10124 | 0.172084 | ||||||||
\(569\) | −26.8881 | −1.12721 | −0.563603 | − | 0.826046i | \(-0.690585\pi\) | ||||
−0.563603 | + | 0.826046i | \(0.690585\pi\) | |||||||
\(570\) | 2.19568 | 0.0919671 | ||||||||
\(571\) | −30.0109 | −1.25592 | −0.627959 | − | 0.778247i | \(-0.716109\pi\) | ||||
−0.627959 | + | 0.778247i | \(0.716109\pi\) | |||||||
\(572\) | −39.0006 | −1.63070 | ||||||||
\(573\) | 1.55942 | 0.0651458 | ||||||||
\(574\) | 1.32475 | 0.0552941 | ||||||||
\(575\) | −2.99723 | −0.124993 | ||||||||
\(576\) | −7.25729 | −0.302387 | ||||||||
\(577\) | −2.86591 | −0.119309 | −0.0596546 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596546 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(578\) | −1.33908 | −0.0556985 | ||||||||
\(579\) | 13.3775 | 0.555949 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.9390 | 1.11762 | ||||||||
\(582\) | −2.53611 | −0.105125 | ||||||||
\(583\) | −46.8035 | −1.93840 | ||||||||
\(584\) | 7.41357 | 0.306776 | ||||||||
\(585\) | 16.0254 | 0.662567 | ||||||||
\(586\) | 2.19860 | 0.0908234 | ||||||||
\(587\) | 21.8403 | 0.901446 | 0.450723 | − | 0.892664i | \(-0.351166\pi\) | ||||
0.450723 | + | 0.892664i | \(0.351166\pi\) | |||||||
\(588\) | −14.5751 | −0.601068 | ||||||||
\(589\) | 16.2472 | 0.669455 | ||||||||
\(590\) | 3.70965 | 0.152724 | ||||||||
\(591\) | −12.7756 | −0.525519 | ||||||||
\(592\) | 24.1275 | 0.991635 | ||||||||
\(593\) | 19.9669 | 0.819941 | 0.409971 | − | 0.912099i | \(-0.365539\pi\) | ||||
0.409971 | + | 0.912099i | \(0.365539\pi\) | |||||||
\(594\) | −0.755521 | −0.0309994 | ||||||||
\(595\) | −40.2409 | −1.64971 | ||||||||
\(596\) | 18.4826 | 0.757077 | ||||||||
\(597\) | 8.82206 | 0.361063 | ||||||||
\(598\) | 0.356494 | 0.0145781 | ||||||||
\(599\) | −25.8925 | −1.05794 | −0.528969 | − | 0.848641i | \(-0.677421\pi\) | ||||
−0.528969 | + | 0.848641i | \(0.677421\pi\) | |||||||
\(600\) | −4.85759 | −0.198310 | ||||||||
\(601\) | 24.1209 | 0.983911 | 0.491956 | − | 0.870620i | \(-0.336282\pi\) | ||||
0.491956 | + | 0.870620i | \(0.336282\pi\) | |||||||
\(602\) | 0.168799 | 0.00687973 | ||||||||
\(603\) | −5.26714 | −0.214495 | ||||||||
\(604\) | −38.7100 | −1.57509 | ||||||||
\(605\) | −24.8675 | −1.01101 | ||||||||
\(606\) | 0.144570 | 0.00587276 | ||||||||
\(607\) | −5.67771 | −0.230451 | −0.115226 | − | 0.993339i | \(-0.536759\pi\) | ||||
−0.115226 | + | 0.993339i | \(0.536759\pi\) | |||||||
\(608\) | −7.47505 | −0.303153 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.31734 | −0.0938262 | ||||||||
\(611\) | 22.3626 | 0.904693 | ||||||||
\(612\) | 6.04783 | 0.244469 | ||||||||
\(613\) | −44.8240 | −1.81042 | −0.905212 | − | 0.424961i | \(-0.860288\pi\) | ||||
−0.905212 | + | 0.424961i | \(0.860288\pi\) | |||||||
\(614\) | 4.25660 | 0.171782 | ||||||||
\(615\) | 6.80372 | 0.274353 | ||||||||
\(616\) | −11.3795 | −0.458495 | ||||||||
\(617\) | −29.0434 | −1.16924 | −0.584622 | − | 0.811306i | \(-0.698757\pi\) | ||||
−0.584622 | + | 0.811306i | \(0.698757\pi\) | |||||||
\(618\) | −0.877917 | −0.0353150 | ||||||||
\(619\) | −7.61305 | −0.305994 | −0.152997 | − | 0.988227i | \(-0.548893\pi\) | ||||
−0.152997 | + | 0.988227i | \(0.548893\pi\) | |||||||
\(620\) | −30.7274 | −1.23404 | ||||||||
\(621\) | −0.433603 | −0.0173999 | ||||||||
\(622\) | −5.53432 | −0.221906 | ||||||||
\(623\) | 53.0426 | 2.12511 | ||||||||
\(624\) | −17.7035 | −0.708707 | ||||||||
\(625\) | −11.7810 | −0.471238 | ||||||||
\(626\) | −3.72753 | −0.148982 | ||||||||
\(627\) | 15.3290 | 0.612182 | ||||||||
\(628\) | 5.14716 | 0.205394 | ||||||||
\(629\) | −19.4399 | −0.775121 | ||||||||
\(630\) | 2.31946 | 0.0924094 | ||||||||
\(631\) | 43.7635 | 1.74220 | 0.871099 | − | 0.491107i | \(-0.163408\pi\) | ||||
0.871099 | + | 0.491107i | \(0.163408\pi\) | |||||||
\(632\) | −7.05316 | −0.280560 | ||||||||
\(633\) | −15.0234 | −0.597126 | ||||||||
\(634\) | −2.77144 | −0.110068 | ||||||||
\(635\) | −4.26146 | −0.169111 | ||||||||
\(636\) | −21.5949 | −0.856292 | ||||||||
\(637\) | −34.3758 | −1.36202 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.83609 | −0.230872 | ||||||||
\(640\) | 18.7976 | 0.743041 | ||||||||
\(641\) | 15.3364 | 0.605750 | 0.302875 | − | 0.953030i | \(-0.402053\pi\) | ||||
0.302875 | + | 0.953030i | \(0.402053\pi\) | |||||||
\(642\) | −2.04269 | −0.0806184 | ||||||||
\(643\) | 27.2674 | 1.07532 | 0.537661 | − | 0.843161i | \(-0.319308\pi\) | ||||
0.537661 | + | 0.843161i | \(0.319308\pi\) | |||||||
\(644\) | −3.23963 | −0.127659 | ||||||||
\(645\) | 0.866924 | 0.0341351 | ||||||||
\(646\) | 1.95435 | 0.0768930 | ||||||||
\(647\) | −24.1819 | −0.950690 | −0.475345 | − | 0.879800i | \(-0.657677\pi\) | ||||
−0.475345 | + | 0.879800i | \(0.657677\pi\) | |||||||
\(648\) | −0.702739 | −0.0276062 | ||||||||
\(649\) | 25.8986 | 1.01661 | ||||||||
\(650\) | −5.68313 | −0.222911 | ||||||||
\(651\) | 17.1631 | 0.672675 | ||||||||
\(652\) | 1.03905 | 0.0406923 | ||||||||
\(653\) | −25.1321 | −0.983497 | −0.491748 | − | 0.870737i | \(-0.663642\pi\) | ||||
−0.491748 | + | 0.870737i | \(0.663642\pi\) | |||||||
\(654\) | 1.53118 | 0.0598739 | ||||||||
\(655\) | 13.7907 | 0.538846 | ||||||||
\(656\) | −7.51619 | −0.293458 | ||||||||
\(657\) | −10.5495 | −0.411577 | ||||||||
\(658\) | 3.23668 | 0.126179 | ||||||||
\(659\) | 9.64762 | 0.375818 | 0.187909 | − | 0.982186i | \(-0.439829\pi\) | ||||
0.187909 | + | 0.982186i | \(0.439829\pi\) | |||||||
\(660\) | −28.9909 | −1.12847 | ||||||||
\(661\) | 15.7907 | 0.614188 | 0.307094 | − | 0.951679i | \(-0.400643\pi\) | ||||
0.307094 | + | 0.951679i | \(0.400643\pi\) | |||||||
\(662\) | −3.44575 | −0.133923 | ||||||||
\(663\) | 14.2640 | 0.553967 | ||||||||
\(664\) | 4.98815 | 0.193578 | ||||||||
\(665\) | −47.0603 | −1.82492 | ||||||||
\(666\) | 1.12051 | 0.0434187 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 29.6260 | 1.14627 | ||||||||
\(669\) | 23.9456 | 0.925791 | ||||||||
\(670\) | 3.21904 | 0.124362 | ||||||||
\(671\) | −16.1783 | −0.624557 | ||||||||
\(672\) | −7.89643 | −0.304611 | ||||||||
\(673\) | −16.3293 | −0.629450 | −0.314725 | − | 0.949183i | \(-0.601912\pi\) | ||||
−0.314725 | + | 0.949183i | \(0.601912\pi\) | |||||||
\(674\) | 3.57297 | 0.137625 | ||||||||
\(675\) | 6.91237 | 0.266057 | ||||||||
\(676\) | −16.8485 | −0.648021 | ||||||||
\(677\) | 11.3525 | 0.436314 | 0.218157 | − | 0.975914i | \(-0.429996\pi\) | ||||
0.218157 | + | 0.975914i | \(0.429996\pi\) | |||||||
\(678\) | 1.34319 | 0.0515848 | ||||||||
\(679\) | 54.3566 | 2.08602 | ||||||||
\(680\) | −7.45118 | −0.285740 | ||||||||
\(681\) | −5.15851 | −0.197674 | ||||||||
\(682\) | 3.41670 | 0.130832 | ||||||||
\(683\) | 21.0754 | 0.806426 | 0.403213 | − | 0.915106i | \(-0.367893\pi\) | ||||
0.403213 | + | 0.915106i | \(0.367893\pi\) | |||||||
\(684\) | 7.07272 | 0.270432 | ||||||||
\(685\) | −57.4797 | −2.19619 | ||||||||
\(686\) | −0.271248 | −0.0103563 | ||||||||
\(687\) | −8.10170 | −0.309099 | ||||||||
\(688\) | −0.957706 | −0.0365122 | ||||||||
\(689\) | −50.9321 | −1.94036 | ||||||||
\(690\) | 0.264998 | 0.0100883 | ||||||||
\(691\) | 5.59507 | 0.212846 | 0.106423 | − | 0.994321i | \(-0.466060\pi\) | ||||
0.106423 | + | 0.994321i | \(0.466060\pi\) | |||||||
\(692\) | −0.203229 | −0.00772561 | ||||||||
\(693\) | 16.1931 | 0.615126 | ||||||||
\(694\) | 0.139596 | 0.00529899 | ||||||||
\(695\) | −28.5470 | −1.08285 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.05592 | 0.229384 | ||||||||
\(698\) | 3.70820 | 0.140357 | ||||||||
\(699\) | 24.5153 | 0.927255 | ||||||||
\(700\) | 51.6453 | 1.95201 | ||||||||
\(701\) | −17.3045 | −0.653583 | −0.326791 | − | 0.945097i | \(-0.605967\pi\) | ||||
−0.326791 | + | 0.945097i | \(0.605967\pi\) | |||||||
\(702\) | −0.822167 | −0.0310307 | ||||||||
\(703\) | −22.7343 | −0.857440 | ||||||||
\(704\) | 30.9649 | 1.16703 | ||||||||
\(705\) | 16.6231 | 0.626062 | ||||||||
\(706\) | −6.39023 | −0.240500 | ||||||||
\(707\) | −3.09858 | −0.116534 | ||||||||
\(708\) | 11.9495 | 0.449089 | ||||||||
\(709\) | 18.6967 | 0.702171 | 0.351085 | − | 0.936343i | \(-0.385813\pi\) | ||||
0.351085 | + | 0.936343i | \(0.385813\pi\) | |||||||
\(710\) | 3.56675 | 0.133858 | ||||||||
\(711\) | 10.0367 | 0.376405 | ||||||||
\(712\) | 9.82162 | 0.368081 | ||||||||
\(713\) | 1.96089 | 0.0734357 | ||||||||
\(714\) | 2.06452 | 0.0772628 | ||||||||
\(715\) | −68.3759 | −2.55711 | ||||||||
\(716\) | 7.97137 | 0.297904 | ||||||||
\(717\) | −27.9408 | −1.04347 | ||||||||
\(718\) | 3.29761 | 0.123066 | ||||||||
\(719\) | −17.2847 | −0.644610 | −0.322305 | − | 0.946636i | \(-0.604458\pi\) | ||||
−0.322305 | + | 0.946636i | \(0.604458\pi\) | |||||||
\(720\) | −13.1598 | −0.490437 | ||||||||
\(721\) | 18.8164 | 0.700761 | ||||||||
\(722\) | −1.07884 | −0.0401501 | ||||||||
\(723\) | 3.96836 | 0.147585 | ||||||||
\(724\) | 22.6832 | 0.843015 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.27581 | 0.0473496 | ||||||||
\(727\) | 2.87185 | 0.106511 | 0.0532556 | − | 0.998581i | \(-0.483040\pi\) | ||||
0.0532556 | + | 0.998581i | \(0.483040\pi\) | |||||||
\(728\) | −12.3834 | −0.458958 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.44739 | 0.238629 | ||||||||
\(731\) | 0.771639 | 0.0285401 | ||||||||
\(732\) | −7.46459 | −0.275899 | ||||||||
\(733\) | 46.8195 | 1.72932 | 0.864659 | − | 0.502359i | \(-0.167534\pi\) | ||||
0.864659 | + | 0.502359i | \(0.167534\pi\) | |||||||
\(734\) | 2.85657 | 0.105438 | ||||||||
\(735\) | −25.5531 | −0.942540 | ||||||||
\(736\) | −0.902168 | −0.0332543 | ||||||||
\(737\) | 22.4735 | 0.827821 | ||||||||
\(738\) | −0.349059 | −0.0128490 | ||||||||
\(739\) | 25.0754 | 0.922415 | 0.461208 | − | 0.887292i | \(-0.347416\pi\) | ||||
0.461208 | + | 0.887292i | \(0.347416\pi\) | |||||||
\(740\) | 42.9961 | 1.58057 | ||||||||
\(741\) | 16.6812 | 0.612800 | ||||||||
\(742\) | −7.37175 | −0.270626 | ||||||||
\(743\) | 28.1550 | 1.03291 | 0.516453 | − | 0.856316i | \(-0.327252\pi\) | ||||
0.516453 | + | 0.856316i | \(0.327252\pi\) | |||||||
\(744\) | 3.17800 | 0.116511 | ||||||||
\(745\) | 32.4037 | 1.18718 | ||||||||
\(746\) | 0.201140 | 0.00736426 | ||||||||
\(747\) | −7.09816 | −0.259708 | ||||||||
\(748\) | −25.8045 | −0.943505 | ||||||||
\(749\) | 43.7810 | 1.59972 | ||||||||
\(750\) | −1.16876 | −0.0426769 | ||||||||
\(751\) | −40.8050 | −1.48900 | −0.744498 | − | 0.667624i | \(-0.767311\pi\) | ||||
−0.744498 | + | 0.667624i | \(0.767311\pi\) | |||||||
\(752\) | −18.3638 | −0.669660 | ||||||||
\(753\) | −31.6093 | −1.15191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −67.8664 | −2.46991 | ||||||||
\(756\) | 7.47142 | 0.271733 | ||||||||
\(757\) | 40.8015 | 1.48296 | 0.741478 | − | 0.670977i | \(-0.234125\pi\) | ||||
0.741478 | + | 0.670977i | \(0.234125\pi\) | |||||||
\(758\) | 5.35601 | 0.194539 | ||||||||
\(759\) | 1.85007 | 0.0671532 | ||||||||
\(760\) | −8.71389 | −0.316086 | ||||||||
\(761\) | −41.6230 | −1.50883 | −0.754417 | − | 0.656395i | \(-0.772080\pi\) | ||||
−0.754417 | + | 0.656395i | \(0.772080\pi\) | |||||||
\(762\) | 0.218631 | 0.00792015 | ||||||||
\(763\) | −32.8179 | −1.18809 | ||||||||
\(764\) | −3.06995 | −0.111067 | ||||||||
\(765\) | 10.6031 | 0.383355 | ||||||||
\(766\) | −3.11288 | −0.112473 | ||||||||
\(767\) | 28.1832 | 1.01764 | ||||||||
\(768\) | 13.5502 | 0.488950 | ||||||||
\(769\) | −9.30333 | −0.335487 | −0.167743 | − | 0.985831i | \(-0.553648\pi\) | ||||
−0.167743 | + | 0.985831i | \(0.553648\pi\) | |||||||
\(770\) | −9.89650 | −0.356645 | ||||||||
\(771\) | −4.05027 | −0.145867 | ||||||||
\(772\) | −26.3355 | −0.947836 | ||||||||
\(773\) | 14.4098 | 0.518284 | 0.259142 | − | 0.965839i | \(-0.416560\pi\) | ||||
0.259142 | + | 0.965839i | \(0.416560\pi\) | |||||||
\(774\) | −0.0444768 | −0.00159869 | ||||||||
\(775\) | −31.2599 | −1.12289 | ||||||||
\(776\) | 10.0649 | 0.361310 | ||||||||
\(777\) | −24.0159 | −0.861564 | ||||||||
\(778\) | 6.82512 | 0.244692 | ||||||||
\(779\) | 7.08218 | 0.253745 | ||||||||
\(780\) | −31.5483 | −1.12961 | ||||||||
\(781\) | 24.9010 | 0.891028 | ||||||||
\(782\) | 0.235872 | 0.00843476 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.2289 | 1.00818 | ||||||||
\(785\) | 9.02400 | 0.322080 | ||||||||
\(786\) | −0.707518 | −0.0252363 | ||||||||
\(787\) | 31.0529 | 1.10692 | 0.553459 | − | 0.832877i | \(-0.313308\pi\) | ||||
0.553459 | + | 0.832877i | \(0.313308\pi\) | |||||||
\(788\) | 25.1507 | 0.895957 | ||||||||
\(789\) | −14.3001 | −0.509097 | ||||||||
\(790\) | −6.13395 | −0.218236 | ||||||||
\(791\) | −28.7886 | −1.02360 | ||||||||
\(792\) | 2.99840 | 0.106543 | ||||||||
\(793\) | −17.6055 | −0.625188 | ||||||||
\(794\) | −3.73166 | −0.132432 | ||||||||
\(795\) | −37.8602 | −1.34276 | ||||||||
\(796\) | −17.3675 | −0.615575 | ||||||||
\(797\) | −33.4931 | −1.18639 | −0.593193 | − | 0.805060i | \(-0.702133\pi\) | ||||
−0.593193 | + | 0.805060i | \(0.702133\pi\) | |||||||
\(798\) | 2.41439 | 0.0854683 | ||||||||
\(799\) | 14.7960 | 0.523446 | ||||||||
\(800\) | 14.3821 | 0.508484 | ||||||||
\(801\) | −13.9762 | −0.493825 | ||||||||
\(802\) | −6.14883 | −0.217123 | ||||||||
\(803\) | 45.0120 | 1.58844 | ||||||||
\(804\) | 10.3691 | 0.365691 | ||||||||
\(805\) | −5.67973 | −0.200184 | ||||||||
\(806\) | 3.71809 | 0.130964 | ||||||||
\(807\) | 21.5174 | 0.757449 | ||||||||
\(808\) | −0.573747 | −0.0201844 | ||||||||
\(809\) | 17.9475 | 0.631000 | 0.315500 | − | 0.948926i | \(-0.397828\pi\) | ||||
0.315500 | + | 0.948926i | \(0.397828\pi\) | |||||||
\(810\) | −0.611154 | −0.0214738 | ||||||||
\(811\) | 6.11810 | 0.214836 | 0.107418 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107418 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.7901 | −0.694068 | ||||||||
\(814\) | −4.78089 | −0.167570 | ||||||||
\(815\) | 1.82166 | 0.0638101 | ||||||||
\(816\) | −11.7134 | −0.410051 | ||||||||
\(817\) | 0.902404 | 0.0315711 | ||||||||
\(818\) | −0.555063 | −0.0194073 | ||||||||
\(819\) | 17.6216 | 0.615747 | ||||||||
\(820\) | −13.3941 | −0.467743 | ||||||||
\(821\) | −38.5521 | −1.34548 | −0.672738 | − | 0.739881i | \(-0.734882\pi\) | ||||
−0.672738 | + | 0.739881i | \(0.734882\pi\) | |||||||
\(822\) | 2.94895 | 0.102856 | ||||||||
\(823\) | −15.0217 | −0.523625 | −0.261813 | − | 0.965119i | \(-0.584320\pi\) | ||||
−0.261813 | + | 0.965119i | \(0.584320\pi\) | |||||||
\(824\) | 3.48414 | 0.121376 | ||||||||
\(825\) | −29.4932 | −1.02682 | ||||||||
\(826\) | 4.07915 | 0.141932 | ||||||||
\(827\) | 17.5838 | 0.611448 | 0.305724 | − | 0.952120i | \(-0.401101\pi\) | ||||
0.305724 | + | 0.952120i | \(0.401101\pi\) | |||||||
\(828\) | 0.853611 | 0.0296650 | ||||||||
\(829\) | −27.9182 | −0.969640 | −0.484820 | − | 0.874614i | \(-0.661115\pi\) | ||||
−0.484820 | + | 0.874614i | \(0.661115\pi\) | |||||||
\(830\) | 4.33807 | 0.150577 | ||||||||
\(831\) | 5.60355 | 0.194385 | ||||||||
\(832\) | 33.6964 | 1.16821 | ||||||||
\(833\) | −22.7445 | −0.788051 | ||||||||
\(834\) | 1.46458 | 0.0507142 | ||||||||
\(835\) | 51.9404 | 1.79747 | ||||||||
\(836\) | −30.1774 | −1.04371 | ||||||||
\(837\) | −4.52230 | −0.156314 | ||||||||
\(838\) | −1.53753 | −0.0531131 | ||||||||
\(839\) | −22.1987 | −0.766384 | −0.383192 | − | 0.923669i | \(-0.625175\pi\) | ||||
−0.383192 | + | 0.923669i | \(0.625175\pi\) | |||||||
\(840\) | −9.20511 | −0.317606 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 5.02585 | 0.173202 | ||||||||
\(843\) | −10.8186 | −0.372611 | ||||||||
\(844\) | 29.5757 | 1.01804 | ||||||||
\(845\) | −29.5389 | −1.01617 | ||||||||
\(846\) | −0.852834 | −0.0293210 | ||||||||
\(847\) | −27.3444 | −0.939566 | ||||||||
\(848\) | 41.8248 | 1.43627 | ||||||||
\(849\) | −7.43490 | −0.255165 | ||||||||
\(850\) | −3.76020 | −0.128974 | ||||||||
\(851\) | −2.74381 | −0.0940568 | ||||||||
\(852\) | 11.4892 | 0.393613 | ||||||||
\(853\) | 26.4548 | 0.905794 | 0.452897 | − | 0.891563i | \(-0.350391\pi\) | ||||
0.452897 | + | 0.891563i | \(0.350391\pi\) | |||||||
\(854\) | −2.54816 | −0.0871961 | ||||||||
\(855\) | 12.3999 | 0.424068 | ||||||||
\(856\) | 8.10670 | 0.277081 | ||||||||
\(857\) | −45.8418 | −1.56592 | −0.782962 | − | 0.622069i | \(-0.786292\pi\) | ||||
−0.782962 | + | 0.622069i | \(0.786292\pi\) | |||||||
\(858\) | 3.50797 | 0.119760 | ||||||||
\(859\) | 8.29444 | 0.283003 | 0.141501 | − | 0.989938i | \(-0.454807\pi\) | ||||
0.141501 | + | 0.989938i | \(0.454807\pi\) | |||||||
\(860\) | −1.70667 | −0.0581968 | ||||||||
\(861\) | 7.48141 | 0.254966 | ||||||||
\(862\) | 0.0145820 | 0.000496666 0 | ||||||||
\(863\) | −7.74485 | −0.263638 | −0.131819 | − | 0.991274i | \(-0.542082\pi\) | ||||
−0.131819 | + | 0.991274i | \(0.542082\pi\) | |||||||
\(864\) | 2.08063 | 0.0707845 | ||||||||
\(865\) | −0.356301 | −0.0121146 | ||||||||
\(866\) | 0.223908 | 0.00760869 | ||||||||
\(867\) | −7.56234 | −0.256830 | ||||||||
\(868\) | −33.7880 | −1.14684 | ||||||||
\(869\) | −42.8238 | −1.45270 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4559 | 0.828657 | ||||||||
\(872\) | −6.07671 | −0.205783 | ||||||||
\(873\) | −14.3224 | −0.484741 | ||||||||
\(874\) | 0.275844 | 0.00933055 | ||||||||
\(875\) | 25.0500 | 0.846845 | ||||||||
\(876\) | 20.7683 | 0.701696 | ||||||||
\(877\) | 37.2741 | 1.25866 | 0.629328 | − | 0.777139i | \(-0.283330\pi\) | ||||
0.629328 | + | 0.777139i | \(0.283330\pi\) | |||||||
\(878\) | 5.16639 | 0.174357 | ||||||||
\(879\) | 12.4164 | 0.418794 | ||||||||
\(880\) | 56.1493 | 1.89279 | ||||||||
\(881\) | −15.2380 | −0.513382 | −0.256691 | − | 0.966493i | \(-0.582632\pi\) | ||||
−0.256691 | + | 0.966493i | \(0.582632\pi\) | |||||||
\(882\) | 1.31098 | 0.0441430 | ||||||||
\(883\) | −48.7085 | −1.63917 | −0.819586 | − | 0.572956i | \(-0.805797\pi\) | ||||
−0.819586 | + | 0.572956i | \(0.805797\pi\) | |||||||
\(884\) | −28.0807 | −0.944457 | ||||||||
\(885\) | 20.9499 | 0.704222 | ||||||||
\(886\) | −3.23983 | −0.108844 | ||||||||
\(887\) | −8.21801 | −0.275934 | −0.137967 | − | 0.990437i | \(-0.544057\pi\) | ||||
−0.137967 | + | 0.990437i | \(0.544057\pi\) | |||||||
\(888\) | −4.44689 | −0.149228 | ||||||||
\(889\) | −4.68592 | −0.157161 | ||||||||
\(890\) | 8.54161 | 0.286315 | ||||||||
\(891\) | −4.26673 | −0.142941 | ||||||||
\(892\) | −47.1404 | −1.57838 | ||||||||
\(893\) | 17.3034 | 0.579037 | ||||||||
\(894\) | −1.66244 | −0.0556004 | ||||||||
\(895\) | 13.9754 | 0.467146 | ||||||||
\(896\) | 20.6700 | 0.690535 | ||||||||
\(897\) | 2.01327 | 0.0672210 | ||||||||
\(898\) | −1.88462 | −0.0628906 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −13.6080 | −0.453600 | ||||||||
\(901\) | −33.6989 | −1.12267 | ||||||||
\(902\) | 1.48934 | 0.0495896 | ||||||||
\(903\) | 0.953274 | 0.0317230 | ||||||||
\(904\) | −5.33063 | −0.177294 | ||||||||
\(905\) | 39.7682 | 1.32194 | ||||||||
\(906\) | 3.48183 | 0.115676 | ||||||||
\(907\) | −4.20133 | −0.139503 | −0.0697514 | − | 0.997564i | \(-0.522221\pi\) | ||||
−0.0697514 | + | 0.997564i | \(0.522221\pi\) | |||||||
\(908\) | 10.1553 | 0.337014 | ||||||||
\(909\) | 0.816445 | 0.0270798 | ||||||||
\(910\) | −10.7695 | −0.357005 | ||||||||
\(911\) | −13.0361 | −0.431906 | −0.215953 | − | 0.976404i | \(-0.569286\pi\) | ||||
−0.215953 | + | 0.976404i | \(0.569286\pi\) | |||||||
\(912\) | −13.6984 | −0.453599 | ||||||||
\(913\) | 30.2859 | 1.00232 | ||||||||
\(914\) | 5.34805 | 0.176898 | ||||||||
\(915\) | −13.0869 | −0.432640 | ||||||||
\(916\) | 15.9494 | 0.526982 | ||||||||
\(917\) | 15.1643 | 0.500769 | ||||||||
\(918\) | −0.543981 | −0.0179541 | ||||||||
\(919\) | 2.15993 | 0.0712497 | 0.0356248 | − | 0.999365i | \(-0.488658\pi\) | ||||
0.0356248 | + | 0.999365i | \(0.488658\pi\) | |||||||
\(920\) | −1.05168 | −0.0346730 | ||||||||
\(921\) | 24.0387 | 0.792102 | ||||||||
\(922\) | −6.45595 | −0.212616 | ||||||||
\(923\) | 27.0976 | 0.891927 | ||||||||
\(924\) | −31.8785 | −1.04873 | ||||||||
\(925\) | 43.7411 | 1.43820 | ||||||||
\(926\) | 3.22129 | 0.105858 | ||||||||
\(927\) | −4.95795 | −0.162840 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.52224 | 0.181179 | 0.0905894 | − | 0.995888i | \(-0.471125\pi\) | ||||
0.0905894 | + | 0.995888i | \(0.471125\pi\) | |||||||
\(930\) | 2.76382 | 0.0906294 | ||||||||
\(931\) | −26.5989 | −0.871744 | ||||||||
\(932\) | −48.2620 | −1.58087 | ||||||||
\(933\) | −31.2545 | −1.02323 | ||||||||
\(934\) | 1.75530 | 0.0574353 | ||||||||
\(935\) | −45.2404 | −1.47952 | ||||||||
\(936\) | 3.26289 | 0.106651 | ||||||||
\(937\) | 55.7255 | 1.82047 | 0.910237 | − | 0.414089i | \(-0.135900\pi\) | ||||
0.910237 | + | 0.414089i | \(0.135900\pi\) | |||||||
\(938\) | 3.53967 | 0.115574 | ||||||||
\(939\) | −21.0508 | −0.686968 | ||||||||
\(940\) | −32.7250 | −1.06737 | ||||||||
\(941\) | 52.7691 | 1.72022 | 0.860112 | − | 0.510105i | \(-0.170394\pi\) | ||||
0.860112 | + | 0.510105i | \(0.170394\pi\) | |||||||
\(942\) | −0.462969 | −0.0150843 | ||||||||
\(943\) | 0.854752 | 0.0278345 | ||||||||
\(944\) | −23.1437 | −0.753262 | ||||||||
\(945\) | 13.0989 | 0.426107 | ||||||||
\(946\) | 0.189770 | 0.00616997 | ||||||||
\(947\) | 42.3685 | 1.37679 | 0.688396 | − | 0.725335i | \(-0.258315\pi\) | ||||
0.688396 | + | 0.725335i | \(0.258315\pi\) | |||||||
\(948\) | −19.7586 | −0.641731 | ||||||||
\(949\) | 48.9826 | 1.59004 | ||||||||
\(950\) | −4.39742 | −0.142671 | ||||||||
\(951\) | −15.6515 | −0.507533 | ||||||||
\(952\) | −8.19336 | −0.265548 | ||||||||
\(953\) | 1.43433 | 0.0464623 | 0.0232312 | − | 0.999730i | \(-0.492605\pi\) | ||||
0.0232312 | + | 0.999730i | \(0.492605\pi\) | |||||||
\(954\) | 1.94238 | 0.0628870 | ||||||||
\(955\) | −5.38224 | −0.174165 | ||||||||
\(956\) | 55.0055 | 1.77900 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.56626 | 0.244455 | ||||||||
\(959\) | −63.2050 | −2.04100 | ||||||||
\(960\) | 25.0480 | 0.808421 | ||||||||
\(961\) | −10.5488 | −0.340283 | ||||||||
\(962\) | −5.20263 | −0.167739 | ||||||||
\(963\) | −11.5359 | −0.371738 | ||||||||
\(964\) | −7.81230 | −0.251617 | ||||||||
\(965\) | −46.1715 | −1.48631 | ||||||||
\(966\) | 0.291394 | 0.00937543 | ||||||||
\(967\) | −10.4202 | −0.335092 | −0.167546 | − | 0.985864i | \(-0.553584\pi\) | ||||
−0.167546 | + | 0.985864i | \(0.553584\pi\) | |||||||
\(968\) | −5.06322 | −0.162738 | ||||||||
\(969\) | 11.0370 | 0.354560 | ||||||||
\(970\) | 8.75321 | 0.281049 | ||||||||
\(971\) | −39.4639 | −1.26646 | −0.633228 | − | 0.773965i | \(-0.718271\pi\) | ||||
−0.633228 | + | 0.773965i | \(0.718271\pi\) | |||||||
\(972\) | −1.96865 | −0.0631443 | ||||||||
\(973\) | −31.3904 | −1.00633 | ||||||||
\(974\) | −4.50408 | −0.144320 | ||||||||
\(975\) | −32.0949 | −1.02786 | ||||||||
\(976\) | 14.4574 | 0.462769 | ||||||||
\(977\) | 7.31111 | 0.233903 | 0.116952 | − | 0.993138i | \(-0.462688\pi\) | ||||
0.116952 | + | 0.993138i | \(0.462688\pi\) | |||||||
\(978\) | −0.0934589 | −0.00298849 | ||||||||
\(979\) | 59.6327 | 1.90587 | ||||||||
\(980\) | 50.3050 | 1.60693 | ||||||||
\(981\) | 8.64718 | 0.276083 | ||||||||
\(982\) | 5.56390 | 0.177551 | ||||||||
\(983\) | −39.1740 | −1.24946 | −0.624728 | − | 0.780842i | \(-0.714790\pi\) | ||||
−0.624728 | + | 0.780842i | \(0.714790\pi\) | |||||||
\(984\) | 1.38529 | 0.0441615 | ||||||||
\(985\) | 44.0942 | 1.40496 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.2788 | 0.581822 | ||||||||
\(988\) | −32.8394 | −1.04476 | ||||||||
\(989\) | 0.108912 | 0.00346319 | ||||||||
\(990\) | 2.60763 | 0.0828759 | ||||||||
\(991\) | −47.8488 | −1.51997 | −0.759983 | − | 0.649942i | \(-0.774793\pi\) | ||||
−0.759983 | + | 0.649942i | \(0.774793\pi\) | |||||||
\(992\) | −9.40924 | −0.298744 | ||||||||
\(993\) | −19.4595 | −0.617530 | ||||||||
\(994\) | 3.92201 | 0.124399 | ||||||||
\(995\) | −30.4487 | −0.965290 | ||||||||
\(996\) | 13.9738 | 0.442776 | ||||||||
\(997\) | 51.3829 | 1.62731 | 0.813656 | − | 0.581347i | \(-0.197474\pi\) | ||||
0.813656 | + | 0.581347i | \(0.197474\pi\) | |||||||
\(998\) | −1.23005 | −0.0389367 | ||||||||
\(999\) | 6.32794 | 0.200207 |
(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 | 2523.2.a.r.1.5 | 9 | ||
3.2 | odd | 2 | 7569.2.a.bj.1.5 | 9 | |||
29.16 | even | 7 | 87.2.g.a.82.2 | yes | 18 | ||
29.20 | even | 7 | 87.2.g.a.52.2 | ✓ | 18 | ||
29.28 | even | 2 | 2523.2.a.o.1.5 | 9 | |||
87.20 | odd | 14 | 261.2.k.c.226.2 | 18 | |||
87.74 | odd | 14 | 261.2.k.c.82.2 | 18 | |||
87.86 | odd | 2 | 7569.2.a.bm.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.g.a.52.2 | ✓ | 18 | 29.20 | even | 7 | ||
87.2.g.a.82.2 | yes | 18 | 29.16 | even | 7 | ||
261.2.k.c.82.2 | 18 | 87.74 | odd | 14 | |||
261.2.k.c.226.2 | 18 | 87.20 | odd | 14 | |||
2523.2.a.o.1.5 | 9 | 29.28 | even | 2 | |||
2523.2.a.r.1.5 | 9 | 1.1 | even | 1 | trivial | ||
7569.2.a.bj.1.5 | 9 | 3.2 | odd | 2 | |||
7569.2.a.bm.1.5 | 9 | 87.86 | odd | 2 |