Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2280,2,Mod(1,2280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2280.a (trivial) |
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: | yes |
Analytic conductor: | \(18.2058916609\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.585786 | −0.221406 | −0.110703 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110703 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.585786 | −0.127829 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.24264 | −1.15923 | −0.579615 | − | 0.814891i | \(-0.696797\pi\) | ||||
−0.579615 | + | 0.814891i | \(0.696797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.17157 | −0.569631 | −0.284816 | − | 0.958582i | \(-0.591932\pi\) | ||||
−0.284816 | + | 0.958582i | \(0.591932\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41421 | 0.246183 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.585786 | 0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.07107 | 1.16248 | 0.581238 | − | 0.813733i | \(-0.302568\pi\) | ||||
0.581238 | + | 0.813733i | \(0.302568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.24264 | −0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.24264 | −0.974937 | −0.487468 | − | 0.873141i | \(-0.662080\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2426 | −1.56199 | −0.780994 | − | 0.624538i | \(-0.785287\pi\) | ||||
−0.780994 | + | 0.624538i | \(0.785287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.828427 | −0.120839 | −0.0604193 | − | 0.998173i | \(-0.519244\pi\) | ||||
−0.0604193 | + | 0.998173i | \(0.519244\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.82843 | −0.396059 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.48528 | 0.616101 | 0.308050 | − | 0.951370i | \(-0.400323\pi\) | ||||
0.308050 | + | 0.951370i | \(0.400323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843 | 0.368230 | 0.184115 | − | 0.982905i | \(-0.441058\pi\) | ||||
0.184115 | + | 0.982905i | \(0.441058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.585786 | −0.0738022 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.24264 | 0.526235 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3137 | 1.38219 | 0.691095 | − | 0.722764i | \(-0.257129\pi\) | ||||
0.691095 | + | 0.722764i | \(0.257129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8284 | −1.28510 | −0.642549 | − | 0.766245i | \(-0.722123\pi\) | ||||
−0.642549 | + | 0.766245i | \(0.722123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.65685 | 0.896167 | 0.448084 | − | 0.893992i | \(-0.352107\pi\) | ||||
0.448084 | + | 0.893992i | \(0.352107\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.828427 | −0.0944080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6569 | −1.53652 | −0.768258 | − | 0.640140i | \(-0.778876\pi\) | ||||
−0.768258 | + | 0.640140i | \(0.778876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82843 | 0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.24264 | −0.669281 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.5563 | 1.86097 | 0.930485 | − | 0.366331i | \(-0.119386\pi\) | ||||
0.930485 | + | 0.366331i | \(0.119386\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.48528 | 0.260528 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.17157 | −0.328877 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.89949 | −1.00514 | −0.502571 | − | 0.864536i | \(-0.667612\pi\) | ||||
−0.502571 | + | 0.864536i | \(0.667612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.41421 | 0.142134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.17157 | −0.713598 | −0.356799 | − | 0.934181i | \(-0.616132\pi\) | ||||
−0.356799 | + | 0.934181i | \(0.616132\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.585786 | 0.0571669 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.34315 | 0.226520 | 0.113260 | − | 0.993565i | \(-0.463871\pi\) | ||||
0.113260 | + | 0.993565i | \(0.463871\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.1421 | −1.54614 | −0.773068 | − | 0.634323i | \(-0.781279\pi\) | ||||
−0.773068 | + | 0.634323i | \(0.781279\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.07107 | 0.671156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.65685 | −0.155864 | −0.0779319 | − | 0.996959i | \(-0.524832\pi\) | ||||
−0.0779319 | + | 0.996959i | \(0.524832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.828427 | −0.0772512 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.24264 | −0.392232 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.65685 | 0.151884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.24264 | −0.562880 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9706 | −1.50589 | −0.752947 | − | 0.658081i | \(-0.771368\pi\) | ||||
−0.752947 | + | 0.658081i | \(0.771368\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.2426 | −0.901814 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.0711 | 1.66625 | 0.833123 | − | 0.553087i | \(-0.186550\pi\) | ||||
0.833123 | + | 0.553087i | \(0.186550\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.585786 | 0.0507941 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.9706 | 1.62076 | 0.810382 | − | 0.585901i | \(-0.199259\pi\) | ||||
0.810382 | + | 0.585901i | \(0.199259\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.48528 | 0.380437 | 0.190218 | − | 0.981742i | \(-0.439080\pi\) | ||||
0.190218 | + | 0.981742i | \(0.439080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.828427 | −0.0697661 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00000 | −0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.24264 | 0.518423 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.65685 | −0.549048 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.343146 | 0.0281116 | 0.0140558 | − | 0.999901i | \(-0.495526\pi\) | ||||
0.0140558 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8284 | −1.36948 | −0.684739 | − | 0.728788i | \(-0.740084\pi\) | ||||
−0.684739 | + | 0.728788i | \(0.740084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.82843 | −0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.17157 | 0.254747 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1421 | 1.60752 | 0.803759 | − | 0.594955i | \(-0.202830\pi\) | ||||
0.803759 | + | 0.594955i | \(0.202830\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.48528 | 0.355706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.485281 | −0.0382455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.8995 | −1.55865 | −0.779324 | − | 0.626621i | \(-0.784438\pi\) | ||||
−0.779324 | + | 0.626621i | \(0.784438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.41421 | −0.110096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.34315 | 0.336083 | 0.168041 | − | 0.985780i | \(-0.446256\pi\) | ||||
0.168041 | + | 0.985780i | \(0.446256\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.34315 | 0.178146 | 0.0890730 | − | 0.996025i | \(-0.471610\pi\) | ||||
0.0890730 | + | 0.996025i | \(0.471610\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.585786 | −0.0442813 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.82843 | 0.212598 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7990 | −1.18087 | −0.590436 | − | 0.807084i | \(-0.701044\pi\) | ||||
−0.590436 | + | 0.807084i | \(0.701044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.828427 | −0.0615765 | −0.0307883 | − | 0.999526i | \(-0.509802\pi\) | ||||
−0.0307883 | + | 0.999526i | \(0.509802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.07107 | −0.519875 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.585786 | −0.0426097 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5858 | 0.765961 | 0.382980 | − | 0.923757i | \(-0.374898\pi\) | ||||
0.382980 | + | 0.923757i | \(0.374898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.92893 | 0.642719 | 0.321359 | − | 0.946957i | \(-0.395860\pi\) | ||||
0.321359 | + | 0.946957i | \(0.395860\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.24264 | 0.303822 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.48528 | −0.604551 | −0.302276 | − | 0.953221i | \(-0.597746\pi\) | ||||
−0.302276 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1421 | 1.00251 | 0.501255 | − | 0.865300i | \(-0.332872\pi\) | ||||
0.501255 | + | 0.865300i | \(0.332872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3137 | 0.798007 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.65685 | 0.256661 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.24264 | 0.436005 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.828427 | 0.0575797 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.41421 | −0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.8284 | −0.741952 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.2426 | 0.698542 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.85786 | 0.126120 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.65685 | 0.517402 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.68629 | −0.313817 | −0.156909 | − | 0.987613i | \(-0.550153\pi\) | ||||
−0.156909 | + | 0.987613i | \(0.550153\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.3137 | 1.14915 | 0.574576 | − | 0.818452i | \(-0.305167\pi\) | ||||
0.574576 | + | 0.818452i | \(0.305167\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.6274 | 1.75959 | 0.879795 | − | 0.475354i | \(-0.157680\pi\) | ||||
0.879795 | + | 0.475354i | \(0.157680\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.828427 | −0.0545065 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.65685 | −0.239568 | −0.119784 | − | 0.992800i | \(-0.538220\pi\) | ||||
−0.119784 | + | 0.992800i | \(0.538220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.828427 | 0.0540406 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.6569 | −0.887108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.75736 | −0.243043 | −0.121522 | − | 0.992589i | \(-0.538777\pi\) | ||||
−0.121522 | + | 0.992589i | \(0.538777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.9706 | 1.22200 | 0.611001 | − | 0.791630i | \(-0.290767\pi\) | ||||
0.611001 | + | 0.791630i | \(0.290767\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.65685 | 0.425291 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.24264 | 0.269953 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.727922 | −0.0459460 | −0.0229730 | − | 0.999736i | \(-0.507313\pi\) | ||||
−0.0229730 | + | 0.999736i | \(0.507313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.17157 | 0.0736562 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.82843 | 0.177123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.34315 | 0.395675 | 0.197837 | − | 0.980235i | \(-0.436608\pi\) | ||||
0.197837 | + | 0.980235i | \(0.436608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.14214 | −0.257380 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.24264 | −0.386410 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.34315 | −0.514460 | −0.257230 | − | 0.966350i | \(-0.582810\pi\) | ||||
−0.257230 | + | 0.966350i | \(0.582810\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.48528 | −0.275529 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.5563 | 1.07443 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.8995 | 1.45718 | 0.728589 | − | 0.684951i | \(-0.240176\pi\) | ||||
0.728589 | + | 0.684951i | \(0.240176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1421 | −1.58802 | −0.794011 | − | 0.607904i | \(-0.792011\pi\) | ||||
−0.794011 | + | 0.607904i | \(0.792011\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.48528 | 0.150416 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.41421 | 0.0852803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.3137 | 1.04028 | 0.520140 | − | 0.854081i | \(-0.325880\pi\) | ||||
0.520140 | + | 0.854081i | \(0.325880\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.17157 | −0.189877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.75736 | 0.343455 | 0.171728 | − | 0.985144i | \(-0.445065\pi\) | ||||
0.171728 | + | 0.985144i | \(0.445065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.8995 | −1.42068 | −0.710339 | − | 0.703860i | \(-0.751458\pi\) | ||||
−0.710339 | + | 0.703860i | \(0.751458\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.65685 | 0.215857 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.89949 | −0.580319 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.82843 | −0.164677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.41421 | 0.0820610 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.51472 | −0.203261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.17157 | −0.411996 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.82843 | 0.389719 | 0.194859 | − | 0.980831i | \(-0.437575\pi\) | ||||
0.194859 | + | 0.980831i | \(0.437575\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.58579 | −0.373446 | −0.186723 | − | 0.982413i | \(-0.559787\pi\) | ||||
−0.186723 | + | 0.982413i | \(0.559787\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.79899 | −0.553872 | −0.276936 | − | 0.960888i | \(-0.589319\pi\) | ||||
−0.276936 | + | 0.960888i | \(0.589319\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.585786 | 0.0330053 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.48528 | −0.476581 | −0.238290 | − | 0.971194i | \(-0.576587\pi\) | ||||
−0.238290 | + | 0.971194i | \(0.576587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.82843 | −0.494297 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.34315 | 0.130782 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.82843 | 0.157378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24264 | −0.235339 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.1421 | −0.892662 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.485281 | 0.0267544 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.17157 | −0.394185 | −0.197093 | − | 0.980385i | \(-0.563150\pi\) | ||||
−0.197093 | + | 0.980385i | \(0.563150\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.07107 | 0.387492 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3137 | −0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8995 | 0.975048 | 0.487524 | − | 0.873110i | \(-0.337900\pi\) | ||||
0.487524 | + | 0.873110i | \(0.337900\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.65685 | −0.0899880 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.48528 | −0.242892 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.828427 | −0.0446010 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6569 | 0.625773 | 0.312886 | − | 0.949791i | \(-0.398704\pi\) | ||||
0.312886 | + | 0.949791i | \(0.398704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.24264 | −0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8284 | 0.574713 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.65685 | 0.0876900 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.0416 | −1.47998 | −0.739990 | − | 0.672618i | \(-0.765170\pi\) | ||||
−0.739990 | + | 0.672618i | \(0.765170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.00000 | −0.472377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.65685 | −0.400778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.07107 | 0.473506 | 0.236753 | − | 0.971570i | \(-0.423917\pi\) | ||||
0.236753 | + | 0.971570i | \(0.423917\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.24264 | −0.324979 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.62742 | −0.136409 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0416 | 1.03772 | 0.518858 | − | 0.854860i | \(-0.326357\pi\) | ||||
0.518858 | + | 0.854860i | \(0.326357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.4853 | 1.36406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.48528 | 0.333127 | 0.166563 | − | 0.986031i | \(-0.446733\pi\) | ||||
0.166563 | + | 0.986031i | \(0.446733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.9706 | −0.869428 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.686292 | −0.0350679 | −0.0175339 | − | 0.999846i | \(-0.505582\pi\) | ||||
−0.0175339 | + | 0.999846i | \(0.505582\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.828427 | 0.0422206 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2426 | −0.520663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.3431 | −0.625822 | −0.312911 | − | 0.949782i | \(-0.601304\pi\) | ||||
−0.312911 | + | 0.949782i | \(0.601304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.34315 | −0.118498 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.0711 | 0.962008 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.6569 | 0.687151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000 | 1.30490 | 0.652451 | − | 0.757831i | \(-0.273741\pi\) | ||||
0.652451 | + | 0.757831i | \(0.273741\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.585786 | 0.0293260 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.2132 | 1.55871 | 0.779356 | − | 0.626581i | \(-0.215546\pi\) | ||||
0.779356 | + | 0.626581i | \(0.215546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.4558 | 0.670283 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000 | 0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.85786 | −0.388546 | −0.194273 | − | 0.980947i | \(-0.562235\pi\) | ||||
−0.194273 | + | 0.980947i | \(0.562235\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.9706 | 0.935749 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.65685 | −0.0815285 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.48528 | 0.219645 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7574 | 0.965210 | 0.482605 | − | 0.875838i | \(-0.339691\pi\) | ||||
0.482605 | + | 0.875838i | \(0.339691\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.68629 | 0.130922 | 0.0654609 | − | 0.997855i | \(-0.479148\pi\) | ||||
0.0654609 | + | 0.997855i | \(0.479148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.828427 | −0.0402795 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.82843 | −0.137199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.68629 | 0.226786 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.85786 | −0.282163 | −0.141082 | − | 0.989998i | \(-0.545058\pi\) | ||||
−0.141082 | + | 0.989998i | \(0.545058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2426 | 0.972799 | 0.486400 | − | 0.873736i | \(-0.338310\pi\) | ||||
0.486400 | + | 0.873736i | \(0.338310\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.24264 | 0.299312 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.828427 | −0.0396290 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.3137 | −1.30361 | −0.651806 | − | 0.758386i | \(-0.725988\pi\) | ||||
−0.651806 | + | 0.758386i | \(0.725988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.65685 | −0.316993 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.1421 | −1.14703 | −0.573514 | − | 0.819196i | \(-0.694420\pi\) | ||||
−0.573514 | + | 0.819196i | \(0.694420\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.5563 | −0.832251 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.343146 | 0.0162302 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.5269 | −1.81820 | −0.909099 | − | 0.416581i | \(-0.863228\pi\) | ||||
−0.909099 | + | 0.416581i | \(0.863228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.82843 | −0.415714 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.8284 | −0.790668 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.48528 | −0.116512 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.14214 | −0.380873 | −0.190437 | − | 0.981700i | \(-0.560990\pi\) | ||||
−0.190437 | + | 0.981700i | \(0.560990\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.82843 | −0.132020 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6274 | 1.14701 | 0.573507 | − | 0.819201i | \(-0.305583\pi\) | ||||
0.573507 | + | 0.819201i | \(0.305583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.2426 | −1.59139 | −0.795695 | − | 0.605697i | \(-0.792894\pi\) | ||||
−0.795695 | + | 0.605697i | \(0.792894\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.17157 | 0.147078 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.14214 | 0.376773 | 0.188387 | − | 0.982095i | \(-0.439674\pi\) | ||||
0.188387 | + | 0.982095i | \(0.439674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.62742 | −0.306026 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.1421 | 0.928101 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.4853 | −0.666034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.48528 | 0.205367 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.3848 | 1.75385 | 0.876923 | − | 0.480632i | \(-0.159593\pi\) | ||||
0.876923 | + | 0.480632i | \(0.159593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.0000 | −1.36788 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.485281 | −0.0220811 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.89949 | 0.449513 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.1716 | 0.596861 | 0.298430 | − | 0.954431i | \(-0.403537\pi\) | ||||
0.298430 | + | 0.954431i | \(0.403537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.8995 | −0.899886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.2426 | 1.81612 | 0.908062 | − | 0.418835i | \(-0.137561\pi\) | ||||
0.908062 | + | 0.418835i | \(0.137561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.6569 | 0.795225 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.41421 | −0.0635642 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.34315 | 0.284529 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.17157 | 0.410576 | 0.205288 | − | 0.978702i | \(-0.434187\pi\) | ||||
0.205288 | + | 0.978702i | \(0.434187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.34315 | 0.194037 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.2843 | 1.35031 | 0.675154 | − | 0.737676i | \(-0.264077\pi\) | ||||
0.675154 | + | 0.737676i | \(0.264077\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.17157 | 0.319131 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.07107 | −0.0474742 | −0.0237371 | − | 0.999718i | \(-0.507556\pi\) | ||||
−0.0237371 | + | 0.999718i | \(0.507556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.48528 | −0.198417 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.17157 | −0.0515257 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.34315 | 0.102853 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3848 | 0.717830 | 0.358915 | − | 0.933370i | \(-0.383147\pi\) | ||||
0.358915 | + | 0.933370i | \(0.383147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.85786 | 0.431054 | 0.215527 | − | 0.976498i | \(-0.430853\pi\) | ||||
0.215527 | + | 0.976498i | \(0.430853\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.585786 | −0.0255658 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.97056 | 0.390764 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.82843 | 0.122743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.4853 | 1.14720 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.34315 | −0.101303 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.7990 | −0.681777 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.41421 | −0.405499 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.3137 | 1.77622 | 0.888108 | − | 0.459636i | \(-0.152020\pi\) | ||||
0.888108 | + | 0.459636i | \(0.152020\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.828427 | −0.0355512 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.1421 | 0.691453 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.5147 | 0.492334 | 0.246167 | − | 0.969227i | \(-0.420829\pi\) | ||||
0.246167 | + | 0.969227i | \(0.420829\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.00000 | −0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.24264 | 0.265945 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.07107 | −0.300150 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.9706 | −0.973294 | −0.486647 | − | 0.873599i | \(-0.661780\pi\) | ||||
−0.486647 | + | 0.873599i | \(0.661780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.4558 | 1.83799 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6863 | 0.450373 | 0.225187 | − | 0.974316i | \(-0.427701\pi\) | ||||
0.225187 | + | 0.974316i | \(0.427701\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.65685 | 0.0697044 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.585786 | −0.0246007 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.8995 | −1.00192 | −0.500959 | − | 0.865471i | \(-0.667019\pi\) | ||||
−0.500959 | + | 0.865471i | \(0.667019\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.4853 | −0.689888 | −0.344944 | − | 0.938623i | \(-0.612102\pi\) | ||||
−0.344944 | + | 0.938623i | \(0.612102\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5858 | 0.442228 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.828427 | 0.0345478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4853 | 0.769552 | 0.384776 | − | 0.923010i | \(-0.374279\pi\) | ||||
0.384776 | + | 0.923010i | \(0.374279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.92893 | 0.371074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.51472 | 0.145815 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.34315 | 0.262706 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.24264 | 0.175412 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.8284 | 0.529486 | 0.264743 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264743 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.17157 | 0.130682 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.48528 | −0.349038 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.31371 | 0.0539475 | 0.0269738 | − | 0.999636i | \(-0.491413\pi\) | ||||
0.0269738 | + | 0.999636i | \(0.491413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.65685 | −0.0679244 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.1421 | 0.578799 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9706 | 0.693398 | 0.346699 | − | 0.937976i | \(-0.387302\pi\) | ||||
0.346699 | + | 0.937976i | \(0.387302\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.8579 | −0.483692 | −0.241846 | − | 0.970315i | \(-0.577753\pi\) | ||||
−0.241846 | + | 0.970315i | \(0.577753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3137 | 0.460730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.00000 | 0.365902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.85786 | 0.237763 | 0.118882 | − | 0.992908i | \(-0.462069\pi\) | ||||
0.118882 | + | 0.992908i | \(0.462069\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.65685 | 0.148183 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.51472 | 0.142190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.1421 | −1.13665 | −0.568325 | − | 0.822804i | \(-0.692408\pi\) | ||||
−0.568325 | + | 0.822804i | \(0.692408\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.24264 | 0.251728 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1127 | 1.25255 | 0.626275 | − | 0.779602i | \(-0.284579\pi\) | ||||
0.626275 | + | 0.779602i | \(0.284579\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.8284 | −0.435231 | −0.217616 | − | 0.976035i | \(-0.569828\pi\) | ||||
−0.217616 | + | 0.976035i | \(0.569828\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.828427 | 0.0332436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.2843 | −0.412031 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.41421 | −0.0564782 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.9706 | −0.994062 | −0.497031 | − | 0.867733i | \(-0.665577\pi\) | ||||
−0.497031 | + | 0.867733i | \(0.665577\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.9706 | 0.673456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2426 | 1.11901 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.8284 | −0.428366 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.7574 | −1.01735 | −0.508677 | − | 0.860957i | \(-0.669865\pi\) | ||||
−0.508677 | + | 0.860957i | \(0.669865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2426 | 0.403930 | 0.201965 | − | 0.979393i | \(-0.435267\pi\) | ||||
0.201965 | + | 0.979393i | \(0.435267\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.2426 | 0.403304 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.6569 | 1.24456 | 0.622280 | − | 0.782795i | \(-0.286207\pi\) | ||||
0.622280 | + | 0.782795i | \(0.286207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.85786 | 0.0728154 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.48528 | 0.175523 | 0.0877613 | − | 0.996142i | \(-0.472029\pi\) | ||||
0.0877613 | + | 0.996142i | \(0.472029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.0711 | −0.745168 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.65685 | 0.298722 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.6569 | −0.687813 | −0.343907 | − | 0.939004i | \(-0.611750\pi\) | ||||
−0.343907 | + | 0.939004i | \(0.611750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.1127 | −1.44352 | −0.721758 | − | 0.692145i | \(-0.756666\pi\) | ||||
−0.721758 | + | 0.692145i | \(0.756666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.0000 | 0.466041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.585786 | −0.0227158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.17157 | −0.200244 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.68629 | −0.181182 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.3137 | −0.436761 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.1005 | −0.389346 | −0.194673 | − | 0.980868i | \(-0.562365\pi\) | ||||
−0.194673 | + | 0.980868i | \(0.562365\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.201010 | 0.00772545 | 0.00386272 | − | 0.999993i | \(-0.498770\pi\) | ||||
0.00386272 | + | 0.999993i | \(0.498770\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.79899 | 0.222545 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.3137 | 0.663463 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.3137 | −1.65735 | −0.828676 | − | 0.559728i | \(-0.810906\pi\) | ||||
−0.828676 | + | 0.559728i | \(0.810906\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.9706 | −0.724828 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.6274 | 1.01590 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.0294 | −0.724964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1127 | 1.18358 | 0.591791 | − | 0.806091i | \(-0.298421\pi\) | ||||
0.591791 | + | 0.806091i | \(0.298421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.828427 | −0.0314693 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.48528 | −0.170136 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.6569 | 0.668801 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.65685 | −0.138315 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.6569 | 0.440273 | 0.220137 | − | 0.975469i | \(-0.429350\pi\) | ||||
0.220137 | + | 0.975469i | \(0.429350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.07107 | −0.266690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.828427 | 0.0312004 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.20101 | 0.157995 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.6569 | −1.11379 | −0.556893 | − | 0.830584i | \(-0.688007\pi\) | ||||
−0.556893 | + | 0.830584i | \(0.688007\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.6569 | −0.512172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.62742 | −0.0983975 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.75736 | −0.140321 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.61522 | 0.358587 | 0.179294 | − | 0.983796i | \(-0.442619\pi\) | ||||
0.179294 | + | 0.983796i | \(0.442619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.68629 | 0.174527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.9706 | 0.705523 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.24264 | −0.231846 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.3848 | −1.05273 | −0.526367 | − | 0.850258i | \(-0.676446\pi\) | ||||
−0.526367 | + | 0.850258i | \(0.676446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.9706 | 1.07151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0000 | 0.960332 | 0.480166 | − | 0.877178i | \(-0.340576\pi\) | ||||
0.480166 | + | 0.877178i | \(0.340576\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.65685 | 0.245542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3137 | 1.15189 | 0.575947 | − | 0.817487i | \(-0.304634\pi\) | ||||
0.575947 | + | 0.817487i | \(0.304634\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.24264 | 0.155857 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.9411 | −0.804942 | −0.402471 | − | 0.915433i | \(-0.631849\pi\) | ||||
−0.402471 | + | 0.915433i | \(0.631849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.343146 | −0.0125719 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.37258 | −0.0501531 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.1421 | 1.02692 | 0.513461 | − | 0.858113i | \(-0.328363\pi\) | ||||
0.513461 | + | 0.858113i | \(0.328363\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.727922 | −0.0265270 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.8284 | 0.612449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.7696 | −0.972956 | −0.486478 | − | 0.873693i | \(-0.661719\pi\) | ||||
−0.486478 | + | 0.873693i | \(0.661719\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.17157 | 0.0425254 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.9706 | −0.687682 | −0.343841 | − | 0.939028i | \(-0.611728\pi\) | ||||
−0.343841 | + | 0.939028i | \(0.611728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.45584 | 0.342325 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.82843 | 0.102262 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.34315 | −0.300862 | −0.150431 | − | 0.988621i | \(-0.548066\pi\) | ||||
−0.150431 | + | 0.988621i | \(0.548066\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.34315 | 0.228443 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.51472 | 0.270286 | 0.135143 | − | 0.990826i | \(-0.456851\pi\) | ||||
0.135143 | + | 0.990826i | \(0.456851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.17157 | −0.113926 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.14214 | −0.148598 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.24264 | 0.223666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.3137 | −0.547968 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.24264 | −0.223094 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.1421 | −0.718904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.48528 | 0.302468 | 0.151234 | − | 0.988498i | \(-0.451675\pi\) | ||||
0.151234 | + | 0.988498i | \(0.451675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.34315 | −0.297024 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.970563 | 0.0345092 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.9411 | 1.20528 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.48528 | −0.159077 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.02944 | −0.248995 | −0.124498 | − | 0.992220i | \(-0.539732\pi\) | ||||
−0.124498 | + | 0.992220i | \(0.539732\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.34315 | 0.0828945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.5563 | 0.620323 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.8284 | 0.382127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.485281 | 0.0171039 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.8995 | 0.841302 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.3137 | 0.889983 | 0.444991 | − | 0.895535i | \(-0.353207\pi\) | ||||
0.444991 | + | 0.895535i | \(0.353207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.28427 | 0.290900 | 0.145450 | − | 0.989366i | \(-0.453537\pi\) | ||||
0.145450 | + | 0.989366i | \(0.453537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.1421 | −0.916845 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.8995 | 0.697049 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2426 | 0.358345 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.48528 | 0.0868428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.51472 | −0.192465 | −0.0962325 | − | 0.995359i | \(-0.530679\pi\) | ||||
−0.0962325 | + | 0.995359i | \(0.530679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2132 | −0.809161 | −0.404581 | − | 0.914502i | \(-0.632583\pi\) | ||||
−0.404581 | + | 0.914502i | \(0.632583\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.41421 | 0.0492366 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0000 | 0.904109 | 0.452054 | − | 0.891990i | \(-0.350691\pi\) | ||||
0.452054 | + | 0.891990i | \(0.350691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.7990 | 1.31281 | 0.656407 | − | 0.754407i | \(-0.272076\pi\) | ||||
0.656407 | + | 0.754407i | \(0.272076\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.3137 | 0.600606 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.8284 | 0.652366 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.34315 | −0.150301 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.17157 | −0.109626 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.4853 | −1.39771 | −0.698854 | − | 0.715265i | \(-0.746306\pi\) | ||||
−0.698854 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.97056 | 0.343813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.75736 | 0.198294 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.00000 | −0.172005 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.27208 | 0.181151 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.8995 | −0.820229 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.85786 | 0.200805 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.45584 | 0.118326 | 0.0591629 | − | 0.998248i | \(-0.481157\pi\) | ||||
0.0591629 | + | 0.998248i | \(0.481157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.0833 | −1.77913 | −0.889565 | − | 0.456808i | \(-0.848993\pi\) | ||||
−0.889565 | + | 0.456808i | \(0.848993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.9411 | −0.612143 | −0.306072 | − | 0.952008i | \(-0.599015\pi\) | ||||
−0.306072 | + | 0.952008i | \(0.599015\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.65685 | 0.124625 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.34315 | −0.0796693 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.00000 | −0.305656 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.3137 | −0.655173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.89949 | −0.335047 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.585786 | 0.0198032 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.5858 | 1.16788 | 0.583940 | − | 0.811797i | \(-0.301511\pi\) | ||||
0.583940 | + | 0.811797i | \(0.301511\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.00000 | 0.134917 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.1127 | −0.980832 | −0.490416 | − | 0.871489i | \(-0.663155\pi\) | ||||
−0.490416 | + | 0.871489i | \(0.663155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.7279 | 1.16869 | 0.584344 | − | 0.811506i | \(-0.301352\pi\) | ||||
0.584344 | + | 0.811506i | \(0.301352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.82843 | −0.0950765 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.9706 | −0.569816 | −0.284908 | − | 0.958555i | \(-0.591963\pi\) | ||||
−0.284908 | + | 0.958555i | \(0.591963\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.94113 | 0.333415 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.41421 | 0.0473779 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.828427 | 0.0277223 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.7990 | 0.528102 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.51472 | −0.117353 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.7990 | 0.660333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6863 | −0.422642 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00000 | 0.199667 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.828427 | 0.0275378 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.1421 | −1.39931 | −0.699653 | − | 0.714482i | \(-0.746662\pi\) | ||||
−0.699653 | + | 0.714482i | \(0.746662\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.17157 | −0.237866 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.0000 | −0.662630 | −0.331315 | − | 0.943520i | \(-0.607492\pi\) | ||||
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.48528 | −0.280822 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.00000 | 0.264472 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1716 | −0.368918 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.34315 | −0.209241 | −0.104621 | − | 0.994512i | \(-0.533363\pi\) | ||||
−0.104621 | + | 0.994512i | \(0.533363\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.82843 | 0.225004 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.9411 | 1.51217 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.07107 | 0.232495 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.1716 | −0.628999 | −0.314499 | − | 0.949258i | \(-0.601837\pi\) | ||||
−0.314499 | + | 0.949258i | \(0.601837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.65685 | 0.218170 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.58579 | −0.215609 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.1127 | 1.60444 | 0.802221 | − | 0.597027i | \(-0.203652\pi\) | ||||
0.802221 | + | 0.597027i | \(0.203652\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.79899 | −0.319778 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0416 | −0.848933 | −0.424466 | − | 0.905444i | \(-0.639538\pi\) | ||||
−0.424466 | + | 0.905444i | \(0.639538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.17157 | −0.168410 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.585786 | 0.0190556 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.68629 | 0.0872927 | 0.0436464 | − | 0.999047i | \(-0.486103\pi\) | ||||
0.0436464 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.4853 | −1.05452 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.48528 | −0.275154 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.9411 | 1.48818 | 0.744090 | − | 0.668080i | \(-0.232884\pi\) | ||||
0.744090 | + | 0.668080i | \(0.232884\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5858 | −0.342548 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.82843 | −0.285383 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.1127 | −0.358848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9411 | −0.675520 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.34315 | 0.0755068 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.92893 | −0.287432 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.8995 | 0.382662 | 0.191331 | − | 0.981526i | \(-0.438720\pi\) | ||||
0.191331 | + | 0.981526i | \(0.438720\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.82843 | 0.0908622 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.3137 | 0.748173 | 0.374086 | − | 0.927394i | \(-0.377956\pi\) | ||||
0.374086 | + | 0.927394i | \(0.377956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.62742 | −0.0842311 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.24264 | −0.135873 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −59.7990 | −1.91314 | −0.956570 | − | 0.291504i | \(-0.905844\pi\) | ||||
−0.956570 | + | 0.291504i | \(0.905844\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.8284 | 0.793520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.1421 | −0.515379 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −57.5980 | −1.83709 | −0.918545 | − | 0.395316i | \(-0.870635\pi\) | ||||
−0.918545 | + | 0.395316i | \(0.870635\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.48528 | 0.270364 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.485281 | 0.0154467 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.48528 | −0.269816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.9706 | −1.55560 | −0.777801 | − | 0.628511i | \(-0.783665\pi\) | ||||
−0.777801 | + | 0.628511i | \(0.783665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.17157 | −0.227583 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.1421 | −0.448336 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2010 | 0.323069 | 0.161535 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161535 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.07107 | 0.223719 |
(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 | 2280.2.a.o.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6840.2.a.x.1.2 | 2 | |||
4.3 | odd | 2 | 4560.2.a.bg.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.o.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4560.2.a.bg.1.1 | 2 | 4.3 | odd | 2 | |||
6840.2.a.x.1.2 | 2 | 3.2 | odd | 2 |