Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(293,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.g (of order \(4\), 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: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 22 x^{14} - 52 x^{13} + 72 x^{12} - 32 x^{11} + 148 x^{10} + 268 x^{9} - 461 x^{8} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(0.510680 + 3.87900i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.293 |
Dual form | 350.2.g.b.307.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −2.28737 | + | 2.28737i | −1.32061 | + | 1.32061i | −0.407332 | + | 0.913280i | \(0.633541\pi\) |
−0.913280 | + | 0.407332i | \(0.866459\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 3.23483i | − | 1.32061i | ||||||
\(7\) | 0.835798 | − | 2.51027i | 0.315902 | − | 0.948792i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 7.46410i | − | 2.48803i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73205 | −0.522233 | −0.261116 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261116 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(12\) | 2.28737 | + | 2.28737i | 0.660306 | + | 0.660306i | ||||
\(13\) | 1.67447 | − | 1.67447i | 0.464414 | − | 0.464414i | −0.435685 | − | 0.900099i | \(-0.643494\pi\) |
0.900099 | + | 0.435685i | \(0.143494\pi\) | |||||||
\(14\) | 1.18403 | + | 2.36603i | 0.316445 | + | 0.632347i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.96184 | − | 3.96184i | −0.960887 | − | 0.960887i | 0.0383767 | − | 0.999263i | \(-0.487781\pi\) |
−0.999263 | + | 0.0383767i | \(0.987781\pi\) | |||||||
\(18\) | 5.27792 | + | 5.27792i | 1.24402 | + | 1.24402i | ||||
\(19\) | 5.60288 | 1.28539 | 0.642695 | − | 0.766122i | \(-0.277816\pi\) | ||||
0.642695 | + | 0.766122i | \(0.277816\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.83013 | + | 7.65368i | 0.835802 | + | 1.67017i | ||||
\(22\) | 1.22474 | − | 1.22474i | 0.261116 | − | 0.261116i | ||||
\(23\) | 1.55291 | + | 1.55291i | 0.323805 | + | 0.323805i | 0.850225 | − | 0.526420i | \(-0.176466\pi\) |
−0.526420 | + | 0.850225i | \(0.676466\pi\) | |||||||
\(24\) | −3.23483 | −0.660306 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.36806i | 0.464414i | ||||||||
\(27\) | 10.2110 | + | 10.2110i | 1.96512 | + | 1.96512i | ||||
\(28\) | −2.51027 | − | 0.835798i | −0.474396 | − | 0.157951i | ||||
\(29\) | 1.26795i | 0.235452i | 0.993046 | + | 0.117726i | \(0.0375605\pi\) | ||||
−0.993046 | + | 0.117726i | \(0.962440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.10160i | 0.736668i | 0.929693 | + | 0.368334i | \(0.120072\pi\) | ||||
−0.929693 | + | 0.368334i | \(0.879928\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 3.96184 | − | 3.96184i | 0.689667 | − | 0.689667i | ||||
\(34\) | 5.60288 | 0.960887 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.46410 | −1.24402 | ||||||||
\(37\) | 5.79555 | − | 5.79555i | 0.952783 | − | 0.952783i | −0.0461511 | − | 0.998934i | \(-0.514696\pi\) |
0.998934 | + | 0.0461511i | \(0.0146956\pi\) | |||||||
\(38\) | −3.96184 | + | 3.96184i | −0.642695 | + | 0.642695i | ||||
\(39\) | 7.66025i | 1.22662i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.70448i | − | 1.51559i | −0.652496 | − | 0.757793i | \(-0.726278\pi\) | ||
0.652496 | − | 0.757793i | \(-0.273722\pi\) | |||||||
\(42\) | −8.12028 | − | 2.70366i | −1.25299 | − | 0.417184i | ||||
\(43\) | −2.44949 | − | 2.44949i | −0.373544 | − | 0.373544i | 0.495222 | − | 0.868766i | \(-0.335087\pi\) |
−0.868766 | + | 0.495222i | \(0.835087\pi\) | |||||||
\(44\) | 1.73205i | 0.261116i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.19615 | −0.323805 | ||||||||
\(47\) | −2.90027 | − | 2.90027i | −0.423047 | − | 0.423047i | 0.463204 | − | 0.886252i | \(-0.346700\pi\) |
−0.886252 | + | 0.463204i | \(0.846700\pi\) | |||||||
\(48\) | 2.28737 | − | 2.28737i | 0.330153 | − | 0.330153i | ||||
\(49\) | −5.60288 | − | 4.19615i | −0.800412 | − | 0.599450i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.1244 | 2.53792 | ||||||||
\(52\) | −1.67447 | − | 1.67447i | −0.232207 | − | 0.232207i | ||||
\(53\) | 2.68973 | + | 2.68973i | 0.369462 | + | 0.369462i | 0.867281 | − | 0.497819i | \(-0.165866\pi\) |
−0.497819 | + | 0.867281i | \(0.665866\pi\) | |||||||
\(54\) | −14.4406 | −1.96512 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.36603 | − | 1.18403i | 0.316173 | − | 0.158222i | ||||
\(57\) | −12.8159 | + | 12.8159i | −1.69750 | + | 1.69750i | ||||
\(58\) | −0.896575 | − | 0.896575i | −0.117726 | − | 0.117726i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.2058i | − | 1.43475i | −0.696686 | − | 0.717376i | \(-0.745343\pi\) | ||
0.696686 | − | 0.717376i | \(-0.254657\pi\) | |||||||
\(62\) | −2.90027 | − | 2.90027i | −0.368334 | − | 0.368334i | ||||
\(63\) | −18.7369 | − | 6.23848i | −2.36063 | − | 0.785975i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.60288i | 0.689667i | ||||||||
\(67\) | 2.77766 | − | 2.77766i | 0.339345 | − | 0.339345i | −0.516776 | − | 0.856121i | \(-0.672868\pi\) |
0.856121 | + | 0.516776i | \(0.172868\pi\) | |||||||
\(68\) | −3.96184 | + | 3.96184i | −0.480443 | + | 0.480443i | ||||
\(69\) | −7.10417 | −0.855242 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.19615 | −0.260635 | −0.130318 | − | 0.991472i | \(-0.541600\pi\) | ||||
−0.130318 | + | 0.991472i | \(0.541600\pi\) | |||||||
\(72\) | 5.27792 | − | 5.27792i | 0.622008 | − | 0.622008i | ||||
\(73\) | 5.18763 | − | 5.18763i | 0.607167 | − | 0.607167i | −0.335038 | − | 0.942205i | \(-0.608749\pi\) |
0.942205 | + | 0.335038i | \(0.108749\pi\) | |||||||
\(74\) | 8.19615i | 0.952783i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.60288i | − | 0.642695i | ||||||
\(77\) | −1.44764 | + | 4.34791i | −0.164974 | + | 0.495490i | ||||
\(78\) | −5.41662 | − | 5.41662i | −0.613311 | − | 0.613311i | ||||
\(79\) | 2.00000i | 0.225018i | 0.993651 | + | 0.112509i | \(0.0358886\pi\) | ||||
−0.993651 | + | 0.112509i | \(0.964111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −24.3205 | −2.70228 | ||||||||
\(82\) | 6.86210 | + | 6.86210i | 0.757793 | + | 0.757793i | ||||
\(83\) | 6.86210 | − | 6.86210i | 0.753214 | − | 0.753214i | −0.221864 | − | 0.975078i | \(-0.571214\pi\) |
0.975078 | + | 0.221864i | \(0.0712141\pi\) | |||||||
\(84\) | 7.65368 | − | 3.83013i | 0.835085 | − | 0.417901i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.46410 | 0.373544 | ||||||||
\(87\) | −2.90027 | − | 2.90027i | −0.310941 | − | 0.310941i | ||||
\(88\) | −1.22474 | − | 1.22474i | −0.130558 | − | 0.130558i | ||||
\(89\) | 9.70448 | 1.02867 | 0.514336 | − | 0.857589i | \(-0.328038\pi\) | ||||
0.514336 | + | 0.857589i | \(0.328038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.80385 | − | 5.60288i | −0.293923 | − | 0.587342i | ||||
\(92\) | 1.55291 | − | 1.55291i | 0.161903 | − | 0.161903i | ||||
\(93\) | −9.38186 | − | 9.38186i | −0.972853 | − | 0.972853i | ||||
\(94\) | 4.10160 | 0.423047 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.23483i | 0.330153i | ||||||||
\(97\) | −3.34894 | − | 3.34894i | −0.340033 | − | 0.340033i | 0.516347 | − | 0.856380i | \(-0.327292\pi\) |
−0.856380 | + | 0.516347i | \(0.827292\pi\) | |||||||
\(98\) | 6.92896 | − | 0.994709i | 0.699931 | − | 0.100481i | ||||
\(99\) | 12.9282i | 1.29933i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.10417i | 0.706892i | 0.935455 | + | 0.353446i | \(0.114990\pi\) | ||||
−0.935455 | + | 0.353446i | \(0.885010\pi\) | |||||||
\(102\) | −12.8159 | + | 12.8159i | −1.26896 | + | 1.26896i | ||||
\(103\) | −3.34894 | + | 3.34894i | −0.329981 | + | 0.329981i | −0.852579 | − | 0.522598i | \(-0.824963\pi\) |
0.522598 | + | 0.852579i | \(0.324963\pi\) | |||||||
\(104\) | 2.36806 | 0.232207 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.80385 | −0.369462 | ||||||||
\(107\) | −9.46979 | + | 9.46979i | −0.915479 | + | 0.915479i | −0.996696 | − | 0.0812173i | \(-0.974119\pi\) |
0.0812173 | + | 0.996696i | \(0.474119\pi\) | |||||||
\(108\) | 10.2110 | − | 10.2110i | 0.982558 | − | 0.982558i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.5131i | 2.51651i | ||||||||
\(112\) | −0.835798 | + | 2.51027i | −0.0789755 | + | 0.237198i | ||||
\(113\) | 7.91688 | + | 7.91688i | 0.744757 | + | 0.744757i | 0.973489 | − | 0.228732i | \(-0.0734581\pi\) |
−0.228732 | + | 0.973489i | \(0.573458\pi\) | |||||||
\(114\) | − | 18.1244i | − | 1.69750i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.26795 | 0.117726 | ||||||||
\(117\) | −12.4984 | − | 12.4984i | −1.15548 | − | 1.15548i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.2566 | + | 6.63397i | −1.21523 | + | 0.608135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 7.92367 | + | 7.92367i | 0.717376 | + | 0.717376i | ||||
\(123\) | 22.1977 | + | 22.1977i | 2.00150 | + | 2.00150i | ||||
\(124\) | 4.10160 | 0.368334 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 17.6603 | − | 8.83771i | 1.57330 | − | 0.787326i | ||||
\(127\) | 12.7279 | − | 12.7279i | 1.12942 | − | 1.12942i | 0.139149 | − | 0.990271i | \(-0.455563\pi\) |
0.990271 | − | 0.139149i | \(-0.0444367\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 11.2058 | 0.986613 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | −3.96184 | − | 3.96184i | −0.344834 | − | 0.344834i | ||||
\(133\) | 4.68288 | − | 14.0647i | 0.406057 | − | 1.21957i | ||||
\(134\) | 3.92820i | 0.339345i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.60288i | − | 0.480443i | ||||||
\(137\) | −0.568406 | + | 0.568406i | −0.0485622 | + | 0.0485622i | −0.730971 | − | 0.682409i | \(-0.760932\pi\) |
0.682409 | + | 0.730971i | \(0.260932\pi\) | |||||||
\(138\) | 5.02341 | − | 5.02341i | 0.427621 | − | 0.427621i | ||||
\(139\) | −2.60031 | −0.220555 | −0.110278 | − | 0.993901i | \(-0.535174\pi\) | ||||
−0.110278 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.2679 | 1.11736 | ||||||||
\(142\) | 1.55291 | − | 1.55291i | 0.130318 | − | 0.130318i | ||||
\(143\) | −2.90027 | + | 2.90027i | −0.242532 | + | 0.242532i | ||||
\(144\) | 7.46410i | 0.622008i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.33642i | 0.607167i | ||||||||
\(147\) | 22.4140 | − | 3.21771i | 1.84868 | − | 0.265392i | ||||
\(148\) | −5.79555 | − | 5.79555i | −0.476392 | − | 0.476392i | ||||
\(149\) | − | 16.3923i | − | 1.34291i | −0.741045 | − | 0.671455i | \(-0.765670\pi\) | ||
0.741045 | − | 0.671455i | \(-0.234330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5885 | −1.34995 | −0.674975 | − | 0.737841i | \(-0.735845\pi\) | ||||
−0.674975 | + | 0.737841i | \(0.735845\pi\) | |||||||
\(152\) | 3.96184 | + | 3.96184i | 0.321347 | + | 0.321347i | ||||
\(153\) | −29.5716 | + | 29.5716i | −2.39072 | + | 2.39072i | ||||
\(154\) | −2.05080 | − | 4.09808i | −0.165258 | − | 0.330232i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.66025 | 0.613311 | ||||||||
\(157\) | 15.3987 | + | 15.3987i | 1.22895 | + | 1.22895i | 0.964362 | + | 0.264586i | \(0.0852353\pi\) |
0.264586 | + | 0.964362i | \(0.414765\pi\) | |||||||
\(158\) | −1.41421 | − | 1.41421i | −0.112509 | − | 0.112509i | ||||
\(159\) | −12.3048 | −0.975833 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.19615 | − | 2.60031i | 0.409514 | − | 0.204933i | ||||
\(162\) | 17.1972 | − | 17.1972i | 1.35114 | − | 1.35114i | ||||
\(163\) | −2.77766 | − | 2.77766i | −0.217563 | − | 0.217563i | 0.589908 | − | 0.807471i | \(-0.299164\pi\) |
−0.807471 | + | 0.589908i | \(0.799164\pi\) | |||||||
\(164\) | −9.70448 | −0.757793 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.70448i | 0.753214i | ||||||||
\(167\) | −15.8473 | − | 15.8473i | −1.22630 | − | 1.22630i | −0.965351 | − | 0.260953i | \(-0.915963\pi\) |
−0.260953 | − | 0.965351i | \(-0.584037\pi\) | |||||||
\(168\) | −2.70366 | + | 8.12028i | −0.208592 | + | 0.626493i | ||||
\(169\) | 7.39230i | 0.568639i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 41.8205i | − | 3.19809i | ||||||
\(172\) | −2.44949 | + | 2.44949i | −0.186772 | + | 0.186772i | ||||
\(173\) | −10.8239 | + | 10.8239i | −0.822929 | + | 0.822929i | −0.986527 | − | 0.163598i | \(-0.947690\pi\) |
0.163598 | + | 0.986527i | \(0.447690\pi\) | |||||||
\(174\) | 4.10160 | 0.310941 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.73205 | 0.130558 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.86210 | + | 6.86210i | −0.514336 | + | 0.514336i | ||||
\(179\) | − | 6.80385i | − | 0.508543i | −0.967133 | − | 0.254272i | \(-0.918164\pi\) | ||
0.967133 | − | 0.254272i | \(-0.0818358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.00258i | − | 0.223180i | −0.993754 | − | 0.111590i | \(-0.964406\pi\) | ||
0.993754 | − | 0.111590i | \(-0.0355943\pi\) | |||||||
\(182\) | 5.94446 | + | 1.97922i | 0.440632 | + | 0.146709i | ||||
\(183\) | 25.6317 | + | 25.6317i | 1.89475 | + | 1.89475i | ||||
\(184\) | 2.19615i | 0.161903i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.2679 | 0.972853 | ||||||||
\(187\) | 6.86210 | + | 6.86210i | 0.501807 | + | 0.501807i | ||||
\(188\) | −2.90027 | + | 2.90027i | −0.211524 | + | 0.211524i | ||||
\(189\) | 34.1668 | − | 17.0981i | 2.48527 | − | 1.24370i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9282 | 0.935452 | 0.467726 | − | 0.883874i | \(-0.345073\pi\) | ||||
0.467726 | + | 0.883874i | \(0.345073\pi\) | |||||||
\(192\) | −2.28737 | − | 2.28737i | −0.165077 | − | 0.165077i | ||||
\(193\) | −4.33057 | − | 4.33057i | −0.311721 | − | 0.311721i | 0.533855 | − | 0.845576i | \(-0.320743\pi\) |
−0.845576 | + | 0.533855i | \(0.820743\pi\) | |||||||
\(194\) | 4.73611 | 0.340033 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.19615 | + | 5.60288i | −0.299725 | + | 0.400206i | ||||
\(197\) | −15.8338 | + | 15.8338i | −1.12811 | + | 1.12811i | −0.137623 | + | 0.990485i | \(0.543946\pi\) |
−0.990485 | + | 0.137623i | \(0.956054\pi\) | |||||||
\(198\) | −9.14162 | − | 9.14162i | −0.649667 | − | 0.649667i | ||||
\(199\) | −15.3074 | −1.08511 | −0.542555 | − | 0.840020i | \(-0.682543\pi\) | ||||
−0.542555 | + | 0.840020i | \(0.682543\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.7071i | 0.896287i | ||||||||
\(202\) | −5.02341 | − | 5.02341i | −0.353446 | − | 0.353446i | ||||
\(203\) | 3.18289 | + | 1.05975i | 0.223395 | + | 0.0743798i | ||||
\(204\) | − | 18.1244i | − | 1.26896i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 4.73611i | − | 0.329981i | ||||||
\(207\) | 11.5911 | − | 11.5911i | 0.805638 | − | 0.805638i | ||||
\(208\) | −1.67447 | + | 1.67447i | −0.116104 | + | 0.116104i | ||||
\(209\) | −9.70448 | −0.671273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.19615 | 0.633089 | 0.316545 | − | 0.948578i | \(-0.397477\pi\) | ||||
0.316545 | + | 0.948578i | \(0.397477\pi\) | |||||||
\(212\) | 2.68973 | − | 2.68973i | 0.184731 | − | 0.184731i | ||||
\(213\) | 5.02341 | − | 5.02341i | 0.344198 | − | 0.344198i | ||||
\(214\) | − | 13.3923i | − | 0.915479i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.4406i | 0.982558i | ||||||||
\(217\) | 10.2961 | + | 3.42811i | 0.698945 | + | 0.232715i | ||||
\(218\) | 1.41421 | + | 1.41421i | 0.0957826 | + | 0.0957826i | ||||
\(219\) | 23.7321i | 1.60366i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2679 | −0.892499 | ||||||||
\(222\) | −18.7476 | − | 18.7476i | −1.25826 | − | 1.25826i | ||||
\(223\) | 12.0497 | − | 12.0497i | 0.806910 | − | 0.806910i | −0.177255 | − | 0.984165i | \(-0.556722\pi\) |
0.984165 | + | 0.177255i | \(0.0567217\pi\) | |||||||
\(224\) | −1.18403 | − | 2.36603i | −0.0791112 | − | 0.158087i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.1962 | −0.744757 | ||||||||
\(227\) | 7.92367 | + | 7.92367i | 0.525913 | + | 0.525913i | 0.919351 | − | 0.393438i | \(-0.128715\pi\) |
−0.393438 | + | 0.919351i | \(0.628715\pi\) | |||||||
\(228\) | 12.8159 | + | 12.8159i | 0.848751 | + | 0.848751i | ||||
\(229\) | 4.10160 | 0.271041 | 0.135521 | − | 0.990775i | \(-0.456729\pi\) | ||||
0.135521 | + | 0.990775i | \(0.456729\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.63397 | − | 13.2566i | −0.436483 | − | 0.872218i | ||||
\(232\) | −0.896575 | + | 0.896575i | −0.0588631 | + | 0.0588631i | ||||
\(233\) | 7.34847 | + | 7.34847i | 0.481414 | + | 0.481414i | 0.905583 | − | 0.424169i | \(-0.139434\pi\) |
−0.424169 | + | 0.905583i | \(0.639434\pi\) | |||||||
\(234\) | 17.6754 | 1.15548 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.57474 | − | 4.57474i | −0.297161 | − | 0.297161i | ||||
\(238\) | 4.68288 | − | 14.0647i | 0.303546 | − | 0.911681i | ||||
\(239\) | − | 25.8564i | − | 1.67251i | −0.548339 | − | 0.836256i | \(-0.684740\pi\) | ||
0.548339 | − | 0.836256i | \(-0.315260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50129i | 0.0967065i | 0.998830 | + | 0.0483532i | \(0.0153973\pi\) | ||||
−0.998830 | + | 0.0483532i | \(0.984603\pi\) | |||||||
\(242\) | 5.65685 | − | 5.65685i | 0.363636 | − | 0.363636i | ||||
\(243\) | 24.9968 | − | 24.9968i | 1.60355 | − | 1.60355i | ||||
\(244\) | −11.2058 | −0.717376 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −31.3923 | −2.00150 | ||||||||
\(247\) | 9.38186 | − | 9.38186i | 0.596953 | − | 0.596953i | ||||
\(248\) | −2.90027 | + | 2.90027i | −0.184167 | + | 0.184167i | ||||
\(249\) | 31.3923i | 1.98941i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.8087i | 1.06095i | 0.847700 | + | 0.530476i | \(0.177987\pi\) | ||||
−0.847700 | + | 0.530476i | \(0.822013\pi\) | |||||||
\(252\) | −6.23848 | + | 18.7369i | −0.392987 | + | 1.18031i | ||||
\(253\) | −2.68973 | − | 2.68973i | −0.169102 | − | 0.169102i | ||||
\(254\) | 18.0000i | 1.12942i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.7242 | + | 13.7242i | 0.856092 | + | 0.856092i | 0.990875 | − | 0.134783i | \(-0.0430336\pi\) |
−0.134783 | + | 0.990875i | \(0.543034\pi\) | |||||||
\(258\) | −7.92367 | + | 7.92367i | −0.493306 | + | 0.493306i | ||||
\(259\) | −9.70448 | − | 19.3923i | −0.603007 | − | 1.20498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.46410 | 0.585813 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.8338 | − | 15.8338i | −0.976351 | − | 0.976351i | 0.0233759 | − | 0.999727i | \(-0.492559\pi\) |
−0.999727 | + | 0.0233759i | \(0.992559\pi\) | |||||||
\(264\) | 5.60288 | 0.344834 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.63397 | + | 13.2566i | 0.406755 | + | 0.812812i | ||||
\(267\) | −22.1977 | + | 22.1977i | −1.35848 | + | 1.35848i | ||||
\(268\) | −2.77766 | − | 2.77766i | −0.169673 | − | 0.169673i | ||||
\(269\) | 12.3048 | 0.750236 | 0.375118 | − | 0.926977i | \(-0.377602\pi\) | ||||
0.375118 | + | 0.926977i | \(0.377602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4090i | 1.17901i | 0.807765 | + | 0.589505i | \(0.200677\pi\) | ||||
−0.807765 | + | 0.589505i | \(0.799323\pi\) | |||||||
\(272\) | 3.96184 | + | 3.96184i | 0.240222 | + | 0.240222i | ||||
\(273\) | 19.2293 | + | 6.40242i | 1.16381 | + | 0.387492i | ||||
\(274\) | − | 0.803848i | − | 0.0485622i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.10417i | 0.427621i | ||||||||
\(277\) | −14.9372 | + | 14.9372i | −0.897488 | + | 0.897488i | −0.995213 | − | 0.0977255i | \(-0.968843\pi\) |
0.0977255 | + | 0.995213i | \(0.468843\pi\) | |||||||
\(278\) | 1.83869 | − | 1.83869i | 0.110278 | − | 0.110278i | ||||
\(279\) | 30.6147 | 1.83286 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8564 | −0.826604 | −0.413302 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413302 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(282\) | −9.38186 | + | 9.38186i | −0.558681 | + | 0.558681i | ||||
\(283\) | −10.2110 | + | 10.2110i | −0.606983 | + | 0.606983i | −0.942157 | − | 0.335173i | \(-0.891205\pi\) |
0.335173 | + | 0.942157i | \(0.391205\pi\) | |||||||
\(284\) | 2.19615i | 0.130318i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4.10160i | − | 0.242532i | ||||||
\(287\) | −24.3608 | − | 8.11098i | −1.43797 | − | 0.478776i | ||||
\(288\) | −5.27792 | − | 5.27792i | −0.311004 | − | 0.311004i | ||||
\(289\) | 14.3923i | 0.846606i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.3205 | 0.898104 | ||||||||
\(292\) | −5.18763 | − | 5.18763i | −0.303583 | − | 0.303583i | ||||
\(293\) | 2.12314 | − | 2.12314i | 0.124035 | − | 0.124035i | −0.642364 | − | 0.766400i | \(-0.722046\pi\) |
0.766400 | + | 0.642364i | \(0.222046\pi\) | |||||||
\(294\) | −13.5738 | + | 18.1244i | −0.791642 | + | 1.05703i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.19615 | 0.476392 | ||||||||
\(297\) | −17.6860 | − | 17.6860i | −1.02625 | − | 1.02625i | ||||
\(298\) | 11.5911 | + | 11.5911i | 0.671455 | + | 0.671455i | ||||
\(299\) | 5.20061 | 0.300759 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.19615 | + | 4.10160i | −0.472418 | + | 0.236412i | ||||
\(302\) | 11.7298 | − | 11.7298i | 0.674975 | − | 0.674975i | ||||
\(303\) | −16.2499 | − | 16.2499i | −0.933530 | − | 0.933530i | ||||
\(304\) | −5.60288 | −0.321347 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 41.8205i | − | 2.39072i | ||||||
\(307\) | −3.51316 | − | 3.51316i | −0.200507 | − | 0.200507i | 0.599710 | − | 0.800217i | \(-0.295282\pi\) |
−0.800217 | + | 0.599710i | \(0.795282\pi\) | |||||||
\(308\) | 4.34791 | + | 1.44764i | 0.247745 | + | 0.0824872i | ||||
\(309\) | − | 15.3205i | − | 0.871553i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.4090i | 1.10058i | 0.834973 | + | 0.550291i | \(0.185483\pi\) | ||||
−0.834973 | + | 0.550291i | \(0.814517\pi\) | |||||||
\(312\) | −5.41662 | + | 5.41662i | −0.306656 | + | 0.306656i | ||||
\(313\) | −20.4221 | + | 20.4221i | −1.15432 | + | 1.15432i | −0.168648 | + | 0.985676i | \(0.553940\pi\) |
−0.985676 | + | 0.168648i | \(0.946060\pi\) | |||||||
\(314\) | −21.7770 | −1.22895 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −11.5911 | + | 11.5911i | −0.651022 | + | 0.651022i | −0.953239 | − | 0.302217i | \(-0.902273\pi\) |
0.302217 | + | 0.953239i | \(0.402273\pi\) | |||||||
\(318\) | 8.70080 | − | 8.70080i | 0.487917 | − | 0.487917i | ||||
\(319\) | − | 2.19615i | − | 0.122961i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 43.3218i | − | 2.41799i | ||||||
\(322\) | −1.83554 | + | 5.51293i | −0.102291 | + | 0.307224i | ||||
\(323\) | −22.1977 | − | 22.1977i | −1.23511 | − | 1.23511i | ||||
\(324\) | 24.3205i | 1.35114i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.92820 | 0.217563 | ||||||||
\(327\) | 4.57474 | + | 4.57474i | 0.252983 | + | 0.252983i | ||||
\(328\) | 6.86210 | − | 6.86210i | 0.378896 | − | 0.378896i | ||||
\(329\) | −9.70448 | + | 4.85641i | −0.535025 | + | 0.267742i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.5885 | −1.29654 | −0.648269 | − | 0.761411i | \(-0.724507\pi\) | ||||
−0.648269 | + | 0.761411i | \(0.724507\pi\) | |||||||
\(332\) | −6.86210 | − | 6.86210i | −0.376607 | − | 0.376607i | ||||
\(333\) | −43.2586 | − | 43.2586i | −2.37056 | − | 2.37056i | ||||
\(334\) | 22.4115 | 1.22630 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.83013 | − | 7.65368i | −0.208951 | − | 0.417543i | ||||
\(337\) | 18.1953 | − | 18.1953i | 0.991162 | − | 0.991162i | −0.00879972 | − | 0.999961i | \(-0.502801\pi\) |
0.999961 | + | 0.00879972i | \(0.00280107\pi\) | |||||||
\(338\) | −5.22715 | − | 5.22715i | −0.284319 | − | 0.284319i | ||||
\(339\) | −36.2176 | −1.96707 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7.10417i | − | 0.384712i | ||||||
\(342\) | 29.5716 | + | 29.5716i | 1.59905 | + | 1.59905i | ||||
\(343\) | −15.2163 | + | 10.5576i | −0.821605 | + | 0.570057i | ||||
\(344\) | − | 3.46410i | − | 0.186772i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.3074i | − | 0.822929i | ||||||
\(347\) | 21.0609 | − | 21.0609i | 1.13061 | − | 1.13061i | 0.140532 | − | 0.990076i | \(-0.455119\pi\) |
0.990076 | − | 0.140532i | \(-0.0448814\pi\) | |||||||
\(348\) | −2.90027 | + | 2.90027i | −0.155471 | + | 0.155471i | ||||
\(349\) | −7.10417 | −0.380278 | −0.190139 | − | 0.981757i | \(-0.560894\pi\) | ||||
−0.190139 | + | 0.981757i | \(0.560894\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.1962 | 1.82526 | ||||||||
\(352\) | −1.22474 | + | 1.22474i | −0.0652791 | + | 0.0652791i | ||||
\(353\) | 19.5247 | − | 19.5247i | 1.03920 | − | 1.03920i | 0.0399971 | − | 0.999200i | \(-0.487265\pi\) |
0.999200 | − | 0.0399971i | \(-0.0127349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 9.70448i | − | 0.514336i | ||||||
\(357\) | 15.1483 | − | 45.4970i | 0.801733 | − | 2.40796i | ||||
\(358\) | 4.81105 | + | 4.81105i | 0.254272 | + | 0.254272i | ||||
\(359\) | − | 10.3923i | − | 0.548485i | −0.961661 | − | 0.274242i | \(-0.911573\pi\) | ||
0.961661 | − | 0.274242i | \(-0.0884271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3923 | 0.652227 | ||||||||
\(362\) | 2.12314 | + | 2.12314i | 0.111590 | + | 0.111590i | ||||
\(363\) | 18.2989 | − | 18.2989i | 0.960445 | − | 0.960445i | ||||
\(364\) | −5.60288 | + | 2.80385i | −0.293671 | + | 0.146962i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −36.2487 | −1.89475 | ||||||||
\(367\) | −3.34894 | − | 3.34894i | −0.174813 | − | 0.174813i | 0.614277 | − | 0.789090i | \(-0.289448\pi\) |
−0.789090 | + | 0.614277i | \(0.789448\pi\) | |||||||
\(368\) | −1.55291 | − | 1.55291i | −0.0809513 | − | 0.0809513i | ||||
\(369\) | −72.4352 | −3.77083 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.00000 | − | 4.50386i | 0.467257 | − | 0.233829i | ||||
\(372\) | −9.38186 | + | 9.38186i | −0.486427 | + | 0.486427i | ||||
\(373\) | 9.38186 | + | 9.38186i | 0.485774 | + | 0.485774i | 0.906970 | − | 0.421196i | \(-0.138389\pi\) |
−0.421196 | + | 0.906970i | \(0.638389\pi\) | |||||||
\(374\) | −9.70448 | −0.501807 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 4.10160i | − | 0.211524i | ||||||
\(377\) | 2.12314 | + | 2.12314i | 0.109347 | + | 0.109347i | ||||
\(378\) | −12.0694 | + | 36.2497i | −0.620784 | + | 1.86449i | ||||
\(379\) | 33.9808i | 1.74547i | 0.488190 | + | 0.872737i | \(0.337657\pi\) | ||||
−0.488190 | + | 0.872737i | \(0.662343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 58.2269i | 2.98305i | ||||||||
\(382\) | −9.14162 | + | 9.14162i | −0.467726 | + | 0.467726i | ||||
\(383\) | −13.7242 | + | 13.7242i | −0.701274 | + | 0.701274i | −0.964684 | − | 0.263410i | \(-0.915153\pi\) |
0.263410 | + | 0.964684i | \(0.415153\pi\) | |||||||
\(384\) | 3.23483 | 0.165077 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.12436 | 0.311721 | ||||||||
\(387\) | −18.2832 | + | 18.2832i | −0.929389 | + | 0.929389i | ||||
\(388\) | −3.34894 | + | 3.34894i | −0.170017 | + | 0.170017i | ||||
\(389\) | 0.339746i | 0.0172258i | 0.999963 | + | 0.00861290i | \(0.00274161\pi\) | ||||
−0.999963 | + | 0.00861290i | \(0.997258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.3048i | − | 0.622280i | ||||||
\(392\) | −0.994709 | − | 6.92896i | −0.0502404 | − | 0.349966i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 22.3923i | − | 1.12811i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.9282 | 0.649667 | ||||||||
\(397\) | 8.37235 | + | 8.37235i | 0.420196 | + | 0.420196i | 0.885271 | − | 0.465075i | \(-0.153973\pi\) |
−0.465075 | + | 0.885271i | \(0.653973\pi\) | |||||||
\(398\) | 10.8239 | − | 10.8239i | 0.542555 | − | 0.542555i | ||||
\(399\) | 21.4598 | + | 42.8827i | 1.07433 | + | 2.14682i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.0718 | 0.702712 | 0.351356 | − | 0.936242i | \(-0.385721\pi\) | ||||
0.351356 | + | 0.936242i | \(0.385721\pi\) | |||||||
\(402\) | −8.98525 | − | 8.98525i | −0.448143 | − | 0.448143i | ||||
\(403\) | 6.86800 | + | 6.86800i | 0.342119 | + | 0.342119i | ||||
\(404\) | 7.10417 | 0.353446 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | + | 1.50129i | −0.148888 | + | 0.0745077i | ||||
\(407\) | −10.0382 | + | 10.0382i | −0.497575 | + | 0.497575i | ||||
\(408\) | 12.8159 | + | 12.8159i | 0.634479 | + | 0.634479i | ||||
\(409\) | 35.1186 | 1.73650 | 0.868251 | − | 0.496125i | \(-0.165244\pi\) | ||||
0.868251 | + | 0.496125i | \(0.165244\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.60031i | − | 0.128264i | ||||||
\(412\) | 3.34894 | + | 3.34894i | 0.164990 | + | 0.164990i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.3923i | 0.805638i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 2.36806i | − | 0.116104i | ||||||
\(417\) | 5.94786 | − | 5.94786i | 0.291268 | − | 0.291268i | ||||
\(418\) | 6.86210 | − | 6.86210i | 0.335636 | − | 0.335636i | ||||
\(419\) | 36.2176 | 1.76935 | 0.884673 | − | 0.466212i | \(-0.154382\pi\) | ||||
0.884673 | + | 0.466212i | \(0.154382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.1769 | 1.42200 | 0.710998 | − | 0.703194i | \(-0.248244\pi\) | ||||
0.710998 | + | 0.703194i | \(0.248244\pi\) | |||||||
\(422\) | −6.50266 | + | 6.50266i | −0.316545 | + | 0.316545i | ||||
\(423\) | −21.6479 | + | 21.6479i | −1.05256 | + | 1.05256i | ||||
\(424\) | 3.80385i | 0.184731i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.10417i | 0.344198i | ||||||||
\(427\) | −28.1295 | − | 9.36576i | −1.36128 | − | 0.453241i | ||||
\(428\) | 9.46979 | + | 9.46979i | 0.457740 | + | 0.457740i | ||||
\(429\) | − | 13.2679i | − | 0.640583i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.51666 | 0.362065 | 0.181032 | − | 0.983477i | \(-0.442056\pi\) | ||||
0.181032 | + | 0.983477i | \(0.442056\pi\) | |||||||
\(432\) | −10.2110 | − | 10.2110i | −0.491279 | − | 0.491279i | ||||
\(433\) | 15.2344 | − | 15.2344i | 0.732121 | − | 0.732121i | −0.238919 | − | 0.971040i | \(-0.576793\pi\) |
0.971040 | + | 0.238919i | \(0.0767929\pi\) | |||||||
\(434\) | −9.70448 | + | 4.85641i | −0.465830 | + | 0.233115i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | 8.70080 | + | 8.70080i | 0.416216 | + | 0.416216i | ||||
\(438\) | −16.7811 | − | 16.7811i | −0.801832 | − | 0.801832i | ||||
\(439\) | 8.20319 | 0.391517 | 0.195758 | − | 0.980652i | \(-0.437283\pi\) | ||||
0.195758 | + | 0.980652i | \(0.437283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.3205 | + | 41.8205i | −1.49145 | + | 1.99145i | ||||
\(442\) | 9.38186 | − | 9.38186i | 0.446249 | − | 0.446249i | ||||
\(443\) | −10.6066 | − | 10.6066i | −0.503935 | − | 0.503935i | 0.408723 | − | 0.912658i | \(-0.365974\pi\) |
−0.912658 | + | 0.408723i | \(0.865974\pi\) | |||||||
\(444\) | 26.5131 | 1.25826 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.0409i | 0.806910i | ||||||||
\(447\) | 37.4952 | + | 37.4952i | 1.77346 | + | 1.77346i | ||||
\(448\) | 2.51027 | + | 0.835798i | 0.118599 | + | 0.0394877i | ||||
\(449\) | 1.14359i | 0.0539695i | 0.999636 | + | 0.0269848i | \(0.00859056\pi\) | ||||
−0.999636 | + | 0.0269848i | \(0.991409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.8087i | 0.791488i | ||||||||
\(452\) | 7.91688 | − | 7.91688i | 0.372378 | − | 0.372378i | ||||
\(453\) | 37.9439 | − | 37.9439i | 1.78276 | − | 1.78276i | ||||
\(454\) | −11.2058 | −0.525913 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.1244 | −0.848751 | ||||||||
\(457\) | −9.05369 | + | 9.05369i | −0.423514 | + | 0.423514i | −0.886412 | − | 0.462898i | \(-0.846810\pi\) |
0.462898 | + | 0.886412i | \(0.346810\pi\) | |||||||
\(458\) | −2.90027 | + | 2.90027i | −0.135521 | + | 0.135521i | ||||
\(459\) | − | 80.9090i | − | 3.77651i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 26.5131i | − | 1.23484i | −0.786634 | − | 0.617420i | \(-0.788178\pi\) | ||
0.786634 | − | 0.617420i | \(-0.211822\pi\) | |||||||
\(462\) | 14.0647 | + | 4.68288i | 0.654351 | + | 0.217867i | ||||
\(463\) | 26.2880 | + | 26.2880i | 1.22171 | + | 1.22171i | 0.967024 | + | 0.254685i | \(0.0819718\pi\) |
0.254685 | + | 0.967024i | \(0.418028\pi\) | |||||||
\(464\) | − | 1.26795i | − | 0.0588631i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.3923 | −0.481414 | ||||||||
\(467\) | 5.80053 | + | 5.80053i | 0.268417 | + | 0.268417i | 0.828462 | − | 0.560045i | \(-0.189216\pi\) |
−0.560045 | + | 0.828462i | \(0.689216\pi\) | |||||||
\(468\) | −12.4984 | + | 12.4984i | −0.577739 | + | 0.577739i | ||||
\(469\) | −4.65111 | − | 9.29423i | −0.214768 | − | 0.429168i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −70.4449 | −3.24593 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.24264 | + | 4.24264i | 0.195077 | + | 0.195077i | ||||
\(474\) | 6.46965 | 0.297161 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.63397 | + | 13.2566i | 0.304068 | + | 0.607614i | ||||
\(477\) | 20.0764 | − | 20.0764i | 0.919235 | − | 0.919235i | ||||
\(478\) | 18.2832 | + | 18.2832i | 0.836256 | + | 0.836256i | ||||
\(479\) | 19.4090 | 0.886818 | 0.443409 | − | 0.896319i | \(-0.353769\pi\) | ||||
0.443409 | + | 0.896319i | \(0.353769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 19.4090i | − | 0.884972i | ||||||
\(482\) | −1.06157 | − | 1.06157i | −0.0483532 | − | 0.0483532i | ||||
\(483\) | −5.93765 | + | 17.8334i | −0.270173 | + | 0.811446i | ||||
\(484\) | 8.00000i | 0.363636i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 35.3508i | 1.60355i | ||||||||
\(487\) | −14.5211 | + | 14.5211i | −0.658013 | + | 0.658013i | −0.954910 | − | 0.296897i | \(-0.904048\pi\) |
0.296897 | + | 0.954910i | \(0.404048\pi\) | |||||||
\(488\) | 7.92367 | − | 7.92367i | 0.358688 | − | 0.358688i | ||||
\(489\) | 12.7071 | 0.574633 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9282 | −0.854218 | −0.427109 | − | 0.904200i | \(-0.640468\pi\) | ||||
−0.427109 | + | 0.904200i | \(0.640468\pi\) | |||||||
\(492\) | 22.1977 | − | 22.1977i | 1.00075 | − | 1.00075i | ||||
\(493\) | 5.02341 | − | 5.02341i | 0.226243 | − | 0.226243i | ||||
\(494\) | 13.2679i | 0.596953i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.10160i | − | 0.184167i | ||||||
\(497\) | −1.83554 | + | 5.51293i | −0.0823352 | + | 0.247289i | ||||
\(498\) | −22.1977 | − | 22.1977i | −0.994703 | − | 0.994703i | ||||
\(499\) | 24.7846i | 1.10951i | 0.832013 | + | 0.554756i | \(0.187188\pi\) | ||||
−0.832013 | + | 0.554756i | \(0.812812\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 72.4974 | 3.23895 | ||||||||
\(502\) | −11.8855 | − | 11.8855i | −0.530476 | − | 0.530476i | ||||
\(503\) | 12.9471 | − | 12.9471i | 0.577282 | − | 0.577282i | −0.356872 | − | 0.934153i | \(-0.616157\pi\) |
0.934153 | + | 0.356872i | \(0.116157\pi\) | |||||||
\(504\) | −8.83771 | − | 17.6603i | −0.393663 | − | 0.786650i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.80385 | 0.169102 | ||||||||
\(507\) | −16.9089 | − | 16.9089i | −0.750951 | − | 0.750951i | ||||
\(508\) | −12.7279 | − | 12.7279i | −0.564710 | − | 0.564710i | ||||
\(509\) | 33.6173 | 1.49006 | 0.745030 | − | 0.667031i | \(-0.232435\pi\) | ||||
0.745030 | + | 0.667031i | \(0.232435\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.68653 | − | 17.3582i | −0.384270 | − | 0.767880i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 57.2113 | + | 57.2113i | 2.52594 | + | 2.52594i | ||||
\(514\) | −19.4090 | −0.856092 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 11.2058i | − | 0.493306i | ||||||
\(517\) | 5.02341 | + | 5.02341i | 0.220929 | + | 0.220929i | ||||
\(518\) | 20.5745 | + | 6.85033i | 0.903993 | + | 0.300986i | ||||
\(519\) | − | 49.5167i | − | 2.17354i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.1134i | − | 1.27548i | −0.770251 | − | 0.637741i | \(-0.779869\pi\) | ||
0.770251 | − | 0.637741i | \(-0.220131\pi\) | |||||||
\(522\) | −6.69213 | + | 6.69213i | −0.292907 | + | 0.292907i | ||||
\(523\) | −23.9352 | + | 23.9352i | −1.04662 | + | 1.04662i | −0.0477563 | + | 0.998859i | \(0.515207\pi\) |
−0.998859 | + | 0.0477563i | \(0.984793\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.3923 | 0.976351 | ||||||||
\(527\) | 16.2499 | − | 16.2499i | 0.707855 | − | 0.707855i | ||||
\(528\) | −3.96184 | + | 3.96184i | −0.172417 | + | 0.172417i | ||||
\(529\) | − | 18.1769i | − | 0.790301i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.0647 | − | 4.68288i | −0.609784 | − | 0.203029i | ||||
\(533\) | −16.2499 | − | 16.2499i | −0.703859 | − | 0.703859i | ||||
\(534\) | − | 31.3923i | − | 1.35848i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.92820 | 0.169673 | ||||||||
\(537\) | 15.5629 | + | 15.5629i | 0.671589 | + | 0.671589i | ||||
\(538\) | −8.70080 | + | 8.70080i | −0.375118 | + | 0.375118i | ||||
\(539\) | 9.70448 | + | 7.26795i | 0.418002 | + | 0.313053i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.5885 | 1.91701 | 0.958504 | − | 0.285080i | \(-0.0920201\pi\) | ||||
0.958504 | + | 0.285080i | \(0.0920201\pi\) | |||||||
\(542\) | −13.7242 | − | 13.7242i | −0.589505 | − | 0.589505i | ||||
\(543\) | 6.86800 | + | 6.86800i | 0.294734 | + | 0.294734i | ||||
\(544\) | −5.60288 | −0.240222 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.1244 | + | 9.06996i | −0.775651 | + | 0.388158i | ||||
\(547\) | −5.22715 | + | 5.22715i | −0.223497 | + | 0.223497i | −0.809969 | − | 0.586472i | \(-0.800516\pi\) |
0.586472 | + | 0.809969i | \(0.300516\pi\) | |||||||
\(548\) | 0.568406 | + | 0.568406i | 0.0242811 | + | 0.0242811i | ||||
\(549\) | −83.6410 | −3.56971 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.10417i | 0.302648i | ||||||||
\(552\) | −5.02341 | − | 5.02341i | −0.213810 | − | 0.213810i | ||||
\(553\) | 5.02053 | + | 1.67160i | 0.213495 | + | 0.0710835i | ||||
\(554\) | − | 21.1244i | − | 0.897488i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.60031i | 0.110278i | ||||||||
\(557\) | 23.1822 | − | 23.1822i | 0.982262 | − | 0.982262i | −0.0175832 | − | 0.999845i | \(-0.505597\pi\) |
0.999845 | + | 0.0175832i | \(0.00559720\pi\) | |||||||
\(558\) | −21.6479 | + | 21.6479i | −0.916428 | + | 0.916428i | ||||
\(559\) | −8.20319 | −0.346958 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.3923 | −1.32538 | ||||||||
\(562\) | 9.79796 | − | 9.79796i | 0.413302 | − | 0.413302i | ||||
\(563\) | −13.7242 | + | 13.7242i | −0.578406 | + | 0.578406i | −0.934464 | − | 0.356058i | \(-0.884121\pi\) |
0.356058 | + | 0.934464i | \(0.384121\pi\) | |||||||
\(564\) | − | 13.2679i | − | 0.558681i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 14.4406i | − | 0.606983i | ||||||
\(567\) | −20.3270 | + | 61.0510i | −0.853655 | + | 2.56390i | ||||
\(568\) | −1.55291 | − | 1.55291i | −0.0651588 | − | 0.0651588i | ||||
\(569\) | 16.1769i | 0.678172i | 0.940755 | + | 0.339086i | \(0.110118\pi\) | ||||
−0.940755 | + | 0.339086i | \(0.889882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.60770 | 0.402070 | 0.201035 | − | 0.979584i | \(-0.435570\pi\) | ||||
0.201035 | + | 0.979584i | \(0.435570\pi\) | |||||||
\(572\) | 2.90027 | + | 2.90027i | 0.121266 | + | 0.121266i | ||||
\(573\) | −29.5716 | + | 29.5716i | −1.23537 | + | 1.23537i | ||||
\(574\) | 22.9610 | − | 11.4904i | 0.958375 | − | 0.479599i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.46410 | 0.311004 | ||||||||
\(577\) | −12.2140 | − | 12.2140i | −0.508474 | − | 0.508474i | 0.405584 | − | 0.914058i | \(-0.367068\pi\) |
−0.914058 | + | 0.405584i | \(0.867068\pi\) | |||||||
\(578\) | −10.1769 | − | 10.1769i | −0.423303 | − | 0.423303i | ||||
\(579\) | 19.8112 | 0.823327 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.4904 | − | 22.9610i | −0.476701 | − | 0.952585i | ||||
\(582\) | −10.8332 | + | 10.8332i | −0.449052 | + | 0.449052i | ||||
\(583\) | −4.65874 | − | 4.65874i | −0.192945 | − | 0.192945i | ||||
\(584\) | 7.33642 | 0.303583 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.00258i | 0.124035i | ||||||||
\(587\) | −3.18471 | − | 3.18471i | −0.131447 | − | 0.131447i | 0.638322 | − | 0.769769i | \(-0.279629\pi\) |
−0.769769 | + | 0.638322i | \(0.779629\pi\) | |||||||
\(588\) | −3.21771 | − | 22.4140i | −0.132696 | − | 0.924338i | ||||
\(589\) | 22.9808i | 0.946906i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 72.4352i | − | 2.97959i | ||||||
\(592\) | −5.79555 | + | 5.79555i | −0.238196 | + | 0.238196i | ||||
\(593\) | −14.0087 | + | 14.0087i | −0.575266 | + | 0.575266i | −0.933595 | − | 0.358329i | \(-0.883347\pi\) |
0.358329 | + | 0.933595i | \(0.383347\pi\) | |||||||
\(594\) | 25.0118 | 1.02625 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.3923 | −0.671455 | ||||||||
\(597\) | 35.0136 | − | 35.0136i | 1.43301 | − | 1.43301i | ||||
\(598\) | −3.67739 | + | 3.67739i | −0.150380 | + | 0.150380i | ||||
\(599\) | − | 22.7321i | − | 0.928806i | −0.885624 | − | 0.464403i | \(-0.846269\pi\) | ||
0.885624 | − | 0.464403i | \(-0.153731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7071i | 0.518332i | 0.965833 | + | 0.259166i | \(0.0834476\pi\) | ||||
−0.965833 | + | 0.259166i | \(0.916552\pi\) | |||||||
\(602\) | 2.89529 | − | 8.69582i | 0.118003 | − | 0.354415i | ||||
\(603\) | −20.7327 | − | 20.7327i | −0.844302 | − | 0.844302i | ||||
\(604\) | 16.5885i | 0.674975i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22.9808 | 0.933530 | ||||||||
\(607\) | 3.34894 | + | 3.34894i | 0.135929 | + | 0.135929i | 0.771798 | − | 0.635868i | \(-0.219358\pi\) |
−0.635868 | + | 0.771798i | \(0.719358\pi\) | |||||||
\(608\) | 3.96184 | − | 3.96184i | 0.160674 | − | 0.160674i | ||||
\(609\) | −9.70448 | + | 4.85641i | −0.393245 | + | 0.196792i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.71281 | −0.392938 | ||||||||
\(612\) | 29.5716 | + | 29.5716i | 1.19536 | + | 1.19536i | ||||
\(613\) | −4.24264 | − | 4.24264i | −0.171359 | − | 0.171359i | 0.616217 | − | 0.787576i | \(-0.288664\pi\) |
−0.787576 | + | 0.616217i | \(0.788664\pi\) | |||||||
\(614\) | 4.96836 | 0.200507 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.09808 | + | 2.05080i | −0.165116 | + | 0.0826290i | ||||
\(617\) | −8.48528 | + | 8.48528i | −0.341605 | + | 0.341605i | −0.856970 | − | 0.515366i | \(-0.827656\pi\) |
0.515366 | + | 0.856970i | \(0.327656\pi\) | |||||||
\(618\) | 10.8332 | + | 10.8332i | 0.435777 | + | 0.435777i | ||||
\(619\) | 47.0211 | 1.88994 | 0.944969 | − | 0.327160i | \(-0.106092\pi\) | ||||
0.944969 | + | 0.327160i | \(0.106092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.7137i | 1.27263i | ||||||||
\(622\) | −13.7242 | − | 13.7242i | −0.550291 | − | 0.550291i | ||||
\(623\) | 8.11098 | − | 24.3608i | 0.324960 | − | 0.975996i | ||||
\(624\) | − | 7.66025i | − | 0.306656i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 28.8812i | − | 1.15432i | ||||||
\(627\) | 22.1977 | − | 22.1977i | 0.886491 | − | 0.886491i | ||||
\(628\) | 15.3987 | − | 15.3987i | 0.614474 | − | 0.614474i | ||||
\(629\) | −45.9221 | −1.83103 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.9808 | 1.47218 | 0.736090 | − | 0.676883i | \(-0.236670\pi\) | ||||
0.736090 | + | 0.676883i | \(0.236670\pi\) | |||||||
\(632\) | −1.41421 | + | 1.41421i | −0.0562544 | + | 0.0562544i | ||||
\(633\) | −21.0350 | + | 21.0350i | −0.836065 | + | 0.836065i | ||||
\(634\) | − | 16.3923i | − | 0.651022i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.3048i | 0.487917i | ||||||||
\(637\) | −16.4082 | + | 2.35553i | −0.650116 | + | 0.0933294i | ||||
\(638\) | 1.55291 | + | 1.55291i | 0.0614805 | + | 0.0614805i | ||||
\(639\) | 16.3923i | 0.648470i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.0000 | −1.42191 | −0.710957 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710957 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(642\) | 30.6331 | + | 30.6331i | 1.20899 | + | 1.20899i | ||||
\(643\) | −20.4221 | + | 20.4221i | −0.805368 | + | 0.805368i | −0.983929 | − | 0.178561i | \(-0.942856\pi\) |
0.178561 | + | 0.983929i | \(0.442856\pi\) | |||||||
\(644\) | −2.60031 | − | 5.19615i | −0.102466 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 31.3923 | 1.23511 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | −17.1972 | − | 17.1972i | −0.675570 | − | 0.675570i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.3923 | + | 15.7096i | −1.23036 | + | 0.615709i | ||||
\(652\) | −2.77766 | + | 2.77766i | −0.108782 | + | 0.108782i | ||||
\(653\) | 35.1894 | + | 35.1894i | 1.37707 | + | 1.37707i | 0.849532 | + | 0.527537i | \(0.176884\pi\) |
0.527537 | + | 0.849532i | \(0.323116\pi\) | |||||||
\(654\) | −6.46965 | −0.252983 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.70448i | 0.378896i | ||||||||
\(657\) | −38.7210 | − | 38.7210i | −1.51065 | − | 1.51065i | ||||
\(658\) | 3.42811 | − | 10.2961i | 0.133641 | − | 0.401384i | ||||
\(659\) | 11.8756i | 0.462609i | 0.972881 | + | 0.231305i | \(0.0742994\pi\) | ||||
−0.972881 | + | 0.231305i | \(0.925701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.5131i | 1.03124i | 0.856817 | + | 0.515621i | \(0.172439\pi\) | ||||
−0.856817 | + | 0.515621i | \(0.827561\pi\) | |||||||
\(662\) | 16.6796 | − | 16.6796i | 0.648269 | − | 0.648269i | ||||
\(663\) | 30.3487 | − | 30.3487i | 1.17864 | − | 1.17864i | ||||
\(664\) | 9.70448 | 0.376607 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 61.1769 | 2.37056 | ||||||||
\(667\) | −1.96902 | + | 1.96902i | −0.0762406 | + | 0.0762406i | ||||
\(668\) | −15.8473 | + | 15.8473i | −0.613152 | + | 0.613152i | ||||
\(669\) | 55.1244i | 2.13123i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.4090i | 0.749275i | ||||||||
\(672\) | 8.12028 | + | 2.70366i | 0.313247 | + | 0.104296i | ||||
\(673\) | 1.13681 | + | 1.13681i | 0.0438209 | + | 0.0438209i | 0.728678 | − | 0.684857i | \(-0.240135\pi\) |
−0.684857 | + | 0.728678i | \(0.740135\pi\) | |||||||
\(674\) | 25.7321i | 0.991162i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.39230 | 0.284319 | ||||||||
\(677\) | −33.2489 | − | 33.2489i | −1.27786 | − | 1.27786i | −0.941863 | − | 0.335998i | \(-0.890926\pi\) |
−0.335998 | − | 0.941863i | \(-0.609074\pi\) | |||||||
\(678\) | 25.6097 | − | 25.6097i | 0.983535 | − | 0.983535i | ||||
\(679\) | −11.2058 | + | 5.60770i | −0.430038 | + | 0.215204i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.2487 | −1.38905 | ||||||||
\(682\) | 5.02341 | + | 5.02341i | 0.192356 | + | 0.192356i | ||||
\(683\) | −0.152304 | − | 0.152304i | −0.00582775 | − | 0.00582775i | 0.704187 | − | 0.710015i | \(-0.251312\pi\) |
−0.710015 | + | 0.704187i | \(0.751312\pi\) | |||||||
\(684\) | −41.8205 | −1.59905 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.29423 | − | 18.2249i | 0.125774 | − | 0.695831i | ||||
\(687\) | −9.38186 | + | 9.38186i | −0.357940 | + | 0.357940i | ||||
\(688\) | 2.44949 | + | 2.44949i | 0.0933859 | + | 0.0933859i | ||||
\(689\) | 9.00773 | 0.343167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8087i | 0.639431i | 0.947514 | + | 0.319716i | \(0.103587\pi\) | ||||
−0.947514 | + | 0.319716i | \(0.896413\pi\) | |||||||
\(692\) | 10.8239 | + | 10.8239i | 0.411464 | + | 0.411464i | ||||
\(693\) | 32.4532 | + | 10.8054i | 1.23280 | + | 0.410462i | ||||
\(694\) | 29.7846i | 1.13061i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 4.10160i | − | 0.155471i | ||||||
\(697\) | −38.4476 | + | 38.4476i | −1.45631 | + | 1.45631i | ||||
\(698\) | 5.02341 | − | 5.02341i | 0.190139 | − | 0.190139i | ||||
\(699\) | −33.6173 | −1.27152 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.9282 | −0.714908 | −0.357454 | − | 0.933931i | \(-0.616355\pi\) | ||||
−0.357454 | + | 0.933931i | \(0.616355\pi\) | |||||||
\(702\) | −24.1803 | + | 24.1803i | −0.912628 | + | 0.912628i | ||||
\(703\) | 32.4718 | − | 32.4718i | 1.22470 | − | 1.22470i | ||||
\(704\) | − | 1.73205i | − | 0.0652791i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.6121i | 1.03920i | ||||||||
\(707\) | 17.8334 | + | 5.93765i | 0.670693 | + | 0.223308i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.392305i | 0.0147333i | 0.999973 | + | 0.00736666i | \(0.00234490\pi\) | ||||
−0.999973 | + | 0.00736666i | \(0.997655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.9282 | 0.559851 | ||||||||
\(712\) | 6.86210 | + | 6.86210i | 0.257168 | + | 0.257168i | ||||
\(713\) | −6.36943 | + | 6.36943i | −0.238537 | + | 0.238537i | ||||
\(714\) | 21.4598 | + | 42.8827i | 0.803111 | + | 1.60484i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.80385 | −0.254272 | ||||||||
\(717\) | 59.1431 | + | 59.1431i | 2.20874 | + | 2.20874i | ||||
\(718\) | 7.34847 | + | 7.34847i | 0.274242 | + | 0.274242i | ||||
\(719\) | −26.5131 | −0.988773 | −0.494386 | − | 0.869242i | \(-0.664607\pi\) | ||||
−0.494386 | + | 0.869242i | \(0.664607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.60770 | + | 11.2058i | 0.208841 | + | 0.417325i | ||||
\(722\) | −8.76268 | + | 8.76268i | −0.326113 | + | 0.326113i | ||||
\(723\) | −3.43400 | − | 3.43400i | −0.127712 | − | 0.127712i | ||||
\(724\) | −3.00258 | −0.111590 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.8786i | 0.960445i | ||||||||
\(727\) | −25.4455 | − | 25.4455i | −0.943721 | − | 0.943721i | 0.0547775 | − | 0.998499i | \(-0.482555\pi\) |
−0.998499 | + | 0.0547775i | \(0.982555\pi\) | |||||||
\(728\) | 1.97922 | − | 5.94446i | 0.0733547 | − | 0.220316i | ||||
\(729\) | 41.3923i | 1.53305i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.4090i | 0.717866i | ||||||||
\(732\) | 25.6317 | − | 25.6317i | 0.947375 | − | 0.947375i | ||||
\(733\) | 3.34894 | − | 3.34894i | 0.123696 | − | 0.123696i | −0.642549 | − | 0.766245i | \(-0.722123\pi\) |
0.766245 | + | 0.642549i | \(0.222123\pi\) | |||||||
\(734\) | 4.73611 | 0.174813 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.19615 | 0.0809513 | ||||||||
\(737\) | −4.81105 | + | 4.81105i | −0.177217 | + | 0.177217i | ||||
\(738\) | 51.2194 | − | 51.2194i | 1.88541 | − | 1.88541i | ||||
\(739\) | − | 16.7846i | − | 0.617432i | −0.951154 | − | 0.308716i | \(-0.900101\pi\) | ||
0.951154 | − | 0.308716i | \(-0.0998992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.9195i | 1.57669i | ||||||||
\(742\) | −3.17925 | + | 9.54867i | −0.116714 | + | 0.350543i | ||||
\(743\) | −4.65874 | − | 4.65874i | −0.170913 | − | 0.170913i | 0.616468 | − | 0.787380i | \(-0.288563\pi\) |
−0.787380 | + | 0.616468i | \(0.788563\pi\) | |||||||
\(744\) | − | 13.2679i | − | 0.486427i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.2679 | −0.485774 | ||||||||
\(747\) | −51.2194 | − | 51.2194i | −1.87402 | − | 1.87402i | ||||
\(748\) | 6.86210 | − | 6.86210i | 0.250903 | − | 0.250903i | ||||
\(749\) | 15.8569 | + | 31.6865i | 0.579398 | + | 1.15780i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8038 | −0.503710 | −0.251855 | − | 0.967765i | \(-0.581041\pi\) | ||||
−0.251855 | + | 0.967765i | \(0.581041\pi\) | |||||||
\(752\) | 2.90027 | + | 2.90027i | 0.105762 | + | 0.105762i | ||||
\(753\) | −38.4476 | − | 38.4476i | −1.40111 | − | 1.40111i | ||||
\(754\) | −3.00258 | −0.109347 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −17.0981 | − | 34.1668i | −0.621851 | − | 1.24263i | ||||
\(757\) | 28.8019 | − | 28.8019i | 1.04682 | − | 1.04682i | 0.0479746 | − | 0.998849i | \(-0.484723\pi\) |
0.998849 | − | 0.0479746i | \(-0.0152767\pi\) | |||||||
\(758\) | −24.0280 | − | 24.0280i | −0.872737 | − | 0.872737i | ||||
\(759\) | 12.3048 | 0.446635 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29.1134i | − | 1.05536i | −0.849443 | − | 0.527681i | \(-0.823062\pi\) | ||
0.849443 | − | 0.527681i | \(-0.176938\pi\) | |||||||
\(762\) | −41.1726 | − | 41.1726i | −1.49153 | − | 1.49153i | ||||
\(763\) | −5.02053 | − | 1.67160i | −0.181756 | − | 0.0605158i | ||||
\(764\) | − | 12.9282i | − | 0.467726i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 19.4090i | − | 0.701274i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.28737 | + | 2.28737i | −0.0825383 | + | 0.0825383i | ||||
\(769\) | −1.50129 | −0.0541378 | −0.0270689 | − | 0.999634i | \(-0.508617\pi\) | ||||
−0.0270689 | + | 0.999634i | \(0.508617\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −62.7846 | −2.26113 | ||||||||
\(772\) | −4.33057 | + | 4.33057i | −0.155861 | + | 0.155861i | ||||
\(773\) | 11.6011 | − | 11.6011i | 0.417261 | − | 0.417261i | −0.466997 | − | 0.884259i | \(-0.654664\pi\) |
0.884259 | + | 0.466997i | \(0.154664\pi\) | |||||||
\(774\) | − | 25.8564i | − | 0.929389i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 4.73611i | − | 0.170017i | ||||||
\(777\) | 66.5550 | + | 22.1596i | 2.38765 | + | 0.794972i | ||||
\(778\) | −0.240237 | − | 0.240237i | −0.00861290 | − | 0.00861290i | ||||
\(779\) | − | 54.3731i | − | 1.94812i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.80385 | 0.136112 | ||||||||
\(782\) | 8.70080 | + | 8.70080i | 0.311140 | + | 0.311140i | ||||
\(783\) | −12.9471 | + | 12.9471i | −0.462691 | + | 0.462691i | ||||
\(784\) | 5.60288 | + | 4.19615i | 0.200103 | + | 0.149863i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.3753 | − | 10.3753i | −0.369838 | − | 0.369838i | 0.497580 | − | 0.867418i | \(-0.334222\pi\) |
−0.867418 | + | 0.497580i | \(0.834222\pi\) | |||||||
\(788\) | 15.8338 | + | 15.8338i | 0.564054 | + | 0.564054i | ||||
\(789\) | 72.4352 | 2.57876 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.4904 | − | 13.2566i | 0.941890 | − | 0.471349i | ||||
\(792\) | −9.14162 | + | 9.14162i | −0.324833 | + | 0.324833i | ||||
\(793\) | −18.7637 | − | 18.7637i | −0.666319 | − | 0.666319i | ||||
\(794\) | −11.8403 | −0.420196 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.3074i | 0.542555i | ||||||||
\(797\) | 25.3253 | + | 25.3253i | 0.897067 | + | 0.897067i | 0.995176 | − | 0.0981086i | \(-0.0312793\pi\) |
−0.0981086 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(798\) | −45.4970 | − | 15.1483i | −1.61058 | − | 0.536244i | ||||
\(799\) | 22.9808i | 0.813001i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 72.4352i | − | 2.55937i | ||||||
\(802\) | −9.95026 | + | 9.95026i | −0.351356 | + | 0.351356i | ||||
\(803\) | −8.98525 | + | 8.98525i | −0.317082 | + | 0.317082i | ||||
\(804\) | 12.7071 | 0.448143 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.71281 | −0.342119 | ||||||||
\(807\) | −28.1456 | + | 28.1456i | −0.990771 | + | 0.990771i | ||||
\(808\) | −5.02341 | + | 5.02341i | −0.176723 | + | 0.176723i | ||||
\(809\) | 51.0333i | 1.79424i | 0.441791 | + | 0.897118i | \(0.354343\pi\) | ||||
−0.441791 | + | 0.897118i | \(0.645657\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.8205i | 1.46852i | 0.678870 | + | 0.734258i | \(0.262470\pi\) | ||||
−0.678870 | + | 0.734258i | \(0.737530\pi\) | |||||||
\(812\) | 1.05975 | − | 3.18289i | 0.0371899 | − | 0.111698i | ||||
\(813\) | −44.3954 | − | 44.3954i | −1.55702 | − | 1.55702i | ||||
\(814\) | − | 14.1962i | − | 0.497575i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −18.1244 | −0.634479 | ||||||||
\(817\) | −13.7242 | − | 13.7242i | −0.480149 | − | 0.480149i | ||||
\(818\) | −24.8326 | + | 24.8326i | −0.868251 | + | 0.868251i | ||||
\(819\) | −41.8205 | + | 20.9282i | −1.46133 | + | 0.731291i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.1244 | −1.15605 | −0.578024 | − | 0.816020i | \(-0.696176\pi\) | ||||
−0.578024 | + | 0.816020i | \(0.696176\pi\) | |||||||
\(822\) | 1.83869 | + | 1.83869i | 0.0641319 | + | 0.0641319i | ||||
\(823\) | 0.896575 | + | 0.896575i | 0.0312527 | + | 0.0312527i | 0.722560 | − | 0.691308i | \(-0.242965\pi\) |
−0.691308 | + | 0.722560i | \(0.742965\pi\) | |||||||
\(824\) | −4.73611 | −0.164990 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.9241 | − | 19.9241i | 0.692828 | − | 0.692828i | −0.270025 | − | 0.962853i | \(-0.587032\pi\) |
0.962853 | + | 0.270025i | \(0.0870319\pi\) | |||||||
\(828\) | −11.5911 | − | 11.5911i | −0.402819 | − | 0.402819i | ||||
\(829\) | −14.2083 | −0.493476 | −0.246738 | − | 0.969082i | \(-0.579359\pi\) | ||||
−0.246738 | + | 0.969082i | \(0.579359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 68.3336i | − | 2.37047i | ||||||
\(832\) | 1.67447 | + | 1.67447i | 0.0580518 | + | 0.0580518i | ||||
\(833\) | 5.57324 | + | 38.8222i | 0.193101 | + | 1.34511i | ||||
\(834\) | 8.41154i | 0.291268i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.70448i | 0.335636i | ||||||||
\(837\) | −41.8816 | + | 41.8816i | −1.44764 | + | 1.44764i | ||||
\(838\) | −25.6097 | + | 25.6097i | −0.884673 | + | 0.884673i | ||||
\(839\) | −21.3125 | −0.735790 | −0.367895 | − | 0.929867i | \(-0.619921\pi\) | ||||
−0.367895 | + | 0.929867i | \(0.619921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3923 | 0.944562 | ||||||||
\(842\) | −20.6312 | + | 20.6312i | −0.710998 | + | 0.710998i | ||||
\(843\) | 31.6947 | − | 31.6947i | 1.09162 | − | 1.09162i | ||||
\(844\) | − | 9.19615i | − | 0.316545i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 30.6147i | − | 1.05256i | ||||||
\(847\) | −6.68638 | + | 20.0821i | −0.229747 | + | 0.690030i | ||||
\(848\) | −2.68973 | − | 2.68973i | −0.0923656 | − | 0.0923656i | ||||
\(849\) | − | 46.7128i | − | 1.60318i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | 0.617032 | ||||||||
\(852\) | −5.02341 | − | 5.02341i | −0.172099 | − | 0.172099i | ||||
\(853\) | −7.02633 | + | 7.02633i | −0.240577 | + | 0.240577i | −0.817089 | − | 0.576512i | \(-0.804413\pi\) |
0.576512 | + | 0.817089i | \(0.304413\pi\) | |||||||
\(854\) | 26.5131 | − | 13.2679i | 0.907261 | − | 0.454020i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.3923 | −0.457740 | ||||||||
\(857\) | −15.5629 | − | 15.5629i | −0.531619 | − | 0.531619i | 0.389435 | − | 0.921054i | \(-0.372670\pi\) |
−0.921054 | + | 0.389435i | \(0.872670\pi\) | |||||||
\(858\) | 9.38186 | + | 9.38186i | 0.320291 | + | 0.320291i | ||||
\(859\) | −36.2176 | −1.23573 | −0.617864 | − | 0.786285i | \(-0.712002\pi\) | ||||
−0.617864 | + | 0.786285i | \(0.712002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 74.2750 | − | 37.1694i | 2.53128 | − | 1.26673i | ||||
\(862\) | −5.31508 | + | 5.31508i | −0.181032 | + | 0.181032i | ||||
\(863\) | 22.3500 | + | 22.3500i | 0.760803 | + | 0.760803i | 0.976468 | − | 0.215664i | \(-0.0691917\pi\) |
−0.215664 | + | 0.976468i | \(0.569192\pi\) | |||||||
\(864\) | 14.4406 | 0.491279 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21.5448i | 0.732121i | ||||||||
\(867\) | −32.9205 | − | 32.9205i | −1.11804 | − | 1.11804i | ||||
\(868\) | 3.42811 | − | 10.2961i | 0.116357 | − | 0.349472i | ||||
\(869\) | − | 3.46410i | − | 0.117512i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.30221i | − | 0.315193i | ||||||
\(872\) | 1.41421 | − | 1.41421i | 0.0478913 | − | 0.0478913i | ||||
\(873\) | −24.9968 | + | 24.9968i | −0.846014 | + | 0.846014i | ||||
\(874\) | −12.3048 | −0.416216 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.7321 | 0.801832 | ||||||||
\(877\) | 1.31268 | − | 1.31268i | 0.0443260 | − | 0.0443260i | −0.684596 | − | 0.728922i | \(-0.740022\pi\) |
0.728922 | + | 0.684596i | \(0.240022\pi\) | |||||||
\(878\) | −5.80053 | + | 5.80053i | −0.195758 | + | 0.195758i | ||||
\(879\) | 9.71281i | 0.327605i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.0263i | 1.78650i | 0.449560 | + | 0.893250i | \(0.351581\pi\) | ||||
−0.449560 | + | 0.893250i | \(0.648419\pi\) | |||||||
\(882\) | −7.42461 | − | 51.7185i | −0.250000 | − | 1.74145i | ||||
\(883\) | 12.3998 | + | 12.3998i | 0.417285 | + | 0.417285i | 0.884267 | − | 0.466982i | \(-0.154659\pi\) |
−0.466982 | + | 0.884267i | \(0.654659\pi\) | |||||||
\(884\) | 13.2679i | 0.446249i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0000 | 0.503935 | ||||||||
\(887\) | 8.70080 | + | 8.70080i | 0.292144 | + | 0.292144i | 0.837927 | − | 0.545783i | \(-0.183768\pi\) |
−0.545783 | + | 0.837927i | \(0.683768\pi\) | |||||||
\(888\) | −18.7476 | + | 18.7476i | −0.629129 | + | 0.629129i | ||||
\(889\) | −21.3125 | − | 42.5885i | −0.714799 | − | 1.42837i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.1244 | 1.41122 | ||||||||
\(892\) | −12.0497 | − | 12.0497i | −0.403455 | − | 0.403455i | ||||
\(893\) | −16.2499 | − | 16.2499i | −0.543781 | − | 0.543781i | ||||
\(894\) | −53.0263 | −1.77346 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.36603 | + | 1.18403i | −0.0790434 | + | 0.0395556i | ||||
\(897\) | −11.8957 | + | 11.8957i | −0.397186 | + | 0.397186i | ||||
\(898\) | −0.808643 | − | 0.808643i | −0.0269848 | − | 0.0269848i | ||||
\(899\) | −5.20061 | −0.173450 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 21.3125i | − | 0.710023i | ||||||
\(902\) | −11.8855 | − | 11.8855i | −0.395744 | − | 0.395744i | ||||
\(903\) | 9.36576 | − | 28.1295i | 0.311673 | − | 0.936090i | ||||
\(904\) | 11.1962i | 0.372378i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 53.6608i | 1.78276i | ||||||||
\(907\) | −31.6675 | + | 31.6675i | −1.05150 | + | 1.05150i | −0.0529024 | + | 0.998600i | \(0.516847\pi\) |
−0.998600 | + | 0.0529024i | \(0.983153\pi\) | |||||||
\(908\) | 7.92367 | − | 7.92367i | 0.262956 | − | 0.262956i | ||||
\(909\) | 53.0263 | 1.75877 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 12.8159 | − | 12.8159i | 0.424375 | − | 0.424375i | ||||
\(913\) | −11.8855 | + | 11.8855i | −0.393353 | + | 0.393353i | ||||
\(914\) | − | 12.8038i | − | 0.423514i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 4.10160i | − | 0.135521i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 57.2113 | + | 57.2113i | 1.88825 | + | 1.88825i | ||||
\(919\) | 9.60770i | 0.316929i | 0.987365 | + | 0.158464i | \(0.0506543\pi\) | ||||
−0.987365 | + | 0.158464i | \(0.949346\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.0718 | 0.529584 | ||||||||
\(922\) | 18.7476 | + | 18.7476i | 0.617420 | + | 0.617420i | ||||
\(923\) | −3.67739 | + | 3.67739i | −0.121043 | + | 0.121043i | ||||
\(924\) | −13.2566 | + | 6.63397i | −0.436109 | + | 0.218242i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −37.1769 | −1.22171 | ||||||||
\(927\) | 24.9968 | + | 24.9968i | 0.821003 | + | 0.821003i | ||||
\(928\) | 0.896575 | + | 0.896575i | 0.0294315 | + | 0.0294315i | ||||
\(929\) | −38.8179 | −1.27357 | −0.636787 | − | 0.771040i | \(-0.719737\pi\) | ||||
−0.636787 | + | 0.771040i | \(0.719737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.3923 | − | 23.5106i | −1.02884 | − | 0.770527i | ||||
\(932\) | 7.34847 | − | 7.34847i | 0.240707 | − | 0.240707i | ||||
\(933\) | −44.3954 | − | 44.3954i | −1.45344 | − | 1.45344i | ||||
\(934\) | −8.20319 | −0.268417 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 17.6754i | − | 0.577739i | ||||||
\(937\) | 35.9850 | + | 35.9850i | 1.17558 | + | 1.17558i | 0.980859 | + | 0.194719i | \(0.0623795\pi\) |
0.194719 | + | 0.980859i | \(0.437620\pi\) | |||||||
\(938\) | 9.86084 | + | 3.28318i | 0.321968 | + | 0.107200i | ||||
\(939\) | − | 93.4256i | − | 3.04883i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.2083i | 0.463179i | 0.972814 | + | 0.231589i | \(0.0743926\pi\) | ||||
−0.972814 | + | 0.231589i | \(0.925607\pi\) | |||||||
\(942\) | 49.8120 | − | 49.8120i | 1.62296 | − | 1.62296i | ||||
\(943\) | 15.0702 | − | 15.0702i | 0.490754 | − | 0.490754i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | −5.07484 | + | 5.07484i | −0.164910 | + | 0.164910i | −0.784738 | − | 0.619828i | \(-0.787202\pi\) |
0.619828 | + | 0.784738i | \(0.287202\pi\) | |||||||
\(948\) | −4.57474 | + | 4.57474i | −0.148580 | + | 0.148580i | ||||
\(949\) | − | 17.3731i | − | 0.563954i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 53.0263i | − | 1.71949i | ||||||
\(952\) | −14.0647 | − | 4.68288i | −0.455841 | − | 0.151773i | ||||
\(953\) | 3.67423 | + | 3.67423i | 0.119020 | + | 0.119020i | 0.764108 | − | 0.645088i | \(-0.223179\pi\) |
−0.645088 | + | 0.764108i | \(0.723179\pi\) | |||||||
\(954\) | 28.3923i | 0.919235i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25.8564 | −0.836256 | ||||||||
\(957\) | 5.02341 | + | 5.02341i | 0.162384 | + | 0.162384i | ||||
\(958\) | −13.7242 | + | 13.7242i | −0.443409 | + | 0.443409i | ||||
\(959\) | 0.951779 | + | 1.90192i | 0.0307345 | + | 0.0614163i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1769 | 0.457320 | ||||||||
\(962\) | 13.7242 | + | 13.7242i | 0.442486 | + | 0.442486i | ||||
\(963\) | 70.6835 | + | 70.6835i | 2.27774 | + | 2.27774i | ||||
\(964\) | 1.50129 | 0.0483532 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.41154 | − | 16.8087i | −0.270637 | − | 0.540809i | ||||
\(967\) | 14.2808 | − | 14.2808i | 0.459241 | − | 0.459241i | −0.439165 | − | 0.898406i | \(-0.644726\pi\) |
0.898406 | + | 0.439165i | \(0.144726\pi\) | |||||||
\(968\) | −5.65685 | − | 5.65685i | −0.181818 | − | 0.181818i | ||||
\(969\) | 101.549 | 3.26221 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 11.6080i | − | 0.372520i | −0.982501 | − | 0.186260i | \(-0.940363\pi\) | ||
0.982501 | − | 0.186260i | \(-0.0596366\pi\) | |||||||
\(972\) | −24.9968 | − | 24.9968i | −0.801773 | − | 0.801773i | ||||
\(973\) | −2.17333 | + | 6.52747i | −0.0696738 | + | 0.209261i | ||||
\(974\) | − | 20.5359i | − | 0.658013i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.2058i | 0.358688i | ||||||||
\(977\) | 36.4785 | − | 36.4785i | 1.16705 | − | 1.16705i | 0.184155 | − | 0.982897i | \(-0.441045\pi\) |
0.982897 | − | 0.184155i | \(-0.0589548\pi\) | |||||||
\(978\) | −8.98525 | + | 8.98525i | −0.287316 | + | 0.287316i | ||||
\(979\) | −16.8087 | −0.537207 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9282 | −0.476621 | ||||||||
\(982\) | 13.3843 | − | 13.3843i | 0.427109 | − | 0.427109i | ||||
\(983\) | 26.6713 | − | 26.6713i | 0.850682 | − | 0.850682i | −0.139535 | − | 0.990217i | \(-0.544561\pi\) |
0.990217 | + | 0.139535i | \(0.0445608\pi\) | |||||||
\(984\) | 31.3923i | 1.00075i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.10417i | 0.226243i | ||||||||
\(987\) | 11.0893 | − | 33.3061i | 0.352977 | − | 1.06014i | ||||
\(988\) | −9.38186 | − | 9.38186i | −0.298477 | − | 0.298477i | ||||
\(989\) | − | 7.60770i | − | 0.241911i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.19615 | −0.133295 | −0.0666476 | − | 0.997777i | \(-0.521230\pi\) | ||||
−0.0666476 | + | 0.997777i | \(0.521230\pi\) | |||||||
\(992\) | 2.90027 | + | 2.90027i | 0.0920835 | + | 0.0920835i | ||||
\(993\) | 53.9555 | − | 53.9555i | 1.71223 | − | 1.71223i | ||||
\(994\) | −2.60031 | − | 5.19615i | −0.0824767 | − | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 31.3923 | 0.994703 | ||||||||
\(997\) | −8.37235 | − | 8.37235i | −0.265155 | − | 0.265155i | 0.561989 | − | 0.827144i | \(-0.310036\pi\) |
−0.827144 | + | 0.561989i | \(0.810036\pi\) | |||||||
\(998\) | −17.5254 | − | 17.5254i | −0.554756 | − | 0.554756i | ||||
\(999\) | 118.357 | 3.74466 |
(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 | 350.2.g.b.293.1 | ✓ | 16 | |
5.2 | odd | 4 | inner | 350.2.g.b.307.4 | yes | 16 | |
5.3 | odd | 4 | inner | 350.2.g.b.307.5 | yes | 16 | |
5.4 | even | 2 | inner | 350.2.g.b.293.8 | yes | 16 | |
7.6 | odd | 2 | inner | 350.2.g.b.293.4 | yes | 16 | |
35.13 | even | 4 | inner | 350.2.g.b.307.8 | yes | 16 | |
35.27 | even | 4 | inner | 350.2.g.b.307.1 | yes | 16 | |
35.34 | odd | 2 | inner | 350.2.g.b.293.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.g.b.293.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
350.2.g.b.293.4 | yes | 16 | 7.6 | odd | 2 | inner | |
350.2.g.b.293.5 | yes | 16 | 35.34 | odd | 2 | inner | |
350.2.g.b.293.8 | yes | 16 | 5.4 | even | 2 | inner | |
350.2.g.b.307.1 | yes | 16 | 35.27 | even | 4 | inner | |
350.2.g.b.307.4 | yes | 16 | 5.2 | odd | 4 | inner | |
350.2.g.b.307.5 | yes | 16 | 5.3 | odd | 4 | inner | |
350.2.g.b.307.8 | yes | 16 | 35.13 | even | 4 | inner |