Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(307,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.k (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: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.11 | ||
Character | \(\chi\) | \(=\) | 975.343 |
Dual form | 975.2.k.d.307.4 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.58074i | 1.11775i | 0.829252 | + | 0.558875i | \(0.188767\pi\) | ||||
−0.829252 | + | 0.558875i | \(0.811233\pi\) | |||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −0.498726 | −0.249363 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.11775 | − | 1.11775i | 0.456319 | − | 0.456319i | ||||
\(7\) | −0.974287 | −0.368246 | −0.184123 | − | 0.982903i | \(-0.558944\pi\) | ||||
−0.184123 | + | 0.982903i | \(0.558944\pi\) | |||||||
\(8\) | 2.37312i | 0.839024i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.601309 | − | 0.601309i | −0.181302 | − | 0.181302i | 0.610621 | − | 0.791923i | \(-0.290920\pi\) |
−0.791923 | + | 0.610621i | \(0.790920\pi\) | |||||||
\(12\) | 0.352653 | + | 0.352653i | 0.101802 | + | 0.101802i | ||||
\(13\) | −3.34435 | + | 1.34733i | −0.927557 | + | 0.373682i | ||||
\(14\) | − | 1.54009i | − | 0.411606i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.74872 | −1.18718 | ||||||||
\(17\) | −1.16444 | − | 1.16444i | −0.282419 | − | 0.282419i | 0.551654 | − | 0.834073i | \(-0.313997\pi\) |
−0.834073 | + | 0.551654i | \(0.813997\pi\) | |||||||
\(18\) | −1.58074 | −0.372583 | ||||||||
\(19\) | 0.691537 | + | 0.691537i | 0.158649 | + | 0.158649i | 0.781968 | − | 0.623319i | \(-0.214216\pi\) |
−0.623319 | + | 0.781968i | \(0.714216\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.688925 | + | 0.688925i | 0.150336 | + | 0.150336i | ||||
\(22\) | 0.950511 | − | 0.950511i | 0.202650 | − | 0.202650i | ||||
\(23\) | 1.66029 | − | 1.66029i | 0.346195 | − | 0.346195i | −0.512495 | − | 0.858690i | \(-0.671279\pi\) |
0.858690 | + | 0.512495i | \(0.171279\pi\) | |||||||
\(24\) | 1.67805 | − | 1.67805i | 0.342530 | − | 0.342530i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.12977 | − | 5.28654i | −0.417683 | − | 1.03678i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0.485902 | 0.0918269 | ||||||||
\(29\) | 6.37081i | 1.18303i | 0.806294 | + | 0.591515i | \(0.201470\pi\) | ||||
−0.806294 | + | 0.591515i | \(0.798530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.57606 | + | 7.57606i | −1.36070 | + | 1.36070i | −0.487674 | + | 0.873026i | \(0.662155\pi\) |
−0.873026 | + | 0.487674i | \(0.837845\pi\) | |||||||
\(32\) | − | 2.76024i | − | 0.487947i | ||||||
\(33\) | 0.850380i | 0.148032i | ||||||||
\(34\) | 1.84067 | − | 1.84067i | 0.315673 | − | 0.315673i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 0.498726i | − | 0.0831210i | ||||||
\(37\) | −7.22558 | −1.18788 | −0.593939 | − | 0.804510i | \(-0.702428\pi\) | ||||
−0.593939 | + | 0.804510i | \(0.702428\pi\) | |||||||
\(38\) | −1.09314 | + | 1.09314i | −0.177330 | + | 0.177330i | ||||
\(39\) | 3.31752 | + | 1.41211i | 0.531229 | + | 0.226118i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65114 | − | 3.65114i | 0.570212 | − | 0.570212i | −0.361975 | − | 0.932188i | \(-0.617898\pi\) |
0.932188 | + | 0.361975i | \(0.117898\pi\) | |||||||
\(42\) | −1.08901 | + | 1.08901i | −0.168038 | + | 0.168038i | ||||
\(43\) | −2.71746 | + | 2.71746i | −0.414409 | + | 0.414409i | −0.883271 | − | 0.468862i | \(-0.844664\pi\) |
0.468862 | + | 0.883271i | \(0.344664\pi\) | |||||||
\(44\) | 0.299889 | + | 0.299889i | 0.0452099 | + | 0.0452099i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.62449 | + | 2.62449i | 0.386959 | + | 0.386959i | ||||
\(47\) | −3.25740 | −0.475140 | −0.237570 | − | 0.971370i | \(-0.576351\pi\) | ||||
−0.237570 | + | 0.971370i | \(0.576351\pi\) | |||||||
\(48\) | 3.35786 | + | 3.35786i | 0.484665 | + | 0.484665i | ||||
\(49\) | −6.05077 | −0.864395 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.64677i | 0.230594i | ||||||||
\(52\) | 1.66792 | − | 0.671949i | 0.231298 | − | 0.0931826i | ||||
\(53\) | −5.65843 | − | 5.65843i | −0.777245 | − | 0.777245i | 0.202117 | − | 0.979361i | \(-0.435218\pi\) |
−0.979361 | + | 0.202117i | \(0.935218\pi\) | |||||||
\(54\) | 1.11775 | + | 1.11775i | 0.152106 | + | 0.152106i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 2.31210i | − | 0.308967i | ||||||
\(57\) | − | 0.977981i | − | 0.129537i | ||||||
\(58\) | −10.0706 | −1.32233 | ||||||||
\(59\) | −5.91615 | + | 5.91615i | −0.770218 | + | 0.770218i | −0.978144 | − | 0.207927i | \(-0.933328\pi\) |
0.207927 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69124 | 0.344578 | 0.172289 | − | 0.985046i | \(-0.444884\pi\) | ||||
0.172289 | + | 0.985046i | \(0.444884\pi\) | |||||||
\(62\) | −11.9757 | − | 11.9757i | −1.52092 | − | 1.52092i | ||||
\(63\) | − | 0.974287i | − | 0.122749i | ||||||
\(64\) | −5.13423 | −0.641779 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.34423 | −0.165463 | ||||||||
\(67\) | − | 6.40792i | − | 0.782851i | −0.920210 | − | 0.391426i | \(-0.871982\pi\) | ||
0.920210 | − | 0.391426i | \(-0.128018\pi\) | |||||||
\(68\) | 0.580737 | + | 0.580737i | 0.0704247 | + | 0.0704247i | ||||
\(69\) | −2.34801 | −0.282667 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.17864 | − | 7.17864i | 0.851948 | − | 0.851948i | −0.138425 | − | 0.990373i | \(-0.544204\pi\) |
0.990373 | + | 0.138425i | \(0.0442040\pi\) | |||||||
\(72\) | −2.37312 | −0.279675 | ||||||||
\(73\) | 10.2299i | 1.19732i | 0.801004 | + | 0.598659i | \(0.204299\pi\) | ||||
−0.801004 | + | 0.598659i | \(0.795701\pi\) | |||||||
\(74\) | − | 11.4217i | − | 1.32775i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.344887 | − | 0.344887i | −0.0395613 | − | 0.0395613i | ||||
\(77\) | 0.585848 | + | 0.585848i | 0.0667635 | + | 0.0667635i | ||||
\(78\) | −2.23217 | + | 5.24413i | −0.252744 | + | 0.593780i | ||||
\(79\) | − | 7.43682i | − | 0.836708i | −0.908284 | − | 0.418354i | \(-0.862607\pi\) | ||
0.908284 | − | 0.418354i | \(-0.137393\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 5.77149 | + | 5.77149i | 0.637354 | + | 0.637354i | ||||
\(83\) | 14.2841 | 1.56788 | 0.783940 | − | 0.620837i | \(-0.213207\pi\) | ||||
0.783940 | + | 0.620837i | \(0.213207\pi\) | |||||||
\(84\) | −0.343585 | − | 0.343585i | −0.0374882 | − | 0.0374882i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.29559 | − | 4.29559i | −0.463205 | − | 0.463205i | ||||
\(87\) | 4.50484 | − | 4.50484i | 0.482970 | − | 0.482970i | ||||
\(88\) | 1.42698 | − | 1.42698i | 0.152116 | − | 0.152116i | ||||
\(89\) | −10.6606 | + | 10.6606i | −1.13002 | + | 1.13002i | −0.139846 | + | 0.990173i | \(0.544661\pi\) |
−0.990173 | + | 0.139846i | \(0.955339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.25836 | − | 1.31269i | 0.341569 | − | 0.137607i | ||||
\(92\) | −0.828032 | + | 0.828032i | −0.0863283 | + | 0.0863283i | ||||
\(93\) | 10.7142 | 1.11101 | ||||||||
\(94\) | − | 5.14908i | − | 0.531087i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.95179 | + | 1.95179i | −0.199203 | + | 0.199203i | ||||
\(97\) | 14.4866i | 1.47089i | 0.677583 | + | 0.735446i | \(0.263027\pi\) | ||||
−0.677583 | + | 0.735446i | \(0.736973\pi\) | |||||||
\(98\) | − | 9.56466i | − | 0.966177i | ||||||
\(99\) | 0.601309 | − | 0.601309i | 0.0604339 | − | 0.0604339i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 5.61850i | − | 0.559062i | −0.960137 | − | 0.279531i | \(-0.909821\pi\) | ||
0.960137 | − | 0.279531i | \(-0.0901789\pi\) | |||||||
\(102\) | −2.60311 | −0.257746 | ||||||||
\(103\) | 0.00240087 | − | 0.00240087i | 0.000236565 | − | 0.000236565i | −0.706988 | − | 0.707225i | \(-0.749947\pi\) |
0.707225 | + | 0.706988i | \(0.249947\pi\) | |||||||
\(104\) | −3.19737 | − | 7.93654i | −0.313528 | − | 0.778242i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.94448 | − | 8.94448i | 0.868765 | − | 0.868765i | ||||
\(107\) | 5.70114 | − | 5.70114i | 0.551150 | − | 0.551150i | −0.375623 | − | 0.926773i | \(-0.622571\pi\) |
0.926773 | + | 0.375623i | \(0.122571\pi\) | |||||||
\(108\) | −0.352653 | + | 0.352653i | −0.0339340 | + | 0.0339340i | ||||
\(109\) | −2.16428 | − | 2.16428i | −0.207300 | − | 0.207300i | 0.595819 | − | 0.803119i | \(-0.296828\pi\) |
−0.803119 | + | 0.595819i | \(0.796828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.10926 | + | 5.10926i | 0.484949 | + | 0.484949i | ||||
\(112\) | 4.62662 | 0.437174 | ||||||||
\(113\) | 11.5213 | + | 11.5213i | 1.08383 | + | 1.08383i | 0.996149 | + | 0.0876801i | \(0.0279453\pi\) |
0.0876801 | + | 0.996149i | \(0.472055\pi\) | |||||||
\(114\) | 1.54593 | 0.144790 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.17729i | − | 0.295004i | ||||||
\(117\) | −1.34733 | − | 3.34435i | −0.124561 | − | 0.309186i | ||||
\(118\) | −9.35188 | − | 9.35188i | −0.860910 | − | 0.860910i | ||||
\(119\) | 1.13450 | + | 1.13450i | 0.103999 | + | 0.103999i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.2769i | − | 0.934259i | ||||||
\(122\) | 4.25414i | 0.385151i | ||||||||
\(123\) | −5.16349 | −0.465576 | ||||||||
\(124\) | 3.77838 | − | 3.77838i | 0.339308 | − | 0.339308i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.54009 | 0.137202 | ||||||||
\(127\) | −4.66491 | − | 4.66491i | −0.413943 | − | 0.413943i | 0.469166 | − | 0.883110i | \(-0.344554\pi\) |
−0.883110 | + | 0.469166i | \(0.844554\pi\) | |||||||
\(128\) | − | 13.6364i | − | 1.20529i | ||||||
\(129\) | 3.84307 | 0.338363 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.57885 | 0.137945 | 0.0689725 | − | 0.997619i | \(-0.478028\pi\) | ||||
0.0689725 | + | 0.997619i | \(0.478028\pi\) | |||||||
\(132\) | − | 0.424107i | − | 0.0369137i | ||||||
\(133\) | −0.673755 | − | 0.673755i | −0.0584220 | − | 0.0584220i | ||||
\(134\) | 10.1292 | 0.875031 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.76336 | − | 2.76336i | 0.236956 | − | 0.236956i | ||||
\(137\) | −3.52318 | −0.301006 | −0.150503 | − | 0.988610i | \(-0.548089\pi\) | ||||
−0.150503 | + | 0.988610i | \(0.548089\pi\) | |||||||
\(138\) | − | 3.71159i | − | 0.315951i | ||||||
\(139\) | 18.8913i | 1.60234i | 0.598439 | + | 0.801168i | \(0.295788\pi\) | ||||
−0.598439 | + | 0.801168i | \(0.704212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.30333 | + | 2.30333i | 0.193975 | + | 0.193975i | ||||
\(142\) | 11.3475 | + | 11.3475i | 0.952264 | + | 0.952264i | ||||
\(143\) | 2.82115 | + | 1.20083i | 0.235917 | + | 0.100418i | ||||
\(144\) | − | 4.74872i | − | 0.395727i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.1707 | −1.33830 | ||||||||
\(147\) | 4.27854 | + | 4.27854i | 0.352888 | + | 0.352888i | ||||
\(148\) | 3.60359 | 0.296213 | ||||||||
\(149\) | −9.84579 | − | 9.84579i | −0.806599 | − | 0.806599i | 0.177519 | − | 0.984117i | \(-0.443193\pi\) |
−0.984117 | + | 0.177519i | \(0.943193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8809 | + | 11.8809i | 0.966858 | + | 0.966858i | 0.999468 | − | 0.0326102i | \(-0.0103820\pi\) |
−0.0326102 | + | 0.999468i | \(0.510382\pi\) | |||||||
\(152\) | −1.64110 | + | 1.64110i | −0.133111 | + | 0.133111i | ||||
\(153\) | 1.16444 | − | 1.16444i | 0.0941395 | − | 0.0941395i | ||||
\(154\) | −0.926070 | + | 0.926070i | −0.0746249 | + | 0.0746249i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.65453 | − | 0.704255i | −0.132469 | − | 0.0563855i | ||||
\(157\) | −4.93383 | + | 4.93383i | −0.393763 | + | 0.393763i | −0.876026 | − | 0.482264i | \(-0.839815\pi\) |
0.482264 | + | 0.876026i | \(0.339815\pi\) | |||||||
\(158\) | 11.7556 | 0.935229 | ||||||||
\(159\) | 8.00223i | 0.634618i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.61760 | + | 1.61760i | −0.127485 | + | 0.127485i | ||||
\(162\) | − | 1.58074i | − | 0.124194i | ||||||
\(163\) | 17.8032i | 1.39445i | 0.716851 | + | 0.697226i | \(0.245583\pi\) | ||||
−0.716851 | + | 0.697226i | \(0.754417\pi\) | |||||||
\(164\) | −1.82092 | + | 1.82092i | −0.142190 | + | 0.142190i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.5793i | 1.75250i | ||||||||
\(167\) | 8.68228 | 0.671855 | 0.335928 | − | 0.941888i | \(-0.390950\pi\) | ||||
0.335928 | + | 0.941888i | \(0.390950\pi\) | |||||||
\(168\) | −1.63490 | + | 1.63490i | −0.126135 | + | 0.126135i | ||||
\(169\) | 9.36940 | − | 9.01190i | 0.720723 | − | 0.693223i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.691537 | + | 0.691537i | −0.0528831 | + | 0.0528831i | ||||
\(172\) | 1.35527 | − | 1.35527i | 0.103338 | − | 0.103338i | ||||
\(173\) | 7.68305 | − | 7.68305i | 0.584131 | − | 0.584131i | −0.351905 | − | 0.936036i | \(-0.614466\pi\) |
0.936036 | + | 0.351905i | \(0.114466\pi\) | |||||||
\(174\) | 7.12097 | + | 7.12097i | 0.539839 | + | 0.539839i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.85545 | + | 2.85545i | 0.215238 | + | 0.215238i | ||||
\(177\) | 8.36670 | 0.628880 | ||||||||
\(178\) | −16.8516 | − | 16.8516i | −1.26308 | − | 1.26308i | ||||
\(179\) | 23.0188 | 1.72051 | 0.860253 | − | 0.509867i | \(-0.170305\pi\) | ||||
0.860253 | + | 0.509867i | \(0.170305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.94015i | − | 0.367199i | −0.983001 | − | 0.183599i | \(-0.941225\pi\) | ||
0.983001 | − | 0.183599i | \(-0.0587749\pi\) | |||||||
\(182\) | 2.07501 | + | 5.15060i | 0.153810 | + | 0.381788i | ||||
\(183\) | −1.90299 | − | 1.90299i | −0.140673 | − | 0.140673i | ||||
\(184\) | 3.94007 | + | 3.94007i | 0.290466 | + | 0.290466i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.9363i | 1.24183i | ||||||||
\(187\) | 1.40038i | 0.102406i | ||||||||
\(188\) | 1.62455 | 0.118482 | ||||||||
\(189\) | −0.688925 | + | 0.688925i | −0.0501119 | + | 0.0501119i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.77759 | −0.490409 | −0.245205 | − | 0.969471i | \(-0.578855\pi\) | ||||
−0.245205 | + | 0.969471i | \(0.578855\pi\) | |||||||
\(192\) | 3.63045 | + | 3.63045i | 0.262005 | + | 0.262005i | ||||
\(193\) | 8.23243i | 0.592583i | 0.955098 | + | 0.296292i | \(0.0957500\pi\) | ||||
−0.955098 | + | 0.296292i | \(0.904250\pi\) | |||||||
\(194\) | −22.8995 | −1.64409 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.01767 | 0.215548 | ||||||||
\(197\) | − | 23.1914i | − | 1.65232i | −0.563434 | − | 0.826161i | \(-0.690520\pi\) | ||
0.563434 | − | 0.826161i | \(-0.309480\pi\) | |||||||
\(198\) | 0.950511 | + | 0.950511i | 0.0675499 | + | 0.0675499i | ||||
\(199\) | 19.1896 | 1.36031 | 0.680156 | − | 0.733068i | \(-0.261912\pi\) | ||||
0.680156 | + | 0.733068i | \(0.261912\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.53108 | + | 4.53108i | −0.319598 | + | 0.319598i | ||||
\(202\) | 8.88137 | 0.624891 | ||||||||
\(203\) | − | 6.20700i | − | 0.435646i | ||||||
\(204\) | − | 0.821287i | − | 0.0575016i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.00379514 | + | 0.00379514i | 0.000264420 | + | 0.000264420i | ||||
\(207\) | 1.66029 | + | 1.66029i | 0.115398 | + | 0.115398i | ||||
\(208\) | 15.8814 | − | 6.39810i | 1.10118 | − | 0.443629i | ||||
\(209\) | − | 0.831655i | − | 0.0575268i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.9847 | −1.58233 | −0.791165 | − | 0.611602i | \(-0.790525\pi\) | ||||
−0.791165 | + | 0.611602i | \(0.790525\pi\) | |||||||
\(212\) | 2.82201 | + | 2.82201i | 0.193816 | + | 0.193816i | ||||
\(213\) | −10.1521 | −0.695613 | ||||||||
\(214\) | 9.01200 | + | 9.01200i | 0.616048 | + | 0.616048i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.67805 | + | 1.67805i | 0.114177 | + | 0.114177i | ||||
\(217\) | 7.38125 | − | 7.38125i | 0.501072 | − | 0.501072i | ||||
\(218\) | 3.42115 | − | 3.42115i | 0.231709 | − | 0.231709i | ||||
\(219\) | 7.23362 | − | 7.23362i | 0.488803 | − | 0.488803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.46319 | + | 2.32542i | 0.367494 | + | 0.156424i | ||||
\(222\) | −8.07639 | + | 8.07639i | −0.542052 | + | 0.542052i | ||||
\(223\) | 23.3874 | 1.56614 | 0.783069 | − | 0.621935i | \(-0.213653\pi\) | ||||
0.783069 | + | 0.621935i | \(0.213653\pi\) | |||||||
\(224\) | 2.68927i | 0.179684i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.2121 | + | 18.2121i | −1.21145 | + | 1.21145i | ||||
\(227\) | 17.4176i | 1.15605i | 0.816020 | + | 0.578024i | \(0.196176\pi\) | ||||
−0.816020 | + | 0.578024i | \(0.803824\pi\) | |||||||
\(228\) | 0.487745i | 0.0323017i | ||||||||
\(229\) | −8.50725 | + | 8.50725i | −0.562175 | + | 0.562175i | −0.929925 | − | 0.367750i | \(-0.880128\pi\) |
0.367750 | + | 0.929925i | \(0.380128\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.828514i | − | 0.0545122i | ||||||
\(232\) | −15.1187 | −0.992590 | ||||||||
\(233\) | −19.9157 | + | 19.9157i | −1.30472 | + | 1.30472i | −0.379555 | + | 0.925169i | \(0.623923\pi\) |
−0.925169 | + | 0.379555i | \(0.876077\pi\) | |||||||
\(234\) | 5.28654 | − | 2.12977i | 0.345592 | − | 0.139228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.95054 | − | 2.95054i | 0.192064 | − | 0.192064i | ||||
\(237\) | −5.25863 | + | 5.25863i | −0.341584 | + | 0.341584i | ||||
\(238\) | −1.79334 | + | 1.79334i | −0.116245 | + | 0.116245i | ||||
\(239\) | 7.69506 | + | 7.69506i | 0.497752 | + | 0.497752i | 0.910738 | − | 0.412985i | \(-0.135514\pi\) |
−0.412985 | + | 0.910738i | \(0.635514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.69323 | − | 2.69323i | −0.173486 | − | 0.173486i | 0.615023 | − | 0.788509i | \(-0.289147\pi\) |
−0.788509 | + | 0.615023i | \(0.789147\pi\) | |||||||
\(242\) | 16.2450 | 1.04427 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −1.34219 | −0.0859249 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 8.16212i | − | 0.520398i | ||||||
\(247\) | −3.24447 | − | 1.38101i | −0.206441 | − | 0.0878719i | ||||
\(248\) | −17.9789 | − | 17.9789i | −1.14166 | − | 1.14166i | ||||
\(249\) | −10.1004 | − | 10.1004i | −0.640084 | − | 0.640084i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1070i | 0.701070i | 0.936550 | + | 0.350535i | \(0.114000\pi\) | ||||
−0.936550 | + | 0.350535i | \(0.886000\pi\) | |||||||
\(252\) | 0.485902i | 0.0306090i | ||||||||
\(253\) | −1.99670 | −0.125532 | ||||||||
\(254\) | 7.37398 | − | 7.37398i | 0.462685 | − | 0.462685i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.2870 | 0.705438 | ||||||||
\(257\) | 6.59109 | + | 6.59109i | 0.411141 | + | 0.411141i | 0.882136 | − | 0.470995i | \(-0.156105\pi\) |
−0.470995 | + | 0.882136i | \(0.656105\pi\) | |||||||
\(258\) | 6.07488i | 0.378205i | ||||||||
\(259\) | 7.03979 | 0.437431 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.37081 | −0.394343 | ||||||||
\(262\) | 2.49575i | 0.154188i | ||||||||
\(263\) | −9.97308 | − | 9.97308i | −0.614966 | − | 0.614966i | 0.329270 | − | 0.944236i | \(-0.393198\pi\) |
−0.944236 | + | 0.329270i | \(0.893198\pi\) | |||||||
\(264\) | −2.01805 | −0.124202 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.06503 | − | 1.06503i | 0.0653011 | − | 0.0653011i | ||||
\(267\) | 15.0763 | 0.922657 | ||||||||
\(268\) | 3.19579i | 0.195214i | ||||||||
\(269\) | 6.04616i | 0.368641i | 0.982866 | + | 0.184320i | \(0.0590084\pi\) | ||||
−0.982866 | + | 0.184320i | \(0.940992\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.75407 | + | 2.75407i | 0.167298 | + | 0.167298i | 0.785791 | − | 0.618493i | \(-0.212256\pi\) |
−0.618493 | + | 0.785791i | \(0.712256\pi\) | |||||||
\(272\) | 5.52961 | + | 5.52961i | 0.335282 | + | 0.335282i | ||||
\(273\) | −3.23222 | − | 1.37580i | −0.195623 | − | 0.0832671i | ||||
\(274\) | − | 5.56922i | − | 0.336449i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.17101 | 0.0704868 | ||||||||
\(277\) | 3.74616 | + | 3.74616i | 0.225085 | + | 0.225085i | 0.810636 | − | 0.585551i | \(-0.199122\pi\) |
−0.585551 | + | 0.810636i | \(0.699122\pi\) | |||||||
\(278\) | −29.8621 | −1.79101 | ||||||||
\(279\) | −7.57606 | − | 7.57606i | −0.453567 | − | 0.453567i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.0861 | + | 23.0861i | 1.37720 | + | 1.37720i | 0.849317 | + | 0.527883i | \(0.177014\pi\) |
0.527883 | + | 0.849317i | \(0.322986\pi\) | |||||||
\(282\) | −3.64095 | + | 3.64095i | −0.216815 | + | 0.216815i | ||||
\(283\) | 10.9905 | − | 10.9905i | 0.653319 | − | 0.653319i | −0.300472 | − | 0.953791i | \(-0.597144\pi\) |
0.953791 | + | 0.300472i | \(0.0971441\pi\) | |||||||
\(284\) | −3.58018 | + | 3.58018i | −0.212444 | + | 0.212444i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.89819 | + | 4.45950i | −0.112242 | + | 0.263696i | ||||
\(287\) | −3.55726 | + | 3.55726i | −0.209978 | + | 0.209978i | ||||
\(288\) | 2.76024 | 0.162649 | ||||||||
\(289\) | − | 14.2882i | − | 0.840480i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.2436 | − | 10.2436i | 0.600489 | − | 0.600489i | ||||
\(292\) | − | 5.10191i | − | 0.298567i | ||||||
\(293\) | 1.95323i | 0.114109i | 0.998371 | + | 0.0570544i | \(0.0181708\pi\) | ||||
−0.998371 | + | 0.0570544i | \(0.981829\pi\) | |||||||
\(294\) | −6.76324 | + | 6.76324i | −0.394440 | + | 0.394440i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 17.1472i | − | 0.996658i | ||||||
\(297\) | −0.850380 | −0.0493440 | ||||||||
\(298\) | 15.5636 | − | 15.5636i | 0.901575 | − | 0.901575i | ||||
\(299\) | −3.31565 | + | 7.78958i | −0.191749 | + | 0.450483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.64758 | − | 2.64758i | 0.152604 | − | 0.152604i | ||||
\(302\) | −18.7806 | + | 18.7806i | −1.08070 | + | 1.08070i | ||||
\(303\) | −3.97288 | + | 3.97288i | −0.228236 | + | 0.228236i | ||||
\(304\) | −3.28392 | − | 3.28392i | −0.188346 | − | 0.188346i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.84067 | + | 1.84067i | 0.105224 | + | 0.105224i | ||||
\(307\) | 23.6877 | 1.35193 | 0.675965 | − | 0.736933i | \(-0.263727\pi\) | ||||
0.675965 | + | 0.736933i | \(0.263727\pi\) | |||||||
\(308\) | −0.292177 | − | 0.292177i | −0.0166484 | − | 0.0166484i | ||||
\(309\) | −0.00339534 | −0.000193154 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.782006i | 0.0443435i | 0.999754 | + | 0.0221717i | \(0.00705806\pi\) | ||||
−0.999754 | + | 0.0221717i | \(0.992942\pi\) | |||||||
\(312\) | −3.35110 | + | 7.87287i | −0.189719 | + | 0.445713i | ||||
\(313\) | −1.09467 | − | 1.09467i | −0.0618743 | − | 0.0618743i | 0.675493 | − | 0.737367i | \(-0.263931\pi\) |
−0.737367 | + | 0.675493i | \(0.763931\pi\) | |||||||
\(314\) | −7.79909 | − | 7.79909i | −0.440128 | − | 0.440128i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.70894i | 0.208644i | ||||||||
\(317\) | 21.0388i | 1.18166i | 0.806797 | + | 0.590828i | \(0.201199\pi\) | ||||
−0.806797 | + | 0.590828i | \(0.798801\pi\) | |||||||
\(318\) | −12.6494 | −0.709343 | ||||||||
\(319\) | 3.83083 | − | 3.83083i | 0.214485 | − | 0.214485i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.06263 | −0.450012 | ||||||||
\(322\) | −2.55700 | − | 2.55700i | −0.142496 | − | 0.142496i | ||||
\(323\) | − | 1.61051i | − | 0.0896111i | ||||||
\(324\) | 0.498726 | 0.0277070 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −28.1421 | −1.55865 | ||||||||
\(327\) | 3.06075i | 0.169260i | ||||||||
\(328\) | 8.66458 | + | 8.66458i | 0.478422 | + | 0.478422i | ||||
\(329\) | 3.17364 | 0.174968 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0574 | + | 10.0574i | −0.552804 | + | 0.552804i | −0.927249 | − | 0.374445i | \(-0.877833\pi\) |
0.374445 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(332\) | −7.12384 | −0.390971 | ||||||||
\(333\) | − | 7.22558i | − | 0.395959i | ||||||
\(334\) | 13.7244i | 0.750965i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.27151 | − | 3.27151i | −0.178476 | − | 0.178476i | ||||
\(337\) | −19.9405 | − | 19.9405i | −1.08623 | − | 1.08623i | −0.995913 | − | 0.0903167i | \(-0.971212\pi\) |
−0.0903167 | − | 0.995913i | \(-0.528788\pi\) | |||||||
\(338\) | 14.2454 | + | 14.8105i | 0.774849 | + | 0.805588i | ||||
\(339\) | − | 16.2935i | − | 0.884943i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.11111 | 0.493394 | ||||||||
\(342\) | −1.09314 | − | 1.09314i | −0.0591101 | − | 0.0591101i | ||||
\(343\) | 12.7152 | 0.686555 | ||||||||
\(344\) | −6.44885 | − | 6.44885i | −0.347699 | − | 0.347699i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1449 | + | 12.1449i | 0.652912 | + | 0.652912i | ||||
\(347\) | −11.4590 | + | 11.4590i | −0.615150 | + | 0.615150i | −0.944283 | − | 0.329133i | \(-0.893243\pi\) |
0.329133 | + | 0.944283i | \(0.393243\pi\) | |||||||
\(348\) | −2.24668 | + | 2.24668i | −0.120435 | + | 0.120435i | ||||
\(349\) | −19.4188 | + | 19.4188i | −1.03946 | + | 1.03946i | −0.0402751 | + | 0.999189i | \(0.512823\pi\) |
−0.999189 | + | 0.0402751i | \(0.987177\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.41211 | + | 3.31752i | −0.0753728 | + | 0.177076i | ||||
\(352\) | −1.65976 | + | 1.65976i | −0.0884655 | + | 0.0884655i | ||||
\(353\) | 19.1849 | 1.02111 | 0.510556 | − | 0.859845i | \(-0.329440\pi\) | ||||
0.510556 | + | 0.859845i | \(0.329440\pi\) | |||||||
\(354\) | 13.2255i | 0.702930i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.31671 | − | 5.31671i | 0.281785 | − | 0.281785i | ||||
\(357\) | − | 1.60442i | − | 0.0849152i | ||||||
\(358\) | 36.3867i | 1.92309i | ||||||||
\(359\) | −7.19553 | + | 7.19553i | −0.379766 | + | 0.379766i | −0.871018 | − | 0.491252i | \(-0.836539\pi\) |
0.491252 | + | 0.871018i | \(0.336539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.0436i | − | 0.949661i | ||||||
\(362\) | 7.80908 | 0.410436 | ||||||||
\(363\) | −7.26683 | + | 7.26683i | −0.381410 | + | 0.381410i | ||||
\(364\) | −1.62503 | + | 0.654671i | −0.0851746 | + | 0.0343141i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.00813 | − | 3.00813i | 0.157237 | − | 0.157237i | ||||
\(367\) | 25.6674 | − | 25.6674i | 1.33983 | − | 1.33983i | 0.443602 | − | 0.896224i | \(-0.353700\pi\) |
0.896224 | − | 0.443602i | \(-0.146300\pi\) | |||||||
\(368\) | −7.88428 | + | 7.88428i | −0.410997 | + | 0.410997i | ||||
\(369\) | 3.65114 | + | 3.65114i | 0.190071 | + | 0.190071i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.51293 | + | 5.51293i | 0.286217 | + | 0.286217i | ||||
\(372\) | −5.34343 | −0.277044 | ||||||||
\(373\) | −10.6993 | − | 10.6993i | −0.553988 | − | 0.553988i | 0.373602 | − | 0.927589i | \(-0.378123\pi\) |
−0.927589 | + | 0.373602i | \(0.878123\pi\) | |||||||
\(374\) | −2.21363 | −0.114464 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 7.73018i | − | 0.398654i | ||||||
\(377\) | −8.58359 | − | 21.3062i | −0.442077 | − | 1.09733i | ||||
\(378\) | −1.08901 | − | 1.08901i | −0.0560125 | − | 0.0560125i | ||||
\(379\) | 4.27043 | + | 4.27043i | 0.219357 | + | 0.219357i | 0.808228 | − | 0.588870i | \(-0.200427\pi\) |
−0.588870 | + | 0.808228i | \(0.700427\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.59717i | 0.337983i | ||||||||
\(382\) | − | 10.7136i | − | 0.548155i | ||||||
\(383\) | 8.57646 | 0.438237 | 0.219118 | − | 0.975698i | \(-0.429682\pi\) | ||||
0.219118 | + | 0.975698i | \(0.429682\pi\) | |||||||
\(384\) | −9.64236 | + | 9.64236i | −0.492060 | + | 0.492060i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0133 | −0.662359 | ||||||||
\(387\) | −2.71746 | − | 2.71746i | −0.138136 | − | 0.138136i | ||||
\(388\) | − | 7.22485i | − | 0.366786i | ||||||
\(389\) | 1.83143 | 0.0928571 | 0.0464286 | − | 0.998922i | \(-0.485216\pi\) | ||||
0.0464286 | + | 0.998922i | \(0.485216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.86663 | −0.195544 | ||||||||
\(392\) | − | 14.3592i | − | 0.725248i | ||||||
\(393\) | −1.11642 | − | 1.11642i | −0.0563158 | − | 0.0563158i | ||||
\(394\) | 36.6596 | 1.84688 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.299889 | + | 0.299889i | −0.0150700 | + | 0.0150700i | ||||
\(397\) | −22.1034 | −1.10934 | −0.554668 | − | 0.832071i | \(-0.687155\pi\) | ||||
−0.554668 | + | 0.832071i | \(0.687155\pi\) | |||||||
\(398\) | 30.3336i | 1.52049i | ||||||||
\(399\) | 0.952834i | 0.0477013i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.6339 | − | 22.6339i | −1.13028 | − | 1.13028i | −0.990130 | − | 0.140155i | \(-0.955240\pi\) |
−0.140155 | − | 0.990130i | \(-0.544760\pi\) | |||||||
\(402\) | −7.16244 | − | 7.16244i | −0.357230 | − | 0.357230i | ||||
\(403\) | 15.1296 | − | 35.5445i | 0.753657 | − | 1.77060i | ||||
\(404\) | 2.80209i | 0.139409i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.81162 | 0.486943 | ||||||||
\(407\) | 4.34481 | + | 4.34481i | 0.215364 | + | 0.215364i | ||||
\(408\) | −3.90798 | −0.193474 | ||||||||
\(409\) | −1.79506 | − | 1.79506i | −0.0887598 | − | 0.0887598i | 0.661333 | − | 0.750093i | \(-0.269991\pi\) |
−0.750093 | + | 0.661333i | \(0.769991\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.49127 | + | 2.49127i | 0.122885 | + | 0.122885i | ||||
\(412\) | −0.00119738 | + | 0.00119738i | −5.89905e−5 | + | 5.89905e-5i | ||||
\(413\) | 5.76403 | − | 5.76403i | 0.283629 | − | 0.283629i | ||||
\(414\) | −2.62449 | + | 2.62449i | −0.128986 | + | 0.128986i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.71896 | + | 9.23123i | 0.182337 | + | 0.452598i | ||||
\(417\) | 13.3581 | − | 13.3581i | 0.654151 | − | 0.654151i | ||||
\(418\) | 1.31463 | 0.0643005 | ||||||||
\(419\) | − | 9.83778i | − | 0.480607i | −0.970698 | − | 0.240304i | \(-0.922753\pi\) | ||
0.970698 | − | 0.240304i | \(-0.0772470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.1987 | − | 11.1987i | 0.545789 | − | 0.545789i | −0.379431 | − | 0.925220i | \(-0.623880\pi\) |
0.925220 | + | 0.379431i | \(0.123880\pi\) | |||||||
\(422\) | − | 36.3327i | − | 1.76865i | ||||||
\(423\) | − | 3.25740i | − | 0.158380i | ||||||
\(424\) | 13.4281 | − | 13.4281i | 0.652127 | − | 0.652127i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 16.0478i | − | 0.777520i | ||||||
\(427\) | −2.62204 | −0.126889 | ||||||||
\(428\) | −2.84331 | + | 2.84331i | −0.137436 | + | 0.137436i | ||||
\(429\) | −1.14574 | − | 2.84397i | −0.0553170 | − | 0.137308i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.8983 | − | 21.8983i | 1.05480 | − | 1.05480i | 0.0563955 | − | 0.998409i | \(-0.482039\pi\) |
0.998409 | − | 0.0563955i | \(-0.0179608\pi\) | |||||||
\(432\) | −3.35786 | + | 3.35786i | −0.161555 | + | 0.161555i | ||||
\(433\) | −7.01215 | + | 7.01215i | −0.336982 | + | 0.336982i | −0.855230 | − | 0.518248i | \(-0.826584\pi\) |
0.518248 | + | 0.855230i | \(0.326584\pi\) | |||||||
\(434\) | 11.6678 | + | 11.6678i | 0.560073 | + | 0.560073i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.07938 | + | 1.07938i | 0.0516930 | + | 0.0516930i | ||||
\(437\) | 2.29631 | 0.109847 | ||||||||
\(438\) | 11.4344 | + | 11.4344i | 0.546359 | + | 0.546359i | ||||
\(439\) | −15.7738 | −0.752841 | −0.376420 | − | 0.926449i | \(-0.622845\pi\) | ||||
−0.376420 | + | 0.926449i | \(0.622845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 6.05077i | − | 0.288132i | ||||||
\(442\) | −3.67587 | + | 8.63586i | −0.174843 | + | 0.410766i | ||||
\(443\) | −0.477834 | − | 0.477834i | −0.0227026 | − | 0.0227026i | 0.695664 | − | 0.718367i | \(-0.255110\pi\) |
−0.718367 | + | 0.695664i | \(0.755110\pi\) | |||||||
\(444\) | −2.54812 | − | 2.54812i | −0.120928 | − | 0.120928i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 36.9694i | 1.75055i | ||||||||
\(447\) | 13.9241i | 0.658585i | ||||||||
\(448\) | 5.00221 | 0.236332 | ||||||||
\(449\) | 10.9559 | − | 10.9559i | 0.517039 | − | 0.517039i | −0.399635 | − | 0.916674i | \(-0.630863\pi\) |
0.916674 | + | 0.399635i | \(0.130863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.39093 | −0.206761 | ||||||||
\(452\) | −5.74595 | − | 5.74595i | −0.270267 | − | 0.270267i | ||||
\(453\) | − | 16.8022i | − | 0.789436i | ||||||
\(454\) | −27.5327 | −1.29217 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.32086 | 0.108684 | ||||||||
\(457\) | − | 22.0567i | − | 1.03177i | −0.856659 | − | 0.515884i | \(-0.827464\pi\) | ||
0.856659 | − | 0.515884i | \(-0.172536\pi\) | |||||||
\(458\) | −13.4477 | − | 13.4477i | −0.628371 | − | 0.628371i | ||||
\(459\) | −1.64677 | −0.0768646 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.75708 | + | 5.75708i | −0.268134 | + | 0.268134i | −0.828348 | − | 0.560214i | \(-0.810719\pi\) |
0.560214 | + | 0.828348i | \(0.310719\pi\) | |||||||
\(462\) | 1.30966 | 0.0609310 | ||||||||
\(463\) | 26.2127i | 1.21821i | 0.793091 | + | 0.609103i | \(0.208470\pi\) | ||||
−0.793091 | + | 0.609103i | \(0.791530\pi\) | |||||||
\(464\) | − | 30.2532i | − | 1.40447i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31.4815 | − | 31.4815i | −1.45835 | − | 1.45835i | ||||
\(467\) | 0.905259 | + | 0.905259i | 0.0418904 | + | 0.0418904i | 0.727742 | − | 0.685851i | \(-0.240570\pi\) |
−0.685851 | + | 0.727742i | \(0.740570\pi\) | |||||||
\(468\) | 0.671949 | + | 1.66792i | 0.0310609 | + | 0.0770995i | ||||
\(469\) | 6.24315i | 0.288282i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.97749 | 0.321506 | ||||||||
\(472\) | −14.0397 | − | 14.0397i | −0.646231 | − | 0.646231i | ||||
\(473\) | 3.26807 | 0.150266 | ||||||||
\(474\) | −8.31250 | − | 8.31250i | −0.381806 | − | 0.381806i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.565805 | − | 0.565805i | −0.0259336 | − | 0.0259336i | ||||
\(477\) | 5.65843 | − | 5.65843i | 0.259082 | − | 0.259082i | ||||
\(478\) | −12.1639 | + | 12.1639i | −0.556362 | + | 0.556362i | ||||
\(479\) | −1.36271 | + | 1.36271i | −0.0622640 | + | 0.0622640i | −0.737553 | − | 0.675289i | \(-0.764019\pi\) |
0.675289 | + | 0.737553i | \(0.264019\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.1649 | − | 9.73525i | 1.10182 | − | 0.443889i | ||||
\(482\) | 4.25728 | − | 4.25728i | 0.193914 | − | 0.193914i | ||||
\(483\) | 2.28764 | 0.104091 | ||||||||
\(484\) | 5.12534i | 0.232970i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.11775 | + | 1.11775i | −0.0507021 | + | 0.0507021i | ||||
\(487\) | 15.2289i | 0.690086i | 0.938587 | + | 0.345043i | \(0.112136\pi\) | ||||
−0.938587 | + | 0.345043i | \(0.887864\pi\) | |||||||
\(488\) | 6.38662i | 0.289109i | ||||||||
\(489\) | 12.5887 | − | 12.5887i | 0.569283 | − | 0.569283i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.1779i | − | 0.549581i | −0.961504 | − | 0.274791i | \(-0.911391\pi\) | ||
0.961504 | − | 0.274791i | \(-0.0886085\pi\) | |||||||
\(492\) | 2.57517 | 0.116098 | ||||||||
\(493\) | 7.41844 | − | 7.41844i | 0.334110 | − | 0.334110i | ||||
\(494\) | 2.18302 | − | 5.12865i | 0.0982187 | − | 0.230749i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 35.9766 | − | 35.9766i | 1.61540 | − | 1.61540i | ||||
\(497\) | −6.99405 | + | 6.99405i | −0.313726 | + | 0.313726i | ||||
\(498\) | 15.9660 | − | 15.9660i | 0.715454 | − | 0.715454i | ||||
\(499\) | −23.1658 | − | 23.1658i | −1.03704 | − | 1.03704i | −0.999287 | − | 0.0377562i | \(-0.987979\pi\) |
−0.0377562 | − | 0.999287i | \(-0.512021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.13930 | − | 6.13930i | −0.274284 | − | 0.274284i | ||||
\(502\) | −17.5573 | −0.783620 | ||||||||
\(503\) | −15.0692 | − | 15.0692i | −0.671901 | − | 0.671901i | 0.286253 | − | 0.958154i | \(-0.407590\pi\) |
−0.958154 | + | 0.286253i | \(0.907590\pi\) | |||||||
\(504\) | 2.31210 | 0.102989 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 3.15626i | − | 0.140313i | ||||||
\(507\) | −12.9975 | − | 0.252790i | −0.577241 | − | 0.0112268i | ||||
\(508\) | 2.32651 | + | 2.32651i | 0.103222 | + | 0.103222i | ||||
\(509\) | −1.14746 | − | 1.14746i | −0.0508604 | − | 0.0508604i | 0.681219 | − | 0.732080i | \(-0.261450\pi\) |
−0.732080 | + | 0.681219i | \(0.761450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 9.96684i | − | 0.440907i | ||||||
\(512\) | − | 9.43092i | − | 0.416792i | ||||||
\(513\) | 0.977981 | 0.0431789 | ||||||||
\(514\) | −10.4188 | + | 10.4188i | −0.459552 | + | 0.459552i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.91664 | −0.0843753 | ||||||||
\(517\) | 1.95870 | + | 1.95870i | 0.0861436 | + | 0.0861436i | ||||
\(518\) | 11.1280i | 0.488938i | ||||||||
\(519\) | −10.8655 | −0.476941 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.617681 | −0.0270611 | −0.0135306 | − | 0.999908i | \(-0.504307\pi\) | ||||
−0.0135306 | + | 0.999908i | \(0.504307\pi\) | |||||||
\(522\) | − | 10.0706i | − | 0.440777i | ||||||
\(523\) | −30.8113 | − | 30.8113i | −1.34728 | − | 1.34728i | −0.888600 | − | 0.458684i | \(-0.848321\pi\) |
−0.458684 | − | 0.888600i | \(-0.651679\pi\) | |||||||
\(524\) | −0.787415 | −0.0343984 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.7648 | − | 15.7648i | 0.687378 | − | 0.687378i | ||||
\(527\) | 17.6437 | 0.768574 | ||||||||
\(528\) | − | 4.03822i | − | 0.175741i | ||||||
\(529\) | 17.4868i | 0.760298i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.91615 | − | 5.91615i | −0.256739 | − | 0.256739i | ||||
\(532\) | 0.336019 | + | 0.336019i | 0.0145683 | + | 0.0145683i | ||||
\(533\) | −7.29141 | + | 17.1300i | −0.315826 | + | 0.741982i | ||||
\(534\) | 23.8317i | 1.03130i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.2067 | 0.656831 | ||||||||
\(537\) | −16.2768 | − | 16.2768i | −0.702394 | − | 0.702394i | ||||
\(538\) | −9.55738 | −0.412048 | ||||||||
\(539\) | 3.63838 | + | 3.63838i | 0.156716 | + | 0.156716i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.1597 | − | 18.1597i | −0.780745 | − | 0.780745i | 0.199212 | − | 0.979956i | \(-0.436162\pi\) |
−0.979956 | + | 0.199212i | \(0.936162\pi\) | |||||||
\(542\) | −4.35346 | + | 4.35346i | −0.186997 | + | 0.186997i | ||||
\(543\) | −3.49322 | + | 3.49322i | −0.149908 | + | 0.149908i | ||||
\(544\) | −3.21414 | + | 3.21414i | −0.137805 | + | 0.137805i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.17477 | − | 5.10928i | 0.0930717 | − | 0.218657i | ||||
\(547\) | −5.87516 | + | 5.87516i | −0.251204 | + | 0.251204i | −0.821464 | − | 0.570260i | \(-0.806842\pi\) |
0.570260 | + | 0.821464i | \(0.306842\pi\) | |||||||
\(548\) | 1.75710 | 0.0750597 | ||||||||
\(549\) | 2.69124i | 0.114859i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.40565 | + | 4.40565i | −0.187687 | + | 0.187687i | ||||
\(552\) | − | 5.57211i | − | 0.237165i | ||||||
\(553\) | 7.24559i | 0.308114i | ||||||||
\(554\) | −5.92169 | + | 5.92169i | −0.251588 | + | 0.251588i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.42157i | − | 0.399564i | ||||||
\(557\) | −6.73062 | −0.285185 | −0.142593 | − | 0.989781i | \(-0.545544\pi\) | ||||
−0.142593 | + | 0.989781i | \(0.545544\pi\) | |||||||
\(558\) | 11.9757 | − | 11.9757i | 0.506974 | − | 0.506974i | ||||
\(559\) | 5.42683 | − | 12.7495i | 0.229530 | − | 0.539245i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.990217 | − | 0.990217i | 0.0418070 | − | 0.0418070i | ||||
\(562\) | −36.4930 | + | 36.4930i | −1.53936 | + | 1.53936i | ||||
\(563\) | −11.5415 | + | 11.5415i | −0.486415 | + | 0.486415i | −0.907173 | − | 0.420758i | \(-0.861764\pi\) |
0.420758 | + | 0.907173i | \(0.361764\pi\) | |||||||
\(564\) | −1.14873 | − | 1.14873i | −0.0483702 | − | 0.0483702i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.3731 | + | 17.3731i | 0.730247 | + | 0.730247i | ||||
\(567\) | 0.974287 | 0.0409162 | ||||||||
\(568\) | 17.0358 | + | 17.0358i | 0.714805 | + | 0.714805i | ||||
\(569\) | 20.2098 | 0.847240 | 0.423620 | − | 0.905840i | \(-0.360759\pi\) | ||||
0.423620 | + | 0.905840i | \(0.360759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.257974i | − | 0.0107959i | −0.999985 | − | 0.00539793i | \(-0.998282\pi\) | ||
0.999985 | − | 0.00539793i | \(-0.00171822\pi\) | |||||||
\(572\) | −1.40698 | − | 0.598884i | −0.0588289 | − | 0.0250406i | ||||
\(573\) | 4.79248 | + | 4.79248i | 0.200209 | + | 0.200209i | ||||
\(574\) | −5.62308 | − | 5.62308i | −0.234703 | − | 0.234703i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 5.13423i | − | 0.213926i | ||||||
\(577\) | 4.50480i | 0.187537i | 0.995594 | + | 0.0937687i | \(0.0298914\pi\) | ||||
−0.995594 | + | 0.0937687i | \(0.970109\pi\) | |||||||
\(578\) | 22.5858 | 0.939445 | ||||||||
\(579\) | 5.82121 | − | 5.82121i | 0.241921 | − | 0.241921i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.9168 | −0.577365 | ||||||||
\(582\) | 16.1924 | + | 16.1924i | 0.671196 | + | 0.671196i | ||||
\(583\) | 6.80493i | 0.281831i | ||||||||
\(584\) | −24.2767 | −1.00458 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.08754 | −0.127545 | ||||||||
\(587\) | 27.5111i | 1.13550i | 0.823200 | + | 0.567752i | \(0.192187\pi\) | ||||
−0.823200 | + | 0.567752i | \(0.807813\pi\) | |||||||
\(588\) | −2.13382 | − | 2.13382i | −0.0879972 | − | 0.0879972i | ||||
\(589\) | −10.4782 | −0.431749 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.3988 | + | 16.3988i | −0.674558 | + | 0.674558i | ||||
\(592\) | 34.3123 | 1.41023 | ||||||||
\(593\) | 46.1002i | 1.89311i | 0.322548 | + | 0.946553i | \(0.395461\pi\) | ||||
−0.322548 | + | 0.946553i | \(0.604539\pi\) | |||||||
\(594\) | − | 1.34423i | − | 0.0551543i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.91035 | + | 4.91035i | 0.201136 | + | 0.201136i | ||||
\(597\) | −13.5691 | − | 13.5691i | −0.555345 | − | 0.555345i | ||||
\(598\) | −12.3133 | − | 5.24116i | −0.503527 | − | 0.214327i | ||||
\(599\) | − | 22.5207i | − | 0.920169i | −0.887875 | − | 0.460084i | \(-0.847819\pi\) | ||
0.887875 | − | 0.460084i | \(-0.152181\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.0110 | −1.42813 | −0.714064 | − | 0.700081i | \(-0.753147\pi\) | ||||
−0.714064 | + | 0.700081i | \(0.753147\pi\) | |||||||
\(602\) | 4.18513 | + | 4.18513i | 0.170573 | + | 0.170573i | ||||
\(603\) | 6.40792 | 0.260950 | ||||||||
\(604\) | −5.92534 | − | 5.92534i | −0.241099 | − | 0.241099i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.28008 | − | 6.28008i | −0.255111 | − | 0.255111i | ||||
\(607\) | −19.4448 | + | 19.4448i | −0.789241 | + | 0.789241i | −0.981370 | − | 0.192129i | \(-0.938461\pi\) |
0.192129 | + | 0.981370i | \(0.438461\pi\) | |||||||
\(608\) | 1.90881 | − | 1.90881i | 0.0774125 | − | 0.0774125i | ||||
\(609\) | −4.38901 | + | 4.38901i | −0.177852 | + | 0.177852i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.8939 | − | 4.38879i | 0.440719 | − | 0.177551i | ||||
\(612\) | −0.580737 | + | 0.580737i | −0.0234749 | + | 0.0234749i | ||||
\(613\) | −20.6580 | −0.834367 | −0.417184 | − | 0.908822i | \(-0.636983\pi\) | ||||
−0.417184 | + | 0.908822i | \(0.636983\pi\) | |||||||
\(614\) | 37.4441i | 1.51112i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.39029 | + | 1.39029i | −0.0560162 | + | 0.0560162i | ||||
\(617\) | − | 37.6970i | − | 1.51762i | −0.651309 | − | 0.758812i | \(-0.725780\pi\) | ||
0.651309 | − | 0.758812i | \(-0.274220\pi\) | |||||||
\(618\) | − | 0.00536714i | − | 0.000215898i | ||||||
\(619\) | 14.7879 | − | 14.7879i | 0.594375 | − | 0.594375i | −0.344435 | − | 0.938810i | \(-0.611930\pi\) |
0.938810 | + | 0.344435i | \(0.111930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2.34801i | − | 0.0942224i | ||||||
\(622\) | −1.23614 | −0.0495649 | ||||||||
\(623\) | 10.3865 | − | 10.3865i | 0.416125 | − | 0.416125i | ||||
\(624\) | −15.7540 | − | 6.70571i | −0.630665 | − | 0.268443i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.73038 | − | 1.73038i | 0.0691600 | − | 0.0691600i | ||||
\(627\) | −0.588069 | + | 0.588069i | −0.0234852 | + | 0.0234852i | ||||
\(628\) | 2.46063 | − | 2.46063i | 0.0981899 | − | 0.0981899i | ||||
\(629\) | 8.41376 | + | 8.41376i | 0.335479 | + | 0.335479i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.91402 | + | 1.91402i | 0.0761958 | + | 0.0761958i | 0.744178 | − | 0.667982i | \(-0.232842\pi\) |
−0.667982 | + | 0.744178i | \(0.732842\pi\) | |||||||
\(632\) | 17.6485 | 0.702018 | ||||||||
\(633\) | 16.2526 | + | 16.2526i | 0.645984 | + | 0.645984i | ||||
\(634\) | −33.2568 | −1.32080 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 3.99092i | − | 0.158250i | ||||||
\(637\) | 20.2359 | − | 8.15238i | 0.801776 | − | 0.323009i | ||||
\(638\) | 6.05553 | + | 6.05553i | 0.239741 | + | 0.239741i | ||||
\(639\) | 7.17864 | + | 7.17864i | 0.283983 | + | 0.283983i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.1627i | 1.58633i | 0.609005 | + | 0.793166i | \(0.291569\pi\) | ||||
−0.609005 | + | 0.793166i | \(0.708431\pi\) | |||||||
\(642\) | − | 12.7449i | − | 0.503001i | ||||||
\(643\) | −11.9456 | −0.471088 | −0.235544 | − | 0.971864i | \(-0.575687\pi\) | ||||
−0.235544 | + | 0.971864i | \(0.575687\pi\) | |||||||
\(644\) | 0.806741 | − | 0.806741i | 0.0317900 | − | 0.0317900i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.54579 | 0.100163 | ||||||||
\(647\) | 14.4871 | + | 14.4871i | 0.569546 | + | 0.569546i | 0.932001 | − | 0.362455i | \(-0.118061\pi\) |
−0.362455 | + | 0.932001i | \(0.618061\pi\) | |||||||
\(648\) | − | 2.37312i | − | 0.0932249i | ||||||
\(649\) | 7.11488 | 0.279283 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4387 | −0.409124 | ||||||||
\(652\) | − | 8.87891i | − | 0.347725i | ||||||
\(653\) | −31.1908 | − | 31.1908i | −1.22059 | − | 1.22059i | −0.967422 | − | 0.253168i | \(-0.918528\pi\) |
−0.253168 | − | 0.967422i | \(-0.581472\pi\) | |||||||
\(654\) | −4.83823 | −0.189190 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.3383 | + | 17.3383i | −0.676945 | + | 0.676945i | ||||
\(657\) | −10.2299 | −0.399106 | ||||||||
\(658\) | 5.01668i | 0.195571i | ||||||||
\(659\) | 29.4886i | 1.14871i | 0.818606 | + | 0.574356i | \(0.194748\pi\) | ||||
−0.818606 | + | 0.574356i | \(0.805252\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.86425 | + | 3.86425i | 0.150302 | + | 0.150302i | 0.778253 | − | 0.627951i | \(-0.216106\pi\) |
−0.627951 | + | 0.778253i | \(0.716106\pi\) | |||||||
\(662\) | −15.8981 | − | 15.8981i | −0.617897 | − | 0.617897i | ||||
\(663\) | −2.21874 | − | 5.50738i | −0.0861688 | − | 0.213889i | ||||
\(664\) | 33.8978i | 1.31549i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.4217 | 0.442583 | ||||||||
\(667\) | 10.5774 | + | 10.5774i | 0.409560 | + | 0.409560i | ||||
\(668\) | −4.33008 | −0.167536 | ||||||||
\(669\) | −16.5374 | − | 16.5374i | −0.639373 | − | 0.639373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.61827 | − | 1.61827i | −0.0624725 | − | 0.0624725i | ||||
\(672\) | 1.90160 | − | 1.90160i | 0.0733558 | − | 0.0733558i | ||||
\(673\) | −10.2250 | + | 10.2250i | −0.394143 | + | 0.394143i | −0.876161 | − | 0.482018i | \(-0.839904\pi\) |
0.482018 | + | 0.876161i | \(0.339904\pi\) | |||||||
\(674\) | 31.5207 | − | 31.5207i | 1.21413 | − | 1.21413i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.67276 | + | 4.49447i | −0.179722 | + | 0.172864i | ||||
\(677\) | −28.6819 | + | 28.6819i | −1.10234 | + | 1.10234i | −0.108207 | + | 0.994128i | \(0.534511\pi\) |
−0.994128 | + | 0.108207i | \(0.965489\pi\) | |||||||
\(678\) | 25.7558 | 0.989144 | ||||||||
\(679\) | − | 14.1141i | − | 0.541650i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.3161 | − | 12.3161i | 0.471955 | − | 0.471955i | ||||
\(682\) | 14.4023i | 0.551491i | ||||||||
\(683\) | − | 2.15178i | − | 0.0823357i | −0.999152 | − | 0.0411679i | \(-0.986892\pi\) | ||
0.999152 | − | 0.0411679i | \(-0.0131078\pi\) | |||||||
\(684\) | 0.344887 | − | 0.344887i | 0.0131871 | − | 0.0131871i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0994i | 0.767397i | ||||||||
\(687\) | 12.0311 | 0.459014 | ||||||||
\(688\) | 12.9045 | − | 12.9045i | 0.491978 | − | 0.491978i | ||||
\(689\) | 26.5476 | + | 11.3000i | 1.01138 | + | 0.430496i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.15129 | + | 2.15129i | −0.0818390 | + | 0.0818390i | −0.746841 | − | 0.665002i | \(-0.768431\pi\) |
0.665002 | + | 0.746841i | \(0.268431\pi\) | |||||||
\(692\) | −3.83174 | + | 3.83174i | −0.145661 | + | 0.145661i | ||||
\(693\) | −0.585848 | + | 0.585848i | −0.0222545 | + | 0.0222545i | ||||
\(694\) | −18.1136 | − | 18.1136i | −0.687583 | − | 0.687583i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.6905 | + | 10.6905i | 0.405223 | + | 0.405223i | ||||
\(697\) | −8.50308 | −0.322077 | ||||||||
\(698\) | −30.6960 | − | 30.6960i | −1.16186 | − | 1.16186i | ||||
\(699\) | 28.1651 | 1.06530 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.1324i | 0.987007i | 0.869744 | + | 0.493503i | \(0.164284\pi\) | ||||
−0.869744 | + | 0.493503i | \(0.835716\pi\) | |||||||
\(702\) | −5.24413 | − | 2.23217i | −0.197927 | − | 0.0842478i | ||||
\(703\) | −4.99676 | − | 4.99676i | −0.188456 | − | 0.188456i | ||||
\(704\) | 3.08726 | + | 3.08726i | 0.116356 | + | 0.116356i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.3263i | 1.14135i | ||||||||
\(707\) | 5.47403i | 0.205872i | ||||||||
\(708\) | −4.17269 | −0.156819 | ||||||||
\(709\) | 19.5616 | − | 19.5616i | 0.734651 | − | 0.734651i | −0.236886 | − | 0.971537i | \(-0.576127\pi\) |
0.971537 | + | 0.236886i | \(0.0761268\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.43682 | 0.278903 | ||||||||
\(712\) | −25.2988 | − | 25.2988i | −0.948113 | − | 0.948113i | ||||
\(713\) | 25.1570i | 0.942136i | ||||||||
\(714\) | 2.53617 | 0.0949138 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.4801 | −0.429031 | ||||||||
\(717\) | − | 10.8825i | − | 0.406413i | ||||||
\(718\) | −11.3742 | − | 11.3742i | −0.424483 | − | 0.424483i | ||||
\(719\) | −31.4983 | −1.17469 | −0.587345 | − | 0.809337i | \(-0.699827\pi\) | ||||
−0.587345 | + | 0.809337i | \(0.699827\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.00233914 | + | 0.00233914i | −8.71140e−5 | + | 8.71140e-5i | ||||
\(722\) | 28.5221 | 1.06148 | ||||||||
\(723\) | 3.80880i | 0.141651i | ||||||||
\(724\) | 2.46378i | 0.0915658i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.4869 | − | 11.4869i | −0.426320 | − | 0.426320i | ||||
\(727\) | 15.0417 | + | 15.0417i | 0.557864 | + | 0.557864i | 0.928699 | − | 0.370835i | \(-0.120928\pi\) |
−0.370835 | + | 0.928699i | \(0.620928\pi\) | |||||||
\(728\) | 3.11516 | + | 7.73247i | 0.115455 | + | 0.286584i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.32864 | 0.234073 | ||||||||
\(732\) | 0.949072 | + | 0.949072i | 0.0350787 | + | 0.0350787i | ||||
\(733\) | −24.6952 | −0.912139 | −0.456070 | − | 0.889944i | \(-0.650743\pi\) | ||||
−0.456070 | + | 0.889944i | \(0.650743\pi\) | |||||||
\(734\) | 40.5733 | + | 40.5733i | 1.49759 | + | 1.49759i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.58282 | − | 4.58282i | −0.168925 | − | 0.168925i | ||||
\(737\) | −3.85314 | + | 3.85314i | −0.141932 | + | 0.141932i | ||||
\(738\) | −5.77149 | + | 5.77149i | −0.212451 | + | 0.212451i | ||||
\(739\) | −27.5591 | + | 27.5591i | −1.01378 | + | 1.01378i | −0.0138749 | + | 0.999904i | \(0.504417\pi\) |
−0.999904 | + | 0.0138749i | \(0.995583\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31766 | + | 3.27071i | 0.0484056 | + | 0.120153i | ||||
\(742\) | −8.71449 | + | 8.71449i | −0.319919 | + | 0.319919i | ||||
\(743\) | 15.3445 | 0.562934 | 0.281467 | − | 0.959571i | \(-0.409179\pi\) | ||||
0.281467 | + | 0.959571i | \(0.409179\pi\) | |||||||
\(744\) | 25.4260i | 0.932161i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.9127 | − | 16.9127i | 0.619219 | − | 0.619219i | ||||
\(747\) | 14.2841i | 0.522627i | ||||||||
\(748\) | − | 0.698406i | − | 0.0255362i | ||||||
\(749\) | −5.55455 | + | 5.55455i | −0.202959 | + | 0.202959i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.8827i | 1.49183i | 0.666041 | + | 0.745915i | \(0.267988\pi\) | ||||
−0.666041 | + | 0.745915i | \(0.732012\pi\) | |||||||
\(752\) | 15.4685 | 0.564077 | ||||||||
\(753\) | 7.85386 | − | 7.85386i | 0.286210 | − | 0.286210i | ||||
\(754\) | 33.6796 | − | 13.5684i | 1.22654 | − | 0.494132i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.343585 | − | 0.343585i | 0.0124961 | − | 0.0124961i | ||||
\(757\) | 3.88542 | − | 3.88542i | 0.141218 | − | 0.141218i | −0.632964 | − | 0.774182i | \(-0.718162\pi\) |
0.774182 | + | 0.632964i | \(0.218162\pi\) | |||||||
\(758\) | −6.75042 | + | 6.75042i | −0.245186 | + | 0.245186i | ||||
\(759\) | 1.41188 | + | 1.41188i | 0.0512480 | + | 0.0512480i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.29974 | − | 6.29974i | −0.228366 | − | 0.228366i | 0.583644 | − | 0.812010i | \(-0.301626\pi\) |
−0.812010 | + | 0.583644i | \(0.801626\pi\) | |||||||
\(762\) | −10.4284 | −0.377781 | ||||||||
\(763\) | 2.10862 | + | 2.10862i | 0.0763373 | + | 0.0763373i | ||||
\(764\) | 3.38016 | 0.122290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.5571i | 0.489839i | ||||||||
\(767\) | 11.8147 | − | 27.7567i | 0.426604 | − | 1.00224i | ||||
\(768\) | −7.98112 | − | 7.98112i | −0.287994 | − | 0.287994i | ||||
\(769\) | −8.18663 | − | 8.18663i | −0.295217 | − | 0.295217i | 0.543920 | − | 0.839137i | \(-0.316940\pi\) |
−0.839137 | + | 0.543920i | \(0.816940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 9.32121i | − | 0.335695i | ||||||
\(772\) | − | 4.10573i | − | 0.147768i | ||||||
\(773\) | −17.5543 | −0.631385 | −0.315692 | − | 0.948862i | \(-0.602237\pi\) | ||||
−0.315692 | + | 0.948862i | \(0.602237\pi\) | |||||||
\(774\) | 4.29559 | − | 4.29559i | 0.154402 | − | 0.154402i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −34.3784 | −1.23411 | ||||||||
\(777\) | −4.97788 | − | 4.97788i | −0.178580 | − | 0.178580i | ||||
\(778\) | 2.89501i | 0.103791i | ||||||||
\(779\) | 5.04980 | 0.180928 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.63317 | −0.308919 | ||||||||
\(782\) | − | 6.11212i | − | 0.218569i | ||||||
\(783\) | 4.50484 | + | 4.50484i | 0.160990 | + | 0.160990i | ||||
\(784\) | 28.7334 | 1.02619 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.76476 | − | 1.76476i | 0.0629469 | − | 0.0629469i | ||||
\(787\) | −8.38195 | −0.298784 | −0.149392 | − | 0.988778i | \(-0.547732\pi\) | ||||
−0.149392 | + | 0.988778i | \(0.547732\pi\) | |||||||
\(788\) | 11.5662i | 0.412028i | ||||||||
\(789\) | 14.1041i | 0.502118i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2250 | − | 11.2250i | −0.399115 | − | 0.399115i | ||||
\(792\) | 1.42698 | + | 1.42698i | 0.0507054 | + | 0.0507054i | ||||
\(793\) | −9.00045 | + | 3.62599i | −0.319615 | + | 0.128763i | ||||
\(794\) | − | 34.9396i | − | 1.23996i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.57033 | −0.339211 | ||||||||
\(797\) | −21.7988 | − | 21.7988i | −0.772152 | − | 0.772152i | 0.206331 | − | 0.978482i | \(-0.433848\pi\) |
−0.978482 | + | 0.206331i | \(0.933848\pi\) | |||||||
\(798\) | −1.50618 | −0.0533181 | ||||||||
\(799\) | 3.79305 | + | 3.79305i | 0.134188 | + | 0.134188i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6606 | − | 10.6606i | −0.376673 | − | 0.376673i | ||||
\(802\) | 35.7783 | − | 35.7783i | 1.26337 | − | 1.26337i | ||||
\(803\) | 6.15132 | − | 6.15132i | 0.217076 | − | 0.217076i | ||||
\(804\) | 2.25977 | − | 2.25977i | 0.0796959 | − | 0.0796959i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 56.1864 | + | 23.9158i | 1.97908 | + | 0.842399i | ||||
\(807\) | 4.27528 | − | 4.27528i | 0.150497 | − | 0.150497i | ||||
\(808\) | 13.3334 | 0.469066 | ||||||||
\(809\) | 20.0206i | 0.703887i | 0.936021 | + | 0.351943i | \(0.114479\pi\) | ||||
−0.936021 | + | 0.351943i | \(0.885521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6145 | + | 34.6145i | −1.21548 | + | 1.21548i | −0.246279 | + | 0.969199i | \(0.579208\pi\) |
−0.969199 | + | 0.246279i | \(0.920792\pi\) | |||||||
\(812\) | 3.09559i | 0.108634i | ||||||||
\(813\) | − | 3.89484i | − | 0.136598i | ||||||
\(814\) | −6.86800 | + | 6.86800i | −0.240723 | + | 0.240723i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 7.82005i | − | 0.273757i | ||||||
\(817\) | −3.75845 | −0.131491 | ||||||||
\(818\) | 2.83751 | − | 2.83751i | 0.0992112 | − | 0.0992112i | ||||
\(819\) | 1.31269 | + | 3.25836i | 0.0458690 | + | 0.113856i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.8296 | + | 15.8296i | −0.552457 | + | 0.552457i | −0.927149 | − | 0.374692i | \(-0.877748\pi\) |
0.374692 | + | 0.927149i | \(0.377748\pi\) | |||||||
\(822\) | −3.93803 | + | 3.93803i | −0.137355 | + | 0.137355i | ||||
\(823\) | −13.5057 | + | 13.5057i | −0.470780 | + | 0.470780i | −0.902167 | − | 0.431387i | \(-0.858024\pi\) |
0.431387 | + | 0.902167i | \(0.358024\pi\) | |||||||
\(824\) | 0.00569755 | + | 0.00569755i | 0.000198483 | + | 0.000198483i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.11141 | + | 9.11141i | 0.317026 | + | 0.317026i | ||||
\(827\) | 6.62864 | 0.230500 | 0.115250 | − | 0.993337i | \(-0.463233\pi\) | ||||
0.115250 | + | 0.993337i | \(0.463233\pi\) | |||||||
\(828\) | −0.828032 | − | 0.828032i | −0.0287761 | − | 0.0287761i | ||||
\(829\) | −22.1289 | −0.768570 | −0.384285 | − | 0.923215i | \(-0.625552\pi\) | ||||
−0.384285 | + | 0.923215i | \(0.625552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 5.29787i | − | 0.183781i | ||||||
\(832\) | 17.1707 | − | 6.91751i | 0.595286 | − | 0.239821i | ||||
\(833\) | 7.04576 | + | 7.04576i | 0.244121 | + | 0.244121i | ||||
\(834\) | 21.1157 | + | 21.1157i | 0.731177 | + | 0.731177i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.414768i | 0.0143451i | ||||||||
\(837\) | 10.7142i | 0.370336i | ||||||||
\(838\) | 15.5509 | 0.537198 | ||||||||
\(839\) | 31.6130 | − | 31.6130i | 1.09140 | − | 1.09140i | 0.0960213 | − | 0.995379i | \(-0.469388\pi\) |
0.995379 | − | 0.0960213i | \(-0.0306117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5873 | −0.399561 | ||||||||
\(842\) | 17.7021 | + | 17.7021i | 0.610056 | + | 0.610056i | ||||
\(843\) | − | 32.6487i | − | 1.12448i | ||||||
\(844\) | 11.4631 | 0.394575 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.14908 | 0.177029 | ||||||||
\(847\) | 10.0126i | 0.344037i | ||||||||
\(848\) | 26.8703 | + | 26.8703i | 0.922730 | + | 0.922730i | ||||
\(849\) | −15.5430 | −0.533433 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.9966 | + | 11.9966i | −0.411238 | + | 0.411238i | ||||
\(852\) | 5.06313 | 0.173460 | ||||||||
\(853\) | − | 51.1679i | − | 1.75196i | −0.482352 | − | 0.875978i | \(-0.660217\pi\) | ||
0.482352 | − | 0.875978i | \(-0.339783\pi\) | |||||||
\(854\) | − | 4.14475i | − | 0.141830i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.5295 | + | 13.5295i | 0.462428 | + | 0.462428i | ||||
\(857\) | 34.0042 | + | 34.0042i | 1.16156 | + | 1.16156i | 0.984134 | + | 0.177426i | \(0.0567770\pi\) |
0.177426 | + | 0.984134i | \(0.443223\pi\) | |||||||
\(858\) | 4.49557 | − | 1.81112i | 0.153476 | − | 0.0618305i | ||||
\(859\) | 27.1852i | 0.927546i | 0.885954 | + | 0.463773i | \(0.153505\pi\) | ||||
−0.885954 | + | 0.463773i | \(0.846495\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.03072 | 0.171446 | ||||||||
\(862\) | 34.6154 | + | 34.6154i | 1.17901 | + | 1.17901i | ||||
\(863\) | 24.8172 | 0.844786 | 0.422393 | − | 0.906413i | \(-0.361190\pi\) | ||||
0.422393 | + | 0.906413i | \(0.361190\pi\) | |||||||
\(864\) | −1.95179 | − | 1.95179i | −0.0664012 | − | 0.0664012i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.0843 | − | 11.0843i | −0.376662 | − | 0.376662i | ||||
\(867\) | −10.1032 | + | 10.1032i | −0.343124 | + | 0.343124i | ||||
\(868\) | −3.68122 | + | 3.68122i | −0.124949 | + | 0.124949i | ||||
\(869\) | −4.47183 | + | 4.47183i | −0.151696 | + | 0.151696i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.63358 | + | 21.4303i | 0.292538 | + | 0.726139i | ||||
\(872\) | 5.13608 | − | 5.13608i | 0.173930 | − | 0.173930i | ||||
\(873\) | −14.4866 | −0.490297 | ||||||||
\(874\) | 3.62986i | 0.122782i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.60760 | + | 3.60760i | −0.121889 | + | 0.121889i | ||||
\(877\) | 8.63720i | 0.291657i | 0.989310 | + | 0.145829i | \(0.0465848\pi\) | ||||
−0.989310 | + | 0.145829i | \(0.953415\pi\) | |||||||
\(878\) | − | 24.9342i | − | 0.841487i | ||||||
\(879\) | 1.38114 | − | 1.38114i | 0.0465847 | − | 0.0465847i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.5330i | − | 0.523320i | −0.965160 | − | 0.261660i | \(-0.915730\pi\) | ||
0.965160 | − | 0.261660i | \(-0.0842700\pi\) | |||||||
\(882\) | 9.56466 | 0.322059 | ||||||||
\(883\) | 20.1472 | − | 20.1472i | 0.678006 | − | 0.678006i | −0.281542 | − | 0.959549i | \(-0.590846\pi\) |
0.959549 | + | 0.281542i | \(0.0908460\pi\) | |||||||
\(884\) | −2.72464 | − | 1.15975i | −0.0916394 | − | 0.0390065i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.755329 | − | 0.755329i | 0.0253758 | − | 0.0253758i | ||||
\(887\) | −25.0749 | + | 25.0749i | −0.841933 | + | 0.841933i | −0.989110 | − | 0.147177i | \(-0.952981\pi\) |
0.147177 | + | 0.989110i | \(0.452981\pi\) | |||||||
\(888\) | −12.1249 | + | 12.1249i | −0.406884 | + | 0.406884i | ||||
\(889\) | 4.54495 | + | 4.54495i | 0.152433 | + | 0.152433i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.601309 | + | 0.601309i | 0.0201446 | + | 0.0201446i | ||||
\(892\) | −11.6639 | −0.390537 | ||||||||
\(893\) | −2.25261 | − | 2.25261i | −0.0753807 | − | 0.0753807i | ||||
\(894\) | −22.0103 | −0.736133 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.2857i | 0.443845i | ||||||||
\(897\) | 7.85258 | − | 3.16355i | 0.262190 | − | 0.105628i | ||||
\(898\) | 17.3183 | + | 17.3183i | 0.577920 | + | 0.577920i | ||||
\(899\) | −48.2656 | − | 48.2656i | −1.60975 | − | 1.60975i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1778i | 0.439017i | ||||||||
\(902\) | − | 6.94090i | − | 0.231107i | ||||||
\(903\) | −3.74425 | −0.124601 | ||||||||
\(904\) | −27.3413 | + | 27.3413i | −0.909358 | + | 0.909358i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 26.5598 | 0.882392 | ||||||||
\(907\) | 15.8243 | + | 15.8243i | 0.525439 | + | 0.525439i | 0.919209 | − | 0.393770i | \(-0.128829\pi\) |
−0.393770 | + | 0.919209i | \(0.628829\pi\) | |||||||
\(908\) | − | 8.68663i | − | 0.288276i | ||||||
\(909\) | 5.61850 | 0.186354 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.9928 | 0.728655 | 0.364327 | − | 0.931271i | \(-0.381299\pi\) | ||||
0.364327 | + | 0.931271i | \(0.381299\pi\) | |||||||
\(912\) | 4.64416i | 0.153784i | ||||||||
\(913\) | −8.58914 | − | 8.58914i | −0.284259 | − | 0.284259i | ||||
\(914\) | 34.8658 | 1.15326 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.24279 | − | 4.24279i | 0.140186 | − | 0.140186i | ||||
\(917\) | −1.53825 | −0.0507976 | ||||||||
\(918\) | − | 2.60311i | − | 0.0859153i | ||||||
\(919\) | − | 53.4478i | − | 1.76308i | −0.472108 | − | 0.881541i | \(-0.656507\pi\) | ||
0.472108 | − | 0.881541i | \(-0.343493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.7498 | − | 16.7498i | −0.551923 | − | 0.551923i | ||||
\(922\) | −9.10043 | − | 9.10043i | −0.299707 | − | 0.299707i | ||||
\(923\) | −14.3359 | + | 33.6799i | −0.471872 | + | 1.10859i | ||||
\(924\) | 0.413201i | 0.0135933i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −41.4353 | −1.36165 | ||||||||
\(927\) | 0.00240087 | + | 0.00240087i | 7.88549e−5 | + | 7.88549e-5i | ||||
\(928\) | 17.5850 | 0.577256 | ||||||||
\(929\) | 7.45064 | + | 7.45064i | 0.244448 | + | 0.244448i | 0.818687 | − | 0.574240i | \(-0.194702\pi\) |
−0.574240 | + | 0.818687i | \(0.694702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.18433 | − | 4.18433i | −0.137136 | − | 0.137136i | ||||
\(932\) | 9.93250 | − | 9.93250i | 0.325350 | − | 0.325350i | ||||
\(933\) | 0.552962 | − | 0.552962i | 0.0181031 | − | 0.0181031i | ||||
\(934\) | −1.43098 | + | 1.43098i | −0.0468230 | + | 0.0468230i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.93654 | − | 3.19737i | 0.259414 | − | 0.104509i | ||||
\(937\) | 13.8571 | − | 13.8571i | 0.452693 | − | 0.452693i | −0.443555 | − | 0.896247i | \(-0.646283\pi\) |
0.896247 | + | 0.443555i | \(0.146283\pi\) | |||||||
\(938\) | −9.86876 | −0.322227 | ||||||||
\(939\) | 1.54810i | 0.0505202i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.55621 | − | 3.55621i | 0.115929 | − | 0.115929i | −0.646762 | − | 0.762692i | \(-0.723877\pi\) |
0.762692 | + | 0.646762i | \(0.223877\pi\) | |||||||
\(942\) | 11.0296i | 0.359363i | ||||||||
\(943\) | − | 12.1239i | − | 0.394810i | ||||||
\(944\) | 28.0942 | − | 28.0942i | 0.914388 | − | 0.914388i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.16595i | 0.167960i | ||||||||
\(947\) | −28.4349 | −0.924010 | −0.462005 | − | 0.886877i | \(-0.652870\pi\) | ||||
−0.462005 | + | 0.886877i | \(0.652870\pi\) | |||||||
\(948\) | 2.62261 | − | 2.62261i | 0.0851785 | − | 0.0851785i | ||||
\(949\) | −13.7830 | − | 34.2123i | −0.447416 | − | 1.11058i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.8767 | − | 14.8767i | 0.482409 | − | 0.482409i | ||||
\(952\) | −2.69230 | + | 2.69230i | −0.0872580 | + | 0.0872580i | ||||
\(953\) | −1.81293 | + | 1.81293i | −0.0587266 | + | 0.0587266i | −0.735860 | − | 0.677134i | \(-0.763222\pi\) |
0.677134 | + | 0.735860i | \(0.263222\pi\) | |||||||
\(954\) | 8.94448 | + | 8.94448i | 0.289588 | + | 0.289588i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.83773 | − | 3.83773i | −0.124121 | − | 0.124121i | ||||
\(957\) | −5.41761 | −0.175126 | ||||||||
\(958\) | −2.15409 | − | 2.15409i | −0.0695956 | − | 0.0695956i | ||||
\(959\) | 3.43259 | 0.110844 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 83.7933i | − | 2.70301i | ||||||
\(962\) | 15.3889 | + | 38.1983i | 0.496157 | + | 1.23156i | ||||
\(963\) | 5.70114 | + | 5.70114i | 0.183717 | + | 0.183717i | ||||
\(964\) | 1.34318 | + | 1.34318i | 0.0432610 | + | 0.0432610i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.61615i | 0.116348i | ||||||||
\(967\) | − | 7.13250i | − | 0.229366i | −0.993402 | − | 0.114683i | \(-0.963415\pi\) | ||
0.993402 | − | 0.114683i | \(-0.0365852\pi\) | |||||||
\(968\) | 24.3882 | 0.783866 | ||||||||
\(969\) | −1.13880 | + | 1.13880i | −0.0365836 | + | 0.0365836i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.6017 | 1.62389 | 0.811943 | − | 0.583737i | \(-0.198410\pi\) | ||||
0.811943 | + | 0.583737i | \(0.198410\pi\) | |||||||
\(972\) | −0.352653 | − | 0.352653i | −0.0113113 | − | 0.0113113i | ||||
\(973\) | − | 18.4055i | − | 0.590054i | ||||||
\(974\) | −24.0728 | −0.771343 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.7799 | −0.409076 | ||||||||
\(977\) | 34.3015i | 1.09740i | 0.836019 | + | 0.548701i | \(0.184877\pi\) | ||||
−0.836019 | + | 0.548701i | \(0.815123\pi\) | |||||||
\(978\) | 19.8995 | + | 19.8995i | 0.636315 | + | 0.636315i | ||||
\(979\) | 12.8206 | 0.409749 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.16428 | − | 2.16428i | 0.0691000 | − | 0.0691000i | ||||
\(982\) | 19.2501 | 0.614294 | ||||||||
\(983\) | − | 47.7005i | − | 1.52141i | −0.649097 | − | 0.760705i | \(-0.724853\pi\) | ||
0.649097 | − | 0.760705i | \(-0.275147\pi\) | |||||||
\(984\) | − | 12.2536i | − | 0.390630i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.7266 | + | 11.7266i | 0.373451 | + | 0.373451i | ||||
\(987\) | −2.24410 | − | 2.24410i | −0.0714305 | − | 0.0714305i | ||||
\(988\) | 1.61810 | + | 0.688748i | 0.0514787 | + | 0.0219120i | ||||
\(989\) | 9.02357i | 0.286933i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9606 | −0.443474 | −0.221737 | − | 0.975107i | \(-0.571173\pi\) | ||||
−0.221737 | + | 0.975107i | \(0.571173\pi\) | |||||||
\(992\) | 20.9118 | + | 20.9118i | 0.663949 | + | 0.663949i | ||||
\(993\) | 14.2233 | 0.451363 | ||||||||
\(994\) | −11.0558 | − | 11.0558i | −0.350667 | − | 0.350667i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.03731 | + | 5.03731i | 0.159613 | + | 0.159613i | ||||
\(997\) | −30.9797 | + | 30.9797i | −0.981136 | + | 0.981136i | −0.999825 | − | 0.0186893i | \(-0.994051\pi\) |
0.0186893 | + | 0.999825i | \(0.494051\pi\) | |||||||
\(998\) | 36.6190 | − | 36.6190i | 1.15915 | − | 1.15915i | ||||
\(999\) | −5.10926 | + | 5.10926i | −0.161650 | + | 0.161650i |
(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 | 975.2.k.d.343.11 | 28 | ||
5.2 | odd | 4 | 975.2.t.d.382.4 | 28 | |||
5.3 | odd | 4 | 195.2.t.a.187.11 | yes | 28 | ||
5.4 | even | 2 | 195.2.k.a.148.4 | yes | 28 | ||
13.8 | odd | 4 | 975.2.t.d.268.4 | 28 | |||
15.8 | even | 4 | 585.2.w.g.577.4 | 28 | |||
15.14 | odd | 2 | 585.2.n.g.343.11 | 28 | |||
65.8 | even | 4 | 195.2.k.a.112.11 | ✓ | 28 | ||
65.34 | odd | 4 | 195.2.t.a.73.11 | yes | 28 | ||
65.47 | even | 4 | inner | 975.2.k.d.307.4 | 28 | ||
195.8 | odd | 4 | 585.2.n.g.307.4 | 28 | |||
195.164 | even | 4 | 585.2.w.g.73.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.k.a.112.11 | ✓ | 28 | 65.8 | even | 4 | ||
195.2.k.a.148.4 | yes | 28 | 5.4 | even | 2 | ||
195.2.t.a.73.11 | yes | 28 | 65.34 | odd | 4 | ||
195.2.t.a.187.11 | yes | 28 | 5.3 | odd | 4 | ||
585.2.n.g.307.4 | 28 | 195.8 | odd | 4 | |||
585.2.n.g.343.11 | 28 | 15.14 | odd | 2 | |||
585.2.w.g.73.4 | 28 | 195.164 | even | 4 | |||
585.2.w.g.577.4 | 28 | 15.8 | even | 4 | |||
975.2.k.d.307.4 | 28 | 65.47 | even | 4 | inner | ||
975.2.k.d.343.11 | 28 | 1.1 | even | 1 | trivial | ||
975.2.t.d.268.4 | 28 | 13.8 | odd | 4 | |||
975.2.t.d.382.4 | 28 | 5.2 | odd | 4 |