Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(26,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 26.5 | ||
Root | \(-0.928369 + 1.60798i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.26 |
Dual form | 475.2.e.f.201.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.740597 | + | 1.28275i | 0.523681 | + | 0.907043i | 0.999620 | + | 0.0275641i | \(0.00877505\pi\) |
−0.475939 | + | 0.879478i | \(0.657892\pi\) | |||||||
\(3\) | −1.42837 | − | 2.47401i | −0.824669 | − | 1.42837i | −0.902172 | − | 0.431377i | \(-0.858028\pi\) |
0.0775023 | − | 0.996992i | \(-0.475305\pi\) | |||||||
\(4\) | −0.0969683 | + | 0.167954i | −0.0484841 | + | 0.0839770i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.11569 | − | 3.66449i | 0.863728 | − | 1.49602i | ||||
\(7\) | 3.78541 | 1.43075 | 0.715375 | − | 0.698740i | \(-0.246256\pi\) | ||||
0.715375 | + | 0.698740i | \(0.246256\pi\) | |||||||
\(8\) | 2.67513 | 0.945802 | ||||||||
\(9\) | −2.58048 | + | 4.46952i | −0.860159 | + | 1.48984i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59460 | −1.68684 | −0.843418 | − | 0.537258i | \(-0.819460\pi\) | ||||
−0.843418 | + | 0.537258i | \(0.819460\pi\) | |||||||
\(12\) | 0.554026 | 0.159934 | ||||||||
\(13\) | 2.45326 | − | 4.24917i | 0.680411 | − | 1.17851i | −0.294444 | − | 0.955669i | \(-0.595134\pi\) |
0.974855 | − | 0.222838i | \(-0.0715322\pi\) | |||||||
\(14\) | 2.80346 | + | 4.85574i | 0.749257 | + | 1.29775i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.17513 | + | 3.76744i | 0.543783 | + | 0.941859i | ||||
\(17\) | −0.875095 | − | 1.51571i | −0.212242 | − | 0.367614i | 0.740174 | − | 0.672415i | \(-0.234743\pi\) |
−0.952416 | + | 0.304802i | \(0.901410\pi\) | |||||||
\(18\) | −7.64438 | −1.80180 | ||||||||
\(19\) | 0.636061 | − | 4.31224i | 0.145922 | − | 0.989296i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.40696 | − | 9.36514i | −1.17990 | − | 2.04364i | ||||
\(22\) | −4.14335 | − | 7.17648i | −0.883364 | − | 1.53003i | ||||
\(23\) | 0.290768 | − | 0.503625i | 0.0606294 | − | 0.105013i | −0.834118 | − | 0.551587i | \(-0.814023\pi\) |
0.894747 | + | 0.446574i | \(0.147356\pi\) | |||||||
\(24\) | −3.82107 | − | 6.61830i | −0.779974 | − | 1.35095i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.26750 | 1.42527 | ||||||||
\(27\) | 6.17328 | 1.18805 | ||||||||
\(28\) | −0.367065 | + | 0.635775i | −0.0693687 | + | 0.120150i | ||||
\(29\) | −0.832153 | + | 1.44133i | −0.154527 | + | 0.267649i | −0.932887 | − | 0.360170i | \(-0.882719\pi\) |
0.778360 | + | 0.627819i | \(0.216052\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.01680 | 1.26025 | 0.630127 | − | 0.776492i | \(-0.283003\pi\) | ||||
0.630127 | + | 0.776492i | \(0.283003\pi\) | |||||||
\(32\) | −0.546661 | + | 0.946844i | −0.0966369 | + | 0.167380i | ||||
\(33\) | 7.99116 | + | 13.8411i | 1.39108 | + | 2.40942i | ||||
\(34\) | 1.29619 | − | 2.24506i | 0.222294 | − | 0.385025i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500449 | − | 0.866803i | −0.0834082 | − | 0.144467i | ||||
\(37\) | −2.36322 | −0.388510 | −0.194255 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194255 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(38\) | 6.00260 | − | 2.37773i | 0.973750 | − | 0.385718i | ||||
\(39\) | −14.0166 | −2.24446 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.417676 | − | 0.723435i | −0.0652300 | − | 0.112982i | 0.831566 | − | 0.555426i | \(-0.187445\pi\) |
−0.896796 | + | 0.442444i | \(0.854111\pi\) | |||||||
\(42\) | 8.00877 | − | 13.8716i | 1.23578 | − | 2.14043i | ||||
\(43\) | −0.535664 | − | 0.927797i | −0.0816880 | − | 0.141488i | 0.822287 | − | 0.569073i | \(-0.192698\pi\) |
−0.903975 | + | 0.427585i | \(0.859364\pi\) | |||||||
\(44\) | 0.542499 | − | 0.939635i | 0.0817848 | − | 0.141655i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.861369 | 0.127002 | ||||||||
\(47\) | 1.93378 | − | 3.34941i | 0.282071 | − | 0.488561i | −0.689824 | − | 0.723977i | \(-0.742312\pi\) |
0.971895 | + | 0.235416i | \(0.0756453\pi\) | |||||||
\(48\) | 6.21378 | − | 10.7626i | 0.896882 | − | 1.55345i | ||||
\(49\) | 7.32934 | 1.04705 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.49992 | + | 4.32999i | −0.350059 | + | 0.606319i | ||||
\(52\) | 0.475776 | + | 0.824069i | 0.0659783 | + | 0.114278i | ||||
\(53\) | −3.39842 | + | 5.88624i | −0.466809 | + | 0.808537i | −0.999281 | − | 0.0379106i | \(-0.987930\pi\) |
0.532472 | + | 0.846448i | \(0.321263\pi\) | |||||||
\(54\) | 4.57192 | + | 7.91879i | 0.622159 | + | 1.07761i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.1265 | 1.35321 | ||||||||
\(57\) | −11.5771 | + | 4.58585i | −1.53342 | + | 0.607411i | ||||
\(58\) | −2.46516 | −0.323691 | ||||||||
\(59\) | 0.204282 | + | 0.353827i | 0.0265953 | + | 0.0460643i | 0.879017 | − | 0.476791i | \(-0.158200\pi\) |
−0.852421 | + | 0.522855i | \(0.824867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.98016 | + | 12.0900i | −0.893718 | + | 1.54796i | −0.0583341 | + | 0.998297i | \(0.518579\pi\) |
−0.835384 | + | 0.549667i | \(0.814754\pi\) | |||||||
\(62\) | 5.19662 | + | 9.00081i | 0.659971 | + | 1.14310i | ||||
\(63\) | −9.76817 | + | 16.9190i | −1.23067 | + | 2.13159i | ||||
\(64\) | 7.08110 | 0.885138 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.8365 | + | 20.5013i | −1.45697 | + | 2.52354i | ||||
\(67\) | 0.390703 | − | 0.676717i | 0.0477319 | − | 0.0826742i | −0.841172 | − | 0.540767i | \(-0.818134\pi\) |
0.888904 | + | 0.458093i | \(0.151467\pi\) | |||||||
\(68\) | 0.339426 | 0.0411614 | ||||||||
\(69\) | −1.66130 | −0.199997 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.18919 | − | 5.52384i | −0.378487 | − | 0.655559i | 0.612355 | − | 0.790583i | \(-0.290222\pi\) |
−0.990842 | + | 0.135024i | \(0.956889\pi\) | |||||||
\(72\) | −6.90312 | + | 11.9565i | −0.813540 | + | 1.40909i | ||||
\(73\) | 1.44458 | + | 2.50208i | 0.169075 | + | 0.292846i | 0.938095 | − | 0.346378i | \(-0.112589\pi\) |
−0.769020 | + | 0.639225i | \(0.779255\pi\) | |||||||
\(74\) | −1.75019 | − | 3.03142i | −0.203456 | − | 0.352395i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.662580 | + | 0.524980i | 0.0760032 | + | 0.0602193i | ||||
\(77\) | −21.1779 | −2.41344 | ||||||||
\(78\) | −10.3807 | − | 17.9799i | −1.17538 | − | 2.03582i | ||||
\(79\) | 6.25135 | + | 10.8276i | 0.703331 | + | 1.21821i | 0.967290 | + | 0.253672i | \(0.0816383\pi\) |
−0.263959 | + | 0.964534i | \(0.585028\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.07630 | − | 1.86420i | −0.119589 | − | 0.207133i | ||||
\(82\) | 0.618659 | − | 1.07155i | 0.0683194 | − | 0.118333i | ||||
\(83\) | 10.3903 | 1.14048 | 0.570240 | − | 0.821478i | \(-0.306850\pi\) | ||||
0.570240 | + | 0.821478i | \(0.306850\pi\) | |||||||
\(84\) | 2.09722 | 0.228825 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.793422 | − | 1.37425i | 0.0855569 | − | 0.148189i | ||||
\(87\) | 4.75449 | 0.509735 | ||||||||
\(88\) | −14.9663 | −1.59541 | ||||||||
\(89\) | −8.92106 | + | 15.4517i | −0.945631 | + | 1.63788i | −0.191148 | + | 0.981561i | \(0.561221\pi\) |
−0.754483 | + | 0.656320i | \(0.772112\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.28659 | − | 16.0848i | 0.973499 | − | 1.68615i | ||||
\(92\) | 0.0563906 | + | 0.0976714i | 0.00587913 | + | 0.0101829i | ||||
\(93\) | −10.0226 | − | 17.3596i | −1.03929 | − | 1.80011i | ||||
\(94\) | 5.72861 | 0.590861 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.12333 | 0.318774 | ||||||||
\(97\) | 5.49995 | + | 9.52619i | 0.558435 | + | 0.967238i | 0.997627 | + | 0.0688448i | \(0.0219313\pi\) |
−0.439192 | + | 0.898393i | \(0.644735\pi\) | |||||||
\(98\) | 5.42809 | + | 9.40172i | 0.548319 | + | 0.949717i | ||||
\(99\) | 14.4367 | − | 25.0052i | 1.45095 | − | 2.51311i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.57944 | + | 4.46772i | −0.256664 | + | 0.444555i | −0.965346 | − | 0.260973i | \(-0.915957\pi\) |
0.708682 | + | 0.705528i | \(0.249290\pi\) | |||||||
\(102\) | −7.40573 | −0.733277 | ||||||||
\(103\) | 7.75851 | 0.764469 | 0.382235 | − | 0.924065i | \(-0.375155\pi\) | ||||
0.382235 | + | 0.924065i | \(0.375155\pi\) | |||||||
\(104\) | 6.56279 | − | 11.3671i | 0.643534 | − | 1.11463i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0674 | −0.977837 | ||||||||
\(107\) | 12.6521 | 1.22313 | 0.611564 | − | 0.791195i | \(-0.290541\pi\) | ||||
0.611564 | + | 0.791195i | \(0.290541\pi\) | |||||||
\(108\) | −0.598613 | + | 1.03683i | −0.0576015 | + | 0.0997688i | ||||
\(109\) | 4.09697 | + | 7.09616i | 0.392418 | + | 0.679689i | 0.992768 | − | 0.120049i | \(-0.0383052\pi\) |
−0.600350 | + | 0.799738i | \(0.704972\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.37554 | + | 5.84661i | 0.320392 | + | 0.554936i | ||||
\(112\) | 8.23376 | + | 14.2613i | 0.778018 | + | 1.34757i | ||||
\(113\) | 12.5551 | 1.18108 | 0.590541 | − | 0.807007i | \(-0.298914\pi\) | ||||
0.590541 | + | 0.807007i | \(0.298914\pi\) | |||||||
\(114\) | −14.4564 | − | 11.4542i | −1.35397 | − | 1.07279i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.161385 | − | 0.279527i | −0.0149842 | − | 0.0259534i | ||||
\(117\) | 12.6612 | + | 21.9298i | 1.17052 | + | 2.02741i | ||||
\(118\) | −0.302581 | + | 0.524086i | −0.0278549 | + | 0.0482461i | ||||
\(119\) | −3.31260 | − | 5.73758i | −0.303665 | − | 0.525963i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.2996 | 1.84541 | ||||||||
\(122\) | −20.6779 | −1.87209 | ||||||||
\(123\) | −1.19319 | + | 2.06667i | −0.107586 | + | 0.186345i | ||||
\(124\) | −0.680407 | + | 1.17850i | −0.0611023 | + | 0.105832i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −28.9371 | −2.57792 | ||||||||
\(127\) | −4.07957 | + | 7.06602i | −0.362003 | + | 0.627007i | −0.988290 | − | 0.152585i | \(-0.951240\pi\) |
0.626287 | + | 0.779592i | \(0.284574\pi\) | |||||||
\(128\) | 6.33757 | + | 10.9770i | 0.560167 | + | 0.970238i | ||||
\(129\) | −1.53025 | + | 2.65047i | −0.134731 | + | 0.233361i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.62491 | − | 16.6708i | −0.840932 | − | 1.45654i | −0.889108 | − | 0.457698i | \(-0.848674\pi\) |
0.0481757 | − | 0.998839i | \(-0.484659\pi\) | |||||||
\(132\) | −3.09955 | −0.269782 | ||||||||
\(133\) | 2.40775 | − | 16.3236i | 0.208779 | − | 1.41544i | ||||
\(134\) | 1.15741 | 0.0999853 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.34099 | − | 4.05472i | −0.200739 | − | 0.347689i | ||||
\(137\) | −0.785955 | + | 1.36131i | −0.0671487 | + | 0.116305i | −0.897645 | − | 0.440719i | \(-0.854724\pi\) |
0.830496 | + | 0.557024i | \(0.188057\pi\) | |||||||
\(138\) | −1.23035 | − | 2.13103i | −0.104735 | − | 0.181406i | ||||
\(139\) | 1.02459 | − | 1.77464i | 0.0869047 | − | 0.150523i | −0.819297 | − | 0.573370i | \(-0.805636\pi\) |
0.906201 | + | 0.422847i | \(0.138969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0486 | −0.930461 | ||||||||
\(142\) | 4.72381 | − | 8.18188i | 0.396413 | − | 0.686608i | ||||
\(143\) | −13.7250 | + | 23.7724i | −1.14774 | + | 1.98795i | ||||
\(144\) | −22.4515 | −1.87096 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.13970 | + | 3.70607i | −0.177083 | + | 0.306716i | ||||
\(147\) | −10.4690 | − | 18.1328i | −0.863468 | − | 1.49557i | ||||
\(148\) | 0.229157 | − | 0.396911i | 0.0188366 | − | 0.0326259i | ||||
\(149\) | 0.737839 | + | 1.27797i | 0.0604461 | + | 0.104696i | 0.894665 | − | 0.446738i | \(-0.147414\pi\) |
−0.834219 | + | 0.551434i | \(0.814081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.42543 | 0.522894 | 0.261447 | − | 0.965218i | \(-0.415800\pi\) | ||||
0.261447 | + | 0.965218i | \(0.415800\pi\) | |||||||
\(152\) | 1.70155 | − | 11.5358i | 0.138014 | − | 0.935678i | ||||
\(153\) | 9.03266 | 0.730247 | ||||||||
\(154\) | −15.6843 | − | 27.1659i | −1.26387 | − | 2.18909i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.35917 | − | 2.35415i | 0.108821 | − | 0.188483i | ||||
\(157\) | −11.1445 | − | 19.3028i | −0.889425 | − | 1.54053i | −0.840556 | − | 0.541724i | \(-0.817772\pi\) |
−0.0488688 | − | 0.998805i | \(-0.515562\pi\) | |||||||
\(158\) | −9.25946 | + | 16.0379i | −0.736643 | + | 1.27590i | ||||
\(159\) | 19.4168 | 1.53985 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.10068 | − | 1.90643i | 0.0867455 | − | 0.150248i | ||||
\(162\) | 1.59420 | − | 2.76124i | 0.125253 | − | 0.216944i | ||||
\(163\) | −15.0321 | −1.17741 | −0.588703 | − | 0.808350i | \(-0.700361\pi\) | ||||
−0.588703 | + | 0.808350i | \(0.700361\pi\) | |||||||
\(164\) | 0.162005 | 0.0126505 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.69500 | + | 13.3281i | 0.597248 | + | 1.03446i | ||||
\(167\) | −4.79928 | + | 8.31260i | −0.371380 | + | 0.643249i | −0.989778 | − | 0.142616i | \(-0.954449\pi\) |
0.618398 | + | 0.785865i | \(0.287782\pi\) | |||||||
\(168\) | −14.4643 | − | 25.0530i | −1.11595 | − | 1.93288i | ||||
\(169\) | −5.53695 | − | 9.59028i | −0.425919 | − | 0.737714i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.6323 | + | 13.9705i | 1.34838 | + | 1.06835i | ||||
\(172\) | 0.207770 | 0.0158423 | ||||||||
\(173\) | 4.41611 | + | 7.64894i | 0.335751 | + | 0.581538i | 0.983629 | − | 0.180207i | \(-0.0576766\pi\) |
−0.647878 | + | 0.761744i | \(0.724343\pi\) | |||||||
\(174\) | 3.52116 | + | 6.09883i | 0.266938 | + | 0.462351i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.1690 | − | 21.0773i | −0.917272 | − | 1.58876i | ||||
\(177\) | 0.583580 | − | 1.01079i | 0.0438646 | − | 0.0759757i | ||||
\(178\) | −26.4277 | −1.98084 | ||||||||
\(179\) | 10.8178 | 0.808564 | 0.404282 | − | 0.914634i | \(-0.367522\pi\) | ||||
0.404282 | + | 0.914634i | \(0.367522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.37359 | + | 9.30733i | −0.399416 | + | 0.691808i | −0.993654 | − | 0.112481i | \(-0.964120\pi\) |
0.594238 | + | 0.804289i | \(0.297454\pi\) | |||||||
\(182\) | 27.5105 | 2.03921 | ||||||||
\(183\) | 39.8810 | 2.94809 | ||||||||
\(184\) | 0.777843 | − | 1.34726i | 0.0573434 | − | 0.0993216i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.8454 | − | 25.7130i | 1.08852 | − | 1.88537i | ||||
\(187\) | 4.89581 | + | 8.47979i | 0.358017 | + | 0.620104i | ||||
\(188\) | 0.375031 | + | 0.649573i | 0.0273519 | + | 0.0473750i | ||||
\(189\) | 23.3684 | 1.69980 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.28362 | −0.454667 | −0.227334 | − | 0.973817i | \(-0.573001\pi\) | ||||
−0.227334 | + | 0.973817i | \(0.573001\pi\) | |||||||
\(192\) | −10.1144 | − | 17.5187i | −0.729946 | − | 1.26430i | ||||
\(193\) | −8.91459 | − | 15.4405i | −0.641686 | − | 1.11143i | −0.985056 | − | 0.172233i | \(-0.944902\pi\) |
0.343370 | − | 0.939200i | \(-0.388431\pi\) | |||||||
\(194\) | −8.14649 | + | 14.1101i | −0.584884 | + | 1.01305i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.710713 | + | 1.23099i | −0.0507652 | + | 0.0879279i | ||||
\(197\) | −16.9925 | −1.21066 | −0.605332 | − | 0.795973i | \(-0.706959\pi\) | ||||
−0.605332 | + | 0.795973i | \(0.706959\pi\) | |||||||
\(198\) | 42.7672 | 3.03934 | ||||||||
\(199\) | −8.22212 | + | 14.2411i | −0.582850 | + | 1.00953i | 0.412289 | + | 0.911053i | \(0.364729\pi\) |
−0.995140 | + | 0.0984735i | \(0.968604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.23227 | −0.157452 | ||||||||
\(202\) | −7.64131 | −0.537641 | ||||||||
\(203\) | −3.15004 | + | 5.45603i | −0.221090 | + | 0.382938i | ||||
\(204\) | −0.484826 | − | 0.839743i | −0.0339446 | − | 0.0587937i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.74593 | + | 9.95225i | 0.400338 | + | 0.693406i | ||||
\(207\) | 1.50064 | + | 2.59919i | 0.104302 | + | 0.180656i | ||||
\(208\) | 21.3446 | 1.47998 | ||||||||
\(209\) | −3.55851 | + | 24.1253i | −0.246147 | + | 1.66878i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.79632 | − | 13.5036i | −0.536721 | − | 0.929628i | −0.999078 | − | 0.0429343i | \(-0.986329\pi\) |
0.462357 | − | 0.886694i | \(-0.347004\pi\) | |||||||
\(212\) | −0.659078 | − | 1.14156i | −0.0452657 | − | 0.0784024i | ||||
\(213\) | −9.11068 | + | 15.7802i | −0.624253 | + | 1.08124i | ||||
\(214\) | 9.37013 | + | 16.2295i | 0.640529 | + | 1.10943i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 16.5143 | 1.12366 | ||||||||
\(217\) | 26.5615 | 1.80311 | ||||||||
\(218\) | −6.06841 | + | 10.5108i | −0.411004 | + | 0.711880i | ||||
\(219\) | 4.12678 | − | 7.14779i | 0.278862 | − | 0.483003i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.58734 | −0.577647 | ||||||||
\(222\) | −4.99984 | + | 8.65997i | −0.335567 | + | 0.581219i | ||||
\(223\) | −3.90313 | − | 6.76042i | −0.261373 | − | 0.452711i | 0.705234 | − | 0.708974i | \(-0.250842\pi\) |
−0.966607 | + | 0.256263i | \(0.917509\pi\) | |||||||
\(224\) | −2.06933 | + | 3.58419i | −0.138263 | + | 0.239479i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.29826 | + | 16.1051i | 0.618511 | + | 1.07129i | ||||
\(227\) | 16.8511 | 1.11845 | 0.559223 | − | 0.829017i | \(-0.311100\pi\) | ||||
0.559223 | + | 0.829017i | \(0.311100\pi\) | |||||||
\(228\) | 0.352394 | − | 2.38909i | 0.0233379 | − | 0.158222i | ||||
\(229\) | −0.251385 | −0.0166120 | −0.00830600 | − | 0.999966i | \(-0.502644\pi\) | ||||
−0.00830600 | + | 0.999966i | \(0.502644\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 30.2498 | + | 52.3942i | 1.99029 | + | 3.44729i | ||||
\(232\) | −2.22612 | + | 3.85575i | −0.146152 | + | 0.253142i | ||||
\(233\) | −11.6014 | − | 20.0943i | −0.760035 | − | 1.31642i | −0.942832 | − | 0.333269i | \(-0.891848\pi\) |
0.182797 | − | 0.983151i | \(-0.441485\pi\) | |||||||
\(234\) | −18.7536 | + | 32.4822i | −1.22596 | + | 2.12343i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.0792355 | −0.00515779 | ||||||||
\(237\) | 17.8585 | − | 30.9318i | 1.16003 | − | 2.00923i | ||||
\(238\) | 4.90660 | − | 8.49848i | 0.318047 | − | 0.550874i | ||||
\(239\) | −7.58778 | −0.490813 | −0.245406 | − | 0.969420i | \(-0.578921\pi\) | ||||
−0.245406 | + | 0.969420i | \(0.578921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.75808 | − | 4.77714i | 0.177664 | − | 0.307723i | −0.763416 | − | 0.645907i | \(-0.776479\pi\) |
0.941080 | + | 0.338184i | \(0.109813\pi\) | |||||||
\(242\) | 15.0338 | + | 26.0393i | 0.966409 | + | 1.67387i | ||||
\(243\) | 6.18523 | − | 10.7131i | 0.396783 | − | 0.687248i | ||||
\(244\) | −1.35371 | − | 2.34469i | −0.0866623 | − | 0.150103i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.53469 | −0.225364 | ||||||||
\(247\) | −16.7630 | − | 13.2818i | −1.06661 | − | 0.845099i | ||||
\(248\) | 18.7708 | 1.19195 | ||||||||
\(249\) | −14.8411 | − | 25.7056i | −0.940519 | − | 1.62903i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.32933 | − | 16.1589i | 0.588862 | − | 1.01994i | −0.405520 | − | 0.914086i | \(-0.632910\pi\) |
0.994382 | − | 0.105852i | \(-0.0337571\pi\) | |||||||
\(252\) | −1.89441 | − | 3.28121i | −0.119336 | − | 0.206697i | ||||
\(253\) | −1.62673 | + | 2.81758i | −0.102272 | + | 0.177140i | ||||
\(254\) | −12.0853 | −0.758297 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.30606 | + | 3.99422i | −0.144129 | + | 0.249639i | ||||
\(257\) | −0.346352 | + | 0.599899i | −0.0216048 | + | 0.0374207i | −0.876626 | − | 0.481173i | \(-0.840211\pi\) |
0.855021 | + | 0.518594i | \(0.173544\pi\) | |||||||
\(258\) | −4.53320 | −0.282225 | ||||||||
\(259\) | −8.94574 | −0.555861 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.29470 | − | 7.43865i | −0.265836 | − | 0.460441i | ||||
\(262\) | 14.2564 | − | 24.6927i | 0.880761 | − | 1.52552i | ||||
\(263\) | −5.81338 | − | 10.0691i | −0.358468 | − | 0.620885i | 0.629237 | − | 0.777214i | \(-0.283368\pi\) |
−0.987705 | + | 0.156328i | \(0.950034\pi\) | |||||||
\(264\) | 21.3774 | + | 37.0267i | 1.31569 | + | 2.27884i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 22.7223 | − | 9.00067i | 1.39319 | − | 0.551866i | ||||
\(267\) | 50.9703 | 3.11933 | ||||||||
\(268\) | 0.0757716 | + | 0.131240i | 0.00462849 | + | 0.00801677i | ||||
\(269\) | 11.8057 | + | 20.4481i | 0.719809 | + | 1.24675i | 0.961075 | + | 0.276286i | \(0.0891038\pi\) |
−0.241267 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.81995 | + | 6.61635i | 0.232046 | + | 0.401915i | 0.958410 | − | 0.285395i | \(-0.0921248\pi\) |
−0.726364 | + | 0.687310i | \(0.758791\pi\) | |||||||
\(272\) | 3.80689 | − | 6.59373i | 0.230827 | − | 0.399804i | ||||
\(273\) | −53.0587 | −3.21126 | ||||||||
\(274\) | −2.32830 | −0.140658 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.161093 | − | 0.279022i | 0.00969667 | − | 0.0167951i | ||||
\(277\) | −18.6537 | −1.12079 | −0.560397 | − | 0.828224i | \(-0.689352\pi\) | ||||
−0.560397 | + | 0.828224i | \(0.689352\pi\) | |||||||
\(278\) | 3.03524 | 0.182041 | ||||||||
\(279\) | −18.1067 | + | 31.3617i | −1.08402 | + | 1.87758i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.99489 | + | 12.1155i | −0.417280 | + | 0.722750i | −0.995665 | − | 0.0930139i | \(-0.970350\pi\) |
0.578385 | + | 0.815764i | \(0.303683\pi\) | |||||||
\(282\) | −8.18257 | − | 14.1726i | −0.487265 | − | 0.843968i | ||||
\(283\) | 12.3334 | + | 21.3620i | 0.733143 | + | 1.26984i | 0.955533 | + | 0.294884i | \(0.0952809\pi\) |
−0.222390 | + | 0.974958i | \(0.571386\pi\) | |||||||
\(284\) | 1.23700 | 0.0734025 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −40.6588 | −2.40420 | ||||||||
\(287\) | −1.58107 | − | 2.73850i | −0.0933278 | − | 0.161649i | ||||
\(288\) | −2.82129 | − | 4.88662i | −0.166246 | − | 0.287947i | ||||
\(289\) | 6.96842 | − | 12.0697i | 0.409907 | − | 0.709979i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.7119 | − | 27.2138i | 0.921049 | − | 1.59530i | ||||
\(292\) | −0.560312 | −0.0327898 | ||||||||
\(293\) | 10.5784 | 0.617994 | 0.308997 | − | 0.951063i | \(-0.400007\pi\) | ||||
0.308997 | + | 0.951063i | \(0.400007\pi\) | |||||||
\(294\) | 15.5066 | − | 26.8583i | 0.904365 | − | 1.56641i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.32191 | −0.367454 | ||||||||
\(297\) | −34.5371 | −2.00404 | ||||||||
\(298\) | −1.09288 | + | 1.89293i | −0.0633090 | + | 0.109654i | ||||
\(299\) | −1.42666 | − | 2.47105i | −0.0825058 | − | 0.142904i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.02771 | − | 3.51209i | −0.116875 | − | 0.202434i | ||||
\(302\) | 4.75866 | + | 8.24223i | 0.273830 | + | 0.474287i | ||||
\(303\) | 14.7376 | 0.846652 | ||||||||
\(304\) | 17.6296 | − | 6.98337i | 1.01113 | − | 0.400524i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.68956 | + | 11.5867i | 0.382417 | + | 0.662365i | ||||
\(307\) | 6.41222 | + | 11.1063i | 0.365965 | + | 0.633870i | 0.988931 | − | 0.148379i | \(-0.0474057\pi\) |
−0.622966 | + | 0.782249i | \(0.714072\pi\) | |||||||
\(308\) | 2.05358 | − | 3.55691i | 0.117014 | − | 0.202674i | ||||
\(309\) | −11.0820 | − | 19.1946i | −0.630434 | − | 1.09194i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.42706 | 0.194331 | 0.0971655 | − | 0.995268i | \(-0.469022\pi\) | ||||
0.0971655 | + | 0.995268i | \(0.469022\pi\) | |||||||
\(312\) | −37.4963 | −2.12281 | ||||||||
\(313\) | −1.42224 | + | 2.46339i | −0.0803896 | + | 0.139239i | −0.903417 | − | 0.428762i | \(-0.858950\pi\) |
0.823028 | + | 0.568001i | \(0.192283\pi\) | |||||||
\(314\) | 16.5071 | − | 28.5912i | 0.931551 | − | 1.61349i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.42473 | −0.136402 | ||||||||
\(317\) | −2.33072 | + | 4.03693i | −0.130907 | + | 0.226737i | −0.924026 | − | 0.382329i | \(-0.875122\pi\) |
0.793120 | + | 0.609066i | \(0.208455\pi\) | |||||||
\(318\) | 14.3800 | + | 24.9069i | 0.806392 | + | 1.39671i | ||||
\(319\) | 4.65556 | − | 8.06367i | 0.260662 | − | 0.451479i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0719 | − | 31.3015i | −1.00868 | − | 1.74708i | ||||
\(322\) | 3.26063 | 0.181708 | ||||||||
\(323\) | −7.09272 | + | 2.80954i | −0.394649 | + | 0.156327i | ||||
\(324\) | 0.417467 | 0.0231926 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.1327 | − | 19.2825i | −0.616585 | − | 1.06796i | ||||
\(327\) | 11.7040 | − | 20.2719i | 0.647231 | − | 1.12104i | ||||
\(328\) | −1.11734 | − | 1.93528i | −0.0616946 | − | 0.106858i | ||||
\(329\) | 7.32016 | − | 12.6789i | 0.403573 | − | 0.699010i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00260 | −0.384898 | −0.192449 | − | 0.981307i | \(-0.561643\pi\) | ||||
−0.192449 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(332\) | −1.00753 | + | 1.74509i | −0.0552952 | + | 0.0957741i | ||||
\(333\) | 6.09822 | − | 10.5624i | 0.334181 | − | 0.578818i | ||||
\(334\) | −14.2173 | −0.777938 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 23.5217 | − | 40.7408i | 1.28321 | − | 2.22259i | ||||
\(337\) | −6.76881 | − | 11.7239i | −0.368721 | − | 0.638643i | 0.620645 | − | 0.784092i | \(-0.286871\pi\) |
−0.989366 | + | 0.145449i | \(0.953537\pi\) | |||||||
\(338\) | 8.20130 | − | 14.2051i | 0.446092 | − | 0.772654i | ||||
\(339\) | −17.9333 | − | 31.0614i | −0.974003 | − | 1.68702i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.2562 | −2.12584 | ||||||||
\(342\) | −4.86229 | + | 32.9644i | −0.262923 | + | 1.78251i | ||||
\(343\) | 1.24667 | 0.0673140 | ||||||||
\(344\) | −1.43297 | − | 2.48198i | −0.0772606 | − | 0.133819i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.54112 | + | 11.3296i | −0.351653 | + | 0.609081i | ||||
\(347\) | 10.9817 | + | 19.0208i | 0.589527 | + | 1.02109i | 0.994294 | + | 0.106671i | \(0.0340190\pi\) |
−0.404768 | + | 0.914420i | \(0.632648\pi\) | |||||||
\(348\) | −0.461034 | + | 0.798535i | −0.0247140 | + | 0.0428060i | ||||
\(349\) | −22.1930 | −1.18796 | −0.593981 | − | 0.804479i | \(-0.702445\pi\) | ||||
−0.593981 | + | 0.804479i | \(0.702445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.1447 | − | 26.2313i | 0.808362 | − | 1.40012i | ||||
\(352\) | 3.05835 | − | 5.29721i | 0.163010 | − | 0.282342i | ||||
\(353\) | 0.679013 | 0.0361402 | 0.0180701 | − | 0.999837i | \(-0.494248\pi\) | ||||
0.0180701 | + | 0.999837i | \(0.494248\pi\) | |||||||
\(354\) | 1.72879 | 0.0918843 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.73012 | − | 2.99666i | −0.0916962 | − | 0.158822i | ||||
\(357\) | −9.46322 | + | 16.3908i | −0.500847 | + | 0.867492i | ||||
\(358\) | 8.01166 | + | 13.8766i | 0.423430 | + | 0.733402i | ||||
\(359\) | 12.6627 | + | 21.9325i | 0.668314 | + | 1.15755i | 0.978375 | + | 0.206837i | \(0.0663170\pi\) |
−0.310062 | + | 0.950716i | \(0.600350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1909 | − | 5.48570i | −0.957413 | − | 0.288721i | ||||
\(362\) | −15.9187 | −0.836666 | ||||||||
\(363\) | −28.9953 | − | 50.2213i | −1.52186 | − | 2.63593i | ||||
\(364\) | 1.80101 | + | 3.11944i | 0.0943985 | + | 0.163503i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 29.5357 | + | 51.1574i | 1.54386 | + | 2.67404i | ||||
\(367\) | 5.83153 | − | 10.1005i | 0.304404 | − | 0.527243i | −0.672725 | − | 0.739893i | \(-0.734876\pi\) |
0.977128 | + | 0.212650i | \(0.0682095\pi\) | |||||||
\(368\) | 2.52984 | 0.131877 | ||||||||
\(369\) | 4.31121 | 0.224433 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.8644 | + | 22.2818i | −0.667887 | + | 1.15681i | ||||
\(372\) | 3.88749 | 0.201557 | ||||||||
\(373\) | 13.0913 | 0.677843 | 0.338921 | − | 0.940815i | \(-0.389938\pi\) | ||||
0.338921 | + | 0.940815i | \(0.389938\pi\) | |||||||
\(374\) | −7.25164 | + | 12.5602i | −0.374974 | + | 0.649473i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.17312 | − | 8.96010i | 0.266783 | − | 0.462082i | ||||
\(377\) | 4.08297 | + | 7.07192i | 0.210284 | + | 0.364222i | ||||
\(378\) | 17.3066 | + | 29.9759i | 0.890155 | + | 1.54179i | ||||
\(379\) | −32.7566 | −1.68259 | −0.841297 | − | 0.540573i | \(-0.818208\pi\) | ||||
−0.841297 | + | 0.540573i | \(0.818208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.3085 | 1.19413 | ||||||||
\(382\) | −4.65363 | − | 8.06033i | −0.238101 | − | 0.412402i | ||||
\(383\) | −12.8227 | − | 22.2096i | −0.655211 | − | 1.13486i | −0.981841 | − | 0.189707i | \(-0.939246\pi\) |
0.326630 | − | 0.945152i | \(-0.394087\pi\) | |||||||
\(384\) | 18.1048 | − | 31.3584i | 0.923905 | − | 1.60025i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.2042 | − | 22.8704i | 0.672078 | − | 1.16407i | ||||
\(387\) | 5.52907 | 0.281059 | ||||||||
\(388\) | −2.13328 | −0.108301 | ||||||||
\(389\) | 9.27329 | − | 16.0618i | 0.470174 | − | 0.814366i | −0.529244 | − | 0.848470i | \(-0.677524\pi\) |
0.999418 | + | 0.0341039i | \(0.0108577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.01780 | −0.0514723 | ||||||||
\(392\) | 19.6069 | 0.990300 | ||||||||
\(393\) | −27.4958 | + | 47.6242i | −1.38698 | + | 2.40232i | ||||
\(394\) | −12.5846 | − | 21.7971i | −0.634002 | − | 1.09812i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.79981 | + | 4.84942i | 0.140696 | + | 0.243692i | ||||
\(397\) | 7.69806 | + | 13.3334i | 0.386355 | + | 0.669186i | 0.991956 | − | 0.126582i | \(-0.0404007\pi\) |
−0.605601 | + | 0.795768i | \(0.707067\pi\) | |||||||
\(398\) | −24.3571 | −1.22091 | ||||||||
\(399\) | −43.8239 | + | 17.3593i | −2.19394 | + | 0.869054i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.2956 | + | 17.8326i | 0.514140 | + | 0.890517i | 0.999865 | + | 0.0164054i | \(0.00522222\pi\) |
−0.485725 | + | 0.874112i | \(0.661444\pi\) | |||||||
\(402\) | −1.65321 | − | 2.86345i | −0.0824548 | − | 0.142816i | ||||
\(403\) | 17.2140 | − | 29.8155i | 0.857491 | − | 1.48522i | ||||
\(404\) | −0.500248 | − | 0.866455i | −0.0248883 | − | 0.0431078i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.33165 | −0.463122 | ||||||||
\(407\) | 13.2212 | 0.655353 | ||||||||
\(408\) | −6.68761 | + | 11.5833i | −0.331086 | + | 0.573458i | ||||
\(409\) | 0.811919 | − | 1.40629i | 0.0401468 | − | 0.0695363i | −0.845254 | − | 0.534365i | \(-0.820551\pi\) |
0.885401 | + | 0.464829i | \(0.153884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.49054 | 0.221502 | ||||||||
\(412\) | −0.752330 | + | 1.30307i | −0.0370646 | + | 0.0641978i | ||||
\(413\) | 0.773292 | + | 1.33938i | 0.0380512 | + | 0.0659066i | ||||
\(414\) | −2.22274 | + | 3.84990i | −0.109242 | + | 0.189212i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.68220 | + | 4.64570i | 0.131506 | + | 0.227774i | ||||
\(417\) | −5.85398 | −0.286671 | ||||||||
\(418\) | −33.5822 | + | 13.3024i | −1.64256 | + | 0.650643i | ||||
\(419\) | 16.8087 | 0.821161 | 0.410580 | − | 0.911824i | \(-0.365326\pi\) | ||||
0.410580 | + | 0.911824i | \(0.365326\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4718 | − | 18.1377i | −0.510365 | − | 0.883977i | −0.999928 | − | 0.0120096i | \(-0.996177\pi\) |
0.489563 | − | 0.871968i | \(-0.337156\pi\) | |||||||
\(422\) | 11.5479 | − | 20.0015i | 0.562142 | − | 0.973658i | ||||
\(423\) | 9.98016 | + | 17.2861i | 0.485252 | + | 0.840481i | ||||
\(424\) | −9.09122 | + | 15.7465i | −0.441509 | + | 0.764716i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −26.9894 | −1.30764 | ||||||||
\(427\) | −26.4228 | + | 45.7656i | −1.27869 | + | 2.21475i | ||||
\(428\) | −1.22686 | + | 2.12498i | −0.0593023 | + | 0.102715i | ||||
\(429\) | 78.4175 | 3.78603 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.8908 | + | 29.2557i | −0.813600 | + | 1.40920i | 0.0967292 | + | 0.995311i | \(0.469162\pi\) |
−0.910329 | + | 0.413885i | \(0.864171\pi\) | |||||||
\(432\) | 13.4277 | + | 23.2575i | 0.646041 | + | 1.11898i | ||||
\(433\) | 7.51443 | − | 13.0154i | 0.361120 | − | 0.625479i | −0.627025 | − | 0.778999i | \(-0.715728\pi\) |
0.988146 | + | 0.153520i | \(0.0490610\pi\) | |||||||
\(434\) | 19.6713 | + | 34.0718i | 0.944254 | + | 1.63550i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.58910 | −0.0761043 | ||||||||
\(437\) | −1.98681 | − | 1.57420i | −0.0950419 | − | 0.0753042i | ||||
\(438\) | 12.2251 | 0.584139 | ||||||||
\(439\) | −18.8607 | − | 32.6677i | −0.900173 | − | 1.55915i | −0.827269 | − | 0.561807i | \(-0.810106\pi\) |
−0.0729045 | − | 0.997339i | \(-0.523227\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.9132 | + | 32.7586i | −0.900628 | + | 1.55993i | ||||
\(442\) | −6.35976 | − | 11.0154i | −0.302503 | − | 0.523950i | ||||
\(443\) | −6.55722 | + | 11.3574i | −0.311543 | + | 0.539608i | −0.978697 | − | 0.205312i | \(-0.934179\pi\) |
0.667154 | + | 0.744920i | \(0.267512\pi\) | |||||||
\(444\) | −1.30928 | −0.0621358 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.78129 | − | 10.0135i | 0.273752 | − | 0.474153i | ||||
\(447\) | 2.10781 | − | 3.65084i | 0.0996961 | − | 0.172679i | ||||
\(448\) | 26.8049 | 1.26641 | ||||||||
\(449\) | 11.6905 | 0.551711 | 0.275855 | − | 0.961199i | \(-0.411039\pi\) | ||||
0.275855 | + | 0.961199i | \(0.411039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.33673 | + | 4.04733i | 0.110032 | + | 0.190581i | ||||
\(452\) | −1.21744 | + | 2.10868i | −0.0572638 | + | 0.0991838i | ||||
\(453\) | −9.17789 | − | 15.8966i | −0.431215 | − | 0.746886i | ||||
\(454\) | 12.4799 | + | 21.6158i | 0.585709 | + | 1.01448i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.9701 | + | 12.2678i | −1.45031 | + | 0.574490i | ||||
\(457\) | −21.4290 | −1.00240 | −0.501202 | − | 0.865330i | \(-0.667109\pi\) | ||||
−0.501202 | + | 0.865330i | \(0.667109\pi\) | |||||||
\(458\) | −0.186175 | − | 0.322465i | −0.00869939 | − | 0.0150678i | ||||
\(459\) | −5.40221 | − | 9.35691i | −0.252154 | − | 0.436743i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.82920 | + | 8.36442i | 0.224918 | + | 0.389570i | 0.956295 | − | 0.292404i | \(-0.0944551\pi\) |
−0.731377 | + | 0.681974i | \(0.761122\pi\) | |||||||
\(462\) | −44.8058 | + | 77.6060i | −2.08456 | + | 3.61056i | ||||
\(463\) | 1.24981 | 0.0580838 | 0.0290419 | − | 0.999578i | \(-0.490754\pi\) | ||||
0.0290419 | + | 0.999578i | \(0.490754\pi\) | |||||||
\(464\) | −7.24017 | −0.336116 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.1840 | − | 29.7635i | 0.796032 | − | 1.37877i | ||||
\(467\) | −31.3476 | −1.45059 | −0.725296 | − | 0.688437i | \(-0.758297\pi\) | ||||
−0.725296 | + | 0.688437i | \(0.758297\pi\) | |||||||
\(468\) | −4.91092 | −0.227007 | ||||||||
\(469\) | 1.47897 | − | 2.56165i | 0.0682925 | − | 0.118286i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.8368 | + | 55.1430i | −1.46696 | + | 2.54085i | ||||
\(472\) | 0.546481 | + | 0.946533i | 0.0251538 | + | 0.0435677i | ||||
\(473\) | 2.99682 | + | 5.19065i | 0.137794 | + | 0.238666i | ||||
\(474\) | 52.9037 | 2.42995 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.28487 | 0.0588918 | ||||||||
\(477\) | −17.5391 | − | 30.3786i | −0.803060 | − | 1.39094i | ||||
\(478\) | −5.61949 | − | 9.73324i | −0.257029 | − | 0.445188i | ||||
\(479\) | −2.37730 | + | 4.11760i | −0.108622 | + | 0.188138i | −0.915212 | − | 0.402973i | \(-0.867977\pi\) |
0.806591 | + | 0.591111i | \(0.201310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.79758 | + | 10.0417i | −0.264347 | + | 0.457862i | ||||
\(482\) | 8.17052 | 0.372157 | ||||||||
\(483\) | −6.28870 | −0.286146 | ||||||||
\(484\) | −1.96841 | + | 3.40939i | −0.0894733 | + | 0.154972i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18.3230 | 0.831150 | ||||||||
\(487\) | 17.0491 | 0.772569 | 0.386285 | − | 0.922380i | \(-0.373758\pi\) | ||||
0.386285 | + | 0.922380i | \(0.373758\pi\) | |||||||
\(488\) | −18.6728 | + | 32.3423i | −0.845280 | + | 1.46407i | ||||
\(489\) | 21.4714 | + | 37.1896i | 0.970970 | + | 1.68177i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.14031 | + | 3.70713i | 0.0965910 | + | 0.167301i | 0.910272 | − | 0.414012i | \(-0.135873\pi\) |
−0.813680 | + | 0.581312i | \(0.802539\pi\) | |||||||
\(492\) | −0.231403 | − | 0.400802i | −0.0104325 | − | 0.0180696i | ||||
\(493\) | 2.91285 | 0.131188 | ||||||||
\(494\) | 4.62258 | − | 31.3392i | 0.207980 | − | 1.41002i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.2624 | + | 26.4353i | 0.685304 | + | 1.18698i | ||||
\(497\) | −12.0724 | − | 20.9100i | −0.541521 | − | 0.937942i | ||||
\(498\) | 21.9826 | − | 38.0750i | 0.985064 | − | 1.70618i | ||||
\(499\) | 2.41284 | + | 4.17916i | 0.108013 | + | 0.187085i | 0.914965 | − | 0.403532i | \(-0.132218\pi\) |
−0.806952 | + | 0.590617i | \(0.798884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.4206 | 1.22506 | ||||||||
\(502\) | 27.6371 | 1.23350 | ||||||||
\(503\) | 12.1368 | − | 21.0215i | 0.541153 | − | 0.937304i | −0.457685 | − | 0.889114i | \(-0.651321\pi\) |
0.998838 | − | 0.0481900i | \(-0.0153453\pi\) | |||||||
\(504\) | −26.1311 | + | 45.2604i | −1.16397 | + | 2.01606i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.81901 | −0.214231 | ||||||||
\(507\) | −15.8176 | + | 27.3969i | −0.702485 | + | 1.21674i | ||||
\(508\) | −0.791177 | − | 1.37036i | −0.0351028 | − | 0.0607998i | ||||
\(509\) | 5.05690 | − | 8.75880i | 0.224143 | − | 0.388227i | −0.731919 | − | 0.681392i | \(-0.761375\pi\) |
0.956062 | + | 0.293165i | \(0.0947084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.46831 | + | 9.47140i | 0.241904 | + | 0.418990i | ||||
\(512\) | 18.5188 | 0.818423 | ||||||||
\(513\) | 3.92659 | − | 26.6207i | 0.173363 | − | 1.17533i | ||||
\(514\) | −1.02603 | −0.0452562 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.296772 | − | 0.514024i | −0.0130646 | − | 0.0226286i | ||||
\(517\) | −10.8187 | + | 18.7386i | −0.475807 | + | 0.824123i | ||||
\(518\) | −6.62519 | − | 11.4752i | −0.291094 | − | 0.504190i | ||||
\(519\) | 12.6157 | − | 21.8510i | 0.553767 | − | 0.959153i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3729 | 1.28685 | 0.643426 | − | 0.765508i | \(-0.277513\pi\) | ||||
0.643426 | + | 0.765508i | \(0.277513\pi\) | |||||||
\(522\) | 6.36129 | − | 11.0181i | 0.278426 | − | 0.482248i | ||||
\(523\) | 5.59998 | − | 9.69944i | 0.244870 | − | 0.424127i | −0.717225 | − | 0.696842i | \(-0.754588\pi\) |
0.962095 | + | 0.272714i | \(0.0879214\pi\) | |||||||
\(524\) | 3.73324 | 0.163087 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.61074 | − | 14.9142i | 0.375446 | − | 0.650292i | ||||
\(527\) | −6.14037 | − | 10.6354i | −0.267479 | − | 0.463286i | ||||
\(528\) | −34.7636 | + | 60.2124i | −1.51289 | + | 2.62041i | ||||
\(529\) | 11.3309 | + | 19.6257i | 0.492648 | + | 0.853292i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.10858 | −0.0915046 | ||||||||
\(532\) | 2.50814 | + | 1.98726i | 0.108742 | + | 0.0861588i | ||||
\(533\) | −4.09866 | −0.177533 | ||||||||
\(534\) | 37.7485 | + | 65.3822i | 1.63354 | + | 2.82937i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.04518 | − | 1.81031i | 0.0451450 | − | 0.0781934i | ||||
\(537\) | −15.4519 | − | 26.7634i | −0.666798 | − | 1.15493i | ||||
\(538\) | −17.4866 | + | 30.2877i | −0.753901 | + | 1.30579i | ||||
\(539\) | −41.0047 | −1.76620 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.84691 | + | 4.93100i | −0.122398 | + | 0.212000i | −0.920713 | − | 0.390241i | \(-0.872392\pi\) |
0.798315 | + | 0.602241i | \(0.205725\pi\) | |||||||
\(542\) | −5.65809 | + | 9.80010i | −0.243036 | + | 0.420950i | ||||
\(543\) | 30.7019 | 1.31754 | ||||||||
\(544\) | 1.91352 | 0.0820415 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −39.2951 | − | 68.0612i | −1.68168 | − | 2.91275i | ||||
\(547\) | −5.99088 | + | 10.3765i | −0.256151 | + | 0.443667i | −0.965208 | − | 0.261485i | \(-0.915788\pi\) |
0.709056 | + | 0.705152i | \(0.249121\pi\) | |||||||
\(548\) | −0.152425 | − | 0.264009i | −0.00651129 | − | 0.0112779i | ||||
\(549\) | −36.0243 | − | 62.3959i | −1.53748 | − | 2.66299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.68607 | + | 4.50522i | 0.242235 | + | 0.191929i | ||||
\(552\) | −4.44419 | −0.189157 | ||||||||
\(553\) | 23.6639 | + | 40.9871i | 1.00629 | + | 1.74295i | ||||
\(554\) | −13.8149 | − | 23.9281i | −0.586939 | − | 1.01661i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.198706 | + | 0.344168i | 0.00842700 | + | 0.0145960i | ||||
\(557\) | 17.2786 | − | 29.9275i | 0.732119 | − | 1.26807i | −0.223857 | − | 0.974622i | \(-0.571865\pi\) |
0.955976 | − | 0.293446i | \(-0.0948019\pi\) | |||||||
\(558\) | −53.6390 | −2.27072 | ||||||||
\(559\) | −5.25649 | −0.222326 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.9860 | − | 24.2245i | 0.590491 | − | 1.02276i | ||||
\(562\) | −20.7216 | −0.874087 | ||||||||
\(563\) | 24.8817 | 1.04864 | 0.524318 | − | 0.851522i | \(-0.324320\pi\) | ||||
0.524318 | + | 0.851522i | \(0.324320\pi\) | |||||||
\(564\) | 1.07137 | − | 1.85566i | 0.0451126 | − | 0.0781374i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.2681 | + | 31.6413i | −0.767867 | + | 1.32998i | ||||
\(567\) | −4.07422 | − | 7.05676i | −0.171101 | − | 0.296356i | ||||
\(568\) | −8.53150 | − | 14.7770i | −0.357974 | − | 0.620029i | ||||
\(569\) | −38.7345 | −1.62384 | −0.811918 | − | 0.583771i | \(-0.801577\pi\) | ||||
−0.811918 | + | 0.583771i | \(0.801577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.53514 | −0.189790 | −0.0948948 | − | 0.995487i | \(-0.530251\pi\) | ||||
−0.0948948 | + | 0.995487i | \(0.530251\pi\) | |||||||
\(572\) | −2.66178 | − | 4.61034i | −0.111295 | − | 0.192768i | ||||
\(573\) | 8.97534 | + | 15.5457i | 0.374950 | + | 0.649433i | ||||
\(574\) | 2.34188 | − | 4.05625i | 0.0977481 | − | 0.169305i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −18.2726 | + | 31.6491i | −0.761359 | + | 1.31871i | ||||
\(577\) | 21.9514 | 0.913847 | 0.456923 | − | 0.889506i | \(-0.348951\pi\) | ||||
0.456923 | + | 0.889506i | \(0.348951\pi\) | |||||||
\(578\) | 20.6432 | 0.858642 | ||||||||
\(579\) | −25.4666 | + | 44.1095i | −1.05836 | + | 1.83313i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.3314 | 1.63174 | ||||||||
\(582\) | 46.5448 | 1.92934 | ||||||||
\(583\) | 19.0128 | − | 32.9311i | 0.787430 | − | 1.36387i | ||||
\(584\) | 3.86443 | + | 6.69339i | 0.159911 | + | 0.276974i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.83430 | + | 13.5694i | 0.323632 | + | 0.560547i | ||||
\(587\) | −20.5232 | − | 35.5472i | −0.847084 | − | 1.46719i | −0.883799 | − | 0.467866i | \(-0.845023\pi\) |
0.0367158 | − | 0.999326i | \(-0.488310\pi\) | |||||||
\(588\) | 4.06064 | 0.167458 | ||||||||
\(589\) | 4.46311 | − | 30.2581i | 0.183899 | − | 1.24676i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.2715 | + | 42.0395i | 0.998397 | + | 1.72927i | ||||
\(592\) | −5.14030 | − | 8.90327i | −0.211265 | − | 0.365922i | ||||
\(593\) | −4.85982 | + | 8.41745i | −0.199569 | + | 0.345663i | −0.948389 | − | 0.317110i | \(-0.897287\pi\) |
0.748820 | + | 0.662774i | \(0.230621\pi\) | |||||||
\(594\) | −25.5780 | − | 44.3025i | −1.04948 | − | 1.81775i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.286188 | −0.0117227 | ||||||||
\(597\) | 46.9769 | 1.92264 | ||||||||
\(598\) | 2.11316 | − | 3.66010i | 0.0864135 | − | 0.149673i | ||||
\(599\) | 15.2247 | − | 26.3700i | 0.622065 | − | 1.07745i | −0.367036 | − | 0.930207i | \(-0.619627\pi\) |
0.989101 | − | 0.147241i | \(-0.0470392\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.5483 | 1.00135 | 0.500673 | − | 0.865637i | \(-0.333086\pi\) | ||||
0.500673 | + | 0.865637i | \(0.333086\pi\) | |||||||
\(602\) | 3.00343 | − | 5.20209i | 0.122411 | − | 0.212021i | ||||
\(603\) | 2.01640 | + | 3.49251i | 0.0821142 | + | 0.142226i | ||||
\(604\) | −0.623063 | + | 1.07918i | −0.0253521 | + | 0.0439111i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.9146 | + | 18.9047i | 0.443376 | + | 0.767949i | ||||
\(607\) | −39.0162 | −1.58362 | −0.791810 | − | 0.610767i | \(-0.790861\pi\) | ||||
−0.791810 | + | 0.610767i | \(0.790861\pi\) | |||||||
\(608\) | 3.73531 | + | 2.95958i | 0.151487 | + | 0.120027i | ||||
\(609\) | 17.9977 | 0.729303 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.48813 | − | 16.4339i | −0.383849 | − | 0.664845i | ||||
\(612\) | −0.875881 | + | 1.51707i | −0.0354054 | + | 0.0613239i | ||||
\(613\) | 2.48708 | + | 4.30775i | 0.100452 | + | 0.173988i | 0.911871 | − | 0.410477i | \(-0.134638\pi\) |
−0.811419 | + | 0.584465i | \(0.801304\pi\) | |||||||
\(614\) | −9.49775 | + | 16.4506i | −0.383298 | + | 0.663891i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −56.6536 | −2.28264 | ||||||||
\(617\) | −19.3210 | + | 33.4649i | −0.777834 | + | 1.34725i | 0.155354 | + | 0.987859i | \(0.450348\pi\) |
−0.933188 | + | 0.359389i | \(0.882985\pi\) | |||||||
\(618\) | 16.4146 | − | 28.4310i | 0.660293 | − | 1.14366i | ||||
\(619\) | −27.9053 | −1.12161 | −0.560804 | − | 0.827949i | \(-0.689508\pi\) | ||||
−0.560804 | + | 0.827949i | \(0.689508\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.79500 | − | 3.10902i | 0.0720307 | − | 0.124761i | ||||
\(622\) | 2.53807 | + | 4.39607i | 0.101767 | + | 0.176266i | ||||
\(623\) | −33.7699 | + | 58.4912i | −1.35296 | + | 2.34340i | ||||
\(624\) | −30.4880 | − | 52.8068i | −1.22050 | − | 2.11396i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.21322 | −0.168394 | ||||||||
\(627\) | 64.7690 | − | 25.6560i | 2.58662 | − | 1.02460i | ||||
\(628\) | 4.32264 | 0.172492 | ||||||||
\(629\) | 2.06804 | + | 3.58195i | 0.0824581 | + | 0.142822i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.62012 | − | 11.4664i | 0.263543 | − | 0.456469i | −0.703638 | − | 0.710559i | \(-0.748442\pi\) |
0.967181 | + | 0.254089i | \(0.0817757\pi\) | |||||||
\(632\) | 16.7232 | + | 28.9654i | 0.665212 | + | 1.15218i | ||||
\(633\) | −22.2721 | + | 38.5763i | −0.885235 | + | 1.53327i | ||||
\(634\) | −6.90451 | −0.274213 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.88281 | + | 3.26113i | −0.0746584 | + | 0.129312i | ||||
\(637\) | 17.9808 | − | 31.1436i | 0.712423 | − | 1.23395i | ||||
\(638\) | 13.7916 | 0.546014 | ||||||||
\(639\) | 32.9185 | 1.30224 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.7555 | − | 32.4854i | −0.740796 | − | 1.28310i | −0.952133 | − | 0.305684i | \(-0.901115\pi\) |
0.211337 | − | 0.977413i | \(-0.432218\pi\) | |||||||
\(642\) | 26.7680 | − | 46.3636i | 1.05645 | − | 1.82982i | ||||
\(643\) | −12.1969 | − | 21.1257i | −0.481000 | − | 0.833117i | 0.518762 | − | 0.854919i | \(-0.326393\pi\) |
−0.999762 | + | 0.0218020i | \(0.993060\pi\) | |||||||
\(644\) | 0.213462 | + | 0.369726i | 0.00841157 | + | 0.0145693i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.85679 | − | 7.01746i | −0.348466 | − | 0.276098i | ||||
\(647\) | −8.05266 | −0.316583 | −0.158291 | − | 0.987392i | \(-0.550599\pi\) | ||||
−0.158291 | + | 0.987392i | \(0.550599\pi\) | |||||||
\(648\) | −2.87923 | − | 4.98698i | −0.113107 | − | 0.195907i | ||||
\(649\) | −1.14288 | − | 1.97952i | −0.0448618 | − | 0.0777030i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.9396 | − | 65.7133i | −1.48697 | − | 2.57551i | ||||
\(652\) | 1.45764 | − | 2.52470i | 0.0570855 | − | 0.0988750i | ||||
\(653\) | 19.9890 | 0.782228 | 0.391114 | − | 0.920342i | \(-0.372090\pi\) | ||||
0.391114 | + | 0.920342i | \(0.372090\pi\) | |||||||
\(654\) | 34.6717 | 1.35577 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.81700 | − | 3.14713i | 0.0709419 | − | 0.122875i | ||||
\(657\) | −14.9108 | −0.581725 | ||||||||
\(658\) | 21.6852 | 0.845375 | ||||||||
\(659\) | 16.2197 | − | 28.0933i | 0.631829 | − | 1.09436i | −0.355349 | − | 0.934734i | \(-0.615638\pi\) |
0.987178 | − | 0.159626i | \(-0.0510287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.7771 | − | 30.7908i | 0.691448 | − | 1.19762i | −0.279915 | − | 0.960025i | \(-0.590306\pi\) |
0.971363 | − | 0.237599i | \(-0.0763603\pi\) | |||||||
\(662\) | −5.18610 | − | 8.98260i | −0.201564 | − | 0.349118i | ||||
\(663\) | 12.2659 | + | 21.2451i | 0.476368 | + | 0.825093i | ||||
\(664\) | 27.7953 | 1.07867 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.0653 | 0.700017 | ||||||||
\(667\) | 0.483927 | + | 0.838187i | 0.0187377 | + | 0.0324547i | ||||
\(668\) | −0.930757 | − | 1.61212i | −0.0360121 | − | 0.0623747i | ||||
\(669\) | −11.1502 | + | 19.3127i | −0.431092 | + | 0.746674i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.0512 | − | 67.6387i | 1.50755 | − | 2.61116i | ||||
\(672\) | 11.8231 | 0.456086 | ||||||||
\(673\) | −27.5963 | −1.06376 | −0.531880 | − | 0.846820i | \(-0.678514\pi\) | ||||
−0.531880 | + | 0.846820i | \(0.678514\pi\) | |||||||
\(674\) | 10.0259 | − | 17.3654i | 0.386184 | − | 0.668891i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.14763 | 0.0826013 | ||||||||
\(677\) | −21.2114 | −0.815221 | −0.407610 | − | 0.913156i | \(-0.633638\pi\) | ||||
−0.407610 | + | 0.913156i | \(0.633638\pi\) | |||||||
\(678\) | 26.5627 | − | 46.0079i | 1.02013 | − | 1.76692i | ||||
\(679\) | 20.8196 | + | 36.0605i | 0.798981 | + | 1.38388i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.0696 | − | 41.6897i | −0.922348 | − | 1.59755i | ||||
\(682\) | −29.0730 | − | 50.3559i | −1.11326 | − | 1.92823i | ||||
\(683\) | −19.3626 | −0.740891 | −0.370446 | − | 0.928854i | \(-0.620795\pi\) | ||||
−0.370446 | + | 0.928854i | \(0.620795\pi\) | |||||||
\(684\) | −4.05618 | + | 1.60672i | −0.155092 | + | 0.0614344i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.923282 | + | 1.59917i | 0.0352511 | + | 0.0610567i | ||||
\(687\) | 0.359071 | + | 0.621929i | 0.0136994 | + | 0.0237281i | ||||
\(688\) | 2.33028 | − | 4.03616i | 0.0888410 | − | 0.153877i | ||||
\(689\) | 16.6744 | + | 28.8809i | 0.635244 | + | 1.10028i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.28081 | −0.0487241 | −0.0243621 | − | 0.999703i | \(-0.507755\pi\) | ||||
−0.0243621 | + | 0.999703i | \(0.507755\pi\) | |||||||
\(692\) | −1.71289 | −0.0651144 | ||||||||
\(693\) | 54.6490 | − | 94.6548i | 2.07594 | − | 3.59564i | ||||
\(694\) | −16.2660 | + | 28.1735i | −0.617448 | + | 1.06945i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.7189 | 0.482108 | ||||||||
\(697\) | −0.731012 | + | 1.26615i | −0.0276891 | + | 0.0479588i | ||||
\(698\) | −16.4361 | − | 28.4681i | −0.622114 | − | 1.07753i | ||||
\(699\) | −33.1423 | + | 57.4041i | −1.25356 | + | 2.17122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.5649 | + | 32.1553i | 0.701185 | + | 1.21449i | 0.968051 | + | 0.250754i | \(0.0806787\pi\) |
−0.266866 | + | 0.963734i | \(0.585988\pi\) | |||||||
\(702\) | 44.8644 | 1.69330 | ||||||||
\(703\) | −1.50315 | + | 10.1908i | −0.0566924 | + | 0.384352i | ||||
\(704\) | −39.6159 | −1.49308 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.502875 | + | 0.871005i | 0.0189260 | + | 0.0327807i | ||||
\(707\) | −9.76425 | + | 16.9122i | −0.367222 | + | 0.636048i | ||||
\(708\) | 0.113178 | + | 0.196029i | 0.00425347 | + | 0.00736723i | ||||
\(709\) | −6.57886 | + | 11.3949i | −0.247074 | + | 0.427945i | −0.962713 | − | 0.270526i | \(-0.912802\pi\) |
0.715638 | + | 0.698471i | \(0.246136\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −64.5258 | −2.41991 | ||||||||
\(712\) | −23.8650 | + | 41.3354i | −0.894379 | + | 1.54911i | ||||
\(713\) | 2.04026 | − | 3.53384i | 0.0764084 | − | 0.132343i | ||||
\(714\) | −28.0337 | −1.04914 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.04899 | + | 1.81690i | −0.0392025 | + | 0.0679007i | ||||
\(717\) | 10.8382 | + | 18.7722i | 0.404758 | + | 0.701062i | ||||
\(718\) | −18.7560 | + | 32.4863i | −0.699967 | + | 1.21238i | ||||
\(719\) | −7.27853 | − | 12.6068i | −0.271443 | − | 0.470153i | 0.697788 | − | 0.716304i | \(-0.254168\pi\) |
−0.969232 | + | 0.246150i | \(0.920834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.3692 | 1.09376 | ||||||||
\(722\) | −6.43530 | − | 27.3970i | −0.239497 | − | 1.01961i | ||||
\(723\) | −15.7583 | −0.586056 | ||||||||
\(724\) | −1.04214 | − | 1.80503i | −0.0387306 | − | 0.0670834i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 42.9476 | − | 74.3874i | 1.59394 | − | 2.76078i | ||||
\(727\) | 4.48581 | + | 7.76966i | 0.166370 | + | 0.288161i | 0.937141 | − | 0.348951i | \(-0.113462\pi\) |
−0.770771 | + | 0.637112i | \(0.780129\pi\) | |||||||
\(728\) | 24.8428 | − | 43.0291i | 0.920737 | − | 1.59476i | ||||
\(729\) | −41.7969 | −1.54803 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.937514 | + | 1.62382i | −0.0346752 | + | 0.0600592i | ||||
\(732\) | −3.86719 | + | 6.69817i | −0.142935 | + | 0.247571i | ||||
\(733\) | −24.7325 | −0.913516 | −0.456758 | − | 0.889591i | \(-0.650990\pi\) | ||||
−0.456758 | + | 0.889591i | \(0.650990\pi\) | |||||||
\(734\) | 17.2753 | 0.637642 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.317903 | + | 0.550624i | 0.0117181 | + | 0.0202963i | ||||
\(737\) | −2.18583 | + | 3.78596i | −0.0805159 | + | 0.139458i | ||||
\(738\) | 3.19287 | + | 5.53021i | 0.117531 | + | 0.203570i | ||||
\(739\) | 0.784588 | + | 1.35895i | 0.0288615 | + | 0.0499896i | 0.880095 | − | 0.474797i | \(-0.157478\pi\) |
−0.851234 | + | 0.524787i | \(0.824145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.91543 | + | 60.4431i | −0.327517 | + | 2.22043i | ||||
\(742\) | −38.1094 | −1.39904 | ||||||||
\(743\) | −12.1463 | − | 21.0380i | −0.445604 | − | 0.771808i | 0.552490 | − | 0.833519i | \(-0.313678\pi\) |
−0.998094 | + | 0.0617109i | \(0.980344\pi\) | |||||||
\(744\) | −26.8117 | − | 46.4392i | −0.982965 | − | 1.70254i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.69539 | + | 16.7929i | 0.354974 | + | 0.614832i | ||||
\(747\) | −26.8119 | + | 46.4395i | −0.980994 | + | 1.69913i | ||||
\(748\) | −1.89895 | −0.0694326 | ||||||||
\(749\) | 47.8935 | 1.74999 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4771 | + | 30.2712i | −0.637748 | + | 1.10461i | 0.348178 | + | 0.937429i | \(0.386801\pi\) |
−0.985926 | + | 0.167184i | \(0.946533\pi\) | |||||||
\(752\) | 16.8249 | 0.613541 | ||||||||
\(753\) | −53.3029 | −1.94247 | ||||||||
\(754\) | −6.04768 | + | 10.4749i | −0.220243 | + | 0.381473i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.26600 | + | 3.92482i | −0.0824135 | + | 0.142744i | ||||
\(757\) | −1.61043 | − | 2.78935i | −0.0585321 | − | 0.101381i | 0.835275 | − | 0.549833i | \(-0.185309\pi\) |
−0.893807 | + | 0.448452i | \(0.851975\pi\) | |||||||
\(758\) | −24.2595 | − | 42.0186i | −0.881143 | − | 1.52619i | ||||
\(759\) | 9.29430 | 0.337362 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.72402 | 0.134996 | 0.0674979 | − | 0.997719i | \(-0.478498\pi\) | ||||
0.0674979 | + | 0.997719i | \(0.478498\pi\) | |||||||
\(762\) | 17.2622 | + | 29.8990i | 0.625344 | + | 1.08313i | ||||
\(763\) | 15.5087 | + | 26.8619i | 0.561453 | + | 0.972465i | ||||
\(764\) | 0.609312 | − | 1.05536i | 0.0220441 | − | 0.0381816i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.9930 | − | 32.8968i | 0.686244 | − | 1.18861i | ||||
\(767\) | 2.00463 | 0.0723829 | ||||||||
\(768\) | 13.1756 | 0.475435 | ||||||||
\(769\) | 16.1032 | − | 27.8915i | 0.580695 | − | 1.00579i | −0.414702 | − | 0.909957i | \(-0.636114\pi\) |
0.995397 | − | 0.0958365i | \(-0.0305526\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.97887 | 0.0712674 | ||||||||
\(772\) | 3.45773 | 0.124446 | ||||||||
\(773\) | 10.3416 | − | 17.9122i | 0.371963 | − | 0.644259i | −0.617904 | − | 0.786253i | \(-0.712018\pi\) |
0.989867 | + | 0.141994i | \(0.0453515\pi\) | |||||||
\(774\) | 4.09482 | + | 7.09243i | 0.147185 | + | 0.254932i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.7131 | + | 25.4838i | 0.528169 | + | 0.914815i | ||||
\(777\) | 12.7778 | + | 22.1318i | 0.458402 | + | 0.793975i | ||||
\(778\) | 27.4711 | 0.984886 | ||||||||
\(779\) | −3.38530 | + | 1.34097i | −0.121291 | + | 0.0480452i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.8422 | + | 30.9037i | 0.638446 | + | 1.10582i | ||||
\(782\) | −0.753780 | − | 1.30558i | −0.0269551 | − | 0.0466876i | ||||
\(783\) | −5.13712 | + | 8.89775i | −0.183586 | + | 0.317980i | ||||
\(784\) | 15.9423 | + | 27.6128i | 0.569367 | + | 0.986172i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −81.4534 | −2.90535 | ||||||||
\(787\) | 46.0227 | 1.64053 | 0.820266 | − | 0.571982i | \(-0.193825\pi\) | ||||
0.820266 | + | 0.571982i | \(0.193825\pi\) | |||||||
\(788\) | 1.64773 | − | 2.85395i | 0.0586980 | − | 0.101668i | ||||
\(789\) | −16.6073 | + | 28.7647i | −0.591236 | + | 1.02405i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.5261 | 1.68983 | ||||||||
\(792\) | 38.6202 | − | 66.8921i | 1.37231 | − | 2.37691i | ||||
\(793\) | 34.2483 | + | 59.3197i | 1.21619 | + | 2.10651i | ||||
\(794\) | −11.4023 | + | 19.7494i | −0.404654 | + | 0.700880i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.59457 | − | 2.76187i | −0.0565180 | − | 0.0978920i | ||||
\(797\) | 25.0847 | 0.888546 | 0.444273 | − | 0.895891i | \(-0.353462\pi\) | ||||
0.444273 | + | 0.895891i | \(0.353462\pi\) | |||||||
\(798\) | −54.7236 | − | 43.3589i | −1.93719 | − | 1.53489i | ||||
\(799\) | −6.76897 | −0.239469 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −46.0412 | − | 79.7457i | −1.62679 | − | 2.81768i | ||||
\(802\) | −15.2499 | + | 26.4135i | −0.538491 | + | 0.932694i | ||||
\(803\) | −8.08183 | − | 13.9981i | −0.285201 | − | 0.493983i | ||||
\(804\) | 0.216460 | − | 0.374919i | 0.00763394 | − | 0.0132224i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.9946 | 1.79621 | ||||||||
\(807\) | 33.7259 | − | 58.4150i | 1.18721 | − | 2.05631i | ||||
\(808\) | −6.90034 | + | 11.9517i | −0.242753 | + | 0.420461i | ||||
\(809\) | 27.6272 | 0.971319 | 0.485660 | − | 0.874148i | \(-0.338579\pi\) | ||||
0.485660 | + | 0.874148i | \(0.338579\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.2254 | − | 33.2993i | 0.675094 | − | 1.16930i | −0.301347 | − | 0.953514i | \(-0.597436\pi\) |
0.976441 | − | 0.215783i | \(-0.0692304\pi\) | |||||||
\(812\) | −0.610908 | − | 1.05812i | −0.0214387 | − | 0.0371329i | ||||
\(813\) | 10.9126 | − | 18.9012i | 0.382722 | − | 0.662893i | ||||
\(814\) | 9.79162 | + | 16.9596i | 0.343196 | + | 0.594433i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −21.7506 | −0.761423 | ||||||||
\(817\) | −4.34160 | + | 1.71978i | −0.151893 | + | 0.0601674i | ||||
\(818\) | 2.40522 | 0.0840966 | ||||||||
\(819\) | 47.9277 | + | 83.0132i | 1.67473 | + | 2.90071i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.3339 | + | 45.6117i | −0.919060 | + | 1.59186i | −0.118215 | + | 0.992988i | \(0.537717\pi\) |
−0.800845 | + | 0.598871i | \(0.795616\pi\) | |||||||
\(822\) | 3.32568 | + | 5.76024i | 0.115996 | + | 0.200912i | ||||
\(823\) | −2.33597 | + | 4.04602i | −0.0814269 | + | 0.141035i | −0.903863 | − | 0.427822i | \(-0.859281\pi\) |
0.822436 | + | 0.568857i | \(0.192614\pi\) | |||||||
\(824\) | 20.7550 | 0.723036 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.14540 | + | 1.98388i | −0.0398534 | + | 0.0690281i | ||||
\(827\) | −13.7124 | + | 23.7506i | −0.476827 | + | 0.825888i | −0.999647 | − | 0.0265546i | \(-0.991546\pi\) |
0.522821 | + | 0.852443i | \(0.324880\pi\) | |||||||
\(828\) | −0.582059 | −0.0202279 | ||||||||
\(829\) | 0.156181 | 0.00542438 | 0.00271219 | − | 0.999996i | \(-0.499137\pi\) | ||||
0.00271219 | + | 0.999996i | \(0.499137\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.6444 | + | 46.1495i | 0.924285 | + | 1.60091i | ||||
\(832\) | 17.3718 | − | 30.0888i | 0.602258 | − | 1.04314i | ||||
\(833\) | −6.41387 | − | 11.1091i | −0.222227 | − | 0.384909i | ||||
\(834\) | −4.33544 | − | 7.50920i | −0.150124 | − | 0.260022i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.70687 | − | 2.93705i | −0.128205 | − | 0.101580i | ||||
\(837\) | 43.3167 | 1.49724 | ||||||||
\(838\) | 12.4485 | + | 21.5615i | 0.430027 | + | 0.744828i | ||||
\(839\) | 14.5946 | + | 25.2786i | 0.503862 | + | 0.872715i | 0.999990 | + | 0.00446519i | \(0.00142132\pi\) |
−0.496128 | + | 0.868249i | \(0.665245\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.1150 | + | 22.7159i | 0.452243 | + | 0.783308i | ||||
\(842\) | 15.5108 | − | 26.8655i | 0.534537 | − | 0.925845i | ||||
\(843\) | 39.9651 | 1.37647 | ||||||||
\(844\) | 3.02398 | 0.104090 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −14.7826 | + | 25.6041i | −0.508235 | + | 0.880288i | ||||
\(847\) | 76.8421 | 2.64033 | ||||||||
\(848\) | −29.5680 | −1.01537 | ||||||||
\(849\) | 35.2332 | − | 61.0258i | 1.20920 | − | 2.09440i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.687148 | + | 1.19018i | −0.0235551 | + | 0.0407987i | ||||
\(852\) | −1.76689 | − | 3.06035i | −0.0605328 | − | 0.104846i | ||||
\(853\) | 22.8832 | + | 39.6348i | 0.783505 | + | 1.35707i | 0.929888 | + | 0.367842i | \(0.119903\pi\) |
−0.146384 | + | 0.989228i | \(0.546763\pi\) | |||||||
\(854\) | −78.2745 | −2.67850 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.8461 | 1.15684 | ||||||||
\(857\) | −7.45807 | − | 12.9177i | −0.254763 | − | 0.441262i | 0.710068 | − | 0.704133i | \(-0.248664\pi\) |
−0.964831 | + | 0.262871i | \(0.915331\pi\) | |||||||
\(858\) | 58.0757 | + | 100.590i | 1.98267 | + | 3.43409i | ||||
\(859\) | −24.6100 | + | 42.6258i | −0.839682 | + | 1.45437i | 0.0504787 | + | 0.998725i | \(0.483925\pi\) |
−0.890161 | + | 0.455647i | \(0.849408\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.51671 | + | 7.82318i | −0.153929 | + | 0.266613i | ||||
\(862\) | −50.0370 | −1.70427 | ||||||||
\(863\) | 20.9577 | 0.713407 | 0.356704 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356704 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(864\) | −3.37469 | + | 5.84514i | −0.114809 | + | 0.198856i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.2607 | 0.756448 | ||||||||
\(867\) | −39.8139 | −1.35215 | ||||||||
\(868\) | −2.57562 | + | 4.46110i | −0.0874222 | + | 0.151420i | ||||
\(869\) | −34.9738 | − | 60.5764i | −1.18640 | − | 2.05491i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.91699 | − | 3.32032i | −0.0649547 | − | 0.112505i | ||||
\(872\) | 10.9599 | + | 18.9831i | 0.371150 | + | 0.642851i | ||||
\(873\) | −56.7700 | −1.92137 | ||||||||
\(874\) | 0.547883 | − | 3.71443i | 0.0185324 | − | 0.125642i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.800333 | + | 1.38622i | 0.0270407 | + | 0.0468359i | ||||
\(877\) | 13.1009 | + | 22.6914i | 0.442385 | + | 0.766233i | 0.997866 | − | 0.0652963i | \(-0.0207993\pi\) |
−0.555481 | + | 0.831529i | \(0.687466\pi\) | |||||||
\(878\) | 27.9364 | − | 48.3873i | 0.942808 | − | 1.63299i | ||||
\(879\) | −15.1098 | − | 26.1709i | −0.509641 | − | 0.882724i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.3499 | −1.52788 | −0.763938 | − | 0.645289i | \(-0.776737\pi\) | ||||
−0.763938 | + | 0.645289i | \(0.776737\pi\) | |||||||
\(882\) | −56.0282 | −1.88657 | ||||||||
\(883\) | 21.6585 | − | 37.5136i | 0.728867 | − | 1.26243i | −0.228495 | − | 0.973545i | \(-0.573381\pi\) |
0.957362 | − | 0.288890i | \(-0.0932861\pi\) | |||||||
\(884\) | 0.832699 | − | 1.44228i | 0.0280067 | − | 0.0485090i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.4250 | −0.652597 | ||||||||
\(887\) | −19.5073 | + | 33.7877i | −0.654992 | + | 1.13448i | 0.326904 | + | 0.945058i | \(0.393995\pi\) |
−0.981896 | + | 0.189422i | \(0.939339\pi\) | |||||||
\(888\) | 9.03002 | + | 15.6405i | 0.303028 | + | 0.524859i | ||||
\(889\) | −15.4428 | + | 26.7478i | −0.517936 | + | 0.897091i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.02145 | + | 10.4295i | 0.201726 | + | 0.349400i | ||||
\(892\) | 1.51392 | 0.0506898 | ||||||||
\(893\) | −13.2135 | − | 10.4694i | −0.442171 | − | 0.350344i | ||||
\(894\) | 6.24416 | 0.208836 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23.9903 | + | 41.5524i | 0.801459 | + | 1.38817i | ||||
\(897\) | −4.07559 | + | 7.05913i | −0.136080 | + | 0.235698i | ||||
\(898\) | 8.65798 | + | 14.9961i | 0.288921 | + | 0.500425i | ||||
\(899\) | −5.83905 | + | 10.1135i | −0.194743 | + | 0.337305i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8958 | 0.396306 | ||||||||
\(902\) | −3.46115 | + | 5.99488i | −0.115244 | + | 0.199608i | ||||
\(903\) | −5.79263 | + | 10.0331i | −0.192767 | + | 0.333882i | ||||
\(904\) | 33.5865 | 1.11707 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13.5942 | − | 23.5459i | 0.451638 | − | 0.782260i | ||||
\(907\) | 25.0804 | + | 43.4405i | 0.832780 | + | 1.44242i | 0.895825 | + | 0.444407i | \(0.146586\pi\) |
−0.0630443 | + | 0.998011i | \(0.520081\pi\) | |||||||
\(908\) | −1.63402 | + | 2.83021i | −0.0542269 | + | 0.0939237i | ||||
\(909\) | −13.3124 | − | 23.0577i | −0.441544 | − | 0.764776i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.4028 | −1.66992 | −0.834959 | − | 0.550312i | \(-0.814509\pi\) | ||||
−0.834959 | + | 0.550312i | \(0.814509\pi\) | |||||||
\(912\) | −42.4585 | − | 33.6410i | −1.40594 | − | 1.11396i | ||||
\(913\) | −58.1294 | −1.92380 | ||||||||
\(914\) | −15.8702 | − | 27.4880i | −0.524940 | − | 0.909223i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.0243764 | − | 0.0422211i | 0.000805418 | − | 0.00139503i | ||||
\(917\) | −36.4342 | − | 63.1059i | −1.20316 | − | 2.08394i | ||||
\(918\) | 8.00173 | − | 13.8594i | 0.264096 | − | 0.457428i | ||||
\(919\) | 48.7246 | 1.60728 | 0.803638 | − | 0.595118i | \(-0.202895\pi\) | ||||
0.803638 | + | 0.595118i | \(0.202895\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.3180 | − | 31.7278i | 0.603600 | − | 1.04547i | ||||
\(922\) | −7.15299 | + | 12.3893i | −0.235571 | + | 0.408021i | ||||
\(923\) | −31.2956 | −1.03011 | ||||||||
\(924\) | −11.7331 | −0.385990 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.925608 | + | 1.60320i | 0.0304174 | + | 0.0526844i | ||||
\(927\) | −20.0207 | + | 34.6768i | −0.657565 | + | 1.13894i | ||||
\(928\) | −0.909811 | − | 1.57584i | −0.0298660 | − | 0.0517294i | ||||
\(929\) | −4.01832 | − | 6.95993i | −0.131837 | − | 0.228348i | 0.792548 | − | 0.609810i | \(-0.208754\pi\) |
−0.924385 | + | 0.381462i | \(0.875421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.66191 | − | 31.6059i | 0.152788 | − | 1.03584i | ||||
\(932\) | 4.49989 | 0.147399 | ||||||||
\(933\) | −4.89511 | − | 8.47858i | −0.160259 | − | 0.277576i | ||||
\(934\) | −23.2159 | − | 40.2111i | −0.759648 | − | 1.31575i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 33.8702 | + | 58.6650i | 1.10708 | + | 1.91752i | ||||
\(937\) | 12.7713 | − | 22.1206i | 0.417221 | − | 0.722647i | −0.578438 | − | 0.815726i | \(-0.696338\pi\) |
0.995659 | + | 0.0930789i | \(0.0296709\pi\) | |||||||
\(938\) | 4.38129 | 0.143054 | ||||||||
\(939\) | 8.12592 | 0.265179 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.30747 | + | 7.46075i | −0.140419 | + | 0.243214i | −0.927655 | − | 0.373439i | \(-0.878178\pi\) |
0.787235 | + | 0.616653i | \(0.211512\pi\) | |||||||
\(942\) | −94.3130 | −3.07288 | ||||||||
\(943\) | −0.485787 | −0.0158194 | ||||||||
\(944\) | −0.888680 | + | 1.53924i | −0.0289241 | + | 0.0500980i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.43888 | + | 7.68837i | −0.144320 | + | 0.249970i | ||||
\(947\) | −19.2138 | − | 33.2793i | −0.624364 | − | 1.08143i | −0.988663 | − | 0.150149i | \(-0.952025\pi\) |
0.364299 | − | 0.931282i | \(-0.381309\pi\) | |||||||
\(948\) | 3.46341 | + | 5.99880i | 0.112486 | + | 0.194832i | ||||
\(949\) | 14.1757 | 0.460162 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.3165 | 0.431819 | ||||||||
\(952\) | −8.86163 | − | 15.3488i | −0.287207 | − | 0.497457i | ||||
\(953\) | 4.44520 | + | 7.69932i | 0.143994 | + | 0.249405i | 0.928997 | − | 0.370087i | \(-0.120672\pi\) |
−0.785003 | + | 0.619492i | \(0.787339\pi\) | |||||||
\(954\) | 25.9788 | − | 44.9966i | 0.841095 | − | 1.45682i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.735774 | − | 1.27440i | 0.0237966 | − | 0.0412170i | ||||
\(957\) | −26.5995 | −0.859838 | ||||||||
\(958\) | −7.04248 | −0.227532 | ||||||||
\(959\) | −2.97516 | + | 5.15313i | −0.0960730 | + | 0.166403i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.2354 | 0.588239 | ||||||||
\(962\) | −17.1747 | −0.553734 | ||||||||
\(963\) | −32.6485 | + | 56.5489i | −1.05208 | + | 1.82226i | ||||
\(964\) | 0.534893 | + | 0.926463i | 0.0172278 | + | 0.0298394i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.65739 | − | 8.06684i | −0.149849 | − | 0.259546i | ||||
\(967\) | −30.8149 | − | 53.3729i | −0.990939 | − | 1.71636i | −0.611789 | − | 0.791021i | \(-0.709550\pi\) |
−0.379150 | − | 0.925335i | \(-0.623784\pi\) | |||||||
\(968\) | 54.3040 | 1.74540 | ||||||||
\(969\) | 17.0818 | + | 13.5344i | 0.548748 | + | 0.434787i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.92998 | − | 5.07488i | −0.0940277 | − | 0.162861i | 0.815175 | − | 0.579215i | \(-0.196641\pi\) |
−0.909202 | + | 0.416354i | \(0.863308\pi\) | |||||||
\(972\) | 1.19954 | + | 2.07767i | 0.0384753 | + | 0.0666412i | ||||
\(973\) | 3.87850 | − | 6.71776i | 0.124339 | − | 0.215361i | ||||
\(974\) | 12.6265 | + | 21.8698i | 0.404580 | + | 0.700753i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −60.7310 | −1.94395 | ||||||||
\(977\) | −2.40082 | −0.0768089 | −0.0384044 | − | 0.999262i | \(-0.512228\pi\) | ||||
−0.0384044 | + | 0.999262i | \(0.512228\pi\) | |||||||
\(978\) | −31.8033 | + | 55.0850i | −1.01696 | + | 1.76142i | ||||
\(979\) | 49.9098 | − | 86.4463i | 1.59512 | − | 2.76284i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.2885 | −1.35017 | ||||||||
\(982\) | −3.17022 | + | 5.49098i | −0.101166 | + | 0.175224i | ||||
\(983\) | −9.18425 | − | 15.9076i | −0.292932 | − | 0.507373i | 0.681570 | − | 0.731753i | \(-0.261298\pi\) |
−0.974502 | + | 0.224380i | \(0.927964\pi\) | |||||||
\(984\) | −3.19194 | + | 5.52860i | −0.101755 | + | 0.176245i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.15725 | + | 3.73647i | 0.0687009 | + | 0.118993i | ||||
\(987\) | −41.8236 | −1.33126 | ||||||||
\(988\) | 3.85621 | − | 1.52750i | 0.122682 | − | 0.0485964i | ||||
\(989\) | −0.623016 | −0.0198108 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.14734 | − | 8.91546i | −0.163511 | − | 0.283209i | 0.772615 | − | 0.634875i | \(-0.218948\pi\) |
−0.936125 | + | 0.351666i | \(0.885615\pi\) | |||||||
\(992\) | −3.83581 | + | 6.64381i | −0.121787 | + | 0.210941i | ||||
\(993\) | 10.0023 | + | 17.3245i | 0.317413 | + | 0.549776i | ||||
\(994\) | 17.8816 | − | 30.9718i | 0.567169 | − | 0.982365i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.75648 | 0.182401 | ||||||||
\(997\) | −1.15115 | + | 1.99385i | −0.0364573 | + | 0.0631459i | −0.883678 | − | 0.468095i | \(-0.844941\pi\) |
0.847221 | + | 0.531241i | \(0.178274\pi\) | |||||||
\(998\) | −3.57388 | + | 6.19014i | −0.113129 | + | 0.195946i | ||||
\(999\) | −14.5888 | −0.461569 |
(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 | 475.2.e.f.26.5 | ✓ | 12 | |
5.2 | odd | 4 | 475.2.j.d.349.3 | 24 | |||
5.3 | odd | 4 | 475.2.j.d.349.10 | 24 | |||
5.4 | even | 2 | 475.2.e.h.26.2 | yes | 12 | ||
19.7 | even | 3 | 9025.2.a.bz.1.2 | 6 | |||
19.11 | even | 3 | inner | 475.2.e.f.201.5 | yes | 12 | |
19.12 | odd | 6 | 9025.2.a.bs.1.5 | 6 | |||
95.49 | even | 6 | 475.2.e.h.201.2 | yes | 12 | ||
95.64 | even | 6 | 9025.2.a.br.1.5 | 6 | |||
95.68 | odd | 12 | 475.2.j.d.49.3 | 24 | |||
95.69 | odd | 6 | 9025.2.a.by.1.2 | 6 | |||
95.87 | odd | 12 | 475.2.j.d.49.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.e.f.26.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
475.2.e.f.201.5 | yes | 12 | 19.11 | even | 3 | inner | |
475.2.e.h.26.2 | yes | 12 | 5.4 | even | 2 | ||
475.2.e.h.201.2 | yes | 12 | 95.49 | even | 6 | ||
475.2.j.d.49.3 | 24 | 95.68 | odd | 12 | |||
475.2.j.d.49.10 | 24 | 95.87 | odd | 12 | |||
475.2.j.d.349.3 | 24 | 5.2 | odd | 4 | |||
475.2.j.d.349.10 | 24 | 5.3 | odd | 4 | |||
9025.2.a.br.1.5 | 6 | 95.64 | even | 6 | |||
9025.2.a.bs.1.5 | 6 | 19.12 | odd | 6 | |||
9025.2.a.by.1.2 | 6 | 95.69 | odd | 6 | |||
9025.2.a.bz.1.2 | 6 | 19.7 | even | 3 |