Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.3352656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 6x - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.81031\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.81031 | 1.28009 | 0.640043 | − | 0.768339i | \(-0.278917\pi\) | ||||
0.640043 | + | 0.768339i | \(0.278917\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.27724 | 0.638619 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.42503 | 1.67250 | 0.836252 | − | 0.548346i | \(-0.184742\pi\) | ||||
0.836252 | + | 0.548346i | \(0.184742\pi\) | |||||||
\(8\) | −1.30843 | −0.462598 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.81031 | 0.572472 | ||||||||
\(11\) | −1.61471 | −0.486854 | −0.243427 | − | 0.969919i | \(-0.578272\pi\) | ||||
−0.243427 | + | 0.969919i | \(0.578272\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 8.01069 | 2.14095 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.92314 | −1.23078 | ||||||||
\(17\) | 1.25584 | 0.304585 | 0.152293 | − | 0.988335i | \(-0.451334\pi\) | ||||
0.152293 | + | 0.988335i | \(0.451334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.722761 | 0.165813 | 0.0829064 | − | 0.996557i | \(-0.473580\pi\) | ||||
0.0829064 | + | 0.996557i | \(0.473580\pi\) | |||||||
\(20\) | 1.27724 | 0.285599 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.92314 | −0.623215 | ||||||||
\(23\) | −1.30843 | −0.272826 | −0.136413 | − | 0.990652i | \(-0.543557\pi\) | ||||
−0.136413 | + | 0.990652i | \(0.543557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.65182 | 1.06809 | ||||||||
\(29\) | −1.16064 | −0.215525 | −0.107762 | − | 0.994177i | \(-0.534369\pi\) | ||||
−0.107762 | + | 0.994177i | \(0.534369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.64968 | 0.296291 | 0.148145 | − | 0.988966i | \(-0.452670\pi\) | ||||
0.148145 | + | 0.988966i | \(0.452670\pi\) | |||||||
\(32\) | −6.29558 | −1.11291 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.27346 | 0.389895 | ||||||||
\(35\) | 4.42503 | 0.747966 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.92314 | −0.809359 | −0.404680 | − | 0.914459i | \(-0.632617\pi\) | ||||
−0.404680 | + | 0.914459i | \(0.632617\pi\) | |||||||
\(38\) | 1.30843 | 0.212255 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.30843 | −0.206880 | ||||||||
\(41\) | 8.56517 | 1.33765 | 0.668827 | − | 0.743418i | \(-0.266797\pi\) | ||||
0.668827 | + | 0.743418i | \(0.266797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.15370 | 1.09093 | 0.545465 | − | 0.838134i | \(-0.316353\pi\) | ||||
0.545465 | + | 0.838134i | \(0.316353\pi\) | |||||||
\(44\) | −2.06237 | −0.310915 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.36866 | −0.349240 | ||||||||
\(47\) | 12.3482 | 1.80117 | 0.900583 | − | 0.434685i | \(-0.143140\pi\) | ||||
0.900583 | + | 0.434685i | \(0.143140\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.5809 | 1.79727 | ||||||||
\(50\) | 1.81031 | 0.256017 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4045 | 1.84125 | 0.920627 | − | 0.390443i | \(-0.127678\pi\) | ||||
0.920627 | + | 0.390443i | \(0.127678\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.61471 | −0.217728 | ||||||||
\(56\) | −5.78982 | −0.773697 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.10112 | −0.275890 | ||||||||
\(59\) | 4.28489 | 0.557845 | 0.278922 | − | 0.960314i | \(-0.410023\pi\) | ||||
0.278922 | + | 0.960314i | \(0.410023\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.64968 | 0.723367 | 0.361684 | − | 0.932301i | \(-0.382202\pi\) | ||||
0.361684 | + | 0.932301i | \(0.382202\pi\) | |||||||
\(62\) | 2.98644 | 0.379278 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.55070 | −0.193837 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.218735 | −0.0267227 | −0.0133613 | − | 0.999911i | \(-0.504253\pi\) | ||||
−0.0133613 | + | 0.999911i | \(0.504253\pi\) | |||||||
\(68\) | 1.60400 | 0.194514 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.01069 | 0.957461 | ||||||||
\(71\) | 5.84150 | 0.693259 | 0.346629 | − | 0.938002i | \(-0.387326\pi\) | ||||
0.346629 | + | 0.938002i | \(0.387326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.91448 | −1.16040 | −0.580201 | − | 0.814473i | \(-0.697026\pi\) | ||||
−0.580201 | + | 0.814473i | \(0.697026\pi\) | |||||||
\(74\) | −8.91243 | −1.03605 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.923139 | 0.105891 | ||||||||
\(77\) | −7.14515 | −0.814266 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.1353 | −1.59035 | −0.795175 | − | 0.606379i | \(-0.792621\pi\) | ||||
−0.795175 | + | 0.606379i | \(0.792621\pi\) | |||||||
\(80\) | −4.92314 | −0.550424 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.5056 | 1.71231 | ||||||||
\(83\) | 11.0342 | 1.21116 | 0.605582 | − | 0.795783i | \(-0.292940\pi\) | ||||
0.605582 | + | 0.795783i | \(0.292940\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.25584 | 0.136215 | ||||||||
\(86\) | 12.9505 | 1.39648 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.11273 | 0.225218 | ||||||||
\(89\) | −0.845279 | −0.0895994 | −0.0447997 | − | 0.998996i | \(-0.514265\pi\) | ||||
−0.0447997 | + | 0.998996i | \(0.514265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.67117 | −0.174232 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22.3541 | 2.30565 | ||||||||
\(95\) | 0.722761 | 0.0741538 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5545 | −1.37625 | −0.688123 | − | 0.725594i | \(-0.741565\pi\) | ||||
−0.688123 | + | 0.725594i | \(0.741565\pi\) | |||||||
\(98\) | 22.7753 | 2.30066 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.27724 | 0.127724 | ||||||||
\(101\) | 17.9221 | 1.78332 | 0.891659 | − | 0.452708i | \(-0.149542\pi\) | ||||
0.891659 | + | 0.452708i | \(0.149542\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8134 | 1.36107 | 0.680535 | − | 0.732715i | \(-0.261747\pi\) | ||||
0.680535 | + | 0.732715i | \(0.261747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.2664 | 2.35696 | ||||||||
\(107\) | −9.73132 | −0.940762 | −0.470381 | − | 0.882463i | \(-0.655883\pi\) | ||||
−0.470381 | + | 0.882463i | \(0.655883\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.36061 | −0.417671 | −0.208835 | − | 0.977951i | \(-0.566967\pi\) | ||||
−0.208835 | + | 0.977951i | \(0.566967\pi\) | |||||||
\(110\) | −2.92314 | −0.278710 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −21.7850 | −2.05849 | ||||||||
\(113\) | 19.1927 | 1.80550 | 0.902749 | − | 0.430167i | \(-0.141545\pi\) | ||||
0.902749 | + | 0.430167i | \(0.141545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.30843 | −0.122011 | ||||||||
\(116\) | −1.48241 | −0.137638 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.75699 | 0.714089 | ||||||||
\(119\) | 5.55712 | 0.509420 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.39270 | −0.762973 | ||||||||
\(122\) | 10.2277 | 0.925972 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.10703 | 0.189217 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04076 | −0.269824 | −0.134912 | − | 0.990858i | \(-0.543075\pi\) | ||||
−0.134912 | + | 0.990858i | \(0.543075\pi\) | |||||||
\(128\) | 9.78390 | 0.864783 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.4894 | −1.35332 | −0.676659 | − | 0.736297i | \(-0.736573\pi\) | ||||
−0.676659 | + | 0.736297i | \(0.736573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.19824 | 0.277323 | ||||||||
\(134\) | −0.395979 | −0.0342073 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.64317 | −0.140901 | ||||||||
\(137\) | −8.69838 | −0.743153 | −0.371576 | − | 0.928402i | \(-0.621183\pi\) | ||||
−0.371576 | + | 0.928402i | \(0.621183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.02832 | 0.172039 | 0.0860197 | − | 0.996293i | \(-0.472585\pi\) | ||||
0.0860197 | + | 0.996293i | \(0.472585\pi\) | |||||||
\(140\) | 5.65182 | 0.477666 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.5750 | 0.887430 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.16064 | −0.0963856 | ||||||||
\(146\) | −17.9483 | −1.48541 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.28802 | −0.516872 | ||||||||
\(149\) | 5.61044 | 0.459625 | 0.229812 | − | 0.973235i | \(-0.426189\pi\) | ||||
0.229812 | + | 0.973235i | \(0.426189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5158 | −1.26266 | −0.631331 | − | 0.775514i | \(-0.717491\pi\) | ||||
−0.631331 | + | 0.775514i | \(0.717491\pi\) | |||||||
\(152\) | −0.945680 | −0.0767047 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.9350 | −1.04233 | ||||||||
\(155\) | 1.64968 | 0.132505 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4852 | −1.15604 | −0.578021 | − | 0.816022i | \(-0.696175\pi\) | ||||
−0.578021 | + | 0.816022i | \(0.696175\pi\) | |||||||
\(158\) | −25.5894 | −2.03579 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.29558 | −0.497709 | ||||||||
\(161\) | −5.78982 | −0.456302 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5340 | −1.21672 | −0.608358 | − | 0.793663i | \(-0.708171\pi\) | ||||
−0.608358 | + | 0.793663i | \(0.708171\pi\) | |||||||
\(164\) | 10.9398 | 0.854252 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.9754 | 1.55039 | ||||||||
\(167\) | −20.3288 | −1.57309 | −0.786545 | − | 0.617533i | \(-0.788132\pi\) | ||||
−0.786545 | + | 0.617533i | \(0.788132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.27346 | 0.174366 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.13699 | 0.696689 | ||||||||
\(173\) | 19.1021 | 1.45231 | 0.726153 | − | 0.687533i | \(-0.241306\pi\) | ||||
0.726153 | + | 0.687533i | \(0.241306\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.42503 | 0.334501 | ||||||||
\(176\) | 7.94946 | 0.599213 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.53022 | −0.114695 | ||||||||
\(179\) | 10.9429 | 0.817911 | 0.408955 | − | 0.912554i | \(-0.365893\pi\) | ||||
0.408955 | + | 0.912554i | \(0.365893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.45122 | −0.107869 | −0.0539343 | − | 0.998544i | \(-0.517176\pi\) | ||||
−0.0539343 | + | 0.998544i | \(0.517176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.71198 | 0.126209 | ||||||||
\(185\) | −4.92314 | −0.361956 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.02782 | −0.148289 | ||||||||
\(188\) | 15.7716 | 1.15026 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.30843 | 0.0949232 | ||||||||
\(191\) | −14.6797 | −1.06219 | −0.531094 | − | 0.847313i | \(-0.678219\pi\) | ||||
−0.531094 | + | 0.847313i | \(0.678219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.8338 | 1.42767 | 0.713835 | − | 0.700314i | \(-0.246956\pi\) | ||||
0.713835 | + | 0.700314i | \(0.246956\pi\) | |||||||
\(194\) | −24.5378 | −1.76171 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.0688 | 1.14777 | ||||||||
\(197\) | −12.3917 | −0.882871 | −0.441436 | − | 0.897293i | \(-0.645531\pi\) | ||||
−0.441436 | + | 0.897293i | \(0.645531\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.1127 | 1.63842 | 0.819208 | − | 0.573497i | \(-0.194413\pi\) | ||||
0.819208 | + | 0.573497i | \(0.194413\pi\) | |||||||
\(200\) | −1.30843 | −0.0925197 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32.4447 | 2.28280 | ||||||||
\(203\) | −5.13585 | −0.360466 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.56517 | 0.598217 | ||||||||
\(206\) | 25.0065 | 1.74229 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.16705 | −0.0807267 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.85383 | −0.609523 | −0.304762 | − | 0.952429i | \(-0.598577\pi\) | ||||
−0.304762 | + | 0.952429i | \(0.598577\pi\) | |||||||
\(212\) | 17.1208 | 1.17586 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.6167 | −1.20426 | ||||||||
\(215\) | 7.15370 | 0.487879 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.29987 | 0.495548 | ||||||||
\(218\) | −7.89407 | −0.534654 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.06237 | −0.139045 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.27532 | 0.286296 | 0.143148 | − | 0.989701i | \(-0.454277\pi\) | ||||
0.143148 | + | 0.989701i | \(0.454277\pi\) | |||||||
\(224\) | −27.8581 | −1.86135 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 34.7448 | 2.31119 | ||||||||
\(227\) | 21.4143 | 1.42132 | 0.710659 | − | 0.703537i | \(-0.248397\pi\) | ||||
0.710659 | + | 0.703537i | \(0.248397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.661510 | −0.0437138 | −0.0218569 | − | 0.999761i | \(-0.506958\pi\) | ||||
−0.0218569 | + | 0.999761i | \(0.506958\pi\) | |||||||
\(230\) | −2.36866 | −0.156185 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.51861 | 0.0997014 | ||||||||
\(233\) | −13.3665 | −0.875670 | −0.437835 | − | 0.899055i | \(-0.644255\pi\) | ||||
−0.437835 | + | 0.899055i | \(0.644255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3482 | 0.805506 | ||||||||
\(236\) | 5.47282 | 0.356250 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.0601 | 0.652101 | ||||||||
\(239\) | 4.44339 | 0.287419 | 0.143709 | − | 0.989620i | \(-0.454097\pi\) | ||||
0.143709 | + | 0.989620i | \(0.454097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4226 | 0.929039 | 0.464519 | − | 0.885563i | \(-0.346227\pi\) | ||||
0.464519 | + | 0.885563i | \(0.346227\pi\) | |||||||
\(242\) | −15.1934 | −0.976671 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.21599 | 0.461956 | ||||||||
\(245\) | 12.5809 | 0.803762 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.15848 | −0.137064 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.81031 | 0.114494 | ||||||||
\(251\) | 3.36540 | 0.212422 | 0.106211 | − | 0.994344i | \(-0.466128\pi\) | ||||
0.106211 | + | 0.994344i | \(0.466128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.11273 | 0.132826 | ||||||||
\(254\) | −5.50473 | −0.345397 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.8133 | 1.30083 | ||||||||
\(257\) | −23.8116 | −1.48533 | −0.742664 | − | 0.669665i | \(-0.766438\pi\) | ||||
−0.742664 | + | 0.669665i | \(0.766438\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.7850 | −1.35366 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −28.0407 | −1.73236 | ||||||||
\(263\) | −20.2963 | −1.25152 | −0.625762 | − | 0.780014i | \(-0.715212\pi\) | ||||
−0.625762 | + | 0.780014i | \(0.715212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.4045 | 0.823434 | ||||||||
\(266\) | 5.78982 | 0.354997 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.279376 | −0.0170656 | ||||||||
\(269\) | −0.205576 | −0.0125342 | −0.00626711 | − | 0.999980i | \(-0.501995\pi\) | ||||
−0.00626711 | + | 0.999980i | \(0.501995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1985 | 0.619512 | 0.309756 | − | 0.950816i | \(-0.399753\pi\) | ||||
0.309756 | + | 0.950816i | \(0.399753\pi\) | |||||||
\(272\) | −6.18266 | −0.374879 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.7468 | −0.951299 | ||||||||
\(275\) | −1.61471 | −0.0973709 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.1858 | 1.69352 | 0.846760 | − | 0.531976i | \(-0.178550\pi\) | ||||
0.846760 | + | 0.531976i | \(0.178550\pi\) | |||||||
\(278\) | 3.67189 | 0.220225 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.78982 | −0.346008 | ||||||||
\(281\) | 17.2672 | 1.03008 | 0.515039 | − | 0.857167i | \(-0.327778\pi\) | ||||
0.515039 | + | 0.857167i | \(0.327778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.0197 | 1.66560 | 0.832798 | − | 0.553577i | \(-0.186738\pi\) | ||||
0.832798 | + | 0.553577i | \(0.186738\pi\) | |||||||
\(284\) | 7.46099 | 0.442728 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.9011 | 2.23723 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4229 | −0.907228 | ||||||||
\(290\) | −2.10112 | −0.123382 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.6631 | −0.741055 | ||||||||
\(293\) | −7.03495 | −0.410986 | −0.205493 | − | 0.978659i | \(-0.565880\pi\) | ||||
−0.205493 | + | 0.978659i | \(0.565880\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.28489 | 0.249476 | ||||||||
\(296\) | 6.44156 | 0.374408 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.1567 | 0.588359 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.6553 | 1.82458 | ||||||||
\(302\) | −28.0886 | −1.61631 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.55825 | −0.204080 | ||||||||
\(305\) | 5.64968 | 0.323500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.9307 | −1.02336 | −0.511679 | − | 0.859177i | \(-0.670976\pi\) | ||||
−0.511679 | + | 0.859177i | \(0.670976\pi\) | |||||||
\(308\) | −9.12606 | −0.520006 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.98644 | 0.169618 | ||||||||
\(311\) | 8.59247 | 0.487234 | 0.243617 | − | 0.969871i | \(-0.421666\pi\) | ||||
0.243617 | + | 0.969871i | \(0.421666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8298 | −1.23389 | −0.616946 | − | 0.787006i | \(-0.711630\pi\) | ||||
−0.616946 | + | 0.787006i | \(0.711630\pi\) | |||||||
\(314\) | −26.2227 | −1.47983 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.0542 | −1.01563 | ||||||||
\(317\) | −20.4269 | −1.14729 | −0.573645 | − | 0.819104i | \(-0.694471\pi\) | ||||
−0.573645 | + | 0.819104i | \(0.694471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.87409 | 0.104929 | ||||||||
\(320\) | −1.55070 | −0.0866867 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.4814 | −0.584105 | ||||||||
\(323\) | 0.907671 | 0.0505042 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −28.1214 | −1.55750 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.2069 | −0.618797 | ||||||||
\(329\) | 54.6410 | 3.01245 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.08491 | 0.0596323 | 0.0298162 | − | 0.999555i | \(-0.490508\pi\) | ||||
0.0298162 | + | 0.999555i | \(0.490508\pi\) | |||||||
\(332\) | 14.0933 | 0.773473 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −36.8015 | −2.01369 | ||||||||
\(335\) | −0.218735 | −0.0119508 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.3641 | −0.836934 | −0.418467 | − | 0.908232i | \(-0.637432\pi\) | ||||
−0.418467 | + | 0.908232i | \(0.637432\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.60400 | 0.0869893 | ||||||||
\(341\) | −2.66376 | −0.144251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.6955 | 1.33343 | ||||||||
\(344\) | −9.36009 | −0.504662 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.5808 | 1.85908 | ||||||||
\(347\) | −31.7743 | −1.70573 | −0.852867 | − | 0.522128i | \(-0.825138\pi\) | ||||
−0.852867 | + | 0.522128i | \(0.825138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.01456 | −0.375481 | −0.187740 | − | 0.982219i | \(-0.560116\pi\) | ||||
−0.187740 | + | 0.982219i | \(0.560116\pi\) | |||||||
\(350\) | 8.01069 | 0.428189 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.1656 | 0.541826 | ||||||||
\(353\) | 30.2070 | 1.60776 | 0.803878 | − | 0.594794i | \(-0.202766\pi\) | ||||
0.803878 | + | 0.594794i | \(0.202766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.84150 | 0.310035 | ||||||||
\(356\) | −1.07962 | −0.0572199 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.8101 | 1.04700 | ||||||||
\(359\) | −16.5984 | −0.876029 | −0.438015 | − | 0.898968i | \(-0.644318\pi\) | ||||
−0.438015 | + | 0.898968i | \(0.644318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4776 | −0.972506 | ||||||||
\(362\) | −2.62717 | −0.138081 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.91448 | −0.518947 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.3285 | 1.06114 | 0.530569 | − | 0.847641i | \(-0.321978\pi\) | ||||
0.530569 | + | 0.847641i | \(0.321978\pi\) | |||||||
\(368\) | 6.44156 | 0.335790 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.91243 | −0.463335 | ||||||||
\(371\) | 59.3154 | 3.07950 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7527 | −1.07453 | −0.537267 | − | 0.843412i | \(-0.680543\pi\) | ||||
−0.537267 | + | 0.843412i | \(0.680543\pi\) | |||||||
\(374\) | −3.67099 | −0.189822 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.1567 | −0.833216 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.865150 | 0.0444398 | 0.0222199 | − | 0.999753i | \(-0.492927\pi\) | ||||
0.0222199 | + | 0.999753i | \(0.492927\pi\) | |||||||
\(380\) | 0.923139 | 0.0473560 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.5749 | −1.35969 | ||||||||
\(383\) | 2.82316 | 0.144257 | 0.0721284 | − | 0.997395i | \(-0.477021\pi\) | ||||
0.0721284 | + | 0.997395i | \(0.477021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.14515 | −0.364151 | ||||||||
\(386\) | 35.9055 | 1.82754 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.3123 | −0.878898 | ||||||||
\(389\) | −13.4514 | −0.682015 | −0.341008 | − | 0.940061i | \(-0.610768\pi\) | ||||
−0.341008 | + | 0.940061i | \(0.610768\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.64317 | −0.0830987 | ||||||||
\(392\) | −16.4611 | −0.831413 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.4328 | −1.13015 | ||||||||
\(395\) | −14.1353 | −0.711227 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.04013 | −0.403523 | −0.201761 | − | 0.979435i | \(-0.564667\pi\) | ||||
−0.201761 | + | 0.979435i | \(0.564667\pi\) | |||||||
\(398\) | 41.8413 | 2.09731 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.92314 | −0.246157 | ||||||||
\(401\) | 34.3620 | 1.71596 | 0.857978 | − | 0.513686i | \(-0.171720\pi\) | ||||
0.857978 | + | 0.513686i | \(0.171720\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 22.8908 | 1.13886 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.29750 | −0.461427 | ||||||||
\(407\) | 7.94946 | 0.394040 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.4668 | 0.962571 | 0.481286 | − | 0.876564i | \(-0.340170\pi\) | ||||
0.481286 | + | 0.876564i | \(0.340170\pi\) | |||||||
\(410\) | 15.5056 | 0.765769 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.6430 | 0.869206 | ||||||||
\(413\) | 18.9607 | 0.932997 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0342 | 0.541649 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.11273 | −0.103337 | ||||||||
\(419\) | 24.4720 | 1.19554 | 0.597768 | − | 0.801669i | \(-0.296055\pi\) | ||||
0.597768 | + | 0.801669i | \(0.296055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.6979 | −1.34991 | −0.674956 | − | 0.737858i | \(-0.735837\pi\) | ||||
−0.674956 | + | 0.737858i | \(0.735837\pi\) | |||||||
\(422\) | −16.0282 | −0.780242 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.5388 | −0.851761 | ||||||||
\(425\) | 1.25584 | 0.0609171 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.0000 | 1.20983 | ||||||||
\(428\) | −12.4292 | −0.600789 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.9505 | 0.624526 | ||||||||
\(431\) | −4.36771 | −0.210385 | −0.105193 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105193 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.05717 | −0.435260 | −0.217630 | − | 0.976031i | \(-0.569833\pi\) | ||||
−0.217630 | + | 0.976031i | \(0.569833\pi\) | |||||||
\(434\) | 13.2151 | 0.634343 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.56954 | −0.266732 | ||||||||
\(437\) | −0.945680 | −0.0452380 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.1793 | −0.772195 | −0.386097 | − | 0.922458i | \(-0.626177\pi\) | ||||
−0.386097 | + | 0.922458i | \(0.626177\pi\) | |||||||
\(440\) | 2.11273 | 0.100721 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.6295 | −0.647555 | −0.323778 | − | 0.946133i | \(-0.604953\pi\) | ||||
−0.323778 | + | 0.946133i | \(0.604953\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.845279 | −0.0400701 | ||||||||
\(446\) | 7.73967 | 0.366484 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.86189 | −0.324194 | ||||||||
\(449\) | 11.0543 | 0.521686 | 0.260843 | − | 0.965381i | \(-0.416000\pi\) | ||||
0.260843 | + | 0.965381i | \(0.416000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8303 | −0.651243 | ||||||||
\(452\) | 24.5137 | 1.15303 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 38.7667 | 1.81941 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.2352 | −1.13367 | −0.566836 | − | 0.823830i | \(-0.691833\pi\) | ||||
−0.566836 | + | 0.823830i | \(0.691833\pi\) | |||||||
\(458\) | −1.19754 | −0.0559574 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.67117 | −0.0779188 | ||||||||
\(461\) | 26.6958 | 1.24335 | 0.621674 | − | 0.783276i | \(-0.286453\pi\) | ||||
0.621674 | + | 0.783276i | \(0.286453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8137 | −0.920819 | −0.460410 | − | 0.887707i | \(-0.652297\pi\) | ||||
−0.460410 | + | 0.887707i | \(0.652297\pi\) | |||||||
\(464\) | 5.71397 | 0.265265 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.1976 | −1.12093 | ||||||||
\(467\) | −22.4652 | −1.03956 | −0.519782 | − | 0.854299i | \(-0.673987\pi\) | ||||
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.967907 | −0.0446938 | ||||||||
\(470\) | 22.3541 | 1.03112 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.60646 | −0.258058 | ||||||||
\(473\) | −11.5512 | −0.531124 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.722761 | 0.0331626 | ||||||||
\(476\) | 7.09776 | 0.325325 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.04392 | 0.367921 | ||||||||
\(479\) | −25.1683 | −1.14997 | −0.574985 | − | 0.818164i | \(-0.694992\pi\) | ||||
−0.574985 | + | 0.818164i | \(0.694992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 26.1094 | 1.18925 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7195 | −0.487249 | ||||||||
\(485\) | −13.5545 | −0.615476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.5542 | 1.33923 | 0.669613 | − | 0.742710i | \(-0.266460\pi\) | ||||
0.669613 | + | 0.742710i | \(0.266460\pi\) | |||||||
\(488\) | −7.39218 | −0.334628 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 22.7753 | 1.02888 | ||||||||
\(491\) | 15.4585 | 0.697630 | 0.348815 | − | 0.937192i | \(-0.386584\pi\) | ||||
0.348815 | + | 0.937192i | \(0.386584\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.45757 | −0.0656457 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.12159 | −0.364670 | ||||||||
\(497\) | 25.8488 | 1.15948 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.38273 | 0.0618993 | 0.0309497 | − | 0.999521i | \(-0.490147\pi\) | ||||
0.0309497 | + | 0.999521i | \(0.490147\pi\) | |||||||
\(500\) | 1.27724 | 0.0571198 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.09244 | 0.271919 | ||||||||
\(503\) | −40.5920 | −1.80991 | −0.904953 | − | 0.425511i | \(-0.860094\pi\) | ||||
−0.904953 | + | 0.425511i | \(0.860094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.9221 | 0.797524 | ||||||||
\(506\) | 3.82471 | 0.170029 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.88377 | −0.172315 | ||||||||
\(509\) | −6.37142 | −0.282408 | −0.141204 | − | 0.989980i | \(-0.545097\pi\) | ||||
−0.141204 | + | 0.989980i | \(0.545097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −43.8718 | −1.94078 | ||||||||
\(512\) | 18.1109 | 0.800396 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −43.1065 | −1.90135 | ||||||||
\(515\) | 13.8134 | 0.608689 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.9387 | −0.876905 | ||||||||
\(518\) | −39.4377 | −1.73280 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.54817 | −0.0678264 | −0.0339132 | − | 0.999425i | \(-0.510797\pi\) | ||||
−0.0339132 | + | 0.999425i | \(0.510797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0971 | 1.44723 | 0.723617 | − | 0.690201i | \(-0.242478\pi\) | ||||
0.723617 | + | 0.690201i | \(0.242478\pi\) | |||||||
\(524\) | −19.7837 | −0.864255 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −36.7427 | −1.60206 | ||||||||
\(527\) | 2.07173 | 0.0902459 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.2880 | −0.925566 | ||||||||
\(530\) | 24.2664 | 1.05407 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.08491 | 0.177104 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.73132 | −0.420721 | ||||||||
\(536\) | 0.286198 | 0.0123619 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.372158 | −0.0160449 | ||||||||
\(539\) | −20.3145 | −0.875007 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.149945 | 0.00644662 | 0.00322331 | − | 0.999995i | \(-0.498974\pi\) | ||||
0.00322331 | + | 0.999995i | \(0.498974\pi\) | |||||||
\(542\) | 18.4624 | 0.793029 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.90622 | −0.338977 | ||||||||
\(545\) | −4.36061 | −0.186788 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.12882 | −0.219293 | −0.109646 | − | 0.993971i | \(-0.534972\pi\) | ||||
−0.109646 | + | 0.993971i | \(0.534972\pi\) | |||||||
\(548\) | −11.1099 | −0.474592 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.92314 | −0.124643 | ||||||||
\(551\) | −0.838863 | −0.0357368 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −62.5493 | −2.65987 | ||||||||
\(554\) | 51.0251 | 2.16785 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.59064 | 0.109868 | ||||||||
\(557\) | −3.27399 | −0.138723 | −0.0693617 | − | 0.997592i | \(-0.522096\pi\) | ||||
−0.0693617 | + | 0.997592i | \(0.522096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −21.7850 | −0.920585 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.2591 | 1.31859 | ||||||||
\(563\) | −7.77432 | −0.327648 | −0.163824 | − | 0.986490i | \(-0.552383\pi\) | ||||
−0.163824 | + | 0.986490i | \(0.552383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.1927 | 0.807443 | ||||||||
\(566\) | 50.7244 | 2.13210 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.64317 | −0.320700 | ||||||||
\(569\) | −7.87472 | −0.330125 | −0.165063 | − | 0.986283i | \(-0.552783\pi\) | ||||
−0.165063 | + | 0.986283i | \(0.552783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.4994 | −0.481236 | −0.240618 | − | 0.970620i | \(-0.577350\pi\) | ||||
−0.240618 | + | 0.970620i | \(0.577350\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 68.6129 | 2.86385 | ||||||||
\(575\) | −1.30843 | −0.0545651 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.797701 | 0.0332087 | 0.0166044 | − | 0.999862i | \(-0.494714\pi\) | ||||
0.0166044 | + | 0.999862i | \(0.494714\pi\) | |||||||
\(578\) | −27.9202 | −1.16133 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.48241 | −0.0615537 | ||||||||
\(581\) | 48.8268 | 2.02568 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.6445 | −0.896423 | ||||||||
\(584\) | 12.9724 | 0.536800 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.7355 | −0.526097 | ||||||||
\(587\) | −18.5437 | −0.765379 | −0.382689 | − | 0.923877i | \(-0.625002\pi\) | ||||
−0.382689 | + | 0.923877i | \(0.625002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.19232 | 0.0491288 | ||||||||
\(590\) | 7.75699 | 0.319350 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24.2373 | 0.996147 | ||||||||
\(593\) | 11.6068 | 0.476633 | 0.238316 | − | 0.971188i | \(-0.423404\pi\) | ||||
0.238316 | + | 0.971188i | \(0.423404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.55712 | 0.227820 | ||||||||
\(596\) | 7.16587 | 0.293525 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.2656 | 1.44091 | 0.720457 | − | 0.693500i | \(-0.243932\pi\) | ||||
0.720457 | + | 0.693500i | \(0.243932\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.63747 | −0.0667938 | −0.0333969 | − | 0.999442i | \(-0.510633\pi\) | ||||
−0.0333969 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(602\) | 57.3061 | 2.33562 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.8174 | −0.806360 | ||||||||
\(605\) | −8.39270 | −0.341212 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2721 | 1.14753 | 0.573765 | − | 0.819020i | \(-0.305482\pi\) | ||||
0.573765 | + | 0.819020i | \(0.305482\pi\) | |||||||
\(608\) | −4.55020 | −0.184535 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.2277 | 0.414107 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.9945 | −0.847959 | −0.423980 | − | 0.905672i | \(-0.639367\pi\) | ||||
−0.423980 | + | 0.905672i | \(0.639367\pi\) | |||||||
\(614\) | −32.4602 | −1.30999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.34890 | 0.376678 | ||||||||
\(617\) | −5.35694 | −0.215662 | −0.107831 | − | 0.994169i | \(-0.534391\pi\) | ||||
−0.107831 | + | 0.994169i | \(0.534391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.1621 | 1.53386 | 0.766931 | − | 0.641729i | \(-0.221783\pi\) | ||||
0.766931 | + | 0.641729i | \(0.221783\pi\) | |||||||
\(620\) | 2.10703 | 0.0846205 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.5551 | 0.623701 | ||||||||
\(623\) | −3.74038 | −0.149855 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −39.5188 | −1.57949 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.5010 | −0.738270 | ||||||||
\(629\) | −6.18266 | −0.246519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.48325 | −0.297903 | −0.148952 | − | 0.988844i | \(-0.547590\pi\) | ||||
−0.148952 | + | 0.988844i | \(0.547590\pi\) | |||||||
\(632\) | 18.4950 | 0.735694 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −36.9792 | −1.46863 | ||||||||
\(635\) | −3.04076 | −0.120669 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.39270 | 0.134318 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.78390 | 0.386743 | ||||||||
\(641\) | −45.4922 | −1.79683 | −0.898416 | − | 0.439145i | \(-0.855282\pi\) | ||||
−0.898416 | + | 0.439145i | \(0.855282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7806 | 1.21387 | 0.606935 | − | 0.794752i | \(-0.292399\pi\) | ||||
0.606935 | + | 0.794752i | \(0.292399\pi\) | |||||||
\(644\) | −7.39498 | −0.291403 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.64317 | 0.0646496 | ||||||||
\(647\) | −47.7652 | −1.87784 | −0.938922 | − | 0.344130i | \(-0.888174\pi\) | ||||
−0.938922 | + | 0.344130i | \(0.888174\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.91886 | −0.271589 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.8406 | −0.777018 | ||||||||
\(653\) | 9.03547 | 0.353585 | 0.176793 | − | 0.984248i | \(-0.443428\pi\) | ||||
0.176793 | + | 0.984248i | \(0.443428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.4894 | −0.605222 | ||||||||
\(656\) | −42.1675 | −1.64636 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 98.9174 | 3.85620 | ||||||||
\(659\) | −40.0775 | −1.56120 | −0.780598 | − | 0.625034i | \(-0.785085\pi\) | ||||
−0.780598 | + | 0.625034i | \(0.785085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.9194 | −0.735878 | −0.367939 | − | 0.929850i | \(-0.619936\pi\) | ||||
−0.367939 | + | 0.929850i | \(0.619936\pi\) | |||||||
\(662\) | 1.96404 | 0.0763345 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.4375 | −0.560282 | ||||||||
\(665\) | 3.19824 | 0.124022 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.51861 | 0.0588007 | ||||||||
\(668\) | −25.9647 | −1.00461 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.395979 | −0.0152980 | ||||||||
\(671\) | −9.12261 | −0.352174 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0031 | −0.886706 | −0.443353 | − | 0.896347i | \(-0.646211\pi\) | ||||
−0.443353 | + | 0.896347i | \(0.646211\pi\) | |||||||
\(674\) | −27.8138 | −1.07135 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0126 | 1.57624 | 0.788121 | − | 0.615520i | \(-0.211054\pi\) | ||||
0.788121 | + | 0.615520i | \(0.211054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −59.9789 | −2.30178 | ||||||||
\(680\) | −1.64317 | −0.0630127 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.82224 | −0.184653 | ||||||||
\(683\) | 2.52625 | 0.0966644 | 0.0483322 | − | 0.998831i | \(-0.484609\pi\) | ||||
0.0483322 | + | 0.998831i | \(0.484609\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.69838 | −0.332348 | ||||||||
\(686\) | 44.7066 | 1.70691 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −35.2187 | −1.34270 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.7869 | −1.43748 | −0.718741 | − | 0.695278i | \(-0.755281\pi\) | ||||
−0.718741 | + | 0.695278i | \(0.755281\pi\) | |||||||
\(692\) | 24.3980 | 0.927471 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −57.5215 | −2.18349 | ||||||||
\(695\) | 2.02832 | 0.0769384 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.7565 | 0.407430 | ||||||||
\(698\) | −12.6986 | −0.480648 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.65182 | 0.213619 | ||||||||
\(701\) | 9.12075 | 0.344486 | 0.172243 | − | 0.985054i | \(-0.444899\pi\) | ||||
0.172243 | + | 0.985054i | \(0.444899\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.55825 | −0.134202 | ||||||||
\(704\) | 2.50393 | 0.0943706 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54.6842 | 2.05807 | ||||||||
\(707\) | 79.3059 | 2.98261 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.7403 | 0.816473 | 0.408236 | − | 0.912876i | \(-0.366144\pi\) | ||||
0.408236 | + | 0.912876i | \(0.366144\pi\) | |||||||
\(710\) | 10.5750 | 0.396871 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.10599 | 0.0414485 | ||||||||
\(713\) | −2.15848 | −0.0808357 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.9767 | 0.522334 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.0483 | −1.12139 | ||||||||
\(719\) | 14.3709 | 0.535945 | 0.267973 | − | 0.963427i | \(-0.413646\pi\) | ||||
0.267973 | + | 0.963427i | \(0.413646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.1245 | 2.27640 | ||||||||
\(722\) | −33.4503 | −1.24489 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.85356 | −0.0688869 | ||||||||
\(725\) | −1.16064 | −0.0431050 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.5088 | −1.42821 | −0.714106 | − | 0.700038i | \(-0.753166\pi\) | ||||
−0.714106 | + | 0.700038i | \(0.753166\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.9483 | −0.664297 | ||||||||
\(731\) | 8.98389 | 0.332281 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.95952 | 0.0723767 | 0.0361884 | − | 0.999345i | \(-0.488478\pi\) | ||||
0.0361884 | + | 0.999345i | \(0.488478\pi\) | |||||||
\(734\) | 36.8010 | 1.35835 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.23730 | 0.303631 | ||||||||
\(737\) | 0.353194 | 0.0130101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.4603 | 1.45157 | 0.725784 | − | 0.687922i | \(-0.241477\pi\) | ||||
0.725784 | + | 0.687922i | \(0.241477\pi\) | |||||||
\(740\) | −6.28802 | −0.231152 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 107.380 | 3.94203 | ||||||||
\(743\) | 33.4899 | 1.22862 | 0.614312 | − | 0.789063i | \(-0.289434\pi\) | ||||
0.614312 | + | 0.789063i | \(0.289434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.61044 | 0.205551 | ||||||||
\(746\) | −37.5689 | −1.37550 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.59001 | −0.0947000 | ||||||||
\(749\) | −43.0613 | −1.57343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.1750 | −0.626725 | −0.313362 | − | 0.949634i | \(-0.601455\pi\) | ||||
−0.313362 | + | 0.949634i | \(0.601455\pi\) | |||||||
\(752\) | −60.7917 | −2.21685 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.5158 | −0.564679 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.3190 | −1.53811 | −0.769055 | − | 0.639183i | \(-0.779273\pi\) | ||||
−0.769055 | + | 0.639183i | \(0.779273\pi\) | |||||||
\(758\) | 1.56619 | 0.0568867 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.945680 | −0.0343034 | ||||||||
\(761\) | 12.4474 | 0.451219 | 0.225610 | − | 0.974218i | \(-0.427563\pi\) | ||||
0.225610 | + | 0.974218i | \(0.427563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.2958 | −0.698555 | ||||||||
\(764\) | −18.7495 | −0.678334 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.11081 | 0.184661 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.35494 | 0.265226 | 0.132613 | − | 0.991168i | \(-0.457663\pi\) | ||||
0.132613 | + | 0.991168i | \(0.457663\pi\) | |||||||
\(770\) | −12.9350 | −0.466144 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.3325 | 0.911738 | ||||||||
\(773\) | 12.8701 | 0.462907 | 0.231453 | − | 0.972846i | \(-0.425652\pi\) | ||||
0.231453 | + | 0.972846i | \(0.425652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.64968 | 0.0592582 | ||||||||
\(776\) | 17.7350 | 0.636649 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.3513 | −0.873038 | ||||||||
\(779\) | 6.19057 | 0.221800 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.43235 | −0.337516 | ||||||||
\(782\) | −2.97465 | −0.106373 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −61.9374 | −2.21205 | ||||||||
\(785\) | −14.4852 | −0.516997 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.96901 | 0.177126 | 0.0885631 | − | 0.996071i | \(-0.471772\pi\) | ||||
0.0885631 | + | 0.996071i | \(0.471772\pi\) | |||||||
\(788\) | −15.8271 | −0.563818 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.5894 | −0.910431 | ||||||||
\(791\) | 84.9283 | 3.01970 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −14.5552 | −0.516543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 29.5204 | 1.04632 | ||||||||
\(797\) | 21.1244 | 0.748266 | 0.374133 | − | 0.927375i | \(-0.377940\pi\) | ||||
0.374133 | + | 0.927375i | \(0.377940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.5073 | 0.548608 | ||||||||
\(800\) | −6.29558 | −0.222582 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 62.2060 | 2.19657 | ||||||||
\(803\) | 16.0090 | 0.564947 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.78982 | −0.204064 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.4498 | −0.824960 | ||||||||
\(809\) | 11.2608 | 0.395910 | 0.197955 | − | 0.980211i | \(-0.436570\pi\) | ||||
0.197955 | + | 0.980211i | \(0.436570\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.9957 | −1.08841 | −0.544203 | − | 0.838954i | \(-0.683168\pi\) | ||||
−0.544203 | + | 0.838954i | \(0.683168\pi\) | |||||||
\(812\) | −6.55970 | −0.230200 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.3910 | 0.504405 | ||||||||
\(815\) | −15.5340 | −0.544132 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.17042 | 0.180890 | ||||||||
\(818\) | 35.2410 | 1.23217 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.9398 | 0.382033 | ||||||||
\(821\) | 43.8685 | 1.53102 | 0.765510 | − | 0.643424i | \(-0.222487\pi\) | ||||
0.765510 | + | 0.643424i | \(0.222487\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.08060 | −0.211957 | −0.105978 | − | 0.994368i | \(-0.533797\pi\) | ||||
−0.105978 | + | 0.994368i | \(0.533797\pi\) | |||||||
\(824\) | −18.0738 | −0.629629 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.3249 | 1.19432 | ||||||||
\(827\) | 11.0488 | 0.384205 | 0.192102 | − | 0.981375i | \(-0.438469\pi\) | ||||
0.192102 | + | 0.981375i | \(0.438469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5605 | 1.09614 | 0.548070 | − | 0.836433i | \(-0.315363\pi\) | ||||
0.548070 | + | 0.836433i | \(0.315363\pi\) | |||||||
\(830\) | 19.9754 | 0.693357 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.7995 | 0.547421 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.3288 | −0.703507 | ||||||||
\(836\) | −1.49060 | −0.0515536 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 44.3020 | 1.53039 | ||||||||
\(839\) | 16.0683 | 0.554739 | 0.277369 | − | 0.960763i | \(-0.410537\pi\) | ||||
0.277369 | + | 0.960763i | \(0.410537\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6529 | −0.953549 | ||||||||
\(842\) | −50.1419 | −1.72800 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.3085 | −0.389253 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.1379 | −1.27607 | ||||||||
\(848\) | −65.9924 | −2.26619 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.27346 | 0.0779791 | ||||||||
\(851\) | 6.44156 | 0.220814 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5424 | −0.395205 | −0.197602 | − | 0.980282i | \(-0.563315\pi\) | ||||
−0.197602 | + | 0.980282i | \(0.563315\pi\) | |||||||
\(854\) | 45.2578 | 1.54869 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.7327 | 0.435195 | ||||||||
\(857\) | −53.7559 | −1.83627 | −0.918134 | − | 0.396270i | \(-0.870304\pi\) | ||||
−0.918134 | + | 0.396270i | \(0.870304\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.28910 | 0.112223 | 0.0561113 | − | 0.998425i | \(-0.482130\pi\) | ||||
0.0561113 | + | 0.998425i | \(0.482130\pi\) | |||||||
\(860\) | 9.13699 | 0.311569 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.90693 | −0.269311 | ||||||||
\(863\) | 32.7600 | 1.11516 | 0.557581 | − | 0.830123i | \(-0.311730\pi\) | ||||
0.557581 | + | 0.830123i | \(0.311730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.1021 | 0.649491 | ||||||||
\(866\) | −16.3963 | −0.557170 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.32368 | 0.316466 | ||||||||
\(869\) | 22.8245 | 0.774269 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.70553 | 0.193214 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.71198 | −0.0579085 | ||||||||
\(875\) | 4.42503 | 0.149593 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.92654 | 0.301428 | 0.150714 | − | 0.988577i | \(-0.451843\pi\) | ||||
0.150714 | + | 0.988577i | \(0.451843\pi\) | |||||||
\(878\) | −29.2896 | −0.988475 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.94946 | 0.267976 | ||||||||
\(881\) | 27.5224 | 0.927252 | 0.463626 | − | 0.886031i | \(-0.346548\pi\) | ||||
0.463626 | + | 0.886031i | \(0.346548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.2667 | 1.45604 | 0.728020 | − | 0.685555i | \(-0.240441\pi\) | ||||
0.728020 | + | 0.685555i | \(0.240441\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.6736 | −0.828926 | ||||||||
\(887\) | −29.3318 | −0.984866 | −0.492433 | − | 0.870350i | \(-0.663892\pi\) | ||||
−0.492433 | + | 0.870350i | \(0.663892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.4554 | −0.451281 | ||||||||
\(890\) | −1.53022 | −0.0512931 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.46060 | 0.182834 | ||||||||
\(893\) | 8.92478 | 0.298656 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.9429 | 0.365781 | ||||||||
\(896\) | 43.2940 | 1.44635 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.0118 | 0.667802 | ||||||||
\(899\) | −1.91468 | −0.0638580 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.8339 | 0.560819 | ||||||||
\(902\) | −25.0372 | −0.833647 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.1122 | −0.835220 | ||||||||
\(905\) | −1.45122 | −0.0482403 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.3799 | −1.17477 | −0.587385 | − | 0.809308i | \(-0.699842\pi\) | ||||
−0.587385 | + | 0.809308i | \(0.699842\pi\) | |||||||
\(908\) | 27.3512 | 0.907681 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.6105 | −1.54428 | −0.772138 | − | 0.635455i | \(-0.780812\pi\) | ||||
−0.772138 | + | 0.635455i | \(0.780812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.8171 | −0.589661 | ||||||||
\(914\) | −43.8732 | −1.45120 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.844906 | −0.0279165 | ||||||||
\(917\) | −68.5412 | −2.26343 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.3865 | −0.870410 | −0.435205 | − | 0.900331i | \(-0.643324\pi\) | ||||
−0.435205 | + | 0.900331i | \(0.643324\pi\) | |||||||
\(920\) | 1.71198 | 0.0564422 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 48.3279 | 1.59159 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.92314 | −0.161872 | ||||||||
\(926\) | −35.8690 | −1.17873 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.30688 | 0.239860 | ||||||||
\(929\) | 5.52357 | 0.181223 | 0.0906113 | − | 0.995886i | \(-0.471118\pi\) | ||||
0.0906113 | + | 0.995886i | \(0.471118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.09297 | 0.298010 | ||||||||
\(932\) | −17.0722 | −0.559220 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40.6690 | −1.33073 | ||||||||
\(935\) | −2.02782 | −0.0663167 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.15026 | 0.233589 | 0.116794 | − | 0.993156i | \(-0.462738\pi\) | ||||
0.116794 | + | 0.993156i | \(0.462738\pi\) | |||||||
\(938\) | −1.75222 | −0.0572119 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.7716 | 0.514411 | ||||||||
\(941\) | 19.8331 | 0.646541 | 0.323271 | − | 0.946307i | \(-0.395218\pi\) | ||||
0.323271 | + | 0.946307i | \(0.395218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.2069 | −0.364946 | ||||||||
\(944\) | −21.0951 | −0.686587 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.9113 | −0.679884 | ||||||||
\(947\) | 3.19122 | 0.103701 | 0.0518503 | − | 0.998655i | \(-0.483488\pi\) | ||||
0.0518503 | + | 0.998655i | \(0.483488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.30843 | 0.0424509 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.27107 | −0.235657 | ||||||||
\(953\) | −40.9786 | −1.32743 | −0.663713 | − | 0.747987i | \(-0.731020\pi\) | ||||
−0.663713 | + | 0.747987i | \(0.731020\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.6797 | −0.475025 | ||||||||
\(956\) | 5.67526 | 0.183551 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45.5626 | −1.47206 | ||||||||
\(959\) | −38.4906 | −1.24293 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2786 | −0.912212 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.4211 | 0.593302 | ||||||||
\(965\) | 19.8338 | 0.638474 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.6355 | 1.33891 | 0.669453 | − | 0.742854i | \(-0.266529\pi\) | ||||
0.669453 | + | 0.742854i | \(0.266529\pi\) | |||||||
\(968\) | 10.9812 | 0.352950 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.5378 | −0.787862 | ||||||||
\(971\) | −21.1935 | −0.680133 | −0.340067 | − | 0.940401i | \(-0.610450\pi\) | ||||
−0.340067 | + | 0.940401i | \(0.610450\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.97535 | 0.287737 | ||||||||
\(974\) | 53.5023 | 1.71433 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.8141 | −0.890309 | ||||||||
\(977\) | 16.2332 | 0.519346 | 0.259673 | − | 0.965697i | \(-0.416385\pi\) | ||||
0.259673 | + | 0.965697i | \(0.416385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.36488 | 0.0436219 | ||||||||
\(980\) | 16.0688 | 0.513298 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27.9847 | 0.893027 | ||||||||
\(983\) | −27.0181 | −0.861743 | −0.430872 | − | 0.902413i | \(-0.641794\pi\) | ||||
−0.430872 | + | 0.902413i | \(0.641794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.3917 | −0.394832 | ||||||||
\(986\) | −2.63866 | −0.0840321 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.36009 | −0.297634 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9905 | −0.539722 | −0.269861 | − | 0.962899i | \(-0.586978\pi\) | ||||
−0.269861 | + | 0.962899i | \(0.586978\pi\) | |||||||
\(992\) | −10.3857 | −0.329746 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 46.7945 | 1.48423 | ||||||||
\(995\) | 23.1127 | 0.732722 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.4255 | 1.24862 | 0.624309 | − | 0.781177i | \(-0.285380\pi\) | ||||
0.624309 | + | 0.781177i | \(0.285380\pi\) | |||||||
\(998\) | 2.50317 | 0.0792364 | ||||||||
\(999\) | 0 | 0 |
(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 | 7605.2.a.cn.1.4 | 5 | ||
3.2 | odd | 2 | 7605.2.a.cl.1.2 | 5 | |||
13.4 | even | 6 | 585.2.j.i.406.4 | yes | 10 | ||
13.10 | even | 6 | 585.2.j.i.451.4 | yes | 10 | ||
13.12 | even | 2 | 7605.2.a.cm.1.2 | 5 | |||
39.17 | odd | 6 | 585.2.j.h.406.2 | ✓ | 10 | ||
39.23 | odd | 6 | 585.2.j.h.451.2 | yes | 10 | ||
39.38 | odd | 2 | 7605.2.a.co.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.j.h.406.2 | ✓ | 10 | 39.17 | odd | 6 | ||
585.2.j.h.451.2 | yes | 10 | 39.23 | odd | 6 | ||
585.2.j.i.406.4 | yes | 10 | 13.4 | even | 6 | ||
585.2.j.i.451.4 | yes | 10 | 13.10 | even | 6 | ||
7605.2.a.cl.1.2 | 5 | 3.2 | odd | 2 | |||
7605.2.a.cm.1.2 | 5 | 13.12 | even | 2 | |||
7605.2.a.cn.1.4 | 5 | 1.1 | even | 1 | trivial | ||
7605.2.a.co.1.4 | 5 | 39.38 | odd | 2 |