Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(506,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.506");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 34x^{16} + 407x^{14} + 2175x^{12} + 5555x^{10} + 6664x^{8} + 3544x^{6} + 681x^{4} + 47x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 506.15 | ||
Root | \(-1.03381i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.506 |
Dual form | 845.2.c.h.506.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.28079i | 1.61276i | 0.591397 | + | 0.806380i | \(0.298576\pi\) | ||||
−0.591397 | + | 0.806380i | \(0.701424\pi\) | |||||||
\(3\) | 3.21428 | 1.85576 | 0.927882 | − | 0.372874i | \(-0.121628\pi\) | ||||
0.927882 | + | 0.372874i | \(0.121628\pi\) | |||||||
\(4\) | −3.20199 | −1.60100 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 7.33108i | 2.99290i | ||||||||
\(7\) | 2.30369i | 0.870714i | 0.900258 | + | 0.435357i | \(0.143378\pi\) | ||||
−0.900258 | + | 0.435357i | \(0.856622\pi\) | |||||||
\(8\) | − 2.74149i | − 0.969263i | ||||||||
\(9\) | 7.33158 | 2.44386 | ||||||||
\(10\) | 2.28079 | 0.721248 | ||||||||
\(11\) | 1.25954i | 0.379765i | 0.981807 | + | 0.189882i | \(0.0608107\pi\) | ||||
−0.981807 | + | 0.189882i | \(0.939189\pi\) | |||||||
\(12\) | −10.2921 | −2.97107 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.25423 | −1.40425 | ||||||||
\(15\) | − 3.21428i | − 0.829923i | ||||||||
\(16\) | −0.151230 | −0.0378075 | ||||||||
\(17\) | −2.43159 | −0.589748 | −0.294874 | − | 0.955536i | \(-0.595278\pi\) | ||||
−0.294874 | + | 0.955536i | \(0.595278\pi\) | |||||||
\(18\) | 16.7218i | 3.94136i | ||||||||
\(19\) | − 0.586893i | − 0.134643i | −0.997731 | − | 0.0673213i | \(-0.978555\pi\) | ||||
0.997731 | − | 0.0673213i | \(-0.0214453\pi\) | |||||||
\(20\) | 3.20199i | 0.715987i | ||||||||
\(21\) | 7.40470i | 1.61584i | ||||||||
\(22\) | −2.87274 | −0.612470 | ||||||||
\(23\) | 8.37020 | 1.74531 | 0.872654 | − | 0.488339i | \(-0.162397\pi\) | ||||
0.872654 | + | 0.488339i | \(0.162397\pi\) | |||||||
\(24\) | − 8.81191i | − 1.79872i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.9229 | 2.67946 | ||||||||
\(28\) | − 7.37640i | − 1.39401i | ||||||||
\(29\) | −3.09157 | −0.574090 | −0.287045 | − | 0.957917i | \(-0.592673\pi\) | ||||
−0.287045 | + | 0.957917i | \(0.592673\pi\) | |||||||
\(30\) | 7.33108 | 1.33847 | ||||||||
\(31\) | − 0.394069i | − 0.0707770i | −0.999374 | − | 0.0353885i | \(-0.988733\pi\) | ||||
0.999374 | − | 0.0353885i | \(-0.0112669\pi\) | |||||||
\(32\) | − 5.82790i | − 1.03024i | ||||||||
\(33\) | 4.04850i | 0.704754i | ||||||||
\(34\) | − 5.54595i | − 0.951122i | ||||||||
\(35\) | 2.30369 | 0.389395 | ||||||||
\(36\) | −23.4757 | −3.91261 | ||||||||
\(37\) | − 2.01774i | − 0.331715i | −0.986150 | − | 0.165857i | \(-0.946961\pi\) | ||||
0.986150 | − | 0.165857i | \(-0.0530391\pi\) | |||||||
\(38\) | 1.33858 | 0.217146 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.74149 | −0.433467 | ||||||||
\(41\) | 5.58749i | 0.872619i | 0.899797 | + | 0.436309i | \(0.143715\pi\) | ||||
−0.899797 | + | 0.436309i | \(0.856285\pi\) | |||||||
\(42\) | −16.8886 | −2.60596 | ||||||||
\(43\) | −5.87653 | −0.896162 | −0.448081 | − | 0.893993i | \(-0.647892\pi\) | ||||
−0.448081 | + | 0.893993i | \(0.647892\pi\) | |||||||
\(44\) | − 4.03303i | − 0.608002i | ||||||||
\(45\) | − 7.33158i | − 1.09293i | ||||||||
\(46\) | 19.0907i | 2.81476i | ||||||||
\(47\) | − 1.92869i | − 0.281329i | −0.990057 | − | 0.140664i | \(-0.955076\pi\) | ||||
0.990057 | − | 0.140664i | \(-0.0449239\pi\) | |||||||
\(48\) | −0.486096 | −0.0701619 | ||||||||
\(49\) | 1.69301 | 0.241858 | ||||||||
\(50\) | − 2.28079i | − 0.322552i | ||||||||
\(51\) | −7.81582 | −1.09443 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.6727 | −1.87809 | −0.939044 | − | 0.343797i | \(-0.888287\pi\) | ||||
−0.939044 | + | 0.343797i | \(0.888287\pi\) | |||||||
\(54\) | 31.7552i | 4.32133i | ||||||||
\(55\) | 1.25954 | 0.169836 | ||||||||
\(56\) | 6.31554 | 0.843950 | ||||||||
\(57\) | − 1.88644i | − 0.249865i | ||||||||
\(58\) | − 7.05121i | − 0.925869i | ||||||||
\(59\) | − 14.6844i | − 1.91175i | −0.293770 | − | 0.955876i | \(-0.594910\pi\) | ||||
0.293770 | − | 0.955876i | \(-0.405090\pi\) | |||||||
\(60\) | 10.2921i | 1.32870i | ||||||||
\(61\) | 5.85222 | 0.749300 | 0.374650 | − | 0.927166i | \(-0.377763\pi\) | ||||
0.374650 | + | 0.927166i | \(0.377763\pi\) | |||||||
\(62\) | 0.898789 | 0.114146 | ||||||||
\(63\) | 16.8897i | 2.12790i | ||||||||
\(64\) | 12.9897 | 1.62372 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.23378 | −1.13660 | ||||||||
\(67\) | − 1.99420i | − 0.243630i | −0.992553 | − | 0.121815i | \(-0.961128\pi\) | ||||
0.992553 | − | 0.121815i | \(-0.0388715\pi\) | |||||||
\(68\) | 7.78594 | 0.944184 | ||||||||
\(69\) | 26.9042 | 3.23888 | ||||||||
\(70\) | 5.25423i | 0.628001i | ||||||||
\(71\) | 9.59141i | 1.13829i | 0.822237 | + | 0.569146i | \(0.192726\pi\) | ||||
−0.822237 | + | 0.569146i | \(0.807274\pi\) | |||||||
\(72\) | − 20.0994i | − 2.36874i | ||||||||
\(73\) | − 4.38231i | − 0.512910i | −0.966556 | − | 0.256455i | \(-0.917445\pi\) | ||||
0.966556 | − | 0.256455i | \(-0.0825546\pi\) | |||||||
\(74\) | 4.60204 | 0.534976 | ||||||||
\(75\) | −3.21428 | −0.371153 | ||||||||
\(76\) | 1.87923i | 0.215562i | ||||||||
\(77\) | −2.90159 | −0.330666 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.217237 | −0.0244411 | −0.0122206 | − | 0.999925i | \(-0.503890\pi\) | ||||
−0.0122206 | + | 0.999925i | \(0.503890\pi\) | |||||||
\(80\) | 0.151230i | 0.0169080i | ||||||||
\(81\) | 22.7573 | 2.52859 | ||||||||
\(82\) | −12.7439 | −1.40733 | ||||||||
\(83\) | − 11.0119i | − 1.20871i | −0.796716 | − | 0.604354i | \(-0.793431\pi\) | ||||
0.796716 | − | 0.604354i | \(-0.206569\pi\) | |||||||
\(84\) | − 23.7098i | − 2.58695i | ||||||||
\(85\) | 2.43159i | 0.263743i | ||||||||
\(86\) | − 13.4031i | − 1.44529i | ||||||||
\(87\) | −9.93715 | −1.06537 | ||||||||
\(88\) | 3.45301 | 0.368092 | ||||||||
\(89\) | 6.37458i | 0.675704i | 0.941199 | + | 0.337852i | \(0.109700\pi\) | ||||
−0.941199 | + | 0.337852i | \(0.890300\pi\) | |||||||
\(90\) | 16.7218 | 1.76263 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −26.8013 | −2.79423 | ||||||||
\(93\) | − 1.26665i | − 0.131345i | ||||||||
\(94\) | 4.39894 | 0.453716 | ||||||||
\(95\) | −0.586893 | −0.0602140 | ||||||||
\(96\) | − 18.7325i | − 1.91188i | ||||||||
\(97\) | − 16.3061i | − 1.65563i | −0.560998 | − | 0.827817i | \(-0.689582\pi\) | ||||
0.560998 | − | 0.827817i | \(-0.310418\pi\) | |||||||
\(98\) | 3.86139i | 0.390059i | ||||||||
\(99\) | 9.23440i | 0.928092i | ||||||||
\(100\) | 3.20199 | 0.320199 | ||||||||
\(101\) | 6.90971 | 0.687541 | 0.343771 | − | 0.939054i | \(-0.388296\pi\) | ||||
0.343771 | + | 0.939054i | \(0.388296\pi\) | |||||||
\(102\) | − 17.8262i | − 1.76506i | ||||||||
\(103\) | −9.09928 | −0.896579 | −0.448289 | − | 0.893888i | \(-0.647967\pi\) | ||||
−0.448289 | + | 0.893888i | \(0.647967\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.40470 | 0.722625 | ||||||||
\(106\) | − 31.1845i | − 3.02891i | ||||||||
\(107\) | 8.96050 | 0.866244 | 0.433122 | − | 0.901335i | \(-0.357412\pi\) | ||||
0.433122 | + | 0.901335i | \(0.357412\pi\) | |||||||
\(108\) | −44.5810 | −4.28981 | ||||||||
\(109\) | − 4.39646i | − 0.421105i | −0.977583 | − | 0.210552i | \(-0.932474\pi\) | ||||
0.977583 | − | 0.210552i | \(-0.0675262\pi\) | |||||||
\(110\) | 2.87274i | 0.273905i | ||||||||
\(111\) | − 6.48558i | − 0.615584i | ||||||||
\(112\) | − 0.348388i | − 0.0329195i | ||||||||
\(113\) | 10.4452 | 0.982600 | 0.491300 | − | 0.870990i | \(-0.336522\pi\) | ||||
0.491300 | + | 0.870990i | \(0.336522\pi\) | |||||||
\(114\) | 4.30256 | 0.402972 | ||||||||
\(115\) | − 8.37020i | − 0.780525i | ||||||||
\(116\) | 9.89917 | 0.919115 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 33.4921 | 3.08320 | ||||||||
\(119\) | − 5.60164i | − 0.513502i | ||||||||
\(120\) | −8.81191 | −0.804413 | ||||||||
\(121\) | 9.41357 | 0.855779 | ||||||||
\(122\) | 13.3477i | 1.20844i | ||||||||
\(123\) | 17.9597i | 1.61937i | ||||||||
\(124\) | 1.26181i | 0.113314i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −38.5218 | −3.43180 | ||||||||
\(127\) | −14.9712 | −1.32848 | −0.664240 | − | 0.747520i | \(-0.731245\pi\) | ||||
−0.664240 | + | 0.747520i | \(0.731245\pi\) | |||||||
\(128\) | 17.9710i | 1.58843i | ||||||||
\(129\) | −18.8888 | −1.66306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7370 | 0.938098 | 0.469049 | − | 0.883172i | \(-0.344597\pi\) | ||||
0.469049 | + | 0.883172i | \(0.344597\pi\) | |||||||
\(132\) | − 12.9633i | − 1.12831i | ||||||||
\(133\) | 1.35202 | 0.117235 | ||||||||
\(134\) | 4.54835 | 0.392918 | ||||||||
\(135\) | − 13.9229i | − 1.19829i | ||||||||
\(136\) | 6.66619i | 0.571621i | ||||||||
\(137\) | − 2.89958i | − 0.247728i | −0.992299 | − | 0.123864i | \(-0.960471\pi\) | ||||
0.992299 | − | 0.123864i | \(-0.0395286\pi\) | |||||||
\(138\) | 61.3627i | 5.22354i | ||||||||
\(139\) | −16.4802 | −1.39784 | −0.698918 | − | 0.715202i | \(-0.746335\pi\) | ||||
−0.698918 | + | 0.715202i | \(0.746335\pi\) | |||||||
\(140\) | −7.37640 | −0.623420 | ||||||||
\(141\) | − 6.19936i | − 0.522080i | ||||||||
\(142\) | −21.8760 | −1.83579 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.10876 | −0.0923963 | ||||||||
\(145\) | 3.09157i | 0.256741i | ||||||||
\(146\) | 9.99512 | 0.827202 | ||||||||
\(147\) | 5.44179 | 0.448831 | ||||||||
\(148\) | 6.46079i | 0.531074i | ||||||||
\(149\) | − 1.08944i | − 0.0892501i | −0.999004 | − | 0.0446251i | \(-0.985791\pi\) | ||||
0.999004 | − | 0.0446251i | \(-0.0142093\pi\) | |||||||
\(150\) | − 7.33108i | − 0.598580i | ||||||||
\(151\) | − 18.9559i | − 1.54261i | −0.636466 | − | 0.771305i | \(-0.719604\pi\) | ||||
0.636466 | − | 0.771305i | \(-0.280396\pi\) | |||||||
\(152\) | −1.60896 | −0.130504 | ||||||||
\(153\) | −17.8274 | −1.44126 | ||||||||
\(154\) | − 6.61790i | − 0.533286i | ||||||||
\(155\) | −0.394069 | −0.0316524 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.27488 | 0.420981 | 0.210491 | − | 0.977596i | \(-0.432494\pi\) | ||||
0.210491 | + | 0.977596i | \(0.432494\pi\) | |||||||
\(158\) | − 0.495472i | − 0.0394177i | ||||||||
\(159\) | −43.9478 | −3.48529 | ||||||||
\(160\) | −5.82790 | −0.460736 | ||||||||
\(161\) | 19.2824i | 1.51966i | ||||||||
\(162\) | 51.9046i | 4.07801i | ||||||||
\(163\) | − 20.4979i | − 1.60552i | −0.596300 | − | 0.802762i | \(-0.703363\pi\) | ||||
0.596300 | − | 0.802762i | \(-0.296637\pi\) | |||||||
\(164\) | − 17.8911i | − 1.39706i | ||||||||
\(165\) | 4.04850 | 0.315176 | ||||||||
\(166\) | 25.1157 | 1.94936 | ||||||||
\(167\) | 19.1053i | 1.47841i | 0.673479 | + | 0.739206i | \(0.264799\pi\) | ||||
−0.673479 | + | 0.739206i | \(0.735201\pi\) | |||||||
\(168\) | 20.2999 | 1.56617 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −5.54595 | −0.425355 | ||||||||
\(171\) | − 4.30285i | − 0.329048i | ||||||||
\(172\) | 18.8166 | 1.43475 | ||||||||
\(173\) | −5.28584 | −0.401875 | −0.200937 | − | 0.979604i | \(-0.564399\pi\) | ||||
−0.200937 | + | 0.979604i | \(0.564399\pi\) | |||||||
\(174\) | − 22.6645i | − 1.71819i | ||||||||
\(175\) | − 2.30369i | − 0.174143i | ||||||||
\(176\) | − 0.190480i | − 0.0143580i | ||||||||
\(177\) | − 47.1999i | − 3.54776i | ||||||||
\(178\) | −14.5391 | −1.08975 | ||||||||
\(179\) | 10.8357 | 0.809896 | 0.404948 | − | 0.914340i | \(-0.367290\pi\) | ||||
0.404948 | + | 0.914340i | \(0.367290\pi\) | |||||||
\(180\) | 23.4757i | 1.74977i | ||||||||
\(181\) | −13.4202 | −0.997517 | −0.498758 | − | 0.866741i | \(-0.666211\pi\) | ||||
−0.498758 | + | 0.866741i | \(0.666211\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.8107 | 1.39052 | ||||||||
\(184\) | − 22.9468i | − 1.69166i | ||||||||
\(185\) | −2.01774 | −0.148347 | ||||||||
\(186\) | 2.88896 | 0.211829 | ||||||||
\(187\) | − 3.06268i | − 0.223966i | ||||||||
\(188\) | 6.17566i | 0.450406i | ||||||||
\(189\) | 32.0740i | 2.33304i | ||||||||
\(190\) | − 1.33858i | − 0.0971107i | ||||||||
\(191\) | 7.19596 | 0.520681 | 0.260341 | − | 0.965517i | \(-0.416165\pi\) | ||||
0.260341 | + | 0.965517i | \(0.416165\pi\) | |||||||
\(192\) | 41.7526 | 3.01324 | ||||||||
\(193\) | 12.6806i | 0.912770i | 0.889782 | + | 0.456385i | \(0.150856\pi\) | ||||
−0.889782 | + | 0.456385i | \(0.849144\pi\) | |||||||
\(194\) | 37.1908 | 2.67014 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.42099 | −0.387214 | ||||||||
\(197\) | 18.9898i | 1.35296i | 0.736459 | + | 0.676482i | \(0.236496\pi\) | ||||
−0.736459 | + | 0.676482i | \(0.763504\pi\) | |||||||
\(198\) | −21.0617 | −1.49679 | ||||||||
\(199\) | −10.1534 | −0.719757 | −0.359878 | − | 0.932999i | \(-0.617182\pi\) | ||||
−0.359878 | + | 0.932999i | \(0.617182\pi\) | |||||||
\(200\) | 2.74149i | 0.193853i | ||||||||
\(201\) | − 6.40992i | − 0.452121i | ||||||||
\(202\) | 15.7596i | 1.10884i | ||||||||
\(203\) | − 7.12202i | − 0.499868i | ||||||||
\(204\) | 25.0262 | 1.75218 | ||||||||
\(205\) | 5.58749 | 0.390247 | ||||||||
\(206\) | − 20.7535i | − 1.44597i | ||||||||
\(207\) | 61.3668 | 4.26529 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.739214 | 0.0511325 | ||||||||
\(210\) | 16.8886i | 1.16542i | ||||||||
\(211\) | 3.78159 | 0.260336 | 0.130168 | − | 0.991492i | \(-0.458448\pi\) | ||||
0.130168 | + | 0.991492i | \(0.458448\pi\) | |||||||
\(212\) | 43.7798 | 3.00681 | ||||||||
\(213\) | 30.8295i | 2.11240i | ||||||||
\(214\) | 20.4370i | 1.39704i | ||||||||
\(215\) | 5.87653i | 0.400776i | ||||||||
\(216\) | − 38.1695i | − 2.59710i | ||||||||
\(217\) | 0.907814 | 0.0616265 | ||||||||
\(218\) | 10.0274 | 0.679141 | ||||||||
\(219\) | − 14.0860i | − 0.951841i | ||||||||
\(220\) | −4.03303 | −0.271907 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 14.7922 | 0.992789 | ||||||||
\(223\) | 3.03624i | 0.203322i | 0.994819 | + | 0.101661i | \(0.0324157\pi\) | ||||
−0.994819 | + | 0.101661i | \(0.967584\pi\) | |||||||
\(224\) | 13.4257 | 0.897042 | ||||||||
\(225\) | −7.33158 | −0.488772 | ||||||||
\(226\) | 23.8232i | 1.58470i | ||||||||
\(227\) | − 5.63181i | − 0.373796i | −0.982379 | − | 0.186898i | \(-0.940157\pi\) | ||||
0.982379 | − | 0.186898i | \(-0.0598434\pi\) | |||||||
\(228\) | 6.04036i | 0.400033i | ||||||||
\(229\) | 13.5479i | 0.895269i | 0.894217 | + | 0.447635i | \(0.147733\pi\) | ||||
−0.894217 | + | 0.447635i | \(0.852267\pi\) | |||||||
\(230\) | 19.0907 | 1.25880 | ||||||||
\(231\) | −9.32650 | −0.613639 | ||||||||
\(232\) | 8.47550i | 0.556444i | ||||||||
\(233\) | 18.8311 | 1.23367 | 0.616834 | − | 0.787093i | \(-0.288415\pi\) | ||||
0.616834 | + | 0.787093i | \(0.288415\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.92869 | −0.125814 | ||||||||
\(236\) | 47.0195i | 3.06071i | ||||||||
\(237\) | −0.698261 | −0.0453569 | ||||||||
\(238\) | 12.7762 | 0.828155 | ||||||||
\(239\) | 13.0244i | 0.842477i | 0.906950 | + | 0.421239i | \(0.138404\pi\) | ||||
−0.906950 | + | 0.421239i | \(0.861596\pi\) | |||||||
\(240\) | 0.486096i | 0.0313773i | ||||||||
\(241\) | − 18.1149i | − 1.16688i | −0.812154 | − | 0.583442i | \(-0.801705\pi\) | ||||
0.812154 | − | 0.583442i | \(-0.198295\pi\) | |||||||
\(242\) | 21.4703i | 1.38017i | ||||||||
\(243\) | 31.3796 | 2.01300 | ||||||||
\(244\) | −18.7388 | −1.19963 | ||||||||
\(245\) | − 1.69301i | − 0.108162i | ||||||||
\(246\) | −40.9623 | −2.61166 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.08034 | −0.0686015 | ||||||||
\(249\) | − 35.3952i | − 2.24308i | ||||||||
\(250\) | −2.28079 | −0.144250 | ||||||||
\(251\) | −0.814081 | −0.0513844 | −0.0256922 | − | 0.999670i | \(-0.508179\pi\) | ||||
−0.0256922 | + | 0.999670i | \(0.508179\pi\) | |||||||
\(252\) | − 54.0807i | − 3.40676i | ||||||||
\(253\) | 10.5426i | 0.662807i | ||||||||
\(254\) | − 34.1461i | − 2.14252i | ||||||||
\(255\) | 7.81582i | 0.489445i | ||||||||
\(256\) | −15.0087 | −0.938041 | ||||||||
\(257\) | −5.91635 | −0.369052 | −0.184526 | − | 0.982828i | \(-0.559075\pi\) | ||||
−0.184526 | + | 0.982828i | \(0.559075\pi\) | |||||||
\(258\) | − 43.0813i | − 2.68212i | ||||||||
\(259\) | 4.64825 | 0.288828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.6661 | −1.40299 | ||||||||
\(262\) | 24.4889i | 1.51293i | ||||||||
\(263\) | −22.8064 | −1.40630 | −0.703151 | − | 0.711041i | \(-0.748224\pi\) | ||||
−0.703151 | + | 0.711041i | \(0.748224\pi\) | |||||||
\(264\) | 11.0989 | 0.683092 | ||||||||
\(265\) | 13.6727i | 0.839907i | ||||||||
\(266\) | 3.08367i | 0.189072i | ||||||||
\(267\) | 20.4897i | 1.25395i | ||||||||
\(268\) | 6.38542i | 0.390051i | ||||||||
\(269\) | −11.4958 | −0.700914 | −0.350457 | − | 0.936579i | \(-0.613974\pi\) | ||||
−0.350457 | + | 0.936579i | \(0.613974\pi\) | |||||||
\(270\) | 31.7552 | 1.93256 | ||||||||
\(271\) | − 3.85160i | − 0.233968i | −0.993134 | − | 0.116984i | \(-0.962677\pi\) | ||||
0.993134 | − | 0.116984i | \(-0.0373227\pi\) | |||||||
\(272\) | 0.367730 | 0.0222969 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.61332 | 0.399525 | ||||||||
\(275\) | − 1.25954i | − 0.0759530i | ||||||||
\(276\) | −86.1469 | −5.18543 | ||||||||
\(277\) | −14.2174 | −0.854238 | −0.427119 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427119 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(278\) | − 37.5879i | − 2.25437i | ||||||||
\(279\) | − 2.88915i | − 0.172969i | ||||||||
\(280\) | − 6.31554i | − 0.377426i | ||||||||
\(281\) | 27.3326i | 1.63053i | 0.579090 | + | 0.815264i | \(0.303408\pi\) | ||||
−0.579090 | + | 0.815264i | \(0.696592\pi\) | |||||||
\(282\) | 14.1394 | 0.841990 | ||||||||
\(283\) | 12.4611 | 0.740736 | 0.370368 | − | 0.928885i | \(-0.379232\pi\) | ||||
0.370368 | + | 0.928885i | \(0.379232\pi\) | |||||||
\(284\) | − 30.7116i | − 1.82240i | ||||||||
\(285\) | −1.88644 | −0.111743 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.8718 | −0.759801 | ||||||||
\(288\) | − 42.7277i | − 2.51775i | ||||||||
\(289\) | −11.0874 | −0.652197 | ||||||||
\(290\) | −7.05121 | −0.414061 | ||||||||
\(291\) | − 52.4123i | − 3.07247i | ||||||||
\(292\) | 14.0321i | 0.821168i | ||||||||
\(293\) | 19.1635i | 1.11955i | 0.828646 | + | 0.559773i | \(0.189111\pi\) | ||||
−0.828646 | + | 0.559773i | \(0.810889\pi\) | |||||||
\(294\) | 12.4116i | 0.723857i | ||||||||
\(295\) | −14.6844 | −0.854962 | ||||||||
\(296\) | −5.53161 | −0.321519 | ||||||||
\(297\) | 17.5364i | 1.01757i | ||||||||
\(298\) | 2.48477 | 0.143939 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 10.2921 | 0.594214 | ||||||||
\(301\) | − 13.5377i | − 0.780300i | ||||||||
\(302\) | 43.2344 | 2.48786 | ||||||||
\(303\) | 22.2097 | 1.27591 | ||||||||
\(304\) | 0.0887560i | 0.00509050i | ||||||||
\(305\) | − 5.85222i | − 0.335097i | ||||||||
\(306\) | − 40.6606i | − 2.32441i | ||||||||
\(307\) | 25.3229i | 1.44526i | 0.691237 | + | 0.722628i | \(0.257066\pi\) | ||||
−0.691237 | + | 0.722628i | \(0.742934\pi\) | |||||||
\(308\) | 9.29086 | 0.529396 | ||||||||
\(309\) | −29.2476 | −1.66384 | ||||||||
\(310\) | − 0.898789i | − 0.0510478i | ||||||||
\(311\) | 8.34852 | 0.473401 | 0.236701 | − | 0.971583i | \(-0.423934\pi\) | ||||
0.236701 | + | 0.971583i | \(0.423934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9850 | −1.07310 | −0.536548 | − | 0.843870i | \(-0.680272\pi\) | ||||
−0.536548 | + | 0.843870i | \(0.680272\pi\) | |||||||
\(314\) | 12.0309i | 0.678942i | ||||||||
\(315\) | 16.8897 | 0.951626 | ||||||||
\(316\) | 0.695592 | 0.0391301 | ||||||||
\(317\) | 22.0449i | 1.23816i | 0.785326 | + | 0.619082i | \(0.212495\pi\) | ||||
−0.785326 | + | 0.619082i | \(0.787505\pi\) | |||||||
\(318\) | − 100.236i | − 5.62093i | ||||||||
\(319\) | − 3.89395i | − 0.218019i | ||||||||
\(320\) | − 12.9897i | − 0.726149i | ||||||||
\(321\) | 28.8015 | 1.60754 | ||||||||
\(322\) | −43.9790 | −2.45085 | ||||||||
\(323\) | 1.42709i | 0.0794052i | ||||||||
\(324\) | −72.8687 | −4.04826 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 46.7515 | 2.58932 | ||||||||
\(327\) | − 14.1314i | − 0.781471i | ||||||||
\(328\) | 15.3180 | 0.845797 | ||||||||
\(329\) | 4.44312 | 0.244957 | ||||||||
\(330\) | 9.23378i | 0.508303i | ||||||||
\(331\) | 11.8953i | 0.653826i | 0.945054 | + | 0.326913i | \(0.106008\pi\) | ||||
−0.945054 | + | 0.326913i | \(0.893992\pi\) | |||||||
\(332\) | 35.2599i | 1.93514i | ||||||||
\(333\) | − 14.7932i | − 0.810664i | ||||||||
\(334\) | −43.5751 | −2.38433 | ||||||||
\(335\) | −1.99420 | −0.108955 | ||||||||
\(336\) | − 1.11981i | − 0.0610909i | ||||||||
\(337\) | −35.1499 | −1.91474 | −0.957368 | − | 0.288871i | \(-0.906720\pi\) | ||||
−0.957368 | + | 0.288871i | \(0.906720\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.5737 | 1.82347 | ||||||||
\(340\) | − 7.78594i | − 0.422252i | ||||||||
\(341\) | 0.496345 | 0.0268786 | ||||||||
\(342\) | 9.81390 | 0.530675 | ||||||||
\(343\) | 20.0260i | 1.08130i | ||||||||
\(344\) | 16.1104i | 0.868616i | ||||||||
\(345\) | − 26.9042i | − 1.44847i | ||||||||
\(346\) | − 12.0559i | − 0.648128i | ||||||||
\(347\) | 17.7972 | 0.955405 | 0.477702 | − | 0.878522i | \(-0.341470\pi\) | ||||
0.477702 | + | 0.878522i | \(0.341470\pi\) | |||||||
\(348\) | 31.8187 | 1.70566 | ||||||||
\(349\) | − 17.0901i | − 0.914814i | −0.889257 | − | 0.457407i | \(-0.848778\pi\) | ||||
0.889257 | − | 0.457407i | \(-0.151222\pi\) | |||||||
\(350\) | 5.25423 | 0.280850 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.34046 | 0.391248 | ||||||||
\(353\) | 8.20354i | 0.436630i | 0.975878 | + | 0.218315i | \(0.0700561\pi\) | ||||
−0.975878 | + | 0.218315i | \(0.929944\pi\) | |||||||
\(354\) | 107.653 | 5.72169 | ||||||||
\(355\) | 9.59141 | 0.509059 | ||||||||
\(356\) | − 20.4114i | − 1.08180i | ||||||||
\(357\) | − 18.0052i | − 0.952938i | ||||||||
\(358\) | 24.7139i | 1.30617i | ||||||||
\(359\) | 4.83618i | 0.255244i | 0.991823 | + | 0.127622i | \(0.0407344\pi\) | ||||
−0.991823 | + | 0.127622i | \(0.959266\pi\) | |||||||
\(360\) | −20.0994 | −1.05933 | ||||||||
\(361\) | 18.6556 | 0.981871 | ||||||||
\(362\) | − 30.6087i | − 1.60876i | ||||||||
\(363\) | 30.2578 | 1.58812 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.38231 | −0.229381 | ||||||||
\(366\) | 42.9031i | 2.24258i | ||||||||
\(367\) | −19.9703 | −1.04244 | −0.521221 | − | 0.853421i | \(-0.674523\pi\) | ||||
−0.521221 | + | 0.853421i | \(0.674523\pi\) | |||||||
\(368\) | −1.26583 | −0.0659858 | ||||||||
\(369\) | 40.9651i | 2.13256i | ||||||||
\(370\) | − 4.60204i | − 0.239249i | ||||||||
\(371\) | − 31.4977i | − 1.63528i | ||||||||
\(372\) | 4.05580i | 0.210283i | ||||||||
\(373\) | −20.4576 | −1.05925 | −0.529626 | − | 0.848231i | \(-0.677668\pi\) | ||||
−0.529626 | + | 0.848231i | \(0.677668\pi\) | |||||||
\(374\) | 6.98533 | 0.361203 | ||||||||
\(375\) | 3.21428i | 0.165985i | ||||||||
\(376\) | −5.28749 | −0.272682 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −73.1541 | −3.76264 | ||||||||
\(379\) | 0.189284i | 0.00972284i | 0.999988 | + | 0.00486142i | \(0.00154744\pi\) | ||||
−0.999988 | + | 0.00486142i | \(0.998453\pi\) | |||||||
\(380\) | 1.87923 | 0.0964024 | ||||||||
\(381\) | −48.1216 | −2.46534 | ||||||||
\(382\) | 16.4125i | 0.839735i | ||||||||
\(383\) | − 16.8652i | − 0.861773i | −0.902406 | − | 0.430886i | \(-0.858201\pi\) | ||||
0.902406 | − | 0.430886i | \(-0.141799\pi\) | |||||||
\(384\) | 57.7639i | 2.94775i | ||||||||
\(385\) | 2.90159i | 0.147879i | ||||||||
\(386\) | −28.9218 | −1.47208 | ||||||||
\(387\) | −43.0842 | −2.19009 | ||||||||
\(388\) | 52.2120i | 2.65066i | ||||||||
\(389\) | 0.569132 | 0.0288561 | 0.0144281 | − | 0.999896i | \(-0.495407\pi\) | ||||
0.0144281 | + | 0.999896i | \(0.495407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.3529 | −1.02929 | ||||||||
\(392\) | − 4.64136i | − 0.234424i | ||||||||
\(393\) | 34.5118 | 1.74089 | ||||||||
\(394\) | −43.3116 | −2.18201 | ||||||||
\(395\) | 0.217237i | 0.0109304i | ||||||||
\(396\) | − 29.5685i | − 1.48587i | ||||||||
\(397\) | − 22.0794i | − 1.10813i | −0.832472 | − | 0.554067i | \(-0.813075\pi\) | ||||
0.832472 | − | 0.554067i | \(-0.186925\pi\) | |||||||
\(398\) | − 23.1578i | − 1.16080i | ||||||||
\(399\) | 4.34577 | 0.217561 | ||||||||
\(400\) | 0.151230 | 0.00756151 | ||||||||
\(401\) | 16.2825i | 0.813107i | 0.913627 | + | 0.406554i | \(0.133270\pi\) | ||||
−0.913627 | + | 0.406554i | \(0.866730\pi\) | |||||||
\(402\) | 14.6197 | 0.729162 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −22.1248 | −1.10075 | ||||||||
\(405\) | − 22.7573i | − 1.13082i | ||||||||
\(406\) | 16.2438 | 0.806167 | ||||||||
\(407\) | 2.54142 | 0.125974 | ||||||||
\(408\) | 21.4270i | 1.06079i | ||||||||
\(409\) | 21.9413i | 1.08493i | 0.840079 | + | 0.542464i | \(0.182508\pi\) | ||||
−0.840079 | + | 0.542464i | \(0.817492\pi\) | |||||||
\(410\) | 12.7439i | 0.629375i | ||||||||
\(411\) | − 9.32005i | − 0.459724i | ||||||||
\(412\) | 29.1358 | 1.43542 | ||||||||
\(413\) | 33.8284 | 1.66459 | ||||||||
\(414\) | 139.965i | 6.87889i | ||||||||
\(415\) | −11.0119 | −0.540551 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −52.9721 | −2.59405 | ||||||||
\(418\) | 1.68599i | 0.0824645i | ||||||||
\(419\) | −12.6663 | −0.618788 | −0.309394 | − | 0.950934i | \(-0.600126\pi\) | ||||
−0.309394 | + | 0.950934i | \(0.600126\pi\) | |||||||
\(420\) | −23.7098 | −1.15692 | ||||||||
\(421\) | − 18.8977i | − 0.921018i | −0.887655 | − | 0.460509i | \(-0.847667\pi\) | ||||
0.887655 | − | 0.460509i | \(-0.152333\pi\) | |||||||
\(422\) | 8.62501i | 0.419859i | ||||||||
\(423\) | − 14.1404i | − 0.687528i | ||||||||
\(424\) | 37.4835i | 1.82036i | ||||||||
\(425\) | 2.43159 | 0.117950 | ||||||||
\(426\) | −70.3154 | −3.40679 | ||||||||
\(427\) | 13.4817i | 0.652426i | ||||||||
\(428\) | −28.6914 | −1.38685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.4031 | −0.646355 | ||||||||
\(431\) | 31.7845i | 1.53100i | 0.643434 | + | 0.765502i | \(0.277509\pi\) | ||||
−0.643434 | + | 0.765502i | \(0.722491\pi\) | |||||||
\(432\) | −2.10556 | −0.101304 | ||||||||
\(433\) | 26.4695 | 1.27204 | 0.636021 | − | 0.771671i | \(-0.280579\pi\) | ||||
0.636021 | + | 0.771671i | \(0.280579\pi\) | |||||||
\(434\) | 2.07053i | 0.0993887i | ||||||||
\(435\) | 9.93715i | 0.476450i | ||||||||
\(436\) | 14.0774i | 0.674187i | ||||||||
\(437\) | − 4.91242i | − 0.234993i | ||||||||
\(438\) | 32.1271 | 1.53509 | ||||||||
\(439\) | −10.7064 | −0.510988 | −0.255494 | − | 0.966811i | \(-0.582238\pi\) | ||||
−0.255494 | + | 0.966811i | \(0.582238\pi\) | |||||||
\(440\) | − 3.45301i | − 0.164616i | ||||||||
\(441\) | 12.4124 | 0.591067 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.14146 | −0.101744 | −0.0508718 | − | 0.998705i | \(-0.516200\pi\) | ||||
−0.0508718 | + | 0.998705i | \(0.516200\pi\) | |||||||
\(444\) | 20.7668i | 0.985547i | ||||||||
\(445\) | 6.37458 | 0.302184 | ||||||||
\(446\) | −6.92503 | −0.327910 | ||||||||
\(447\) | − 3.50175i | − 0.165627i | ||||||||
\(448\) | 29.9244i | 1.41379i | ||||||||
\(449\) | − 1.10953i | − 0.0523620i | −0.999657 | − | 0.0261810i | \(-0.991665\pi\) | ||||
0.999657 | − | 0.0261810i | \(-0.00833462\pi\) | |||||||
\(450\) | − 16.7218i | − 0.788272i | ||||||||
\(451\) | −7.03765 | −0.331390 | ||||||||
\(452\) | −33.4454 | −1.57314 | ||||||||
\(453\) | − 60.9295i | − 2.86272i | ||||||||
\(454\) | 12.8450 | 0.602844 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.17165 | −0.242185 | ||||||||
\(457\) | − 7.94953i | − 0.371863i | −0.982563 | − | 0.185932i | \(-0.940470\pi\) | ||||
0.982563 | − | 0.185932i | \(-0.0595303\pi\) | |||||||
\(458\) | −30.8998 | −1.44385 | ||||||||
\(459\) | −33.8548 | −1.58021 | ||||||||
\(460\) | 26.8013i | 1.24962i | ||||||||
\(461\) | − 18.2179i | − 0.848494i | −0.905546 | − | 0.424247i | \(-0.860539\pi\) | ||||
0.905546 | − | 0.424247i | \(-0.139461\pi\) | |||||||
\(462\) | − 21.2718i | − 0.989652i | ||||||||
\(463\) | 25.1740i | 1.16993i | 0.811057 | + | 0.584967i | \(0.198893\pi\) | ||||
−0.811057 | + | 0.584967i | \(0.801107\pi\) | |||||||
\(464\) | 0.467538 | 0.0217049 | ||||||||
\(465\) | −1.26665 | −0.0587394 | ||||||||
\(466\) | 42.9498i | 1.98961i | ||||||||
\(467\) | −0.530268 | −0.0245379 | −0.0122689 | − | 0.999925i | \(-0.503905\pi\) | ||||
−0.0122689 | + | 0.999925i | \(0.503905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.59402 | 0.212132 | ||||||||
\(470\) | − 4.39894i | − 0.202908i | ||||||||
\(471\) | 16.9549 | 0.781242 | ||||||||
\(472\) | −40.2572 | −1.85299 | ||||||||
\(473\) | − 7.40170i | − 0.340331i | ||||||||
\(474\) | − 1.59259i | − 0.0731499i | ||||||||
\(475\) | 0.586893i | 0.0269285i | ||||||||
\(476\) | 17.9364i | 0.822114i | ||||||||
\(477\) | −100.242 | −4.58978 | ||||||||
\(478\) | −29.7058 | −1.35871 | ||||||||
\(479\) | 17.8049i | 0.813525i | 0.913534 | + | 0.406762i | \(0.133342\pi\) | ||||
−0.913534 | + | 0.406762i | \(0.866658\pi\) | |||||||
\(480\) | −18.7325 | −0.855017 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 41.3163 | 1.88191 | ||||||||
\(483\) | 61.9789i | 2.82014i | ||||||||
\(484\) | −30.1422 | −1.37010 | ||||||||
\(485\) | −16.3061 | −0.740422 | ||||||||
\(486\) | 71.5702i | 3.24649i | ||||||||
\(487\) | 24.3801i | 1.10477i | 0.833590 | + | 0.552384i | \(0.186282\pi\) | ||||
−0.833590 | + | 0.552384i | \(0.813718\pi\) | |||||||
\(488\) | − 16.0438i | − 0.726269i | ||||||||
\(489\) | − 65.8861i | − 2.97947i | ||||||||
\(490\) | 3.86139 | 0.174440 | ||||||||
\(491\) | −26.3116 | −1.18742 | −0.593712 | − | 0.804677i | \(-0.702338\pi\) | ||||
−0.593712 | + | 0.804677i | \(0.702338\pi\) | |||||||
\(492\) | − 57.5069i | − 2.59261i | ||||||||
\(493\) | 7.51744 | 0.338568 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.23440 | 0.415055 | ||||||||
\(496\) | 0.0595952i | 0.00267590i | ||||||||
\(497\) | −22.0957 | −0.991126 | ||||||||
\(498\) | 80.7289 | 3.61755 | ||||||||
\(499\) | − 24.0669i | − 1.07738i | −0.842504 | − | 0.538691i | \(-0.818919\pi\) | ||||
0.842504 | − | 0.538691i | \(-0.181081\pi\) | |||||||
\(500\) | − 3.20199i | − 0.143197i | ||||||||
\(501\) | 61.4097i | 2.74358i | ||||||||
\(502\) | − 1.85675i | − 0.0828707i | ||||||||
\(503\) | −20.1923 | −0.900332 | −0.450166 | − | 0.892945i | \(-0.648635\pi\) | ||||
−0.450166 | + | 0.892945i | \(0.648635\pi\) | |||||||
\(504\) | 46.3029 | 2.06250 | ||||||||
\(505\) | − 6.90971i | − 0.307478i | ||||||||
\(506\) | −24.0454 | −1.06895 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 47.9377 | 2.12689 | ||||||||
\(509\) | − 29.7451i | − 1.31843i | −0.751955 | − | 0.659214i | \(-0.770889\pi\) | ||||
0.751955 | − | 0.659214i | \(-0.229111\pi\) | |||||||
\(510\) | −17.8262 | −0.789358 | ||||||||
\(511\) | 10.0955 | 0.446598 | ||||||||
\(512\) | 1.71055i | 0.0755962i | ||||||||
\(513\) | − 8.17125i | − 0.360770i | ||||||||
\(514\) | − 13.4939i | − 0.595192i | ||||||||
\(515\) | 9.09928i | 0.400962i | ||||||||
\(516\) | 60.4817 | 2.66256 | ||||||||
\(517\) | 2.42926 | 0.106839 | ||||||||
\(518\) | 10.6017i | 0.465811i | ||||||||
\(519\) | −16.9901 | −0.745785 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.9231 | 1.44239 | 0.721194 | − | 0.692733i | \(-0.243594\pi\) | ||||
0.721194 | + | 0.692733i | \(0.243594\pi\) | |||||||
\(522\) | − 51.6965i | − 2.26269i | ||||||||
\(523\) | 20.9654 | 0.916751 | 0.458375 | − | 0.888759i | \(-0.348432\pi\) | ||||
0.458375 | + | 0.888759i | \(0.348432\pi\) | |||||||
\(524\) | −34.3799 | −1.50189 | ||||||||
\(525\) | − 7.40470i | − 0.323168i | ||||||||
\(526\) | − 52.0165i | − 2.26803i | ||||||||
\(527\) | 0.958217i | 0.0417406i | ||||||||
\(528\) | − 0.612256i | − 0.0266450i | ||||||||
\(529\) | 47.0603 | 2.04610 | ||||||||
\(530\) | −31.1845 | −1.35457 | ||||||||
\(531\) | − 107.660i | − 4.67205i | ||||||||
\(532\) | −4.32916 | −0.187693 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −46.7326 | −2.02232 | ||||||||
\(535\) | − 8.96050i | − 0.387396i | ||||||||
\(536\) | −5.46708 | −0.236142 | ||||||||
\(537\) | 34.8289 | 1.50298 | ||||||||
\(538\) | − 26.2196i | − 1.13041i | ||||||||
\(539\) | 2.13240i | 0.0918491i | ||||||||
\(540\) | 44.5810i | 1.91846i | ||||||||
\(541\) | − 0.397145i | − 0.0170746i | −0.999964 | − | 0.00853729i | \(-0.997282\pi\) | ||||
0.999964 | − | 0.00853729i | \(-0.00271754\pi\) | |||||||
\(542\) | 8.78469 | 0.377335 | ||||||||
\(543\) | −43.1363 | −1.85116 | ||||||||
\(544\) | 14.1711i | 0.607580i | ||||||||
\(545\) | −4.39646 | −0.188324 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.7287 | −0.886295 | −0.443147 | − | 0.896449i | \(-0.646138\pi\) | ||||
−0.443147 | + | 0.896449i | \(0.646138\pi\) | |||||||
\(548\) | 9.28443i | 0.396611i | ||||||||
\(549\) | 42.9060 | 1.83118 | ||||||||
\(550\) | 2.87274 | 0.122494 | ||||||||
\(551\) | 1.81442i | 0.0772969i | ||||||||
\(552\) | − 73.7574i | − 3.13932i | ||||||||
\(553\) | − 0.500448i | − 0.0212812i | ||||||||
\(554\) | − 32.4268i | − 1.37768i | ||||||||
\(555\) | −6.48558 | −0.275297 | ||||||||
\(556\) | 52.7696 | 2.23793 | ||||||||
\(557\) | − 14.0049i | − 0.593406i | −0.954970 | − | 0.296703i | \(-0.904113\pi\) | ||||
0.954970 | − | 0.296703i | \(-0.0958872\pi\) | |||||||
\(558\) | 6.58954 | 0.278957 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.348388 | −0.0147221 | ||||||||
\(561\) | − 9.84431i | − 0.415627i | ||||||||
\(562\) | −62.3399 | −2.62965 | ||||||||
\(563\) | −28.1488 | −1.18633 | −0.593164 | − | 0.805081i | \(-0.702122\pi\) | ||||
−0.593164 | + | 0.805081i | \(0.702122\pi\) | |||||||
\(564\) | 19.8503i | 0.835848i | ||||||||
\(565\) | − 10.4452i | − 0.439432i | ||||||||
\(566\) | 28.4211i | 1.19463i | ||||||||
\(567\) | 52.4258i | 2.20168i | ||||||||
\(568\) | 26.2948 | 1.10330 | ||||||||
\(569\) | 1.24816 | 0.0523254 | 0.0261627 | − | 0.999658i | \(-0.491671\pi\) | ||||
0.0261627 | + | 0.999658i | \(0.491671\pi\) | |||||||
\(570\) | − 4.30256i | − 0.180215i | ||||||||
\(571\) | −29.0651 | −1.21633 | −0.608167 | − | 0.793809i | \(-0.708095\pi\) | ||||
−0.608167 | + | 0.793809i | \(0.708095\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.1298 | 0.966262 | ||||||||
\(574\) | − 29.3579i | − 1.22538i | ||||||||
\(575\) | −8.37020 | −0.349062 | ||||||||
\(576\) | 95.2353 | 3.96814 | ||||||||
\(577\) | − 26.7191i | − 1.11233i | −0.831072 | − | 0.556165i | \(-0.812272\pi\) | ||||
0.831072 | − | 0.556165i | \(-0.187728\pi\) | |||||||
\(578\) | − 25.2879i | − 1.05184i | ||||||||
\(579\) | 40.7590i | 1.69389i | ||||||||
\(580\) | − 9.89917i | − 0.411041i | ||||||||
\(581\) | 25.3679 | 1.05244 | ||||||||
\(582\) | 119.541 | 4.95515 | ||||||||
\(583\) | − 17.2213i | − 0.713232i | ||||||||
\(584\) | −12.0141 | −0.497145 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −43.7079 | −1.80556 | ||||||||
\(587\) | − 26.1925i | − 1.08108i | −0.841319 | − | 0.540539i | \(-0.818220\pi\) | ||||
0.841319 | − | 0.540539i | \(-0.181780\pi\) | |||||||
\(588\) | −17.4246 | −0.718577 | ||||||||
\(589\) | −0.231277 | −0.00952959 | ||||||||
\(590\) | − 33.4921i | − 1.37885i | ||||||||
\(591\) | 61.0384i | 2.51078i | ||||||||
\(592\) | 0.305143i | 0.0125413i | ||||||||
\(593\) | 14.8254i | 0.608806i | 0.952543 | + | 0.304403i | \(0.0984570\pi\) | ||||
−0.952543 | + | 0.304403i | \(0.901543\pi\) | |||||||
\(594\) | −39.9968 | −1.64109 | ||||||||
\(595\) | −5.60164 | −0.229645 | ||||||||
\(596\) | 3.48837i | 0.142889i | ||||||||
\(597\) | −32.6359 | −1.33570 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0326 | 0.491639 | 0.245820 | − | 0.969316i | \(-0.420943\pi\) | ||||
0.245820 | + | 0.969316i | \(0.420943\pi\) | |||||||
\(600\) | 8.81191i | 0.359745i | ||||||||
\(601\) | 14.9028 | 0.607899 | 0.303950 | − | 0.952688i | \(-0.401695\pi\) | ||||
0.303950 | + | 0.952688i | \(0.401695\pi\) | |||||||
\(602\) | 30.8766 | 1.25844 | ||||||||
\(603\) | − 14.6206i | − 0.595399i | ||||||||
\(604\) | 60.6966i | 2.46971i | ||||||||
\(605\) | − 9.41357i | − 0.382716i | ||||||||
\(606\) | 50.6556i | 2.05774i | ||||||||
\(607\) | 29.2262 | 1.18626 | 0.593128 | − | 0.805108i | \(-0.297893\pi\) | ||||
0.593128 | + | 0.805108i | \(0.297893\pi\) | |||||||
\(608\) | −3.42036 | −0.138714 | ||||||||
\(609\) | − 22.8921i | − 0.927636i | ||||||||
\(610\) | 13.3477 | 0.540432 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 57.0833 | 2.30745 | ||||||||
\(613\) | 32.1313i | 1.29777i | 0.760887 | + | 0.648885i | \(0.224764\pi\) | ||||
−0.760887 | + | 0.648885i | \(0.775236\pi\) | |||||||
\(614\) | −57.7562 | −2.33085 | ||||||||
\(615\) | 17.9597 | 0.724206 | ||||||||
\(616\) | 7.95467i | 0.320503i | ||||||||
\(617\) | − 13.0350i | − 0.524771i | −0.964963 | − | 0.262385i | \(-0.915491\pi\) | ||||
0.964963 | − | 0.262385i | \(-0.0845092\pi\) | |||||||
\(618\) | − 66.7076i | − 2.68337i | ||||||||
\(619\) | − 28.6664i | − 1.15220i | −0.817379 | − | 0.576100i | \(-0.804574\pi\) | ||||
0.817379 | − | 0.576100i | \(-0.195426\pi\) | |||||||
\(620\) | 1.26181 | 0.0506754 | ||||||||
\(621\) | 116.537 | 4.67649 | ||||||||
\(622\) | 19.0412i | 0.763483i | ||||||||
\(623\) | −14.6851 | −0.588345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 43.3008i | − 1.73065i | ||||||||
\(627\) | 2.37604 | 0.0948899 | ||||||||
\(628\) | −16.8901 | −0.673990 | ||||||||
\(629\) | 4.90633i | 0.195628i | ||||||||
\(630\) | 38.5218i | 1.53475i | ||||||||
\(631\) | − 26.4497i | − 1.05295i | −0.850191 | − | 0.526474i | \(-0.823514\pi\) | ||||
0.850191 | − | 0.526474i | \(-0.176486\pi\) | |||||||
\(632\) | 0.595554i | 0.0236899i | ||||||||
\(633\) | 12.1551 | 0.483121 | ||||||||
\(634\) | −50.2797 | −1.99686 | ||||||||
\(635\) | 14.9712i | 0.594114i | ||||||||
\(636\) | 140.721 | 5.57993 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.88126 | 0.351613 | ||||||||
\(639\) | 70.3202i | 2.78182i | ||||||||
\(640\) | 17.9710 | 0.710368 | ||||||||
\(641\) | 26.6673 | 1.05330 | 0.526648 | − | 0.850084i | \(-0.323449\pi\) | ||||
0.526648 | + | 0.850084i | \(0.323449\pi\) | |||||||
\(642\) | 65.6902i | 2.59258i | ||||||||
\(643\) | 28.0533i | 1.10631i | 0.833077 | + | 0.553157i | \(0.186577\pi\) | ||||
−0.833077 | + | 0.553157i | \(0.813423\pi\) | |||||||
\(644\) | − 61.7420i | − 2.43297i | ||||||||
\(645\) | 18.8888i | 0.743745i | ||||||||
\(646\) | −3.25488 | −0.128062 | ||||||||
\(647\) | 23.1563 | 0.910368 | 0.455184 | − | 0.890397i | \(-0.349573\pi\) | ||||
0.455184 | + | 0.890397i | \(0.349573\pi\) | |||||||
\(648\) | − 62.3889i | − 2.45087i | ||||||||
\(649\) | 18.4956 | 0.726016 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.91797 | 0.114364 | ||||||||
\(652\) | 65.6343i | 2.57044i | ||||||||
\(653\) | −23.7386 | −0.928962 | −0.464481 | − | 0.885583i | \(-0.653759\pi\) | ||||
−0.464481 | + | 0.885583i | \(0.653759\pi\) | |||||||
\(654\) | 32.2308 | 1.26032 | ||||||||
\(655\) | − 10.7370i | − 0.419530i | ||||||||
\(656\) | − 0.844996i | − 0.0329916i | ||||||||
\(657\) | − 32.1292i | − 1.25348i | ||||||||
\(658\) | 10.1338i | 0.395057i | ||||||||
\(659\) | 4.26802 | 0.166259 | 0.0831293 | − | 0.996539i | \(-0.473509\pi\) | ||||
0.0831293 | + | 0.996539i | \(0.473509\pi\) | |||||||
\(660\) | −12.9633 | −0.504595 | ||||||||
\(661\) | 12.0531i | 0.468812i | 0.972139 | + | 0.234406i | \(0.0753145\pi\) | ||||
−0.972139 | + | 0.234406i | \(0.924685\pi\) | |||||||
\(662\) | −27.1307 | −1.05446 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30.1889 | −1.17156 | ||||||||
\(665\) | − 1.35202i | − 0.0524291i | ||||||||
\(666\) | 33.7402 | 1.30741 | ||||||||
\(667\) | −25.8770 | −1.00196 | ||||||||
\(668\) | − 61.1750i | − 2.36693i | ||||||||
\(669\) | 9.75933i | 0.377318i | ||||||||
\(670\) | − 4.54835i | − 0.175718i | ||||||||
\(671\) | 7.37109i | 0.284558i | ||||||||
\(672\) | 43.1539 | 1.66470 | ||||||||
\(673\) | 2.44006 | 0.0940576 | 0.0470288 | − | 0.998894i | \(-0.485025\pi\) | ||||
0.0470288 | + | 0.998894i | \(0.485025\pi\) | |||||||
\(674\) | − 80.1694i | − 3.08801i | ||||||||
\(675\) | −13.9229 | −0.535892 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.5620 | −0.674964 | −0.337482 | − | 0.941332i | \(-0.609575\pi\) | ||||
−0.337482 | + | 0.941332i | \(0.609575\pi\) | |||||||
\(678\) | 76.5745i | 2.94083i | ||||||||
\(679\) | 37.5642 | 1.44158 | ||||||||
\(680\) | 6.66619 | 0.255637 | ||||||||
\(681\) | − 18.1022i | − 0.693677i | ||||||||
\(682\) | 1.13206i | 0.0433487i | ||||||||
\(683\) | 35.9632i | 1.37609i | 0.725667 | + | 0.688046i | \(0.241531\pi\) | ||||
−0.725667 | + | 0.688046i | \(0.758469\pi\) | |||||||
\(684\) | 13.7777i | 0.526804i | ||||||||
\(685\) | −2.89958 | −0.110787 | ||||||||
\(686\) | −45.6751 | −1.74388 | ||||||||
\(687\) | 43.5467i | 1.66141i | ||||||||
\(688\) | 0.888708 | 0.0338817 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 61.3627 | 2.33604 | ||||||||
\(691\) | − 40.6980i | − 1.54822i | −0.633049 | − | 0.774112i | \(-0.718197\pi\) | ||||
0.633049 | − | 0.774112i | \(-0.281803\pi\) | |||||||
\(692\) | 16.9252 | 0.643400 | ||||||||
\(693\) | −21.2732 | −0.808102 | ||||||||
\(694\) | 40.5917i | 1.54084i | ||||||||
\(695\) | 16.4802i | 0.625131i | ||||||||
\(696\) | 27.2426i | 1.03263i | ||||||||
\(697\) | − 13.5865i | − 0.514625i | ||||||||
\(698\) | 38.9790 | 1.47538 | ||||||||
\(699\) | 60.5285 | 2.28940 | ||||||||
\(700\) | 7.37640i | 0.278802i | ||||||||
\(701\) | 42.3583 | 1.59985 | 0.799926 | − | 0.600099i | \(-0.204872\pi\) | ||||
0.799926 | + | 0.600099i | \(0.204872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.18420 | −0.0446629 | ||||||||
\(704\) | 16.3611i | 0.616631i | ||||||||
\(705\) | −6.19936 | −0.233481 | ||||||||
\(706\) | −18.7105 | −0.704180 | ||||||||
\(707\) | 15.9178i | 0.598652i | ||||||||
\(708\) | 151.134i | 5.67995i | ||||||||
\(709\) | 10.5529i | 0.396322i | 0.980169 | + | 0.198161i | \(0.0634969\pi\) | ||||
−0.980169 | + | 0.198161i | \(0.936503\pi\) | |||||||
\(710\) | 21.8760i | 0.820991i | ||||||||
\(711\) | −1.59269 | −0.0597306 | ||||||||
\(712\) | 17.4758 | 0.654935 | ||||||||
\(713\) | − 3.29844i | − 0.123528i | ||||||||
\(714\) | 41.0661 | 1.53686 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −34.6958 | −1.29664 | ||||||||
\(717\) | 41.8640i | 1.56344i | ||||||||
\(718\) | −11.0303 | −0.411647 | ||||||||
\(719\) | −39.9389 | −1.48947 | −0.744734 | − | 0.667361i | \(-0.767424\pi\) | ||||
−0.744734 | + | 0.667361i | \(0.767424\pi\) | |||||||
\(720\) | 1.10876i | 0.0413209i | ||||||||
\(721\) | − 20.9619i | − 0.780663i | ||||||||
\(722\) | 42.5494i | 1.58352i | ||||||||
\(723\) | − 58.2264i | − 2.16546i | ||||||||
\(724\) | 42.9714 | 1.59702 | ||||||||
\(725\) | 3.09157 | 0.114818 | ||||||||
\(726\) | 69.0116i | 2.56126i | ||||||||
\(727\) | −16.4466 | −0.609969 | −0.304985 | − | 0.952357i | \(-0.598651\pi\) | ||||
−0.304985 | + | 0.952357i | \(0.598651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.5908 | 1.20707 | ||||||||
\(730\) | − 9.99512i | − 0.369936i | ||||||||
\(731\) | 14.2893 | 0.528510 | ||||||||
\(732\) | −60.2316 | −2.22622 | ||||||||
\(733\) | − 34.8676i | − 1.28786i | −0.765083 | − | 0.643931i | \(-0.777302\pi\) | ||||
0.765083 | − | 0.643931i | \(-0.222698\pi\) | |||||||
\(734\) | − 45.5481i | − 1.68121i | ||||||||
\(735\) | − 5.44179i | − 0.200723i | ||||||||
\(736\) | − 48.7807i | − 1.79808i | ||||||||
\(737\) | 2.51177 | 0.0925223 | ||||||||
\(738\) | −93.4327 | −3.43930 | ||||||||
\(739\) | − 3.02112i | − 0.111134i | −0.998455 | − | 0.0555669i | \(-0.982303\pi\) | ||||
0.998455 | − | 0.0555669i | \(-0.0176966\pi\) | |||||||
\(740\) | 6.46079 | 0.237503 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 71.8395 | 2.63731 | ||||||||
\(743\) | − 43.9749i | − 1.61328i | −0.591042 | − | 0.806641i | \(-0.701283\pi\) | ||||
0.591042 | − | 0.806641i | \(-0.298717\pi\) | |||||||
\(744\) | −3.47250 | −0.127308 | ||||||||
\(745\) | −1.08944 | −0.0399139 | ||||||||
\(746\) | − 46.6594i | − 1.70832i | ||||||||
\(747\) | − 80.7343i | − 2.95391i | ||||||||
\(748\) | 9.80669i | 0.358568i | ||||||||
\(749\) | 20.6422i | 0.754250i | ||||||||
\(750\) | −7.33108 | −0.267693 | ||||||||
\(751\) | −2.30363 | −0.0840606 | −0.0420303 | − | 0.999116i | \(-0.513383\pi\) | ||||
−0.0420303 | + | 0.999116i | \(0.513383\pi\) | |||||||
\(752\) | 0.291677i | 0.0106364i | ||||||||
\(753\) | −2.61668 | −0.0953572 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.9559 | −0.689876 | ||||||||
\(756\) | − 102.701i | − 3.73519i | ||||||||
\(757\) | −20.2683 | −0.736665 | −0.368332 | − | 0.929694i | \(-0.620071\pi\) | ||||
−0.368332 | + | 0.929694i | \(0.620071\pi\) | |||||||
\(758\) | −0.431716 | −0.0156806 | ||||||||
\(759\) | 33.8868i | 1.23001i | ||||||||
\(760\) | 1.60896i | 0.0583632i | ||||||||
\(761\) | − 15.0956i | − 0.547214i | −0.961842 | − | 0.273607i | \(-0.911783\pi\) | ||||
0.961842 | − | 0.273607i | \(-0.0882168\pi\) | |||||||
\(762\) | − 109.755i | − 3.97601i | ||||||||
\(763\) | 10.1281 | 0.366661 | ||||||||
\(764\) | −23.0414 | −0.833609 | ||||||||
\(765\) | 17.8274i | 0.644552i | ||||||||
\(766\) | 38.4660 | 1.38983 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −48.2420 | −1.74078 | ||||||||
\(769\) | 19.9278i | 0.718616i | 0.933219 | + | 0.359308i | \(0.116987\pi\) | ||||
−0.933219 | + | 0.359308i | \(0.883013\pi\) | |||||||
\(770\) | −6.61790 | −0.238493 | ||||||||
\(771\) | −19.0168 | −0.684873 | ||||||||
\(772\) | − 40.6032i | − 1.46134i | ||||||||
\(773\) | 2.92060i | 0.105047i | 0.998620 | + | 0.0525233i | \(0.0167264\pi\) | ||||
−0.998620 | + | 0.0525233i | \(0.983274\pi\) | |||||||
\(774\) | − 98.2659i | − 3.53210i | ||||||||
\(775\) | 0.394069i | 0.0141554i | ||||||||
\(776\) | −44.7030 | −1.60474 | ||||||||
\(777\) | 14.9408 | 0.535997 | ||||||||
\(778\) | 1.29807i | 0.0465380i | ||||||||
\(779\) | 3.27926 | 0.117492 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0807 | −0.432283 | ||||||||
\(782\) | − 46.4207i | − 1.66000i | ||||||||
\(783\) | −43.0436 | −1.53825 | ||||||||
\(784\) | −0.256033 | −0.00914405 | ||||||||
\(785\) | − 5.27488i | − 0.188269i | ||||||||
\(786\) | 78.7140i | 2.80764i | ||||||||
\(787\) | 5.51034i | 0.196423i | 0.995166 | + | 0.0982113i | \(0.0313121\pi\) | ||||
−0.995166 | + | 0.0982113i | \(0.968688\pi\) | |||||||
\(788\) | − 60.8051i | − 2.16609i | ||||||||
\(789\) | −73.3060 | −2.60976 | ||||||||
\(790\) | −0.495472 | −0.0176281 | ||||||||
\(791\) | 24.0625i | 0.855563i | ||||||||
\(792\) | 25.3160 | 0.899565 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 50.3585 | 1.78716 | ||||||||
\(795\) | 43.9478i | 1.55867i | ||||||||
\(796\) | 32.5112 | 1.15233 | ||||||||
\(797\) | 50.5977 | 1.79226 | 0.896131 | − | 0.443789i | \(-0.146366\pi\) | ||||
0.896131 | + | 0.443789i | \(0.146366\pi\) | |||||||
\(798\) | 9.91178i | 0.350873i | ||||||||
\(799\) | 4.68980i | 0.165913i | ||||||||
\(800\) | 5.82790i | 0.206047i | ||||||||
\(801\) | 46.7357i | 1.65133i | ||||||||
\(802\) | −37.1368 | −1.31135 | ||||||||
\(803\) | 5.51968 | 0.194785 | ||||||||
\(804\) | 20.5245i | 0.723843i | ||||||||
\(805\) | 19.2824 | 0.679614 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.9508 | −1.30073 | ||||||||
\(808\) | − 18.9429i | − 0.666408i | ||||||||
\(809\) | −24.7359 | −0.869670 | −0.434835 | − | 0.900510i | \(-0.643193\pi\) | ||||
−0.434835 | + | 0.900510i | \(0.643193\pi\) | |||||||
\(810\) | 51.9046 | 1.82374 | ||||||||
\(811\) | 45.9957i | 1.61513i | 0.589780 | + | 0.807564i | \(0.299214\pi\) | ||||
−0.589780 | + | 0.807564i | \(0.700786\pi\) | |||||||
\(812\) | 22.8046i | 0.800286i | ||||||||
\(813\) | − 12.3801i | − 0.434190i | ||||||||
\(814\) | 5.79644i | 0.203165i | ||||||||
\(815\) | −20.4979 | −0.718012 | ||||||||
\(816\) | 1.18199 | 0.0413778 | ||||||||
\(817\) | 3.44889i | 0.120662i | ||||||||
\(818\) | −50.0435 | −1.74973 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.8911 | −0.624784 | ||||||||
\(821\) | − 1.19931i | − 0.0418563i | −0.999781 | − | 0.0209281i | \(-0.993338\pi\) | ||||
0.999781 | − | 0.0209281i | \(-0.00666212\pi\) | |||||||
\(822\) | 21.2570 | 0.741425 | ||||||||
\(823\) | −22.1824 | −0.773229 | −0.386615 | − | 0.922241i | \(-0.626356\pi\) | ||||
−0.386615 | + | 0.922241i | \(0.626356\pi\) | |||||||
\(824\) | 24.9456i | 0.869020i | ||||||||
\(825\) | − 4.04850i | − 0.140951i | ||||||||
\(826\) | 77.1555i | 2.68458i | ||||||||
\(827\) | 46.3610i | 1.61213i | 0.591828 | + | 0.806065i | \(0.298407\pi\) | ||||
−0.591828 | + | 0.806065i | \(0.701593\pi\) | |||||||
\(828\) | −196.496 | −6.82871 | ||||||||
\(829\) | 20.3120 | 0.705466 | 0.352733 | − | 0.935724i | \(-0.385252\pi\) | ||||
0.352733 | + | 0.935724i | \(0.385252\pi\) | |||||||
\(830\) | − 25.1157i | − 0.871779i | ||||||||
\(831\) | −45.6985 | −1.58526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.11670 | −0.142635 | ||||||||
\(834\) | − 120.818i | − 4.18359i | ||||||||
\(835\) | 19.1053 | 0.661166 | ||||||||
\(836\) | −2.36696 | −0.0818630 | ||||||||
\(837\) | − 5.48659i | − 0.189644i | ||||||||
\(838\) | − 28.8891i | − 0.997956i | ||||||||
\(839\) | 44.2056i | 1.52615i | 0.646311 | + | 0.763074i | \(0.276311\pi\) | ||||
−0.646311 | + | 0.763074i | \(0.723689\pi\) | |||||||
\(840\) | − 20.2999i | − 0.700414i | ||||||||
\(841\) | −19.4422 | −0.670421 | ||||||||
\(842\) | 43.1017 | 1.48538 | ||||||||
\(843\) | 87.8546i | 3.02587i | ||||||||
\(844\) | −12.1086 | −0.416796 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 32.2512 | 1.10882 | ||||||||
\(847\) | 21.6859i | 0.745138i | ||||||||
\(848\) | 2.06772 | 0.0710059 | ||||||||
\(849\) | 40.0535 | 1.37463 | ||||||||
\(850\) | 5.54595i | 0.190224i | ||||||||
\(851\) | − 16.8889i | − 0.578944i | ||||||||
\(852\) | − 98.7157i | − 3.38194i | ||||||||
\(853\) | 21.5463i | 0.737731i | 0.929483 | + | 0.368865i | \(0.120254\pi\) | ||||
−0.929483 | + | 0.368865i | \(0.879746\pi\) | |||||||
\(854\) | −30.7489 | −1.05221 | ||||||||
\(855\) | −4.30285 | −0.147155 | ||||||||
\(856\) | − 24.5651i | − 0.839618i | ||||||||
\(857\) | 46.4540 | 1.58684 | 0.793419 | − | 0.608676i | \(-0.208299\pi\) | ||||
0.793419 | + | 0.608676i | \(0.208299\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.4901 | 0.426158 | 0.213079 | − | 0.977035i | \(-0.431651\pi\) | ||||
0.213079 | + | 0.977035i | \(0.431651\pi\) | |||||||
\(860\) | − 18.8166i | − 0.641640i | ||||||||
\(861\) | −41.3737 | −1.41001 | ||||||||
\(862\) | −72.4936 | −2.46914 | ||||||||
\(863\) | − 15.2521i | − 0.519187i | −0.965718 | − | 0.259593i | \(-0.916411\pi\) | ||||
0.965718 | − | 0.259593i | \(-0.0835886\pi\) | |||||||
\(864\) | − 81.1412i | − 2.76048i | ||||||||
\(865\) | 5.28584i | 0.179724i | ||||||||
\(866\) | 60.3713i | 2.05150i | ||||||||
\(867\) | −35.6378 | −1.21032 | ||||||||
\(868\) | −2.90681 | −0.0986637 | ||||||||
\(869\) | − 0.273619i | − 0.00928188i | ||||||||
\(870\) | −22.6645 | −0.768400 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −12.0528 | −0.408161 | ||||||||
\(873\) | − 119.549i | − 4.04614i | ||||||||
\(874\) | 11.2042 | 0.378987 | ||||||||
\(875\) | −2.30369 | −0.0778790 | ||||||||
\(876\) | 45.1031i | 1.52389i | ||||||||
\(877\) | 53.6346i | 1.81111i | 0.424227 | + | 0.905556i | \(0.360546\pi\) | ||||
−0.424227 | + | 0.905556i | \(0.639454\pi\) | |||||||
\(878\) | − 24.4190i | − 0.824102i | ||||||||
\(879\) | 61.5969i | 2.07761i | ||||||||
\(880\) | −0.190480 | −0.00642108 | ||||||||
\(881\) | −37.8813 | −1.27625 | −0.638127 | − | 0.769931i | \(-0.720290\pi\) | ||||
−0.638127 | + | 0.769931i | \(0.720290\pi\) | |||||||
\(882\) | 28.3101i | 0.953249i | ||||||||
\(883\) | −28.9953 | −0.975771 | −0.487885 | − | 0.872908i | \(-0.662232\pi\) | ||||
−0.487885 | + | 0.872908i | \(0.662232\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −47.1999 | −1.58661 | ||||||||
\(886\) | − 4.88421i | − 0.164088i | ||||||||
\(887\) | 2.16393 | 0.0726575 | 0.0363287 | − | 0.999340i | \(-0.488434\pi\) | ||||
0.0363287 | + | 0.999340i | \(0.488434\pi\) | |||||||
\(888\) | −17.7801 | −0.596663 | ||||||||
\(889\) | − 34.4890i | − 1.15673i | ||||||||
\(890\) | 14.5391i | 0.487350i | ||||||||
\(891\) | 28.6637i | 0.960269i | ||||||||
\(892\) | − 9.72203i | − 0.325518i | ||||||||
\(893\) | −1.13194 | −0.0378788 | ||||||||
\(894\) | 7.98675 | 0.267117 | ||||||||
\(895\) | − 10.8357i | − 0.362197i | ||||||||
\(896\) | −41.3998 | −1.38307 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.53060 | 0.0844474 | ||||||||
\(899\) | 1.21829i | 0.0406323i | ||||||||
\(900\) | 23.4757 | 0.782522 | ||||||||
\(901\) | 33.2464 | 1.10760 | ||||||||
\(902\) | − 16.0514i | − 0.534453i | ||||||||
\(903\) | − 43.5139i | − 1.44805i | ||||||||
\(904\) | − 28.6354i | − 0.952398i | ||||||||
\(905\) | 13.4202i | 0.446103i | ||||||||
\(906\) | 138.967 | 4.61688 | ||||||||
\(907\) | −18.5788 | −0.616900 | −0.308450 | − | 0.951241i | \(-0.599810\pi\) | ||||
−0.308450 | + | 0.951241i | \(0.599810\pi\) | |||||||
\(908\) | 18.0330i | 0.598446i | ||||||||
\(909\) | 50.6590 | 1.68025 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.55425 | 0.316546 | 0.158273 | − | 0.987395i | \(-0.449407\pi\) | ||||
0.158273 | + | 0.987395i | \(0.449407\pi\) | |||||||
\(912\) | 0.285286i | 0.00944677i | ||||||||
\(913\) | 13.8699 | 0.459025 | ||||||||
\(914\) | 18.1312 | 0.599726 | ||||||||
\(915\) | − 18.8107i | − 0.621861i | ||||||||
\(916\) | − 43.3802i | − 1.43332i | ||||||||
\(917\) | 24.7348i | 0.816815i | ||||||||
\(918\) | − 77.2156i | − 2.54850i | ||||||||
\(919\) | 32.9746 | 1.08773 | 0.543866 | − | 0.839172i | \(-0.316960\pi\) | ||||
0.543866 | + | 0.839172i | \(0.316960\pi\) | |||||||
\(920\) | −22.9468 | −0.756534 | ||||||||
\(921\) | 81.3949i | 2.68205i | ||||||||
\(922\) | 41.5513 | 1.36842 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 29.8634 | 0.982433 | ||||||||
\(925\) | 2.01774i | 0.0663429i | ||||||||
\(926\) | −57.4165 | −1.88682 | ||||||||
\(927\) | −66.7121 | −2.19111 | ||||||||
\(928\) | 18.0174i | 0.591449i | ||||||||
\(929\) | − 7.17296i | − 0.235337i | −0.993053 | − | 0.117669i | \(-0.962458\pi\) | ||||
0.993053 | − | 0.117669i | \(-0.0375421\pi\) | |||||||
\(930\) | − 2.88896i | − 0.0947326i | ||||||||
\(931\) | − 0.993614i | − 0.0325644i | ||||||||
\(932\) | −60.2971 | −1.97510 | ||||||||
\(933\) | 26.8345 | 0.878521 | ||||||||
\(934\) | − 1.20943i | − 0.0395737i | ||||||||
\(935\) | −3.06268 | −0.100160 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.7912 | 1.59394 | 0.796970 | − | 0.604019i | \(-0.206435\pi\) | ||||
0.796970 | + | 0.604019i | \(0.206435\pi\) | |||||||
\(938\) | 10.4780i | 0.342119i | ||||||||
\(939\) | −61.0231 | −1.99141 | ||||||||
\(940\) | 6.17566 | 0.201428 | ||||||||
\(941\) | 28.4075i | 0.926059i | 0.886343 | + | 0.463029i | \(0.153238\pi\) | ||||
−0.886343 | + | 0.463029i | \(0.846762\pi\) | |||||||
\(942\) | 38.6706i | 1.25996i | ||||||||
\(943\) | 46.7684i | 1.52299i | ||||||||
\(944\) | 2.22073i | 0.0722786i | ||||||||
\(945\) | 32.0740 | 1.04337 | ||||||||
\(946\) | 16.8817 | 0.548872 | ||||||||
\(947\) | 35.7589i | 1.16201i | 0.813901 | + | 0.581004i | \(0.197340\pi\) | ||||
−0.813901 | + | 0.581004i | \(0.802660\pi\) | |||||||
\(948\) | 2.23583 | 0.0726163 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.33858 | −0.0434292 | ||||||||
\(951\) | 70.8583i | 2.29774i | ||||||||
\(952\) | −15.3568 | −0.497718 | ||||||||
\(953\) | 6.41209 | 0.207708 | 0.103854 | − | 0.994593i | \(-0.466883\pi\) | ||||
0.103854 | + | 0.994593i | \(0.466883\pi\) | |||||||
\(954\) | − 228.632i | − 7.40222i | ||||||||
\(955\) | − 7.19596i | − 0.232856i | ||||||||
\(956\) | − 41.7040i | − 1.34880i | ||||||||
\(957\) | − 12.5162i | − 0.404592i | ||||||||
\(958\) | −40.6091 | −1.31202 | ||||||||
\(959\) | 6.67973 | 0.215700 | ||||||||
\(960\) | − 41.7526i | − 1.34756i | ||||||||
\(961\) | 30.8447 | 0.994991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 65.6946 | 2.11698 | ||||||||
\(964\) | 58.0039i | 1.86818i | ||||||||
\(965\) | 12.6806 | 0.408203 | ||||||||
\(966\) | −141.361 | −4.54820 | ||||||||
\(967\) | − 7.78138i | − 0.250232i | −0.992142 | − | 0.125116i | \(-0.960070\pi\) | ||||
0.992142 | − | 0.125116i | \(-0.0399304\pi\) | |||||||
\(968\) | − 25.8072i | − 0.829474i | ||||||||
\(969\) | 4.58705i | 0.147357i | ||||||||
\(970\) | − 37.1908i | − 1.19412i | ||||||||
\(971\) | −45.0741 | −1.44650 | −0.723249 | − | 0.690587i | \(-0.757352\pi\) | ||||
−0.723249 | + | 0.690587i | \(0.757352\pi\) | |||||||
\(972\) | −100.477 | −3.22281 | ||||||||
\(973\) | − 37.9654i | − 1.21711i | ||||||||
\(974\) | −55.6059 | −1.78173 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.885032 | −0.0283292 | ||||||||
\(977\) | − 27.6147i | − 0.883474i | −0.897145 | − | 0.441737i | \(-0.854362\pi\) | ||||
0.897145 | − | 0.441737i | \(-0.145638\pi\) | |||||||
\(978\) | 150.272 | 4.80517 | ||||||||
\(979\) | −8.02902 | −0.256609 | ||||||||
\(980\) | 5.42099i | 0.173167i | ||||||||
\(981\) | − 32.2330i | − 1.02912i | ||||||||
\(982\) | − 60.0111i | − 1.91503i | ||||||||
\(983\) | 40.7921i | 1.30107i | 0.759478 | + | 0.650533i | \(0.225455\pi\) | ||||
−0.759478 | + | 0.650533i | \(0.774545\pi\) | |||||||
\(984\) | 49.2364 | 1.56960 | ||||||||
\(985\) | 18.9898 | 0.605064 | ||||||||
\(986\) | 17.1457i | 0.546029i | ||||||||
\(987\) | 14.2814 | 0.454582 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −49.1877 | −1.56408 | ||||||||
\(990\) | 21.0617i | 0.669385i | ||||||||
\(991\) | 48.3304 | 1.53527 | 0.767633 | − | 0.640890i | \(-0.221435\pi\) | ||||
0.767633 | + | 0.640890i | \(0.221435\pi\) | |||||||
\(992\) | −2.29660 | −0.0729171 | ||||||||
\(993\) | 38.2348i | 1.21335i | ||||||||
\(994\) | − 50.3955i | − 1.59845i | ||||||||
\(995\) | 10.1534i | 0.321885i | ||||||||
\(996\) | 113.335i | 3.59116i | ||||||||
\(997\) | −9.25930 | −0.293245 | −0.146622 | − | 0.989193i | \(-0.546840\pi\) | ||||
−0.146622 | + | 0.989193i | \(0.546840\pi\) | |||||||
\(998\) | 54.8914 | 1.73756 | ||||||||
\(999\) | − 28.0928i | − 0.888816i |
(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 | 845.2.c.h.506.15 | 18 | ||
13.2 | odd | 12 | 845.2.e.p.191.2 | 18 | |||
13.3 | even | 3 | 845.2.m.j.316.4 | 36 | |||
13.4 | even | 6 | 845.2.m.j.361.4 | 36 | |||
13.5 | odd | 4 | 845.2.a.n.1.8 | ✓ | 9 | ||
13.6 | odd | 12 | 845.2.e.p.146.2 | 18 | |||
13.7 | odd | 12 | 845.2.e.o.146.8 | 18 | |||
13.8 | odd | 4 | 845.2.a.o.1.2 | yes | 9 | ||
13.9 | even | 3 | 845.2.m.j.361.15 | 36 | |||
13.10 | even | 6 | 845.2.m.j.316.15 | 36 | |||
13.11 | odd | 12 | 845.2.e.o.191.8 | 18 | |||
13.12 | even | 2 | inner | 845.2.c.h.506.4 | 18 | ||
39.5 | even | 4 | 7605.2.a.cs.1.2 | 9 | |||
39.8 | even | 4 | 7605.2.a.cp.1.8 | 9 | |||
65.34 | odd | 4 | 4225.2.a.bs.1.8 | 9 | |||
65.44 | odd | 4 | 4225.2.a.bt.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.a.n.1.8 | ✓ | 9 | 13.5 | odd | 4 | ||
845.2.a.o.1.2 | yes | 9 | 13.8 | odd | 4 | ||
845.2.c.h.506.4 | 18 | 13.12 | even | 2 | inner | ||
845.2.c.h.506.15 | 18 | 1.1 | even | 1 | trivial | ||
845.2.e.o.146.8 | 18 | 13.7 | odd | 12 | |||
845.2.e.o.191.8 | 18 | 13.11 | odd | 12 | |||
845.2.e.p.146.2 | 18 | 13.6 | odd | 12 | |||
845.2.e.p.191.2 | 18 | 13.2 | odd | 12 | |||
845.2.m.j.316.4 | 36 | 13.3 | even | 3 | |||
845.2.m.j.316.15 | 36 | 13.10 | even | 6 | |||
845.2.m.j.361.4 | 36 | 13.4 | even | 6 | |||
845.2.m.j.361.15 | 36 | 13.9 | even | 3 | |||
4225.2.a.bs.1.8 | 9 | 65.34 | odd | 4 | |||
4225.2.a.bt.1.2 | 9 | 65.44 | odd | 4 | |||
7605.2.a.cp.1.8 | 9 | 39.8 | even | 4 | |||
7605.2.a.cs.1.2 | 9 | 39.5 | even | 4 |