Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22159 | 0.863792 | 0.431896 | − | 0.901923i | \(-0.357845\pi\) | ||||
0.431896 | + | 0.901923i | \(0.357845\pi\) | |||||||
\(3\) | 0.804421 | 0.464432 | 0.232216 | − | 0.972664i | \(-0.425402\pi\) | ||||
0.232216 | + | 0.972664i | \(0.425402\pi\) | |||||||
\(4\) | −0.507728 | −0.253864 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.982669 | 0.401173 | ||||||||
\(7\) | 3.79180 | 1.43317 | 0.716583 | − | 0.697502i | \(-0.245705\pi\) | ||||
0.716583 | + | 0.697502i | \(0.245705\pi\) | |||||||
\(8\) | −3.06341 | −1.08308 | ||||||||
\(9\) | −2.35291 | −0.784303 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23733 | −0.373068 | −0.186534 | − | 0.982449i | \(-0.559725\pi\) | ||||
−0.186534 | + | 0.982449i | \(0.559725\pi\) | |||||||
\(12\) | −0.408427 | −0.117903 | ||||||||
\(13\) | −3.45598 | −0.958517 | −0.479259 | − | 0.877674i | \(-0.659094\pi\) | ||||
−0.479259 | + | 0.877674i | \(0.659094\pi\) | |||||||
\(14\) | 4.63201 | 1.23796 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.72676 | −0.681689 | ||||||||
\(17\) | 3.00695 | 0.729293 | 0.364647 | − | 0.931146i | \(-0.381190\pi\) | ||||
0.364647 | + | 0.931146i | \(0.381190\pi\) | |||||||
\(18\) | −2.87428 | −0.677474 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.05020 | 0.665608 | ||||||||
\(22\) | −1.51150 | −0.322253 | ||||||||
\(23\) | 6.14780 | 1.28191 | 0.640953 | − | 0.767580i | \(-0.278539\pi\) | ||||
0.640953 | + | 0.767580i | \(0.278539\pi\) | |||||||
\(24\) | −2.46427 | −0.503016 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.22178 | −0.827959 | ||||||||
\(27\) | −4.30599 | −0.828688 | ||||||||
\(28\) | −1.92520 | −0.363829 | ||||||||
\(29\) | 4.28727 | 0.796126 | 0.398063 | − | 0.917358i | \(-0.369683\pi\) | ||||
0.398063 | + | 0.917358i | \(0.369683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.10134 | −0.916227 | −0.458114 | − | 0.888894i | \(-0.651475\pi\) | ||||
−0.458114 | + | 0.888894i | \(0.651475\pi\) | |||||||
\(32\) | 2.79584 | 0.494240 | ||||||||
\(33\) | −0.995330 | −0.173265 | ||||||||
\(34\) | 3.67325 | 0.629958 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.19464 | 0.199106 | ||||||||
\(37\) | −9.13084 | −1.50110 | −0.750550 | − | 0.660813i | \(-0.770211\pi\) | ||||
−0.750550 | + | 0.660813i | \(0.770211\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.78006 | −0.445167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.33021 | −0.832440 | −0.416220 | − | 0.909264i | \(-0.636645\pi\) | ||||
−0.416220 | + | 0.909264i | \(0.636645\pi\) | |||||||
\(42\) | 3.72608 | 0.574947 | ||||||||
\(43\) | −9.12495 | −1.39154 | −0.695771 | − | 0.718264i | \(-0.744937\pi\) | ||||
−0.695771 | + | 0.718264i | \(0.744937\pi\) | |||||||
\(44\) | 0.628225 | 0.0947084 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.51007 | 1.10730 | ||||||||
\(47\) | 7.30333 | 1.06530 | 0.532650 | − | 0.846336i | \(-0.321196\pi\) | ||||
0.532650 | + | 0.846336i | \(0.321196\pi\) | |||||||
\(48\) | −2.19346 | −0.316599 | ||||||||
\(49\) | 7.37774 | 1.05396 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.41886 | 0.338707 | ||||||||
\(52\) | 1.75470 | 0.243333 | ||||||||
\(53\) | 3.33235 | 0.457734 | 0.228867 | − | 0.973458i | \(-0.426498\pi\) | ||||
0.228867 | + | 0.973458i | \(0.426498\pi\) | |||||||
\(54\) | −5.26014 | −0.715814 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.6158 | −1.55223 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.23727 | 0.687687 | ||||||||
\(59\) | 0.817318 | 0.106406 | 0.0532029 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532029 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.40201 | 0.819693 | 0.409847 | − | 0.912154i | \(-0.365582\pi\) | ||||
0.409847 | + | 0.912154i | \(0.365582\pi\) | |||||||
\(62\) | −6.23172 | −0.791430 | ||||||||
\(63\) | −8.92175 | −1.12404 | ||||||||
\(64\) | 8.86888 | 1.10861 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.21588 | −0.149665 | ||||||||
\(67\) | 1.01092 | 0.123504 | 0.0617520 | − | 0.998092i | \(-0.480331\pi\) | ||||
0.0617520 | + | 0.998092i | \(0.480331\pi\) | |||||||
\(68\) | −1.52671 | −0.185141 | ||||||||
\(69\) | 4.94542 | 0.595359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6795 | −1.62346 | −0.811731 | − | 0.584032i | \(-0.801474\pi\) | ||||
−0.811731 | + | 0.584032i | \(0.801474\pi\) | |||||||
\(72\) | 7.20791 | 0.849460 | ||||||||
\(73\) | −11.0627 | −1.29479 | −0.647395 | − | 0.762155i | \(-0.724142\pi\) | ||||
−0.647395 | + | 0.762155i | \(0.724142\pi\) | |||||||
\(74\) | −11.1541 | −1.29664 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.69169 | −0.534668 | ||||||||
\(78\) | −3.39609 | −0.384531 | ||||||||
\(79\) | 1.38420 | 0.155735 | 0.0778673 | − | 0.996964i | \(-0.475189\pi\) | ||||
0.0778673 | + | 0.996964i | \(0.475189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.59490 | 0.399433 | ||||||||
\(82\) | −6.51132 | −0.719054 | ||||||||
\(83\) | −2.52052 | −0.276663 | −0.138332 | − | 0.990386i | \(-0.544174\pi\) | ||||
−0.138332 | + | 0.990386i | \(0.544174\pi\) | |||||||
\(84\) | −1.54867 | −0.168974 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.1469 | −1.20200 | ||||||||
\(87\) | 3.44877 | 0.369747 | ||||||||
\(88\) | 3.79043 | 0.404061 | ||||||||
\(89\) | −2.69842 | −0.286032 | −0.143016 | − | 0.989720i | \(-0.545680\pi\) | ||||
−0.143016 | + | 0.989720i | \(0.545680\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.1044 | −1.37371 | ||||||||
\(92\) | −3.12141 | −0.325430 | ||||||||
\(93\) | −4.10362 | −0.425526 | ||||||||
\(94\) | 8.92164 | 0.920197 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.24903 | 0.229541 | ||||||||
\(97\) | −3.06253 | −0.310953 | −0.155476 | − | 0.987840i | \(-0.549691\pi\) | ||||
−0.155476 | + | 0.987840i | \(0.549691\pi\) | |||||||
\(98\) | 9.01254 | 0.910404 | ||||||||
\(99\) | 2.91131 | 0.292598 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.72705 | 0.370856 | 0.185428 | − | 0.982658i | \(-0.440633\pi\) | ||||
0.185428 | + | 0.982658i | \(0.440633\pi\) | |||||||
\(102\) | 2.95484 | 0.292573 | ||||||||
\(103\) | −13.2086 | −1.30149 | −0.650743 | − | 0.759298i | \(-0.725543\pi\) | ||||
−0.650743 | + | 0.759298i | \(0.725543\pi\) | |||||||
\(104\) | 10.5871 | 1.03815 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.07076 | 0.395387 | ||||||||
\(107\) | −5.13305 | −0.496230 | −0.248115 | − | 0.968731i | \(-0.579811\pi\) | ||||
−0.248115 | + | 0.968731i | \(0.579811\pi\) | |||||||
\(108\) | 2.18627 | 0.210374 | ||||||||
\(109\) | 1.58777 | 0.152081 | 0.0760404 | − | 0.997105i | \(-0.475772\pi\) | ||||
0.0760404 | + | 0.997105i | \(0.475772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.34503 | −0.697160 | ||||||||
\(112\) | −10.3393 | −0.976973 | ||||||||
\(113\) | −20.0832 | −1.88927 | −0.944634 | − | 0.328126i | \(-0.893583\pi\) | ||||
−0.944634 | + | 0.328126i | \(0.893583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.17676 | −0.202108 | ||||||||
\(117\) | 8.13161 | 0.751768 | ||||||||
\(118\) | 0.998424 | 0.0919124 | ||||||||
\(119\) | 11.4018 | 1.04520 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.46903 | −0.860821 | ||||||||
\(122\) | 7.82061 | 0.708044 | ||||||||
\(123\) | −4.28773 | −0.386612 | ||||||||
\(124\) | 2.59009 | 0.232597 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.8987 | −0.970932 | ||||||||
\(127\) | −3.45304 | −0.306408 | −0.153204 | − | 0.988195i | \(-0.548959\pi\) | ||||
−0.153204 | + | 0.988195i | \(0.548959\pi\) | |||||||
\(128\) | 5.24241 | 0.463368 | ||||||||
\(129\) | −7.34030 | −0.646277 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.58746 | −0.662920 | −0.331460 | − | 0.943469i | \(-0.607541\pi\) | ||||
−0.331460 | + | 0.943469i | \(0.607541\pi\) | |||||||
\(132\) | 0.505357 | 0.0439857 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.23493 | 0.106682 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.21152 | −0.789881 | ||||||||
\(137\) | −3.68633 | −0.314944 | −0.157472 | − | 0.987523i | \(-0.550334\pi\) | ||||
−0.157472 | + | 0.987523i | \(0.550334\pi\) | |||||||
\(138\) | 6.04126 | 0.514266 | ||||||||
\(139\) | −18.6273 | −1.57994 | −0.789972 | − | 0.613143i | \(-0.789905\pi\) | ||||
−0.789972 | + | 0.613143i | \(0.789905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.87494 | 0.494760 | ||||||||
\(142\) | −16.7107 | −1.40233 | ||||||||
\(143\) | 4.27618 | 0.357592 | ||||||||
\(144\) | 6.41581 | 0.534651 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.5140 | −1.11843 | ||||||||
\(147\) | 5.93480 | 0.489494 | ||||||||
\(148\) | 4.63598 | 0.381075 | ||||||||
\(149\) | 1.68785 | 0.138274 | 0.0691369 | − | 0.997607i | \(-0.477975\pi\) | ||||
0.0691369 | + | 0.997607i | \(0.477975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.33890 | −0.108958 | −0.0544791 | − | 0.998515i | \(-0.517350\pi\) | ||||
−0.0544791 | + | 0.998515i | \(0.517350\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.07508 | −0.571987 | ||||||||
\(154\) | −5.73130 | −0.461841 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.41152 | 0.113012 | ||||||||
\(157\) | 6.04267 | 0.482258 | 0.241129 | − | 0.970493i | \(-0.422482\pi\) | ||||
0.241129 | + | 0.970493i | \(0.422482\pi\) | |||||||
\(158\) | 1.69092 | 0.134522 | ||||||||
\(159\) | 2.68061 | 0.212587 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.3112 | 1.83718 | ||||||||
\(162\) | 4.39147 | 0.345027 | ||||||||
\(163\) | −9.79728 | −0.767382 | −0.383691 | − | 0.923462i | \(-0.625347\pi\) | ||||
−0.383691 | + | 0.923462i | \(0.625347\pi\) | |||||||
\(164\) | 2.70630 | 0.211326 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.07903 | −0.238979 | ||||||||
\(167\) | −3.87632 | −0.299959 | −0.149979 | − | 0.988689i | \(-0.547921\pi\) | ||||
−0.149979 | + | 0.988689i | \(0.547921\pi\) | |||||||
\(168\) | −9.34400 | −0.720905 | ||||||||
\(169\) | −1.05618 | −0.0812444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.63299 | 0.353262 | ||||||||
\(173\) | 4.73220 | 0.359782 | 0.179891 | − | 0.983687i | \(-0.442425\pi\) | ||||
0.179891 | + | 0.983687i | \(0.442425\pi\) | |||||||
\(174\) | 4.21296 | 0.319384 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.37389 | 0.254316 | ||||||||
\(177\) | 0.657468 | 0.0494183 | ||||||||
\(178\) | −3.29635 | −0.247072 | ||||||||
\(179\) | 9.37815 | 0.700956 | 0.350478 | − | 0.936571i | \(-0.386019\pi\) | ||||
0.350478 | + | 0.936571i | \(0.386019\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.5008 | 1.44948 | 0.724741 | − | 0.689022i | \(-0.241960\pi\) | ||||
0.724741 | + | 0.689022i | \(0.241960\pi\) | |||||||
\(182\) | −16.0081 | −1.18660 | ||||||||
\(183\) | 5.14991 | 0.380692 | ||||||||
\(184\) | −18.8332 | −1.38840 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.01293 | −0.367566 | ||||||||
\(187\) | −3.72058 | −0.272076 | ||||||||
\(188\) | −3.70810 | −0.270441 | ||||||||
\(189\) | −16.3274 | −1.18765 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.5024 | 1.12171 | 0.560857 | − | 0.827913i | \(-0.310472\pi\) | ||||
0.560857 | + | 0.827913i | \(0.310472\pi\) | |||||||
\(192\) | 7.13431 | 0.514874 | ||||||||
\(193\) | −19.8432 | −1.42834 | −0.714172 | − | 0.699970i | \(-0.753196\pi\) | ||||
−0.714172 | + | 0.699970i | \(0.753196\pi\) | |||||||
\(194\) | −3.74114 | −0.268598 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.74588 | −0.267563 | ||||||||
\(197\) | −25.9708 | −1.85034 | −0.925170 | − | 0.379553i | \(-0.876078\pi\) | ||||
−0.925170 | + | 0.379553i | \(0.876078\pi\) | |||||||
\(198\) | 3.55642 | 0.252744 | ||||||||
\(199\) | −5.41593 | −0.383925 | −0.191963 | − | 0.981402i | \(-0.561485\pi\) | ||||
−0.191963 | + | 0.981402i | \(0.561485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.813208 | 0.0573593 | ||||||||
\(202\) | 4.55291 | 0.320342 | ||||||||
\(203\) | 16.2565 | 1.14098 | ||||||||
\(204\) | −1.22812 | −0.0859856 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.1355 | −1.12421 | ||||||||
\(207\) | −14.4652 | −1.00540 | ||||||||
\(208\) | 9.42363 | 0.653411 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1197 | 1.38510 | 0.692550 | − | 0.721370i | \(-0.256487\pi\) | ||||
0.692550 | + | 0.721370i | \(0.256487\pi\) | |||||||
\(212\) | −1.69193 | −0.116202 | ||||||||
\(213\) | −11.0041 | −0.753988 | ||||||||
\(214\) | −6.27046 | −0.428640 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.1910 | 0.897533 | ||||||||
\(217\) | −19.3432 | −1.31311 | ||||||||
\(218\) | 1.93960 | 0.131366 | ||||||||
\(219\) | −8.89905 | −0.601342 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.3920 | −0.699040 | ||||||||
\(222\) | −8.97259 | −0.602201 | ||||||||
\(223\) | 10.8496 | 0.726546 | 0.363273 | − | 0.931683i | \(-0.381659\pi\) | ||||
0.363273 | + | 0.931683i | \(0.381659\pi\) | |||||||
\(224\) | 10.6013 | 0.708327 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.5333 | −1.63193 | ||||||||
\(227\) | −8.78226 | −0.582899 | −0.291449 | − | 0.956586i | \(-0.594138\pi\) | ||||
−0.291449 | + | 0.956586i | \(0.594138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0824 | 1.19492 | 0.597459 | − | 0.801899i | \(-0.296177\pi\) | ||||
0.597459 | + | 0.801899i | \(0.296177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.77409 | −0.248317 | ||||||||
\(232\) | −13.1336 | −0.862265 | ||||||||
\(233\) | 26.3658 | 1.72728 | 0.863640 | − | 0.504109i | \(-0.168179\pi\) | ||||
0.863640 | + | 0.504109i | \(0.168179\pi\) | |||||||
\(234\) | 9.93346 | 0.649371 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.414975 | −0.0270126 | ||||||||
\(237\) | 1.11348 | 0.0723282 | ||||||||
\(238\) | 13.9282 | 0.902833 | ||||||||
\(239\) | −9.16897 | −0.593091 | −0.296546 | − | 0.955019i | \(-0.595835\pi\) | ||||
−0.296546 | + | 0.955019i | \(0.595835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.5167 | −1.70809 | −0.854045 | − | 0.520199i | \(-0.825858\pi\) | ||||
−0.854045 | + | 0.520199i | \(0.825858\pi\) | |||||||
\(242\) | −11.5672 | −0.743570 | ||||||||
\(243\) | 15.8098 | 1.01420 | ||||||||
\(244\) | −3.25048 | −0.208091 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.23784 | −0.333952 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 15.6275 | 0.992345 | ||||||||
\(249\) | −2.02756 | −0.128491 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9471 | −0.943451 | −0.471726 | − | 0.881745i | \(-0.656369\pi\) | ||||
−0.471726 | + | 0.881745i | \(0.656369\pi\) | |||||||
\(252\) | 4.52982 | 0.285352 | ||||||||
\(253\) | −7.60684 | −0.478238 | ||||||||
\(254\) | −4.21819 | −0.264673 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.3337 | −0.708356 | ||||||||
\(257\) | 10.7988 | 0.673610 | 0.336805 | − | 0.941574i | \(-0.390654\pi\) | ||||
0.336805 | + | 0.941574i | \(0.390654\pi\) | |||||||
\(258\) | −8.96680 | −0.558249 | ||||||||
\(259\) | −34.6223 | −2.15132 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0875 | −0.624403 | ||||||||
\(262\) | −9.26874 | −0.572624 | ||||||||
\(263\) | −0.549168 | −0.0338632 | −0.0169316 | − | 0.999857i | \(-0.505390\pi\) | ||||
−0.0169316 | + | 0.999857i | \(0.505390\pi\) | |||||||
\(264\) | 3.04910 | 0.187659 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.17066 | −0.132842 | ||||||||
\(268\) | −0.513275 | −0.0313532 | ||||||||
\(269\) | −21.9270 | −1.33691 | −0.668455 | − | 0.743752i | \(-0.733044\pi\) | ||||
−0.668455 | + | 0.743752i | \(0.733044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.28538 | −0.321064 | −0.160532 | − | 0.987031i | \(-0.551321\pi\) | ||||
−0.160532 | + | 0.987031i | \(0.551321\pi\) | |||||||
\(272\) | −8.19923 | −0.497151 | ||||||||
\(273\) | −10.5414 | −0.637997 | ||||||||
\(274\) | −4.50316 | −0.272046 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.51093 | −0.151140 | ||||||||
\(277\) | −17.4391 | −1.04781 | −0.523906 | − | 0.851776i | \(-0.675526\pi\) | ||||
−0.523906 | + | 0.851776i | \(0.675526\pi\) | |||||||
\(278\) | −22.7548 | −1.36474 | ||||||||
\(279\) | 12.0030 | 0.718599 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.1841 | 1.38305 | 0.691524 | − | 0.722354i | \(-0.256940\pi\) | ||||
0.691524 | + | 0.722354i | \(0.256940\pi\) | |||||||
\(282\) | 7.17675 | 0.427369 | ||||||||
\(283\) | −4.59388 | −0.273078 | −0.136539 | − | 0.990635i | \(-0.543598\pi\) | ||||
−0.136539 | + | 0.990635i | \(0.543598\pi\) | |||||||
\(284\) | 6.94548 | 0.412138 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.22372 | 0.308885 | ||||||||
\(287\) | −20.2111 | −1.19302 | ||||||||
\(288\) | −6.57836 | −0.387633 | ||||||||
\(289\) | −7.95823 | −0.468131 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.46356 | −0.144416 | ||||||||
\(292\) | 5.61684 | 0.328700 | ||||||||
\(293\) | −18.1326 | −1.05932 | −0.529659 | − | 0.848211i | \(-0.677680\pi\) | ||||
−0.529659 | + | 0.848211i | \(0.677680\pi\) | |||||||
\(294\) | 7.24987 | 0.422821 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 27.9715 | 1.62581 | ||||||||
\(297\) | 5.32791 | 0.309157 | ||||||||
\(298\) | 2.06185 | 0.119440 | ||||||||
\(299\) | −21.2467 | −1.22873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.6000 | −1.99431 | ||||||||
\(302\) | −1.63558 | −0.0941171 | ||||||||
\(303\) | 2.99812 | 0.172237 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.64282 | −0.494077 | ||||||||
\(307\) | 4.41407 | 0.251924 | 0.125962 | − | 0.992035i | \(-0.459798\pi\) | ||||
0.125962 | + | 0.992035i | \(0.459798\pi\) | |||||||
\(308\) | 2.38210 | 0.135733 | ||||||||
\(309\) | −10.6253 | −0.604452 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0338 | 0.852487 | 0.426243 | − | 0.904609i | \(-0.359837\pi\) | ||||
0.426243 | + | 0.904609i | \(0.359837\pi\) | |||||||
\(312\) | 8.51646 | 0.482150 | ||||||||
\(313\) | −7.80549 | −0.441193 | −0.220596 | − | 0.975365i | \(-0.570800\pi\) | ||||
−0.220596 | + | 0.975365i | \(0.570800\pi\) | |||||||
\(314\) | 7.38164 | 0.416570 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.702796 | −0.0395354 | ||||||||
\(317\) | 27.2310 | 1.52944 | 0.764722 | − | 0.644361i | \(-0.222877\pi\) | ||||
0.764722 | + | 0.644361i | \(0.222877\pi\) | |||||||
\(318\) | 3.27460 | 0.183631 | ||||||||
\(319\) | −5.30474 | −0.297009 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.12913 | −0.230466 | ||||||||
\(322\) | 28.4767 | 1.58694 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.82523 | −0.101402 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.9682 | −0.662858 | ||||||||
\(327\) | 1.27724 | 0.0706313 | ||||||||
\(328\) | 16.3286 | 0.901596 | ||||||||
\(329\) | 27.6927 | 1.52675 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9800 | 0.658480 | 0.329240 | − | 0.944246i | \(-0.393208\pi\) | ||||
0.329240 | + | 0.944246i | \(0.393208\pi\) | |||||||
\(332\) | 1.27974 | 0.0702348 | ||||||||
\(333\) | 21.4840 | 1.17732 | ||||||||
\(334\) | −4.73526 | −0.259102 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.31716 | −0.453738 | ||||||||
\(337\) | 4.14343 | 0.225707 | 0.112853 | − | 0.993612i | \(-0.464001\pi\) | ||||
0.112853 | + | 0.993612i | \(0.464001\pi\) | |||||||
\(338\) | −1.29021 | −0.0701782 | ||||||||
\(339\) | −16.1553 | −0.877437 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.31201 | 0.341815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.43230 | 0.0773370 | ||||||||
\(344\) | 27.9534 | 1.50715 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.78078 | 0.310777 | ||||||||
\(347\) | 9.16935 | 0.492237 | 0.246118 | − | 0.969240i | \(-0.420845\pi\) | ||||
0.246118 | + | 0.969240i | \(0.420845\pi\) | |||||||
\(348\) | −1.75103 | −0.0938653 | ||||||||
\(349\) | −32.6883 | −1.74976 | −0.874881 | − | 0.484337i | \(-0.839061\pi\) | ||||
−0.874881 | + | 0.484337i | \(0.839061\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.8814 | 0.794312 | ||||||||
\(352\) | −3.45937 | −0.184385 | ||||||||
\(353\) | −26.4701 | −1.40886 | −0.704431 | − | 0.709773i | \(-0.748798\pi\) | ||||
−0.704431 | + | 0.709773i | \(0.748798\pi\) | |||||||
\(354\) | 0.803153 | 0.0426871 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.37006 | 0.0726131 | ||||||||
\(357\) | 9.17181 | 0.485424 | ||||||||
\(358\) | 11.4562 | 0.605480 | ||||||||
\(359\) | 12.4121 | 0.655083 | 0.327542 | − | 0.944837i | \(-0.393780\pi\) | ||||
0.327542 | + | 0.944837i | \(0.393780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 23.8219 | 1.25205 | ||||||||
\(363\) | −7.61708 | −0.399793 | ||||||||
\(364\) | 6.65347 | 0.348736 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.29106 | 0.328839 | ||||||||
\(367\) | 5.32121 | 0.277765 | 0.138882 | − | 0.990309i | \(-0.455649\pi\) | ||||
0.138882 | + | 0.990309i | \(0.455649\pi\) | |||||||
\(368\) | −16.7636 | −0.873861 | ||||||||
\(369\) | 12.5415 | 0.652885 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.6356 | 0.656009 | ||||||||
\(372\) | 2.08352 | 0.108026 | ||||||||
\(373\) | 19.3050 | 0.999575 | 0.499788 | − | 0.866148i | \(-0.333411\pi\) | ||||
0.499788 | + | 0.866148i | \(0.333411\pi\) | |||||||
\(374\) | −4.54501 | −0.235017 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.3730 | −1.15380 | ||||||||
\(377\) | −14.8167 | −0.763100 | ||||||||
\(378\) | −19.9454 | −1.02588 | ||||||||
\(379\) | −20.5109 | −1.05357 | −0.526787 | − | 0.849997i | \(-0.676603\pi\) | ||||
−0.526787 | + | 0.849997i | \(0.676603\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.77770 | −0.142306 | ||||||||
\(382\) | 18.9375 | 0.968927 | ||||||||
\(383\) | 22.7253 | 1.16121 | 0.580605 | − | 0.814186i | \(-0.302816\pi\) | ||||
0.580605 | + | 0.814186i | \(0.302816\pi\) | |||||||
\(384\) | 4.21710 | 0.215203 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.2402 | −1.23379 | ||||||||
\(387\) | 21.4702 | 1.09139 | ||||||||
\(388\) | 1.55493 | 0.0789396 | ||||||||
\(389\) | 5.04493 | 0.255788 | 0.127894 | − | 0.991788i | \(-0.459178\pi\) | ||||
0.127894 | + | 0.991788i | \(0.459178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.4862 | 0.934885 | ||||||||
\(392\) | −22.6010 | −1.14152 | ||||||||
\(393\) | −6.10351 | −0.307881 | ||||||||
\(394\) | −31.7255 | −1.59831 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.47815 | −0.0742800 | ||||||||
\(397\) | 22.9429 | 1.15147 | 0.575735 | − | 0.817636i | \(-0.304716\pi\) | ||||
0.575735 | + | 0.817636i | \(0.304716\pi\) | |||||||
\(398\) | −6.61603 | −0.331632 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.7649 | 1.13683 | 0.568413 | − | 0.822744i | \(-0.307558\pi\) | ||||
0.568413 | + | 0.822744i | \(0.307558\pi\) | |||||||
\(402\) | 0.993404 | 0.0495465 | ||||||||
\(403\) | 17.6301 | 0.878220 | ||||||||
\(404\) | −1.89233 | −0.0941468 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.8587 | 0.985568 | ||||||||
\(407\) | 11.2978 | 0.560012 | ||||||||
\(408\) | −7.40993 | −0.366846 | ||||||||
\(409\) | −23.8028 | −1.17697 | −0.588486 | − | 0.808507i | \(-0.700276\pi\) | ||||
−0.588486 | + | 0.808507i | \(0.700276\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.96536 | −0.146270 | ||||||||
\(412\) | 6.70640 | 0.330400 | ||||||||
\(413\) | 3.09911 | 0.152497 | ||||||||
\(414\) | −17.6705 | −0.868458 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.66239 | −0.473737 | ||||||||
\(417\) | −14.9842 | −0.733777 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.9374 | −0.778593 | −0.389296 | − | 0.921113i | \(-0.627282\pi\) | ||||
−0.389296 | + | 0.921113i | \(0.627282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.65354 | 0.129326 | 0.0646629 | − | 0.997907i | \(-0.479403\pi\) | ||||
0.0646629 | + | 0.997907i | \(0.479403\pi\) | |||||||
\(422\) | 24.5780 | 1.19644 | ||||||||
\(423\) | −17.1840 | −0.835517 | ||||||||
\(424\) | −10.2084 | −0.495761 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.4424 | −0.651289 | ||||||||
\(427\) | 24.2751 | 1.17476 | ||||||||
\(428\) | 2.60619 | 0.125975 | ||||||||
\(429\) | 3.43984 | 0.166077 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.3222 | −1.60507 | −0.802536 | − | 0.596604i | \(-0.796516\pi\) | ||||
−0.802536 | + | 0.596604i | \(0.796516\pi\) | |||||||
\(432\) | 11.7414 | 0.564908 | ||||||||
\(433\) | −22.3800 | −1.07552 | −0.537758 | − | 0.843099i | \(-0.680728\pi\) | ||||
−0.537758 | + | 0.843099i | \(0.680728\pi\) | |||||||
\(434\) | −23.6294 | −1.13425 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.806155 | −0.0386078 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −10.8710 | −0.519435 | ||||||||
\(439\) | 17.4561 | 0.833132 | 0.416566 | − | 0.909105i | \(-0.363233\pi\) | ||||
0.416566 | + | 0.909105i | \(0.363233\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.3591 | −0.826625 | ||||||||
\(442\) | −12.6947 | −0.603825 | ||||||||
\(443\) | 1.49859 | 0.0712001 | 0.0356001 | − | 0.999366i | \(-0.488666\pi\) | ||||
0.0356001 | + | 0.999366i | \(0.488666\pi\) | |||||||
\(444\) | 3.72928 | 0.176984 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.2538 | 0.627584 | ||||||||
\(447\) | 1.35774 | 0.0642189 | ||||||||
\(448\) | 33.6290 | 1.58882 | ||||||||
\(449\) | −11.9911 | −0.565896 | −0.282948 | − | 0.959135i | \(-0.591312\pi\) | ||||
−0.282948 | + | 0.959135i | \(0.591312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.59521 | 0.310556 | ||||||||
\(452\) | 10.1968 | 0.479617 | ||||||||
\(453\) | −1.07704 | −0.0506037 | ||||||||
\(454\) | −10.7283 | −0.503503 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.9472 | −0.605646 | −0.302823 | − | 0.953047i | \(-0.597929\pi\) | ||||
−0.302823 | + | 0.953047i | \(0.597929\pi\) | |||||||
\(458\) | 22.0892 | 1.03216 | ||||||||
\(459\) | −12.9479 | −0.604357 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8680 | 0.645899 | 0.322949 | − | 0.946416i | \(-0.395326\pi\) | ||||
0.322949 | + | 0.946416i | \(0.395326\pi\) | |||||||
\(462\) | −4.61038 | −0.214494 | ||||||||
\(463\) | −4.18473 | −0.194481 | −0.0972405 | − | 0.995261i | \(-0.531002\pi\) | ||||
−0.0972405 | + | 0.995261i | \(0.531002\pi\) | |||||||
\(464\) | −11.6903 | −0.542710 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.2081 | 1.49201 | ||||||||
\(467\) | 23.3019 | 1.07828 | 0.539141 | − | 0.842216i | \(-0.318749\pi\) | ||||
0.539141 | + | 0.842216i | \(0.318749\pi\) | |||||||
\(468\) | −4.12864 | −0.190847 | ||||||||
\(469\) | 3.83322 | 0.177002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.86085 | 0.223976 | ||||||||
\(472\) | −2.50378 | −0.115246 | ||||||||
\(473\) | 11.2905 | 0.519139 | ||||||||
\(474\) | 1.36021 | 0.0624765 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.78899 | −0.265338 | ||||||||
\(477\) | −7.84072 | −0.359002 | ||||||||
\(478\) | −11.2007 | −0.512307 | ||||||||
\(479\) | 35.1170 | 1.60454 | 0.802268 | − | 0.596963i | \(-0.203626\pi\) | ||||
0.802268 | + | 0.596963i | \(0.203626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.5560 | 1.43883 | ||||||||
\(482\) | −32.3924 | −1.47543 | ||||||||
\(483\) | 18.7520 | 0.853247 | ||||||||
\(484\) | 4.80769 | 0.218531 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.3130 | 0.876055 | ||||||||
\(487\) | 33.4209 | 1.51445 | 0.757223 | − | 0.653156i | \(-0.226556\pi\) | ||||
0.757223 | + | 0.653156i | \(0.226556\pi\) | |||||||
\(488\) | −19.6120 | −0.887791 | ||||||||
\(489\) | −7.88113 | −0.356397 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.5387 | −0.791511 | −0.395755 | − | 0.918356i | \(-0.629517\pi\) | ||||
−0.395755 | + | 0.918356i | \(0.629517\pi\) | |||||||
\(492\) | 2.17700 | 0.0981468 | ||||||||
\(493\) | 12.8916 | 0.580609 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.9101 | 0.624582 | ||||||||
\(497\) | −51.8700 | −2.32669 | ||||||||
\(498\) | −2.47684 | −0.110990 | ||||||||
\(499\) | 32.6830 | 1.46309 | 0.731545 | − | 0.681793i | \(-0.238799\pi\) | ||||
0.731545 | + | 0.681793i | \(0.238799\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.11819 | −0.139310 | ||||||||
\(502\) | −18.2591 | −0.814946 | ||||||||
\(503\) | 17.5243 | 0.781370 | 0.390685 | − | 0.920524i | \(-0.372238\pi\) | ||||
0.390685 | + | 0.920524i | \(0.372238\pi\) | |||||||
\(504\) | 27.3309 | 1.21742 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.29240 | −0.413098 | ||||||||
\(507\) | −0.849611 | −0.0377325 | ||||||||
\(508\) | 1.75321 | 0.0777860 | ||||||||
\(509\) | −29.9995 | −1.32970 | −0.664852 | − | 0.746975i | \(-0.731505\pi\) | ||||
−0.664852 | + | 0.746975i | \(0.731505\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.9475 | −1.85565 | ||||||||
\(512\) | −24.3299 | −1.07524 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.1916 | 0.581858 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.72687 | 0.164066 | ||||||||
\(517\) | −9.03659 | −0.397429 | ||||||||
\(518\) | −42.2941 | −1.85830 | ||||||||
\(519\) | 3.80668 | 0.167094 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4875 | 0.459464 | 0.229732 | − | 0.973254i | \(-0.426215\pi\) | ||||
0.229732 | + | 0.973254i | \(0.426215\pi\) | |||||||
\(522\) | −12.3228 | −0.539354 | ||||||||
\(523\) | −32.7586 | −1.43244 | −0.716218 | − | 0.697877i | \(-0.754128\pi\) | ||||
−0.716218 | + | 0.697877i | \(0.754128\pi\) | |||||||
\(524\) | 3.85237 | 0.168291 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.670856 | −0.0292507 | ||||||||
\(527\) | −15.3395 | −0.668198 | ||||||||
\(528\) | 2.71402 | 0.118113 | ||||||||
\(529\) | 14.7955 | 0.643283 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.92307 | −0.0834543 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.4211 | 0.797908 | ||||||||
\(534\) | −2.65165 | −0.114748 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.09687 | −0.133764 | ||||||||
\(537\) | 7.54398 | 0.325547 | ||||||||
\(538\) | −26.7857 | −1.15481 | ||||||||
\(539\) | −9.12866 | −0.393199 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7958 | 0.636122 | 0.318061 | − | 0.948070i | \(-0.396968\pi\) | ||||
0.318061 | + | 0.948070i | \(0.396968\pi\) | |||||||
\(542\) | −6.45655 | −0.277333 | ||||||||
\(543\) | 15.6868 | 0.673186 | ||||||||
\(544\) | 8.40697 | 0.360446 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.8773 | −0.551097 | ||||||||
\(547\) | 1.61001 | 0.0688390 | 0.0344195 | − | 0.999407i | \(-0.489042\pi\) | ||||
0.0344195 | + | 0.999407i | \(0.489042\pi\) | |||||||
\(548\) | 1.87165 | 0.0799529 | ||||||||
\(549\) | −15.0633 | −0.642888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −15.1498 | −0.644819 | ||||||||
\(553\) | 5.24860 | 0.223193 | ||||||||
\(554\) | −21.3033 | −0.905092 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.45758 | 0.401091 | ||||||||
\(557\) | 22.3165 | 0.945581 | 0.472790 | − | 0.881175i | \(-0.343247\pi\) | ||||
0.472790 | + | 0.881175i | \(0.343247\pi\) | |||||||
\(558\) | 14.6627 | 0.620720 | ||||||||
\(559\) | 31.5357 | 1.33382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.99291 | −0.126361 | ||||||||
\(562\) | 28.3214 | 1.19467 | ||||||||
\(563\) | −2.42120 | −0.102042 | −0.0510208 | − | 0.998698i | \(-0.516247\pi\) | ||||
−0.0510208 | + | 0.998698i | \(0.516247\pi\) | |||||||
\(564\) | −2.98287 | −0.125602 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.61182 | −0.235882 | ||||||||
\(567\) | 13.6311 | 0.572453 | ||||||||
\(568\) | 41.9059 | 1.75833 | ||||||||
\(569\) | −25.3556 | −1.06296 | −0.531481 | − | 0.847070i | \(-0.678364\pi\) | ||||
−0.531481 | + | 0.847070i | \(0.678364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.79252 | 0.158712 | 0.0793561 | − | 0.996846i | \(-0.474714\pi\) | ||||
0.0793561 | + | 0.996846i | \(0.474714\pi\) | |||||||
\(572\) | −2.17113 | −0.0907797 | ||||||||
\(573\) | 12.4704 | 0.520960 | ||||||||
\(574\) | −24.6896 | −1.03052 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −20.8676 | −0.869485 | ||||||||
\(577\) | 36.8138 | 1.53258 | 0.766289 | − | 0.642496i | \(-0.222101\pi\) | ||||
0.766289 | + | 0.642496i | \(0.222101\pi\) | |||||||
\(578\) | −9.72166 | −0.404368 | ||||||||
\(579\) | −15.9623 | −0.663369 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.55731 | −0.396504 | ||||||||
\(582\) | −3.00945 | −0.124746 | ||||||||
\(583\) | −4.12321 | −0.170766 | ||||||||
\(584\) | 33.8895 | 1.40236 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.1505 | −0.915030 | ||||||||
\(587\) | 27.5764 | 1.13820 | 0.569100 | − | 0.822268i | \(-0.307292\pi\) | ||||
0.569100 | + | 0.822268i | \(0.307292\pi\) | |||||||
\(588\) | −3.01326 | −0.124265 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.8914 | −0.859358 | ||||||||
\(592\) | 24.8976 | 1.02328 | ||||||||
\(593\) | −7.43391 | −0.305274 | −0.152637 | − | 0.988282i | \(-0.548777\pi\) | ||||
−0.152637 | + | 0.988282i | \(0.548777\pi\) | |||||||
\(594\) | 6.50850 | 0.267047 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.856967 | −0.0351027 | ||||||||
\(597\) | −4.35669 | −0.178307 | ||||||||
\(598\) | −25.9547 | −1.06137 | ||||||||
\(599\) | −7.48833 | −0.305965 | −0.152982 | − | 0.988229i | \(-0.548888\pi\) | ||||
−0.152982 | + | 0.988229i | \(0.548888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.9173 | 1.01640 | 0.508199 | − | 0.861240i | \(-0.330312\pi\) | ||||
0.508199 | + | 0.861240i | \(0.330312\pi\) | |||||||
\(602\) | −42.2668 | −1.72267 | ||||||||
\(603\) | −2.37861 | −0.0968646 | ||||||||
\(604\) | 0.679797 | 0.0276605 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.66246 | 0.148777 | ||||||||
\(607\) | 13.5201 | 0.548764 | 0.274382 | − | 0.961621i | \(-0.411527\pi\) | ||||
0.274382 | + | 0.961621i | \(0.411527\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.0770 | 0.529908 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.2402 | −1.02111 | ||||||||
\(612\) | 3.59222 | 0.145207 | ||||||||
\(613\) | −5.65406 | −0.228365 | −0.114183 | − | 0.993460i | \(-0.536425\pi\) | ||||
−0.114183 | + | 0.993460i | \(0.536425\pi\) | |||||||
\(614\) | 5.39217 | 0.217610 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.3725 | 0.579086 | ||||||||
\(617\) | −18.4368 | −0.742239 | −0.371120 | − | 0.928585i | \(-0.621026\pi\) | ||||
−0.371120 | + | 0.928585i | \(0.621026\pi\) | |||||||
\(618\) | −12.9797 | −0.522121 | ||||||||
\(619\) | −6.99902 | −0.281314 | −0.140657 | − | 0.990058i | \(-0.544922\pi\) | ||||
−0.140657 | + | 0.990058i | \(0.544922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.4724 | −1.06230 | ||||||||
\(622\) | 18.3650 | 0.736371 | ||||||||
\(623\) | −10.2319 | −0.409931 | ||||||||
\(624\) | 7.58056 | 0.303465 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.53508 | −0.381099 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.06803 | −0.122428 | ||||||||
\(629\) | −27.4560 | −1.09474 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0613 | 1.11710 | 0.558551 | − | 0.829470i | \(-0.311358\pi\) | ||||
0.558551 | + | 0.829470i | \(0.311358\pi\) | |||||||
\(632\) | −4.24036 | −0.168672 | ||||||||
\(633\) | 16.1847 | 0.643285 | ||||||||
\(634\) | 33.2650 | 1.32112 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.36102 | −0.0539681 | ||||||||
\(637\) | −25.4973 | −1.01024 | ||||||||
\(638\) | −6.48020 | −0.256554 | ||||||||
\(639\) | 32.1867 | 1.27328 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.8330 | −1.05984 | −0.529921 | − | 0.848047i | \(-0.677778\pi\) | ||||
−0.529921 | + | 0.848047i | \(0.677778\pi\) | |||||||
\(642\) | −5.04409 | −0.199074 | ||||||||
\(643\) | −26.8783 | −1.05998 | −0.529988 | − | 0.848005i | \(-0.677804\pi\) | ||||
−0.529988 | + | 0.848005i | \(0.677804\pi\) | |||||||
\(644\) | −11.8358 | −0.466394 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.88424 | −0.349275 | −0.174638 | − | 0.984633i | \(-0.555875\pi\) | ||||
−0.174638 | + | 0.984633i | \(0.555875\pi\) | |||||||
\(648\) | −11.0126 | −0.432617 | ||||||||
\(649\) | −1.01129 | −0.0396965 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.5601 | −0.609849 | ||||||||
\(652\) | 4.97435 | 0.194811 | ||||||||
\(653\) | 39.4102 | 1.54224 | 0.771121 | − | 0.636689i | \(-0.219697\pi\) | ||||
0.771121 | + | 0.636689i | \(0.219697\pi\) | |||||||
\(654\) | 1.56025 | 0.0610107 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.5342 | 0.567465 | ||||||||
\(657\) | 26.0295 | 1.01551 | ||||||||
\(658\) | 33.8291 | 1.31879 | ||||||||
\(659\) | −17.3119 | −0.674377 | −0.337189 | − | 0.941437i | \(-0.609476\pi\) | ||||
−0.337189 | + | 0.941437i | \(0.609476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2421 | −0.553952 | −0.276976 | − | 0.960877i | \(-0.589332\pi\) | ||||
−0.276976 | + | 0.960877i | \(0.589332\pi\) | |||||||
\(662\) | 14.6346 | 0.568789 | ||||||||
\(663\) | −8.35952 | −0.324657 | ||||||||
\(664\) | 7.72138 | 0.299647 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 26.2446 | 1.01696 | ||||||||
\(667\) | 26.3573 | 1.02056 | ||||||||
\(668\) | 1.96811 | 0.0761486 | ||||||||
\(669\) | 8.72768 | 0.337431 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.92137 | −0.305801 | ||||||||
\(672\) | 8.52788 | 0.328970 | ||||||||
\(673\) | −3.86700 | −0.149062 | −0.0745310 | − | 0.997219i | \(-0.523746\pi\) | ||||
−0.0745310 | + | 0.997219i | \(0.523746\pi\) | |||||||
\(674\) | 5.06155 | 0.194964 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.536250 | 0.0206250 | ||||||||
\(677\) | −15.7102 | −0.603790 | −0.301895 | − | 0.953341i | \(-0.597619\pi\) | ||||
−0.301895 | + | 0.953341i | \(0.597619\pi\) | |||||||
\(678\) | −19.7351 | −0.757923 | ||||||||
\(679\) | −11.6125 | −0.445646 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.06463 | −0.270717 | ||||||||
\(682\) | 7.71067 | 0.295257 | ||||||||
\(683\) | −11.3613 | −0.434727 | −0.217364 | − | 0.976091i | \(-0.569746\pi\) | ||||
−0.217364 | + | 0.976091i | \(0.569746\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.74968 | 0.0668031 | ||||||||
\(687\) | 14.5458 | 0.554959 | ||||||||
\(688\) | 24.8815 | 0.948599 | ||||||||
\(689\) | −11.5166 | −0.438746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.01088 | −0.0764974 | −0.0382487 | − | 0.999268i | \(-0.512178\pi\) | ||||
−0.0382487 | + | 0.999268i | \(0.512178\pi\) | |||||||
\(692\) | −2.40267 | −0.0913357 | ||||||||
\(693\) | 11.0391 | 0.419341 | ||||||||
\(694\) | 11.2012 | 0.425190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.5650 | −0.400464 | ||||||||
\(697\) | −16.0277 | −0.607093 | ||||||||
\(698\) | −39.9315 | −1.51143 | ||||||||
\(699\) | 21.2092 | 0.802205 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.4628 | 0.470713 | 0.235357 | − | 0.971909i | \(-0.424374\pi\) | ||||
0.235357 | + | 0.971909i | \(0.424374\pi\) | |||||||
\(702\) | 18.1789 | 0.686120 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −10.9737 | −0.413586 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.3355 | −1.21696 | ||||||||
\(707\) | 14.1322 | 0.531497 | ||||||||
\(708\) | −0.333815 | −0.0125455 | ||||||||
\(709\) | −3.52250 | −0.132290 | −0.0661452 | − | 0.997810i | \(-0.521070\pi\) | ||||
−0.0661452 | + | 0.997810i | \(0.521070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.25689 | −0.122143 | ||||||||
\(712\) | 8.26634 | 0.309794 | ||||||||
\(713\) | −31.3620 | −1.17452 | ||||||||
\(714\) | 11.2042 | 0.419305 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.76155 | −0.177947 | ||||||||
\(717\) | −7.37571 | −0.275451 | ||||||||
\(718\) | 15.1624 | 0.565855 | ||||||||
\(719\) | −23.9065 | −0.891563 | −0.445781 | − | 0.895142i | \(-0.647074\pi\) | ||||
−0.445781 | + | 0.895142i | \(0.647074\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.0845 | −1.86524 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.3306 | −0.793293 | ||||||||
\(724\) | −9.90109 | −0.367971 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.30492 | −0.345338 | ||||||||
\(727\) | −5.47926 | −0.203214 | −0.101607 | − | 0.994825i | \(-0.532398\pi\) | ||||
−0.101607 | + | 0.994825i | \(0.532398\pi\) | |||||||
\(728\) | 40.1441 | 1.48784 | ||||||||
\(729\) | 1.93302 | 0.0715933 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.4383 | −1.01484 | ||||||||
\(732\) | −2.61475 | −0.0966440 | ||||||||
\(733\) | 18.8893 | 0.697691 | 0.348846 | − | 0.937180i | \(-0.386574\pi\) | ||||
0.348846 | + | 0.937180i | \(0.386574\pi\) | |||||||
\(734\) | 6.50031 | 0.239931 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.1883 | 0.633569 | ||||||||
\(737\) | −1.25084 | −0.0460754 | ||||||||
\(738\) | 15.3205 | 0.563956 | ||||||||
\(739\) | 34.9585 | 1.28597 | 0.642985 | − | 0.765879i | \(-0.277696\pi\) | ||||
0.642985 | + | 0.765879i | \(0.277696\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.4355 | 0.566655 | ||||||||
\(743\) | −27.6384 | −1.01395 | −0.506976 | − | 0.861960i | \(-0.669237\pi\) | ||||
−0.506976 | + | 0.861960i | \(0.669237\pi\) | |||||||
\(744\) | 12.5711 | 0.460877 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.5827 | 0.863425 | ||||||||
\(747\) | 5.93055 | 0.216988 | ||||||||
\(748\) | 1.88904 | 0.0690702 | ||||||||
\(749\) | −19.4635 | −0.711180 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.7087 | −1.95986 | −0.979929 | − | 0.199348i | \(-0.936118\pi\) | ||||
−0.979929 | + | 0.199348i | \(0.936118\pi\) | |||||||
\(752\) | −19.9144 | −0.726203 | ||||||||
\(753\) | −12.0237 | −0.438169 | ||||||||
\(754\) | −18.0999 | −0.659160 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.28990 | 0.301501 | ||||||||
\(757\) | −24.5798 | −0.893368 | −0.446684 | − | 0.894692i | \(-0.647395\pi\) | ||||
−0.446684 | + | 0.894692i | \(0.647395\pi\) | |||||||
\(758\) | −25.0558 | −0.910068 | ||||||||
\(759\) | −6.11909 | −0.222109 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.906887 | −0.0328746 | −0.0164373 | − | 0.999865i | \(-0.505232\pi\) | ||||
−0.0164373 | + | 0.999865i | \(0.505232\pi\) | |||||||
\(762\) | −3.39320 | −0.122923 | ||||||||
\(763\) | 6.02051 | 0.217957 | ||||||||
\(764\) | −7.87099 | −0.284763 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.7609 | 1.00304 | ||||||||
\(767\) | −2.82464 | −0.101992 | ||||||||
\(768\) | −9.11706 | −0.328984 | ||||||||
\(769\) | 21.3193 | 0.768792 | 0.384396 | − | 0.923168i | \(-0.374410\pi\) | ||||
0.384396 | + | 0.923168i | \(0.374410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.68676 | 0.312846 | ||||||||
\(772\) | 10.0749 | 0.362605 | ||||||||
\(773\) | 16.6037 | 0.597192 | 0.298596 | − | 0.954380i | \(-0.403482\pi\) | ||||
0.298596 | + | 0.954380i | \(0.403482\pi\) | |||||||
\(774\) | 26.2277 | 0.942733 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.38176 | 0.336786 | ||||||||
\(777\) | −27.8509 | −0.999145 | ||||||||
\(778\) | 6.16282 | 0.220948 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9260 | 0.605661 | ||||||||
\(782\) | 22.5824 | 0.807546 | ||||||||
\(783\) | −18.4609 | −0.659740 | ||||||||
\(784\) | −20.1173 | −0.718475 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.45596 | −0.265945 | ||||||||
\(787\) | 41.3474 | 1.47388 | 0.736938 | − | 0.675960i | \(-0.236271\pi\) | ||||
0.736938 | + | 0.675960i | \(0.236271\pi\) | |||||||
\(788\) | 13.1861 | 0.469735 | ||||||||
\(789\) | −0.441762 | −0.0157271 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −76.1514 | −2.70763 | ||||||||
\(792\) | −8.91853 | −0.316906 | ||||||||
\(793\) | −22.1252 | −0.785690 | ||||||||
\(794\) | 28.0267 | 0.994631 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.74982 | 0.0974648 | ||||||||
\(797\) | 22.7002 | 0.804083 | 0.402042 | − | 0.915621i | \(-0.368301\pi\) | ||||
0.402042 | + | 0.915621i | \(0.368301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.9608 | 0.776916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.34913 | 0.224335 | ||||||||
\(802\) | 27.8093 | 0.981980 | ||||||||
\(803\) | 13.6881 | 0.483044 | ||||||||
\(804\) | −0.412889 | −0.0145615 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.5367 | 0.758599 | ||||||||
\(807\) | −17.6385 | −0.620905 | ||||||||
\(808\) | −11.4175 | −0.401665 | ||||||||
\(809\) | −27.1508 | −0.954571 | −0.477285 | − | 0.878748i | \(-0.658379\pi\) | ||||
−0.477285 | + | 0.878748i | \(0.658379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.2598 | 1.58929 | 0.794644 | − | 0.607076i | \(-0.207658\pi\) | ||||
0.794644 | + | 0.607076i | \(0.207658\pi\) | |||||||
\(812\) | −8.25385 | −0.289653 | ||||||||
\(813\) | −4.25167 | −0.149113 | ||||||||
\(814\) | 13.8013 | 0.483734 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.59563 | −0.230893 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −29.0771 | −1.01666 | ||||||||
\(819\) | 30.8334 | 1.07741 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.7796 | 0.515813 | 0.257907 | − | 0.966170i | \(-0.416967\pi\) | ||||
0.257907 | + | 0.966170i | \(0.416967\pi\) | |||||||
\(822\) | −3.62244 | −0.126347 | ||||||||
\(823\) | 38.1769 | 1.33076 | 0.665381 | − | 0.746504i | \(-0.268269\pi\) | ||||
0.665381 | + | 0.746504i | \(0.268269\pi\) | |||||||
\(824\) | 40.4634 | 1.40961 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.78582 | 0.131726 | ||||||||
\(827\) | −45.3277 | −1.57620 | −0.788099 | − | 0.615548i | \(-0.788935\pi\) | ||||
−0.788099 | + | 0.615548i | \(0.788935\pi\) | |||||||
\(828\) | 7.34439 | 0.255235 | ||||||||
\(829\) | −37.9276 | −1.31728 | −0.658640 | − | 0.752458i | \(-0.728868\pi\) | ||||
−0.658640 | + | 0.752458i | \(0.728868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.0284 | −0.486638 | ||||||||
\(832\) | −30.6507 | −1.06262 | ||||||||
\(833\) | 22.1845 | 0.768648 | ||||||||
\(834\) | −18.3044 | −0.633831 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.9663 | 0.759267 | ||||||||
\(838\) | −19.4689 | −0.672542 | ||||||||
\(839\) | 7.14266 | 0.246592 | 0.123296 | − | 0.992370i | \(-0.460654\pi\) | ||||
0.123296 | + | 0.992370i | \(0.460654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6193 | −0.366184 | ||||||||
\(842\) | 3.24153 | 0.111710 | ||||||||
\(843\) | 18.6498 | 0.642332 | ||||||||
\(844\) | −10.2153 | −0.351627 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −20.9918 | −0.721713 | ||||||||
\(847\) | −35.9046 | −1.23370 | ||||||||
\(848\) | −9.08652 | −0.312032 | ||||||||
\(849\) | −3.69541 | −0.126826 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56.1346 | −1.92427 | ||||||||
\(852\) | 5.58709 | 0.191410 | ||||||||
\(853\) | 51.0391 | 1.74755 | 0.873773 | − | 0.486335i | \(-0.161666\pi\) | ||||
0.873773 | + | 0.486335i | \(0.161666\pi\) | |||||||
\(854\) | 29.6542 | 1.01474 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7246 | 0.537456 | ||||||||
\(857\) | 13.6042 | 0.464710 | 0.232355 | − | 0.972631i | \(-0.425357\pi\) | ||||
0.232355 | + | 0.972631i | \(0.425357\pi\) | |||||||
\(858\) | 4.20207 | 0.143456 | ||||||||
\(859\) | −38.4375 | −1.31147 | −0.655735 | − | 0.754991i | \(-0.727641\pi\) | ||||
−0.655735 | + | 0.754991i | \(0.727641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.2582 | −0.554079 | ||||||||
\(862\) | −40.7059 | −1.38645 | ||||||||
\(863\) | 54.3455 | 1.84994 | 0.924970 | − | 0.380039i | \(-0.124090\pi\) | ||||
0.924970 | + | 0.380039i | \(0.124090\pi\) | |||||||
\(864\) | −12.0389 | −0.409571 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27.3391 | −0.929021 | ||||||||
\(867\) | −6.40176 | −0.217415 | ||||||||
\(868\) | 9.82110 | 0.333350 | ||||||||
\(869\) | −1.71270 | −0.0580995 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.49374 | −0.118381 | ||||||||
\(872\) | −4.86398 | −0.164715 | ||||||||
\(873\) | 7.20584 | 0.243881 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.51830 | 0.152659 | ||||||||
\(877\) | −13.5325 | −0.456961 | −0.228481 | − | 0.973548i | \(-0.573376\pi\) | ||||
−0.228481 | + | 0.973548i | \(0.573376\pi\) | |||||||
\(878\) | 21.3241 | 0.719653 | ||||||||
\(879\) | −14.5862 | −0.491982 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.9577 | −0.941920 | −0.470960 | − | 0.882155i | \(-0.656092\pi\) | ||||
−0.470960 | + | 0.882155i | \(0.656092\pi\) | |||||||
\(882\) | −21.2057 | −0.714032 | ||||||||
\(883\) | 54.5487 | 1.83571 | 0.917855 | − | 0.396915i | \(-0.129919\pi\) | ||||
0.917855 | + | 0.396915i | \(0.129919\pi\) | |||||||
\(884\) | 5.27630 | 0.177461 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.83066 | 0.0615021 | ||||||||
\(887\) | 35.9778 | 1.20802 | 0.604008 | − | 0.796979i | \(-0.293570\pi\) | ||||
0.604008 | + | 0.796979i | \(0.293570\pi\) | |||||||
\(888\) | 22.5008 | 0.755078 | ||||||||
\(889\) | −13.0932 | −0.439133 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.44806 | −0.149016 | ||||||||
\(892\) | −5.50867 | −0.184444 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 1.65860 | 0.0554717 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.8782 | 0.664083 | ||||||||
\(897\) | −17.0913 | −0.570662 | ||||||||
\(898\) | −14.6482 | −0.488817 | ||||||||
\(899\) | −21.8708 | −0.729432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0202 | 0.333822 | ||||||||
\(902\) | 8.05662 | 0.268256 | ||||||||
\(903\) | −27.8329 | −0.926222 | ||||||||
\(904\) | 61.5230 | 2.04622 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.31570 | −0.0437110 | ||||||||
\(907\) | 4.40371 | 0.146223 | 0.0731114 | − | 0.997324i | \(-0.476707\pi\) | ||||
0.0731114 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(908\) | 4.45900 | 0.147977 | ||||||||
\(909\) | −8.76941 | −0.290863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2563 | 0.472333 | 0.236166 | − | 0.971713i | \(-0.424109\pi\) | ||||
0.236166 | + | 0.971713i | \(0.424109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.11870 | 0.103214 | ||||||||
\(914\) | −15.8162 | −0.523152 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.18093 | −0.303347 | ||||||||
\(917\) | −28.7701 | −0.950073 | ||||||||
\(918\) | −15.8170 | −0.522038 | ||||||||
\(919\) | −28.7276 | −0.947637 | −0.473819 | − | 0.880622i | \(-0.657125\pi\) | ||||
−0.473819 | + | 0.880622i | \(0.657125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.55077 | 0.117002 | ||||||||
\(922\) | 16.9410 | 0.557922 | ||||||||
\(923\) | 47.2762 | 1.55612 | ||||||||
\(924\) | 1.91621 | 0.0630387 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.11201 | −0.167991 | ||||||||
\(927\) | 31.0787 | 1.02076 | ||||||||
\(928\) | 11.9865 | 0.393477 | ||||||||
\(929\) | −30.6928 | −1.00700 | −0.503499 | − | 0.863996i | \(-0.667954\pi\) | ||||
−0.503499 | + | 0.863996i | \(0.667954\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.3866 | −0.438494 | ||||||||
\(933\) | 12.0935 | 0.395923 | ||||||||
\(934\) | 28.4652 | 0.931411 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −24.9104 | −0.814222 | ||||||||
\(937\) | −50.4315 | −1.64752 | −0.823762 | − | 0.566936i | \(-0.808129\pi\) | ||||
−0.823762 | + | 0.566936i | \(0.808129\pi\) | |||||||
\(938\) | 4.68261 | 0.152893 | ||||||||
\(939\) | −6.27890 | −0.204904 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.54594 | −0.278590 | −0.139295 | − | 0.990251i | \(-0.544484\pi\) | ||||
−0.139295 | + | 0.990251i | \(0.544484\pi\) | |||||||
\(942\) | 5.93795 | 0.193469 | ||||||||
\(943\) | −32.7691 | −1.06711 | ||||||||
\(944\) | −2.22863 | −0.0725357 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.7924 | 0.448428 | ||||||||
\(947\) | 20.5825 | 0.668841 | 0.334421 | − | 0.942424i | \(-0.391459\pi\) | ||||
0.334421 | + | 0.942424i | \(0.391459\pi\) | |||||||
\(948\) | −0.565344 | −0.0183615 | ||||||||
\(949\) | 38.2325 | 1.24108 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.9051 | 0.710323 | ||||||||
\(952\) | −34.9282 | −1.13203 | ||||||||
\(953\) | −59.1921 | −1.91742 | −0.958711 | − | 0.284384i | \(-0.908211\pi\) | ||||
−0.958711 | + | 0.284384i | \(0.908211\pi\) | |||||||
\(954\) | −9.57812 | −0.310103 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.65534 | 0.150564 | ||||||||
\(957\) | −4.26725 | −0.137940 | ||||||||
\(958\) | 42.8984 | 1.38599 | ||||||||
\(959\) | −13.9778 | −0.451367 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.97635 | −0.160528 | ||||||||
\(962\) | 38.5484 | 1.24285 | ||||||||
\(963\) | 12.0776 | 0.389195 | ||||||||
\(964\) | 13.4633 | 0.433623 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 22.9072 | 0.737028 | ||||||||
\(967\) | 10.9970 | 0.353639 | 0.176819 | − | 0.984243i | \(-0.443419\pi\) | ||||
0.176819 | + | 0.984243i | \(0.443419\pi\) | |||||||
\(968\) | 29.0075 | 0.932335 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.3692 | −1.03878 | −0.519389 | − | 0.854538i | \(-0.673840\pi\) | ||||
−0.519389 | + | 0.854538i | \(0.673840\pi\) | |||||||
\(972\) | −8.02706 | −0.257468 | ||||||||
\(973\) | −70.6309 | −2.26432 | ||||||||
\(974\) | 40.8265 | 1.30817 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.4567 | −0.558776 | ||||||||
\(977\) | 11.1038 | 0.355241 | 0.177621 | − | 0.984099i | \(-0.443160\pi\) | ||||
0.177621 | + | 0.984099i | \(0.443160\pi\) | |||||||
\(978\) | −9.62748 | −0.307853 | ||||||||
\(979\) | 3.33882 | 0.106709 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.73588 | −0.119277 | ||||||||
\(982\) | −21.4250 | −0.683701 | ||||||||
\(983\) | −12.5322 | −0.399716 | −0.199858 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199858 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(984\) | 13.1351 | 0.418731 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.7482 | 0.501525 | ||||||||
\(987\) | 22.2766 | 0.709072 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.0984 | −1.78383 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.7597 | −1.16771 | −0.583856 | − | 0.811857i | \(-0.698457\pi\) | ||||
−0.583856 | + | 0.811857i | \(0.698457\pi\) | |||||||
\(992\) | −14.2625 | −0.452836 | ||||||||
\(993\) | 9.63695 | 0.305819 | ||||||||
\(994\) | −63.3637 | −2.00977 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.02945 | 0.0326193 | ||||||||
\(997\) | 24.4801 | 0.775291 | 0.387646 | − | 0.921808i | \(-0.373288\pi\) | ||||
0.387646 | + | 0.921808i | \(0.373288\pi\) | |||||||
\(998\) | 39.9251 | 1.26381 | ||||||||
\(999\) | 39.3173 | 1.24394 |
(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 | 9025.2.a.ct.1.17 | 24 | ||
5.2 | odd | 4 | 1805.2.b.l.1084.17 | 24 | |||
5.3 | odd | 4 | 1805.2.b.l.1084.8 | 24 | |||
5.4 | even | 2 | inner | 9025.2.a.ct.1.8 | 24 | ||
19.3 | odd | 18 | 475.2.l.f.351.3 | 48 | |||
19.13 | odd | 18 | 475.2.l.f.226.3 | 48 | |||
19.18 | odd | 2 | 9025.2.a.cu.1.8 | 24 | |||
95.3 | even | 36 | 95.2.p.a.9.3 | ✓ | 48 | ||
95.13 | even | 36 | 95.2.p.a.74.6 | yes | 48 | ||
95.18 | even | 4 | 1805.2.b.k.1084.17 | 24 | |||
95.22 | even | 36 | 95.2.p.a.9.6 | yes | 48 | ||
95.32 | even | 36 | 95.2.p.a.74.3 | yes | 48 | ||
95.37 | even | 4 | 1805.2.b.k.1084.8 | 24 | |||
95.79 | odd | 18 | 475.2.l.f.351.6 | 48 | |||
95.89 | odd | 18 | 475.2.l.f.226.6 | 48 | |||
95.94 | odd | 2 | 9025.2.a.cu.1.17 | 24 | |||
285.32 | odd | 36 | 855.2.da.b.739.6 | 48 | |||
285.98 | odd | 36 | 855.2.da.b.199.6 | 48 | |||
285.203 | odd | 36 | 855.2.da.b.739.3 | 48 | |||
285.212 | odd | 36 | 855.2.da.b.199.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.9.3 | ✓ | 48 | 95.3 | even | 36 | ||
95.2.p.a.9.6 | yes | 48 | 95.22 | even | 36 | ||
95.2.p.a.74.3 | yes | 48 | 95.32 | even | 36 | ||
95.2.p.a.74.6 | yes | 48 | 95.13 | even | 36 | ||
475.2.l.f.226.3 | 48 | 19.13 | odd | 18 | |||
475.2.l.f.226.6 | 48 | 95.89 | odd | 18 | |||
475.2.l.f.351.3 | 48 | 19.3 | odd | 18 | |||
475.2.l.f.351.6 | 48 | 95.79 | odd | 18 | |||
855.2.da.b.199.3 | 48 | 285.212 | odd | 36 | |||
855.2.da.b.199.6 | 48 | 285.98 | odd | 36 | |||
855.2.da.b.739.3 | 48 | 285.203 | odd | 36 | |||
855.2.da.b.739.6 | 48 | 285.32 | odd | 36 | |||
1805.2.b.k.1084.8 | 24 | 95.37 | even | 4 | |||
1805.2.b.k.1084.17 | 24 | 95.18 | even | 4 | |||
1805.2.b.l.1084.8 | 24 | 5.3 | odd | 4 | |||
1805.2.b.l.1084.17 | 24 | 5.2 | odd | 4 | |||
9025.2.a.ct.1.8 | 24 | 5.4 | even | 2 | inner | ||
9025.2.a.ct.1.17 | 24 | 1.1 | even | 1 | trivial | ||
9025.2.a.cu.1.8 | 24 | 19.18 | odd | 2 | |||
9025.2.a.cu.1.17 | 24 | 95.94 | odd | 2 |