Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), degree \(2\), not 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} + 2x^{2} + x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.809017 - 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.n.177.1 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.61803 | + | 2.80252i | −0.934172 | + | 1.61803i | −0.158069 | + | 0.987428i | \(0.550527\pi\) |
−0.776103 | + | 0.630606i | \(0.782806\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.61803 | + | 2.80252i | 0.723607 | + | 1.25332i | 0.959545 | + | 0.281556i | \(0.0908504\pi\) |
−0.235938 | + | 0.971768i | \(0.575816\pi\) | |||||||
\(6\) | 3.23607 | 1.32112 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.73607 | − | 6.47106i | −1.24536 | − | 2.15702i | ||||
\(10\) | 1.61803 | − | 2.80252i | 0.511667 | − | 0.886234i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | −1.61803 | − | 2.80252i | −0.467086 | − | 0.809017i | ||||
\(13\) | −1.23607 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.4721 | −2.70389 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.23607 | + | 5.60503i | −0.784862 | + | 1.35942i | 0.144220 | + | 0.989546i | \(0.453933\pi\) |
−0.929082 | + | 0.369875i | \(0.879401\pi\) | |||||||
\(18\) | −3.73607 | + | 6.47106i | −0.880600 | + | 1.52524i | ||||
\(19\) | −1.38197 | − | 2.39364i | −0.317045 | − | 0.549138i | 0.662825 | − | 0.748774i | \(-0.269357\pi\) |
−0.979870 | + | 0.199636i | \(0.936024\pi\) | |||||||
\(20\) | −3.23607 | −0.723607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | −1.61803 | + | 2.80252i | −0.330280 | + | 0.572061i | ||||
\(25\) | −2.73607 | + | 4.73901i | −0.547214 | + | 0.947802i | ||||
\(26\) | 0.618034 | + | 1.07047i | 0.121206 | + | 0.209936i | ||||
\(27\) | 14.4721 | 2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 5.23607 | + | 9.06914i | 0.955971 | + | 1.65579i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.61803 | − | 2.80252i | −0.281664 | − | 0.487856i | ||||
\(34\) | 6.47214 | 1.10996 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.47214 | 1.24536 | ||||||||
\(37\) | 5.47214 | + | 9.47802i | 0.899614 | + | 1.55818i | 0.827989 | + | 0.560745i | \(0.189485\pi\) |
0.0716249 | + | 0.997432i | \(0.477182\pi\) | |||||||
\(38\) | −1.38197 | + | 2.39364i | −0.224184 | + | 0.388299i | ||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | 1.61803 | + | 2.80252i | 0.255834 | + | 0.443117i | ||||
\(41\) | −6.47214 | −1.01078 | −0.505389 | − | 0.862892i | \(-0.668651\pi\) | ||||
−0.505389 | + | 0.862892i | \(0.668651\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.52786 | −0.232997 | −0.116499 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116499 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | 12.0902 | − | 20.9408i | 1.80230 | − | 3.12167i | ||||
\(46\) | −2.00000 | + | 3.46410i | −0.294884 | + | 0.510754i | ||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | 3.23607 | 0.467086 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.47214 | 0.773877 | ||||||||
\(51\) | −10.4721 | − | 18.1383i | −1.46639 | − | 2.53987i | ||||
\(52\) | 0.618034 | − | 1.07047i | 0.0857059 | − | 0.148447i | ||||
\(53\) | 0.236068 | − | 0.408882i | 0.0324264 | − | 0.0561642i | −0.849357 | − | 0.527819i | \(-0.823010\pi\) |
0.881783 | + | 0.471655i | \(0.156343\pi\) | |||||||
\(54\) | −7.23607 | − | 12.5332i | −0.984704 | − | 1.70556i | ||||
\(55\) | −3.23607 | −0.436351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.94427 | 1.18470 | ||||||||
\(58\) | 2.23607 | + | 3.87298i | 0.293610 | + | 0.508548i | ||||
\(59\) | 3.61803 | − | 6.26662i | 0.471028 | − | 0.815844i | −0.528423 | − | 0.848981i | \(-0.677216\pi\) |
0.999451 | + | 0.0331370i | \(0.0105498\pi\) | |||||||
\(60\) | 5.23607 | − | 9.06914i | 0.675973 | − | 1.17082i | ||||
\(61\) | −2.61803 | − | 4.53457i | −0.335205 | − | 0.580592i | 0.648319 | − | 0.761369i | \(-0.275472\pi\) |
−0.983524 | + | 0.180777i | \(0.942139\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | −1.61803 | + | 2.80252i | −0.199166 | + | 0.344966i | ||||
\(67\) | 7.70820 | − | 13.3510i | 0.941707 | − | 1.63108i | 0.179493 | − | 0.983759i | \(-0.442554\pi\) |
0.762214 | − | 0.647325i | \(-0.224112\pi\) | |||||||
\(68\) | −3.23607 | − | 5.60503i | −0.392431 | − | 0.679710i | ||||
\(69\) | 12.9443 | 1.55831 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.47214 | −0.293389 | −0.146694 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146694 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(72\) | −3.73607 | − | 6.47106i | −0.440300 | − | 0.762622i | ||||
\(73\) | −2.47214 | + | 4.28187i | −0.289342 | + | 0.501154i | −0.973653 | − | 0.228036i | \(-0.926770\pi\) |
0.684311 | + | 0.729190i | \(0.260103\pi\) | |||||||
\(74\) | 5.47214 | − | 9.47802i | 0.636123 | − | 1.10180i | ||||
\(75\) | −8.85410 | − | 15.3358i | −1.02238 | − | 1.77082i | ||||
\(76\) | 2.76393 | 0.317045 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 1.61803 | − | 2.80252i | 0.180902 | − | 0.313331i | ||||
\(81\) | −12.2082 | + | 21.1452i | −1.35647 | + | 2.34947i | ||||
\(82\) | 3.23607 | + | 5.60503i | 0.357364 | + | 0.618972i | ||||
\(83\) | −10.1803 | −1.11744 | −0.558719 | − | 0.829357i | \(-0.688707\pi\) | ||||
−0.558719 | + | 0.829357i | \(0.688707\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.9443 | −2.27173 | ||||||||
\(86\) | 0.763932 | + | 1.32317i | 0.0823769 | + | 0.142681i | ||||
\(87\) | 7.23607 | − | 12.5332i | 0.775788 | − | 1.34370i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 5.00000 | + | 8.66025i | 0.529999 | + | 0.917985i | 0.999388 | + | 0.0349934i | \(0.0111410\pi\) |
−0.469389 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(90\) | −24.1803 | −2.54883 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 3.23607 | + | 5.60503i | 0.335565 | + | 0.581215i | ||||
\(94\) | −1.00000 | + | 1.73205i | −0.103142 | + | 0.178647i | ||||
\(95\) | 4.47214 | − | 7.74597i | 0.458831 | − | 0.794719i | ||||
\(96\) | −1.61803 | − | 2.80252i | −0.165140 | − | 0.286031i | ||||
\(97\) | −3.52786 | −0.358200 | −0.179100 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179100 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.47214 | 0.750978 | ||||||||
\(100\) | −2.73607 | − | 4.73901i | −0.273607 | − | 0.473901i | ||||
\(101\) | −7.09017 | + | 12.2805i | −0.705498 | + | 1.22196i | 0.261013 | + | 0.965335i | \(0.415943\pi\) |
−0.966511 | + | 0.256624i | \(0.917390\pi\) | |||||||
\(102\) | −10.4721 | + | 18.1383i | −1.03690 | + | 1.79596i | ||||
\(103\) | 1.47214 | + | 2.54981i | 0.145054 | + | 0.251241i | 0.929393 | − | 0.369092i | \(-0.120331\pi\) |
−0.784339 | + | 0.620332i | \(0.786998\pi\) | |||||||
\(104\) | −1.23607 | −0.121206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.472136 | −0.0458579 | ||||||||
\(107\) | 3.23607 | + | 5.60503i | 0.312842 | + | 0.541859i | 0.978977 | − | 0.203973i | \(-0.0653855\pi\) |
−0.666134 | + | 0.745832i | \(0.732052\pi\) | |||||||
\(108\) | −7.23607 | + | 12.5332i | −0.696291 | + | 1.20601i | ||||
\(109\) | 5.00000 | − | 8.66025i | 0.478913 | − | 0.829502i | −0.520794 | − | 0.853682i | \(-0.674364\pi\) |
0.999708 | + | 0.0241802i | \(0.00769755\pi\) | |||||||
\(110\) | 1.61803 | + | 2.80252i | 0.154273 | + | 0.267210i | ||||
\(111\) | −35.4164 | −3.36158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.47214 | 0.796992 | 0.398496 | − | 0.917170i | \(-0.369532\pi\) | ||||
0.398496 | + | 0.917170i | \(0.369532\pi\) | |||||||
\(114\) | −4.47214 | − | 7.74597i | −0.418854 | − | 0.725476i | ||||
\(115\) | 6.47214 | − | 11.2101i | 0.603530 | − | 1.04534i | ||||
\(116\) | 2.23607 | − | 3.87298i | 0.207614 | − | 0.359597i | ||||
\(117\) | 4.61803 | + | 7.99867i | 0.426937 | + | 0.739477i | ||||
\(118\) | −7.23607 | −0.666134 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.4721 | −0.955971 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −2.61803 | + | 4.53457i | −0.237026 | + | 0.410540i | ||||
\(123\) | 10.4721 | − | 18.1383i | 0.944241 | − | 1.63547i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 2.47214 | − | 4.28187i | 0.217659 | − | 0.376997i | ||||
\(130\) | −2.00000 | + | 3.46410i | −0.175412 | + | 0.303822i | ||||
\(131\) | 4.61803 | + | 7.99867i | 0.403480 | + | 0.698847i | 0.994143 | − | 0.108071i | \(-0.0344673\pi\) |
−0.590664 | + | 0.806918i | \(0.701134\pi\) | |||||||
\(132\) | 3.23607 | 0.281664 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −15.4164 | −1.33177 | ||||||||
\(135\) | 23.4164 | + | 40.5584i | 2.01536 | + | 3.49071i | ||||
\(136\) | −3.23607 | + | 5.60503i | −0.277491 | + | 0.480628i | ||||
\(137\) | −7.94427 | + | 13.7599i | −0.678725 | + | 1.17559i | 0.296640 | + | 0.954989i | \(0.404134\pi\) |
−0.975365 | + | 0.220597i | \(0.929200\pi\) | |||||||
\(138\) | −6.47214 | − | 11.2101i | −0.550945 | − | 0.954264i | ||||
\(139\) | 8.29180 | 0.703301 | 0.351650 | − | 0.936131i | \(-0.385621\pi\) | ||||
0.351650 | + | 0.936131i | \(0.385621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.47214 | 0.545052 | ||||||||
\(142\) | 1.23607 | + | 2.14093i | 0.103729 | + | 0.179663i | ||||
\(143\) | 0.618034 | − | 1.07047i | 0.0516826 | − | 0.0895169i | ||||
\(144\) | −3.73607 | + | 6.47106i | −0.311339 | + | 0.539255i | ||||
\(145\) | −7.23607 | − | 12.5332i | −0.600923 | − | 1.04083i | ||||
\(146\) | 4.94427 | 0.409191 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.9443 | −0.899614 | ||||||||
\(149\) | −11.1803 | − | 19.3649i | −0.915929 | − | 1.58644i | −0.805535 | − | 0.592548i | \(-0.798122\pi\) |
−0.110394 | − | 0.993888i | \(-0.535211\pi\) | |||||||
\(150\) | −8.85410 | + | 15.3358i | −0.722934 | + | 1.25216i | ||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | −1.38197 | − | 2.39364i | −0.112092 | − | 0.194149i | ||||
\(153\) | 48.3607 | 3.90973 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.47214 | 0.519854 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | 9.32624 | − | 16.1535i | 0.744315 | − | 1.28919i | −0.206199 | − | 0.978510i | \(-0.566110\pi\) |
0.950514 | − | 0.310681i | \(-0.100557\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.763932 | + | 1.32317i | 0.0605838 | + | 0.104934i | ||||
\(160\) | −3.23607 | −0.255834 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 24.4164 | 1.91833 | ||||||||
\(163\) | −3.70820 | − | 6.42280i | −0.290449 | − | 0.503072i | 0.683467 | − | 0.729981i | \(-0.260471\pi\) |
−0.973916 | + | 0.226909i | \(0.927138\pi\) | |||||||
\(164\) | 3.23607 | − | 5.60503i | 0.252694 | − | 0.437680i | ||||
\(165\) | 5.23607 | − | 9.06914i | 0.407627 | − | 0.706031i | ||||
\(166\) | 5.09017 | + | 8.81643i | 0.395074 | + | 0.684288i | ||||
\(167\) | 15.4164 | 1.19296 | 0.596479 | − | 0.802629i | \(-0.296566\pi\) | ||||
0.596479 | + | 0.802629i | \(0.296566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 10.4721 | + | 18.1383i | 0.803176 | + | 1.39114i | ||||
\(171\) | −10.3262 | + | 17.8856i | −0.789667 | + | 1.36774i | ||||
\(172\) | 0.763932 | − | 1.32317i | 0.0582493 | − | 0.100891i | ||||
\(173\) | 0.618034 | + | 1.07047i | 0.0469883 | + | 0.0813860i | 0.888563 | − | 0.458755i | \(-0.151704\pi\) |
−0.841575 | + | 0.540141i | \(0.818371\pi\) | |||||||
\(174\) | −14.4721 | −1.09713 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 11.7082 | + | 20.2792i | 0.880042 | + | 1.52428i | ||||
\(178\) | 5.00000 | − | 8.66025i | 0.374766 | − | 0.649113i | ||||
\(179\) | −4.47214 | + | 7.74597i | −0.334263 | + | 0.578961i | −0.983343 | − | 0.181760i | \(-0.941821\pi\) |
0.649080 | + | 0.760720i | \(0.275154\pi\) | |||||||
\(180\) | 12.0902 | + | 20.9408i | 0.901148 | + | 1.56083i | ||||
\(181\) | −4.76393 | −0.354100 | −0.177050 | − | 0.984202i | \(-0.556655\pi\) | ||||
−0.177050 | + | 0.984202i | \(0.556655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.9443 | 1.25256 | ||||||||
\(184\) | −2.00000 | − | 3.46410i | −0.147442 | − | 0.255377i | ||||
\(185\) | −17.7082 | + | 30.6715i | −1.30193 | + | 2.25501i | ||||
\(186\) | 3.23607 | − | 5.60503i | 0.237280 | − | 0.410981i | ||||
\(187\) | −3.23607 | − | 5.60503i | −0.236645 | − | 0.409881i | ||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.94427 | −0.648886 | ||||||||
\(191\) | −3.23607 | − | 5.60503i | −0.234154 | − | 0.405566i | 0.724873 | − | 0.688883i | \(-0.241899\pi\) |
−0.959026 | + | 0.283317i | \(0.908565\pi\) | |||||||
\(192\) | −1.61803 | + | 2.80252i | −0.116772 | + | 0.202254i | ||||
\(193\) | −1.47214 | + | 2.54981i | −0.105967 | + | 0.183540i | −0.914133 | − | 0.405415i | \(-0.867127\pi\) |
0.808166 | + | 0.588955i | \(0.200460\pi\) | |||||||
\(194\) | 1.76393 | + | 3.05522i | 0.126643 | + | 0.219352i | ||||
\(195\) | 12.9443 | 0.926959 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | −3.73607 | − | 6.47106i | −0.265511 | − | 0.459878i | ||||
\(199\) | 0.527864 | − | 0.914287i | 0.0374193 | − | 0.0648121i | −0.846709 | − | 0.532056i | \(-0.821420\pi\) |
0.884129 | + | 0.467244i | \(0.154753\pi\) | |||||||
\(200\) | −2.73607 | + | 4.73901i | −0.193469 | + | 0.335099i | ||||
\(201\) | 24.9443 | + | 43.2047i | 1.75943 | + | 3.04743i | ||||
\(202\) | 14.1803 | 0.997725 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 20.9443 | 1.46639 | ||||||||
\(205\) | −10.4721 | − | 18.1383i | −0.731406 | − | 1.26683i | ||||
\(206\) | 1.47214 | − | 2.54981i | 0.102569 | − | 0.177654i | ||||
\(207\) | −14.9443 | + | 25.8842i | −1.03870 | + | 1.79908i | ||||
\(208\) | 0.618034 | + | 1.07047i | 0.0428529 | + | 0.0742235i | ||||
\(209\) | 2.76393 | 0.191185 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4721 | −1.54705 | −0.773523 | − | 0.633768i | \(-0.781507\pi\) | ||||
−0.773523 | + | 0.633768i | \(0.781507\pi\) | |||||||
\(212\) | 0.236068 | + | 0.408882i | 0.0162132 | + | 0.0280821i | ||||
\(213\) | 4.00000 | − | 6.92820i | 0.274075 | − | 0.474713i | ||||
\(214\) | 3.23607 | − | 5.60503i | 0.221213 | − | 0.383152i | ||||
\(215\) | −2.47214 | − | 4.28187i | −0.168598 | − | 0.292021i | ||||
\(216\) | 14.4721 | 0.984704 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | −8.00000 | − | 13.8564i | −0.540590 | − | 0.936329i | ||||
\(220\) | 1.61803 | − | 2.80252i | 0.109088 | − | 0.188946i | ||||
\(221\) | 4.00000 | − | 6.92820i | 0.269069 | − | 0.466041i | ||||
\(222\) | 17.7082 | + | 30.6715i | 1.18850 | + | 2.05854i | ||||
\(223\) | −8.47214 | −0.567336 | −0.283668 | − | 0.958923i | \(-0.591551\pi\) | ||||
−0.283668 | + | 0.958923i | \(0.591551\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40.8885 | 2.72590 | ||||||||
\(226\) | −4.23607 | − | 7.33708i | −0.281779 | − | 0.488056i | ||||
\(227\) | −7.38197 | + | 12.7859i | −0.489958 | + | 0.848633i | −0.999933 | − | 0.0115566i | \(-0.996321\pi\) |
0.509975 | + | 0.860189i | \(0.329655\pi\) | |||||||
\(228\) | −4.47214 | + | 7.74597i | −0.296174 | + | 0.512989i | ||||
\(229\) | 6.38197 | + | 11.0539i | 0.421732 | + | 0.730462i | 0.996109 | − | 0.0881294i | \(-0.0280889\pi\) |
−0.574377 | + | 0.818591i | \(0.694756\pi\) | |||||||
\(230\) | −12.9443 | −0.853520 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.47214 | −0.293610 | ||||||||
\(233\) | −1.47214 | − | 2.54981i | −0.0964428 | − | 0.167044i | 0.813767 | − | 0.581191i | \(-0.197413\pi\) |
−0.910210 | + | 0.414147i | \(0.864080\pi\) | |||||||
\(234\) | 4.61803 | − | 7.99867i | 0.301890 | − | 0.522889i | ||||
\(235\) | 3.23607 | − | 5.60503i | 0.211098 | − | 0.365632i | ||||
\(236\) | 3.61803 | + | 6.26662i | 0.235514 | + | 0.407922i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 5.23607 | + | 9.06914i | 0.337987 | + | 0.585410i | ||||
\(241\) | −5.70820 | + | 9.88690i | −0.367698 | + | 0.636871i | −0.989205 | − | 0.146537i | \(-0.953187\pi\) |
0.621507 | + | 0.783408i | \(0.286521\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | −17.7984 | − | 30.8277i | −1.14177 | − | 1.97760i | ||||
\(244\) | 5.23607 | 0.335205 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.9443 | −1.33536 | ||||||||
\(247\) | 1.70820 | + | 2.95870i | 0.108690 | + | 0.188257i | ||||
\(248\) | 1.00000 | − | 1.73205i | 0.0635001 | − | 0.109985i | ||||
\(249\) | 16.4721 | − | 28.5306i | 1.04388 | − | 1.80805i | ||||
\(250\) | 0.763932 | + | 1.32317i | 0.0483153 | + | 0.0836846i | ||||
\(251\) | −24.7639 | −1.56309 | −0.781543 | − | 0.623852i | \(-0.785567\pi\) | ||||
−0.781543 | + | 0.623852i | \(0.785567\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 6.00000 | + | 10.3923i | 0.376473 | + | 0.652071i | ||||
\(255\) | 33.8885 | − | 58.6967i | 2.12218 | − | 3.67573i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.47214 | − | 9.47802i | −0.341342 | − | 0.591222i | 0.643340 | − | 0.765581i | \(-0.277548\pi\) |
−0.984682 | + | 0.174358i | \(0.944215\pi\) | |||||||
\(258\) | −4.94427 | −0.307817 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 16.7082 | + | 28.9395i | 1.03421 | + | 1.79131i | ||||
\(262\) | 4.61803 | − | 7.99867i | 0.285303 | − | 0.494159i | ||||
\(263\) | −6.47214 | + | 11.2101i | −0.399089 | + | 0.691242i | −0.993614 | − | 0.112835i | \(-0.964007\pi\) |
0.594525 | + | 0.804077i | \(0.297340\pi\) | |||||||
\(264\) | −1.61803 | − | 2.80252i | −0.0995831 | − | 0.172483i | ||||
\(265\) | 1.52786 | 0.0938559 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.3607 | −1.98044 | ||||||||
\(268\) | 7.70820 | + | 13.3510i | 0.470853 | + | 0.815542i | ||||
\(269\) | −13.6180 | + | 23.5871i | −0.830306 | + | 1.43813i | 0.0674893 | + | 0.997720i | \(0.478501\pi\) |
−0.897796 | + | 0.440413i | \(0.854832\pi\) | |||||||
\(270\) | 23.4164 | − | 40.5584i | 1.42508 | − | 2.46831i | ||||
\(271\) | −8.47214 | − | 14.6742i | −0.514646 | − | 0.891392i | −0.999856 | − | 0.0169947i | \(-0.994590\pi\) |
0.485210 | − | 0.874398i | \(-0.338743\pi\) | |||||||
\(272\) | 6.47214 | 0.392431 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.8885 | 0.959862 | ||||||||
\(275\) | −2.73607 | − | 4.73901i | −0.164991 | − | 0.285773i | ||||
\(276\) | −6.47214 | + | 11.2101i | −0.389577 | + | 0.674767i | ||||
\(277\) | −6.23607 | + | 10.8012i | −0.374689 | + | 0.648980i | −0.990280 | − | 0.139085i | \(-0.955584\pi\) |
0.615591 | + | 0.788065i | \(0.288917\pi\) | |||||||
\(278\) | −4.14590 | − | 7.18091i | −0.248654 | − | 0.430682i | ||||
\(279\) | −14.9443 | −0.894690 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.8328 | −1.48140 | −0.740701 | − | 0.671835i | \(-0.765506\pi\) | ||||
−0.740701 | + | 0.671835i | \(0.765506\pi\) | |||||||
\(282\) | −3.23607 | − | 5.60503i | −0.192705 | − | 0.333775i | ||||
\(283\) | −8.32624 | + | 14.4215i | −0.494943 | + | 0.857267i | −0.999983 | − | 0.00582897i | \(-0.998145\pi\) |
0.505040 | + | 0.863096i | \(0.331478\pi\) | |||||||
\(284\) | 1.23607 | − | 2.14093i | 0.0733471 | − | 0.127041i | ||||
\(285\) | 14.4721 | + | 25.0665i | 0.857255 | + | 1.48481i | ||||
\(286\) | −1.23607 | −0.0730902 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.47214 | 0.440300 | ||||||||
\(289\) | −12.4443 | − | 21.5541i | −0.732016 | − | 1.26789i | ||||
\(290\) | −7.23607 | + | 12.5332i | −0.424917 | + | 0.735977i | ||||
\(291\) | 5.70820 | − | 9.88690i | 0.334621 | − | 0.579580i | ||||
\(292\) | −2.47214 | − | 4.28187i | −0.144671 | − | 0.250577i | ||||
\(293\) | −4.65248 | −0.271801 | −0.135900 | − | 0.990723i | \(-0.543393\pi\) | ||||
−0.135900 | + | 0.990723i | \(0.543393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.4164 | 1.36336 | ||||||||
\(296\) | 5.47214 | + | 9.47802i | 0.318061 | + | 0.550899i | ||||
\(297\) | −7.23607 | + | 12.5332i | −0.419879 | + | 0.727252i | ||||
\(298\) | −11.1803 | + | 19.3649i | −0.647660 | + | 1.12178i | ||||
\(299\) | 2.47214 | + | 4.28187i | 0.142967 | + | 0.247627i | ||||
\(300\) | 17.7082 | 1.02238 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −22.9443 | − | 39.7406i | −1.31811 | − | 2.28304i | ||||
\(304\) | −1.38197 | + | 2.39364i | −0.0792612 | + | 0.137284i | ||||
\(305\) | 8.47214 | − | 14.6742i | 0.485113 | − | 0.840241i | ||||
\(306\) | −24.1803 | − | 41.8816i | −1.38230 | − | 2.39421i | ||||
\(307\) | −32.0689 | −1.83027 | −0.915134 | − | 0.403150i | \(-0.867915\pi\) | ||||
−0.915134 | + | 0.403150i | \(0.867915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.52786 | −0.542021 | ||||||||
\(310\) | −3.23607 | − | 5.60503i | −0.183796 | − | 0.318345i | ||||
\(311\) | 2.70820 | − | 4.69075i | 0.153568 | − | 0.265988i | −0.778969 | − | 0.627063i | \(-0.784257\pi\) |
0.932537 | + | 0.361075i | \(0.117590\pi\) | |||||||
\(312\) | 2.00000 | − | 3.46410i | 0.113228 | − | 0.196116i | ||||
\(313\) | 14.2361 | + | 24.6576i | 0.804670 | + | 1.39373i | 0.916514 | + | 0.400004i | \(0.130991\pi\) |
−0.111843 | + | 0.993726i | \(0.535675\pi\) | |||||||
\(314\) | −18.6525 | −1.05262 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.52786 | + | 11.3066i | 0.366641 | + | 0.635041i | 0.989038 | − | 0.147660i | \(-0.0471743\pi\) |
−0.622397 | + | 0.782702i | \(0.713841\pi\) | |||||||
\(318\) | 0.763932 | − | 1.32317i | 0.0428392 | − | 0.0741996i | ||||
\(319\) | 2.23607 | − | 3.87298i | 0.125196 | − | 0.216845i | ||||
\(320\) | 1.61803 | + | 2.80252i | 0.0904508 | + | 0.156665i | ||||
\(321\) | −20.9443 | −1.16900 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.8885 | 0.995345 | ||||||||
\(324\) | −12.2082 | − | 21.1452i | −0.678234 | − | 1.17473i | ||||
\(325\) | 3.38197 | − | 5.85774i | 0.187598 | − | 0.324929i | ||||
\(326\) | −3.70820 | + | 6.42280i | −0.205378 | + | 0.355726i | ||||
\(327\) | 16.1803 | + | 28.0252i | 0.894775 | + | 1.54980i | ||||
\(328\) | −6.47214 | −0.357364 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.4721 | −0.576472 | ||||||||
\(331\) | −0.472136 | − | 0.817763i | −0.0259509 | − | 0.0449483i | 0.852758 | − | 0.522306i | \(-0.174928\pi\) |
−0.878709 | + | 0.477357i | \(0.841595\pi\) | |||||||
\(332\) | 5.09017 | − | 8.81643i | 0.279359 | − | 0.483865i | ||||
\(333\) | 40.8885 | − | 70.8210i | 2.24068 | − | 3.88097i | ||||
\(334\) | −7.70820 | − | 13.3510i | −0.421774 | − | 0.730534i | ||||
\(335\) | 49.8885 | 2.72570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 5.73607 | + | 9.93516i | 0.312001 | + | 0.540402i | ||||
\(339\) | −13.7082 | + | 23.7433i | −0.744527 | + | 1.28956i | ||||
\(340\) | 10.4721 | − | 18.1383i | 0.567931 | − | 0.983686i | ||||
\(341\) | 1.00000 | + | 1.73205i | 0.0541530 | + | 0.0937958i | ||||
\(342\) | 20.6525 | 1.11676 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.52786 | −0.0823769 | ||||||||
\(345\) | 20.9443 | + | 36.2765i | 1.12760 | + | 1.95306i | ||||
\(346\) | 0.618034 | − | 1.07047i | 0.0332257 | − | 0.0575486i | ||||
\(347\) | 3.23607 | − | 5.60503i | 0.173721 | − | 0.300894i | −0.765997 | − | 0.642844i | \(-0.777754\pi\) |
0.939718 | + | 0.341950i | \(0.111087\pi\) | |||||||
\(348\) | 7.23607 | + | 12.5332i | 0.387894 | + | 0.671852i | ||||
\(349\) | −8.29180 | −0.443850 | −0.221925 | − | 0.975064i | \(-0.571234\pi\) | ||||
−0.221925 | + | 0.975064i | \(0.571234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −17.4721 | + | 30.2626i | −0.929948 | + | 1.61072i | −0.146544 | + | 0.989204i | \(0.546815\pi\) |
−0.783404 | + | 0.621513i | \(0.786518\pi\) | |||||||
\(354\) | 11.7082 | − | 20.2792i | 0.622284 | − | 1.07783i | ||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.94427 | 0.472719 | ||||||||
\(359\) | 13.4164 | + | 23.2379i | 0.708091 | + | 1.22645i | 0.965564 | + | 0.260164i | \(0.0837767\pi\) |
−0.257473 | + | 0.966285i | \(0.582890\pi\) | |||||||
\(360\) | 12.0902 | − | 20.9408i | 0.637208 | − | 1.10368i | ||||
\(361\) | 5.68034 | − | 9.83864i | 0.298965 | − | 0.517823i | ||||
\(362\) | 2.38197 | + | 4.12569i | 0.125193 | + | 0.216841i | ||||
\(363\) | 3.23607 | 0.169850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.0000 | −0.837478 | ||||||||
\(366\) | −8.47214 | − | 14.6742i | −0.442846 | − | 0.767031i | ||||
\(367\) | 10.7082 | − | 18.5472i | 0.558964 | − | 0.968154i | −0.438620 | − | 0.898673i | \(-0.644532\pi\) |
0.997583 | − | 0.0694807i | \(-0.0221342\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 24.1803 | + | 41.8816i | 1.25878 | + | 2.18027i | ||||
\(370\) | 35.4164 | 1.84121 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.47214 | −0.335565 | ||||||||
\(373\) | 3.00000 | + | 5.19615i | 0.155334 | + | 0.269047i | 0.933181 | − | 0.359408i | \(-0.117021\pi\) |
−0.777847 | + | 0.628454i | \(0.783688\pi\) | |||||||
\(374\) | −3.23607 | + | 5.60503i | −0.167333 | + | 0.289829i | ||||
\(375\) | 2.47214 | − | 4.28187i | 0.127661 | − | 0.221115i | ||||
\(376\) | −1.00000 | − | 1.73205i | −0.0515711 | − | 0.0893237i | ||||
\(377\) | 5.52786 | 0.284699 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.52786 | 0.283947 | 0.141974 | − | 0.989870i | \(-0.454655\pi\) | ||||
0.141974 | + | 0.989870i | \(0.454655\pi\) | |||||||
\(380\) | 4.47214 | + | 7.74597i | 0.229416 | + | 0.397360i | ||||
\(381\) | 19.4164 | − | 33.6302i | 0.994733 | − | 1.72293i | ||||
\(382\) | −3.23607 | + | 5.60503i | −0.165572 | + | 0.286778i | ||||
\(383\) | 5.94427 | + | 10.2958i | 0.303738 | + | 0.526090i | 0.976980 | − | 0.213333i | \(-0.0684319\pi\) |
−0.673241 | + | 0.739423i | \(0.735099\pi\) | |||||||
\(384\) | 3.23607 | 0.165140 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.94427 | 0.149859 | ||||||||
\(387\) | 5.70820 | + | 9.88690i | 0.290164 | + | 0.502579i | ||||
\(388\) | 1.76393 | − | 3.05522i | 0.0895501 | − | 0.155105i | ||||
\(389\) | −3.29180 | + | 5.70156i | −0.166901 | + | 0.289080i | −0.937329 | − | 0.348447i | \(-0.886709\pi\) |
0.770428 | + | 0.637527i | \(0.220043\pi\) | |||||||
\(390\) | −6.47214 | − | 11.2101i | −0.327729 | − | 0.567644i | ||||
\(391\) | 25.8885 | 1.30924 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.8885 | −1.50768 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.73607 | + | 6.47106i | −0.187744 | + | 0.325183i | ||||
\(397\) | −5.14590 | − | 8.91296i | −0.258265 | − | 0.447328i | 0.707512 | − | 0.706701i | \(-0.249818\pi\) |
−0.965777 | + | 0.259373i | \(0.916484\pi\) | |||||||
\(398\) | −1.05573 | −0.0529189 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.47214 | 0.273607 | ||||||||
\(401\) | 15.1803 | + | 26.2931i | 0.758070 | + | 1.31302i | 0.943834 | + | 0.330421i | \(0.107191\pi\) |
−0.185764 | + | 0.982594i | \(0.559476\pi\) | |||||||
\(402\) | 24.9443 | − | 43.2047i | 1.24411 | − | 2.15486i | ||||
\(403\) | −1.23607 | + | 2.14093i | −0.0615729 | + | 0.106647i | ||||
\(404\) | −7.09017 | − | 12.2805i | −0.352749 | − | 0.610979i | ||||
\(405\) | −79.0132 | −3.92620 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9443 | −0.542487 | ||||||||
\(408\) | −10.4721 | − | 18.1383i | −0.518448 | − | 0.897978i | ||||
\(409\) | −11.7082 | + | 20.2792i | −0.578933 | + | 1.00274i | 0.416669 | + | 0.909058i | \(0.363198\pi\) |
−0.995602 | + | 0.0936836i | \(0.970136\pi\) | |||||||
\(410\) | −10.4721 | + | 18.1383i | −0.517182 | + | 0.895785i | ||||
\(411\) | −25.7082 | − | 44.5279i | −1.26809 | − | 2.19640i | ||||
\(412\) | −2.94427 | −0.145054 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 29.8885 | 1.46894 | ||||||||
\(415\) | −16.4721 | − | 28.5306i | −0.808585 | − | 1.40051i | ||||
\(416\) | 0.618034 | − | 1.07047i | 0.0303016 | − | 0.0524839i | ||||
\(417\) | −13.4164 | + | 23.2379i | −0.657004 | + | 1.13796i | ||||
\(418\) | −1.38197 | − | 2.39364i | −0.0675942 | − | 0.117077i | ||||
\(419\) | −12.7639 | −0.623559 | −0.311779 | − | 0.950155i | \(-0.600925\pi\) | ||||
−0.311779 | + | 0.950155i | \(0.600925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.52786 | 0.366886 | 0.183443 | − | 0.983030i | \(-0.441276\pi\) | ||||
0.183443 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(422\) | 11.2361 | + | 19.4614i | 0.546963 | + | 0.947368i | ||||
\(423\) | −7.47214 | + | 12.9421i | −0.363308 | + | 0.629267i | ||||
\(424\) | 0.236068 | − | 0.408882i | 0.0114645 | − | 0.0198571i | ||||
\(425\) | −17.7082 | − | 30.6715i | −0.858974 | − | 1.48779i | ||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.47214 | −0.312842 | ||||||||
\(429\) | 2.00000 | + | 3.46410i | 0.0965609 | + | 0.167248i | ||||
\(430\) | −2.47214 | + | 4.28187i | −0.119217 | + | 0.206490i | ||||
\(431\) | −20.4721 | + | 35.4588i | −0.986108 | + | 1.70799i | −0.349203 | + | 0.937047i | \(0.613548\pi\) |
−0.636905 | + | 0.770942i | \(0.719786\pi\) | |||||||
\(432\) | −7.23607 | − | 12.5332i | −0.348145 | − | 0.603006i | ||||
\(433\) | −19.5279 | −0.938449 | −0.469225 | − | 0.883079i | \(-0.655467\pi\) | ||||
−0.469225 | + | 0.883079i | \(0.655467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 46.8328 | 2.24546 | ||||||||
\(436\) | 5.00000 | + | 8.66025i | 0.239457 | + | 0.414751i | ||||
\(437\) | −5.52786 | + | 9.57454i | −0.264434 | + | 0.458012i | ||||
\(438\) | −8.00000 | + | 13.8564i | −0.382255 | + | 0.662085i | ||||
\(439\) | −4.47214 | − | 7.74597i | −0.213443 | − | 0.369695i | 0.739347 | − | 0.673325i | \(-0.235135\pi\) |
−0.952790 | + | 0.303630i | \(0.901801\pi\) | |||||||
\(440\) | −3.23607 | −0.154273 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.00000 | −0.380521 | ||||||||
\(443\) | 3.52786 | + | 6.11044i | 0.167614 | + | 0.290316i | 0.937580 | − | 0.347768i | \(-0.113060\pi\) |
−0.769967 | + | 0.638084i | \(0.779727\pi\) | |||||||
\(444\) | 17.7082 | − | 30.6715i | 0.840394 | − | 1.45561i | ||||
\(445\) | −16.1803 | + | 28.0252i | −0.767022 | + | 1.32852i | ||||
\(446\) | 4.23607 | + | 7.33708i | 0.200584 | + | 0.347421i | ||||
\(447\) | 72.3607 | 3.42254 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.05573 | 0.0498229 | 0.0249114 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249114 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(450\) | −20.4443 | − | 35.4105i | −0.963752 | − | 1.66927i | ||||
\(451\) | 3.23607 | − | 5.60503i | 0.152380 | − | 0.263931i | ||||
\(452\) | −4.23607 | + | 7.33708i | −0.199248 | + | 0.345107i | ||||
\(453\) | −19.4164 | − | 33.6302i | −0.912262 | − | 1.58008i | ||||
\(454\) | 14.7639 | 0.692906 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.94427 | 0.418854 | ||||||||
\(457\) | −4.52786 | − | 7.84249i | −0.211805 | − | 0.366856i | 0.740475 | − | 0.672084i | \(-0.234601\pi\) |
−0.952279 | + | 0.305228i | \(0.901267\pi\) | |||||||
\(458\) | 6.38197 | − | 11.0539i | 0.298210 | − | 0.516514i | ||||
\(459\) | −46.8328 | + | 81.1168i | −2.18597 | + | 3.78621i | ||||
\(460\) | 6.47214 | + | 11.2101i | 0.301765 | + | 0.522672i | ||||
\(461\) | −29.2361 | −1.36166 | −0.680830 | − | 0.732442i | \(-0.738381\pi\) | ||||
−0.680830 | + | 0.732442i | \(0.738381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5279 | −1.00048 | −0.500242 | − | 0.865885i | \(-0.666756\pi\) | ||||
−0.500242 | + | 0.865885i | \(0.666756\pi\) | |||||||
\(464\) | 2.23607 | + | 3.87298i | 0.103807 | + | 0.179799i | ||||
\(465\) | −10.4721 | + | 18.1383i | −0.485634 | + | 0.841142i | ||||
\(466\) | −1.47214 | + | 2.54981i | −0.0681954 | + | 0.118118i | ||||
\(467\) | 6.56231 | + | 11.3662i | 0.303667 | + | 0.525967i | 0.976964 | − | 0.213405i | \(-0.0684555\pi\) |
−0.673296 | + | 0.739373i | \(0.735122\pi\) | |||||||
\(468\) | −9.23607 | −0.426937 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.47214 | −0.298537 | ||||||||
\(471\) | 30.1803 | + | 52.2739i | 1.39064 | + | 2.40865i | ||||
\(472\) | 3.61803 | − | 6.26662i | 0.166534 | − | 0.288445i | ||||
\(473\) | 0.763932 | − | 1.32317i | 0.0351256 | − | 0.0608394i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.1246 | 0.693965 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.52786 | −0.161530 | ||||||||
\(478\) | −10.0000 | − | 17.3205i | −0.457389 | − | 0.792222i | ||||
\(479\) | −16.1803 | + | 28.0252i | −0.739299 | + | 1.28050i | 0.213513 | + | 0.976940i | \(0.431509\pi\) |
−0.952812 | + | 0.303562i | \(0.901824\pi\) | |||||||
\(480\) | 5.23607 | − | 9.06914i | 0.238993 | − | 0.413948i | ||||
\(481\) | −6.76393 | − | 11.7155i | −0.308409 | − | 0.534180i | ||||
\(482\) | 11.4164 | 0.520003 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −5.70820 | − | 9.88690i | −0.259196 | − | 0.448941i | ||||
\(486\) | −17.7984 | + | 30.8277i | −0.807351 | + | 1.39837i | ||||
\(487\) | 0.472136 | − | 0.817763i | 0.0213945 | − | 0.0370564i | −0.855130 | − | 0.518414i | \(-0.826523\pi\) |
0.876524 | + | 0.481357i | \(0.159856\pi\) | |||||||
\(488\) | −2.61803 | − | 4.53457i | −0.118513 | − | 0.205270i | ||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.944272 | 0.0426144 | 0.0213072 | − | 0.999773i | \(-0.493217\pi\) | ||||
0.0213072 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(492\) | 10.4721 | + | 18.1383i | 0.472120 | + | 0.817736i | ||||
\(493\) | 14.4721 | − | 25.0665i | 0.651792 | − | 1.12894i | ||||
\(494\) | 1.70820 | − | 2.95870i | 0.0768557 | − | 0.133118i | ||||
\(495\) | 12.0902 | + | 20.9408i | 0.543413 | + | 0.941218i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −32.9443 | −1.47627 | ||||||||
\(499\) | −6.18034 | − | 10.7047i | −0.276670 | − | 0.479207i | 0.693885 | − | 0.720086i | \(-0.255898\pi\) |
−0.970555 | + | 0.240879i | \(0.922564\pi\) | |||||||
\(500\) | 0.763932 | − | 1.32317i | 0.0341641 | − | 0.0591739i | ||||
\(501\) | −24.9443 | + | 43.2047i | −1.11443 | + | 1.93025i | ||||
\(502\) | 12.3820 | + | 21.4462i | 0.552634 | + | 0.957190i | ||||
\(503\) | −4.00000 | −0.178351 | −0.0891756 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891756 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.8885 | −2.04201 | ||||||||
\(506\) | −2.00000 | − | 3.46410i | −0.0889108 | − | 0.153998i | ||||
\(507\) | 18.5623 | − | 32.1509i | 0.824381 | − | 1.42787i | ||||
\(508\) | 6.00000 | − | 10.3923i | 0.266207 | − | 0.461084i | ||||
\(509\) | −17.0344 | − | 29.5045i | −0.755038 | − | 1.30776i | −0.945355 | − | 0.326042i | \(-0.894285\pi\) |
0.190317 | − | 0.981723i | \(-0.439048\pi\) | |||||||
\(510\) | −67.7771 | −3.00122 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −20.0000 | − | 34.6410i | −0.883022 | − | 1.52944i | ||||
\(514\) | −5.47214 | + | 9.47802i | −0.241366 | + | 0.418057i | ||||
\(515\) | −4.76393 | + | 8.25137i | −0.209924 | + | 0.363599i | ||||
\(516\) | 2.47214 | + | 4.28187i | 0.108830 | + | 0.188499i | ||||
\(517\) | 2.00000 | 0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | −2.00000 | − | 3.46410i | −0.0877058 | − | 0.151911i | ||||
\(521\) | 17.1803 | − | 29.7572i | 0.752684 | − | 1.30369i | −0.193833 | − | 0.981035i | \(-0.562092\pi\) |
0.946517 | − | 0.322653i | \(-0.104575\pi\) | |||||||
\(522\) | 16.7082 | − | 28.9395i | 0.731298 | − | 1.26665i | ||||
\(523\) | −13.8541 | − | 23.9960i | −0.605798 | − | 1.04927i | −0.991925 | − | 0.126827i | \(-0.959521\pi\) |
0.386127 | − | 0.922446i | \(-0.373813\pi\) | |||||||
\(524\) | −9.23607 | −0.403480 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.9443 | 0.564397 | ||||||||
\(527\) | 6.47214 | + | 11.2101i | 0.281931 | + | 0.488318i | ||||
\(528\) | −1.61803 | + | 2.80252i | −0.0704159 | + | 0.121964i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −0.763932 | − | 1.32317i | −0.0331831 | − | 0.0574748i | ||||
\(531\) | −54.0689 | −2.34639 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | 16.1803 | + | 28.0252i | 0.700192 | + | 1.21277i | ||||
\(535\) | −10.4721 | + | 18.1383i | −0.452750 | + | 0.784186i | ||||
\(536\) | 7.70820 | − | 13.3510i | 0.332944 | − | 0.576675i | ||||
\(537\) | −14.4721 | − | 25.0665i | −0.624519 | − | 1.08170i | ||||
\(538\) | 27.2361 | 1.17423 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −46.8328 | −2.01536 | ||||||||
\(541\) | 4.52786 | + | 7.84249i | 0.194668 | + | 0.337175i | 0.946792 | − | 0.321847i | \(-0.104304\pi\) |
−0.752124 | + | 0.659022i | \(0.770970\pi\) | |||||||
\(542\) | −8.47214 | + | 14.6742i | −0.363909 | + | 0.630310i | ||||
\(543\) | 7.70820 | − | 13.3510i | 0.330791 | − | 0.572946i | ||||
\(544\) | −3.23607 | − | 5.60503i | −0.138745 | − | 0.240314i | ||||
\(545\) | 32.3607 | 1.38618 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9443 | 0.724485 | 0.362242 | − | 0.932084i | \(-0.382011\pi\) | ||||
0.362242 | + | 0.932084i | \(0.382011\pi\) | |||||||
\(548\) | −7.94427 | − | 13.7599i | −0.339362 | − | 0.587793i | ||||
\(549\) | −19.5623 | + | 33.8829i | −0.834899 | + | 1.44609i | ||||
\(550\) | −2.73607 | + | 4.73901i | −0.116666 | + | 0.202072i | ||||
\(551\) | 6.18034 | + | 10.7047i | 0.263291 | + | 0.456034i | ||||
\(552\) | 12.9443 | 0.550945 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.4721 | 0.529890 | ||||||||
\(555\) | −57.3050 | − | 99.2551i | −2.43246 | − | 4.21314i | ||||
\(556\) | −4.14590 | + | 7.18091i | −0.175825 | + | 0.304538i | ||||
\(557\) | 14.4164 | − | 24.9700i | 0.610843 | − | 1.05801i | −0.380256 | − | 0.924881i | \(-0.624164\pi\) |
0.991099 | − | 0.133129i | \(-0.0425026\pi\) | |||||||
\(558\) | 7.47214 | + | 12.9421i | 0.316321 | + | 0.547884i | ||||
\(559\) | 1.88854 | 0.0798769 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9443 | 0.884268 | ||||||||
\(562\) | 12.4164 | + | 21.5058i | 0.523755 | + | 0.907169i | ||||
\(563\) | 13.3820 | − | 23.1782i | 0.563983 | − | 0.976847i | −0.433161 | − | 0.901317i | \(-0.642602\pi\) |
0.997144 | − | 0.0755300i | \(-0.0240648\pi\) | |||||||
\(564\) | −3.23607 | + | 5.60503i | −0.136263 | + | 0.236015i | ||||
\(565\) | 13.7082 | + | 23.7433i | 0.576708 | + | 0.998888i | ||||
\(566\) | 16.6525 | 0.699956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.47214 | −0.103729 | ||||||||
\(569\) | −8.41641 | − | 14.5776i | −0.352834 | − | 0.611127i | 0.633911 | − | 0.773406i | \(-0.281449\pi\) |
−0.986745 | + | 0.162280i | \(0.948115\pi\) | |||||||
\(570\) | 14.4721 | − | 25.0665i | 0.606171 | − | 1.04992i | ||||
\(571\) | 22.9443 | − | 39.7406i | 0.960188 | − | 1.66309i | 0.238165 | − | 0.971225i | \(-0.423454\pi\) |
0.722022 | − | 0.691870i | \(-0.243213\pi\) | |||||||
\(572\) | 0.618034 | + | 1.07047i | 0.0258413 | + | 0.0447584i | ||||
\(573\) | 20.9443 | 0.874960 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.8885 | 0.912815 | ||||||||
\(576\) | −3.73607 | − | 6.47106i | −0.155669 | − | 0.269627i | ||||
\(577\) | 4.52786 | − | 7.84249i | 0.188497 | − | 0.326487i | −0.756252 | − | 0.654280i | \(-0.772972\pi\) |
0.944749 | + | 0.327793i | \(0.106305\pi\) | |||||||
\(578\) | −12.4443 | + | 21.5541i | −0.517613 | + | 0.896533i | ||||
\(579\) | −4.76393 | − | 8.25137i | −0.197982 | − | 0.342915i | ||||
\(580\) | 14.4721 | 0.600923 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.4164 | −0.473225 | ||||||||
\(583\) | 0.236068 | + | 0.408882i | 0.00977694 | + | 0.0169342i | ||||
\(584\) | −2.47214 | + | 4.28187i | −0.102298 | + | 0.177185i | ||||
\(585\) | −14.9443 | + | 25.8842i | −0.617870 | + | 1.07018i | ||||
\(586\) | 2.32624 | + | 4.02916i | 0.0960960 | + | 0.166443i | ||||
\(587\) | 28.1803 | 1.16313 | 0.581564 | − | 0.813501i | \(-0.302441\pi\) | ||||
0.581564 | + | 0.813501i | \(0.302441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.52786 | −0.227772 | ||||||||
\(590\) | −11.7082 | − | 20.2792i | −0.482019 | − | 0.834882i | ||||
\(591\) | −29.1246 | + | 50.4453i | −1.19803 | + | 2.07504i | ||||
\(592\) | 5.47214 | − | 9.47802i | 0.224903 | − | 0.389544i | ||||
\(593\) | 12.0000 | + | 20.7846i | 0.492781 | + | 0.853522i | 0.999965 | − | 0.00831589i | \(-0.00264706\pi\) |
−0.507184 | + | 0.861838i | \(0.669314\pi\) | |||||||
\(594\) | 14.4721 | 0.593799 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.3607 | 0.915929 | ||||||||
\(597\) | 1.70820 | + | 2.95870i | 0.0699121 | + | 0.121091i | ||||
\(598\) | 2.47214 | − | 4.28187i | 0.101093 | − | 0.175098i | ||||
\(599\) | −6.18034 | + | 10.7047i | −0.252522 | + | 0.437381i | −0.964219 | − | 0.265105i | \(-0.914593\pi\) |
0.711698 | + | 0.702486i | \(0.247927\pi\) | |||||||
\(600\) | −8.85410 | − | 15.3358i | −0.361467 | − | 0.626080i | ||||
\(601\) | −18.8328 | −0.768207 | −0.384103 | − | 0.923290i | \(-0.625489\pi\) | ||||
−0.384103 | + | 0.923290i | \(0.625489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −115.193 | −4.69104 | ||||||||
\(604\) | −6.00000 | − | 10.3923i | −0.244137 | − | 0.422857i | ||||
\(605\) | 1.61803 | − | 2.80252i | 0.0657824 | − | 0.113939i | ||||
\(606\) | −22.9443 | + | 39.7406i | −0.932047 | + | 1.61435i | ||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | 2.76393 | 0.112092 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.9443 | −0.686054 | ||||||||
\(611\) | 1.23607 | + | 2.14093i | 0.0500060 | + | 0.0866129i | ||||
\(612\) | −24.1803 | + | 41.8816i | −0.977432 | + | 1.69296i | ||||
\(613\) | −9.76393 | + | 16.9116i | −0.394362 | + | 0.683054i | −0.993019 | − | 0.117951i | \(-0.962368\pi\) |
0.598658 | + | 0.801005i | \(0.295701\pi\) | |||||||
\(614\) | 16.0344 | + | 27.7725i | 0.647097 | + | 1.12081i | ||||
\(615\) | 67.7771 | 2.73304 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.41641 | −0.218056 | −0.109028 | − | 0.994039i | \(-0.534774\pi\) | ||||
−0.109028 | + | 0.994039i | \(0.534774\pi\) | |||||||
\(618\) | 4.76393 | + | 8.25137i | 0.191633 | + | 0.331919i | ||||
\(619\) | −24.2705 | + | 42.0378i | −0.975514 | + | 1.68964i | −0.297286 | + | 0.954788i | \(0.596082\pi\) |
−0.678228 | + | 0.734852i | \(0.737252\pi\) | |||||||
\(620\) | −3.23607 | + | 5.60503i | −0.129964 | + | 0.225104i | ||||
\(621\) | −28.9443 | − | 50.1329i | −1.16149 | − | 2.01177i | ||||
\(622\) | −5.41641 | −0.217178 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 11.2082 | + | 19.4132i | 0.448328 | + | 0.776527i | ||||
\(626\) | 14.2361 | − | 24.6576i | 0.568988 | − | 0.985516i | ||||
\(627\) | −4.47214 | + | 7.74597i | −0.178600 | + | 0.309344i | ||||
\(628\) | 9.32624 | + | 16.1535i | 0.372157 | + | 0.644596i | ||||
\(629\) | −70.8328 | −2.82429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.58359 | −0.182470 | −0.0912350 | − | 0.995829i | \(-0.529081\pi\) | ||||
−0.0912350 | + | 0.995829i | \(0.529081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.3607 | − | 62.9785i | 1.44521 | − | 2.50317i | ||||
\(634\) | 6.52786 | − | 11.3066i | 0.259255 | − | 0.449042i | ||||
\(635\) | −19.4164 | − | 33.6302i | −0.770517 | − | 1.33457i | ||||
\(636\) | −1.52786 | −0.0605838 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.47214 | −0.177054 | ||||||||
\(639\) | 9.23607 | + | 15.9973i | 0.365373 | + | 0.632845i | ||||
\(640\) | 1.61803 | − | 2.80252i | 0.0639584 | − | 0.110779i | ||||
\(641\) | −18.2361 | + | 31.5858i | −0.720281 | + | 1.24756i | 0.240606 | + | 0.970623i | \(0.422654\pi\) |
−0.960887 | + | 0.276941i | \(0.910679\pi\) | |||||||
\(642\) | 10.4721 | + | 18.1383i | 0.413302 | + | 0.715860i | ||||
\(643\) | 23.2361 | 0.916341 | 0.458171 | − | 0.888864i | \(-0.348505\pi\) | ||||
0.458171 | + | 0.888864i | \(0.348505\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.0000 | 0.629999 | ||||||||
\(646\) | −8.94427 | − | 15.4919i | −0.351908 | − | 0.609522i | ||||
\(647\) | 12.4164 | − | 21.5058i | 0.488139 | − | 0.845482i | −0.511768 | − | 0.859124i | \(-0.671009\pi\) |
0.999907 | + | 0.0136418i | \(0.00434244\pi\) | |||||||
\(648\) | −12.2082 | + | 21.1452i | −0.479584 | + | 0.830663i | ||||
\(649\) | 3.61803 | + | 6.26662i | 0.142020 | + | 0.245986i | ||||
\(650\) | −6.76393 | −0.265303 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.41641 | 0.290449 | ||||||||
\(653\) | −0.819660 | − | 1.41969i | −0.0320758 | − | 0.0555569i | 0.849542 | − | 0.527521i | \(-0.176878\pi\) |
−0.881618 | + | 0.471964i | \(0.843545\pi\) | |||||||
\(654\) | 16.1803 | − | 28.0252i | 0.632701 | − | 1.09587i | ||||
\(655\) | −14.9443 | + | 25.8842i | −0.583921 | + | 1.01138i | ||||
\(656\) | 3.23607 | + | 5.60503i | 0.126347 | + | 0.218840i | ||||
\(657\) | 36.9443 | 1.44133 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.4164 | 1.69126 | 0.845632 | − | 0.533767i | \(-0.179224\pi\) | ||||
0.845632 | + | 0.533767i | \(0.179224\pi\) | |||||||
\(660\) | 5.23607 | + | 9.06914i | 0.203814 | + | 0.353016i | ||||
\(661\) | 18.5623 | − | 32.1509i | 0.721990 | − | 1.25052i | −0.238211 | − | 0.971213i | \(-0.576561\pi\) |
0.960201 | − | 0.279310i | \(-0.0901057\pi\) | |||||||
\(662\) | −0.472136 | + | 0.817763i | −0.0183501 | + | 0.0317833i | ||||
\(663\) | 12.9443 | + | 22.4201i | 0.502714 | + | 0.870726i | ||||
\(664\) | −10.1803 | −0.395074 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −81.7771 | −3.16880 | ||||||||
\(667\) | 8.94427 | + | 15.4919i | 0.346324 | + | 0.599850i | ||||
\(668\) | −7.70820 | + | 13.3510i | −0.298239 | + | 0.516566i | ||||
\(669\) | 13.7082 | − | 23.7433i | 0.529990 | − | 0.917969i | ||||
\(670\) | −24.9443 | − | 43.2047i | −0.963681 | − | 1.66914i | ||||
\(671\) | 5.23607 | 0.202136 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8885 | 1.22921 | 0.614607 | − | 0.788834i | \(-0.289315\pi\) | ||||
0.614607 | + | 0.788834i | \(0.289315\pi\) | |||||||
\(674\) | −9.00000 | − | 15.5885i | −0.346667 | − | 0.600445i | ||||
\(675\) | −39.5967 | + | 68.5836i | −1.52408 | + | 2.63978i | ||||
\(676\) | 5.73607 | − | 9.93516i | 0.220618 | − | 0.382122i | ||||
\(677\) | 16.0344 | + | 27.7725i | 0.616254 | + | 1.06738i | 0.990163 | + | 0.139917i | \(0.0446837\pi\) |
−0.373910 | + | 0.927465i | \(0.621983\pi\) | |||||||
\(678\) | 27.4164 | 1.05292 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.9443 | −0.803176 | ||||||||
\(681\) | −23.8885 | − | 41.3762i | −0.915411 | − | 1.58554i | ||||
\(682\) | 1.00000 | − | 1.73205i | 0.0382920 | − | 0.0663237i | ||||
\(683\) | −7.52786 | + | 13.0386i | −0.288046 | + | 0.498910i | −0.973343 | − | 0.229353i | \(-0.926339\pi\) |
0.685297 | + | 0.728263i | \(0.259672\pi\) | |||||||
\(684\) | −10.3262 | − | 17.8856i | −0.394834 | − | 0.683872i | ||||
\(685\) | −51.4164 | −1.96452 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.3050 | −1.57588 | ||||||||
\(688\) | 0.763932 | + | 1.32317i | 0.0291246 | + | 0.0504453i | ||||
\(689\) | −0.291796 | + | 0.505406i | −0.0111165 | + | 0.0192544i | ||||
\(690\) | 20.9443 | − | 36.2765i | 0.797335 | − | 1.38102i | ||||
\(691\) | −9.32624 | − | 16.1535i | −0.354787 | − | 0.614509i | 0.632295 | − | 0.774728i | \(-0.282113\pi\) |
−0.987081 | + | 0.160219i | \(0.948780\pi\) | |||||||
\(692\) | −1.23607 | −0.0469883 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.47214 | −0.245679 | ||||||||
\(695\) | 13.4164 | + | 23.2379i | 0.508913 | + | 0.881464i | ||||
\(696\) | 7.23607 | − | 12.5332i | 0.274282 | − | 0.475071i | ||||
\(697\) | 20.9443 | − | 36.2765i | 0.793321 | − | 1.37407i | ||||
\(698\) | 4.14590 | + | 7.18091i | 0.156925 | + | 0.271801i | ||||
\(699\) | 9.52786 | 0.360377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.7214 | 1.76464 | 0.882321 | − | 0.470649i | \(-0.155980\pi\) | ||||
0.882321 | + | 0.470649i | \(0.155980\pi\) | |||||||
\(702\) | 8.94427 | + | 15.4919i | 0.337580 | + | 0.584705i | ||||
\(703\) | 15.1246 | − | 26.1966i | 0.570436 | − | 0.988023i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 10.4721 | + | 18.1383i | 0.394403 | + | 0.683127i | ||||
\(706\) | 34.9443 | 1.31515 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −23.4164 | −0.880042 | ||||||||
\(709\) | 2.23607 | + | 3.87298i | 0.0839773 | + | 0.145453i | 0.904955 | − | 0.425507i | \(-0.139904\pi\) |
−0.820978 | + | 0.570960i | \(0.806571\pi\) | |||||||
\(710\) | −4.00000 | + | 6.92820i | −0.150117 | + | 0.260011i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.00000 | + | 8.66025i | 0.187383 | + | 0.324557i | ||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | −4.47214 | − | 7.74597i | −0.167132 | − | 0.289480i | ||||
\(717\) | −32.3607 | + | 56.0503i | −1.20853 | + | 2.09324i | ||||
\(718\) | 13.4164 | − | 23.2379i | 0.500696 | − | 0.867231i | ||||
\(719\) | −18.4164 | − | 31.8982i | −0.686816 | − | 1.18960i | −0.972862 | − | 0.231385i | \(-0.925674\pi\) |
0.286046 | − | 0.958216i | \(-0.407659\pi\) | |||||||
\(720\) | −24.1803 | −0.901148 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.3607 | −0.422801 | ||||||||
\(723\) | −18.4721 | − | 31.9947i | −0.686986 | − | 1.18989i | ||||
\(724\) | 2.38197 | − | 4.12569i | 0.0885251 | − | 0.153330i | ||||
\(725\) | 12.2361 | − | 21.1935i | 0.454436 | − | 0.787107i | ||||
\(726\) | −1.61803 | − | 2.80252i | −0.0600509 | − | 0.104011i | ||||
\(727\) | −18.0000 | −0.667583 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 8.00000 | + | 13.8564i | 0.296093 | + | 0.512849i | ||||
\(731\) | 4.94427 | − | 8.56373i | 0.182871 | − | 0.316741i | ||||
\(732\) | −8.47214 | + | 14.6742i | −0.313139 | + | 0.542373i | ||||
\(733\) | 4.43769 | + | 7.68631i | 0.163910 | + | 0.283900i | 0.936268 | − | 0.351287i | \(-0.114256\pi\) |
−0.772358 | + | 0.635188i | \(0.780923\pi\) | |||||||
\(734\) | −21.4164 | −0.790494 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 7.70820 | + | 13.3510i | 0.283935 | + | 0.491790i | ||||
\(738\) | 24.1803 | − | 41.8816i | 0.890091 | − | 1.54168i | ||||
\(739\) | −10.0000 | + | 17.3205i | −0.367856 | + | 0.637145i | −0.989230 | − | 0.146369i | \(-0.953241\pi\) |
0.621374 | + | 0.783514i | \(0.286575\pi\) | |||||||
\(740\) | −17.7082 | − | 30.6715i | −0.650967 | − | 1.12751i | ||||
\(741\) | −11.0557 | −0.406142 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.8885 | −0.509521 | −0.254761 | − | 0.967004i | \(-0.581997\pi\) | ||||
−0.254761 | + | 0.967004i | \(0.581997\pi\) | |||||||
\(744\) | 3.23607 | + | 5.60503i | 0.118640 | + | 0.205491i | ||||
\(745\) | 36.1803 | − | 62.6662i | 1.32555 | − | 2.29591i | ||||
\(746\) | 3.00000 | − | 5.19615i | 0.109838 | − | 0.190245i | ||||
\(747\) | 38.0344 | + | 65.8776i | 1.39161 | + | 2.41033i | ||||
\(748\) | 6.47214 | 0.236645 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.94427 | −0.180539 | ||||||||
\(751\) | −0.472136 | − | 0.817763i | −0.0172285 | − | 0.0298406i | 0.857283 | − | 0.514846i | \(-0.172151\pi\) |
−0.874511 | + | 0.485005i | \(0.838818\pi\) | |||||||
\(752\) | −1.00000 | + | 1.73205i | −0.0364662 | + | 0.0631614i | ||||
\(753\) | 40.0689 | − | 69.4013i | 1.46019 | − | 2.52913i | ||||
\(754\) | −2.76393 | − | 4.78727i | −0.100656 | − | 0.174342i | ||||
\(755\) | −38.8328 | −1.41327 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3050 | 1.42856 | 0.714281 | − | 0.699859i | \(-0.246754\pi\) | ||||
0.714281 | + | 0.699859i | \(0.246754\pi\) | |||||||
\(758\) | −2.76393 | − | 4.78727i | −0.100391 | − | 0.173882i | ||||
\(759\) | −6.47214 | + | 11.2101i | −0.234924 | + | 0.406900i | ||||
\(760\) | 4.47214 | − | 7.74597i | 0.162221 | − | 0.280976i | ||||
\(761\) | 7.70820 | + | 13.3510i | 0.279422 | + | 0.483973i | 0.971241 | − | 0.238097i | \(-0.0765238\pi\) |
−0.691819 | + | 0.722071i | \(0.743190\pi\) | |||||||
\(762\) | −38.8328 | −1.40676 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.47214 | 0.234154 | ||||||||
\(765\) | 78.2492 | + | 135.532i | 2.82911 | + | 4.90016i | ||||
\(766\) | 5.94427 | − | 10.2958i | 0.214775 | − | 0.372002i | ||||
\(767\) | −4.47214 | + | 7.74597i | −0.161479 | + | 0.279691i | ||||
\(768\) | −1.61803 | − | 2.80252i | −0.0583858 | − | 0.101127i | ||||
\(769\) | 16.5836 | 0.598020 | 0.299010 | − | 0.954250i | \(-0.403344\pi\) | ||||
0.299010 | + | 0.954250i | \(0.403344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.4164 | 1.27549 | ||||||||
\(772\) | −1.47214 | − | 2.54981i | −0.0529833 | − | 0.0917698i | ||||
\(773\) | 1.14590 | − | 1.98475i | 0.0412151 | − | 0.0713866i | −0.844682 | − | 0.535268i | \(-0.820210\pi\) |
0.885897 | + | 0.463882i | \(0.153544\pi\) | |||||||
\(774\) | 5.70820 | − | 9.88690i | 0.205177 | − | 0.355377i | ||||
\(775\) | 5.47214 | + | 9.47802i | 0.196565 | + | 0.340460i | ||||
\(776\) | −3.52786 | −0.126643 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.58359 | 0.236033 | ||||||||
\(779\) | 8.94427 | + | 15.4919i | 0.320462 | + | 0.555056i | ||||
\(780\) | −6.47214 | + | 11.2101i | −0.231740 | + | 0.401385i | ||||
\(781\) | 1.23607 | − | 2.14093i | 0.0442300 | − | 0.0766086i | ||||
\(782\) | −12.9443 | − | 22.4201i | −0.462886 | − | 0.801742i | ||||
\(783\) | −64.7214 | −2.31295 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.3607 | 2.15437 | ||||||||
\(786\) | 14.9443 | + | 25.8842i | 0.533045 | + | 0.923260i | ||||
\(787\) | −2.90983 | + | 5.03997i | −0.103724 | + | 0.179656i | −0.913216 | − | 0.407475i | \(-0.866409\pi\) |
0.809492 | + | 0.587131i | \(0.199743\pi\) | |||||||
\(788\) | −9.00000 | + | 15.5885i | −0.320612 | + | 0.555316i | ||||
\(789\) | −20.9443 | − | 36.2765i | −0.745636 | − | 1.29148i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.47214 | 0.265511 | ||||||||
\(793\) | 3.23607 | + | 5.60503i | 0.114916 | + | 0.199041i | ||||
\(794\) | −5.14590 | + | 8.91296i | −0.182621 | + | 0.316309i | ||||
\(795\) | −2.47214 | + | 4.28187i | −0.0876776 | + | 0.151862i | ||||
\(796\) | 0.527864 | + | 0.914287i | 0.0187096 | + | 0.0324061i | ||||
\(797\) | −7.59675 | −0.269091 | −0.134545 | − | 0.990907i | \(-0.542957\pi\) | ||||
−0.134545 | + | 0.990907i | \(0.542957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9443 | 0.457935 | ||||||||
\(800\) | −2.73607 | − | 4.73901i | −0.0967346 | − | 0.167549i | ||||
\(801\) | 37.3607 | − | 64.7106i | 1.32007 | − | 2.28644i | ||||
\(802\) | 15.1803 | − | 26.2931i | 0.536036 | − | 0.928442i | ||||
\(803\) | −2.47214 | − | 4.28187i | −0.0872398 | − | 0.151104i | ||||
\(804\) | −49.8885 | −1.75943 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.47214 | 0.0870773 | ||||||||
\(807\) | −44.0689 | − | 76.3295i | −1.55130 | − | 2.68693i | ||||
\(808\) | −7.09017 | + | 12.2805i | −0.249431 | + | 0.432028i | ||||
\(809\) | 19.4721 | − | 33.7267i | 0.684604 | − | 1.18577i | −0.288957 | − | 0.957342i | \(-0.593309\pi\) |
0.973561 | − | 0.228427i | \(-0.0733581\pi\) | |||||||
\(810\) | 39.5066 | + | 68.4274i | 1.38812 | + | 2.40429i | ||||
\(811\) | −9.23607 | −0.324322 | −0.162161 | − | 0.986764i | \(-0.551846\pi\) | ||||
−0.162161 | + | 0.986764i | \(0.551846\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 54.8328 | 1.92307 | ||||||||
\(814\) | 5.47214 | + | 9.47802i | 0.191798 | + | 0.332204i | ||||
\(815\) | 12.0000 | − | 20.7846i | 0.420342 | − | 0.728053i | ||||
\(816\) | −10.4721 | + | 18.1383i | −0.366598 | + | 0.634967i | ||||
\(817\) | 2.11146 | + | 3.65715i | 0.0738705 | + | 0.127947i | ||||
\(818\) | 23.4164 | 0.818736 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.9443 | 0.731406 | ||||||||
\(821\) | −12.7082 | − | 22.0113i | −0.443519 | − | 0.768198i | 0.554428 | − | 0.832231i | \(-0.312937\pi\) |
−0.997948 | + | 0.0640333i | \(0.979604\pi\) | |||||||
\(822\) | −25.7082 | + | 44.5279i | −0.896677 | + | 1.55309i | ||||
\(823\) | −17.1246 | + | 29.6607i | −0.596926 | + | 1.03391i | 0.396345 | + | 0.918101i | \(0.370278\pi\) |
−0.993272 | + | 0.115805i | \(0.963055\pi\) | |||||||
\(824\) | 1.47214 | + | 2.54981i | 0.0512843 | + | 0.0888270i | ||||
\(825\) | 17.7082 | 0.616521 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.944272 | −0.0328356 | −0.0164178 | − | 0.999865i | \(-0.505226\pi\) | ||||
−0.0164178 | + | 0.999865i | \(0.505226\pi\) | |||||||
\(828\) | −14.9443 | − | 25.8842i | −0.519349 | − | 0.899539i | ||||
\(829\) | −0.854102 | + | 1.47935i | −0.0296642 | + | 0.0513799i | −0.880476 | − | 0.474090i | \(-0.842777\pi\) |
0.850812 | + | 0.525470i | \(0.176110\pi\) | |||||||
\(830\) | −16.4721 | + | 28.5306i | −0.571756 | + | 0.990311i | ||||
\(831\) | −20.1803 | − | 34.9534i | −0.700048 | − | 1.21252i | ||||
\(832\) | −1.23607 | −0.0428529 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 26.8328 | 0.929144 | ||||||||
\(835\) | 24.9443 | + | 43.2047i | 0.863232 | + | 1.49516i | ||||
\(836\) | −1.38197 | + | 2.39364i | −0.0477963 | + | 0.0827856i | ||||
\(837\) | 14.4721 | − | 25.0665i | 0.500230 | − | 0.866424i | ||||
\(838\) | 6.38197 | + | 11.0539i | 0.220461 | + | 0.381850i | ||||
\(839\) | 36.8328 | 1.27161 | 0.635805 | − | 0.771850i | \(-0.280668\pi\) | ||||
0.635805 | + | 0.771850i | \(0.280668\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | −3.76393 | − | 6.51932i | −0.129714 | − | 0.224671i | ||||
\(843\) | 40.1803 | − | 69.5944i | 1.38388 | − | 2.39696i | ||||
\(844\) | 11.2361 | − | 19.4614i | 0.386761 | − | 0.669890i | ||||
\(845\) | −18.5623 | − | 32.1509i | −0.638563 | − | 1.10602i | ||||
\(846\) | 14.9443 | 0.513795 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | −26.9443 | − | 46.6688i | −0.924725 | − | 1.60167i | ||||
\(850\) | −17.7082 | + | 30.6715i | −0.607386 | + | 1.05202i | ||||
\(851\) | 21.8885 | − | 37.9121i | 0.750330 | − | 1.29961i | ||||
\(852\) | 4.00000 | + | 6.92820i | 0.137038 | + | 0.237356i | ||||
\(853\) | 34.5410 | 1.18266 | 0.591331 | − | 0.806429i | \(-0.298603\pi\) | ||||
0.591331 | + | 0.806429i | \(0.298603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −66.8328 | −2.28563 | ||||||||
\(856\) | 3.23607 | + | 5.60503i | 0.110607 | + | 0.191576i | ||||
\(857\) | −18.7639 | + | 32.5001i | −0.640964 | + | 1.11018i | 0.344254 | + | 0.938876i | \(0.388132\pi\) |
−0.985218 | + | 0.171305i | \(0.945202\pi\) | |||||||
\(858\) | 2.00000 | − | 3.46410i | 0.0682789 | − | 0.118262i | ||||
\(859\) | −12.5623 | − | 21.7586i | −0.428620 | − | 0.742392i | 0.568131 | − | 0.822938i | \(-0.307667\pi\) |
−0.996751 | + | 0.0805462i | \(0.974334\pi\) | |||||||
\(860\) | 4.94427 | 0.168598 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.9443 | 1.39457 | ||||||||
\(863\) | −13.7082 | − | 23.7433i | −0.466633 | − | 0.808232i | 0.532641 | − | 0.846341i | \(-0.321200\pi\) |
−0.999274 | + | 0.0381098i | \(0.987866\pi\) | |||||||
\(864\) | −7.23607 | + | 12.5332i | −0.246176 | + | 0.426389i | ||||
\(865\) | −2.00000 | + | 3.46410i | −0.0680020 | + | 0.117783i | ||||
\(866\) | 9.76393 | + | 16.9116i | 0.331792 | + | 0.574680i | ||||
\(867\) | 80.5410 | 2.73532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −23.4164 | − | 40.5584i | −0.793891 | − | 1.37506i | ||||
\(871\) | −9.52786 | + | 16.5027i | −0.322839 | + | 0.559174i | ||||
\(872\) | 5.00000 | − | 8.66025i | 0.169321 | − | 0.293273i | ||||
\(873\) | 13.1803 | + | 22.8290i | 0.446087 | + | 0.772645i | ||||
\(874\) | 11.0557 | 0.373966 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | −13.4721 | − | 23.3344i | −0.454922 | − | 0.787948i | 0.543762 | − | 0.839239i | \(-0.316999\pi\) |
−0.998684 | + | 0.0512920i | \(0.983666\pi\) | |||||||
\(878\) | −4.47214 | + | 7.74597i | −0.150927 | + | 0.261414i | ||||
\(879\) | 7.52786 | − | 13.0386i | 0.253909 | − | 0.439783i | ||||
\(880\) | 1.61803 | + | 2.80252i | 0.0545439 | + | 0.0944728i | ||||
\(881\) | 24.8328 | 0.836639 | 0.418319 | − | 0.908300i | \(-0.362619\pi\) | ||||
0.418319 | + | 0.908300i | \(0.362619\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.8328 | 1.71066 | 0.855330 | − | 0.518083i | \(-0.173354\pi\) | ||||
0.855330 | + | 0.518083i | \(0.173354\pi\) | |||||||
\(884\) | 4.00000 | + | 6.92820i | 0.134535 | + | 0.233021i | ||||
\(885\) | −37.8885 | + | 65.6249i | −1.27361 | + | 2.20596i | ||||
\(886\) | 3.52786 | − | 6.11044i | 0.118521 | − | 0.205284i | ||||
\(887\) | 0.180340 | + | 0.312358i | 0.00605522 | + | 0.0104880i | 0.869037 | − | 0.494747i | \(-0.164739\pi\) |
−0.862982 | + | 0.505235i | \(0.831406\pi\) | |||||||
\(888\) | −35.4164 | −1.18850 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32.3607 | 1.08473 | ||||||||
\(891\) | −12.2082 | − | 21.1452i | −0.408990 | − | 0.708392i | ||||
\(892\) | 4.23607 | − | 7.33708i | 0.141834 | − | 0.245664i | ||||
\(893\) | −2.76393 | + | 4.78727i | −0.0924915 | + | 0.160200i | ||||
\(894\) | −36.1803 | − | 62.6662i | −1.21005 | − | 2.09587i | ||||
\(895\) | −28.9443 | −0.967500 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | −0.527864 | − | 0.914287i | −0.0176151 | − | 0.0305102i | ||||
\(899\) | −4.47214 | + | 7.74597i | −0.149154 | + | 0.258342i | ||||
\(900\) | −20.4443 | + | 35.4105i | −0.681476 | + | 1.18035i | ||||
\(901\) | 1.52786 | + | 2.64634i | 0.0509005 | + | 0.0881623i | ||||
\(902\) | −6.47214 | −0.215499 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.47214 | 0.281779 | ||||||||
\(905\) | −7.70820 | − | 13.3510i | −0.256229 | − | 0.443802i | ||||
\(906\) | −19.4164 | + | 33.6302i | −0.645067 | + | 1.11729i | ||||
\(907\) | −10.1803 | + | 17.6329i | −0.338033 | + | 0.585490i | −0.984063 | − | 0.177822i | \(-0.943095\pi\) |
0.646030 | + | 0.763312i | \(0.276428\pi\) | |||||||
\(908\) | −7.38197 | − | 12.7859i | −0.244979 | − | 0.424316i | ||||
\(909\) | 105.957 | 3.51439 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0000 | −0.927681 | −0.463841 | − | 0.885919i | \(-0.653529\pi\) | ||||
−0.463841 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(912\) | −4.47214 | − | 7.74597i | −0.148087 | − | 0.256495i | ||||
\(913\) | 5.09017 | − | 8.81643i | 0.168460 | − | 0.291781i | ||||
\(914\) | −4.52786 | + | 7.84249i | −0.149768 | + | 0.259407i | ||||
\(915\) | 27.4164 | + | 47.4866i | 0.906358 | + | 1.56986i | ||||
\(916\) | −12.7639 | −0.421732 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 93.6656 | 3.09143 | ||||||||
\(919\) | 28.9443 | + | 50.1329i | 0.954783 | + | 1.65373i | 0.734863 | + | 0.678216i | \(0.237246\pi\) |
0.219920 | + | 0.975518i | \(0.429420\pi\) | |||||||
\(920\) | 6.47214 | − | 11.2101i | 0.213380 | − | 0.369585i | ||||
\(921\) | 51.8885 | − | 89.8736i | 1.70979 | − | 2.96144i | ||||
\(922\) | 14.6180 | + | 25.3192i | 0.481419 | + | 0.833843i | ||||
\(923\) | 3.05573 | 0.100581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.8885 | −1.96912 | ||||||||
\(926\) | 10.7639 | + | 18.6437i | 0.353725 | + | 0.612669i | ||||
\(927\) | 11.0000 | − | 19.0526i | 0.361287 | − | 0.625768i | ||||
\(928\) | 2.23607 | − | 3.87298i | 0.0734025 | − | 0.127137i | ||||
\(929\) | −20.1246 | − | 34.8569i | −0.660267 | − | 1.14362i | −0.980545 | − | 0.196293i | \(-0.937110\pi\) |
0.320278 | − | 0.947324i | \(-0.396224\pi\) | |||||||
\(930\) | 20.9443 | 0.686790 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.94427 | 0.0964428 | ||||||||
\(933\) | 8.76393 | + | 15.1796i | 0.286918 | + | 0.496957i | ||||
\(934\) | 6.56231 | − | 11.3662i | 0.214725 | − | 0.371915i | ||||
\(935\) | 10.4721 | − | 18.1383i | 0.342475 | − | 0.593185i | ||||
\(936\) | 4.61803 | + | 7.99867i | 0.150945 | + | 0.261445i | ||||
\(937\) | 20.9443 | 0.684220 | 0.342110 | − | 0.939660i | \(-0.388859\pi\) | ||||
0.342110 | + | 0.939660i | \(0.388859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −92.1378 | −3.00680 | ||||||||
\(940\) | 3.23607 | + | 5.60503i | 0.105549 | + | 0.182816i | ||||
\(941\) | −17.0902 | + | 29.6010i | −0.557124 | + | 0.964966i | 0.440611 | + | 0.897698i | \(0.354762\pi\) |
−0.997735 | + | 0.0672684i | \(0.978572\pi\) | |||||||
\(942\) | 30.1803 | − | 52.2739i | 0.983329 | − | 1.70318i | ||||
\(943\) | 12.9443 | + | 22.4201i | 0.421523 | + | 0.730100i | ||||
\(944\) | −7.23607 | −0.235514 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.52786 | −0.0496751 | ||||||||
\(947\) | 0.472136 | + | 0.817763i | 0.0153424 | + | 0.0265737i | 0.873595 | − | 0.486654i | \(-0.161783\pi\) |
−0.858252 | + | 0.513228i | \(0.828450\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.05573 | − | 5.29268i | 0.0991931 | − | 0.171808i | ||||
\(950\) | −7.56231 | − | 13.0983i | −0.245354 | − | 0.424965i | ||||
\(951\) | −42.2492 | −1.37002 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.05573 | 0.163771 | 0.0818855 | − | 0.996642i | \(-0.473906\pi\) | ||||
0.0818855 | + | 0.996642i | \(0.473906\pi\) | |||||||
\(954\) | 1.76393 | + | 3.05522i | 0.0571094 | + | 0.0989164i | ||||
\(955\) | 10.4721 | − | 18.1383i | 0.338870 | − | 0.586941i | ||||
\(956\) | −10.0000 | + | 17.3205i | −0.323423 | + | 0.560185i | ||||
\(957\) | 7.23607 | + | 12.5332i | 0.233909 | + | 0.405142i | ||||
\(958\) | 32.3607 | 1.04553 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.4721 | −0.337987 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −6.76393 | + | 11.7155i | −0.218078 | + | 0.377722i | ||||
\(963\) | 24.1803 | − | 41.8816i | 0.779201 | − | 1.34961i | ||||
\(964\) | −5.70820 | − | 9.88690i | −0.183849 | − | 0.318436i | ||||
\(965\) | −9.52786 | −0.306713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.1115 | 0.325163 | 0.162581 | − | 0.986695i | \(-0.448018\pi\) | ||||
0.162581 | + | 0.986695i | \(0.448018\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | −28.9443 | + | 50.1329i | −0.929824 | + | 1.61050i | ||||
\(970\) | −5.70820 | + | 9.88690i | −0.183279 | + | 0.317449i | ||||
\(971\) | −8.27051 | − | 14.3249i | −0.265413 | − | 0.459709i | 0.702259 | − | 0.711922i | \(-0.252175\pi\) |
−0.967672 | + | 0.252213i | \(0.918842\pi\) | |||||||
\(972\) | 35.5967 | 1.14177 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.944272 | −0.0302564 | ||||||||
\(975\) | 10.9443 | + | 18.9560i | 0.350497 | + | 0.607079i | ||||
\(976\) | −2.61803 | + | 4.53457i | −0.0838012 | + | 0.145148i | ||||
\(977\) | −12.4164 | + | 21.5058i | −0.397236 | + | 0.688033i | −0.993384 | − | 0.114842i | \(-0.963364\pi\) |
0.596148 | + | 0.802875i | \(0.296697\pi\) | |||||||
\(978\) | −12.0000 | − | 20.7846i | −0.383718 | − | 0.664619i | ||||
\(979\) | −10.0000 | −0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −74.7214 | −2.38567 | ||||||||
\(982\) | −0.472136 | − | 0.817763i | −0.0150665 | − | 0.0260959i | ||||
\(983\) | 7.00000 | − | 12.1244i | 0.223265 | − | 0.386707i | −0.732532 | − | 0.680732i | \(-0.761662\pi\) |
0.955798 | + | 0.294025i | \(0.0949950\pi\) | |||||||
\(984\) | 10.4721 | − | 18.1383i | 0.333840 | − | 0.578227i | ||||
\(985\) | 29.1246 | + | 50.4453i | 0.927987 | + | 1.60732i | ||||
\(986\) | −28.9443 | −0.921773 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.41641 | −0.108690 | ||||||||
\(989\) | 3.05573 | + | 5.29268i | 0.0971665 | + | 0.168297i | ||||
\(990\) | 12.0902 | − | 20.9408i | 0.384251 | − | 0.665542i | ||||
\(991\) | −22.1803 | + | 38.4175i | −0.704582 | + | 1.22037i | 0.262261 | + | 0.964997i | \(0.415532\pi\) |
−0.966842 | + | 0.255374i | \(0.917801\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | 3.05573 | 0.0969706 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.41641 | 0.108307 | ||||||||
\(996\) | 16.4721 | + | 28.5306i | 0.521940 | + | 0.904026i | ||||
\(997\) | 0.909830 | − | 1.57587i | 0.0288146 | − | 0.0499084i | −0.851259 | − | 0.524747i | \(-0.824160\pi\) |
0.880073 | + | 0.474838i | \(0.157493\pi\) | |||||||
\(998\) | −6.18034 | + | 10.7047i | −0.195635 | + | 0.338850i | ||||
\(999\) | 79.1935 | + | 137.167i | 2.50557 | + | 4.33978i |
(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 | 1078.2.e.n.67.1 | 4 | ||
7.2 | even | 3 | inner | 1078.2.e.n.177.1 | 4 | ||
7.3 | odd | 6 | 154.2.a.d.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 1078.2.a.w.1.2 | 2 | |||
7.5 | odd | 6 | 1078.2.e.q.177.2 | 4 | |||
7.6 | odd | 2 | 1078.2.e.q.67.2 | 4 | |||
21.11 | odd | 6 | 9702.2.a.cu.1.2 | 2 | |||
21.17 | even | 6 | 1386.2.a.m.1.1 | 2 | |||
28.3 | even | 6 | 1232.2.a.p.1.2 | 2 | |||
28.11 | odd | 6 | 8624.2.a.bf.1.1 | 2 | |||
35.3 | even | 12 | 3850.2.c.q.1849.1 | 4 | |||
35.17 | even | 12 | 3850.2.c.q.1849.4 | 4 | |||
35.24 | odd | 6 | 3850.2.a.bj.1.2 | 2 | |||
56.3 | even | 6 | 4928.2.a.bk.1.1 | 2 | |||
56.45 | odd | 6 | 4928.2.a.bt.1.2 | 2 | |||
77.10 | even | 6 | 1694.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.a.d.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
1078.2.a.w.1.2 | 2 | 7.4 | even | 3 | |||
1078.2.e.n.67.1 | 4 | 1.1 | even | 1 | trivial | ||
1078.2.e.n.177.1 | 4 | 7.2 | even | 3 | inner | ||
1078.2.e.q.67.2 | 4 | 7.6 | odd | 2 | |||
1078.2.e.q.177.2 | 4 | 7.5 | odd | 6 | |||
1232.2.a.p.1.2 | 2 | 28.3 | even | 6 | |||
1386.2.a.m.1.1 | 2 | 21.17 | even | 6 | |||
1694.2.a.l.1.1 | 2 | 77.10 | even | 6 | |||
3850.2.a.bj.1.2 | 2 | 35.24 | odd | 6 | |||
3850.2.c.q.1849.1 | 4 | 35.3 | even | 12 | |||
3850.2.c.q.1849.4 | 4 | 35.17 | even | 12 | |||
4928.2.a.bk.1.1 | 2 | 56.3 | even | 6 | |||
4928.2.a.bt.1.2 | 2 | 56.45 | odd | 6 | |||
8624.2.a.bf.1.1 | 2 | 28.11 | odd | 6 | |||
9702.2.a.cu.1.2 | 2 | 21.11 | odd | 6 |