Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.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: | \(21.5196833447\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 30x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.480122\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.480122 | 0.339497 | 0.169749 | − | 0.985487i | \(-0.445704\pi\) | ||||
0.169749 | + | 0.985487i | \(0.445704\pi\) | |||||||
\(3\) | −0.720208 | −0.415812 | −0.207906 | − | 0.978149i | \(-0.566665\pi\) | ||||
−0.207906 | + | 0.978149i | \(0.566665\pi\) | |||||||
\(4\) | −1.76948 | −0.884741 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.345788 | −0.141167 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.80981 | −0.639865 | ||||||||
\(9\) | −2.48130 | −0.827100 | ||||||||
\(10\) | 0.480122 | 0.151828 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.27440 | 0.367886 | ||||||||
\(13\) | 2.59533 | 0.719815 | 0.359907 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359907 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.720208 | −0.185957 | ||||||||
\(16\) | 2.67004 | 0.667509 | ||||||||
\(17\) | −2.65161 | −0.643111 | −0.321555 | − | 0.946891i | \(-0.604206\pi\) | ||||
−0.321555 | + | 0.946891i | \(0.604206\pi\) | |||||||
\(18\) | −1.19133 | −0.280798 | ||||||||
\(19\) | 2.83072 | 0.649412 | 0.324706 | − | 0.945815i | \(-0.394735\pi\) | ||||
0.324706 | + | 0.945815i | \(0.394735\pi\) | |||||||
\(20\) | −1.76948 | −0.395668 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.480122 | 0.102362 | ||||||||
\(23\) | 2.01184 | 0.419497 | 0.209749 | − | 0.977755i | \(-0.432735\pi\) | ||||
0.209749 | + | 0.977755i | \(0.432735\pi\) | |||||||
\(24\) | 1.30344 | 0.266064 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.24607 | 0.244375 | ||||||||
\(27\) | 3.94768 | 0.759731 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.33190 | −1.17580 | −0.587902 | − | 0.808932i | \(-0.700046\pi\) | ||||
−0.587902 | + | 0.808932i | \(0.700046\pi\) | |||||||
\(30\) | −0.345788 | −0.0631319 | ||||||||
\(31\) | −4.04011 | −0.725625 | −0.362812 | − | 0.931862i | \(-0.618183\pi\) | ||||
−0.362812 | + | 0.931862i | \(0.618183\pi\) | |||||||
\(32\) | 4.90157 | 0.866483 | ||||||||
\(33\) | −0.720208 | −0.125372 | ||||||||
\(34\) | −1.27310 | −0.218334 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.39062 | 0.731770 | ||||||||
\(37\) | 11.6184 | 1.91005 | 0.955024 | − | 0.296528i | \(-0.0958287\pi\) | ||||
0.955024 | + | 0.296528i | \(0.0958287\pi\) | |||||||
\(38\) | 1.35909 | 0.220474 | ||||||||
\(39\) | −1.86918 | −0.299308 | ||||||||
\(40\) | −1.80981 | −0.286156 | ||||||||
\(41\) | −3.25462 | −0.508286 | −0.254143 | − | 0.967167i | \(-0.581793\pi\) | ||||
−0.254143 | + | 0.967167i | \(0.581793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.96803 | −0.605119 | −0.302559 | − | 0.953131i | \(-0.597841\pi\) | ||||
−0.302559 | + | 0.953131i | \(0.597841\pi\) | |||||||
\(44\) | −1.76948 | −0.266760 | ||||||||
\(45\) | −2.48130 | −0.369890 | ||||||||
\(46\) | 0.965927 | 0.142418 | ||||||||
\(47\) | −9.41591 | −1.37345 | −0.686726 | − | 0.726917i | \(-0.740953\pi\) | ||||
−0.686726 | + | 0.726917i | \(0.740953\pi\) | |||||||
\(48\) | −1.92298 | −0.277559 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.480122 | 0.0678995 | ||||||||
\(51\) | 1.90971 | 0.267413 | ||||||||
\(52\) | −4.59239 | −0.636850 | ||||||||
\(53\) | −6.56767 | −0.902139 | −0.451069 | − | 0.892489i | \(-0.648957\pi\) | ||||
−0.451069 | + | 0.892489i | \(0.648957\pi\) | |||||||
\(54\) | 1.89537 | 0.257927 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.03871 | −0.270034 | ||||||||
\(58\) | −3.04008 | −0.399183 | ||||||||
\(59\) | −12.2383 | −1.59328 | −0.796642 | − | 0.604451i | \(-0.793393\pi\) | ||||
−0.796642 | + | 0.604451i | \(0.793393\pi\) | |||||||
\(60\) | 1.27440 | 0.164524 | ||||||||
\(61\) | 5.18390 | 0.663730 | 0.331865 | − | 0.943327i | \(-0.392322\pi\) | ||||
0.331865 | + | 0.943327i | \(0.392322\pi\) | |||||||
\(62\) | −1.93974 | −0.246348 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.98672 | −0.373340 | ||||||||
\(65\) | 2.59533 | 0.321911 | ||||||||
\(66\) | −0.345788 | −0.0425635 | ||||||||
\(67\) | −2.21517 | −0.270626 | −0.135313 | − | 0.990803i | \(-0.543204\pi\) | ||||
−0.135313 | + | 0.990803i | \(0.543204\pi\) | |||||||
\(68\) | 4.69199 | 0.568987 | ||||||||
\(69\) | −1.44894 | −0.174432 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.74766 | −0.444765 | −0.222383 | − | 0.974959i | \(-0.571383\pi\) | ||||
−0.222383 | + | 0.974959i | \(0.571383\pi\) | |||||||
\(72\) | 4.49068 | 0.529232 | ||||||||
\(73\) | −7.99291 | −0.935499 | −0.467750 | − | 0.883861i | \(-0.654935\pi\) | ||||
−0.467750 | + | 0.883861i | \(0.654935\pi\) | |||||||
\(74\) | 5.57823 | 0.648457 | ||||||||
\(75\) | −0.720208 | −0.0831625 | ||||||||
\(76\) | −5.00891 | −0.574562 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.897433 | −0.101614 | ||||||||
\(79\) | 16.3495 | 1.83947 | 0.919733 | − | 0.392545i | \(-0.128405\pi\) | ||||
0.919733 | + | 0.392545i | \(0.128405\pi\) | |||||||
\(80\) | 2.67004 | 0.298519 | ||||||||
\(81\) | 4.60075 | 0.511195 | ||||||||
\(82\) | −1.56262 | −0.172562 | ||||||||
\(83\) | −1.31388 | −0.144217 | −0.0721084 | − | 0.997397i | \(-0.522973\pi\) | ||||
−0.0721084 | + | 0.997397i | \(0.522973\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.65161 | −0.287608 | ||||||||
\(86\) | −1.90514 | −0.205436 | ||||||||
\(87\) | 4.56029 | 0.488914 | ||||||||
\(88\) | −1.80981 | −0.192927 | ||||||||
\(89\) | −7.47273 | −0.792108 | −0.396054 | − | 0.918227i | \(-0.629621\pi\) | ||||
−0.396054 | + | 0.918227i | \(0.629621\pi\) | |||||||
\(90\) | −1.19133 | −0.125577 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.55991 | −0.371146 | ||||||||
\(93\) | 2.90972 | 0.301724 | ||||||||
\(94\) | −4.52078 | −0.466283 | ||||||||
\(95\) | 2.83072 | 0.290426 | ||||||||
\(96\) | −3.53015 | −0.360294 | ||||||||
\(97\) | −6.50946 | −0.660936 | −0.330468 | − | 0.943817i | \(-0.607207\pi\) | ||||
−0.330468 | + | 0.943817i | \(0.607207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.48130 | −0.249380 | ||||||||
\(100\) | −1.76948 | −0.176948 | ||||||||
\(101\) | −11.2053 | −1.11497 | −0.557485 | − | 0.830187i | \(-0.688234\pi\) | ||||
−0.557485 | + | 0.830187i | \(0.688234\pi\) | |||||||
\(102\) | 0.916895 | 0.0907862 | ||||||||
\(103\) | −15.0206 | −1.48003 | −0.740014 | − | 0.672591i | \(-0.765181\pi\) | ||||
−0.740014 | + | 0.672591i | \(0.765181\pi\) | |||||||
\(104\) | −4.69706 | −0.460584 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.15328 | −0.306274 | ||||||||
\(107\) | −5.53990 | −0.535563 | −0.267781 | − | 0.963480i | \(-0.586290\pi\) | ||||
−0.267781 | + | 0.963480i | \(0.586290\pi\) | |||||||
\(108\) | −6.98535 | −0.672165 | ||||||||
\(109\) | −11.2111 | −1.07383 | −0.536913 | − | 0.843638i | \(-0.680410\pi\) | ||||
−0.536913 | + | 0.843638i | \(0.680410\pi\) | |||||||
\(110\) | 0.480122 | 0.0457778 | ||||||||
\(111\) | −8.36765 | −0.794222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.89479 | −0.178246 | −0.0891232 | − | 0.996021i | \(-0.528406\pi\) | ||||
−0.0891232 | + | 0.996021i | \(0.528406\pi\) | |||||||
\(114\) | −0.978829 | −0.0916757 | ||||||||
\(115\) | 2.01184 | 0.187605 | ||||||||
\(116\) | 11.2042 | 1.04028 | ||||||||
\(117\) | −6.43979 | −0.595359 | ||||||||
\(118\) | −5.87585 | −0.540916 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.30344 | 0.118987 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.48890 | 0.225335 | ||||||||
\(123\) | 2.34401 | 0.211352 | ||||||||
\(124\) | 7.14890 | 0.641991 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.718996 | −0.0638006 | −0.0319003 | − | 0.999491i | \(-0.510156\pi\) | ||||
−0.0319003 | + | 0.999491i | \(0.510156\pi\) | |||||||
\(128\) | −11.2371 | −0.993231 | ||||||||
\(129\) | 2.85781 | 0.251616 | ||||||||
\(130\) | 1.24607 | 0.109288 | ||||||||
\(131\) | 16.5681 | 1.44756 | 0.723781 | − | 0.690030i | \(-0.242403\pi\) | ||||
0.723781 | + | 0.690030i | \(0.242403\pi\) | |||||||
\(132\) | 1.27440 | 0.110922 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.06355 | −0.0918768 | ||||||||
\(135\) | 3.94768 | 0.339762 | ||||||||
\(136\) | 4.79892 | 0.411504 | ||||||||
\(137\) | 14.0530 | 1.20063 | 0.600315 | − | 0.799764i | \(-0.295042\pi\) | ||||
0.600315 | + | 0.799764i | \(0.295042\pi\) | |||||||
\(138\) | −0.695669 | −0.0592192 | ||||||||
\(139\) | −14.3025 | −1.21312 | −0.606560 | − | 0.795037i | \(-0.707451\pi\) | ||||
−0.606560 | + | 0.795037i | \(0.707451\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.78141 | 0.571098 | ||||||||
\(142\) | −1.79933 | −0.150997 | ||||||||
\(143\) | 2.59533 | 0.217032 | ||||||||
\(144\) | −6.62516 | −0.552097 | ||||||||
\(145\) | −6.33190 | −0.525836 | ||||||||
\(146\) | −3.83757 | −0.317600 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.5585 | −1.68990 | ||||||||
\(149\) | −23.7598 | −1.94648 | −0.973240 | − | 0.229790i | \(-0.926196\pi\) | ||||
−0.973240 | + | 0.229790i | \(0.926196\pi\) | |||||||
\(150\) | −0.345788 | −0.0282334 | ||||||||
\(151\) | 7.18141 | 0.584415 | 0.292207 | − | 0.956355i | \(-0.405610\pi\) | ||||
0.292207 | + | 0.956355i | \(0.405610\pi\) | |||||||
\(152\) | −5.12307 | −0.415536 | ||||||||
\(153\) | 6.57945 | 0.531917 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.04011 | −0.324509 | ||||||||
\(156\) | 3.30748 | 0.264810 | ||||||||
\(157\) | 7.81328 | 0.623568 | 0.311784 | − | 0.950153i | \(-0.399073\pi\) | ||||
0.311784 | + | 0.950153i | \(0.399073\pi\) | |||||||
\(158\) | 7.84977 | 0.624494 | ||||||||
\(159\) | 4.73009 | 0.375120 | ||||||||
\(160\) | 4.90157 | 0.387503 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.20892 | 0.173549 | ||||||||
\(163\) | −1.78950 | −0.140164 | −0.0700822 | − | 0.997541i | \(-0.522326\pi\) | ||||
−0.0700822 | + | 0.997541i | \(0.522326\pi\) | |||||||
\(164\) | 5.75900 | 0.449702 | ||||||||
\(165\) | −0.720208 | −0.0560681 | ||||||||
\(166\) | −0.630821 | −0.0489612 | ||||||||
\(167\) | −11.9544 | −0.925059 | −0.462529 | − | 0.886604i | \(-0.653058\pi\) | ||||
−0.462529 | + | 0.886604i | \(0.653058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.26426 | −0.481867 | ||||||||
\(170\) | −1.27310 | −0.0976421 | ||||||||
\(171\) | −7.02387 | −0.537129 | ||||||||
\(172\) | 7.02136 | 0.535374 | ||||||||
\(173\) | −20.4569 | −1.55531 | −0.777653 | − | 0.628694i | \(-0.783590\pi\) | ||||
−0.777653 | + | 0.628694i | \(0.783590\pi\) | |||||||
\(174\) | 2.18949 | 0.165985 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.67004 | 0.201262 | ||||||||
\(177\) | 8.81409 | 0.662508 | ||||||||
\(178\) | −3.58782 | −0.268919 | ||||||||
\(179\) | −2.14591 | −0.160393 | −0.0801965 | − | 0.996779i | \(-0.525555\pi\) | ||||
−0.0801965 | + | 0.996779i | \(0.525555\pi\) | |||||||
\(180\) | 4.39062 | 0.327257 | ||||||||
\(181\) | 8.76578 | 0.651556 | 0.325778 | − | 0.945446i | \(-0.394374\pi\) | ||||
0.325778 | + | 0.945446i | \(0.394374\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.73349 | −0.275987 | ||||||||
\(184\) | −3.64105 | −0.268421 | ||||||||
\(185\) | 11.6184 | 0.854200 | ||||||||
\(186\) | 1.39702 | 0.102434 | ||||||||
\(187\) | −2.65161 | −0.193905 | ||||||||
\(188\) | 16.6613 | 1.21515 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.35909 | 0.0985989 | ||||||||
\(191\) | 1.48453 | 0.107417 | 0.0537085 | − | 0.998557i | \(-0.482896\pi\) | ||||
0.0537085 | + | 0.998557i | \(0.482896\pi\) | |||||||
\(192\) | 2.15106 | 0.155240 | ||||||||
\(193\) | 22.5446 | 1.62279 | 0.811397 | − | 0.584495i | \(-0.198707\pi\) | ||||
0.811397 | + | 0.584495i | \(0.198707\pi\) | |||||||
\(194\) | −3.12534 | −0.224386 | ||||||||
\(195\) | −1.86918 | −0.133855 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.11322 | 0.435549 | 0.217774 | − | 0.975999i | \(-0.430120\pi\) | ||||
0.217774 | + | 0.975999i | \(0.430120\pi\) | |||||||
\(198\) | −1.19133 | −0.0846639 | ||||||||
\(199\) | −24.7090 | −1.75158 | −0.875788 | − | 0.482695i | \(-0.839658\pi\) | ||||
−0.875788 | + | 0.482695i | \(0.839658\pi\) | |||||||
\(200\) | −1.80981 | −0.127973 | ||||||||
\(201\) | 1.59538 | 0.112530 | ||||||||
\(202\) | −5.37992 | −0.378530 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.37921 | −0.236592 | ||||||||
\(205\) | −3.25462 | −0.227313 | ||||||||
\(206\) | −7.21174 | −0.502466 | ||||||||
\(207\) | −4.99197 | −0.346966 | ||||||||
\(208\) | 6.92962 | 0.480483 | ||||||||
\(209\) | 2.83072 | 0.195805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.69492 | −0.598583 | −0.299292 | − | 0.954162i | \(-0.596750\pi\) | ||||
−0.299292 | + | 0.954162i | \(0.596750\pi\) | |||||||
\(212\) | 11.6214 | 0.798160 | ||||||||
\(213\) | 2.69909 | 0.184939 | ||||||||
\(214\) | −2.65983 | −0.181822 | ||||||||
\(215\) | −3.96803 | −0.270617 | ||||||||
\(216\) | −7.14455 | −0.486125 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.38268 | −0.364561 | ||||||||
\(219\) | 5.75656 | 0.388992 | ||||||||
\(220\) | −1.76948 | −0.119299 | ||||||||
\(221\) | −6.88181 | −0.462921 | ||||||||
\(222\) | −4.01749 | −0.269636 | ||||||||
\(223\) | 23.8971 | 1.60027 | 0.800134 | − | 0.599822i | \(-0.204762\pi\) | ||||
0.800134 | + | 0.599822i | \(0.204762\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.48130 | −0.165420 | ||||||||
\(226\) | −0.909728 | −0.0605142 | ||||||||
\(227\) | −19.8750 | −1.31915 | −0.659574 | − | 0.751640i | \(-0.729263\pi\) | ||||
−0.659574 | + | 0.751640i | \(0.729263\pi\) | |||||||
\(228\) | 3.60746 | 0.238910 | ||||||||
\(229\) | −7.34417 | −0.485316 | −0.242658 | − | 0.970112i | \(-0.578019\pi\) | ||||
−0.242658 | + | 0.970112i | \(0.578019\pi\) | |||||||
\(230\) | 0.965927 | 0.0636913 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.4595 | 0.752356 | ||||||||
\(233\) | −9.33992 | −0.611879 | −0.305939 | − | 0.952051i | \(-0.598970\pi\) | ||||
−0.305939 | + | 0.952051i | \(0.598970\pi\) | |||||||
\(234\) | −3.09188 | −0.202123 | ||||||||
\(235\) | −9.41591 | −0.614226 | ||||||||
\(236\) | 21.6554 | 1.40965 | ||||||||
\(237\) | −11.7751 | −0.764873 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.14840 | −0.268338 | −0.134169 | − | 0.990958i | \(-0.542836\pi\) | ||||
−0.134169 | + | 0.990958i | \(0.542836\pi\) | |||||||
\(240\) | −1.92298 | −0.124128 | ||||||||
\(241\) | −2.45358 | −0.158049 | −0.0790246 | − | 0.996873i | \(-0.525181\pi\) | ||||
−0.0790246 | + | 0.996873i | \(0.525181\pi\) | |||||||
\(242\) | 0.480122 | 0.0308634 | ||||||||
\(243\) | −15.1565 | −0.972292 | ||||||||
\(244\) | −9.17282 | −0.587230 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.12541 | 0.0717534 | ||||||||
\(247\) | 7.34666 | 0.467457 | ||||||||
\(248\) | 7.31183 | 0.464302 | ||||||||
\(249\) | 0.946265 | 0.0599671 | ||||||||
\(250\) | 0.480122 | 0.0303656 | ||||||||
\(251\) | 6.73338 | 0.425007 | 0.212504 | − | 0.977160i | \(-0.431838\pi\) | ||||
0.212504 | + | 0.977160i | \(0.431838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.01184 | 0.126483 | ||||||||
\(254\) | −0.345206 | −0.0216601 | ||||||||
\(255\) | 1.90971 | 0.119591 | ||||||||
\(256\) | 0.578258 | 0.0361411 | ||||||||
\(257\) | 17.3927 | 1.08493 | 0.542464 | − | 0.840079i | \(-0.317492\pi\) | ||||
0.542464 | + | 0.840079i | \(0.317492\pi\) | |||||||
\(258\) | 1.37210 | 0.0854229 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.59239 | −0.284808 | ||||||||
\(261\) | 15.7114 | 0.972508 | ||||||||
\(262\) | 7.95471 | 0.491443 | ||||||||
\(263\) | 6.31203 | 0.389217 | 0.194608 | − | 0.980881i | \(-0.437656\pi\) | ||||
0.194608 | + | 0.980881i | \(0.437656\pi\) | |||||||
\(264\) | 1.30344 | 0.0802212 | ||||||||
\(265\) | −6.56767 | −0.403449 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.38192 | 0.329368 | ||||||||
\(268\) | 3.91970 | 0.239434 | ||||||||
\(269\) | 0.304989 | 0.0185955 | 0.00929776 | − | 0.999957i | \(-0.497040\pi\) | ||||
0.00929776 | + | 0.999957i | \(0.497040\pi\) | |||||||
\(270\) | 1.89537 | 0.115348 | ||||||||
\(271\) | 5.76238 | 0.350039 | 0.175020 | − | 0.984565i | \(-0.444001\pi\) | ||||
0.175020 | + | 0.984565i | \(0.444001\pi\) | |||||||
\(272\) | −7.07990 | −0.429282 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.74715 | 0.407611 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 2.56388 | 0.154327 | ||||||||
\(277\) | −29.6336 | −1.78051 | −0.890254 | − | 0.455464i | \(-0.849473\pi\) | ||||
−0.890254 | + | 0.455464i | \(0.849473\pi\) | |||||||
\(278\) | −6.86693 | −0.411851 | ||||||||
\(279\) | 10.0247 | 0.600164 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7559 | 0.760951 | 0.380475 | − | 0.924791i | \(-0.375760\pi\) | ||||
0.380475 | + | 0.924791i | \(0.375760\pi\) | |||||||
\(282\) | 3.25590 | 0.193886 | ||||||||
\(283\) | 3.54406 | 0.210672 | 0.105336 | − | 0.994437i | \(-0.466408\pi\) | ||||
0.105336 | + | 0.994437i | \(0.466408\pi\) | |||||||
\(284\) | 6.63141 | 0.393502 | ||||||||
\(285\) | −2.03871 | −0.120763 | ||||||||
\(286\) | 1.24607 | 0.0736819 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −12.1623 | −0.716668 | ||||||||
\(289\) | −9.96894 | −0.586408 | ||||||||
\(290\) | −3.04008 | −0.178520 | ||||||||
\(291\) | 4.68817 | 0.274825 | ||||||||
\(292\) | 14.1433 | 0.827675 | ||||||||
\(293\) | −4.92175 | −0.287532 | −0.143766 | − | 0.989612i | \(-0.545921\pi\) | ||||
−0.143766 | + | 0.989612i | \(0.545921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2383 | −0.712539 | ||||||||
\(296\) | −21.0271 | −1.22217 | ||||||||
\(297\) | 3.94768 | 0.229067 | ||||||||
\(298\) | −11.4076 | −0.660825 | ||||||||
\(299\) | 5.22138 | 0.301960 | ||||||||
\(300\) | 1.27440 | 0.0735773 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.44795 | 0.198407 | ||||||||
\(303\) | 8.07016 | 0.463619 | ||||||||
\(304\) | 7.55813 | 0.433488 | ||||||||
\(305\) | 5.18390 | 0.296829 | ||||||||
\(306\) | 3.15894 | 0.180584 | ||||||||
\(307\) | 1.29737 | 0.0740451 | 0.0370225 | − | 0.999314i | \(-0.488213\pi\) | ||||
0.0370225 | + | 0.999314i | \(0.488213\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8180 | 0.615414 | ||||||||
\(310\) | −1.93974 | −0.110170 | ||||||||
\(311\) | 12.4456 | 0.705725 | 0.352862 | − | 0.935675i | \(-0.385208\pi\) | ||||
0.352862 | + | 0.935675i | \(0.385208\pi\) | |||||||
\(312\) | 3.38286 | 0.191517 | ||||||||
\(313\) | −1.63401 | −0.0923598 | −0.0461799 | − | 0.998933i | \(-0.514705\pi\) | ||||
−0.0461799 | + | 0.998933i | \(0.514705\pi\) | |||||||
\(314\) | 3.75133 | 0.211700 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.9302 | −1.62745 | ||||||||
\(317\) | −8.92497 | −0.501277 | −0.250638 | − | 0.968081i | \(-0.580640\pi\) | ||||
−0.250638 | + | 0.968081i | \(0.580640\pi\) | |||||||
\(318\) | 2.27102 | 0.127352 | ||||||||
\(319\) | −6.33190 | −0.354518 | ||||||||
\(320\) | −2.98672 | −0.166963 | ||||||||
\(321\) | 3.98988 | 0.222694 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.50598 | −0.417644 | ||||||||
\(324\) | −8.14095 | −0.452275 | ||||||||
\(325\) | 2.59533 | 0.143963 | ||||||||
\(326\) | −0.859178 | −0.0475855 | ||||||||
\(327\) | 8.07430 | 0.446510 | ||||||||
\(328\) | 5.89025 | 0.325235 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.345788 | −0.0190350 | ||||||||
\(331\) | 19.5320 | 1.07357 | 0.536787 | − | 0.843718i | \(-0.319638\pi\) | ||||
0.536787 | + | 0.843718i | \(0.319638\pi\) | |||||||
\(332\) | 2.32488 | 0.127595 | ||||||||
\(333\) | −28.8287 | −1.57980 | ||||||||
\(334\) | −5.73957 | −0.314055 | ||||||||
\(335\) | −2.21517 | −0.121028 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4497 | −0.732654 | −0.366327 | − | 0.930486i | \(-0.619385\pi\) | ||||
−0.366327 | + | 0.930486i | \(0.619385\pi\) | |||||||
\(338\) | −3.00761 | −0.163592 | ||||||||
\(339\) | 1.36464 | 0.0741171 | ||||||||
\(340\) | 4.69199 | 0.254459 | ||||||||
\(341\) | −4.04011 | −0.218784 | ||||||||
\(342\) | −3.37231 | −0.182354 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.18138 | 0.387194 | ||||||||
\(345\) | −1.44894 | −0.0780084 | ||||||||
\(346\) | −9.82178 | −0.528022 | ||||||||
\(347\) | 10.5737 | 0.567628 | 0.283814 | − | 0.958879i | \(-0.408400\pi\) | ||||
0.283814 | + | 0.958879i | \(0.408400\pi\) | |||||||
\(348\) | −8.06935 | −0.432563 | ||||||||
\(349\) | 11.5704 | 0.619349 | 0.309675 | − | 0.950843i | \(-0.399780\pi\) | ||||
0.309675 | + | 0.950843i | \(0.399780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.2455 | 0.546866 | ||||||||
\(352\) | 4.90157 | 0.261254 | ||||||||
\(353\) | −15.6700 | −0.834030 | −0.417015 | − | 0.908900i | \(-0.636924\pi\) | ||||
−0.417015 | + | 0.908900i | \(0.636924\pi\) | |||||||
\(354\) | 4.23184 | 0.224920 | ||||||||
\(355\) | −3.74766 | −0.198905 | ||||||||
\(356\) | 13.2229 | 0.700811 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.03030 | −0.0544530 | ||||||||
\(359\) | 29.4977 | 1.55683 | 0.778413 | − | 0.627752i | \(-0.216025\pi\) | ||||
0.778413 | + | 0.627752i | \(0.216025\pi\) | |||||||
\(360\) | 4.49068 | 0.236680 | ||||||||
\(361\) | −10.9870 | −0.578264 | ||||||||
\(362\) | 4.20864 | 0.221201 | ||||||||
\(363\) | −0.720208 | −0.0378011 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.99291 | −0.418368 | ||||||||
\(366\) | −1.79253 | −0.0936970 | ||||||||
\(367\) | −30.8844 | −1.61215 | −0.806076 | − | 0.591812i | \(-0.798413\pi\) | ||||
−0.806076 | + | 0.591812i | \(0.798413\pi\) | |||||||
\(368\) | 5.37168 | 0.280018 | ||||||||
\(369\) | 8.07569 | 0.420404 | ||||||||
\(370\) | 5.57823 | 0.289999 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.14870 | −0.266948 | ||||||||
\(373\) | −21.3841 | −1.10723 | −0.553613 | − | 0.832774i | \(-0.686751\pi\) | ||||
−0.553613 | + | 0.832774i | \(0.686751\pi\) | |||||||
\(374\) | −1.27310 | −0.0658303 | ||||||||
\(375\) | −0.720208 | −0.0371914 | ||||||||
\(376\) | 17.0410 | 0.878823 | ||||||||
\(377\) | −16.4334 | −0.846362 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.60024 | 0.236299 | 0.118149 | − | 0.992996i | \(-0.462304\pi\) | ||||
0.118149 | + | 0.992996i | \(0.462304\pi\) | |||||||
\(380\) | −5.00891 | −0.256952 | ||||||||
\(381\) | 0.517827 | 0.0265291 | ||||||||
\(382\) | 0.712756 | 0.0364678 | ||||||||
\(383\) | −7.77268 | −0.397165 | −0.198583 | − | 0.980084i | \(-0.563634\pi\) | ||||
−0.198583 | + | 0.980084i | \(0.563634\pi\) | |||||||
\(384\) | 8.09307 | 0.412998 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.8241 | 0.550934 | ||||||||
\(387\) | 9.84587 | 0.500494 | ||||||||
\(388\) | 11.5184 | 0.584757 | ||||||||
\(389\) | 7.98574 | 0.404893 | 0.202447 | − | 0.979293i | \(-0.435111\pi\) | ||||
0.202447 | + | 0.979293i | \(0.435111\pi\) | |||||||
\(390\) | −0.897433 | −0.0454433 | ||||||||
\(391\) | −5.33461 | −0.269783 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.9325 | −0.601914 | ||||||||
\(394\) | 2.93509 | 0.147868 | ||||||||
\(395\) | 16.3495 | 0.822634 | ||||||||
\(396\) | 4.39062 | 0.220637 | ||||||||
\(397\) | −1.32722 | −0.0666112 | −0.0333056 | − | 0.999445i | \(-0.510603\pi\) | ||||
−0.0333056 | + | 0.999445i | \(0.510603\pi\) | |||||||
\(398\) | −11.8633 | −0.594656 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.67004 | 0.133502 | ||||||||
\(401\) | −4.94204 | −0.246793 | −0.123397 | − | 0.992357i | \(-0.539379\pi\) | ||||
−0.123397 | + | 0.992357i | \(0.539379\pi\) | |||||||
\(402\) | 0.765978 | 0.0382035 | ||||||||
\(403\) | −10.4854 | −0.522316 | ||||||||
\(404\) | 19.8276 | 0.986461 | ||||||||
\(405\) | 4.60075 | 0.228613 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.6184 | 0.575901 | ||||||||
\(408\) | −3.45622 | −0.171108 | ||||||||
\(409\) | 5.52113 | 0.273002 | 0.136501 | − | 0.990640i | \(-0.456414\pi\) | ||||
0.136501 | + | 0.990640i | \(0.456414\pi\) | |||||||
\(410\) | −1.56262 | −0.0771721 | ||||||||
\(411\) | −10.1211 | −0.499236 | ||||||||
\(412\) | 26.5788 | 1.30944 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.39675 | −0.117794 | ||||||||
\(415\) | −1.31388 | −0.0644957 | ||||||||
\(416\) | 12.7212 | 0.623707 | ||||||||
\(417\) | 10.3008 | 0.504431 | ||||||||
\(418\) | 1.35909 | 0.0664753 | ||||||||
\(419\) | 10.7144 | 0.523432 | 0.261716 | − | 0.965145i | \(-0.415712\pi\) | ||||
0.261716 | + | 0.965145i | \(0.415712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.9844 | 1.41261 | 0.706307 | − | 0.707905i | \(-0.250360\pi\) | ||||
0.706307 | + | 0.707905i | \(0.250360\pi\) | |||||||
\(422\) | −4.17462 | −0.203217 | ||||||||
\(423\) | 23.3637 | 1.13598 | ||||||||
\(424\) | 11.8862 | 0.577247 | ||||||||
\(425\) | −2.65161 | −0.128622 | ||||||||
\(426\) | 1.29589 | 0.0627863 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.80276 | 0.473834 | ||||||||
\(429\) | −1.86918 | −0.0902447 | ||||||||
\(430\) | −1.90514 | −0.0918739 | ||||||||
\(431\) | 26.4566 | 1.27437 | 0.637185 | − | 0.770711i | \(-0.280099\pi\) | ||||
0.637185 | + | 0.770711i | \(0.280099\pi\) | |||||||
\(432\) | 10.5404 | 0.507127 | ||||||||
\(433\) | 13.6978 | 0.658275 | 0.329137 | − | 0.944282i | \(-0.393242\pi\) | ||||
0.329137 | + | 0.944282i | \(0.393242\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.56029 | 0.218649 | ||||||||
\(436\) | 19.8378 | 0.950058 | ||||||||
\(437\) | 5.69495 | 0.272426 | ||||||||
\(438\) | 2.76385 | 0.132062 | ||||||||
\(439\) | 30.8989 | 1.47472 | 0.737362 | − | 0.675498i | \(-0.236071\pi\) | ||||
0.737362 | + | 0.675498i | \(0.236071\pi\) | |||||||
\(440\) | −1.80981 | −0.0862794 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.30411 | −0.157160 | ||||||||
\(443\) | −5.96262 | −0.283292 | −0.141646 | − | 0.989917i | \(-0.545240\pi\) | ||||
−0.141646 | + | 0.989917i | \(0.545240\pi\) | |||||||
\(444\) | 14.8064 | 0.702681 | ||||||||
\(445\) | −7.47273 | −0.354241 | ||||||||
\(446\) | 11.4735 | 0.543287 | ||||||||
\(447\) | 17.1120 | 0.809371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8561 | 1.26742 | 0.633710 | − | 0.773571i | \(-0.281531\pi\) | ||||
0.633710 | + | 0.773571i | \(0.281531\pi\) | |||||||
\(450\) | −1.19133 | −0.0561597 | ||||||||
\(451\) | −3.25462 | −0.153254 | ||||||||
\(452\) | 3.35279 | 0.157702 | ||||||||
\(453\) | −5.17211 | −0.243007 | ||||||||
\(454\) | −9.54241 | −0.447847 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.68968 | 0.172785 | ||||||||
\(457\) | −15.9877 | −0.747874 | −0.373937 | − | 0.927454i | \(-0.621992\pi\) | ||||
−0.373937 | + | 0.927454i | \(0.621992\pi\) | |||||||
\(458\) | −3.52610 | −0.164764 | ||||||||
\(459\) | −10.4677 | −0.488591 | ||||||||
\(460\) | −3.55991 | −0.165982 | ||||||||
\(461\) | −23.7501 | −1.10615 | −0.553077 | − | 0.833130i | \(-0.686547\pi\) | ||||
−0.553077 | + | 0.833130i | \(0.686547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5550 | 0.722903 | 0.361451 | − | 0.932391i | \(-0.382281\pi\) | ||||
0.361451 | + | 0.932391i | \(0.382281\pi\) | |||||||
\(464\) | −16.9064 | −0.784860 | ||||||||
\(465\) | 2.90972 | 0.134935 | ||||||||
\(466\) | −4.48430 | −0.207731 | ||||||||
\(467\) | 16.2132 | 0.750258 | 0.375129 | − | 0.926973i | \(-0.377598\pi\) | ||||
0.375129 | + | 0.926973i | \(0.377598\pi\) | |||||||
\(468\) | 11.3951 | 0.526739 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.52078 | −0.208528 | ||||||||
\(471\) | −5.62719 | −0.259287 | ||||||||
\(472\) | 22.1489 | 1.01949 | ||||||||
\(473\) | −3.96803 | −0.182450 | ||||||||
\(474\) | −5.65347 | −0.259672 | ||||||||
\(475\) | 2.83072 | 0.129882 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.2964 | 0.746159 | ||||||||
\(478\) | −1.99174 | −0.0910999 | ||||||||
\(479\) | 31.7472 | 1.45057 | 0.725283 | − | 0.688451i | \(-0.241709\pi\) | ||||
0.725283 | + | 0.688451i | \(0.241709\pi\) | |||||||
\(480\) | −3.53015 | −0.161128 | ||||||||
\(481\) | 30.1535 | 1.37488 | ||||||||
\(482\) | −1.17802 | −0.0536573 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.76948 | −0.0804310 | ||||||||
\(485\) | −6.50946 | −0.295579 | ||||||||
\(486\) | −7.27698 | −0.330091 | ||||||||
\(487\) | −37.8990 | −1.71737 | −0.858684 | − | 0.512506i | \(-0.828717\pi\) | ||||
−0.858684 | + | 0.512506i | \(0.828717\pi\) | |||||||
\(488\) | −9.38188 | −0.424698 | ||||||||
\(489\) | 1.28881 | 0.0582821 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.6097 | 1.87782 | 0.938910 | − | 0.344164i | \(-0.111838\pi\) | ||||
0.938910 | + | 0.344164i | \(0.111838\pi\) | |||||||
\(492\) | −4.14768 | −0.186992 | ||||||||
\(493\) | 16.7898 | 0.756173 | ||||||||
\(494\) | 3.52729 | 0.158700 | ||||||||
\(495\) | −2.48130 | −0.111526 | ||||||||
\(496\) | −10.7872 | −0.484361 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.454323 | 0.0203587 | ||||||||
\(499\) | 33.9699 | 1.52070 | 0.760351 | − | 0.649513i | \(-0.225027\pi\) | ||||
0.760351 | + | 0.649513i | \(0.225027\pi\) | |||||||
\(500\) | −1.76948 | −0.0791337 | ||||||||
\(501\) | 8.60965 | 0.384651 | ||||||||
\(502\) | 3.23284 | 0.144289 | ||||||||
\(503\) | 32.2366 | 1.43736 | 0.718679 | − | 0.695342i | \(-0.244747\pi\) | ||||
0.718679 | + | 0.695342i | \(0.244747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.2053 | −0.498630 | ||||||||
\(506\) | 0.965927 | 0.0429407 | ||||||||
\(507\) | 4.51158 | 0.200366 | ||||||||
\(508\) | 1.27225 | 0.0564470 | ||||||||
\(509\) | 8.29547 | 0.367690 | 0.183845 | − | 0.982955i | \(-0.441146\pi\) | ||||
0.183845 | + | 0.982955i | \(0.441146\pi\) | |||||||
\(510\) | 0.916895 | 0.0406008 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.7519 | 1.00550 | ||||||||
\(513\) | 11.1748 | 0.493379 | ||||||||
\(514\) | 8.35062 | 0.368330 | ||||||||
\(515\) | −15.0206 | −0.661889 | ||||||||
\(516\) | −5.05684 | −0.222615 | ||||||||
\(517\) | −9.41591 | −0.414111 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.7332 | 0.646715 | ||||||||
\(520\) | −4.69706 | −0.205980 | ||||||||
\(521\) | −19.1556 | −0.839224 | −0.419612 | − | 0.907704i | \(-0.637834\pi\) | ||||
−0.419612 | + | 0.907704i | \(0.637834\pi\) | |||||||
\(522\) | 7.54336 | 0.330164 | ||||||||
\(523\) | −36.4567 | −1.59414 | −0.797069 | − | 0.603888i | \(-0.793617\pi\) | ||||
−0.797069 | + | 0.603888i | \(0.793617\pi\) | |||||||
\(524\) | −29.3170 | −1.28072 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.03055 | 0.132138 | ||||||||
\(527\) | 10.7128 | 0.466657 | ||||||||
\(528\) | −1.92298 | −0.0836870 | ||||||||
\(529\) | −18.9525 | −0.824022 | ||||||||
\(530\) | −3.15328 | −0.136970 | ||||||||
\(531\) | 30.3668 | 1.31781 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.44682 | −0.365872 | ||||||||
\(534\) | 2.58398 | 0.111820 | ||||||||
\(535\) | −5.53990 | −0.239511 | ||||||||
\(536\) | 4.00904 | 0.173164 | ||||||||
\(537\) | 1.54550 | 0.0666934 | ||||||||
\(538\) | 0.146432 | 0.00631313 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.98535 | −0.300602 | ||||||||
\(541\) | 5.09481 | 0.219043 | 0.109522 | − | 0.993984i | \(-0.465068\pi\) | ||||
0.109522 | + | 0.993984i | \(0.465068\pi\) | |||||||
\(542\) | 2.76664 | 0.118837 | ||||||||
\(543\) | −6.31319 | −0.270925 | ||||||||
\(544\) | −12.9971 | −0.557244 | ||||||||
\(545\) | −11.2111 | −0.480229 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.47799 | −0.234222 | −0.117111 | − | 0.993119i | \(-0.537363\pi\) | ||||
−0.117111 | + | 0.993119i | \(0.537363\pi\) | |||||||
\(548\) | −24.8665 | −1.06225 | ||||||||
\(549\) | −12.8628 | −0.548972 | ||||||||
\(550\) | 0.480122 | 0.0204725 | ||||||||
\(551\) | −17.9239 | −0.763582 | ||||||||
\(552\) | 2.62231 | 0.111613 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2277 | −0.604478 | ||||||||
\(555\) | −8.36765 | −0.355187 | ||||||||
\(556\) | 25.3080 | 1.07330 | ||||||||
\(557\) | −40.7436 | −1.72636 | −0.863180 | − | 0.504896i | \(-0.831531\pi\) | ||||
−0.863180 | + | 0.504896i | \(0.831531\pi\) | |||||||
\(558\) | 4.81309 | 0.203754 | ||||||||
\(559\) | −10.2983 | −0.435573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.90971 | 0.0806282 | ||||||||
\(562\) | 6.12437 | 0.258341 | ||||||||
\(563\) | 29.0662 | 1.22499 | 0.612497 | − | 0.790473i | \(-0.290165\pi\) | ||||
0.612497 | + | 0.790473i | \(0.290165\pi\) | |||||||
\(564\) | −11.9996 | −0.505274 | ||||||||
\(565\) | −1.89479 | −0.0797142 | ||||||||
\(566\) | 1.70158 | 0.0715227 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.78255 | 0.284590 | ||||||||
\(569\) | 1.03493 | 0.0433864 | 0.0216932 | − | 0.999765i | \(-0.493094\pi\) | ||||
0.0216932 | + | 0.999765i | \(0.493094\pi\) | |||||||
\(570\) | −0.978829 | −0.0409986 | ||||||||
\(571\) | −2.66578 | −0.111559 | −0.0557796 | − | 0.998443i | \(-0.517764\pi\) | ||||
−0.0557796 | + | 0.998443i | \(0.517764\pi\) | |||||||
\(572\) | −4.59239 | −0.192018 | ||||||||
\(573\) | −1.06917 | −0.0446653 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.01184 | 0.0838994 | ||||||||
\(576\) | 7.41096 | 0.308790 | ||||||||
\(577\) | −14.0006 | −0.582854 | −0.291427 | − | 0.956593i | \(-0.594130\pi\) | ||||
−0.291427 | + | 0.956593i | \(0.594130\pi\) | |||||||
\(578\) | −4.78631 | −0.199084 | ||||||||
\(579\) | −16.2368 | −0.674778 | ||||||||
\(580\) | 11.2042 | 0.465229 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.25089 | 0.0933025 | ||||||||
\(583\) | −6.56767 | −0.272005 | ||||||||
\(584\) | 14.4657 | 0.598593 | ||||||||
\(585\) | −6.43979 | −0.266253 | ||||||||
\(586\) | −2.36304 | −0.0976162 | ||||||||
\(587\) | −13.6037 | −0.561486 | −0.280743 | − | 0.959783i | \(-0.590581\pi\) | ||||
−0.280743 | + | 0.959783i | \(0.590581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.4364 | −0.471230 | ||||||||
\(590\) | −5.87585 | −0.241905 | ||||||||
\(591\) | −4.40279 | −0.181106 | ||||||||
\(592\) | 31.0215 | 1.27497 | ||||||||
\(593\) | −19.7326 | −0.810322 | −0.405161 | − | 0.914245i | \(-0.632784\pi\) | ||||
−0.405161 | + | 0.914245i | \(0.632784\pi\) | |||||||
\(594\) | 1.89537 | 0.0777678 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 42.0426 | 1.72213 | ||||||||
\(597\) | 17.7956 | 0.728327 | ||||||||
\(598\) | 2.50690 | 0.102515 | ||||||||
\(599\) | 5.93747 | 0.242598 | 0.121299 | − | 0.992616i | \(-0.461294\pi\) | ||||
0.121299 | + | 0.992616i | \(0.461294\pi\) | |||||||
\(600\) | 1.30344 | 0.0532128 | ||||||||
\(601\) | −37.1451 | −1.51518 | −0.757590 | − | 0.652731i | \(-0.773623\pi\) | ||||
−0.757590 | + | 0.652731i | \(0.773623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.49650 | 0.223835 | ||||||||
\(604\) | −12.7074 | −0.517056 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 3.87466 | 0.157397 | ||||||||
\(607\) | 7.07506 | 0.287168 | 0.143584 | − | 0.989638i | \(-0.454137\pi\) | ||||
0.143584 | + | 0.989638i | \(0.454137\pi\) | |||||||
\(608\) | 13.8750 | 0.562704 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.48890 | 0.100773 | ||||||||
\(611\) | −24.4374 | −0.988630 | ||||||||
\(612\) | −11.6422 | −0.470609 | ||||||||
\(613\) | 33.2245 | 1.34193 | 0.670963 | − | 0.741491i | \(-0.265881\pi\) | ||||
0.670963 | + | 0.741491i | \(0.265881\pi\) | |||||||
\(614\) | 0.622898 | 0.0251381 | ||||||||
\(615\) | 2.34401 | 0.0945194 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.6813 | 1.87932 | 0.939660 | − | 0.342109i | \(-0.111141\pi\) | ||||
0.939660 | + | 0.342109i | \(0.111141\pi\) | |||||||
\(618\) | 5.19396 | 0.208932 | ||||||||
\(619\) | 1.35992 | 0.0546597 | 0.0273298 | − | 0.999626i | \(-0.491300\pi\) | ||||
0.0273298 | + | 0.999626i | \(0.491300\pi\) | |||||||
\(620\) | 7.14890 | 0.287107 | ||||||||
\(621\) | 7.94208 | 0.318705 | ||||||||
\(622\) | 5.97540 | 0.239592 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.99077 | −0.199791 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.784525 | −0.0313559 | ||||||||
\(627\) | −2.03871 | −0.0814182 | ||||||||
\(628\) | −13.8255 | −0.551696 | ||||||||
\(629\) | −30.8074 | −1.22837 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7939 | 1.34531 | 0.672657 | − | 0.739954i | \(-0.265153\pi\) | ||||
0.672657 | + | 0.739954i | \(0.265153\pi\) | |||||||
\(632\) | −29.5896 | −1.17701 | ||||||||
\(633\) | 6.26215 | 0.248898 | ||||||||
\(634\) | −4.28508 | −0.170182 | ||||||||
\(635\) | −0.718996 | −0.0285325 | ||||||||
\(636\) | −8.36981 | −0.331885 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.04008 | −0.120358 | ||||||||
\(639\) | 9.29906 | 0.367865 | ||||||||
\(640\) | −11.2371 | −0.444186 | ||||||||
\(641\) | −32.7946 | −1.29531 | −0.647655 | − | 0.761934i | \(-0.724250\pi\) | ||||
−0.647655 | + | 0.761934i | \(0.724250\pi\) | |||||||
\(642\) | 1.91563 | 0.0756039 | ||||||||
\(643\) | 5.31001 | 0.209406 | 0.104703 | − | 0.994504i | \(-0.466611\pi\) | ||||
0.104703 | + | 0.994504i | \(0.466611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.85781 | 0.112526 | ||||||||
\(646\) | −3.60379 | −0.141789 | ||||||||
\(647\) | 4.66136 | 0.183257 | 0.0916286 | − | 0.995793i | \(-0.470793\pi\) | ||||
0.0916286 | + | 0.995793i | \(0.470793\pi\) | |||||||
\(648\) | −8.32649 | −0.327095 | ||||||||
\(649\) | −12.2383 | −0.480393 | ||||||||
\(650\) | 1.24607 | 0.0488751 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.16649 | 0.124009 | ||||||||
\(653\) | −45.1554 | −1.76707 | −0.883533 | − | 0.468369i | \(-0.844842\pi\) | ||||
−0.883533 | + | 0.468369i | \(0.844842\pi\) | |||||||
\(654\) | 3.87665 | 0.151589 | ||||||||
\(655\) | 16.5681 | 0.647369 | ||||||||
\(656\) | −8.68996 | −0.339286 | ||||||||
\(657\) | 19.8328 | 0.773751 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.31420 | 0.129103 | 0.0645514 | − | 0.997914i | \(-0.479438\pi\) | ||||
0.0645514 | + | 0.997914i | \(0.479438\pi\) | |||||||
\(660\) | 1.27440 | 0.0496058 | ||||||||
\(661\) | −9.71398 | −0.377830 | −0.188915 | − | 0.981993i | \(-0.560497\pi\) | ||||
−0.188915 | + | 0.981993i | \(0.560497\pi\) | |||||||
\(662\) | 9.37773 | 0.364476 | ||||||||
\(663\) | 4.95634 | 0.192488 | ||||||||
\(664\) | 2.37787 | 0.0922793 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.8413 | −0.536338 | ||||||||
\(667\) | −12.7388 | −0.493247 | ||||||||
\(668\) | 21.1531 | 0.818438 | ||||||||
\(669\) | −17.2109 | −0.665411 | ||||||||
\(670\) | −1.06355 | −0.0410885 | ||||||||
\(671\) | 5.18390 | 0.200122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.16771 | −0.314842 | −0.157421 | − | 0.987532i | \(-0.550318\pi\) | ||||
−0.157421 | + | 0.987532i | \(0.550318\pi\) | |||||||
\(674\) | −6.45752 | −0.248734 | ||||||||
\(675\) | 3.94768 | 0.151946 | ||||||||
\(676\) | 11.0845 | 0.426327 | ||||||||
\(677\) | 39.9698 | 1.53616 | 0.768082 | − | 0.640352i | \(-0.221211\pi\) | ||||
0.768082 | + | 0.640352i | \(0.221211\pi\) | |||||||
\(678\) | 0.655194 | 0.0251626 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.79892 | 0.184030 | ||||||||
\(681\) | 14.3141 | 0.548518 | ||||||||
\(682\) | −1.93974 | −0.0742767 | ||||||||
\(683\) | −37.6069 | −1.43899 | −0.719495 | − | 0.694498i | \(-0.755627\pi\) | ||||
−0.719495 | + | 0.694498i | \(0.755627\pi\) | |||||||
\(684\) | 12.4286 | 0.475220 | ||||||||
\(685\) | 14.0530 | 0.536938 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.28933 | 0.201800 | ||||||||
\(688\) | −10.5948 | −0.403922 | ||||||||
\(689\) | −17.0453 | −0.649373 | ||||||||
\(690\) | −0.695669 | −0.0264836 | ||||||||
\(691\) | 35.2203 | 1.33984 | 0.669921 | − | 0.742432i | \(-0.266328\pi\) | ||||
0.669921 | + | 0.742432i | \(0.266328\pi\) | |||||||
\(692\) | 36.1981 | 1.37604 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.07668 | 0.192708 | ||||||||
\(695\) | −14.3025 | −0.542524 | ||||||||
\(696\) | −8.25326 | −0.312839 | ||||||||
\(697\) | 8.63000 | 0.326885 | ||||||||
\(698\) | 5.55520 | 0.210267 | ||||||||
\(699\) | 6.72669 | 0.254427 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.4463 | 0.507861 | 0.253930 | − | 0.967222i | \(-0.418277\pi\) | ||||
0.253930 | + | 0.967222i | \(0.418277\pi\) | |||||||
\(702\) | 4.91910 | 0.185659 | ||||||||
\(703\) | 32.8884 | 1.24041 | ||||||||
\(704\) | −2.98672 | −0.112566 | ||||||||
\(705\) | 6.78141 | 0.255403 | ||||||||
\(706\) | −7.52351 | −0.283151 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −15.5964 | −0.586148 | ||||||||
\(709\) | 7.19749 | 0.270308 | 0.135154 | − | 0.990825i | \(-0.456847\pi\) | ||||
0.135154 | + | 0.990825i | \(0.456847\pi\) | |||||||
\(710\) | −1.79933 | −0.0675277 | ||||||||
\(711\) | −40.5681 | −1.52142 | ||||||||
\(712\) | 13.5242 | 0.506842 | ||||||||
\(713\) | −8.12804 | −0.304398 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.59533 | 0.0970598 | ||||||||
\(716\) | 3.79716 | 0.141906 | ||||||||
\(717\) | 2.98771 | 0.111578 | ||||||||
\(718\) | 14.1625 | 0.528539 | ||||||||
\(719\) | −43.7755 | −1.63255 | −0.816275 | − | 0.577663i | \(-0.803965\pi\) | ||||
−0.816275 | + | 0.577663i | \(0.803965\pi\) | |||||||
\(720\) | −6.62516 | −0.246905 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.27510 | −0.196319 | ||||||||
\(723\) | 1.76709 | 0.0657188 | ||||||||
\(724\) | −15.5109 | −0.576458 | ||||||||
\(725\) | −6.33190 | −0.235161 | ||||||||
\(726\) | −0.345788 | −0.0128334 | ||||||||
\(727\) | 11.5718 | 0.429173 | 0.214587 | − | 0.976705i | \(-0.431160\pi\) | ||||
0.214587 | + | 0.976705i | \(0.431160\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.88639 | −0.106903 | ||||||||
\(730\) | −3.83757 | −0.142035 | ||||||||
\(731\) | 10.5217 | 0.389158 | ||||||||
\(732\) | 6.60634 | 0.244177 | ||||||||
\(733\) | −52.9098 | −1.95427 | −0.977133 | − | 0.212627i | \(-0.931798\pi\) | ||||
−0.977133 | + | 0.212627i | \(0.931798\pi\) | |||||||
\(734\) | −14.8283 | −0.547322 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.86115 | 0.363487 | ||||||||
\(737\) | −2.21517 | −0.0815968 | ||||||||
\(738\) | 3.87732 | 0.142726 | ||||||||
\(739\) | −1.60903 | −0.0591891 | −0.0295945 | − | 0.999562i | \(-0.509422\pi\) | ||||
−0.0295945 | + | 0.999562i | \(0.509422\pi\) | |||||||
\(740\) | −20.5585 | −0.755746 | ||||||||
\(741\) | −5.29112 | −0.194374 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.4436 | −1.30030 | −0.650150 | − | 0.759806i | \(-0.725294\pi\) | ||||
−0.650150 | + | 0.759806i | \(0.725294\pi\) | |||||||
\(744\) | −5.26604 | −0.193063 | ||||||||
\(745\) | −23.7598 | −0.870493 | ||||||||
\(746\) | −10.2670 | −0.375900 | ||||||||
\(747\) | 3.26012 | 0.119282 | ||||||||
\(748\) | 4.69199 | 0.171556 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.345788 | −0.0126264 | ||||||||
\(751\) | 37.8138 | 1.37984 | 0.689922 | − | 0.723884i | \(-0.257645\pi\) | ||||
0.689922 | + | 0.723884i | \(0.257645\pi\) | |||||||
\(752\) | −25.1408 | −0.916791 | ||||||||
\(753\) | −4.84944 | −0.176723 | ||||||||
\(754\) | −7.89002 | −0.287338 | ||||||||
\(755\) | 7.18141 | 0.261358 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.03504 | 0.328384 | 0.164192 | − | 0.986428i | \(-0.447498\pi\) | ||||
0.164192 | + | 0.986428i | \(0.447498\pi\) | |||||||
\(758\) | 2.20868 | 0.0802228 | ||||||||
\(759\) | −1.44894 | −0.0525932 | ||||||||
\(760\) | −5.12307 | −0.185833 | ||||||||
\(761\) | −41.5744 | −1.50707 | −0.753535 | − | 0.657407i | \(-0.771653\pi\) | ||||
−0.753535 | + | 0.657407i | \(0.771653\pi\) | |||||||
\(762\) | 0.248620 | 0.00900655 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.62685 | −0.0950362 | ||||||||
\(765\) | 6.57945 | 0.237881 | ||||||||
\(766\) | −3.73183 | −0.134837 | ||||||||
\(767\) | −31.7623 | −1.14687 | ||||||||
\(768\) | −0.416466 | −0.0150279 | ||||||||
\(769\) | 20.8863 | 0.753180 | 0.376590 | − | 0.926380i | \(-0.377097\pi\) | ||||
0.376590 | + | 0.926380i | \(0.377097\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.5264 | −0.451126 | ||||||||
\(772\) | −39.8922 | −1.43575 | ||||||||
\(773\) | −50.1351 | −1.80324 | −0.901618 | − | 0.432533i | \(-0.857620\pi\) | ||||
−0.901618 | + | 0.432533i | \(0.857620\pi\) | |||||||
\(774\) | 4.72722 | 0.169916 | ||||||||
\(775\) | −4.04011 | −0.145125 | ||||||||
\(776\) | 11.7809 | 0.422910 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.83413 | 0.137460 | ||||||||
\(779\) | −9.21293 | −0.330087 | ||||||||
\(780\) | 3.30748 | 0.118427 | ||||||||
\(781\) | −3.74766 | −0.134102 | ||||||||
\(782\) | −2.56127 | −0.0915907 | ||||||||
\(783\) | −24.9963 | −0.893295 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.81328 | 0.278868 | ||||||||
\(786\) | −5.72904 | −0.204348 | ||||||||
\(787\) | −9.39061 | −0.334739 | −0.167370 | − | 0.985894i | \(-0.553527\pi\) | ||||
−0.167370 | + | 0.985894i | \(0.553527\pi\) | |||||||
\(788\) | −10.8172 | −0.385348 | ||||||||
\(789\) | −4.54598 | −0.161841 | ||||||||
\(790\) | 7.84977 | 0.279282 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.49068 | 0.159570 | ||||||||
\(793\) | 13.4539 | 0.477763 | ||||||||
\(794\) | −0.637227 | −0.0226143 | ||||||||
\(795\) | 4.73009 | 0.167759 | ||||||||
\(796\) | 43.7222 | 1.54969 | ||||||||
\(797\) | −32.0295 | −1.13454 | −0.567272 | − | 0.823531i | \(-0.692001\pi\) | ||||
−0.567272 | + | 0.823531i | \(0.692001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.9673 | 0.883281 | ||||||||
\(800\) | 4.90157 | 0.173297 | ||||||||
\(801\) | 18.5421 | 0.655153 | ||||||||
\(802\) | −2.37278 | −0.0837858 | ||||||||
\(803\) | −7.99291 | −0.282064 | ||||||||
\(804\) | −2.82300 | −0.0995596 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.03428 | −0.177325 | ||||||||
\(807\) | −0.219656 | −0.00773225 | ||||||||
\(808\) | 20.2795 | 0.713431 | ||||||||
\(809\) | 44.6204 | 1.56877 | 0.784384 | − | 0.620275i | \(-0.212979\pi\) | ||||
0.784384 | + | 0.620275i | \(0.212979\pi\) | |||||||
\(810\) | 2.20892 | 0.0776136 | ||||||||
\(811\) | −22.7734 | −0.799683 | −0.399842 | − | 0.916584i | \(-0.630935\pi\) | ||||
−0.399842 | + | 0.916584i | \(0.630935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.15011 | −0.145551 | ||||||||
\(814\) | 5.57823 | 0.195517 | ||||||||
\(815\) | −1.78950 | −0.0626834 | ||||||||
\(816\) | 5.09901 | 0.178501 | ||||||||
\(817\) | −11.2324 | −0.392971 | ||||||||
\(818\) | 2.65081 | 0.0926835 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.75900 | 0.201113 | ||||||||
\(821\) | 11.9500 | 0.417059 | 0.208529 | − | 0.978016i | \(-0.433132\pi\) | ||||
0.208529 | + | 0.978016i | \(0.433132\pi\) | |||||||
\(822\) | −4.85936 | −0.169490 | ||||||||
\(823\) | 29.4262 | 1.02573 | 0.512867 | − | 0.858468i | \(-0.328584\pi\) | ||||
0.512867 | + | 0.858468i | \(0.328584\pi\) | |||||||
\(824\) | 27.1845 | 0.947018 | ||||||||
\(825\) | −0.720208 | −0.0250744 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.1635 | −0.944569 | −0.472285 | − | 0.881446i | \(-0.656571\pi\) | ||||
−0.472285 | + | 0.881446i | \(0.656571\pi\) | |||||||
\(828\) | 8.83321 | 0.306975 | ||||||||
\(829\) | 51.6294 | 1.79316 | 0.896582 | − | 0.442879i | \(-0.146043\pi\) | ||||
0.896582 | + | 0.442879i | \(0.146043\pi\) | |||||||
\(830\) | −0.630821 | −0.0218961 | ||||||||
\(831\) | 21.3423 | 0.740357 | ||||||||
\(832\) | −7.75153 | −0.268736 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.94562 | 0.171253 | ||||||||
\(835\) | −11.9544 | −0.413699 | ||||||||
\(836\) | −5.00891 | −0.173237 | ||||||||
\(837\) | −15.9490 | −0.551280 | ||||||||
\(838\) | 5.14421 | 0.177704 | ||||||||
\(839\) | 21.4801 | 0.741576 | 0.370788 | − | 0.928718i | \(-0.379088\pi\) | ||||
0.370788 | + | 0.928718i | \(0.379088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0930 | 0.382517 | ||||||||
\(842\) | 13.9161 | 0.479579 | ||||||||
\(843\) | −9.18687 | −0.316413 | ||||||||
\(844\) | 15.3855 | 0.529591 | ||||||||
\(845\) | −6.26426 | −0.215497 | ||||||||
\(846\) | 11.2174 | 0.385663 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.5359 | −0.602186 | ||||||||
\(849\) | −2.55246 | −0.0876002 | ||||||||
\(850\) | −1.27310 | −0.0436669 | ||||||||
\(851\) | 23.3743 | 0.801260 | ||||||||
\(852\) | −4.77600 | −0.163623 | ||||||||
\(853\) | 44.6910 | 1.53019 | 0.765095 | − | 0.643917i | \(-0.222692\pi\) | ||||
0.765095 | + | 0.643917i | \(0.222692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.02387 | −0.240211 | ||||||||
\(856\) | 10.0262 | 0.342688 | ||||||||
\(857\) | 4.48284 | 0.153131 | 0.0765654 | − | 0.997065i | \(-0.475605\pi\) | ||||
0.0765654 | + | 0.997065i | \(0.475605\pi\) | |||||||
\(858\) | −0.897433 | −0.0306379 | ||||||||
\(859\) | −24.6914 | −0.842461 | −0.421230 | − | 0.906954i | \(-0.638402\pi\) | ||||
−0.421230 | + | 0.906954i | \(0.638402\pi\) | |||||||
\(860\) | 7.02136 | 0.239426 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.7024 | 0.432645 | ||||||||
\(863\) | −22.1998 | −0.755689 | −0.377844 | − | 0.925869i | \(-0.623335\pi\) | ||||
−0.377844 | + | 0.925869i | \(0.623335\pi\) | |||||||
\(864\) | 19.3498 | 0.658294 | ||||||||
\(865\) | −20.4569 | −0.695554 | ||||||||
\(866\) | 6.57662 | 0.223483 | ||||||||
\(867\) | 7.17972 | 0.243836 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.3495 | 0.554620 | ||||||||
\(870\) | 2.18949 | 0.0742308 | ||||||||
\(871\) | −5.74909 | −0.194800 | ||||||||
\(872\) | 20.2899 | 0.687103 | ||||||||
\(873\) | 16.1519 | 0.546660 | ||||||||
\(874\) | 2.73427 | 0.0924881 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.1861 | −0.344157 | ||||||||
\(877\) | −48.2069 | −1.62783 | −0.813916 | − | 0.580982i | \(-0.802669\pi\) | ||||
−0.813916 | + | 0.580982i | \(0.802669\pi\) | |||||||
\(878\) | 14.8352 | 0.500665 | ||||||||
\(879\) | 3.54468 | 0.119559 | ||||||||
\(880\) | 2.67004 | 0.0900069 | ||||||||
\(881\) | −46.8659 | −1.57895 | −0.789477 | − | 0.613780i | \(-0.789648\pi\) | ||||
−0.789477 | + | 0.613780i | \(0.789648\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.6461 | −0.492879 | −0.246440 | − | 0.969158i | \(-0.579261\pi\) | ||||
−0.246440 | + | 0.969158i | \(0.579261\pi\) | |||||||
\(884\) | 12.1772 | 0.409565 | ||||||||
\(885\) | 8.81409 | 0.296282 | ||||||||
\(886\) | −2.86278 | −0.0961771 | ||||||||
\(887\) | −41.7705 | −1.40252 | −0.701258 | − | 0.712907i | \(-0.747378\pi\) | ||||
−0.701258 | + | 0.712907i | \(0.747378\pi\) | |||||||
\(888\) | 15.1439 | 0.508195 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.58782 | −0.120264 | ||||||||
\(891\) | 4.60075 | 0.154131 | ||||||||
\(892\) | −42.2855 | −1.41582 | ||||||||
\(893\) | −26.6538 | −0.891936 | ||||||||
\(894\) | 8.21586 | 0.274779 | ||||||||
\(895\) | −2.14591 | −0.0717299 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.76048 | −0.125559 | ||||||||
\(898\) | 12.8942 | 0.430286 | ||||||||
\(899\) | 25.5816 | 0.853193 | ||||||||
\(900\) | 4.39062 | 0.146354 | ||||||||
\(901\) | 17.4149 | 0.580175 | ||||||||
\(902\) | −1.56262 | −0.0520294 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.42920 | 0.114054 | ||||||||
\(905\) | 8.76578 | 0.291385 | ||||||||
\(906\) | −2.48324 | −0.0825002 | ||||||||
\(907\) | 12.4729 | 0.414155 | 0.207077 | − | 0.978325i | \(-0.433605\pi\) | ||||
0.207077 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(908\) | 35.1684 | 1.16711 | ||||||||
\(909\) | 27.8038 | 0.922192 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.1114 | −0.633191 | −0.316595 | − | 0.948561i | \(-0.602540\pi\) | ||||
−0.316595 | + | 0.948561i | \(0.602540\pi\) | |||||||
\(912\) | −5.44343 | −0.180250 | ||||||||
\(913\) | −1.31388 | −0.0434830 | ||||||||
\(914\) | −7.67605 | −0.253901 | ||||||||
\(915\) | −3.73349 | −0.123425 | ||||||||
\(916\) | 12.9954 | 0.429379 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.02578 | −0.165875 | ||||||||
\(919\) | −8.14450 | −0.268662 | −0.134331 | − | 0.990936i | \(-0.542889\pi\) | ||||
−0.134331 | + | 0.990936i | \(0.542889\pi\) | |||||||
\(920\) | −3.64105 | −0.120042 | ||||||||
\(921\) | −0.934380 | −0.0307889 | ||||||||
\(922\) | −11.4030 | −0.375537 | ||||||||
\(923\) | −9.72640 | −0.320148 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6184 | 0.382010 | ||||||||
\(926\) | 7.46830 | 0.245424 | ||||||||
\(927\) | 37.2707 | 1.22413 | ||||||||
\(928\) | −31.0362 | −1.01881 | ||||||||
\(929\) | −23.2542 | −0.762946 | −0.381473 | − | 0.924380i | \(-0.624583\pi\) | ||||
−0.381473 | + | 0.924380i | \(0.624583\pi\) | |||||||
\(930\) | 1.39702 | 0.0458101 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.5268 | 0.541354 | ||||||||
\(933\) | −8.96342 | −0.293449 | ||||||||
\(934\) | 7.78432 | 0.254711 | ||||||||
\(935\) | −2.65161 | −0.0867170 | ||||||||
\(936\) | 11.6548 | 0.380949 | ||||||||
\(937\) | 53.7860 | 1.75711 | 0.878556 | − | 0.477640i | \(-0.158508\pi\) | ||||
0.878556 | + | 0.477640i | \(0.158508\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.17683 | 0.0384044 | ||||||||
\(940\) | 16.6613 | 0.543431 | ||||||||
\(941\) | −33.2193 | −1.08292 | −0.541458 | − | 0.840728i | \(-0.682128\pi\) | ||||
−0.541458 | + | 0.840728i | \(0.682128\pi\) | |||||||
\(942\) | −2.70174 | −0.0880274 | ||||||||
\(943\) | −6.54777 | −0.213225 | ||||||||
\(944\) | −32.6766 | −1.06353 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.90514 | −0.0619414 | ||||||||
\(947\) | 20.6050 | 0.669573 | 0.334786 | − | 0.942294i | \(-0.391336\pi\) | ||||
0.334786 | + | 0.942294i | \(0.391336\pi\) | |||||||
\(948\) | 20.8358 | 0.676715 | ||||||||
\(949\) | −20.7442 | −0.673386 | ||||||||
\(950\) | 1.35909 | 0.0440948 | ||||||||
\(951\) | 6.42784 | 0.208437 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.4071 | 0.337118 | 0.168559 | − | 0.985692i | \(-0.446089\pi\) | ||||
0.168559 | + | 0.985692i | \(0.446089\pi\) | |||||||
\(954\) | 7.82424 | 0.253319 | ||||||||
\(955\) | 1.48453 | 0.0480383 | ||||||||
\(956\) | 7.34052 | 0.237409 | ||||||||
\(957\) | 4.56029 | 0.147413 | ||||||||
\(958\) | 15.2425 | 0.492463 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.15106 | 0.0694252 | ||||||||
\(961\) | −14.6775 | −0.473468 | ||||||||
\(962\) | 14.4774 | 0.466769 | ||||||||
\(963\) | 13.7462 | 0.442964 | ||||||||
\(964\) | 4.34157 | 0.139833 | ||||||||
\(965\) | 22.5446 | 0.725736 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.4271 | −1.78241 | −0.891207 | − | 0.453596i | \(-0.850141\pi\) | ||||
−0.891207 | + | 0.453596i | \(0.850141\pi\) | |||||||
\(968\) | −1.80981 | −0.0581695 | ||||||||
\(969\) | 5.40587 | 0.173662 | ||||||||
\(970\) | −3.12534 | −0.100348 | ||||||||
\(971\) | 26.7900 | 0.859732 | 0.429866 | − | 0.902893i | \(-0.358561\pi\) | ||||
0.429866 | + | 0.902893i | \(0.358561\pi\) | |||||||
\(972\) | 26.8192 | 0.860227 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.1961 | −0.583042 | ||||||||
\(975\) | −1.86918 | −0.0598616 | ||||||||
\(976\) | 13.8412 | 0.443046 | ||||||||
\(977\) | 31.0373 | 0.992970 | 0.496485 | − | 0.868045i | \(-0.334624\pi\) | ||||
0.496485 | + | 0.868045i | \(0.334624\pi\) | |||||||
\(978\) | 0.618787 | 0.0197866 | ||||||||
\(979\) | −7.47273 | −0.238830 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.8180 | 0.888161 | ||||||||
\(982\) | 19.9777 | 0.637515 | ||||||||
\(983\) | −5.26620 | −0.167966 | −0.0839828 | − | 0.996467i | \(-0.526764\pi\) | ||||
−0.0839828 | + | 0.996467i | \(0.526764\pi\) | |||||||
\(984\) | −4.24221 | −0.135237 | ||||||||
\(985\) | 6.11322 | 0.194783 | ||||||||
\(986\) | 8.06113 | 0.256719 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.9998 | −0.413578 | ||||||||
\(989\) | −7.98303 | −0.253845 | ||||||||
\(990\) | −1.19133 | −0.0378628 | ||||||||
\(991\) | −60.3436 | −1.91688 | −0.958439 | − | 0.285298i | \(-0.907908\pi\) | ||||
−0.958439 | + | 0.285298i | \(0.907908\pi\) | |||||||
\(992\) | −19.8029 | −0.628741 | ||||||||
\(993\) | −14.0671 | −0.446406 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.7090 | −0.783329 | ||||||||
\(996\) | −1.67440 | −0.0530554 | ||||||||
\(997\) | −8.84168 | −0.280019 | −0.140009 | − | 0.990150i | \(-0.544713\pi\) | ||||
−0.140009 | + | 0.990150i | \(0.544713\pi\) | |||||||
\(998\) | 16.3097 | 0.516274 | ||||||||
\(999\) | 45.8656 | 1.45112 |
(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 | 2695.2.a.u.1.7 | ✓ | 10 | |
7.6 | odd | 2 | 2695.2.a.v.1.7 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2695.2.a.u.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial | |
2695.2.a.v.1.7 | yes | 10 | 7.6 | odd | 2 |