Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.45308\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45308 | 1.73459 | 0.867293 | − | 0.497797i | \(-0.165858\pi\) | ||||
0.867293 | + | 0.497797i | \(0.165858\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.01758 | 2.00879 | ||||||||
\(5\) | 0.0682999 | 0.0305446 | 0.0152723 | − | 0.999883i | \(-0.495138\pi\) | ||||
0.0152723 | + | 0.999883i | \(0.495138\pi\) | |||||||
\(6\) | 2.45308 | 1.00146 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 4.94928 | 1.74984 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.167545 | 0.0529823 | ||||||||
\(11\) | −0.678230 | −0.204494 | −0.102247 | − | 0.994759i | \(-0.532603\pi\) | ||||
−0.102247 | + | 0.994759i | \(0.532603\pi\) | |||||||
\(12\) | 4.01758 | 1.15978 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.45308 | 0.655612 | ||||||||
\(15\) | 0.0682999 | 0.0176350 | ||||||||
\(16\) | 4.10580 | 1.02645 | ||||||||
\(17\) | −0.934958 | −0.226761 | −0.113380 | − | 0.993552i | \(-0.536168\pi\) | ||||
−0.113380 | + | 0.993552i | \(0.536168\pi\) | |||||||
\(18\) | 2.45308 | 0.578196 | ||||||||
\(19\) | 2.06767 | 0.474356 | 0.237178 | − | 0.971466i | \(-0.423777\pi\) | ||||
0.237178 | + | 0.971466i | \(0.423777\pi\) | |||||||
\(20\) | 0.274400 | 0.0613578 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.66375 | −0.354713 | ||||||||
\(23\) | 4.29948 | 0.896503 | 0.448252 | − | 0.893907i | \(-0.352047\pi\) | ||||
0.448252 | + | 0.893907i | \(0.352047\pi\) | |||||||
\(24\) | 4.94928 | 1.01027 | ||||||||
\(25\) | −4.99534 | −0.999067 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.01758 | 0.759252 | ||||||||
\(29\) | 8.01446 | 1.48825 | 0.744124 | − | 0.668042i | \(-0.232867\pi\) | ||||
0.744124 | + | 0.668042i | \(0.232867\pi\) | |||||||
\(30\) | 0.167545 | 0.0305894 | ||||||||
\(31\) | 10.0622 | 1.80722 | 0.903609 | − | 0.428358i | \(-0.140908\pi\) | ||||
0.903609 | + | 0.428358i | \(0.140908\pi\) | |||||||
\(32\) | 0.173279 | 0.0306316 | ||||||||
\(33\) | −0.678230 | −0.118065 | ||||||||
\(34\) | −2.29352 | −0.393336 | ||||||||
\(35\) | 0.0682999 | 0.0115448 | ||||||||
\(36\) | 4.01758 | 0.669597 | ||||||||
\(37\) | −0.527492 | −0.0867191 | −0.0433596 | − | 0.999060i | \(-0.513806\pi\) | ||||
−0.0433596 | + | 0.999060i | \(0.513806\pi\) | |||||||
\(38\) | 5.07216 | 0.822812 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.338035 | 0.0534481 | ||||||||
\(41\) | 5.13776 | 0.802383 | 0.401191 | − | 0.915994i | \(-0.368596\pi\) | ||||
0.401191 | + | 0.915994i | \(0.368596\pi\) | |||||||
\(42\) | 2.45308 | 0.378518 | ||||||||
\(43\) | −1.78857 | −0.272755 | −0.136377 | − | 0.990657i | \(-0.543546\pi\) | ||||
−0.136377 | + | 0.990657i | \(0.543546\pi\) | |||||||
\(44\) | −2.72485 | −0.410786 | ||||||||
\(45\) | 0.0682999 | 0.0101815 | ||||||||
\(46\) | 10.5470 | 1.55506 | ||||||||
\(47\) | 4.22889 | 0.616846 | 0.308423 | − | 0.951249i | \(-0.400199\pi\) | ||||
0.308423 | + | 0.951249i | \(0.400199\pi\) | |||||||
\(48\) | 4.10580 | 0.592621 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −12.2539 | −1.73297 | ||||||||
\(51\) | −0.934958 | −0.130920 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.21495 | −0.441608 | −0.220804 | − | 0.975318i | \(-0.570868\pi\) | ||||
−0.220804 | + | 0.975318i | \(0.570868\pi\) | |||||||
\(54\) | 2.45308 | 0.333821 | ||||||||
\(55\) | −0.0463231 | −0.00624620 | ||||||||
\(56\) | 4.94928 | 0.661376 | ||||||||
\(57\) | 2.06767 | 0.273870 | ||||||||
\(58\) | 19.6601 | 2.58149 | ||||||||
\(59\) | −8.32746 | −1.08414 | −0.542071 | − | 0.840332i | \(-0.682360\pi\) | ||||
−0.542071 | + | 0.840332i | \(0.682360\pi\) | |||||||
\(60\) | 0.274400 | 0.0354249 | ||||||||
\(61\) | 1.01053 | 0.129386 | 0.0646928 | − | 0.997905i | \(-0.479393\pi\) | ||||
0.0646928 | + | 0.997905i | \(0.479393\pi\) | |||||||
\(62\) | 24.6833 | 3.13478 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −7.78654 | −0.973317 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.66375 | −0.204794 | ||||||||
\(67\) | −7.30030 | −0.891874 | −0.445937 | − | 0.895064i | \(-0.647129\pi\) | ||||
−0.445937 | + | 0.895064i | \(0.647129\pi\) | |||||||
\(68\) | −3.75627 | −0.455515 | ||||||||
\(69\) | 4.29948 | 0.517597 | ||||||||
\(70\) | 0.167545 | 0.0200254 | ||||||||
\(71\) | 9.91104 | 1.17622 | 0.588112 | − | 0.808779i | \(-0.299871\pi\) | ||||
0.588112 | + | 0.808779i | \(0.299871\pi\) | |||||||
\(72\) | 4.94928 | 0.583278 | ||||||||
\(73\) | −3.42254 | −0.400578 | −0.200289 | − | 0.979737i | \(-0.564188\pi\) | ||||
−0.200289 | + | 0.979737i | \(0.564188\pi\) | |||||||
\(74\) | −1.29398 | −0.150422 | ||||||||
\(75\) | −4.99534 | −0.576812 | ||||||||
\(76\) | 8.30704 | 0.952883 | ||||||||
\(77\) | −0.678230 | −0.0772915 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0484 | −1.58057 | −0.790283 | − | 0.612742i | \(-0.790066\pi\) | ||||
−0.790283 | + | 0.612742i | \(0.790066\pi\) | |||||||
\(80\) | 0.280426 | 0.0313526 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.6033 | 1.39180 | ||||||||
\(83\) | −7.03411 | −0.772094 | −0.386047 | − | 0.922479i | \(-0.626160\pi\) | ||||
−0.386047 | + | 0.922479i | \(0.626160\pi\) | |||||||
\(84\) | 4.01758 | 0.438354 | ||||||||
\(85\) | −0.0638575 | −0.00692632 | ||||||||
\(86\) | −4.38750 | −0.473117 | ||||||||
\(87\) | 8.01446 | 0.859240 | ||||||||
\(88\) | −3.35675 | −0.357831 | ||||||||
\(89\) | −15.7543 | −1.66995 | −0.834975 | − | 0.550288i | \(-0.814518\pi\) | ||||
−0.834975 | + | 0.550288i | \(0.814518\pi\) | |||||||
\(90\) | 0.167545 | 0.0176608 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 17.2735 | 1.80089 | ||||||||
\(93\) | 10.0622 | 1.04340 | ||||||||
\(94\) | 10.3738 | 1.06997 | ||||||||
\(95\) | 0.141222 | 0.0144890 | ||||||||
\(96\) | 0.173279 | 0.0176852 | ||||||||
\(97\) | 16.6705 | 1.69263 | 0.846314 | − | 0.532684i | \(-0.178817\pi\) | ||||
0.846314 | + | 0.532684i | \(0.178817\pi\) | |||||||
\(98\) | 2.45308 | 0.247798 | ||||||||
\(99\) | −0.678230 | −0.0681647 | ||||||||
\(100\) | −20.0692 | −2.00692 | ||||||||
\(101\) | −1.50429 | −0.149682 | −0.0748412 | − | 0.997195i | \(-0.523845\pi\) | ||||
−0.0748412 | + | 0.997195i | \(0.523845\pi\) | |||||||
\(102\) | −2.29352 | −0.227093 | ||||||||
\(103\) | −2.21721 | −0.218468 | −0.109234 | − | 0.994016i | \(-0.534840\pi\) | ||||
−0.109234 | + | 0.994016i | \(0.534840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0682999 | 0.00666539 | ||||||||
\(106\) | −7.88652 | −0.766007 | ||||||||
\(107\) | −19.7860 | −1.91278 | −0.956390 | − | 0.292092i | \(-0.905649\pi\) | ||||
−0.956390 | + | 0.292092i | \(0.905649\pi\) | |||||||
\(108\) | 4.01758 | 0.386592 | ||||||||
\(109\) | 1.71086 | 0.163870 | 0.0819352 | − | 0.996638i | \(-0.473890\pi\) | ||||
0.0819352 | + | 0.996638i | \(0.473890\pi\) | |||||||
\(110\) | −0.113634 | −0.0108346 | ||||||||
\(111\) | −0.527492 | −0.0500673 | ||||||||
\(112\) | 4.10580 | 0.387962 | ||||||||
\(113\) | −13.6392 | −1.28307 | −0.641536 | − | 0.767093i | \(-0.721702\pi\) | ||||
−0.641536 | + | 0.767093i | \(0.721702\pi\) | |||||||
\(114\) | 5.07216 | 0.475051 | ||||||||
\(115\) | 0.293654 | 0.0273834 | ||||||||
\(116\) | 32.1987 | 2.98958 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.4279 | −1.88054 | ||||||||
\(119\) | −0.934958 | −0.0857075 | ||||||||
\(120\) | 0.338035 | 0.0308583 | ||||||||
\(121\) | −10.5400 | −0.958182 | ||||||||
\(122\) | 2.47892 | 0.224430 | ||||||||
\(123\) | 5.13776 | 0.463256 | ||||||||
\(124\) | 40.4256 | 3.63032 | ||||||||
\(125\) | −0.682680 | −0.0610608 | ||||||||
\(126\) | 2.45308 | 0.218537 | ||||||||
\(127\) | −8.00439 | −0.710275 | −0.355138 | − | 0.934814i | \(-0.615566\pi\) | ||||
−0.355138 | + | 0.934814i | \(0.615566\pi\) | |||||||
\(128\) | −19.4475 | −1.71893 | ||||||||
\(129\) | −1.78857 | −0.157475 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2912 | −0.899146 | −0.449573 | − | 0.893244i | \(-0.648424\pi\) | ||||
−0.449573 | + | 0.893244i | \(0.648424\pi\) | |||||||
\(132\) | −2.72485 | −0.237167 | ||||||||
\(133\) | 2.06767 | 0.179290 | ||||||||
\(134\) | −17.9082 | −1.54703 | ||||||||
\(135\) | 0.0682999 | 0.00587832 | ||||||||
\(136\) | −4.62737 | −0.396794 | ||||||||
\(137\) | −3.61956 | −0.309239 | −0.154620 | − | 0.987974i | \(-0.549415\pi\) | ||||
−0.154620 | + | 0.987974i | \(0.549415\pi\) | |||||||
\(138\) | 10.5470 | 0.897816 | ||||||||
\(139\) | 1.21815 | 0.103322 | 0.0516610 | − | 0.998665i | \(-0.483548\pi\) | ||||
0.0516610 | + | 0.998665i | \(0.483548\pi\) | |||||||
\(140\) | 0.274400 | 0.0231911 | ||||||||
\(141\) | 4.22889 | 0.356136 | ||||||||
\(142\) | 24.3125 | 2.04026 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.10580 | 0.342150 | ||||||||
\(145\) | 0.547387 | 0.0454580 | ||||||||
\(146\) | −8.39574 | −0.694836 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −2.11924 | −0.174201 | ||||||||
\(149\) | 16.5273 | 1.35397 | 0.676983 | − | 0.735999i | \(-0.263287\pi\) | ||||
0.676983 | + | 0.735999i | \(0.263287\pi\) | |||||||
\(150\) | −12.2539 | −1.00053 | ||||||||
\(151\) | −20.3543 | −1.65641 | −0.828206 | − | 0.560424i | \(-0.810638\pi\) | ||||
−0.828206 | + | 0.560424i | \(0.810638\pi\) | |||||||
\(152\) | 10.2335 | 0.830046 | ||||||||
\(153\) | −0.934958 | −0.0755869 | ||||||||
\(154\) | −1.66375 | −0.134069 | ||||||||
\(155\) | 0.687245 | 0.0552008 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.1583 | 1.20976 | 0.604881 | − | 0.796316i | \(-0.293221\pi\) | ||||
0.604881 | + | 0.796316i | \(0.293221\pi\) | |||||||
\(158\) | −34.4617 | −2.74163 | ||||||||
\(159\) | −3.21495 | −0.254962 | ||||||||
\(160\) | 0.0118349 | 0.000935632 0 | ||||||||
\(161\) | 4.29948 | 0.338846 | ||||||||
\(162\) | 2.45308 | 0.192732 | ||||||||
\(163\) | 16.8412 | 1.31910 | 0.659551 | − | 0.751660i | \(-0.270747\pi\) | ||||
0.659551 | + | 0.751660i | \(0.270747\pi\) | |||||||
\(164\) | 20.6414 | 1.61182 | ||||||||
\(165\) | −0.0463231 | −0.00360625 | ||||||||
\(166\) | −17.2552 | −1.33926 | ||||||||
\(167\) | −1.65129 | −0.127780 | −0.0638902 | − | 0.997957i | \(-0.520351\pi\) | ||||
−0.0638902 | + | 0.997957i | \(0.520351\pi\) | |||||||
\(168\) | 4.94928 | 0.381845 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.156647 | −0.0120143 | ||||||||
\(171\) | 2.06767 | 0.158119 | ||||||||
\(172\) | −7.18574 | −0.547907 | ||||||||
\(173\) | 24.7787 | 1.88389 | 0.941943 | − | 0.335772i | \(-0.108997\pi\) | ||||
0.941943 | + | 0.335772i | \(0.108997\pi\) | |||||||
\(174\) | 19.6601 | 1.49043 | ||||||||
\(175\) | −4.99534 | −0.377612 | ||||||||
\(176\) | −2.78468 | −0.209903 | ||||||||
\(177\) | −8.32746 | −0.625930 | ||||||||
\(178\) | −38.6465 | −2.89667 | ||||||||
\(179\) | −6.30284 | −0.471097 | −0.235548 | − | 0.971863i | \(-0.575689\pi\) | ||||
−0.235548 | + | 0.971863i | \(0.575689\pi\) | |||||||
\(180\) | 0.274400 | 0.0204526 | ||||||||
\(181\) | −18.9468 | −1.40830 | −0.704152 | − | 0.710049i | \(-0.748673\pi\) | ||||
−0.704152 | + | 0.710049i | \(0.748673\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.01053 | 0.0747008 | ||||||||
\(184\) | 21.2793 | 1.56873 | ||||||||
\(185\) | −0.0360276 | −0.00264880 | ||||||||
\(186\) | 24.6833 | 1.80986 | ||||||||
\(187\) | 0.634117 | 0.0463712 | ||||||||
\(188\) | 16.9899 | 1.23912 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0.346428 | 0.0251325 | ||||||||
\(191\) | −8.79410 | −0.636319 | −0.318159 | − | 0.948037i | \(-0.603065\pi\) | ||||
−0.318159 | + | 0.948037i | \(0.603065\pi\) | |||||||
\(192\) | −7.78654 | −0.561945 | ||||||||
\(193\) | −6.19901 | −0.446215 | −0.223107 | − | 0.974794i | \(-0.571620\pi\) | ||||
−0.223107 | + | 0.974794i | \(0.571620\pi\) | |||||||
\(194\) | 40.8939 | 2.93601 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.01758 | 0.286970 | ||||||||
\(197\) | −15.1434 | −1.07892 | −0.539460 | − | 0.842011i | \(-0.681371\pi\) | ||||
−0.539460 | + | 0.842011i | \(0.681371\pi\) | |||||||
\(198\) | −1.66375 | −0.118238 | ||||||||
\(199\) | 15.0372 | 1.06596 | 0.532979 | − | 0.846128i | \(-0.321072\pi\) | ||||
0.532979 | + | 0.846128i | \(0.321072\pi\) | |||||||
\(200\) | −24.7233 | −1.74820 | ||||||||
\(201\) | −7.30030 | −0.514924 | ||||||||
\(202\) | −3.69014 | −0.259637 | ||||||||
\(203\) | 8.01446 | 0.562505 | ||||||||
\(204\) | −3.75627 | −0.262992 | ||||||||
\(205\) | 0.350908 | 0.0245085 | ||||||||
\(206\) | −5.43898 | −0.378952 | ||||||||
\(207\) | 4.29948 | 0.298834 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.40236 | −0.0970031 | ||||||||
\(210\) | 0.167545 | 0.0115617 | ||||||||
\(211\) | 25.4741 | 1.75371 | 0.876856 | − | 0.480752i | \(-0.159636\pi\) | ||||
0.876856 | + | 0.480752i | \(0.159636\pi\) | |||||||
\(212\) | −12.9163 | −0.887097 | ||||||||
\(213\) | 9.91104 | 0.679093 | ||||||||
\(214\) | −48.5365 | −3.31788 | ||||||||
\(215\) | −0.122159 | −0.00833119 | ||||||||
\(216\) | 4.94928 | 0.336756 | ||||||||
\(217\) | 10.0622 | 0.683064 | ||||||||
\(218\) | 4.19686 | 0.284248 | ||||||||
\(219\) | −3.42254 | −0.231274 | ||||||||
\(220\) | −0.186107 | −0.0125473 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.29398 | −0.0868461 | ||||||||
\(223\) | −7.00654 | −0.469192 | −0.234596 | − | 0.972093i | \(-0.575377\pi\) | ||||
−0.234596 | + | 0.972093i | \(0.575377\pi\) | |||||||
\(224\) | 0.173279 | 0.0115777 | ||||||||
\(225\) | −4.99534 | −0.333022 | ||||||||
\(226\) | −33.4581 | −2.22560 | ||||||||
\(227\) | −27.7571 | −1.84230 | −0.921151 | − | 0.389206i | \(-0.872749\pi\) | ||||
−0.921151 | + | 0.389206i | \(0.872749\pi\) | |||||||
\(228\) | 8.30704 | 0.550147 | ||||||||
\(229\) | 3.61011 | 0.238563 | 0.119281 | − | 0.992860i | \(-0.461941\pi\) | ||||
0.119281 | + | 0.992860i | \(0.461941\pi\) | |||||||
\(230\) | 0.720355 | 0.0474988 | ||||||||
\(231\) | −0.678230 | −0.0446243 | ||||||||
\(232\) | 39.6658 | 2.60419 | ||||||||
\(233\) | −15.6176 | −1.02315 | −0.511573 | − | 0.859240i | \(-0.670937\pi\) | ||||
−0.511573 | + | 0.859240i | \(0.670937\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.288832 | 0.0188413 | ||||||||
\(236\) | −33.4562 | −2.17782 | ||||||||
\(237\) | −14.0484 | −0.912540 | ||||||||
\(238\) | −2.29352 | −0.148667 | ||||||||
\(239\) | 27.9831 | 1.81008 | 0.905038 | − | 0.425332i | \(-0.139843\pi\) | ||||
0.905038 | + | 0.425332i | \(0.139843\pi\) | |||||||
\(240\) | 0.280426 | 0.0181014 | ||||||||
\(241\) | 25.9732 | 1.67308 | 0.836541 | − | 0.547904i | \(-0.184574\pi\) | ||||
0.836541 | + | 0.547904i | \(0.184574\pi\) | |||||||
\(242\) | −25.8554 | −1.66205 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.05990 | 0.259909 | ||||||||
\(245\) | 0.0682999 | 0.00436352 | ||||||||
\(246\) | 12.6033 | 0.803558 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 49.8005 | 3.16233 | ||||||||
\(249\) | −7.03411 | −0.445769 | ||||||||
\(250\) | −1.67467 | −0.105915 | ||||||||
\(251\) | −6.38525 | −0.403033 | −0.201517 | − | 0.979485i | \(-0.564587\pi\) | ||||
−0.201517 | + | 0.979485i | \(0.564587\pi\) | |||||||
\(252\) | 4.01758 | 0.253084 | ||||||||
\(253\) | −2.91604 | −0.183330 | ||||||||
\(254\) | −19.6354 | −1.23203 | ||||||||
\(255\) | −0.0638575 | −0.00399891 | ||||||||
\(256\) | −32.1332 | −2.00832 | ||||||||
\(257\) | −13.8179 | −0.861934 | −0.430967 | − | 0.902368i | \(-0.641827\pi\) | ||||
−0.430967 | + | 0.902368i | \(0.641827\pi\) | |||||||
\(258\) | −4.38750 | −0.273154 | ||||||||
\(259\) | −0.527492 | −0.0327767 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.01446 | 0.496083 | ||||||||
\(262\) | −25.2451 | −1.55965 | ||||||||
\(263\) | −11.3364 | −0.699033 | −0.349517 | − | 0.936930i | \(-0.613654\pi\) | ||||
−0.349517 | + | 0.936930i | \(0.613654\pi\) | |||||||
\(264\) | −3.35675 | −0.206594 | ||||||||
\(265\) | −0.219581 | −0.0134887 | ||||||||
\(266\) | 5.07216 | 0.310994 | ||||||||
\(267\) | −15.7543 | −0.964146 | ||||||||
\(268\) | −29.3296 | −1.79159 | ||||||||
\(269\) | 21.0002 | 1.28040 | 0.640202 | − | 0.768206i | \(-0.278851\pi\) | ||||
0.640202 | + | 0.768206i | \(0.278851\pi\) | |||||||
\(270\) | 0.167545 | 0.0101965 | ||||||||
\(271\) | 29.2450 | 1.77651 | 0.888253 | − | 0.459354i | \(-0.151919\pi\) | ||||
0.888253 | + | 0.459354i | \(0.151919\pi\) | |||||||
\(272\) | −3.83875 | −0.232759 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.87904 | −0.536403 | ||||||||
\(275\) | 3.38799 | 0.204303 | ||||||||
\(276\) | 17.2735 | 1.03974 | ||||||||
\(277\) | 16.5036 | 0.991603 | 0.495801 | − | 0.868436i | \(-0.334874\pi\) | ||||
0.495801 | + | 0.868436i | \(0.334874\pi\) | |||||||
\(278\) | 2.98821 | 0.179221 | ||||||||
\(279\) | 10.0622 | 0.602406 | ||||||||
\(280\) | 0.338035 | 0.0202015 | ||||||||
\(281\) | 1.12161 | 0.0669094 | 0.0334547 | − | 0.999440i | \(-0.489349\pi\) | ||||
0.0334547 | + | 0.999440i | \(0.489349\pi\) | |||||||
\(282\) | 10.3738 | 0.617749 | ||||||||
\(283\) | 10.9412 | 0.650387 | 0.325194 | − | 0.945647i | \(-0.394571\pi\) | ||||
0.325194 | + | 0.945647i | \(0.394571\pi\) | |||||||
\(284\) | 39.8184 | 2.36279 | ||||||||
\(285\) | 0.141222 | 0.00836525 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.13776 | 0.303272 | ||||||||
\(288\) | 0.173279 | 0.0102105 | ||||||||
\(289\) | −16.1259 | −0.948580 | ||||||||
\(290\) | 1.34278 | 0.0788508 | ||||||||
\(291\) | 16.6705 | 0.977239 | ||||||||
\(292\) | −13.7503 | −0.804677 | ||||||||
\(293\) | −15.5503 | −0.908457 | −0.454229 | − | 0.890885i | \(-0.650085\pi\) | ||||
−0.454229 | + | 0.890885i | \(0.650085\pi\) | |||||||
\(294\) | 2.45308 | 0.143066 | ||||||||
\(295\) | −0.568764 | −0.0331147 | ||||||||
\(296\) | −2.61071 | −0.151744 | ||||||||
\(297\) | −0.678230 | −0.0393549 | ||||||||
\(298\) | 40.5426 | 2.34857 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −20.0692 | −1.15869 | ||||||||
\(301\) | −1.78857 | −0.103092 | ||||||||
\(302\) | −49.9307 | −2.87319 | ||||||||
\(303\) | −1.50429 | −0.0864192 | ||||||||
\(304\) | 8.48945 | 0.486903 | ||||||||
\(305\) | 0.0690193 | 0.00395203 | ||||||||
\(306\) | −2.29352 | −0.131112 | ||||||||
\(307\) | 0.119003 | 0.00679184 | 0.00339592 | − | 0.999994i | \(-0.498919\pi\) | ||||
0.00339592 | + | 0.999994i | \(0.498919\pi\) | |||||||
\(308\) | −2.72485 | −0.155263 | ||||||||
\(309\) | −2.21721 | −0.126133 | ||||||||
\(310\) | 1.68586 | 0.0957506 | ||||||||
\(311\) | −31.4738 | −1.78472 | −0.892358 | − | 0.451327i | \(-0.850951\pi\) | ||||
−0.892358 | + | 0.451327i | \(0.850951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1243 | 0.798355 | 0.399178 | − | 0.916874i | \(-0.369296\pi\) | ||||
0.399178 | + | 0.916874i | \(0.369296\pi\) | |||||||
\(314\) | 37.1844 | 2.09844 | ||||||||
\(315\) | 0.0682999 | 0.00384826 | ||||||||
\(316\) | −56.4405 | −3.17503 | ||||||||
\(317\) | 18.6470 | 1.04732 | 0.523661 | − | 0.851927i | \(-0.324566\pi\) | ||||
0.523661 | + | 0.851927i | \(0.324566\pi\) | |||||||
\(318\) | −7.88652 | −0.442254 | ||||||||
\(319\) | −5.43565 | −0.304338 | ||||||||
\(320\) | −0.531820 | −0.0297296 | ||||||||
\(321\) | −19.7860 | −1.10434 | ||||||||
\(322\) | 10.5470 | 0.587759 | ||||||||
\(323\) | −1.93319 | −0.107565 | ||||||||
\(324\) | 4.01758 | 0.223199 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 41.3126 | 2.28810 | ||||||||
\(327\) | 1.71086 | 0.0946107 | ||||||||
\(328\) | 25.4282 | 1.40404 | ||||||||
\(329\) | 4.22889 | 0.233146 | ||||||||
\(330\) | −0.113634 | −0.00625535 | ||||||||
\(331\) | 22.0843 | 1.21386 | 0.606930 | − | 0.794755i | \(-0.292401\pi\) | ||||
0.606930 | + | 0.794755i | \(0.292401\pi\) | |||||||
\(332\) | −28.2601 | −1.55098 | ||||||||
\(333\) | −0.527492 | −0.0289064 | ||||||||
\(334\) | −4.05073 | −0.221646 | ||||||||
\(335\) | −0.498610 | −0.0272420 | ||||||||
\(336\) | 4.10580 | 0.223990 | ||||||||
\(337\) | −32.5355 | −1.77232 | −0.886161 | − | 0.463377i | \(-0.846638\pi\) | ||||
−0.886161 | + | 0.463377i | \(0.846638\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.6392 | −0.740782 | ||||||||
\(340\) | −0.256553 | −0.0139135 | ||||||||
\(341\) | −6.82447 | −0.369566 | ||||||||
\(342\) | 5.07216 | 0.274271 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.85215 | −0.477276 | ||||||||
\(345\) | 0.293654 | 0.0158098 | ||||||||
\(346\) | 60.7839 | 3.26776 | ||||||||
\(347\) | 4.41223 | 0.236861 | 0.118431 | − | 0.992962i | \(-0.462214\pi\) | ||||
0.118431 | + | 0.992962i | \(0.462214\pi\) | |||||||
\(348\) | 32.1987 | 1.72603 | ||||||||
\(349\) | 7.12421 | 0.381350 | 0.190675 | − | 0.981653i | \(-0.438932\pi\) | ||||
0.190675 | + | 0.981653i | \(0.438932\pi\) | |||||||
\(350\) | −12.2539 | −0.655000 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.117523 | −0.00626399 | ||||||||
\(353\) | 3.33664 | 0.177591 | 0.0887957 | − | 0.996050i | \(-0.471698\pi\) | ||||
0.0887957 | + | 0.996050i | \(0.471698\pi\) | |||||||
\(354\) | −20.4279 | −1.08573 | ||||||||
\(355\) | 0.676923 | 0.0359273 | ||||||||
\(356\) | −63.2941 | −3.35458 | ||||||||
\(357\) | −0.934958 | −0.0494832 | ||||||||
\(358\) | −15.4614 | −0.817158 | ||||||||
\(359\) | −24.5869 | −1.29765 | −0.648823 | − | 0.760940i | \(-0.724738\pi\) | ||||
−0.648823 | + | 0.760940i | \(0.724738\pi\) | |||||||
\(360\) | 0.338035 | 0.0178160 | ||||||||
\(361\) | −14.7247 | −0.774986 | ||||||||
\(362\) | −46.4779 | −2.44282 | ||||||||
\(363\) | −10.5400 | −0.553207 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.233759 | −0.0122355 | ||||||||
\(366\) | 2.47892 | 0.129575 | ||||||||
\(367\) | −15.0766 | −0.786991 | −0.393495 | − | 0.919327i | \(-0.628734\pi\) | ||||
−0.393495 | + | 0.919327i | \(0.628734\pi\) | |||||||
\(368\) | 17.6528 | 0.920216 | ||||||||
\(369\) | 5.13776 | 0.267461 | ||||||||
\(370\) | −0.0883785 | −0.00459458 | ||||||||
\(371\) | −3.21495 | −0.166912 | ||||||||
\(372\) | 40.4256 | 2.09597 | ||||||||
\(373\) | −25.2471 | −1.30725 | −0.653623 | − | 0.756820i | \(-0.726752\pi\) | ||||
−0.653623 | + | 0.756820i | \(0.726752\pi\) | |||||||
\(374\) | 1.55554 | 0.0804349 | ||||||||
\(375\) | −0.682680 | −0.0352535 | ||||||||
\(376\) | 20.9299 | 1.07938 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.45308 | 0.126173 | ||||||||
\(379\) | 24.0432 | 1.23502 | 0.617508 | − | 0.786565i | \(-0.288142\pi\) | ||||
0.617508 | + | 0.786565i | \(0.288142\pi\) | |||||||
\(380\) | 0.567370 | 0.0291055 | ||||||||
\(381\) | −8.00439 | −0.410077 | ||||||||
\(382\) | −21.5726 | −1.10375 | ||||||||
\(383\) | −4.53923 | −0.231944 | −0.115972 | − | 0.993252i | \(-0.536998\pi\) | ||||
−0.115972 | + | 0.993252i | \(0.536998\pi\) | |||||||
\(384\) | −19.4475 | −0.992427 | ||||||||
\(385\) | −0.0463231 | −0.00236084 | ||||||||
\(386\) | −15.2067 | −0.773998 | ||||||||
\(387\) | −1.78857 | −0.0909182 | ||||||||
\(388\) | 66.9749 | 3.40014 | ||||||||
\(389\) | 19.7847 | 1.00313 | 0.501563 | − | 0.865121i | \(-0.332758\pi\) | ||||
0.501563 | + | 0.865121i | \(0.332758\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.01983 | −0.203292 | ||||||||
\(392\) | 4.94928 | 0.249976 | ||||||||
\(393\) | −10.2912 | −0.519122 | ||||||||
\(394\) | −37.1478 | −1.87148 | ||||||||
\(395\) | −0.959502 | −0.0482778 | ||||||||
\(396\) | −2.72485 | −0.136929 | ||||||||
\(397\) | 10.4584 | 0.524892 | 0.262446 | − | 0.964947i | \(-0.415471\pi\) | ||||
0.262446 | + | 0.964947i | \(0.415471\pi\) | |||||||
\(398\) | 36.8874 | 1.84900 | ||||||||
\(399\) | 2.06767 | 0.103513 | ||||||||
\(400\) | −20.5099 | −1.02549 | ||||||||
\(401\) | 22.4236 | 1.11978 | 0.559891 | − | 0.828566i | \(-0.310843\pi\) | ||||
0.559891 | + | 0.828566i | \(0.310843\pi\) | |||||||
\(402\) | −17.9082 | −0.893180 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.04361 | −0.300681 | ||||||||
\(405\) | 0.0682999 | 0.00339385 | ||||||||
\(406\) | 19.6601 | 0.975713 | ||||||||
\(407\) | 0.357761 | 0.0177336 | ||||||||
\(408\) | −4.62737 | −0.229089 | ||||||||
\(409\) | 24.4405 | 1.20851 | 0.604253 | − | 0.796793i | \(-0.293472\pi\) | ||||
0.604253 | + | 0.796793i | \(0.293472\pi\) | |||||||
\(410\) | 0.860805 | 0.0425121 | ||||||||
\(411\) | −3.61956 | −0.178539 | ||||||||
\(412\) | −8.90782 | −0.438857 | ||||||||
\(413\) | −8.32746 | −0.409767 | ||||||||
\(414\) | 10.5470 | 0.518354 | ||||||||
\(415\) | −0.480429 | −0.0235833 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.21815 | 0.0596529 | ||||||||
\(418\) | −3.44009 | −0.168260 | ||||||||
\(419\) | 27.7961 | 1.35793 | 0.678965 | − | 0.734170i | \(-0.262429\pi\) | ||||
0.678965 | + | 0.734170i | \(0.262429\pi\) | |||||||
\(420\) | 0.274400 | 0.0133894 | ||||||||
\(421\) | −15.8324 | −0.771626 | −0.385813 | − | 0.922577i | \(-0.626079\pi\) | ||||
−0.385813 | + | 0.922577i | \(0.626079\pi\) | |||||||
\(422\) | 62.4900 | 3.04197 | ||||||||
\(423\) | 4.22889 | 0.205615 | ||||||||
\(424\) | −15.9117 | −0.772741 | ||||||||
\(425\) | 4.67043 | 0.226549 | ||||||||
\(426\) | 24.3125 | 1.17795 | ||||||||
\(427\) | 1.01053 | 0.0489031 | ||||||||
\(428\) | −79.4917 | −3.84238 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.299666 | −0.0144512 | ||||||||
\(431\) | 18.2098 | 0.877135 | 0.438567 | − | 0.898698i | \(-0.355486\pi\) | ||||
0.438567 | + | 0.898698i | \(0.355486\pi\) | |||||||
\(432\) | 4.10580 | 0.197540 | ||||||||
\(433\) | −9.40449 | −0.451951 | −0.225975 | − | 0.974133i | \(-0.572557\pi\) | ||||
−0.225975 | + | 0.974133i | \(0.572557\pi\) | |||||||
\(434\) | 24.6833 | 1.18483 | ||||||||
\(435\) | 0.547387 | 0.0262452 | ||||||||
\(436\) | 6.87351 | 0.329182 | ||||||||
\(437\) | 8.88991 | 0.425262 | ||||||||
\(438\) | −8.39574 | −0.401164 | ||||||||
\(439\) | −19.2339 | −0.917984 | −0.458992 | − | 0.888440i | \(-0.651789\pi\) | ||||
−0.458992 | + | 0.888440i | \(0.651789\pi\) | |||||||
\(440\) | −0.229266 | −0.0109298 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.40445 | −0.256773 | −0.128387 | − | 0.991724i | \(-0.540980\pi\) | ||||
−0.128387 | + | 0.991724i | \(0.540980\pi\) | |||||||
\(444\) | −2.11924 | −0.100575 | ||||||||
\(445\) | −1.07602 | −0.0510080 | ||||||||
\(446\) | −17.1876 | −0.813855 | ||||||||
\(447\) | 16.5273 | 0.781713 | ||||||||
\(448\) | −7.78654 | −0.367879 | ||||||||
\(449\) | −13.5534 | −0.639623 | −0.319812 | − | 0.947481i | \(-0.603620\pi\) | ||||
−0.319812 | + | 0.947481i | \(0.603620\pi\) | |||||||
\(450\) | −12.2539 | −0.577656 | ||||||||
\(451\) | −3.48458 | −0.164083 | ||||||||
\(452\) | −54.7968 | −2.57742 | ||||||||
\(453\) | −20.3543 | −0.956329 | ||||||||
\(454\) | −68.0902 | −3.19563 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.2335 | 0.479227 | ||||||||
\(457\) | −29.8229 | −1.39506 | −0.697528 | − | 0.716558i | \(-0.745717\pi\) | ||||
−0.697528 | + | 0.716558i | \(0.745717\pi\) | |||||||
\(458\) | 8.85588 | 0.413808 | ||||||||
\(459\) | −0.934958 | −0.0436401 | ||||||||
\(460\) | 1.17978 | 0.0550075 | ||||||||
\(461\) | 2.22803 | 0.103770 | 0.0518849 | − | 0.998653i | \(-0.483477\pi\) | ||||
0.0518849 | + | 0.998653i | \(0.483477\pi\) | |||||||
\(462\) | −1.66375 | −0.0774047 | ||||||||
\(463\) | 21.6086 | 1.00424 | 0.502118 | − | 0.864799i | \(-0.332554\pi\) | ||||
0.502118 | + | 0.864799i | \(0.332554\pi\) | |||||||
\(464\) | 32.9058 | 1.52761 | ||||||||
\(465\) | 0.687245 | 0.0318702 | ||||||||
\(466\) | −38.3112 | −1.77473 | ||||||||
\(467\) | −24.0068 | −1.11090 | −0.555452 | − | 0.831549i | \(-0.687455\pi\) | ||||
−0.555452 | + | 0.831549i | \(0.687455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.30030 | −0.337097 | ||||||||
\(470\) | 0.708528 | 0.0326819 | ||||||||
\(471\) | 15.1583 | 0.698456 | ||||||||
\(472\) | −41.2149 | −1.89707 | ||||||||
\(473\) | 1.21306 | 0.0557767 | ||||||||
\(474\) | −34.4617 | −1.58288 | ||||||||
\(475\) | −10.3287 | −0.473914 | ||||||||
\(476\) | −3.75627 | −0.172168 | ||||||||
\(477\) | −3.21495 | −0.147203 | ||||||||
\(478\) | 68.6446 | 3.13973 | ||||||||
\(479\) | 30.6921 | 1.40236 | 0.701179 | − | 0.712985i | \(-0.252657\pi\) | ||||
0.701179 | + | 0.712985i | \(0.252657\pi\) | |||||||
\(480\) | 0.0118349 | 0.000540187 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 63.7143 | 2.90211 | ||||||||
\(483\) | 4.29948 | 0.195633 | ||||||||
\(484\) | −42.3453 | −1.92479 | ||||||||
\(485\) | 1.13859 | 0.0517007 | ||||||||
\(486\) | 2.45308 | 0.111274 | ||||||||
\(487\) | −17.8707 | −0.809798 | −0.404899 | − | 0.914361i | \(-0.632693\pi\) | ||||
−0.404899 | + | 0.914361i | \(0.632693\pi\) | |||||||
\(488\) | 5.00142 | 0.226403 | ||||||||
\(489\) | 16.8412 | 0.761583 | ||||||||
\(490\) | 0.167545 | 0.00756890 | ||||||||
\(491\) | −13.5696 | −0.612388 | −0.306194 | − | 0.951969i | \(-0.599056\pi\) | ||||
−0.306194 | + | 0.951969i | \(0.599056\pi\) | |||||||
\(492\) | 20.6414 | 0.930585 | ||||||||
\(493\) | −7.49318 | −0.337476 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0463231 | −0.00208207 | ||||||||
\(496\) | 41.3132 | 1.85502 | ||||||||
\(497\) | 9.91104 | 0.444571 | ||||||||
\(498\) | −17.2552 | −0.773225 | ||||||||
\(499\) | 10.4240 | 0.466644 | 0.233322 | − | 0.972399i | \(-0.425040\pi\) | ||||
0.233322 | + | 0.972399i | \(0.425040\pi\) | |||||||
\(500\) | −2.74272 | −0.122658 | ||||||||
\(501\) | −1.65129 | −0.0737740 | ||||||||
\(502\) | −15.6635 | −0.699096 | ||||||||
\(503\) | 5.04813 | 0.225085 | 0.112543 | − | 0.993647i | \(-0.464101\pi\) | ||||
0.112543 | + | 0.993647i | \(0.464101\pi\) | |||||||
\(504\) | 4.94928 | 0.220459 | ||||||||
\(505\) | −0.102743 | −0.00457199 | ||||||||
\(506\) | −7.15326 | −0.318001 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.1583 | −1.42679 | ||||||||
\(509\) | −8.99245 | −0.398583 | −0.199292 | − | 0.979940i | \(-0.563864\pi\) | ||||
−0.199292 | + | 0.979940i | \(0.563864\pi\) | |||||||
\(510\) | −0.156647 | −0.00693646 | ||||||||
\(511\) | −3.42254 | −0.151404 | ||||||||
\(512\) | −39.9301 | −1.76468 | ||||||||
\(513\) | 2.06767 | 0.0912899 | ||||||||
\(514\) | −33.8962 | −1.49510 | ||||||||
\(515\) | −0.151435 | −0.00667303 | ||||||||
\(516\) | −7.18574 | −0.316334 | ||||||||
\(517\) | −2.86816 | −0.126141 | ||||||||
\(518\) | −1.29398 | −0.0568541 | ||||||||
\(519\) | 24.7787 | 1.08766 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.21666 | −0.403789 | −0.201895 | − | 0.979407i | \(-0.564710\pi\) | ||||
−0.201895 | + | 0.979407i | \(0.564710\pi\) | |||||||
\(522\) | 19.6601 | 0.860498 | ||||||||
\(523\) | 18.6656 | 0.816191 | 0.408096 | − | 0.912939i | \(-0.366193\pi\) | ||||
0.408096 | + | 0.912939i | \(0.366193\pi\) | |||||||
\(524\) | −41.3457 | −1.80620 | ||||||||
\(525\) | −4.99534 | −0.218014 | ||||||||
\(526\) | −27.8091 | −1.21253 | ||||||||
\(527\) | −9.40770 | −0.409806 | ||||||||
\(528\) | −2.78468 | −0.121188 | ||||||||
\(529\) | −4.51447 | −0.196281 | ||||||||
\(530\) | −0.538648 | −0.0233974 | ||||||||
\(531\) | −8.32746 | −0.361381 | ||||||||
\(532\) | 8.30704 | 0.360156 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −38.6465 | −1.67240 | ||||||||
\(535\) | −1.35138 | −0.0584252 | ||||||||
\(536\) | −36.1313 | −1.56063 | ||||||||
\(537\) | −6.30284 | −0.271988 | ||||||||
\(538\) | 51.5151 | 2.22097 | ||||||||
\(539\) | −0.678230 | −0.0292135 | ||||||||
\(540\) | 0.274400 | 0.0118083 | ||||||||
\(541\) | 16.3383 | 0.702437 | 0.351219 | − | 0.936293i | \(-0.385767\pi\) | ||||
0.351219 | + | 0.936293i | \(0.385767\pi\) | |||||||
\(542\) | 71.7402 | 3.08150 | ||||||||
\(543\) | −18.9468 | −0.813085 | ||||||||
\(544\) | −0.162008 | −0.00694605 | ||||||||
\(545\) | 0.116851 | 0.00500536 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.07719 | 0.217085 | 0.108542 | − | 0.994092i | \(-0.465382\pi\) | ||||
0.108542 | + | 0.994092i | \(0.465382\pi\) | |||||||
\(548\) | −14.5419 | −0.621197 | ||||||||
\(549\) | 1.01053 | 0.0431285 | ||||||||
\(550\) | 8.31099 | 0.354382 | ||||||||
\(551\) | 16.5713 | 0.705960 | ||||||||
\(552\) | 21.2793 | 0.905709 | ||||||||
\(553\) | −14.0484 | −0.597398 | ||||||||
\(554\) | 40.4845 | 1.72002 | ||||||||
\(555\) | −0.0360276 | −0.00152929 | ||||||||
\(556\) | 4.89401 | 0.207552 | ||||||||
\(557\) | 1.28369 | 0.0543917 | 0.0271959 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271959 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(558\) | 24.6833 | 1.04493 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.280426 | 0.0118502 | ||||||||
\(561\) | 0.634117 | 0.0267725 | ||||||||
\(562\) | 2.75138 | 0.116060 | ||||||||
\(563\) | 16.9798 | 0.715613 | 0.357807 | − | 0.933796i | \(-0.383525\pi\) | ||||
0.357807 | + | 0.933796i | \(0.383525\pi\) | |||||||
\(564\) | 16.9899 | 0.715404 | ||||||||
\(565\) | −0.931558 | −0.0391909 | ||||||||
\(566\) | 26.8396 | 1.12815 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 49.0525 | 2.05820 | ||||||||
\(569\) | −35.9628 | −1.50764 | −0.753820 | − | 0.657080i | \(-0.771791\pi\) | ||||
−0.753820 | + | 0.657080i | \(0.771791\pi\) | |||||||
\(570\) | 0.346428 | 0.0145103 | ||||||||
\(571\) | −20.6811 | −0.865475 | −0.432738 | − | 0.901520i | \(-0.642452\pi\) | ||||
−0.432738 | + | 0.901520i | \(0.642452\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.79410 | −0.367379 | ||||||||
\(574\) | 12.6033 | 0.526052 | ||||||||
\(575\) | −21.4773 | −0.895667 | ||||||||
\(576\) | −7.78654 | −0.324439 | ||||||||
\(577\) | −3.67781 | −0.153109 | −0.0765546 | − | 0.997065i | \(-0.524392\pi\) | ||||
−0.0765546 | + | 0.997065i | \(0.524392\pi\) | |||||||
\(578\) | −39.5579 | −1.64539 | ||||||||
\(579\) | −6.19901 | −0.257622 | ||||||||
\(580\) | 2.19917 | 0.0913156 | ||||||||
\(581\) | −7.03411 | −0.291824 | ||||||||
\(582\) | 40.8939 | 1.69511 | ||||||||
\(583\) | 2.18048 | 0.0903062 | ||||||||
\(584\) | −16.9391 | −0.700945 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.1460 | −1.57580 | ||||||||
\(587\) | 12.0433 | 0.497078 | 0.248539 | − | 0.968622i | \(-0.420050\pi\) | ||||
0.248539 | + | 0.968622i | \(0.420050\pi\) | |||||||
\(588\) | 4.01758 | 0.165682 | ||||||||
\(589\) | 20.8052 | 0.857265 | ||||||||
\(590\) | −1.39522 | −0.0574404 | ||||||||
\(591\) | −15.1434 | −0.622914 | ||||||||
\(592\) | −2.16578 | −0.0890129 | ||||||||
\(593\) | −24.4737 | −1.00501 | −0.502507 | − | 0.864573i | \(-0.667589\pi\) | ||||
−0.502507 | + | 0.864573i | \(0.667589\pi\) | |||||||
\(594\) | −1.66375 | −0.0682645 | ||||||||
\(595\) | −0.0638575 | −0.00261790 | ||||||||
\(596\) | 66.3996 | 2.71984 | ||||||||
\(597\) | 15.0372 | 0.615431 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.8012 | −0.890773 | −0.445387 | − | 0.895338i | \(-0.646934\pi\) | ||||
−0.445387 | + | 0.895338i | \(0.646934\pi\) | |||||||
\(600\) | −24.7233 | −1.00933 | ||||||||
\(601\) | 6.58213 | 0.268491 | 0.134245 | − | 0.990948i | \(-0.457139\pi\) | ||||
0.134245 | + | 0.990948i | \(0.457139\pi\) | |||||||
\(602\) | −4.38750 | −0.178821 | ||||||||
\(603\) | −7.30030 | −0.297291 | ||||||||
\(604\) | −81.7752 | −3.32738 | ||||||||
\(605\) | −0.719881 | −0.0292673 | ||||||||
\(606\) | −3.69014 | −0.149902 | ||||||||
\(607\) | 45.6933 | 1.85463 | 0.927317 | − | 0.374278i | \(-0.122109\pi\) | ||||
0.927317 | + | 0.374278i | \(0.122109\pi\) | |||||||
\(608\) | 0.358283 | 0.0145303 | ||||||||
\(609\) | 8.01446 | 0.324762 | ||||||||
\(610\) | 0.169310 | 0.00685515 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.75627 | −0.151838 | ||||||||
\(613\) | −41.9953 | −1.69618 | −0.848088 | − | 0.529855i | \(-0.822246\pi\) | ||||
−0.848088 | + | 0.529855i | \(0.822246\pi\) | |||||||
\(614\) | 0.291923 | 0.0117810 | ||||||||
\(615\) | 0.350908 | 0.0141500 | ||||||||
\(616\) | −3.35675 | −0.135247 | ||||||||
\(617\) | 24.4374 | 0.983811 | 0.491906 | − | 0.870648i | \(-0.336300\pi\) | ||||
0.491906 | + | 0.870648i | \(0.336300\pi\) | |||||||
\(618\) | −5.43898 | −0.218788 | ||||||||
\(619\) | 24.1245 | 0.969644 | 0.484822 | − | 0.874613i | \(-0.338884\pi\) | ||||
0.484822 | + | 0.874613i | \(0.338884\pi\) | |||||||
\(620\) | 2.76106 | 0.110887 | ||||||||
\(621\) | 4.29948 | 0.172532 | ||||||||
\(622\) | −77.2077 | −3.09575 | ||||||||
\(623\) | −15.7543 | −0.631182 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9300 | 0.997202 | ||||||||
\(626\) | 34.6481 | 1.38482 | ||||||||
\(627\) | −1.40236 | −0.0560048 | ||||||||
\(628\) | 60.8996 | 2.43016 | ||||||||
\(629\) | 0.493183 | 0.0196645 | ||||||||
\(630\) | 0.167545 | 0.00667514 | ||||||||
\(631\) | 23.5737 | 0.938456 | 0.469228 | − | 0.883077i | \(-0.344532\pi\) | ||||
0.469228 | + | 0.883077i | \(0.344532\pi\) | |||||||
\(632\) | −69.5294 | −2.76573 | ||||||||
\(633\) | 25.4741 | 1.01251 | ||||||||
\(634\) | 45.7426 | 1.81667 | ||||||||
\(635\) | −0.546699 | −0.0216951 | ||||||||
\(636\) | −12.9163 | −0.512166 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.3341 | −0.527901 | ||||||||
\(639\) | 9.91104 | 0.392075 | ||||||||
\(640\) | −1.32826 | −0.0525042 | ||||||||
\(641\) | 36.8958 | 1.45730 | 0.728648 | − | 0.684889i | \(-0.240149\pi\) | ||||
0.728648 | + | 0.684889i | \(0.240149\pi\) | |||||||
\(642\) | −48.5365 | −1.91558 | ||||||||
\(643\) | 25.1777 | 0.992911 | 0.496455 | − | 0.868062i | \(-0.334635\pi\) | ||||
0.496455 | + | 0.868062i | \(0.334635\pi\) | |||||||
\(644\) | 17.2735 | 0.680672 | ||||||||
\(645\) | −0.122159 | −0.00481002 | ||||||||
\(646\) | −4.74225 | −0.186581 | ||||||||
\(647\) | 5.00172 | 0.196638 | 0.0983189 | − | 0.995155i | \(-0.468653\pi\) | ||||
0.0983189 | + | 0.995155i | \(0.468653\pi\) | |||||||
\(648\) | 4.94928 | 0.194426 | ||||||||
\(649\) | 5.64794 | 0.221701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0622 | 0.394367 | ||||||||
\(652\) | 67.6607 | 2.64980 | ||||||||
\(653\) | −27.8545 | −1.09003 | −0.545015 | − | 0.838426i | \(-0.683476\pi\) | ||||
−0.545015 | + | 0.838426i | \(0.683476\pi\) | |||||||
\(654\) | 4.19686 | 0.164110 | ||||||||
\(655\) | −0.702887 | −0.0274641 | ||||||||
\(656\) | 21.0946 | 0.823606 | ||||||||
\(657\) | −3.42254 | −0.133526 | ||||||||
\(658\) | 10.3738 | 0.404412 | ||||||||
\(659\) | 4.79936 | 0.186957 | 0.0934783 | − | 0.995621i | \(-0.470201\pi\) | ||||
0.0934783 | + | 0.995621i | \(0.470201\pi\) | |||||||
\(660\) | −0.186107 | −0.00724419 | ||||||||
\(661\) | −3.05390 | −0.118783 | −0.0593914 | − | 0.998235i | \(-0.518916\pi\) | ||||
−0.0593914 | + | 0.998235i | \(0.518916\pi\) | |||||||
\(662\) | 54.1744 | 2.10555 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34.8138 | −1.35104 | ||||||||
\(665\) | 0.141222 | 0.00547634 | ||||||||
\(666\) | −1.29398 | −0.0501406 | ||||||||
\(667\) | 34.4580 | 1.33422 | ||||||||
\(668\) | −6.63418 | −0.256684 | ||||||||
\(669\) | −7.00654 | −0.270888 | ||||||||
\(670\) | −1.22313 | −0.0472535 | ||||||||
\(671\) | −0.685375 | −0.0264586 | ||||||||
\(672\) | 0.173279 | 0.00668437 | ||||||||
\(673\) | 12.7900 | 0.493016 | 0.246508 | − | 0.969141i | \(-0.420717\pi\) | ||||
0.246508 | + | 0.969141i | \(0.420717\pi\) | |||||||
\(674\) | −79.8121 | −3.07425 | ||||||||
\(675\) | −4.99534 | −0.192271 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6803 | 0.833240 | 0.416620 | − | 0.909081i | \(-0.363215\pi\) | ||||
0.416620 | + | 0.909081i | \(0.363215\pi\) | |||||||
\(678\) | −33.4581 | −1.28495 | ||||||||
\(679\) | 16.6705 | 0.639753 | ||||||||
\(680\) | −0.316049 | −0.0121199 | ||||||||
\(681\) | −27.7571 | −1.06365 | ||||||||
\(682\) | −16.7409 | −0.641043 | ||||||||
\(683\) | 33.9669 | 1.29971 | 0.649854 | − | 0.760059i | \(-0.274830\pi\) | ||||
0.649854 | + | 0.760059i | \(0.274830\pi\) | |||||||
\(684\) | 8.30704 | 0.317628 | ||||||||
\(685\) | −0.247215 | −0.00944561 | ||||||||
\(686\) | 2.45308 | 0.0936589 | ||||||||
\(687\) | 3.61011 | 0.137734 | ||||||||
\(688\) | −7.34352 | −0.279969 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.720355 | 0.0274235 | ||||||||
\(691\) | −43.2170 | −1.64405 | −0.822026 | − | 0.569450i | \(-0.807156\pi\) | ||||
−0.822026 | + | 0.569450i | \(0.807156\pi\) | |||||||
\(692\) | 99.5503 | 3.78433 | ||||||||
\(693\) | −0.678230 | −0.0257638 | ||||||||
\(694\) | 10.8235 | 0.410856 | ||||||||
\(695\) | 0.0831993 | 0.00315593 | ||||||||
\(696\) | 39.6658 | 1.50353 | ||||||||
\(697\) | −4.80359 | −0.181949 | ||||||||
\(698\) | 17.4762 | 0.661485 | ||||||||
\(699\) | −15.6176 | −0.590713 | ||||||||
\(700\) | −20.0692 | −0.758543 | ||||||||
\(701\) | −0.456718 | −0.0172500 | −0.00862500 | − | 0.999963i | \(-0.502745\pi\) | ||||
−0.00862500 | + | 0.999963i | \(0.502745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.09068 | −0.0411358 | ||||||||
\(704\) | 5.28107 | 0.199038 | ||||||||
\(705\) | 0.288832 | 0.0108781 | ||||||||
\(706\) | 8.18503 | 0.308048 | ||||||||
\(707\) | −1.50429 | −0.0565746 | ||||||||
\(708\) | −33.4562 | −1.25736 | ||||||||
\(709\) | 14.8844 | 0.558994 | 0.279497 | − | 0.960147i | \(-0.409832\pi\) | ||||
0.279497 | + | 0.960147i | \(0.409832\pi\) | |||||||
\(710\) | 1.66054 | 0.0623191 | ||||||||
\(711\) | −14.0484 | −0.526855 | ||||||||
\(712\) | −77.9724 | −2.92214 | ||||||||
\(713\) | 43.2621 | 1.62018 | ||||||||
\(714\) | −2.29352 | −0.0858330 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.3222 | −0.946335 | ||||||||
\(717\) | 27.9831 | 1.04505 | ||||||||
\(718\) | −60.3135 | −2.25088 | ||||||||
\(719\) | 9.97486 | 0.372000 | 0.186000 | − | 0.982550i | \(-0.440448\pi\) | ||||
0.186000 | + | 0.982550i | \(0.440448\pi\) | |||||||
\(720\) | 0.280426 | 0.0104509 | ||||||||
\(721\) | −2.21721 | −0.0825732 | ||||||||
\(722\) | −36.1209 | −1.34428 | ||||||||
\(723\) | 25.9732 | 0.965955 | ||||||||
\(724\) | −76.1203 | −2.82899 | ||||||||
\(725\) | −40.0349 | −1.48686 | ||||||||
\(726\) | −25.8554 | −0.959585 | ||||||||
\(727\) | 10.4392 | 0.387169 | 0.193585 | − | 0.981084i | \(-0.437989\pi\) | ||||
0.193585 | + | 0.981084i | \(0.437989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.573428 | −0.0212235 | ||||||||
\(731\) | 1.67224 | 0.0618500 | ||||||||
\(732\) | 4.05990 | 0.150058 | ||||||||
\(733\) | 22.7887 | 0.841718 | 0.420859 | − | 0.907126i | \(-0.361729\pi\) | ||||
0.420859 | + | 0.907126i | \(0.361729\pi\) | |||||||
\(734\) | −36.9840 | −1.36510 | ||||||||
\(735\) | 0.0682999 | 0.00251928 | ||||||||
\(736\) | 0.745008 | 0.0274614 | ||||||||
\(737\) | 4.95129 | 0.182383 | ||||||||
\(738\) | 12.6033 | 0.463934 | ||||||||
\(739\) | −42.2796 | −1.55528 | −0.777640 | − | 0.628710i | \(-0.783583\pi\) | ||||
−0.777640 | + | 0.628710i | \(0.783583\pi\) | |||||||
\(740\) | −0.144744 | −0.00532089 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.88652 | −0.289523 | ||||||||
\(743\) | −6.98202 | −0.256145 | −0.128073 | − | 0.991765i | \(-0.540879\pi\) | ||||
−0.128073 | + | 0.991765i | \(0.540879\pi\) | |||||||
\(744\) | 49.8005 | 1.82577 | ||||||||
\(745\) | 1.12881 | 0.0413564 | ||||||||
\(746\) | −61.9331 | −2.26753 | ||||||||
\(747\) | −7.03411 | −0.257365 | ||||||||
\(748\) | 2.54762 | 0.0931501 | ||||||||
\(749\) | −19.7860 | −0.722963 | ||||||||
\(750\) | −1.67467 | −0.0611502 | ||||||||
\(751\) | 35.5530 | 1.29735 | 0.648673 | − | 0.761067i | \(-0.275324\pi\) | ||||
0.648673 | + | 0.761067i | \(0.275324\pi\) | |||||||
\(752\) | 17.3630 | 0.633162 | ||||||||
\(753\) | −6.38525 | −0.232691 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.39020 | −0.0505945 | ||||||||
\(756\) | 4.01758 | 0.146118 | ||||||||
\(757\) | −13.1171 | −0.476749 | −0.238374 | − | 0.971173i | \(-0.576615\pi\) | ||||
−0.238374 | + | 0.971173i | \(0.576615\pi\) | |||||||
\(758\) | 58.9798 | 2.14224 | ||||||||
\(759\) | −2.91604 | −0.105845 | ||||||||
\(760\) | 0.698946 | 0.0253534 | ||||||||
\(761\) | −3.28595 | −0.119116 | −0.0595578 | − | 0.998225i | \(-0.518969\pi\) | ||||
−0.0595578 | + | 0.998225i | \(0.518969\pi\) | |||||||
\(762\) | −19.6354 | −0.711315 | ||||||||
\(763\) | 1.71086 | 0.0619372 | ||||||||
\(764\) | −35.3310 | −1.27823 | ||||||||
\(765\) | −0.0638575 | −0.00230877 | ||||||||
\(766\) | −11.1351 | −0.402327 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −32.1332 | −1.15951 | ||||||||
\(769\) | 1.28809 | 0.0464498 | 0.0232249 | − | 0.999730i | \(-0.492607\pi\) | ||||
0.0232249 | + | 0.999730i | \(0.492607\pi\) | |||||||
\(770\) | −0.113634 | −0.00409508 | ||||||||
\(771\) | −13.8179 | −0.497638 | ||||||||
\(772\) | −24.9051 | −0.896352 | ||||||||
\(773\) | 22.0147 | 0.791813 | 0.395907 | − | 0.918291i | \(-0.370430\pi\) | ||||
0.395907 | + | 0.918291i | \(0.370430\pi\) | |||||||
\(774\) | −4.38750 | −0.157706 | ||||||||
\(775\) | −50.2639 | −1.80553 | ||||||||
\(776\) | 82.5068 | 2.96182 | ||||||||
\(777\) | −0.527492 | −0.0189237 | ||||||||
\(778\) | 48.5335 | 1.74001 | ||||||||
\(779\) | 10.6232 | 0.380615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.72197 | −0.240531 | ||||||||
\(782\) | −9.86096 | −0.352627 | ||||||||
\(783\) | 8.01446 | 0.286413 | ||||||||
\(784\) | 4.10580 | 0.146636 | ||||||||
\(785\) | 1.03531 | 0.0369517 | ||||||||
\(786\) | −25.2451 | −0.900462 | ||||||||
\(787\) | −5.09721 | −0.181696 | −0.0908479 | − | 0.995865i | \(-0.528958\pi\) | ||||
−0.0908479 | + | 0.995865i | \(0.528958\pi\) | |||||||
\(788\) | −60.8397 | −2.16732 | ||||||||
\(789\) | −11.3364 | −0.403587 | ||||||||
\(790\) | −2.35373 | −0.0837420 | ||||||||
\(791\) | −13.6392 | −0.484955 | ||||||||
\(792\) | −3.35675 | −0.119277 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 25.6553 | 0.910471 | ||||||||
\(795\) | −0.219581 | −0.00778773 | ||||||||
\(796\) | 60.4132 | 2.14129 | ||||||||
\(797\) | −41.5555 | −1.47197 | −0.735986 | − | 0.676997i | \(-0.763281\pi\) | ||||
−0.735986 | + | 0.676997i | \(0.763281\pi\) | |||||||
\(798\) | 5.07216 | 0.179552 | ||||||||
\(799\) | −3.95383 | −0.139877 | ||||||||
\(800\) | −0.865585 | −0.0306031 | ||||||||
\(801\) | −15.7543 | −0.556650 | ||||||||
\(802\) | 55.0068 | 1.94236 | ||||||||
\(803\) | 2.32127 | 0.0819158 | ||||||||
\(804\) | −29.3296 | −1.03437 | ||||||||
\(805\) | 0.293654 | 0.0103499 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.0002 | 0.739242 | ||||||||
\(808\) | −7.44515 | −0.261920 | ||||||||
\(809\) | 22.0300 | 0.774532 | 0.387266 | − | 0.921968i | \(-0.373419\pi\) | ||||
0.387266 | + | 0.921968i | \(0.373419\pi\) | |||||||
\(810\) | 0.167545 | 0.00588692 | ||||||||
\(811\) | 20.0797 | 0.705094 | 0.352547 | − | 0.935794i | \(-0.385316\pi\) | ||||
0.352547 | + | 0.935794i | \(0.385316\pi\) | |||||||
\(812\) | 32.1987 | 1.12995 | ||||||||
\(813\) | 29.2450 | 1.02567 | ||||||||
\(814\) | 0.877615 | 0.0307604 | ||||||||
\(815\) | 1.15025 | 0.0402915 | ||||||||
\(816\) | −3.83875 | −0.134383 | ||||||||
\(817\) | −3.69818 | −0.129383 | ||||||||
\(818\) | 59.9544 | 2.09626 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.40980 | 0.0492324 | ||||||||
\(821\) | −13.8647 | −0.483882 | −0.241941 | − | 0.970291i | \(-0.577784\pi\) | ||||
−0.241941 | + | 0.970291i | \(0.577784\pi\) | |||||||
\(822\) | −8.87904 | −0.309692 | ||||||||
\(823\) | −14.7804 | −0.515213 | −0.257606 | − | 0.966250i | \(-0.582934\pi\) | ||||
−0.257606 | + | 0.966250i | \(0.582934\pi\) | |||||||
\(824\) | −10.9736 | −0.382283 | ||||||||
\(825\) | 3.38799 | 0.117955 | ||||||||
\(826\) | −20.4279 | −0.710777 | ||||||||
\(827\) | −26.2554 | −0.912988 | −0.456494 | − | 0.889726i | \(-0.650895\pi\) | ||||
−0.456494 | + | 0.889726i | \(0.650895\pi\) | |||||||
\(828\) | 17.2735 | 0.600296 | ||||||||
\(829\) | 14.3216 | 0.497408 | 0.248704 | − | 0.968579i | \(-0.419995\pi\) | ||||
0.248704 | + | 0.968579i | \(0.419995\pi\) | |||||||
\(830\) | −1.17853 | −0.0409073 | ||||||||
\(831\) | 16.5036 | 0.572502 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.934958 | −0.0323944 | ||||||||
\(834\) | 2.98821 | 0.103473 | ||||||||
\(835\) | −0.112783 | −0.00390301 | ||||||||
\(836\) | −5.63409 | −0.194859 | ||||||||
\(837\) | 10.0622 | 0.347799 | ||||||||
\(838\) | 68.1861 | 2.35545 | ||||||||
\(839\) | 34.5482 | 1.19274 | 0.596368 | − | 0.802711i | \(-0.296610\pi\) | ||||
0.596368 | + | 0.802711i | \(0.296610\pi\) | |||||||
\(840\) | 0.338035 | 0.0116633 | ||||||||
\(841\) | 35.2315 | 1.21488 | ||||||||
\(842\) | −38.8382 | −1.33845 | ||||||||
\(843\) | 1.12161 | 0.0386302 | ||||||||
\(844\) | 102.344 | 3.52284 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.3738 | 0.356658 | ||||||||
\(847\) | −10.5400 | −0.362159 | ||||||||
\(848\) | −13.2000 | −0.453288 | ||||||||
\(849\) | 10.9412 | 0.375501 | ||||||||
\(850\) | 11.4569 | 0.392969 | ||||||||
\(851\) | −2.26794 | −0.0777440 | ||||||||
\(852\) | 39.8184 | 1.36416 | ||||||||
\(853\) | −40.2048 | −1.37659 | −0.688294 | − | 0.725432i | \(-0.741640\pi\) | ||||
−0.688294 | + | 0.725432i | \(0.741640\pi\) | |||||||
\(854\) | 2.47892 | 0.0848267 | ||||||||
\(855\) | 0.141222 | 0.00482968 | ||||||||
\(856\) | −97.9263 | −3.34705 | ||||||||
\(857\) | 24.2988 | 0.830031 | 0.415015 | − | 0.909814i | \(-0.363776\pi\) | ||||
0.415015 | + | 0.909814i | \(0.363776\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.8589 | −1.32585 | −0.662924 | − | 0.748687i | \(-0.730685\pi\) | ||||
−0.662924 | + | 0.748687i | \(0.730685\pi\) | |||||||
\(860\) | −0.490785 | −0.0167356 | ||||||||
\(861\) | 5.13776 | 0.175094 | ||||||||
\(862\) | 44.6700 | 1.52147 | ||||||||
\(863\) | 30.0838 | 1.02406 | 0.512032 | − | 0.858966i | \(-0.328893\pi\) | ||||
0.512032 | + | 0.858966i | \(0.328893\pi\) | |||||||
\(864\) | 0.173279 | 0.00589506 | ||||||||
\(865\) | 1.69238 | 0.0575426 | ||||||||
\(866\) | −23.0699 | −0.783948 | ||||||||
\(867\) | −16.1259 | −0.547663 | ||||||||
\(868\) | 40.4256 | 1.37213 | ||||||||
\(869\) | 9.52804 | 0.323216 | ||||||||
\(870\) | 1.34278 | 0.0455245 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.46752 | 0.286746 | ||||||||
\(873\) | 16.6705 | 0.564209 | ||||||||
\(874\) | 21.8076 | 0.737654 | ||||||||
\(875\) | −0.682680 | −0.0230788 | ||||||||
\(876\) | −13.7503 | −0.464580 | ||||||||
\(877\) | 14.7532 | 0.498179 | 0.249090 | − | 0.968480i | \(-0.419869\pi\) | ||||
0.249090 | + | 0.968480i | \(0.419869\pi\) | |||||||
\(878\) | −47.1822 | −1.59232 | ||||||||
\(879\) | −15.5503 | −0.524498 | ||||||||
\(880\) | −0.190193 | −0.00641141 | ||||||||
\(881\) | 34.5537 | 1.16414 | 0.582072 | − | 0.813137i | \(-0.302242\pi\) | ||||
0.582072 | + | 0.813137i | \(0.302242\pi\) | |||||||
\(882\) | 2.45308 | 0.0825994 | ||||||||
\(883\) | 7.47582 | 0.251581 | 0.125791 | − | 0.992057i | \(-0.459853\pi\) | ||||
0.125791 | + | 0.992057i | \(0.459853\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.568764 | −0.0191188 | ||||||||
\(886\) | −13.2575 | −0.445396 | ||||||||
\(887\) | −20.3565 | −0.683503 | −0.341752 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341752 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(888\) | −2.61071 | −0.0876095 | ||||||||
\(889\) | −8.00439 | −0.268459 | ||||||||
\(890\) | −2.63955 | −0.0884778 | ||||||||
\(891\) | −0.678230 | −0.0227216 | ||||||||
\(892\) | −28.1493 | −0.942509 | ||||||||
\(893\) | 8.74395 | 0.292605 | ||||||||
\(894\) | 40.5426 | 1.35595 | ||||||||
\(895\) | −0.430484 | −0.0143895 | ||||||||
\(896\) | −19.4475 | −0.649696 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.2475 | −1.10948 | ||||||||
\(899\) | 80.6428 | 2.68959 | ||||||||
\(900\) | −20.0692 | −0.668972 | ||||||||
\(901\) | 3.00585 | 0.100139 | ||||||||
\(902\) | −8.54795 | −0.284616 | ||||||||
\(903\) | −1.78857 | −0.0595200 | ||||||||
\(904\) | −67.5044 | −2.24516 | ||||||||
\(905\) | −1.29406 | −0.0430161 | ||||||||
\(906\) | −49.9307 | −1.65884 | ||||||||
\(907\) | −9.91111 | −0.329093 | −0.164546 | − | 0.986369i | \(-0.552616\pi\) | ||||
−0.164546 | + | 0.986369i | \(0.552616\pi\) | |||||||
\(908\) | −111.516 | −3.70080 | ||||||||
\(909\) | −1.50429 | −0.0498941 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.7109 | −0.387998 | −0.193999 | − | 0.981002i | \(-0.562146\pi\) | ||||
−0.193999 | + | 0.981002i | \(0.562146\pi\) | |||||||
\(912\) | 8.48945 | 0.281114 | ||||||||
\(913\) | 4.77075 | 0.157889 | ||||||||
\(914\) | −73.1578 | −2.41984 | ||||||||
\(915\) | 0.0690193 | 0.00228171 | ||||||||
\(916\) | 14.5039 | 0.479223 | ||||||||
\(917\) | −10.2912 | −0.339845 | ||||||||
\(918\) | −2.29352 | −0.0756976 | ||||||||
\(919\) | −20.7949 | −0.685962 | −0.342981 | − | 0.939342i | \(-0.611437\pi\) | ||||
−0.342981 | + | 0.939342i | \(0.611437\pi\) | |||||||
\(920\) | 1.45338 | 0.0479164 | ||||||||
\(921\) | 0.119003 | 0.00392127 | ||||||||
\(922\) | 5.46553 | 0.179998 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.72485 | −0.0896409 | ||||||||
\(925\) | 2.63500 | 0.0866382 | ||||||||
\(926\) | 53.0075 | 1.74194 | ||||||||
\(927\) | −2.21721 | −0.0728227 | ||||||||
\(928\) | 1.38873 | 0.0455875 | ||||||||
\(929\) | −51.1824 | −1.67924 | −0.839620 | − | 0.543174i | \(-0.817222\pi\) | ||||
−0.839620 | + | 0.543174i | \(0.817222\pi\) | |||||||
\(930\) | 1.68586 | 0.0552816 | ||||||||
\(931\) | 2.06767 | 0.0677652 | ||||||||
\(932\) | −62.7451 | −2.05528 | ||||||||
\(933\) | −31.4738 | −1.03041 | ||||||||
\(934\) | −58.8906 | −1.92696 | ||||||||
\(935\) | 0.0433101 | 0.00141639 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1728 | 1.50840 | 0.754200 | − | 0.656645i | \(-0.228025\pi\) | ||||
0.754200 | + | 0.656645i | \(0.228025\pi\) | |||||||
\(938\) | −17.9082 | −0.584723 | ||||||||
\(939\) | 14.1243 | 0.460931 | ||||||||
\(940\) | 1.16041 | 0.0378483 | ||||||||
\(941\) | −31.6254 | −1.03096 | −0.515480 | − | 0.856902i | \(-0.672386\pi\) | ||||
−0.515480 | + | 0.856902i | \(0.672386\pi\) | |||||||
\(942\) | 37.1844 | 1.21153 | ||||||||
\(943\) | 22.0897 | 0.719339 | ||||||||
\(944\) | −34.1909 | −1.11282 | ||||||||
\(945\) | 0.0682999 | 0.00222180 | ||||||||
\(946\) | 2.97574 | 0.0967496 | ||||||||
\(947\) | −19.2256 | −0.624747 | −0.312373 | − | 0.949959i | \(-0.601124\pi\) | ||||
−0.312373 | + | 0.949959i | \(0.601124\pi\) | |||||||
\(948\) | −56.4405 | −1.83310 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −25.3371 | −0.822045 | ||||||||
\(951\) | 18.6470 | 0.604671 | ||||||||
\(952\) | −4.62737 | −0.149974 | ||||||||
\(953\) | 14.4415 | 0.467806 | 0.233903 | − | 0.972260i | \(-0.424850\pi\) | ||||
0.233903 | + | 0.972260i | \(0.424850\pi\) | |||||||
\(954\) | −7.88652 | −0.255336 | ||||||||
\(955\) | −0.600636 | −0.0194361 | ||||||||
\(956\) | 112.424 | 3.63606 | ||||||||
\(957\) | −5.43565 | −0.175710 | ||||||||
\(958\) | 75.2901 | 2.43251 | ||||||||
\(959\) | −3.61956 | −0.116882 | ||||||||
\(960\) | −0.531820 | −0.0171644 | ||||||||
\(961\) | 70.2471 | 2.26604 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.7860 | −0.637593 | ||||||||
\(964\) | 104.350 | 3.36087 | ||||||||
\(965\) | −0.423392 | −0.0136295 | ||||||||
\(966\) | 10.5470 | 0.339343 | ||||||||
\(967\) | 3.28457 | 0.105625 | 0.0528123 | − | 0.998604i | \(-0.483181\pi\) | ||||
0.0528123 | + | 0.998604i | \(0.483181\pi\) | |||||||
\(968\) | −52.1655 | −1.67666 | ||||||||
\(969\) | −1.93319 | −0.0621029 | ||||||||
\(970\) | 2.79305 | 0.0896794 | ||||||||
\(971\) | −15.9721 | −0.512568 | −0.256284 | − | 0.966601i | \(-0.582498\pi\) | ||||
−0.256284 | + | 0.966601i | \(0.582498\pi\) | |||||||
\(972\) | 4.01758 | 0.128864 | ||||||||
\(973\) | 1.21815 | 0.0390520 | ||||||||
\(974\) | −43.8382 | −1.40467 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.14905 | 0.132808 | ||||||||
\(977\) | −21.9335 | −0.701714 | −0.350857 | − | 0.936429i | \(-0.614110\pi\) | ||||
−0.350857 | + | 0.936429i | \(0.614110\pi\) | |||||||
\(978\) | 41.3126 | 1.32103 | ||||||||
\(979\) | 10.6850 | 0.341495 | ||||||||
\(980\) | 0.274400 | 0.00876540 | ||||||||
\(981\) | 1.71086 | 0.0546235 | ||||||||
\(982\) | −33.2873 | −1.06224 | ||||||||
\(983\) | −22.0867 | −0.704456 | −0.352228 | − | 0.935914i | \(-0.614576\pi\) | ||||
−0.352228 | + | 0.935914i | \(0.614576\pi\) | |||||||
\(984\) | 25.4282 | 0.810622 | ||||||||
\(985\) | −1.03429 | −0.0329552 | ||||||||
\(986\) | −18.3814 | −0.585382 | ||||||||
\(987\) | 4.22889 | 0.134607 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.68993 | −0.244526 | ||||||||
\(990\) | −0.113634 | −0.00361153 | ||||||||
\(991\) | 4.36458 | 0.138645 | 0.0693227 | − | 0.997594i | \(-0.477916\pi\) | ||||
0.0693227 | + | 0.997594i | \(0.477916\pi\) | |||||||
\(992\) | 1.74356 | 0.0553580 | ||||||||
\(993\) | 22.0843 | 0.700823 | ||||||||
\(994\) | 24.3125 | 0.771147 | ||||||||
\(995\) | 1.02704 | 0.0325593 | ||||||||
\(996\) | −28.2601 | −0.895456 | ||||||||
\(997\) | 55.3319 | 1.75238 | 0.876189 | − | 0.481967i | \(-0.160078\pi\) | ||||
0.876189 | + | 0.481967i | \(0.160078\pi\) | |||||||
\(998\) | 25.5710 | 0.809435 | ||||||||
\(999\) | −0.527492 | −0.0166891 |
(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 | 3549.2.a.bd.1.7 | 8 | ||
13.2 | odd | 12 | 273.2.bd.a.43.8 | ✓ | 16 | ||
13.7 | odd | 12 | 273.2.bd.a.127.8 | yes | 16 | ||
13.12 | even | 2 | 3549.2.a.bb.1.2 | 8 | |||
39.2 | even | 12 | 819.2.ct.b.316.1 | 16 | |||
39.20 | even | 12 | 819.2.ct.b.127.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bd.a.43.8 | ✓ | 16 | 13.2 | odd | 12 | ||
273.2.bd.a.127.8 | yes | 16 | 13.7 | odd | 12 | ||
819.2.ct.b.127.1 | 16 | 39.20 | even | 12 | |||
819.2.ct.b.316.1 | 16 | 39.2 | even | 12 | |||
3549.2.a.bb.1.2 | 8 | 13.12 | even | 2 | |||
3549.2.a.bd.1.7 | 8 | 1.1 | even | 1 | trivial |