Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, 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("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-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 | ||||||||
\(7\) | 3.82843 | 1.44701 | 0.723505 | − | 0.690319i | \(-0.242530\pi\) | ||||
0.723505 | + | 0.690319i | \(0.242530\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41421 | 0.946932 | 0.473466 | − | 0.880812i | \(-0.343003\pi\) | ||||
0.473466 | + | 0.880812i | \(0.343003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.414214 | 0.100462 | 0.0502308 | − | 0.998738i | \(-0.484004\pi\) | ||||
0.0502308 | + | 0.998738i | \(0.484004\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.58579 | 1.05205 | 0.526026 | − | 0.850469i | \(-0.323682\pi\) | ||||
0.526026 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.82843 | 0.835431 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.41421 | −1.19109 | −0.595545 | − | 0.803322i | \(-0.703064\pi\) | ||||
−0.595545 | + | 0.803322i | \(0.703064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | 0.0898027 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898027 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.41421 | −0.246183 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.82843 | 0.647122 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.48528 | 1.55937 | 0.779685 | − | 0.626172i | \(-0.215379\pi\) | ||||
0.779685 | + | 0.626172i | \(0.215379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.41421 | 0.546712 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.24264 | −0.194068 | −0.0970339 | − | 0.995281i | \(-0.530936\pi\) | ||||
−0.0970339 | + | 0.995281i | \(0.530936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.65685 | −0.557665 | −0.278833 | − | 0.960340i | \(-0.589947\pi\) | ||||
−0.278833 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.24264 | −0.327123 | −0.163561 | − | 0.986533i | \(-0.552298\pi\) | ||||
−0.163561 | + | 0.986533i | \(0.552298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.65685 | 1.09384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.414214 | 0.0580015 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.24264 | −0.445411 | −0.222705 | − | 0.974886i | \(-0.571489\pi\) | ||||
−0.222705 | + | 0.974886i | \(0.571489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.58579 | 0.607402 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7279 | 1.52685 | 0.763423 | − | 0.645899i | \(-0.223517\pi\) | ||||
0.763423 | + | 0.645899i | \(0.223517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41421 | −0.181071 | −0.0905357 | − | 0.995893i | \(-0.528858\pi\) | ||||
−0.0905357 | + | 0.995893i | \(0.528858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.82843 | 0.482336 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.41421 | 0.423481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.48528 | −0.181456 | −0.0907280 | − | 0.995876i | \(-0.528919\pi\) | ||||
−0.0907280 | + | 0.995876i | \(0.528919\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0710678 | −0.00843420 | −0.00421710 | − | 0.999991i | \(-0.501342\pi\) | ||||
−0.00421710 | + | 0.999991i | \(0.501342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.24264 | −0.730646 | −0.365323 | − | 0.930881i | \(-0.619041\pi\) | ||||
−0.365323 | + | 0.930881i | \(0.619041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.41421 | −0.617007 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9706 | 1.90934 | 0.954669 | − | 0.297670i | \(-0.0962096\pi\) | ||||
0.954669 | + | 0.297670i | \(0.0962096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2426 | −1.23404 | −0.617020 | − | 0.786947i | \(-0.711660\pi\) | ||||
−0.617020 | + | 0.786947i | \(0.711660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.414214 | 0.0449278 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.41421 | −0.687676 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.8284 | −1.57181 | −0.785905 | − | 0.618347i | \(-0.787803\pi\) | ||||
−0.785905 | + | 0.618347i | \(0.787803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.0711 | 1.37022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.58579 | 0.470492 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1421 | −1.02978 | −0.514889 | − | 0.857257i | \(-0.672167\pi\) | ||||
−0.514889 | + | 0.857257i | \(0.672167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.41421 | −0.142134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.07107 | 0.405086 | 0.202543 | − | 0.979273i | \(-0.435079\pi\) | ||||
0.202543 | + | 0.979273i | \(0.435079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4853 | 1.82141 | 0.910704 | − | 0.413059i | \(-0.135540\pi\) | ||||
0.910704 | + | 0.413059i | \(0.135540\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.82843 | 0.373616 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.41421 | −0.620085 | −0.310043 | − | 0.950723i | \(-0.600343\pi\) | ||||
−0.310043 | + | 0.950723i | \(0.600343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.58579 | −0.439239 | −0.219619 | − | 0.975586i | \(-0.570482\pi\) | ||||
−0.219619 | + | 0.975586i | \(0.570482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.48528 | 0.900303 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.899495 | −0.0846174 | −0.0423087 | − | 0.999105i | \(-0.513471\pi\) | ||||
−0.0423087 | + | 0.999105i | \(0.513471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.41421 | 0.315644 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.58579 | 0.145369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.24264 | −0.112045 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5563 | −1.02546 | −0.512730 | − | 0.858550i | \(-0.671366\pi\) | ||||
−0.512730 | + | 0.858550i | \(0.671366\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.65685 | −0.321968 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0000 | 1.39793 | 0.698963 | − | 0.715158i | \(-0.253645\pi\) | ||||
0.698963 | + | 0.715158i | \(0.253645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.5563 | 1.52233 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.82843 | −0.241649 | −0.120824 | − | 0.992674i | \(-0.538554\pi\) | ||||
−0.120824 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.514719 | 0.0436579 | 0.0218289 | − | 0.999762i | \(-0.493051\pi\) | ||||
0.0218289 | + | 0.999762i | \(0.493051\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.24264 | −0.188864 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.82843 | −0.403773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.41421 | −0.532671 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.65685 | 0.631527 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.24264 | 0.511417 | 0.255709 | − | 0.966754i | \(-0.417691\pi\) | ||||
0.255709 | + | 0.966754i | \(0.417691\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.31371 | −0.106908 | −0.0534540 | − | 0.998570i | \(-0.517023\pi\) | ||||
−0.0534540 | + | 0.998570i | \(0.517023\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.414214 | 0.0334872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | −0.239426 | −0.119713 | − | 0.992809i | \(-0.538197\pi\) | ||||
−0.119713 | + | 0.992809i | \(0.538197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.24264 | −0.257158 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.82843 | 0.301722 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.9706 | 1.17258 | 0.586292 | − | 0.810099i | \(-0.300587\pi\) | ||||
0.586292 | + | 0.810099i | \(0.300587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.41421 | −0.110096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2426 | 0.792599 | 0.396300 | − | 0.918121i | \(-0.370294\pi\) | ||||
0.396300 | + | 0.918121i | \(0.370294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.58579 | 0.350684 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3431 | 0.786375 | 0.393187 | − | 0.919458i | \(-0.371372\pi\) | ||||
0.393187 | + | 0.919458i | \(0.371372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.82843 | 0.289402 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.7279 | 0.881525 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.34315 | 0.623596 | 0.311798 | − | 0.950148i | \(-0.399069\pi\) | ||||
0.311798 | + | 0.950148i | \(0.399069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4853 | −1.52266 | −0.761329 | − | 0.648365i | \(-0.775453\pi\) | ||||
−0.761329 | + | 0.648365i | \(0.775453\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.41421 | −0.104542 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.48528 | 0.697372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.585786 | −0.0428369 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.82843 | 0.278477 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2426 | −1.03056 | −0.515281 | − | 0.857021i | \(-0.672312\pi\) | ||||
−0.515281 | + | 0.857021i | \(0.672312\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1421 | −0.730047 | −0.365023 | − | 0.930998i | \(-0.618939\pi\) | ||||
−0.365023 | + | 0.930998i | \(0.618939\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.41421 | 0.244497 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8284 | −0.913988 | −0.456994 | − | 0.889470i | \(-0.651074\pi\) | ||||
−0.456994 | + | 0.889470i | \(0.651074\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.48528 | −0.176177 | −0.0880885 | − | 0.996113i | \(-0.528076\pi\) | ||||
−0.0880885 | + | 0.996113i | \(0.528076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.48528 | −0.104764 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.5563 | −1.72352 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.24264 | −0.0867898 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.48528 | −0.448596 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7990 | 1.29418 | 0.647088 | − | 0.762415i | \(-0.275987\pi\) | ||||
0.647088 | + | 0.762415i | \(0.275987\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0710678 | −0.00486949 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.65685 | −0.249395 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.82843 | 0.259891 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.24264 | −0.421839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.41421 | 0.0951303 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.9706 | −1.00250 | −0.501252 | − | 0.865302i | \(-0.667127\pi\) | ||||
−0.501252 | + | 0.865302i | \(0.667127\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3137 | 1.54739 | 0.773693 | − | 0.633561i | \(-0.218408\pi\) | ||||
0.773693 | + | 0.633561i | \(0.218408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.485281 | 0.0320683 | 0.0160341 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160341 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.41421 | −0.356229 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65685 | 0.370593 | 0.185296 | − | 0.982683i | \(-0.440675\pi\) | ||||
0.185296 | + | 0.982683i | \(0.440675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.24264 | −0.146294 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.9706 | 1.10236 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.58579 | −0.102576 | −0.0512880 | − | 0.998684i | \(-0.516333\pi\) | ||||
−0.0512880 | + | 0.998684i | \(0.516333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.2132 | 1.75296 | 0.876478 | − | 0.481441i | \(-0.159887\pi\) | ||||
0.876478 | + | 0.481441i | \(0.159887\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.65685 | 0.489178 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.6569 | 0.996222 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.2426 | −0.712473 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9706 | −1.19741 | −0.598706 | − | 0.800969i | \(-0.704318\pi\) | ||||
−0.598706 | + | 0.800969i | \(0.704318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.41421 | −0.0889108 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.414214 | 0.0259391 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.58579 | −0.535567 | −0.267783 | − | 0.963479i | \(-0.586291\pi\) | ||||
−0.267783 | + | 0.963479i | \(0.586291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.3137 | 2.25642 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.41421 | −0.397030 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.58579 | −0.591085 | −0.295542 | − | 0.955330i | \(-0.595500\pi\) | ||||
−0.295542 | + | 0.955330i | \(0.595500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.24264 | −0.199194 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.8284 | −0.907485 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.07107 | −0.126275 | −0.0631376 | − | 0.998005i | \(-0.520111\pi\) | ||||
−0.0631376 | + | 0.998005i | \(0.520111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.31371 | 0.262039 | 0.131020 | − | 0.991380i | \(-0.458175\pi\) | ||||
0.131020 | + | 0.991380i | \(0.458175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.0711 | 0.791097 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.41421 | −0.0852803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9706 | −0.899494 | −0.449747 | − | 0.893156i | \(-0.648486\pi\) | ||||
−0.449747 | + | 0.893156i | \(0.648486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2426 | 0.730335 | 0.365167 | − | 0.930942i | \(-0.381012\pi\) | ||||
0.365167 | + | 0.930942i | \(0.381012\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.6274 | −1.16673 | −0.583364 | − | 0.812211i | \(-0.698264\pi\) | ||||
−0.583364 | + | 0.812211i | \(0.698264\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.58579 | 0.271639 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.75736 | −0.280818 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8284 | −0.989907 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1421 | −0.594543 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.89949 | −0.519914 | −0.259957 | − | 0.965620i | \(-0.583708\pi\) | ||||
−0.259957 | + | 0.965620i | \(0.583708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7279 | 0.682826 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.41421 | −0.0820610 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.41421 | 0.197449 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0000 | −0.806947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.07107 | 0.233877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.41421 | −0.0809776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8995 | 0.907432 | 0.453716 | − | 0.891146i | \(-0.350098\pi\) | ||||
0.453716 | + | 0.891146i | \(0.350098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.4853 | 1.05159 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.68629 | −0.492554 | −0.246277 | − | 0.969199i | \(-0.579207\pi\) | ||||
−0.246277 | + | 0.969199i | \(0.579207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.14214 | −0.403697 | −0.201849 | − | 0.979417i | \(-0.564695\pi\) | ||||
−0.201849 | + | 0.979417i | \(0.564695\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.82843 | 0.215707 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.58579 | −0.257563 | −0.128782 | − | 0.991673i | \(-0.541107\pi\) | ||||
−0.128782 | + | 0.991673i | \(0.541107\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.07107 | 0.507882 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.41421 | −0.358006 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.89949 | 0.105691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.41421 | 0.189386 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.58579 | −0.253595 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.58579 | −0.473350 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.1716 | 0.998800 | 0.499400 | − | 0.866372i | \(-0.333554\pi\) | ||||
0.499400 | + | 0.866372i | \(0.333554\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.48528 | 0.519790 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.48528 | −0.0811496 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.6569 | −1.07078 | −0.535389 | − | 0.844606i | \(-0.679835\pi\) | ||||
−0.535389 | + | 0.844606i | \(0.679835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.899495 | −0.0488539 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.41421 | −0.0765840 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.51472 | 0.135782 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.4853 | 0.670245 | 0.335123 | − | 0.942175i | \(-0.391222\pi\) | ||||
0.335123 | + | 0.942175i | \(0.391222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1716 | −0.544472 | −0.272236 | − | 0.962231i | \(-0.587763\pi\) | ||||
−0.272236 | + | 0.962231i | \(0.587763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.41421 | 0.182237 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.0416 | 1.38606 | 0.693028 | − | 0.720911i | \(-0.256276\pi\) | ||||
0.693028 | + | 0.720911i | \(0.256276\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0710678 | −0.00377189 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.58579 | 0.0839287 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.07107 | −0.478753 | −0.239376 | − | 0.970927i | \(-0.576943\pi\) | ||||
−0.239376 | + | 0.970927i | \(0.576943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.02944 | 0.106812 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.00000 | −0.472377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.24264 | −0.326755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.00000 | −0.156599 | −0.0782994 | − | 0.996930i | \(-0.524949\pi\) | ||||
−0.0782994 | + | 0.996930i | \(0.524949\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.24264 | −0.0646893 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.4142 | −0.644514 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.34315 | 0.328436 | 0.164218 | − | 0.986424i | \(-0.447490\pi\) | ||||
0.164218 | + | 0.986424i | \(0.447490\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.8995 | −1.12788 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.6569 | 1.31790 | 0.658952 | − | 0.752185i | \(-0.271000\pi\) | ||||
0.658952 | + | 0.752185i | \(0.271000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.5563 | −0.592050 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7279 | 0.599269 | 0.299634 | − | 0.954054i | \(-0.403135\pi\) | ||||
0.299634 | + | 0.954054i | \(0.403135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.41421 | −0.275934 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.65685 | −0.185888 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.4558 | 1.59487 | 0.797437 | − | 0.603402i | \(-0.206188\pi\) | ||||
0.797437 | + | 0.603402i | \(0.206188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.414214 | 0.0209477 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | 0.807093 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.9706 | 0.853882 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3431 | −0.519108 | −0.259554 | − | 0.965729i | \(-0.583575\pi\) | ||||
−0.259554 | + | 0.965729i | \(0.583575\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.5563 | 0.878917 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.5147 | 1.07439 | 0.537197 | − | 0.843457i | \(-0.319483\pi\) | ||||
0.537197 | + | 0.843457i | \(0.319483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.41421 | 0.170074 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.4142 | −0.664918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1716 | 0.700739 | 0.350370 | − | 0.936612i | \(-0.386056\pi\) | ||||
0.350370 | + | 0.936612i | \(0.386056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.82843 | −0.139516 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.8995 | 2.20936 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.2426 | −0.551880 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.514719 | 0.0252059 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.3553 | 1.72722 | 0.863611 | − | 0.504159i | \(-0.168198\pi\) | ||||
0.863611 | + | 0.504159i | \(0.168198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8701 | −1.01714 | −0.508572 | − | 0.861019i | \(-0.669827\pi\) | ||||
−0.508572 | + | 0.861019i | \(0.669827\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.24264 | −0.109041 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.414214 | 0.0200923 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.41421 | −0.262012 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.82843 | −0.233119 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5147 | −0.554644 | −0.277322 | − | 0.960777i | \(-0.589447\pi\) | ||||
−0.277322 | + | 0.960777i | \(0.589447\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3137 | 1.26456 | 0.632278 | − | 0.774742i | \(-0.282120\pi\) | ||||
0.632278 | + | 0.774742i | \(0.282120\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.41421 | −0.307538 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.58579 | 0.219368 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.79899 | −0.276771 | −0.138385 | − | 0.990378i | \(-0.544191\pi\) | ||||
−0.138385 | + | 0.990378i | \(0.544191\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.65685 | 0.364612 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.89949 | 0.185271 | 0.0926353 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926353 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8284 | −0.702935 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.24264 | 0.295267 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.8995 | 0.986308 | 0.493154 | − | 0.869942i | \(-0.335844\pi\) | ||||
0.493154 | + | 0.869942i | \(0.335844\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75736 | 0.0827508 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.31371 | −0.0617234 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.0711 | 0.612781 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.4558 | 1.89244 | 0.946222 | − | 0.323517i | \(-0.104865\pi\) | ||||
0.946222 | + | 0.323517i | \(0.104865\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.414214 | 0.0193338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.4558 | 1.09245 | 0.546224 | − | 0.837639i | \(-0.316065\pi\) | ||||
0.546224 | + | 0.837639i | \(0.316065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0416 | 1.21026 | 0.605129 | − | 0.796128i | \(-0.293122\pi\) | ||||
0.605129 | + | 0.796128i | \(0.293122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.4142 | −0.667010 | −0.333505 | − | 0.942748i | \(-0.608231\pi\) | ||||
−0.333505 | + | 0.942748i | \(0.608231\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.68629 | −0.262569 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | −0.138233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.17157 | 0.237789 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.58579 | 0.210410 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.24264 | −0.148470 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.8995 | −1.82305 | −0.911527 | − | 0.411240i | \(-0.865096\pi\) | ||||
−0.911527 | + | 0.411240i | \(0.865096\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.3848 | 1.47662 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.82843 | 0.174199 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.1421 | −0.460531 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.9289 | −0.767123 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.9706 | 0.676992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.8995 | −1.93603 | −0.968014 | − | 0.250898i | \(-0.919274\pi\) | ||||
−0.968014 | + | 0.250898i | \(0.919274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.65685 | −0.119659 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.41421 | −0.0635642 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.272078 | −0.0122044 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.4558 | −1.18433 | −0.592163 | − | 0.805818i | \(-0.701726\pi\) | ||||
−0.592163 | + | 0.805818i | \(0.701726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.2426 | 0.457607 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.2426 | −1.30386 | −0.651932 | − | 0.758277i | \(-0.726041\pi\) | ||||
−0.651932 | + | 0.758277i | \(0.726041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.07107 | 0.181160 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.34315 | −0.0596512 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.51472 | −0.155787 | −0.0778936 | − | 0.996962i | \(-0.524819\pi\) | ||||
−0.0778936 | + | 0.996962i | \(0.524819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.8995 | −1.05725 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.58579 | 0.202467 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.4853 | 0.814559 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.17157 | 0.139486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3431 | 0.454014 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.727922 | 0.0318908 | 0.0159454 | − | 0.999873i | \(-0.494924\pi\) | ||||
0.0159454 | + | 0.999873i | \(0.494924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.82843 | 0.167086 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.414214 | 0.0180434 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.7279 | 0.508948 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24264 | −0.183769 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.41421 | −0.277311 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.34315 | 0.360033 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.8284 | −0.466413 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1127 | 0.821719 | 0.410860 | − | 0.911699i | \(-0.365229\pi\) | ||||
0.410860 | + | 0.911699i | \(0.365229\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.4853 | −0.879108 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.58579 | −0.196434 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6569 | −0.754953 | −0.377476 | − | 0.926019i | \(-0.623208\pi\) | ||||
−0.377476 | + | 0.926019i | \(0.623208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.41421 | −0.0603572 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.4142 | −1.25309 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 64.9706 | 2.76283 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.48528 | 0.402628 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.5269 | −1.33584 | −0.667919 | − | 0.744234i | \(-0.732815\pi\) | ||||
−0.667919 | + | 0.744234i | \(0.732815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.4853 | −0.528071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.585786 | −0.0247319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.4142 | 1.95613 | 0.978063 | − | 0.208310i | \(-0.0667962\pi\) | ||||
0.978063 | + | 0.208310i | \(0.0667962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.899495 | −0.0378420 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.82843 | 0.160779 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.51472 | 0.0635003 | 0.0317502 | − | 0.999496i | \(-0.489892\pi\) | ||||
0.0317502 | + | 0.999496i | \(0.489892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.8995 | −0.749071 | −0.374535 | − | 0.927213i | \(-0.622198\pi\) | ||||
−0.374535 | + | 0.927213i | \(0.622198\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.2426 | −0.594995 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.2843 | −1.34401 | −0.672006 | − | 0.740546i | \(-0.734567\pi\) | ||||
−0.672006 | + | 0.740546i | \(0.734567\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.1421 | −0.421493 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.0416 | −1.78567 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.58579 | 0.189924 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.41421 | 0.141160 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.62742 | 0.356092 | 0.178046 | − | 0.984022i | \(-0.443022\pi\) | ||||
0.178046 | + | 0.984022i | \(0.443022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.58579 | 0.188954 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8284 | −0.527691 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.0711 | −0.865285 | −0.432643 | − | 0.901566i | \(-0.642419\pi\) | ||||
−0.432643 | + | 0.901566i | \(0.642419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.58579 | 0.0650109 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.48528 | −0.101716 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.1421 | −0.414396 | −0.207198 | − | 0.978299i | \(-0.566435\pi\) | ||||
−0.207198 | + | 0.978299i | \(0.566435\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.3431 | 0.462697 | 0.231348 | − | 0.972871i | \(-0.425686\pi\) | ||||
0.231348 | + | 0.972871i | \(0.425686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.48528 | −0.0604853 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.00000 | −0.365902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.7279 | −0.516610 | −0.258305 | − | 0.966063i | \(-0.583164\pi\) | ||||
−0.258305 | + | 0.966063i | \(0.583164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.5563 | −0.995073 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.65685 | −0.309763 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.6274 | 1.64093 | 0.820463 | − | 0.571700i | \(-0.193716\pi\) | ||||
0.820463 | + | 0.571700i | \(0.193716\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.24264 | −0.0501081 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.75736 | 0.352558 | 0.176279 | − | 0.984340i | \(-0.443594\pi\) | ||||
0.176279 | + | 0.984340i | \(0.443594\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.2843 | 1.61916 | 0.809581 | − | 0.587008i | \(-0.199694\pi\) | ||||
0.809581 | + | 0.587008i | \(0.199694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −56.7696 | −2.27442 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.48528 | −0.258997 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.92893 | 0.156657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.41421 | 0.0562990 | 0.0281495 | − | 0.999604i | \(-0.491039\pi\) | ||||
0.0281495 | + | 0.999604i | \(0.491039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.7990 | 0.747193 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.5563 | −0.458600 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.1421 | 1.03579 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0710678 | −0.00281140 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.5858 | −0.734094 | −0.367047 | − | 0.930202i | \(-0.619631\pi\) | ||||
−0.367047 | + | 0.930202i | \(0.619631\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.6569 | −1.68222 | −0.841111 | − | 0.540862i | \(-0.818098\pi\) | ||||
−0.841111 | + | 0.540862i | \(0.818098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.65685 | −0.143988 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.3848 | −1.35181 | −0.675903 | − | 0.736991i | \(-0.736246\pi\) | ||||
−0.675903 | + | 0.736991i | \(0.736246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.5858 | −0.651049 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.82843 | 0.150048 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.72792 | 0.341550 | 0.170775 | − | 0.985310i | \(-0.445373\pi\) | ||||
0.170775 | + | 0.985310i | \(0.445373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0000 | 0.625172 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.24264 | −0.243549 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.3848 | −1.18362 | −0.591811 | − | 0.806076i | \(-0.701587\pi\) | ||||
−0.591811 | + | 0.806076i | \(0.701587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.1127 | −1.91026 | −0.955131 | − | 0.296183i | \(-0.904286\pi\) | ||||
−0.955131 | + | 0.296183i | \(0.904286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.41421 | 0.0549235 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.5563 | 0.680806 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.41421 | −0.248359 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.9706 | −0.578795 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.7279 | 1.26157 | 0.630784 | − | 0.775958i | \(-0.282733\pi\) | ||||
0.630784 | + | 0.775958i | \(0.282733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.1838 | 1.27536 | 0.637678 | − | 0.770303i | \(-0.279895\pi\) | ||||
0.637678 | + | 0.770303i | \(0.279895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.8284 | −1.49010 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.3137 | 0.893383 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.0122 | 1.49276 | 0.746380 | − | 0.665520i | \(-0.231790\pi\) | ||||
0.746380 | + | 0.665520i | \(0.231790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.82843 | −0.108069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.485281 | 0.0185146 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0711 | −0.421774 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9706 | −0.721674 | −0.360837 | − | 0.932629i | \(-0.617509\pi\) | ||||
−0.360837 | + | 0.932629i | \(0.617509\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.41421 | −0.205669 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.514719 | 0.0195244 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.514719 | −0.0194964 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.65685 | 0.213962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4437 | 0.696607 | 0.348304 | − | 0.937382i | \(-0.386758\pi\) | ||||
0.348304 | + | 0.937382i | \(0.386758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.4975 | 1.64054 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.24264 | −0.0844627 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.5858 | 0.586164 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6985 | −1.56602 | −0.783010 | − | 0.622009i | \(-0.786317\pi\) | ||||
−0.783010 | + | 0.622009i | \(0.786317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.9706 | 0.636446 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00000 | 0.0374503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.82843 | −0.180573 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.58579 | −0.0592223 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.44365 | −0.0538391 | −0.0269195 | − | 0.999638i | \(-0.508570\pi\) | ||||
−0.0269195 | + | 0.999638i | \(0.508570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 70.7696 | 2.63560 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.2132 | 1.01207 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.41421 | −0.238218 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.00000 | −0.333792 | −0.166896 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166896 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.51472 | −0.0560239 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.31371 | −0.233202 | −0.116601 | − | 0.993179i | \(-0.537200\pi\) | ||||
−0.116601 | + | 0.993179i | \(0.537200\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.65685 | 0.282427 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.10051 | 0.0773731 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.1421 | 0.409870 | 0.204935 | − | 0.978776i | \(-0.434302\pi\) | ||||
0.204935 | + | 0.978776i | \(0.434302\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.6569 | 0.575169 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.00000 | −0.146746 | −0.0733729 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733729 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.24264 | 0.228713 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.2426 | −0.411347 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.5563 | −0.897269 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.9289 | 1.12861 | 0.564306 | − | 0.825565i | \(-0.309144\pi\) | ||||
0.564306 | + | 0.825565i | \(0.309144\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.9706 | −0.691326 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.31371 | −0.0478107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.82843 | 0.139147 | 0.0695733 | − | 0.997577i | \(-0.477836\pi\) | ||||
0.0695733 | + | 0.997577i | \(0.477836\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.41421 | −0.0513327 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.0711 | −1.38008 | −0.690038 | − | 0.723774i | \(-0.742406\pi\) | ||||
−0.690038 | + | 0.723774i | \(0.742406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.5563 | −0.635583 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.414214 | 0.0149759 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.0416 | 1.44582 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.7279 | −1.46869 | −0.734343 | − | 0.678778i | \(-0.762510\pi\) | ||||
−0.734343 | + | 0.678778i | \(0.762510\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.58579 | −0.309210 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.7990 | 0.927925 | 0.463963 | − | 0.885855i | \(-0.346427\pi\) | ||||
0.463963 | + | 0.885855i | \(0.346427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.3137 | 1.30275 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.69848 | −0.204169 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.100505 | 0.00359635 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.41421 | −0.229225 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.00000 | −0.107075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.2843 | −1.32904 | −0.664520 | − | 0.747270i | \(-0.731364\pi\) | ||||
−0.664520 | + | 0.747270i | \(0.731364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.58579 | −0.341263 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.44365 | −0.122442 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.82843 | −0.171462 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.24264 | −0.115005 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.1005 | −0.534887 | −0.267444 | − | 0.963573i | \(-0.586179\pi\) | ||||
−0.267444 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.928932 | −0.0328633 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.8284 | −0.523937 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.82843 | 0.311548 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.82843 | 0.134934 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.07107 | −0.0729050 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.27208 | 0.150198 | 0.0750991 | − | 0.997176i | \(-0.476073\pi\) | ||||
0.0750991 | + | 0.997176i | \(0.476073\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.1421 | −0.812630 | −0.406315 | − | 0.913733i | \(-0.633186\pi\) | ||||
−0.406315 | + | 0.913733i | \(0.633186\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.31371 | 0.151288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.9706 | 0.524396 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.7696 | −0.586692 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.0711 | 0.456740 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.4558 | −0.609213 | −0.304607 | − | 0.952478i | \(-0.598525\pi\) | ||||
−0.304607 | + | 0.952478i | \(0.598525\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.3431 | 1.47599 | 0.737995 | − | 0.674807i | \(-0.235773\pi\) | ||||
0.737995 | + | 0.674807i | \(0.235773\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.41421 | −0.0492366 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.7279 | −0.964194 | −0.482097 | − | 0.876118i | \(-0.660125\pi\) | ||||
−0.482097 | + | 0.876118i | \(0.660125\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.17157 | −0.0754218 | −0.0377109 | − | 0.999289i | \(-0.512007\pi\) | ||||
−0.0377109 | + | 0.999289i | \(0.512007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9706 | −0.519323 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.17157 | 0.109888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.2426 | 0.354461 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.6569 | −1.36911 | −0.684553 | − | 0.728963i | \(-0.740003\pi\) | ||||
−0.684553 | + | 0.728963i | \(0.740003\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1421 | 0.418694 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.2426 | 0.421659 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.34315 | −0.0462056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.4558 | −1.18392 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.6274 | −0.673611 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.48528 | 0.325151 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.4853 | −0.359009 | −0.179505 | − | 0.983757i | \(-0.557449\pi\) | ||||
−0.179505 | + | 0.983757i | \(0.557449\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.58579 | 0.156831 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.3137 | −1.82116 | −0.910581 | − | 0.413331i | \(-0.864365\pi\) | ||||
−0.910581 | + | 0.413331i | \(0.864365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.1716 | 1.64359 | 0.821796 | − | 0.569781i | \(-0.192972\pi\) | ||||
0.821796 | + | 0.569781i | \(0.192972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.75736 | −0.162130 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.5147 | −1.00469 | −0.502346 | − | 0.864666i | \(-0.667530\pi\) | ||||
−0.502346 | + | 0.864666i | \(0.667530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.3431 | 0.351678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8284 | −0.571523 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0000 | −0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.07107 | −0.171827 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.1421 | −0.343259 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.82843 | 0.129424 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.8284 | −0.433185 | −0.216593 | − | 0.976262i | \(-0.569494\pi\) | ||||
−0.216593 | + | 0.976262i | \(0.569494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.89949 | −0.300173 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0711 | −0.844666 | −0.422333 | − | 0.906441i | \(-0.638789\pi\) | ||||
−0.422333 | + | 0.906441i | \(0.638789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.0711 | 1.58407 | 0.792034 | − | 0.610477i | \(-0.209022\pi\) | ||||
0.792034 | + | 0.610477i | \(0.209022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.7279 | 0.394230 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.828427 | −0.0278159 | −0.0139079 | − | 0.999903i | \(-0.504427\pi\) | ||||
−0.0139079 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.2426 | −1.48385 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.41421 | −0.0473779 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.2843 | −0.344150 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.34315 | 0.278881 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.41421 | 0.113997 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.41421 | −0.213926 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.34315 | −0.0447467 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.0000 | −0.465891 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.4853 | −0.680954 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.8284 | −0.791210 | −0.395605 | − | 0.918421i | \(-0.629465\pi\) | ||||
−0.395605 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.07107 | 0.135029 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.97056 | 0.164682 | 0.0823410 | − | 0.996604i | \(-0.473760\pi\) | ||||
0.0823410 | + | 0.996604i | \(0.473760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.8995 | 0.526196 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.41421 | −0.0467525 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 61.2548 | 2.02281 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.2843 | 1.06496 | 0.532480 | − | 0.846443i | \(-0.321260\pi\) | ||||
0.532480 | + | 0.846443i | \(0.321260\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.8995 | 0.523906 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.242641 | −0.00798662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.48528 | 0.311874 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.4853 | 0.607136 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.2426 | −1.35313 | −0.676564 | − | 0.736384i | \(-0.736532\pi\) | ||||
−0.676564 | + | 0.736384i | \(0.736532\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.1127 | 1.15077 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.68629 | −0.284376 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.585786 | −0.0191573 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.485281 | −0.0158535 | −0.00792673 | − | 0.999969i | \(-0.502523\pi\) | ||||
−0.00792673 | + | 0.999969i | \(0.502523\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.14214 | −0.233075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.5269 | −1.90792 | −0.953961 | − | 0.299929i | \(-0.903037\pi\) | ||||
−0.953961 | + | 0.299929i | \(0.903037\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.24264 | −0.0404659 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.82843 | 0.124539 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.5147 | 0.374178 | 0.187089 | − | 0.982343i | \(-0.440095\pi\) | ||||
0.187089 | + | 0.982343i | \(0.440095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.3137 | −0.691872 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.58579 | −0.148704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.6274 | 1.31605 | 0.658026 | − | 0.752996i | \(-0.271392\pi\) | ||||
0.658026 | + | 0.752996i | \(0.271392\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.2426 | −0.460881 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.07107 | 0.293226 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.8284 | −0.349668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.41421 | −0.206695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.1421 | −0.326487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.61522 | −0.180573 | −0.0902867 | − | 0.995916i | \(-0.528778\pi\) | ||||
−0.0902867 | + | 0.995916i | \(0.528778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.89949 | 0.0610206 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.4264 | −1.61826 | −0.809130 | − | 0.587629i | \(-0.800061\pi\) | ||||
−0.809130 | + | 0.587629i | \(0.800061\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.97056 | 0.0631733 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.41421 | 0.109342 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.87006 | 0.123814 | 0.0619071 | − | 0.998082i | \(-0.480282\pi\) | ||||
0.0619071 | + | 0.998082i | \(0.480282\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.9706 | 0.670222 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.58579 | −0.146413 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5269 | −0.877972 | −0.438986 | − | 0.898494i | \(-0.644662\pi\) | ||||
−0.438986 | + | 0.898494i | \(0.644662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8284 | −0.408748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.58579 | −0.273289 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.65685 | −0.116281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.455844 | 0.0144804 | 0.00724018 | − | 0.999974i | \(-0.497695\pi\) | ||||
0.00724018 | + | 0.999974i | \(0.497695\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.1716 | 0.576657 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.48528 | −0.0787887 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.4853 | 1.15550 | 0.577750 | − | 0.816214i | \(-0.303931\pi\) | ||||
0.577750 | + | 0.816214i | \(0.303931\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.48528 | 0.300101 |
(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 | 5520.2.a.bt.1.2 | 2 | ||
4.3 | odd | 2 | 2760.2.a.n.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 8280.2.a.x.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.n.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
5520.2.a.bt.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8280.2.a.x.1.1 | 2 | 12.11 | even | 2 |