Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(461,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.461");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.461 |
Dual form | 483.2.d.b.461.1 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803i | 1.14412i | 0.820211 | + | 0.572061i | \(0.193856\pi\) | ||||
−0.820211 | + | 0.572061i | \(0.806144\pi\) | |||||||
\(3\) | −0.618034 | − | 1.61803i | −0.356822 | − | 0.934172i | ||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | 2.61803 | 1.17082 | 0.585410 | − | 0.810737i | \(-0.300933\pi\) | ||||
0.585410 | + | 0.810737i | \(0.300933\pi\) | |||||||
\(6\) | 2.61803 | − | 1.00000i | 1.06881 | − | 0.408248i | ||||
\(7\) | 2.61803 | − | 0.381966i | 0.989524 | − | 0.144370i | ||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | −2.23607 | + | 2.00000i | −0.745356 | + | 0.666667i | ||||
\(10\) | 4.23607i | 1.33956i | ||||||||
\(11\) | − | 2.23607i | − | 0.674200i | −0.941469 | − | 0.337100i | \(-0.890554\pi\) | ||
0.941469 | − | 0.337100i | \(-0.109446\pi\) | |||||||
\(12\) | 0.381966 | + | 1.00000i | 0.110264 | + | 0.288675i | ||||
\(13\) | − | 6.85410i | − | 1.90099i | −0.310746 | − | 0.950493i | \(-0.600579\pi\) | ||
0.310746 | − | 0.950493i | \(-0.399421\pi\) | |||||||
\(14\) | 0.618034 | + | 4.23607i | 0.165177 | + | 1.13214i | ||||
\(15\) | −1.61803 | − | 4.23607i | −0.417775 | − | 1.09375i | ||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 1.47214 | 0.357045 | 0.178523 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178523 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(18\) | −3.23607 | − | 3.61803i | −0.762749 | − | 0.852779i | ||||
\(19\) | 5.47214i | 1.25539i | 0.778458 | + | 0.627697i | \(0.216002\pi\) | ||||
−0.778458 | + | 0.627697i | \(0.783998\pi\) | |||||||
\(20\) | −1.61803 | −0.361803 | ||||||||
\(21\) | −2.23607 | − | 4.00000i | −0.487950 | − | 0.872872i | ||||
\(22\) | 3.61803 | 0.771367 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 3.61803 | − | 1.38197i | 0.738528 | − | 0.282093i | ||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | 11.0902 | 2.17496 | ||||||||
\(27\) | 4.61803 | + | 2.38197i | 0.888741 | + | 0.458410i | ||||
\(28\) | −1.61803 | + | 0.236068i | −0.305780 | + | 0.0446127i | ||||
\(29\) | 1.76393i | 0.327554i | 0.986497 | + | 0.163777i | \(0.0523677\pi\) | ||||
−0.986497 | + | 0.163777i | \(0.947632\pi\) | |||||||
\(30\) | 6.85410 | − | 2.61803i | 1.25138 | − | 0.477985i | ||||
\(31\) | 0.527864i | 0.0948072i | 0.998876 | + | 0.0474036i | \(0.0150947\pi\) | ||||
−0.998876 | + | 0.0474036i | \(0.984905\pi\) | |||||||
\(32\) | − | 3.38197i | − | 0.597853i | ||||||
\(33\) | −3.61803 | + | 1.38197i | −0.629819 | + | 0.240569i | ||||
\(34\) | 2.38197i | 0.408504i | ||||||||
\(35\) | 6.85410 | − | 1.00000i | 1.15855 | − | 0.169031i | ||||
\(36\) | 1.38197 | − | 1.23607i | 0.230328 | − | 0.206011i | ||||
\(37\) | 5.76393 | 0.947585 | 0.473792 | − | 0.880637i | \(-0.342885\pi\) | ||||
0.473792 | + | 0.880637i | \(0.342885\pi\) | |||||||
\(38\) | −8.85410 | −1.43633 | ||||||||
\(39\) | −11.0902 | + | 4.23607i | −1.77585 | + | 0.678314i | ||||
\(40\) | 5.85410i | 0.925615i | ||||||||
\(41\) | 0.236068 | 0.0368676 | 0.0184338 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184338 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(42\) | 6.47214 | − | 3.61803i | 0.998672 | − | 0.558275i | ||||
\(43\) | 7.61803 | 1.16174 | 0.580870 | − | 0.813997i | \(-0.302713\pi\) | ||||
0.580870 | + | 0.813997i | \(0.302713\pi\) | |||||||
\(44\) | 1.38197i | 0.208339i | ||||||||
\(45\) | −5.85410 | + | 5.23607i | −0.872678 | + | 0.780547i | ||||
\(46\) | 1.61803 | 0.238566 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 3.00000 | + | 7.85410i | 0.433013 | + | 1.13364i | ||||
\(49\) | 6.70820 | − | 2.00000i | 0.958315 | − | 0.285714i | ||||
\(50\) | 3.00000i | 0.424264i | ||||||||
\(51\) | −0.909830 | − | 2.38197i | −0.127402 | − | 0.333542i | ||||
\(52\) | 4.23607i | 0.587437i | ||||||||
\(53\) | 13.5623i | 1.86293i | 0.363836 | + | 0.931463i | \(0.381467\pi\) | ||||
−0.363836 | + | 0.931463i | \(0.618533\pi\) | |||||||
\(54\) | −3.85410 | + | 7.47214i | −0.524477 | + | 1.01683i | ||||
\(55\) | − | 5.85410i | − | 0.789367i | ||||||
\(56\) | 0.854102 | + | 5.85410i | 0.114134 | + | 0.782287i | ||||
\(57\) | 8.85410 | − | 3.38197i | 1.17275 | − | 0.447952i | ||||
\(58\) | −2.85410 | −0.374762 | ||||||||
\(59\) | −7.56231 | −0.984528 | −0.492264 | − | 0.870446i | \(-0.663831\pi\) | ||||
−0.492264 | + | 0.870446i | \(0.663831\pi\) | |||||||
\(60\) | 1.00000 | + | 2.61803i | 0.129099 | + | 0.337987i | ||||
\(61\) | 0.854102i | 0.109357i | 0.998504 | + | 0.0546783i | \(0.0174133\pi\) | ||||
−0.998504 | + | 0.0546783i | \(0.982587\pi\) | |||||||
\(62\) | −0.854102 | −0.108471 | ||||||||
\(63\) | −5.09017 | + | 6.09017i | −0.641301 | + | 0.767289i | ||||
\(64\) | −4.23607 | −0.529508 | ||||||||
\(65\) | − | 17.9443i | − | 2.22571i | ||||||
\(66\) | −2.23607 | − | 5.85410i | −0.275241 | − | 0.720590i | ||||
\(67\) | −10.6180 | −1.29720 | −0.648600 | − | 0.761130i | \(-0.724645\pi\) | ||||
−0.648600 | + | 0.761130i | \(0.724645\pi\) | |||||||
\(68\) | −0.909830 | −0.110333 | ||||||||
\(69\) | −1.61803 | + | 0.618034i | −0.194788 | + | 0.0744025i | ||||
\(70\) | 1.61803 | + | 11.0902i | 0.193392 | + | 1.32553i | ||||
\(71\) | − | 5.32624i | − | 0.632108i | −0.948741 | − | 0.316054i | \(-0.897642\pi\) | ||
0.948741 | − | 0.316054i | \(-0.102358\pi\) | |||||||
\(72\) | −4.47214 | − | 5.00000i | −0.527046 | − | 0.589256i | ||||
\(73\) | − | 8.23607i | − | 0.963959i | −0.876183 | − | 0.481979i | \(-0.839918\pi\) | ||
0.876183 | − | 0.481979i | \(-0.160082\pi\) | |||||||
\(74\) | 9.32624i | 1.08415i | ||||||||
\(75\) | −1.14590 | − | 3.00000i | −0.132317 | − | 0.346410i | ||||
\(76\) | − | 3.38197i | − | 0.387938i | ||||||
\(77\) | −0.854102 | − | 5.85410i | −0.0973340 | − | 0.667137i | ||||
\(78\) | −6.85410 | − | 17.9443i | −0.776074 | − | 2.03179i | ||||
\(79\) | −7.76393 | −0.873511 | −0.436755 | − | 0.899580i | \(-0.643872\pi\) | ||||
−0.436755 | + | 0.899580i | \(0.643872\pi\) | |||||||
\(80\) | −12.7082 | −1.42082 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 0.381966i | 0.0421811i | ||||||||
\(83\) | −10.7082 | −1.17538 | −0.587689 | − | 0.809087i | \(-0.699962\pi\) | ||||
−0.587689 | + | 0.809087i | \(0.699962\pi\) | |||||||
\(84\) | 1.38197 | + | 2.47214i | 0.150785 | + | 0.269732i | ||||
\(85\) | 3.85410 | 0.418036 | ||||||||
\(86\) | 12.3262i | 1.32917i | ||||||||
\(87\) | 2.85410 | − | 1.09017i | 0.305992 | − | 0.116878i | ||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 8.09017 | 0.857556 | 0.428778 | − | 0.903410i | \(-0.358944\pi\) | ||||
0.428778 | + | 0.903410i | \(0.358944\pi\) | |||||||
\(90\) | −8.47214 | − | 9.47214i | −0.893042 | − | 0.998451i | ||||
\(91\) | −2.61803 | − | 17.9443i | −0.274445 | − | 1.88107i | ||||
\(92\) | 0.618034i | 0.0644345i | ||||||||
\(93\) | 0.854102 | − | 0.326238i | 0.0885662 | − | 0.0338293i | ||||
\(94\) | − | 12.9443i | − | 1.33510i | ||||||
\(95\) | 14.3262i | 1.46984i | ||||||||
\(96\) | −5.47214 | + | 2.09017i | −0.558498 | + | 0.213327i | ||||
\(97\) | − | 1.94427i | − | 0.197411i | −0.995117 | − | 0.0987055i | \(-0.968530\pi\) | ||
0.995117 | − | 0.0987055i | \(-0.0314702\pi\) | |||||||
\(98\) | 3.23607 | + | 10.8541i | 0.326892 | + | 1.09643i | ||||
\(99\) | 4.47214 | + | 5.00000i | 0.449467 | + | 0.502519i | ||||
\(100\) | −1.14590 | −0.114590 | ||||||||
\(101\) | −5.09017 | −0.506491 | −0.253245 | − | 0.967402i | \(-0.581498\pi\) | ||||
−0.253245 | + | 0.967402i | \(0.581498\pi\) | |||||||
\(102\) | 3.85410 | − | 1.47214i | 0.381613 | − | 0.145763i | ||||
\(103\) | 10.1803i | 1.00310i | 0.865129 | + | 0.501549i | \(0.167236\pi\) | ||||
−0.865129 | + | 0.501549i | \(0.832764\pi\) | |||||||
\(104\) | 15.3262 | 1.50286 | ||||||||
\(105\) | −5.85410 | − | 10.4721i | −0.571302 | − | 1.02198i | ||||
\(106\) | −21.9443 | −2.13142 | ||||||||
\(107\) | 11.6180i | 1.12316i | 0.827423 | + | 0.561579i | \(0.189806\pi\) | ||||
−0.827423 | + | 0.561579i | \(0.810194\pi\) | |||||||
\(108\) | −2.85410 | − | 1.47214i | −0.274636 | − | 0.141656i | ||||
\(109\) | 3.09017 | 0.295985 | 0.147992 | − | 0.988989i | \(-0.452719\pi\) | ||||
0.147992 | + | 0.988989i | \(0.452719\pi\) | |||||||
\(110\) | 9.47214 | 0.903133 | ||||||||
\(111\) | −3.56231 | − | 9.32624i | −0.338119 | − | 0.885207i | ||||
\(112\) | −12.7082 | + | 1.85410i | −1.20081 | + | 0.175196i | ||||
\(113\) | 10.7984i | 1.01583i | 0.861409 | + | 0.507913i | \(0.169583\pi\) | ||||
−0.861409 | + | 0.507913i | \(0.830417\pi\) | |||||||
\(114\) | 5.47214 | + | 14.3262i | 0.512512 | + | 1.34178i | ||||
\(115\) | − | 2.61803i | − | 0.244133i | ||||||
\(116\) | − | 1.09017i | − | 0.101220i | ||||||
\(117\) | 13.7082 | + | 15.3262i | 1.26732 | + | 1.41691i | ||||
\(118\) | − | 12.2361i | − | 1.12642i | ||||||
\(119\) | 3.85410 | − | 0.562306i | 0.353305 | − | 0.0515465i | ||||
\(120\) | 9.47214 | − | 3.61803i | 0.864684 | − | 0.330280i | ||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | −1.38197 | −0.125117 | ||||||||
\(123\) | −0.145898 | − | 0.381966i | −0.0131552 | − | 0.0344407i | ||||
\(124\) | − | 0.326238i | − | 0.0292970i | ||||||
\(125\) | −8.23607 | −0.736656 | ||||||||
\(126\) | −9.85410 | − | 8.23607i | −0.877873 | − | 0.733727i | ||||
\(127\) | 7.79837 | 0.691994 | 0.345997 | − | 0.938236i | \(-0.387541\pi\) | ||||
0.345997 | + | 0.938236i | \(0.387541\pi\) | |||||||
\(128\) | − | 13.6180i | − | 1.20368i | ||||||
\(129\) | −4.70820 | − | 12.3262i | −0.414534 | − | 1.08526i | ||||
\(130\) | 29.0344 | 2.54649 | ||||||||
\(131\) | −18.7082 | −1.63454 | −0.817272 | − | 0.576253i | \(-0.804514\pi\) | ||||
−0.817272 | + | 0.576253i | \(0.804514\pi\) | |||||||
\(132\) | 2.23607 | − | 0.854102i | 0.194625 | − | 0.0743400i | ||||
\(133\) | 2.09017 | + | 14.3262i | 0.181241 | + | 1.24224i | ||||
\(134\) | − | 17.1803i | − | 1.48416i | ||||||
\(135\) | 12.0902 | + | 6.23607i | 1.04056 | + | 0.536715i | ||||
\(136\) | 3.29180i | 0.282269i | ||||||||
\(137\) | − | 14.2361i | − | 1.21627i | −0.793834 | − | 0.608135i | \(-0.791918\pi\) | ||
0.793834 | − | 0.608135i | \(-0.208082\pi\) | |||||||
\(138\) | −1.00000 | − | 2.61803i | −0.0851257 | − | 0.222862i | ||||
\(139\) | − | 0.909830i | − | 0.0771708i | −0.999255 | − | 0.0385854i | \(-0.987715\pi\) | ||
0.999255 | − | 0.0385854i | \(-0.0122852\pi\) | |||||||
\(140\) | −4.23607 | + | 0.618034i | −0.358013 | + | 0.0522334i | ||||
\(141\) | 4.94427 | + | 12.9443i | 0.416383 | + | 1.09010i | ||||
\(142\) | 8.61803 | 0.723209 | ||||||||
\(143\) | −15.3262 | −1.28164 | ||||||||
\(144\) | 10.8541 | − | 9.70820i | 0.904508 | − | 0.809017i | ||||
\(145\) | 4.61803i | 0.383507i | ||||||||
\(146\) | 13.3262 | 1.10289 | ||||||||
\(147\) | −7.38197 | − | 9.61803i | −0.608854 | − | 0.793282i | ||||
\(148\) | −3.56231 | −0.292820 | ||||||||
\(149\) | − | 7.70820i | − | 0.631481i | −0.948846 | − | 0.315740i | \(-0.897747\pi\) | ||
0.948846 | − | 0.315740i | \(-0.102253\pi\) | |||||||
\(150\) | 4.85410 | − | 1.85410i | 0.396336 | − | 0.151387i | ||||
\(151\) | −2.47214 | −0.201180 | −0.100590 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100590 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(152\) | −12.2361 | −0.992476 | ||||||||
\(153\) | −3.29180 | + | 2.94427i | −0.266126 | + | 0.238030i | ||||
\(154\) | 9.47214 | − | 1.38197i | 0.763286 | − | 0.111362i | ||||
\(155\) | 1.38197i | 0.111002i | ||||||||
\(156\) | 6.85410 | − | 2.61803i | 0.548767 | − | 0.209610i | ||||
\(157\) | 7.52786i | 0.600789i | 0.953815 | + | 0.300394i | \(0.0971183\pi\) | ||||
−0.953815 | + | 0.300394i | \(0.902882\pi\) | |||||||
\(158\) | − | 12.5623i | − | 0.999403i | ||||||
\(159\) | 21.9443 | − | 8.38197i | 1.74029 | − | 0.664733i | ||||
\(160\) | − | 8.85410i | − | 0.699978i | ||||||
\(161\) | −0.381966 | − | 2.61803i | −0.0301031 | − | 0.206330i | ||||
\(162\) | 14.4721 | + | 1.61803i | 1.13704 | + | 0.127125i | ||||
\(163\) | −19.0902 | −1.49526 | −0.747629 | − | 0.664117i | \(-0.768808\pi\) | ||||
−0.747629 | + | 0.664117i | \(0.768808\pi\) | |||||||
\(164\) | −0.145898 | −0.0113927 | ||||||||
\(165\) | −9.47214 | + | 3.61803i | −0.737405 | + | 0.281664i | ||||
\(166\) | − | 17.3262i | − | 1.34478i | ||||||
\(167\) | −19.1803 | −1.48422 | −0.742110 | − | 0.670279i | \(-0.766175\pi\) | ||||
−0.742110 | + | 0.670279i | \(0.766175\pi\) | |||||||
\(168\) | 8.94427 | − | 5.00000i | 0.690066 | − | 0.385758i | ||||
\(169\) | −33.9787 | −2.61375 | ||||||||
\(170\) | 6.23607i | 0.478285i | ||||||||
\(171\) | −10.9443 | − | 12.2361i | −0.836929 | − | 0.935716i | ||||
\(172\) | −4.70820 | −0.358997 | ||||||||
\(173\) | −3.47214 | −0.263982 | −0.131991 | − | 0.991251i | \(-0.542137\pi\) | ||||
−0.131991 | + | 0.991251i | \(0.542137\pi\) | |||||||
\(174\) | 1.76393 | + | 4.61803i | 0.133723 | + | 0.350092i | ||||
\(175\) | 4.85410 | − | 0.708204i | 0.366936 | − | 0.0535352i | ||||
\(176\) | 10.8541i | 0.818159i | ||||||||
\(177\) | 4.67376 | + | 12.2361i | 0.351301 | + | 0.919719i | ||||
\(178\) | 13.0902i | 0.981150i | ||||||||
\(179\) | − | 5.67376i | − | 0.424077i | −0.977261 | − | 0.212038i | \(-0.931990\pi\) | ||
0.977261 | − | 0.212038i | \(-0.0680102\pi\) | |||||||
\(180\) | 3.61803 | − | 3.23607i | 0.269672 | − | 0.241202i | ||||
\(181\) | − | 6.70820i | − | 0.498617i | −0.968424 | − | 0.249308i | \(-0.919797\pi\) | ||
0.968424 | − | 0.249308i | \(-0.0802033\pi\) | |||||||
\(182\) | 29.0344 | − | 4.23607i | 2.15218 | − | 0.313998i | ||||
\(183\) | 1.38197 | − | 0.527864i | 0.102158 | − | 0.0390208i | ||||
\(184\) | 2.23607 | 0.164845 | ||||||||
\(185\) | 15.0902 | 1.10945 | ||||||||
\(186\) | 0.527864 | + | 1.38197i | 0.0387049 | + | 0.101331i | ||||
\(187\) | − | 3.29180i | − | 0.240720i | ||||||
\(188\) | 4.94427 | 0.360598 | ||||||||
\(189\) | 13.0000 | + | 4.47214i | 0.945611 | + | 0.325300i | ||||
\(190\) | −23.1803 | −1.68168 | ||||||||
\(191\) | − | 21.7082i | − | 1.57075i | −0.619020 | − | 0.785375i | \(-0.712470\pi\) | ||
0.619020 | − | 0.785375i | \(-0.287530\pi\) | |||||||
\(192\) | 2.61803 | + | 6.85410i | 0.188940 | + | 0.494652i | ||||
\(193\) | 15.7082 | 1.13070 | 0.565351 | − | 0.824851i | \(-0.308741\pi\) | ||||
0.565351 | + | 0.824851i | \(0.308741\pi\) | |||||||
\(194\) | 3.14590 | 0.225862 | ||||||||
\(195\) | −29.0344 | + | 11.0902i | −2.07920 | + | 0.794184i | ||||
\(196\) | −4.14590 | + | 1.23607i | −0.296136 | + | 0.0882906i | ||||
\(197\) | 26.0902i | 1.85885i | 0.369014 | + | 0.929424i | \(0.379695\pi\) | ||||
−0.369014 | + | 0.929424i | \(0.620305\pi\) | |||||||
\(198\) | −8.09017 | + | 7.23607i | −0.574943 | + | 0.514245i | ||||
\(199\) | 14.6180i | 1.03624i | 0.855306 | + | 0.518122i | \(0.173369\pi\) | ||||
−0.855306 | + | 0.518122i | \(0.826631\pi\) | |||||||
\(200\) | 4.14590i | 0.293159i | ||||||||
\(201\) | 6.56231 | + | 17.1803i | 0.462869 | + | 1.21181i | ||||
\(202\) | − | 8.23607i | − | 0.579488i | ||||||
\(203\) | 0.673762 | + | 4.61803i | 0.0472888 | + | 0.324122i | ||||
\(204\) | 0.562306 | + | 1.47214i | 0.0393693 | + | 0.103070i | ||||
\(205\) | 0.618034 | 0.0431654 | ||||||||
\(206\) | −16.4721 | −1.14767 | ||||||||
\(207\) | 2.00000 | + | 2.23607i | 0.139010 | + | 0.155417i | ||||
\(208\) | 33.2705i | 2.30689i | ||||||||
\(209\) | 12.2361 | 0.846387 | ||||||||
\(210\) | 16.9443 | − | 9.47214i | 1.16927 | − | 0.653639i | ||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | − | 8.38197i | − | 0.575676i | ||||||
\(213\) | −8.61803 | + | 3.29180i | −0.590498 | + | 0.225550i | ||||
\(214\) | −18.7984 | −1.28503 | ||||||||
\(215\) | 19.9443 | 1.36019 | ||||||||
\(216\) | −5.32624 | + | 10.3262i | −0.362405 | + | 0.702611i | ||||
\(217\) | 0.201626 | + | 1.38197i | 0.0136873 | + | 0.0938140i | ||||
\(218\) | 5.00000i | 0.338643i | ||||||||
\(219\) | −13.3262 | + | 5.09017i | −0.900504 | + | 0.343962i | ||||
\(220\) | 3.61803i | 0.243928i | ||||||||
\(221\) | − | 10.0902i | − | 0.678738i | ||||||
\(222\) | 15.0902 | − | 5.76393i | 1.01279 | − | 0.386850i | ||||
\(223\) | 17.0902i | 1.14444i | 0.820099 | + | 0.572221i | \(0.193918\pi\) | ||||
−0.820099 | + | 0.572221i | \(0.806082\pi\) | |||||||
\(224\) | −1.29180 | − | 8.85410i | −0.0863118 | − | 0.591590i | ||||
\(225\) | −4.14590 | + | 3.70820i | −0.276393 | + | 0.247214i | ||||
\(226\) | −17.4721 | −1.16223 | ||||||||
\(227\) | 22.3262 | 1.48184 | 0.740922 | − | 0.671591i | \(-0.234389\pi\) | ||||
0.740922 | + | 0.671591i | \(0.234389\pi\) | |||||||
\(228\) | −5.47214 | + | 2.09017i | −0.362401 | + | 0.138425i | ||||
\(229\) | − | 10.9098i | − | 0.720942i | −0.932770 | − | 0.360471i | \(-0.882616\pi\) | ||
0.932770 | − | 0.360471i | \(-0.117384\pi\) | |||||||
\(230\) | 4.23607 | 0.279318 | ||||||||
\(231\) | −8.94427 | + | 5.00000i | −0.588490 | + | 0.328976i | ||||
\(232\) | −3.94427 | −0.258954 | ||||||||
\(233\) | − | 13.6738i | − | 0.895798i | −0.894084 | − | 0.447899i | \(-0.852172\pi\) | ||
0.894084 | − | 0.447899i | \(-0.147828\pi\) | |||||||
\(234\) | −24.7984 | + | 22.1803i | −1.62112 | + | 1.44997i | ||||
\(235\) | −20.9443 | −1.36625 | ||||||||
\(236\) | 4.67376 | 0.304236 | ||||||||
\(237\) | 4.79837 | + | 12.5623i | 0.311688 | + | 0.816009i | ||||
\(238\) | 0.909830 | + | 6.23607i | 0.0589755 | + | 0.404224i | ||||
\(239\) | − | 5.67376i | − | 0.367005i | −0.983019 | − | 0.183503i | \(-0.941256\pi\) | ||
0.983019 | − | 0.183503i | \(-0.0587436\pi\) | |||||||
\(240\) | 7.85410 | + | 20.5623i | 0.506980 | + | 1.32729i | ||||
\(241\) | 0.527864i | 0.0340027i | 0.999855 | + | 0.0170014i | \(0.00541196\pi\) | ||||
−0.999855 | + | 0.0170014i | \(0.994588\pi\) | |||||||
\(242\) | 9.70820i | 0.624067i | ||||||||
\(243\) | −15.0902 | + | 3.90983i | −0.968035 | + | 0.250816i | ||||
\(244\) | − | 0.527864i | − | 0.0337930i | ||||||
\(245\) | 17.5623 | − | 5.23607i | 1.12201 | − | 0.334520i | ||||
\(246\) | 0.618034 | − | 0.236068i | 0.0394044 | − | 0.0150511i | ||||
\(247\) | 37.5066 | 2.38649 | ||||||||
\(248\) | −1.18034 | −0.0749517 | ||||||||
\(249\) | 6.61803 | + | 17.3262i | 0.419401 | + | 1.09801i | ||||
\(250\) | − | 13.3262i | − | 0.842825i | ||||||
\(251\) | −6.47214 | −0.408518 | −0.204259 | − | 0.978917i | \(-0.565478\pi\) | ||||
−0.204259 | + | 0.978917i | \(0.565478\pi\) | |||||||
\(252\) | 3.14590 | − | 3.76393i | 0.198173 | − | 0.237105i | ||||
\(253\) | −2.23607 | −0.140580 | ||||||||
\(254\) | 12.6180i | 0.791726i | ||||||||
\(255\) | −2.38197 | − | 6.23607i | −0.149164 | − | 0.390518i | ||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 30.9443 | 1.93025 | 0.965125 | − | 0.261788i | \(-0.0843122\pi\) | ||||
0.965125 | + | 0.261788i | \(0.0843122\pi\) | |||||||
\(258\) | 19.9443 | − | 7.61803i | 1.24168 | − | 0.474278i | ||||
\(259\) | 15.0902 | − | 2.20163i | 0.937658 | − | 0.136802i | ||||
\(260\) | 11.0902i | 0.687783i | ||||||||
\(261\) | −3.52786 | − | 3.94427i | −0.218369 | − | 0.244144i | ||||
\(262\) | − | 30.2705i | − | 1.87012i | ||||||
\(263\) | − | 17.9443i | − | 1.10649i | −0.833018 | − | 0.553246i | \(-0.813389\pi\) | ||
0.833018 | − | 0.553246i | \(-0.186611\pi\) | |||||||
\(264\) | −3.09017 | − | 8.09017i | −0.190187 | − | 0.497916i | ||||
\(265\) | 35.5066i | 2.18115i | ||||||||
\(266\) | −23.1803 | + | 3.38197i | −1.42128 | + | 0.207362i | ||||
\(267\) | −5.00000 | − | 13.0902i | −0.305995 | − | 0.801105i | ||||
\(268\) | 6.56231 | 0.400857 | ||||||||
\(269\) | −10.8541 | −0.661786 | −0.330893 | − | 0.943668i | \(-0.607350\pi\) | ||||
−0.330893 | + | 0.943668i | \(0.607350\pi\) | |||||||
\(270\) | −10.0902 | + | 19.5623i | −0.614068 | + | 1.19052i | ||||
\(271\) | − | 2.23607i | − | 0.135831i | −0.997691 | − | 0.0679157i | \(-0.978365\pi\) | ||
0.997691 | − | 0.0679157i | \(-0.0216349\pi\) | |||||||
\(272\) | −7.14590 | −0.433284 | ||||||||
\(273\) | −27.4164 | + | 15.3262i | −1.65932 | + | 0.927586i | ||||
\(274\) | 23.0344 | 1.39156 | ||||||||
\(275\) | − | 4.14590i | − | 0.250007i | ||||||
\(276\) | 1.00000 | − | 0.381966i | 0.0601929 | − | 0.0229917i | ||||
\(277\) | 7.14590 | 0.429355 | 0.214678 | − | 0.976685i | \(-0.431130\pi\) | ||||
0.214678 | + | 0.976685i | \(0.431130\pi\) | |||||||
\(278\) | 1.47214 | 0.0882928 | ||||||||
\(279\) | −1.05573 | − | 1.18034i | −0.0632048 | − | 0.0706651i | ||||
\(280\) | 2.23607 | + | 15.3262i | 0.133631 | + | 0.915918i | ||||
\(281\) | − | 1.05573i | − | 0.0629795i | −0.999504 | − | 0.0314897i | \(-0.989975\pi\) | ||
0.999504 | − | 0.0314897i | \(-0.0100251\pi\) | |||||||
\(282\) | −20.9443 | + | 8.00000i | −1.24721 | + | 0.476393i | ||||
\(283\) | 8.79837i | 0.523009i | 0.965202 | + | 0.261505i | \(0.0842186\pi\) | ||||
−0.965202 | + | 0.261505i | \(0.915781\pi\) | |||||||
\(284\) | 3.29180i | 0.195332i | ||||||||
\(285\) | 23.1803 | − | 8.85410i | 1.37308 | − | 0.524472i | ||||
\(286\) | − | 24.7984i | − | 1.46636i | ||||||
\(287\) | 0.618034 | − | 0.0901699i | 0.0364814 | − | 0.00532256i | ||||
\(288\) | 6.76393 | + | 7.56231i | 0.398569 | + | 0.445613i | ||||
\(289\) | −14.8328 | −0.872519 | ||||||||
\(290\) | −7.47214 | −0.438779 | ||||||||
\(291\) | −3.14590 | + | 1.20163i | −0.184416 | + | 0.0704406i | ||||
\(292\) | 5.09017i | 0.297880i | ||||||||
\(293\) | 14.2918 | 0.834936 | 0.417468 | − | 0.908692i | \(-0.362918\pi\) | ||||
0.417468 | + | 0.908692i | \(0.362918\pi\) | |||||||
\(294\) | 15.5623 | − | 11.9443i | 0.907612 | − | 0.696604i | ||||
\(295\) | −19.7984 | −1.15271 | ||||||||
\(296\) | 12.8885i | 0.749131i | ||||||||
\(297\) | 5.32624 | − | 10.3262i | 0.309060 | − | 0.599189i | ||||
\(298\) | 12.4721 | 0.722491 | ||||||||
\(299\) | −6.85410 | −0.396383 | ||||||||
\(300\) | 0.708204 | + | 1.85410i | 0.0408882 | + | 0.107047i | ||||
\(301\) | 19.9443 | − | 2.90983i | 1.14957 | − | 0.167720i | ||||
\(302\) | − | 4.00000i | − | 0.230174i | ||||||
\(303\) | 3.14590 | + | 8.23607i | 0.180727 | + | 0.473150i | ||||
\(304\) | − | 26.5623i | − | 1.52345i | ||||||
\(305\) | 2.23607i | 0.128037i | ||||||||
\(306\) | −4.76393 | − | 5.32624i | −0.272336 | − | 0.304481i | ||||
\(307\) | 21.4721i | 1.22548i | 0.790285 | + | 0.612740i | \(0.209933\pi\) | ||||
−0.790285 | + | 0.612740i | \(0.790067\pi\) | |||||||
\(308\) | 0.527864 | + | 3.61803i | 0.0300778 | + | 0.206157i | ||||
\(309\) | 16.4721 | − | 6.29180i | 0.937067 | − | 0.357928i | ||||
\(310\) | −2.23607 | −0.127000 | ||||||||
\(311\) | 23.3262 | 1.32271 | 0.661355 | − | 0.750073i | \(-0.269982\pi\) | ||||
0.661355 | + | 0.750073i | \(0.269982\pi\) | |||||||
\(312\) | −9.47214 | − | 24.7984i | −0.536254 | − | 1.40393i | ||||
\(313\) | 10.1803i | 0.575427i | 0.957717 | + | 0.287713i | \(0.0928951\pi\) | ||||
−0.957717 | + | 0.287713i | \(0.907105\pi\) | |||||||
\(314\) | −12.1803 | −0.687376 | ||||||||
\(315\) | −13.3262 | + | 15.9443i | −0.750848 | + | 0.898358i | ||||
\(316\) | 4.79837 | 0.269930 | ||||||||
\(317\) | − | 0.618034i | − | 0.0347122i | −0.999849 | − | 0.0173561i | \(-0.994475\pi\) | ||
0.999849 | − | 0.0173561i | \(-0.00552490\pi\) | |||||||
\(318\) | 13.5623 | + | 35.5066i | 0.760536 | + | 1.99111i | ||||
\(319\) | 3.94427 | 0.220837 | ||||||||
\(320\) | −11.0902 | −0.619959 | ||||||||
\(321\) | 18.7984 | − | 7.18034i | 1.04922 | − | 0.400767i | ||||
\(322\) | 4.23607 | − | 0.618034i | 0.236067 | − | 0.0344417i | ||||
\(323\) | 8.05573i | 0.448233i | ||||||||
\(324\) | −0.618034 | + | 5.52786i | −0.0343352 | + | 0.307104i | ||||
\(325\) | − | 12.7082i | − | 0.704924i | ||||||
\(326\) | − | 30.8885i | − | 1.71076i | ||||||
\(327\) | −1.90983 | − | 5.00000i | −0.105614 | − | 0.276501i | ||||
\(328\) | 0.527864i | 0.0291464i | ||||||||
\(329\) | −20.9443 | + | 3.05573i | −1.15470 | + | 0.168468i | ||||
\(330\) | −5.85410 | − | 15.3262i | −0.322258 | − | 0.843682i | ||||
\(331\) | 36.0689 | 1.98253 | 0.991263 | − | 0.131903i | \(-0.0421089\pi\) | ||||
0.991263 | + | 0.131903i | \(0.0421089\pi\) | |||||||
\(332\) | 6.61803 | 0.363212 | ||||||||
\(333\) | −12.8885 | + | 11.5279i | −0.706288 | + | 0.631723i | ||||
\(334\) | − | 31.0344i | − | 1.69813i | ||||||
\(335\) | −27.7984 | −1.51879 | ||||||||
\(336\) | 10.8541 | + | 19.4164i | 0.592140 | + | 1.05925i | ||||
\(337\) | −32.4508 | −1.76771 | −0.883855 | − | 0.467761i | \(-0.845061\pi\) | ||||
−0.883855 | + | 0.467761i | \(0.845061\pi\) | |||||||
\(338\) | − | 54.9787i | − | 2.99045i | ||||||
\(339\) | 17.4721 | − | 6.67376i | 0.948956 | − | 0.362469i | ||||
\(340\) | −2.38197 | −0.129180 | ||||||||
\(341\) | 1.18034 | 0.0639190 | ||||||||
\(342\) | 19.7984 | − | 17.7082i | 1.07057 | − | 0.957550i | ||||
\(343\) | 16.7984 | − | 7.79837i | 0.907027 | − | 0.421073i | ||||
\(344\) | 17.0344i | 0.918436i | ||||||||
\(345\) | −4.23607 | + | 1.61803i | −0.228062 | + | 0.0871120i | ||||
\(346\) | − | 5.61803i | − | 0.302027i | ||||||
\(347\) | − | 23.1803i | − | 1.24439i | −0.782864 | − | 0.622193i | \(-0.786242\pi\) | ||
0.782864 | − | 0.622193i | \(-0.213758\pi\) | |||||||
\(348\) | −1.76393 | + | 0.673762i | −0.0945567 | + | 0.0361174i | ||||
\(349\) | 31.8541i | 1.70511i | 0.522637 | + | 0.852555i | \(0.324948\pi\) | ||||
−0.522637 | + | 0.852555i | \(0.675052\pi\) | |||||||
\(350\) | 1.14590 | + | 7.85410i | 0.0612508 | + | 0.419819i | ||||
\(351\) | 16.3262 | − | 31.6525i | 0.871430 | − | 1.68948i | ||||
\(352\) | −7.56231 | −0.403072 | ||||||||
\(353\) | 26.5279 | 1.41194 | 0.705968 | − | 0.708244i | \(-0.250512\pi\) | ||||
0.705968 | + | 0.708244i | \(0.250512\pi\) | |||||||
\(354\) | −19.7984 | + | 7.56231i | −1.05227 | + | 0.401932i | ||||
\(355\) | − | 13.9443i | − | 0.740085i | ||||||
\(356\) | −5.00000 | −0.264999 | ||||||||
\(357\) | −3.29180 | − | 5.88854i | −0.174220 | − | 0.311655i | ||||
\(358\) | 9.18034 | 0.485196 | ||||||||
\(359\) | − | 2.90983i | − | 0.153575i | −0.997047 | − | 0.0767875i | \(-0.975534\pi\) | ||
0.997047 | − | 0.0767875i | \(-0.0244663\pi\) | |||||||
\(360\) | −11.7082 | − | 13.0902i | −0.617077 | − | 0.689913i | ||||
\(361\) | −10.9443 | −0.576014 | ||||||||
\(362\) | 10.8541 | 0.570479 | ||||||||
\(363\) | −3.70820 | − | 9.70820i | −0.194630 | − | 0.509549i | ||||
\(364\) | 1.61803 | + | 11.0902i | 0.0848080 | + | 0.581283i | ||||
\(365\) | − | 21.5623i | − | 1.12862i | ||||||
\(366\) | 0.854102 | + | 2.23607i | 0.0446446 | + | 0.116881i | ||||
\(367\) | − | 22.2705i | − | 1.16251i | −0.813721 | − | 0.581256i | \(-0.802562\pi\) | ||
0.813721 | − | 0.581256i | \(-0.197438\pi\) | |||||||
\(368\) | 4.85410i | 0.253038i | ||||||||
\(369\) | −0.527864 | + | 0.472136i | −0.0274795 | + | 0.0245784i | ||||
\(370\) | 24.4164i | 1.26935i | ||||||||
\(371\) | 5.18034 | + | 35.5066i | 0.268950 | + | 1.84341i | ||||
\(372\) | −0.527864 | + | 0.201626i | −0.0273685 | + | 0.0104538i | ||||
\(373\) | −1.00000 | −0.0517780 | −0.0258890 | − | 0.999665i | \(-0.508242\pi\) | ||||
−0.0258890 | + | 0.999665i | \(0.508242\pi\) | |||||||
\(374\) | 5.32624 | 0.275413 | ||||||||
\(375\) | 5.09017 | + | 13.3262i | 0.262855 | + | 0.688164i | ||||
\(376\) | − | 17.8885i | − | 0.922531i | ||||||
\(377\) | 12.0902 | 0.622675 | ||||||||
\(378\) | −7.23607 | + | 21.0344i | −0.372183 | + | 1.08189i | ||||
\(379\) | 24.4721 | 1.25705 | 0.628525 | − | 0.777790i | \(-0.283659\pi\) | ||||
0.628525 | + | 0.777790i | \(0.283659\pi\) | |||||||
\(380\) | − | 8.85410i | − | 0.454206i | ||||||
\(381\) | −4.81966 | − | 12.6180i | −0.246919 | − | 0.646441i | ||||
\(382\) | 35.1246 | 1.79713 | ||||||||
\(383\) | 8.23607 | 0.420843 | 0.210422 | − | 0.977611i | \(-0.432516\pi\) | ||||
0.210422 | + | 0.977611i | \(0.432516\pi\) | |||||||
\(384\) | −22.0344 | + | 8.41641i | −1.12444 | + | 0.429498i | ||||
\(385\) | −2.23607 | − | 15.3262i | −0.113961 | − | 0.781097i | ||||
\(386\) | 25.4164i | 1.29366i | ||||||||
\(387\) | −17.0344 | + | 15.2361i | −0.865909 | + | 0.774493i | ||||
\(388\) | 1.20163i | 0.0610033i | ||||||||
\(389\) | − | 32.7082i | − | 1.65837i | −0.558973 | − | 0.829186i | \(-0.688804\pi\) | ||
0.558973 | − | 0.829186i | \(-0.311196\pi\) | |||||||
\(390\) | −17.9443 | − | 46.9787i | −0.908644 | − | 2.37886i | ||||
\(391\) | − | 1.47214i | − | 0.0744491i | ||||||
\(392\) | 4.47214 | + | 15.0000i | 0.225877 | + | 0.757614i | ||||
\(393\) | 11.5623 | + | 30.2705i | 0.583241 | + | 1.52695i | ||||
\(394\) | −42.2148 | −2.12675 | ||||||||
\(395\) | −20.3262 | −1.02272 | ||||||||
\(396\) | −2.76393 | − | 3.09017i | −0.138893 | − | 0.155287i | ||||
\(397\) | − | 15.2361i | − | 0.764676i | −0.924022 | − | 0.382338i | \(-0.875119\pi\) | ||
0.924022 | − | 0.382338i | \(-0.124881\pi\) | |||||||
\(398\) | −23.6525 | −1.18559 | ||||||||
\(399\) | 21.8885 | − | 12.2361i | 1.09580 | − | 0.612570i | ||||
\(400\) | −9.00000 | −0.450000 | ||||||||
\(401\) | − | 8.41641i | − | 0.420295i | −0.977670 | − | 0.210148i | \(-0.932606\pi\) | ||
0.977670 | − | 0.210148i | \(-0.0673945\pi\) | |||||||
\(402\) | −27.7984 | + | 10.6180i | −1.38646 | + | 0.529579i | ||||
\(403\) | 3.61803 | 0.180227 | ||||||||
\(404\) | 3.14590 | 0.156514 | ||||||||
\(405\) | 2.61803 | − | 23.4164i | 0.130091 | − | 1.16357i | ||||
\(406\) | −7.47214 | + | 1.09017i | −0.370836 | + | 0.0541042i | ||||
\(407\) | − | 12.8885i | − | 0.638861i | ||||||
\(408\) | 5.32624 | − | 2.03444i | 0.263688 | − | 0.100720i | ||||
\(409\) | − | 33.4721i | − | 1.65509i | −0.561399 | − | 0.827545i | \(-0.689737\pi\) | ||
0.561399 | − | 0.827545i | \(-0.310263\pi\) | |||||||
\(410\) | 1.00000i | 0.0493865i | ||||||||
\(411\) | −23.0344 | + | 8.79837i | −1.13621 | + | 0.433992i | ||||
\(412\) | − | 6.29180i | − | 0.309975i | ||||||
\(413\) | −19.7984 | + | 2.88854i | −0.974214 | + | 0.142136i | ||||
\(414\) | −3.61803 | + | 3.23607i | −0.177817 | + | 0.159044i | ||||
\(415\) | −28.0344 | −1.37616 | ||||||||
\(416\) | −23.1803 | −1.13651 | ||||||||
\(417\) | −1.47214 | + | 0.562306i | −0.0720908 | + | 0.0275362i | ||||
\(418\) | 19.7984i | 0.968370i | ||||||||
\(419\) | 24.7984 | 1.21148 | 0.605740 | − | 0.795663i | \(-0.292877\pi\) | ||||
0.605740 | + | 0.795663i | \(0.292877\pi\) | |||||||
\(420\) | 3.61803 | + | 6.47214i | 0.176542 | + | 0.315808i | ||||
\(421\) | 39.6869 | 1.93422 | 0.967111 | − | 0.254355i | \(-0.0818631\pi\) | ||||
0.967111 | + | 0.254355i | \(0.0818631\pi\) | |||||||
\(422\) | − | 4.85410i | − | 0.236294i | ||||||
\(423\) | 17.8885 | − | 16.0000i | 0.869771 | − | 0.777947i | ||||
\(424\) | −30.3262 | −1.47277 | ||||||||
\(425\) | 2.72949 | 0.132400 | ||||||||
\(426\) | −5.32624 | − | 13.9443i | −0.258057 | − | 0.675602i | ||||
\(427\) | 0.326238 | + | 2.23607i | 0.0157878 | + | 0.108211i | ||||
\(428\) | − | 7.18034i | − | 0.347075i | ||||||
\(429\) | 9.47214 | + | 24.7984i | 0.457319 | + | 1.19728i | ||||
\(430\) | 32.2705i | 1.55622i | ||||||||
\(431\) | 21.9098i | 1.05536i | 0.849443 | + | 0.527680i | \(0.176938\pi\) | ||||
−0.849443 | + | 0.527680i | \(0.823062\pi\) | |||||||
\(432\) | −22.4164 | − | 11.5623i | −1.07851 | − | 0.556292i | ||||
\(433\) | − | 1.52786i | − | 0.0734245i | −0.999326 | − | 0.0367122i | \(-0.988312\pi\) | ||
0.999326 | − | 0.0367122i | \(-0.0116885\pi\) | |||||||
\(434\) | −2.23607 | + | 0.326238i | −0.107335 | + | 0.0156599i | ||||
\(435\) | 7.47214 | − | 2.85410i | 0.358261 | − | 0.136844i | ||||
\(436\) | −1.90983 | −0.0914643 | ||||||||
\(437\) | 5.47214 | 0.261768 | ||||||||
\(438\) | −8.23607 | − | 21.5623i | −0.393535 | − | 1.03029i | ||||
\(439\) | 25.4721i | 1.21572i | 0.794045 | + | 0.607859i | \(0.207972\pi\) | ||||
−0.794045 | + | 0.607859i | \(0.792028\pi\) | |||||||
\(440\) | 13.0902 | 0.624049 | ||||||||
\(441\) | −11.0000 | + | 17.8885i | −0.523810 | + | 0.851835i | ||||
\(442\) | 16.3262 | 0.776560 | ||||||||
\(443\) | 22.1803i | 1.05382i | 0.849921 | + | 0.526910i | \(0.176649\pi\) | ||||
−0.849921 | + | 0.526910i | \(0.823351\pi\) | |||||||
\(444\) | 2.20163 | + | 5.76393i | 0.104485 | + | 0.273544i | ||||
\(445\) | 21.1803 | 1.00404 | ||||||||
\(446\) | −27.6525 | −1.30938 | ||||||||
\(447\) | −12.4721 | + | 4.76393i | −0.589912 | + | 0.225326i | ||||
\(448\) | −11.0902 | + | 1.61803i | −0.523961 | + | 0.0764449i | ||||
\(449\) | 10.9098i | 0.514867i | 0.966296 | + | 0.257433i | \(0.0828768\pi\) | ||||
−0.966296 | + | 0.257433i | \(0.917123\pi\) | |||||||
\(450\) | −6.00000 | − | 6.70820i | −0.282843 | − | 0.316228i | ||||
\(451\) | − | 0.527864i | − | 0.0248561i | ||||||
\(452\) | − | 6.67376i | − | 0.313907i | ||||||
\(453\) | 1.52786 | + | 4.00000i | 0.0717853 | + | 0.187936i | ||||
\(454\) | 36.1246i | 1.69541i | ||||||||
\(455\) | −6.85410 | − | 46.9787i | −0.321325 | − | 2.20240i | ||||
\(456\) | 7.56231 | + | 19.7984i | 0.354137 | + | 0.927144i | ||||
\(457\) | 15.5623 | 0.727974 | 0.363987 | − | 0.931404i | \(-0.381415\pi\) | ||||
0.363987 | + | 0.931404i | \(0.381415\pi\) | |||||||
\(458\) | 17.6525 | 0.824846 | ||||||||
\(459\) | 6.79837 | + | 3.50658i | 0.317321 | + | 0.163673i | ||||
\(460\) | 1.61803i | 0.0754412i | ||||||||
\(461\) | −24.6869 | −1.14978 | −0.574892 | − | 0.818229i | \(-0.694956\pi\) | ||||
−0.574892 | + | 0.818229i | \(0.694956\pi\) | |||||||
\(462\) | −8.09017 | − | 14.4721i | −0.376389 | − | 0.673305i | ||||
\(463\) | −16.5279 | −0.768115 | −0.384057 | − | 0.923309i | \(-0.625474\pi\) | ||||
−0.384057 | + | 0.923309i | \(0.625474\pi\) | |||||||
\(464\) | − | 8.56231i | − | 0.397495i | ||||||
\(465\) | 2.23607 | − | 0.854102i | 0.103695 | − | 0.0396080i | ||||
\(466\) | 22.1246 | 1.02490 | ||||||||
\(467\) | 33.8328 | 1.56560 | 0.782798 | − | 0.622276i | \(-0.213792\pi\) | ||||
0.782798 | + | 0.622276i | \(0.213792\pi\) | |||||||
\(468\) | −8.47214 | − | 9.47214i | −0.391625 | − | 0.437850i | ||||
\(469\) | −27.7984 | + | 4.05573i | −1.28361 | + | 0.187276i | ||||
\(470\) | − | 33.8885i | − | 1.56316i | ||||||
\(471\) | 12.1803 | − | 4.65248i | 0.561240 | − | 0.214375i | ||||
\(472\) | − | 16.9098i | − | 0.778338i | ||||||
\(473\) | − | 17.0344i | − | 0.783244i | ||||||
\(474\) | −20.3262 | + | 7.76393i | −0.933615 | + | 0.356609i | ||||
\(475\) | 10.1459i | 0.465526i | ||||||||
\(476\) | −2.38197 | + | 0.347524i | −0.109177 | + | 0.0159287i | ||||
\(477\) | −27.1246 | − | 30.3262i | −1.24195 | − | 1.38854i | ||||
\(478\) | 9.18034 | 0.419899 | ||||||||
\(479\) | −25.6525 | −1.17209 | −0.586046 | − | 0.810278i | \(-0.699316\pi\) | ||||
−0.586046 | + | 0.810278i | \(0.699316\pi\) | |||||||
\(480\) | −14.3262 | + | 5.47214i | −0.653900 | + | 0.249768i | ||||
\(481\) | − | 39.5066i | − | 1.80134i | ||||||
\(482\) | −0.854102 | −0.0389033 | ||||||||
\(483\) | −4.00000 | + | 2.23607i | −0.182006 | + | 0.101745i | ||||
\(484\) | −3.70820 | −0.168555 | ||||||||
\(485\) | − | 5.09017i | − | 0.231133i | ||||||
\(486\) | −6.32624 | − | 24.4164i | −0.286964 | − | 1.10755i | ||||
\(487\) | 14.7082 | 0.666492 | 0.333246 | − | 0.942840i | \(-0.391856\pi\) | ||||
0.333246 | + | 0.942840i | \(0.391856\pi\) | |||||||
\(488\) | −1.90983 | −0.0864539 | ||||||||
\(489\) | 11.7984 | + | 30.8885i | 0.533541 | + | 1.39683i | ||||
\(490\) | 8.47214 | + | 28.4164i | 0.382732 | + | 1.28372i | ||||
\(491\) | 21.9098i | 0.988777i | 0.869241 | + | 0.494388i | \(0.164608\pi\) | ||||
−0.869241 | + | 0.494388i | \(0.835392\pi\) | |||||||
\(492\) | 0.0901699 | + | 0.236068i | 0.00406518 | + | 0.0106428i | ||||
\(493\) | 2.59675i | 0.116952i | ||||||||
\(494\) | 60.6869i | 2.73043i | ||||||||
\(495\) | 11.7082 | + | 13.0902i | 0.526245 | + | 0.588359i | ||||
\(496\) | − | 2.56231i | − | 0.115051i | ||||||
\(497\) | −2.03444 | − | 13.9443i | −0.0912572 | − | 0.625486i | ||||
\(498\) | −28.0344 | + | 10.7082i | −1.25625 | + | 0.479846i | ||||
\(499\) | −17.5623 | −0.786197 | −0.393098 | − | 0.919496i | \(-0.628597\pi\) | ||||
−0.393098 | + | 0.919496i | \(0.628597\pi\) | |||||||
\(500\) | 5.09017 | 0.227639 | ||||||||
\(501\) | 11.8541 | + | 31.0344i | 0.529602 | + | 1.38652i | ||||
\(502\) | − | 10.4721i | − | 0.467394i | ||||||
\(503\) | −0.257354 | −0.0114749 | −0.00573743 | − | 0.999984i | \(-0.501826\pi\) | ||||
−0.00573743 | + | 0.999984i | \(0.501826\pi\) | |||||||
\(504\) | −13.6180 | − | 11.3820i | −0.606595 | − | 0.506993i | ||||
\(505\) | −13.3262 | −0.593010 | ||||||||
\(506\) | − | 3.61803i | − | 0.160841i | ||||||
\(507\) | 21.0000 | + | 54.9787i | 0.932643 | + | 2.44169i | ||||
\(508\) | −4.81966 | −0.213838 | ||||||||
\(509\) | 20.0000 | 0.886484 | 0.443242 | − | 0.896402i | \(-0.353828\pi\) | ||||
0.443242 | + | 0.896402i | \(0.353828\pi\) | |||||||
\(510\) | 10.0902 | − | 3.85410i | 0.446800 | − | 0.170663i | ||||
\(511\) | −3.14590 | − | 21.5623i | −0.139166 | − | 0.953860i | ||||
\(512\) | − | 5.29180i | − | 0.233867i | ||||||
\(513\) | −13.0344 | + | 25.2705i | −0.575485 | + | 1.11572i | ||||
\(514\) | 50.0689i | 2.20844i | ||||||||
\(515\) | 26.6525i | 1.17445i | ||||||||
\(516\) | 2.90983 | + | 7.61803i | 0.128098 | + | 0.335365i | ||||
\(517\) | 17.8885i | 0.786737i | ||||||||
\(518\) | 3.56231 | + | 24.4164i | 0.156519 | + | 1.07280i | ||||
\(519\) | 2.14590 | + | 5.61803i | 0.0941945 | + | 0.246604i | ||||
\(520\) | 40.1246 | 1.75958 | ||||||||
\(521\) | −36.4721 | −1.59787 | −0.798937 | − | 0.601415i | \(-0.794604\pi\) | ||||
−0.798937 | + | 0.601415i | \(0.794604\pi\) | |||||||
\(522\) | 6.38197 | − | 5.70820i | 0.279331 | − | 0.249841i | ||||
\(523\) | − | 25.5967i | − | 1.11927i | −0.828740 | − | 0.559634i | \(-0.810942\pi\) | ||
0.828740 | − | 0.559634i | \(-0.189058\pi\) | |||||||
\(524\) | 11.5623 | 0.505102 | ||||||||
\(525\) | −4.14590 | − | 7.41641i | −0.180942 | − | 0.323679i | ||||
\(526\) | 29.0344 | 1.26596 | ||||||||
\(527\) | 0.777088i | 0.0338505i | ||||||||
\(528\) | 17.5623 | − | 6.70820i | 0.764301 | − | 0.291937i | ||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | −57.4508 | −2.49551 | ||||||||
\(531\) | 16.9098 | − | 15.1246i | 0.733824 | − | 0.656352i | ||||
\(532\) | −1.29180 | − | 8.85410i | −0.0560065 | − | 0.383874i | ||||
\(533\) | − | 1.61803i | − | 0.0700848i | ||||||
\(534\) | 21.1803 | − | 8.09017i | 0.916563 | − | 0.350096i | ||||
\(535\) | 30.4164i | 1.31502i | ||||||||
\(536\) | − | 23.7426i | − | 1.02553i | ||||||
\(537\) | −9.18034 | + | 3.50658i | −0.396161 | + | 0.151320i | ||||
\(538\) | − | 17.5623i | − | 0.757165i | ||||||
\(539\) | −4.47214 | − | 15.0000i | −0.192629 | − | 0.646096i | ||||
\(540\) | −7.47214 | − | 3.85410i | −0.321550 | − | 0.165854i | ||||
\(541\) | −25.2361 | −1.08498 | −0.542492 | − | 0.840061i | \(-0.682519\pi\) | ||||
−0.542492 | + | 0.840061i | \(0.682519\pi\) | |||||||
\(542\) | 3.61803 | 0.155408 | ||||||||
\(543\) | −10.8541 | + | 4.14590i | −0.465794 | + | 0.177918i | ||||
\(544\) | − | 4.97871i | − | 0.213461i | ||||||
\(545\) | 8.09017 | 0.346545 | ||||||||
\(546\) | −24.7984 | − | 44.3607i | −1.06127 | − | 1.89846i | ||||
\(547\) | −20.2148 | −0.864322 | −0.432161 | − | 0.901797i | \(-0.642249\pi\) | ||||
−0.432161 | + | 0.901797i | \(0.642249\pi\) | |||||||
\(548\) | 8.79837i | 0.375848i | ||||||||
\(549\) | −1.70820 | − | 1.90983i | −0.0729044 | − | 0.0815096i | ||||
\(550\) | 6.70820 | 0.286039 | ||||||||
\(551\) | −9.65248 | −0.411209 | ||||||||
\(552\) | −1.38197 | − | 3.61803i | −0.0588204 | − | 0.153994i | ||||
\(553\) | −20.3262 | + | 2.96556i | −0.864360 | + | 0.126108i | ||||
\(554\) | 11.5623i | 0.491235i | ||||||||
\(555\) | −9.32624 | − | 24.4164i | −0.395877 | − | 1.03642i | ||||
\(556\) | 0.562306i | 0.0238471i | ||||||||
\(557\) | 32.0689i | 1.35880i | 0.733767 | + | 0.679401i | \(0.237760\pi\) | ||||
−0.733767 | + | 0.679401i | \(0.762240\pi\) | |||||||
\(558\) | 1.90983 | − | 1.70820i | 0.0808496 | − | 0.0723140i | ||||
\(559\) | − | 52.2148i | − | 2.20845i | ||||||
\(560\) | −33.2705 | + | 4.85410i | −1.40594 | + | 0.205123i | ||||
\(561\) | −5.32624 | + | 2.03444i | −0.224874 | + | 0.0858942i | ||||
\(562\) | 1.70820 | 0.0720562 | ||||||||
\(563\) | −24.8541 | −1.04748 | −0.523738 | − | 0.851880i | \(-0.675463\pi\) | ||||
−0.523738 | + | 0.851880i | \(0.675463\pi\) | |||||||
\(564\) | −3.05573 | − | 8.00000i | −0.128669 | − | 0.336861i | ||||
\(565\) | 28.2705i | 1.18935i | ||||||||
\(566\) | −14.2361 | −0.598387 | ||||||||
\(567\) | −0.798374 | − | 23.7984i | −0.0335286 | − | 0.999438i | ||||
\(568\) | 11.9098 | 0.499725 | ||||||||
\(569\) | − | 35.5967i | − | 1.49229i | −0.665782 | − | 0.746147i | \(-0.731902\pi\) | ||
0.665782 | − | 0.746147i | \(-0.268098\pi\) | |||||||
\(570\) | 14.3262 | + | 37.5066i | 0.600060 | + | 1.57098i | ||||
\(571\) | −16.4164 | −0.687005 | −0.343503 | − | 0.939152i | \(-0.611613\pi\) | ||||
−0.343503 | + | 0.939152i | \(0.611613\pi\) | |||||||
\(572\) | 9.47214 | 0.396050 | ||||||||
\(573\) | −35.1246 | + | 13.4164i | −1.46735 | + | 0.560478i | ||||
\(574\) | 0.145898 | + | 1.00000i | 0.00608967 | + | 0.0417392i | ||||
\(575\) | − | 1.85410i | − | 0.0773214i | ||||||
\(576\) | 9.47214 | − | 8.47214i | 0.394672 | − | 0.353006i | ||||
\(577\) | 33.3050i | 1.38650i | 0.720696 | + | 0.693252i | \(0.243823\pi\) | ||||
−0.720696 | + | 0.693252i | \(0.756177\pi\) | |||||||
\(578\) | − | 24.0000i | − | 0.998268i | ||||||
\(579\) | −9.70820 | − | 25.4164i | −0.403459 | − | 1.05627i | ||||
\(580\) | − | 2.85410i | − | 0.118510i | ||||||
\(581\) | −28.0344 | + | 4.09017i | −1.16306 | + | 0.169689i | ||||
\(582\) | −1.94427 | − | 5.09017i | −0.0805927 | − | 0.210994i | ||||
\(583\) | 30.3262 | 1.25598 | ||||||||
\(584\) | 18.4164 | 0.762076 | ||||||||
\(585\) | 35.8885 | + | 40.1246i | 1.48381 | + | 1.65895i | ||||
\(586\) | 23.1246i | 0.955269i | ||||||||
\(587\) | −13.3262 | −0.550033 | −0.275016 | − | 0.961440i | \(-0.588683\pi\) | ||||
−0.275016 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(588\) | 4.56231 | + | 5.94427i | 0.188146 | + | 0.245138i | ||||
\(589\) | −2.88854 | −0.119020 | ||||||||
\(590\) | − | 32.0344i | − | 1.31884i | ||||||
\(591\) | 42.2148 | − | 16.1246i | 1.73648 | − | 0.663278i | ||||
\(592\) | −27.9787 | −1.14992 | ||||||||
\(593\) | 31.1246 | 1.27813 | 0.639067 | − | 0.769151i | \(-0.279321\pi\) | ||||
0.639067 | + | 0.769151i | \(0.279321\pi\) | |||||||
\(594\) | 16.7082 | + | 8.61803i | 0.685546 | + | 0.353602i | ||||
\(595\) | 10.0902 | − | 1.47214i | 0.413657 | − | 0.0603517i | ||||
\(596\) | 4.76393i | 0.195138i | ||||||||
\(597\) | 23.6525 | − | 9.03444i | 0.968031 | − | 0.369755i | ||||
\(598\) | − | 11.0902i | − | 0.453511i | ||||||
\(599\) | 3.14590i | 0.128538i | 0.997933 | + | 0.0642690i | \(0.0204716\pi\) | ||||
−0.997933 | + | 0.0642690i | \(0.979528\pi\) | |||||||
\(600\) | 6.70820 | − | 2.56231i | 0.273861 | − | 0.104606i | ||||
\(601\) | − | 9.67376i | − | 0.394601i | −0.980343 | − | 0.197300i | \(-0.936783\pi\) | ||
0.980343 | − | 0.197300i | \(-0.0632175\pi\) | |||||||
\(602\) | 4.70820 | + | 32.2705i | 0.191892 | + | 1.31525i | ||||
\(603\) | 23.7426 | − | 21.2361i | 0.966875 | − | 0.864800i | ||||
\(604\) | 1.52786 | 0.0621679 | ||||||||
\(605\) | 15.7082 | 0.638629 | ||||||||
\(606\) | −13.3262 | + | 5.09017i | −0.541341 | + | 0.206774i | ||||
\(607\) | 34.5623i | 1.40284i | 0.712748 | + | 0.701420i | \(0.247450\pi\) | ||||
−0.712748 | + | 0.701420i | \(0.752550\pi\) | |||||||
\(608\) | 18.5066 | 0.750541 | ||||||||
\(609\) | 7.05573 | − | 3.94427i | 0.285913 | − | 0.159830i | ||||
\(610\) | −3.61803 | −0.146490 | ||||||||
\(611\) | 54.8328i | 2.21830i | ||||||||
\(612\) | 2.03444 | − | 1.81966i | 0.0822374 | − | 0.0735554i | ||||
\(613\) | −5.47214 | −0.221017 | −0.110509 | − | 0.993875i | \(-0.535248\pi\) | ||||
−0.110509 | + | 0.993875i | \(0.535248\pi\) | |||||||
\(614\) | −34.7426 | −1.40210 | ||||||||
\(615\) | −0.381966 | − | 1.00000i | −0.0154024 | − | 0.0403239i | ||||
\(616\) | 13.0902 | − | 1.90983i | 0.527418 | − | 0.0769492i | ||||
\(617\) | 9.90983i | 0.398955i | 0.979902 | + | 0.199477i | \(0.0639244\pi\) | ||||
−0.979902 | + | 0.199477i | \(0.936076\pi\) | |||||||
\(618\) | 10.1803 | + | 26.6525i | 0.409513 | + | 1.07212i | ||||
\(619\) | − | 39.9787i | − | 1.60688i | −0.595386 | − | 0.803440i | \(-0.703001\pi\) | ||
0.595386 | − | 0.803440i | \(-0.296999\pi\) | |||||||
\(620\) | − | 0.854102i | − | 0.0343016i | ||||||
\(621\) | 2.38197 | − | 4.61803i | 0.0955850 | − | 0.185315i | ||||
\(622\) | 37.7426i | 1.51334i | ||||||||
\(623\) | 21.1803 | − | 3.09017i | 0.848572 | − | 0.123805i | ||||
\(624\) | 53.8328 | − | 20.5623i | 2.15504 | − | 0.823151i | ||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | −16.4721 | −0.658359 | ||||||||
\(627\) | −7.56231 | − | 19.7984i | −0.302009 | − | 0.790671i | ||||
\(628\) | − | 4.65248i | − | 0.185654i | ||||||
\(629\) | 8.48529 | 0.338331 | ||||||||
\(630\) | −25.7984 | − | 21.5623i | −1.02783 | − | 0.859063i | ||||
\(631\) | −6.81966 | −0.271486 | −0.135743 | − | 0.990744i | \(-0.543342\pi\) | ||||
−0.135743 | + | 0.990744i | \(0.543342\pi\) | |||||||
\(632\) | − | 17.3607i | − | 0.690571i | ||||||
\(633\) | 1.85410 | + | 4.85410i | 0.0736939 | + | 0.192933i | ||||
\(634\) | 1.00000 | 0.0397151 | ||||||||
\(635\) | 20.4164 | 0.810200 | ||||||||
\(636\) | −13.5623 | + | 5.18034i | −0.537780 | + | 0.205414i | ||||
\(637\) | −13.7082 | − | 45.9787i | −0.543139 | − | 1.82174i | ||||
\(638\) | 6.38197i | 0.252664i | ||||||||
\(639\) | 10.6525 | + | 11.9098i | 0.421405 | + | 0.471146i | ||||
\(640\) | − | 35.6525i | − | 1.40929i | ||||||
\(641\) | − | 7.43769i | − | 0.293771i | −0.989153 | − | 0.146886i | \(-0.953075\pi\) | ||
0.989153 | − | 0.146886i | \(-0.0469249\pi\) | |||||||
\(642\) | 11.6180 | + | 30.4164i | 0.458527 | + | 1.20044i | ||||
\(643\) | − | 5.79837i | − | 0.228666i | −0.993443 | − | 0.114333i | \(-0.963527\pi\) | ||
0.993443 | − | 0.114333i | \(-0.0364730\pi\) | |||||||
\(644\) | 0.236068 | + | 1.61803i | 0.00930238 | + | 0.0637595i | ||||
\(645\) | −12.3262 | − | 32.2705i | −0.485345 | − | 1.27065i | ||||
\(646\) | −13.0344 | −0.512833 | ||||||||
\(647\) | 34.0344 | 1.33803 | 0.669016 | − | 0.743248i | \(-0.266716\pi\) | ||||
0.669016 | + | 0.743248i | \(0.266716\pi\) | |||||||
\(648\) | 20.0000 | + | 2.23607i | 0.785674 | + | 0.0878410i | ||||
\(649\) | 16.9098i | 0.663769i | ||||||||
\(650\) | 20.5623 | 0.806520 | ||||||||
\(651\) | 2.11146 | − | 1.18034i | 0.0827545 | − | 0.0462612i | ||||
\(652\) | 11.7984 | 0.462060 | ||||||||
\(653\) | 2.50658i | 0.0980900i | 0.998797 | + | 0.0490450i | \(0.0156178\pi\) | ||||
−0.998797 | + | 0.0490450i | \(0.984382\pi\) | |||||||
\(654\) | 8.09017 | − | 3.09017i | 0.316351 | − | 0.120835i | ||||
\(655\) | −48.9787 | −1.91376 | ||||||||
\(656\) | −1.14590 | −0.0447398 | ||||||||
\(657\) | 16.4721 | + | 18.4164i | 0.642639 | + | 0.718493i | ||||
\(658\) | −4.94427 | − | 33.8885i | −0.192748 | − | 1.32111i | ||||
\(659\) | − | 4.41641i | − | 0.172039i | −0.996293 | − | 0.0860194i | \(-0.972585\pi\) | ||
0.996293 | − | 0.0860194i | \(-0.0274147\pi\) | |||||||
\(660\) | 5.85410 | − | 2.23607i | 0.227871 | − | 0.0870388i | ||||
\(661\) | 16.0557i | 0.624495i | 0.950001 | + | 0.312248i | \(0.101082\pi\) | ||||
−0.950001 | + | 0.312248i | \(0.898918\pi\) | |||||||
\(662\) | 58.3607i | 2.26825i | ||||||||
\(663\) | −16.3262 | + | 6.23607i | −0.634059 | + | 0.242189i | ||||
\(664\) | − | 23.9443i | − | 0.929218i | ||||||
\(665\) | 5.47214 | + | 37.5066i | 0.212200 | + | 1.45444i | ||||
\(666\) | −18.6525 | − | 20.8541i | −0.722769 | − | 0.808080i | ||||
\(667\) | 1.76393 | 0.0682997 | ||||||||
\(668\) | 11.8541 | 0.458649 | ||||||||
\(669\) | 27.6525 | − | 10.5623i | 1.06911 | − | 0.408362i | ||||
\(670\) | − | 44.9787i | − | 1.73768i | ||||||
\(671\) | 1.90983 | 0.0737282 | ||||||||
\(672\) | −13.5279 | + | 7.56231i | −0.521849 | + | 0.291722i | ||||
\(673\) | 6.23607 | 0.240383 | 0.120191 | − | 0.992751i | \(-0.461649\pi\) | ||||
0.120191 | + | 0.992751i | \(0.461649\pi\) | |||||||
\(674\) | − | 52.5066i | − | 2.02248i | ||||||
\(675\) | 8.56231 | + | 4.41641i | 0.329563 | + | 0.169988i | ||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | 13.5066 | 0.519100 | 0.259550 | − | 0.965730i | \(-0.416426\pi\) | ||||
0.259550 | + | 0.965730i | \(0.416426\pi\) | |||||||
\(678\) | 10.7984 | + | 28.2705i | 0.414709 | + | 1.08572i | ||||
\(679\) | −0.742646 | − | 5.09017i | −0.0285001 | − | 0.195343i | ||||
\(680\) | 8.61803i | 0.330487i | ||||||||
\(681\) | −13.7984 | − | 36.1246i | −0.528755 | − | 1.38430i | ||||
\(682\) | 1.90983i | 0.0731312i | ||||||||
\(683\) | − | 28.5967i | − | 1.09422i | −0.837059 | − | 0.547112i | \(-0.815727\pi\) | ||
0.837059 | − | 0.547112i | \(-0.184273\pi\) | |||||||
\(684\) | 6.76393 | + | 7.56231i | 0.258625 | + | 0.289152i | ||||
\(685\) | − | 37.2705i | − | 1.42403i | ||||||
\(686\) | 12.6180 | + | 27.1803i | 0.481759 | + | 1.03775i | ||||
\(687\) | −17.6525 | + | 6.74265i | −0.673484 | + | 0.257248i | ||||
\(688\) | −36.9787 | −1.40980 | ||||||||
\(689\) | 92.9574 | 3.54140 | ||||||||
\(690\) | −2.61803 | − | 6.85410i | −0.0996669 | − | 0.260931i | ||||
\(691\) | − | 8.09017i | − | 0.307765i | −0.988089 | − | 0.153882i | \(-0.950822\pi\) | ||
0.988089 | − | 0.153882i | \(-0.0491777\pi\) | |||||||
\(692\) | 2.14590 | 0.0815748 | ||||||||
\(693\) | 13.6180 | + | 11.3820i | 0.517306 | + | 0.432365i | ||||
\(694\) | 37.5066 | 1.42373 | ||||||||
\(695\) | − | 2.38197i | − | 0.0903531i | ||||||
\(696\) | 2.43769 | + | 6.38197i | 0.0924006 | + | 0.241908i | ||||
\(697\) | 0.347524 | 0.0131634 | ||||||||
\(698\) | −51.5410 | −1.95086 | ||||||||
\(699\) | −22.1246 | + | 8.45085i | −0.836830 | + | 0.319640i | ||||
\(700\) | −3.00000 | + | 0.437694i | −0.113389 | + | 0.0165433i | ||||
\(701\) | − | 31.6312i | − | 1.19469i | −0.801983 | − | 0.597347i | \(-0.796222\pi\) | ||
0.801983 | − | 0.597347i | \(-0.203778\pi\) | |||||||
\(702\) | 51.2148 | + | 26.4164i | 1.93298 | + | 0.997023i | ||||
\(703\) | 31.5410i | 1.18959i | ||||||||
\(704\) | 9.47214i | 0.356995i | ||||||||
\(705\) | 12.9443 | + | 33.8885i | 0.487509 | + | 1.27632i | ||||
\(706\) | 42.9230i | 1.61543i | ||||||||
\(707\) | −13.3262 | + | 1.94427i | −0.501185 | + | 0.0731219i | ||||
\(708\) | −2.88854 | − | 7.56231i | −0.108558 | − | 0.284209i | ||||
\(709\) | 32.5623 | 1.22290 | 0.611452 | − | 0.791282i | \(-0.290586\pi\) | ||||
0.611452 | + | 0.791282i | \(0.290586\pi\) | |||||||
\(710\) | 22.5623 | 0.846748 | ||||||||
\(711\) | 17.3607 | − | 15.5279i | 0.651076 | − | 0.582340i | ||||
\(712\) | 18.0902i | 0.677958i | ||||||||
\(713\) | 0.527864 | 0.0197687 | ||||||||
\(714\) | 9.52786 | − | 5.32624i | 0.356571 | − | 0.199329i | ||||
\(715\) | −40.1246 | −1.50058 | ||||||||
\(716\) | 3.50658i | 0.131047i | ||||||||
\(717\) | −9.18034 | + | 3.50658i | −0.342846 | + | 0.130956i | ||||
\(718\) | 4.70820 | 0.175709 | ||||||||
\(719\) | −17.7639 | −0.662483 | −0.331241 | − | 0.943546i | \(-0.607467\pi\) | ||||
−0.331241 | + | 0.943546i | \(0.607467\pi\) | |||||||
\(720\) | 28.4164 | − | 25.4164i | 1.05902 | − | 0.947214i | ||||
\(721\) | 3.88854 | + | 26.6525i | 0.144817 | + | 0.992590i | ||||
\(722\) | − | 17.7082i | − | 0.659031i | ||||||
\(723\) | 0.854102 | − | 0.326238i | 0.0317644 | − | 0.0121329i | ||||
\(724\) | 4.14590i | 0.154081i | ||||||||
\(725\) | 3.27051i | 0.121464i | ||||||||
\(726\) | 15.7082 | − | 6.00000i | 0.582986 | − | 0.222681i | ||||
\(727\) | 2.52786i | 0.0937533i | 0.998901 | + | 0.0468766i | \(0.0149268\pi\) | ||||
−0.998901 | + | 0.0468766i | \(0.985073\pi\) | |||||||
\(728\) | 40.1246 | − | 5.85410i | 1.48712 | − | 0.216967i | ||||
\(729\) | 15.6525 | + | 22.0000i | 0.579721 | + | 0.814815i | ||||
\(730\) | 34.8885 | 1.29128 | ||||||||
\(731\) | 11.2148 | 0.414794 | ||||||||
\(732\) | −0.854102 | + | 0.326238i | −0.0315685 | + | 0.0120581i | ||||
\(733\) | − | 38.3607i | − | 1.41688i | −0.705769 | − | 0.708442i | \(-0.749398\pi\) | ||
0.705769 | − | 0.708442i | \(-0.250602\pi\) | |||||||
\(734\) | 36.0344 | 1.33006 | ||||||||
\(735\) | −19.3262 | − | 25.1803i | −0.712859 | − | 0.928791i | ||||
\(736\) | −3.38197 | −0.124661 | ||||||||
\(737\) | 23.7426i | 0.874572i | ||||||||
\(738\) | −0.763932 | − | 0.854102i | −0.0281207 | − | 0.0314399i | ||||
\(739\) | −28.4164 | −1.04531 | −0.522657 | − | 0.852543i | \(-0.675059\pi\) | ||||
−0.522657 | + | 0.852543i | \(0.675059\pi\) | |||||||
\(740\) | −9.32624 | −0.342839 | ||||||||
\(741\) | −23.1803 | − | 60.6869i | −0.851551 | − | 2.22939i | ||||
\(742\) | −57.4508 | + | 8.38197i | −2.10909 | + | 0.307712i | ||||
\(743\) | 11.8541i | 0.434885i | 0.976073 | + | 0.217442i | \(0.0697714\pi\) | ||||
−0.976073 | + | 0.217442i | \(0.930229\pi\) | |||||||
\(744\) | 0.729490 | + | 1.90983i | 0.0267444 | + | 0.0700178i | ||||
\(745\) | − | 20.1803i | − | 0.739350i | ||||||
\(746\) | − | 1.61803i | − | 0.0592404i | ||||||
\(747\) | 23.9443 | − | 21.4164i | 0.876075 | − | 0.783585i | ||||
\(748\) | 2.03444i | 0.0743866i | ||||||||
\(749\) | 4.43769 | + | 30.4164i | 0.162150 | + | 1.11139i | ||||
\(750\) | −21.5623 | + | 8.23607i | −0.787344 | + | 0.300739i | ||||
\(751\) | 44.0344 | 1.60684 | 0.803420 | − | 0.595413i | \(-0.203012\pi\) | ||||
0.803420 | + | 0.595413i | \(0.203012\pi\) | |||||||
\(752\) | 38.8328 | 1.41609 | ||||||||
\(753\) | 4.00000 | + | 10.4721i | 0.145768 | + | 0.381626i | ||||
\(754\) | 19.5623i | 0.712417i | ||||||||
\(755\) | −6.47214 | −0.235545 | ||||||||
\(756\) | −8.03444 | − | 2.76393i | −0.292210 | − | 0.100523i | ||||
\(757\) | −17.0000 | −0.617876 | −0.308938 | − | 0.951082i | \(-0.599973\pi\) | ||||
−0.308938 | + | 0.951082i | \(0.599973\pi\) | |||||||
\(758\) | 39.5967i | 1.43822i | ||||||||
\(759\) | 1.38197 | + | 3.61803i | 0.0501622 | + | 0.131326i | ||||
\(760\) | −32.0344 | −1.16201 | ||||||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 20.4164 | − | 7.79837i | 0.739608 | − | 0.282505i | ||||
\(763\) | 8.09017 | − | 1.18034i | 0.292884 | − | 0.0427312i | ||||
\(764\) | 13.4164i | 0.485389i | ||||||||
\(765\) | −8.61803 | + | 7.70820i | −0.311586 | + | 0.278691i | ||||
\(766\) | 13.3262i | 0.481497i | ||||||||
\(767\) | 51.8328i | 1.87157i | ||||||||
\(768\) | −8.38197 | − | 21.9443i | −0.302458 | − | 0.791846i | ||||
\(769\) | 22.1803i | 0.799844i | 0.916549 | + | 0.399922i | \(0.130963\pi\) | ||||
−0.916549 | + | 0.399922i | \(0.869037\pi\) | |||||||
\(770\) | 24.7984 | − | 3.61803i | 0.893671 | − | 0.130385i | ||||
\(771\) | −19.1246 | − | 50.0689i | −0.688756 | − | 1.80319i | ||||
\(772\) | −9.70820 | −0.349406 | ||||||||
\(773\) | −0.708204 | −0.0254723 | −0.0127362 | − | 0.999919i | \(-0.504054\pi\) | ||||
−0.0127362 | + | 0.999919i | \(0.504054\pi\) | |||||||
\(774\) | −24.6525 | − | 27.5623i | −0.886115 | − | 0.990707i | ||||
\(775\) | 0.978714i | 0.0351564i | ||||||||
\(776\) | 4.34752 | 0.156067 | ||||||||
\(777\) | −12.8885 | − | 23.0557i | −0.462374 | − | 0.827120i | ||||
\(778\) | 52.9230 | 1.89738 | ||||||||
\(779\) | 1.29180i | 0.0462834i | ||||||||
\(780\) | 17.9443 | − | 6.85410i | 0.642508 | − | 0.245416i | ||||
\(781\) | −11.9098 | −0.426167 | ||||||||
\(782\) | 2.38197 | 0.0851789 | ||||||||
\(783\) | −4.20163 | + | 8.14590i | −0.150154 | + | 0.291111i | ||||
\(784\) | −32.5623 | + | 9.70820i | −1.16294 | + | 0.346722i | ||||
\(785\) | 19.7082i | 0.703416i | ||||||||
\(786\) | −48.9787 | + | 18.7082i | −1.74701 | + | 0.667300i | ||||
\(787\) | 18.5066i | 0.659688i | 0.944035 | + | 0.329844i | \(0.106996\pi\) | ||||
−0.944035 | + | 0.329844i | \(0.893004\pi\) | |||||||
\(788\) | − | 16.1246i | − | 0.574416i | ||||||
\(789\) | −29.0344 | + | 11.0902i | −1.03365 | + | 0.394821i | ||||
\(790\) | − | 32.8885i | − | 1.17012i | ||||||
\(791\) | 4.12461 | + | 28.2705i | 0.146654 | + | 1.00518i | ||||
\(792\) | −11.1803 | + | 10.0000i | −0.397276 | + | 0.355335i | ||||
\(793\) | 5.85410 | 0.207885 | ||||||||
\(794\) | 24.6525 | 0.874884 | ||||||||
\(795\) | 57.4508 | − | 21.9443i | 2.03757 | − | 0.778283i | ||||
\(796\) | − | 9.03444i | − | 0.320217i | ||||||
\(797\) | −26.5410 | −0.940131 | −0.470066 | − | 0.882631i | \(-0.655770\pi\) | ||||
−0.470066 | + | 0.882631i | \(0.655770\pi\) | |||||||
\(798\) | 19.7984 | + | 35.4164i | 0.700855 | + | 1.25373i | ||||
\(799\) | −11.7771 | −0.416643 | ||||||||
\(800\) | − | 6.27051i | − | 0.221696i | ||||||
\(801\) | −18.0902 | + | 16.1803i | −0.639185 | + | 0.571704i | ||||
\(802\) | 13.6180 | 0.480869 | ||||||||
\(803\) | −18.4164 | −0.649901 | ||||||||
\(804\) | −4.05573 | − | 10.6180i | −0.143035 | − | 0.374469i | ||||
\(805\) | −1.00000 | − | 6.85410i | −0.0352454 | − | 0.241575i | ||||
\(806\) | 5.85410i | 0.206202i | ||||||||
\(807\) | 6.70820 | + | 17.5623i | 0.236140 | + | 0.618222i | ||||
\(808\) | − | 11.3820i | − | 0.400416i | ||||||
\(809\) | − | 23.0344i | − | 0.809848i | −0.914350 | − | 0.404924i | \(-0.867298\pi\) | ||
0.914350 | − | 0.404924i | \(-0.132702\pi\) | |||||||
\(810\) | 37.8885 | + | 4.23607i | 1.33127 | + | 0.148840i | ||||
\(811\) | − | 49.0689i | − | 1.72304i | −0.507722 | − | 0.861521i | \(-0.669512\pi\) | ||
0.507722 | − | 0.861521i | \(-0.330488\pi\) | |||||||
\(812\) | −0.416408 | − | 2.85410i | −0.0146131 | − | 0.100159i | ||||
\(813\) | −3.61803 | + | 1.38197i | −0.126890 | + | 0.0484677i | ||||
\(814\) | 20.8541 | 0.730936 | ||||||||
\(815\) | −49.9787 | −1.75068 | ||||||||
\(816\) | 4.41641 | + | 11.5623i | 0.154605 | + | 0.404762i | ||||
\(817\) | 41.6869i | 1.45844i | ||||||||
\(818\) | 54.1591 | 1.89363 | ||||||||
\(819\) | 41.7426 | + | 34.8885i | 1.45861 | + | 1.21910i | ||||
\(820\) | −0.381966 | −0.0133388 | ||||||||
\(821\) | 26.1803i | 0.913700i | 0.889544 | + | 0.456850i | \(0.151022\pi\) | ||||
−0.889544 | + | 0.456850i | \(0.848978\pi\) | |||||||
\(822\) | −14.2361 | − | 37.2705i | −0.496540 | − | 1.29996i | ||||
\(823\) | 11.5623 | 0.403037 | 0.201518 | − | 0.979485i | \(-0.435412\pi\) | ||||
0.201518 | + | 0.979485i | \(0.435412\pi\) | |||||||
\(824\) | −22.7639 | −0.793019 | ||||||||
\(825\) | −6.70820 | + | 2.56231i | −0.233550 | + | 0.0892080i | ||||
\(826\) | −4.67376 | − | 32.0344i | −0.162621 | − | 1.11462i | ||||
\(827\) | 26.2148i | 0.911577i | 0.890088 | + | 0.455789i | \(0.150643\pi\) | ||||
−0.890088 | + | 0.455789i | \(0.849357\pi\) | |||||||
\(828\) | −1.23607 | − | 1.38197i | −0.0429563 | − | 0.0480266i | ||||
\(829\) | 1.00000i | 0.0347314i | 0.999849 | + | 0.0173657i | \(0.00552796\pi\) | ||||
−0.999849 | + | 0.0173657i | \(0.994472\pi\) | |||||||
\(830\) | − | 45.3607i | − | 1.57449i | ||||||
\(831\) | −4.41641 | − | 11.5623i | −0.153203 | − | 0.401092i | ||||
\(832\) | 29.0344i | 1.00659i | ||||||||
\(833\) | 9.87539 | − | 2.94427i | 0.342162 | − | 0.102013i | ||||
\(834\) | −0.909830 | − | 2.38197i | −0.0315048 | − | 0.0824807i | ||||
\(835\) | −50.2148 | −1.73775 | ||||||||
\(836\) | −7.56231 | −0.261548 | ||||||||
\(837\) | −1.25735 | + | 2.43769i | −0.0434605 | + | 0.0842590i | ||||
\(838\) | 40.1246i | 1.38608i | ||||||||
\(839\) | −10.8541 | −0.374725 | −0.187363 | − | 0.982291i | \(-0.559994\pi\) | ||||
−0.187363 | + | 0.982291i | \(0.559994\pi\) | |||||||
\(840\) | 23.4164 | − | 13.0902i | 0.807943 | − | 0.451654i | ||||
\(841\) | 25.8885 | 0.892708 | ||||||||
\(842\) | 64.2148i | 2.21299i | ||||||||
\(843\) | −1.70820 | + | 0.652476i | −0.0588337 | + | 0.0224725i | ||||
\(844\) | 1.85410 | 0.0638208 | ||||||||
\(845\) | −88.9574 | −3.06023 | ||||||||
\(846\) | 25.8885 | + | 28.9443i | 0.890066 | + | 0.995125i | ||||
\(847\) | 15.7082 | − | 2.29180i | 0.539740 | − | 0.0787470i | ||||
\(848\) | − | 65.8328i | − | 2.26071i | ||||||
\(849\) | 14.2361 | − | 5.43769i | 0.488581 | − | 0.186621i | ||||
\(850\) | 4.41641i | 0.151482i | ||||||||
\(851\) | − | 5.76393i | − | 0.197585i | ||||||
\(852\) | 5.32624 | − | 2.03444i | 0.182474 | − | 0.0696988i | ||||
\(853\) | − | 5.34752i | − | 0.183096i | −0.995801 | − | 0.0915479i | \(-0.970819\pi\) | ||
0.995801 | − | 0.0915479i | \(-0.0291815\pi\) | |||||||
\(854\) | −3.61803 | + | 0.527864i | −0.123807 | + | 0.0180631i | ||||
\(855\) | −28.6525 | − | 32.0344i | −0.979894 | − | 1.09555i | ||||
\(856\) | −25.9787 | −0.887934 | ||||||||
\(857\) | 26.4721 | 0.904271 | 0.452135 | − | 0.891949i | \(-0.350662\pi\) | ||||
0.452135 | + | 0.891949i | \(0.350662\pi\) | |||||||
\(858\) | −40.1246 | + | 15.3262i | −1.36983 | + | 0.523229i | ||||
\(859\) | − | 38.4721i | − | 1.31265i | −0.754477 | − | 0.656326i | \(-0.772110\pi\) | ||
0.754477 | − | 0.656326i | \(-0.227890\pi\) | |||||||
\(860\) | −12.3262 | −0.420321 | ||||||||
\(861\) | −0.527864 | − | 0.944272i | −0.0179896 | − | 0.0321807i | ||||
\(862\) | −35.4508 | −1.20746 | ||||||||
\(863\) | − | 16.3607i | − | 0.556924i | −0.960447 | − | 0.278462i | \(-0.910175\pi\) | ||
0.960447 | − | 0.278462i | \(-0.0898246\pi\) | |||||||
\(864\) | 8.05573 | − | 15.6180i | 0.274061 | − | 0.531336i | ||||
\(865\) | −9.09017 | −0.309075 | ||||||||
\(866\) | 2.47214 | 0.0840066 | ||||||||
\(867\) | 9.16718 | + | 24.0000i | 0.311334 | + | 0.815083i | ||||
\(868\) | −0.124612 | − | 0.854102i | −0.00422960 | − | 0.0289901i | ||||
\(869\) | 17.3607i | 0.588921i | ||||||||
\(870\) | 4.61803 | + | 12.0902i | 0.156566 | + | 0.409895i | ||||
\(871\) | 72.7771i | 2.46596i | ||||||||
\(872\) | 6.90983i | 0.233996i | ||||||||
\(873\) | 3.88854 | + | 4.34752i | 0.131607 | + | 0.147141i | ||||
\(874\) | 8.85410i | 0.299494i | ||||||||
\(875\) | −21.5623 | + | 3.14590i | −0.728939 | + | 0.106351i | ||||
\(876\) | 8.23607 | − | 3.14590i | 0.278271 | − | 0.106290i | ||||
\(877\) | 9.70820 | 0.327823 | 0.163911 | − | 0.986475i | \(-0.447589\pi\) | ||||
0.163911 | + | 0.986475i | \(0.447589\pi\) | |||||||
\(878\) | −41.2148 | −1.39093 | ||||||||
\(879\) | −8.83282 | − | 23.1246i | −0.297923 | − | 0.779974i | ||||
\(880\) | 28.4164i | 0.957917i | ||||||||
\(881\) | 25.8885 | 0.872207 | 0.436104 | − | 0.899896i | \(-0.356358\pi\) | ||||
0.436104 | + | 0.899896i | \(0.356358\pi\) | |||||||
\(882\) | −28.9443 | − | 17.7984i | −0.974604 | − | 0.599302i | ||||
\(883\) | 56.1591 | 1.88990 | 0.944951 | − | 0.327211i | \(-0.106109\pi\) | ||||
0.944951 | + | 0.327211i | \(0.106109\pi\) | |||||||
\(884\) | 6.23607i | 0.209742i | ||||||||
\(885\) | 12.2361 | + | 32.0344i | 0.411311 | + | 1.07683i | ||||
\(886\) | −35.8885 | −1.20570 | ||||||||
\(887\) | −19.9098 | −0.668507 | −0.334253 | − | 0.942483i | \(-0.608484\pi\) | ||||
−0.334253 | + | 0.942483i | \(0.608484\pi\) | |||||||
\(888\) | 20.8541 | − | 7.96556i | 0.699818 | − | 0.267307i | ||||
\(889\) | 20.4164 | − | 2.97871i | 0.684744 | − | 0.0999029i | ||||
\(890\) | 34.2705i | 1.14875i | ||||||||
\(891\) | −20.0000 | − | 2.23607i | −0.670025 | − | 0.0749111i | ||||
\(892\) | − | 10.5623i | − | 0.353652i | ||||||
\(893\) | − | 43.7771i | − | 1.46494i | ||||||
\(894\) | −7.70820 | − | 20.1803i | −0.257801 | − | 0.674932i | ||||
\(895\) | − | 14.8541i | − | 0.496518i | ||||||
\(896\) | −5.20163 | − | 35.6525i | −0.173774 | − | 1.19107i | ||||
\(897\) | 4.23607 | + | 11.0902i | 0.141438 | + | 0.370290i | ||||
\(898\) | −17.6525 | −0.589071 | ||||||||
\(899\) | −0.931116 | −0.0310545 | ||||||||
\(900\) | 2.56231 | − | 2.29180i | 0.0854102 | − | 0.0763932i | ||||
\(901\) | 19.9656i | 0.665149i | ||||||||
\(902\) | 0.854102 | 0.0284385 | ||||||||
\(903\) | −17.0344 | − | 30.4721i | −0.566871 | − | 1.01405i | ||||
\(904\) | −24.1459 | −0.803081 | ||||||||
\(905\) | − | 17.5623i | − | 0.583791i | ||||||
\(906\) | −6.47214 | + | 2.47214i | −0.215022 | + | 0.0821312i | ||||
\(907\) | −4.03444 | −0.133961 | −0.0669807 | − | 0.997754i | \(-0.521337\pi\) | ||||
−0.0669807 | + | 0.997754i | \(0.521337\pi\) | |||||||
\(908\) | −13.7984 | −0.457915 | ||||||||
\(909\) | 11.3820 | − | 10.1803i | 0.377516 | − | 0.337661i | ||||
\(910\) | 76.0132 | − | 11.0902i | 2.51981 | − | 0.367636i | ||||
\(911\) | 15.1246i | 0.501101i | 0.968104 | + | 0.250550i | \(0.0806116\pi\) | ||||
−0.968104 | + | 0.250550i | \(0.919388\pi\) | |||||||
\(912\) | −42.9787 | + | 16.4164i | −1.42317 | + | 0.543602i | ||||
\(913\) | 23.9443i | 0.792440i | ||||||||
\(914\) | 25.1803i | 0.832892i | ||||||||
\(915\) | 3.61803 | − | 1.38197i | 0.119609 | − | 0.0456864i | ||||
\(916\) | 6.74265i | 0.222783i | ||||||||
\(917\) | −48.9787 | + | 7.14590i | −1.61742 | + | 0.235978i | ||||
\(918\) | −5.67376 | + | 11.0000i | −0.187262 | + | 0.363054i | ||||
\(919\) | −14.3475 | −0.473281 | −0.236641 | − | 0.971597i | \(-0.576046\pi\) | ||||
−0.236641 | + | 0.971597i | \(0.576046\pi\) | |||||||
\(920\) | 5.85410 | 0.193004 | ||||||||
\(921\) | 34.7426 | − | 13.2705i | 1.14481 | − | 0.437278i | ||||
\(922\) | − | 39.9443i | − | 1.31549i | ||||||
\(923\) | −36.5066 | −1.20163 | ||||||||
\(924\) | 5.52786 | − | 3.09017i | 0.181853 | − | 0.101659i | ||||
\(925\) | 10.6869 | 0.351384 | ||||||||
\(926\) | − | 26.7426i | − | 0.878818i | ||||||
\(927\) | −20.3607 | − | 22.7639i | −0.668732 | − | 0.747666i | ||||
\(928\) | 5.96556 | 0.195829 | ||||||||
\(929\) | 34.3951 | 1.12847 | 0.564234 | − | 0.825615i | \(-0.309172\pi\) | ||||
0.564234 | + | 0.825615i | \(0.309172\pi\) | |||||||
\(930\) | 1.38197 | + | 3.61803i | 0.0453165 | + | 0.118640i | ||||
\(931\) | 10.9443 | + | 36.7082i | 0.358684 | + | 1.20306i | ||||
\(932\) | 8.45085i | 0.276817i | ||||||||
\(933\) | −14.4164 | − | 37.7426i | −0.471972 | − | 1.23564i | ||||
\(934\) | 54.7426i | 1.79123i | ||||||||
\(935\) | − | 8.61803i | − | 0.281840i | ||||||
\(936\) | −34.2705 | + | 30.6525i | −1.12017 | + | 1.00191i | ||||
\(937\) | 38.7082i | 1.26454i | 0.774747 | + | 0.632271i | \(0.217877\pi\) | ||||
−0.774747 | + | 0.632271i | \(0.782123\pi\) | |||||||
\(938\) | −6.56231 | − | 44.9787i | −0.214267 | − | 1.46861i | ||||
\(939\) | 16.4721 | − | 6.29180i | 0.537548 | − | 0.205325i | ||||
\(940\) | 12.9443 | 0.422196 | ||||||||
\(941\) | −26.4721 | −0.862967 | −0.431483 | − | 0.902121i | \(-0.642010\pi\) | ||||
−0.431483 | + | 0.902121i | \(0.642010\pi\) | |||||||
\(942\) | 7.52786 | + | 19.7082i | 0.245271 | + | 0.642128i | ||||
\(943\) | − | 0.236068i | − | 0.00768743i | ||||||
\(944\) | 36.7082 | 1.19475 | ||||||||
\(945\) | 34.0344 | + | 11.7082i | 1.10714 | + | 0.380868i | ||||
\(946\) | 27.5623 | 0.896128 | ||||||||
\(947\) | 4.83282i | 0.157045i | 0.996912 | + | 0.0785227i | \(0.0250203\pi\) | ||||
−0.996912 | + | 0.0785227i | \(0.974980\pi\) | |||||||
\(948\) | −2.96556 | − | 7.76393i | −0.0963169 | − | 0.252161i | ||||
\(949\) | −56.4508 | −1.83247 | ||||||||
\(950\) | −16.4164 | −0.532619 | ||||||||
\(951\) | −1.00000 | + | 0.381966i | −0.0324272 | + | 0.0123861i | ||||
\(952\) | 1.25735 | + | 8.61803i | 0.0407511 | + | 0.279312i | ||||
\(953\) | 3.03444i | 0.0982952i | 0.998792 | + | 0.0491476i | \(0.0156505\pi\) | ||||
−0.998792 | + | 0.0491476i | \(0.984350\pi\) | |||||||
\(954\) | 49.0689 | − | 43.8885i | 1.58866 | − | 1.42094i | ||||
\(955\) | − | 56.8328i | − | 1.83907i | ||||||
\(956\) | 3.50658i | 0.113411i | ||||||||
\(957\) | −2.43769 | − | 6.38197i | −0.0787995 | − | 0.206300i | ||||
\(958\) | − | 41.5066i | − | 1.34102i | ||||||
\(959\) | −5.43769 | − | 37.2705i | −0.175592 | − | 1.20353i | ||||
\(960\) | 6.85410 | + | 17.9443i | 0.221215 | + | 0.579149i | ||||
\(961\) | 30.7214 | 0.991012 | ||||||||
\(962\) | 63.9230 | 2.06096 | ||||||||
\(963\) | −23.2361 | − | 25.9787i | −0.748772 | − | 0.837152i | ||||
\(964\) | − | 0.326238i | − | 0.0105074i | ||||||
\(965\) | 41.1246 | 1.32385 | ||||||||
\(966\) | −3.61803 | − | 6.47214i | −0.116408 | − | 0.208238i | ||||
\(967\) | 15.8885 | 0.510941 | 0.255471 | − | 0.966817i | \(-0.417770\pi\) | ||||
0.255471 | + | 0.966817i | \(0.417770\pi\) | |||||||
\(968\) | 13.4164i | 0.431220i | ||||||||
\(969\) | 13.0344 | − | 4.97871i | 0.418727 | − | 0.159939i | ||||
\(970\) | 8.23607 | 0.264444 | ||||||||
\(971\) | 6.74265 | 0.216382 | 0.108191 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108191 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(972\) | 9.32624 | − | 2.41641i | 0.299139 | − | 0.0775063i | ||||
\(973\) | −0.347524 | − | 2.38197i | −0.0111411 | − | 0.0763623i | ||||
\(974\) | 23.7984i | 0.762549i | ||||||||
\(975\) | −20.5623 | + | 7.85410i | −0.658521 | + | 0.251533i | ||||
\(976\) | − | 4.14590i | − | 0.132707i | ||||||
\(977\) | − | 7.97871i | − | 0.255262i | −0.991822 | − | 0.127631i | \(-0.959263\pi\) | ||
0.991822 | − | 0.127631i | \(-0.0407373\pi\) | |||||||
\(978\) | −49.9787 | + | 19.0902i | −1.59814 | + | 0.610436i | ||||
\(979\) | − | 18.0902i | − | 0.578164i | ||||||
\(980\) | −10.8541 | + | 3.23607i | −0.346722 | + | 0.103372i | ||||
\(981\) | −6.90983 | + | 6.18034i | −0.220614 | + | 0.197323i | ||||
\(982\) | −35.4508 | −1.13128 | ||||||||
\(983\) | −2.81966 | −0.0899332 | −0.0449666 | − | 0.998988i | \(-0.514318\pi\) | ||||
−0.0449666 | + | 0.998988i | \(0.514318\pi\) | |||||||
\(984\) | 0.854102 | − | 0.326238i | 0.0272278 | − | 0.0104001i | ||||
\(985\) | 68.3050i | 2.17638i | ||||||||
\(986\) | −4.20163 | −0.133807 | ||||||||
\(987\) | 17.8885 | + | 32.0000i | 0.569399 | + | 1.01857i | ||||
\(988\) | −23.1803 | −0.737465 | ||||||||
\(989\) | − | 7.61803i | − | 0.242239i | ||||||
\(990\) | −21.1803 | + | 18.9443i | −0.673155 | + | 0.602088i | ||||
\(991\) | 2.20163 | 0.0699370 | 0.0349685 | − | 0.999388i | \(-0.488867\pi\) | ||||
0.0349685 | + | 0.999388i | \(0.488867\pi\) | |||||||
\(992\) | 1.78522 | 0.0566807 | ||||||||
\(993\) | −22.2918 | − | 58.3607i | −0.707409 | − | 1.85202i | ||||
\(994\) | 22.5623 | − | 3.29180i | 0.715633 | − | 0.104409i | ||||
\(995\) | 38.2705i | 1.21326i | ||||||||
\(996\) | −4.09017 | − | 10.7082i | −0.129602 | − | 0.339302i | ||||
\(997\) | 18.0557i | 0.571831i | 0.958255 | + | 0.285915i | \(0.0922976\pi\) | ||||
−0.958255 | + | 0.285915i | \(0.907702\pi\) | |||||||
\(998\) | − | 28.4164i | − | 0.899506i | ||||||
\(999\) | 26.6180 | + | 13.7295i | 0.842157 | + | 0.434382i |
(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 | 483.2.d.b.461.4 | yes | 4 | |
3.2 | odd | 2 | 483.2.d.a.461.1 | ✓ | 4 | ||
7.6 | odd | 2 | 483.2.d.a.461.4 | yes | 4 | ||
21.20 | even | 2 | inner | 483.2.d.b.461.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.d.a.461.1 | ✓ | 4 | 3.2 | odd | 2 | ||
483.2.d.a.461.4 | yes | 4 | 7.6 | odd | 2 | ||
483.2.d.b.461.1 | yes | 4 | 21.20 | even | 2 | inner | |
483.2.d.b.461.4 | yes | 4 | 1.1 | even | 1 | trivial |