Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1815) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | 5.23607 | 1.45222 | 0.726112 | − | 0.687576i | \(-0.241325\pi\) | ||||
0.726112 | + | 0.687576i | \(0.241325\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −5.47214 | −1.32719 | −0.663594 | − | 0.748093i | \(-0.730970\pi\) | ||||
−0.663594 | + | 0.748093i | \(0.730970\pi\) | |||||||
\(18\) | −0.618034 | −0.145672 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.23607 | 0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.70820 | 0.981728 | 0.490864 | − | 0.871236i | \(-0.336681\pi\) | ||||
0.490864 | + | 0.871236i | \(0.336681\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.23607 | −0.634645 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.23607 | −0.989524 | ||||||||
\(29\) | 1.23607 | 0.229532 | 0.114766 | − | 0.993393i | \(-0.463388\pi\) | ||||
0.114766 | + | 0.993393i | \(0.463388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.70820 | −1.20483 | −0.602414 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602414 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.38197 | 0.580002 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | −0.763932 | −0.125590 | −0.0627948 | − | 0.998026i | \(-0.520001\pi\) | ||||
−0.0627948 | + | 0.998026i | \(0.520001\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 5.23607 | 0.838442 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.52786 | −0.550960 | −0.275480 | − | 0.961307i | \(-0.588837\pi\) | ||||
−0.275480 | + | 0.961307i | \(0.588837\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | −5.23607 | −0.798493 | −0.399246 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399246 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.90983 | −0.429031 | ||||||||
\(47\) | −8.70820 | −1.27022 | −0.635111 | − | 0.772421i | \(-0.719046\pi\) | ||||
−0.635111 | + | 0.772421i | \(0.719046\pi\) | |||||||
\(48\) | 1.85410 | 0.267617 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.47214 | −0.766252 | ||||||||
\(52\) | −8.47214 | −1.17487 | ||||||||
\(53\) | −9.94427 | −1.36595 | −0.682975 | − | 0.730441i | \(-0.739314\pi\) | ||||
−0.682975 | + | 0.730441i | \(0.739314\pi\) | |||||||
\(54\) | −0.618034 | −0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.23607 | 0.966960 | ||||||||
\(57\) | −6.47214 | −0.857255 | ||||||||
\(58\) | −0.763932 | −0.100309 | ||||||||
\(59\) | 11.7082 | 1.52428 | 0.762139 | − | 0.647413i | \(-0.224149\pi\) | ||||
0.762139 | + | 0.647413i | \(0.224149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.47214 | 0.188488 | 0.0942438 | − | 0.995549i | \(-0.469957\pi\) | ||||
0.0942438 | + | 0.995549i | \(0.469957\pi\) | |||||||
\(62\) | 4.14590 | 0.526530 | ||||||||
\(63\) | 3.23607 | 0.407706 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2361 | −1.37270 | −0.686352 | − | 0.727269i | \(-0.740789\pi\) | ||||
−0.686352 | + | 0.727269i | \(0.740789\pi\) | |||||||
\(68\) | 8.85410 | 1.07372 | ||||||||
\(69\) | 4.70820 | 0.566801 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4721 | −1.71753 | −0.858763 | − | 0.512373i | \(-0.828767\pi\) | ||||
−0.858763 | + | 0.512373i | \(0.828767\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −10.4721 | −1.22567 | −0.612835 | − | 0.790211i | \(-0.709971\pi\) | ||||
−0.612835 | + | 0.790211i | \(0.709971\pi\) | |||||||
\(74\) | 0.472136 | 0.0548847 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.4721 | 1.20124 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.23607 | −0.366413 | ||||||||
\(79\) | −12.7082 | −1.42978 | −0.714892 | − | 0.699235i | \(-0.753524\pi\) | ||||
−0.714892 | + | 0.699235i | \(0.753524\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.18034 | 0.240778 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | −5.23607 | −0.571302 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.23607 | 0.348954 | ||||||||
\(87\) | 1.23607 | 0.132520 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.76393 | 0.504976 | 0.252488 | − | 0.967600i | \(-0.418751\pi\) | ||||
0.252488 | + | 0.967600i | \(0.418751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.9443 | 1.77624 | ||||||||
\(92\) | −7.61803 | −0.794235 | ||||||||
\(93\) | −6.70820 | −0.695608 | ||||||||
\(94\) | 5.38197 | 0.555107 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.61803 | −0.573388 | ||||||||
\(97\) | −12.7639 | −1.29598 | −0.647990 | − | 0.761648i | \(-0.724390\pi\) | ||||
−0.647990 | + | 0.761648i | \(0.724390\pi\) | |||||||
\(98\) | −2.14590 | −0.216768 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.52786 | 0.550043 | 0.275022 | − | 0.961438i | \(-0.411315\pi\) | ||||
0.275022 | + | 0.961438i | \(0.411315\pi\) | |||||||
\(102\) | 3.38197 | 0.334865 | ||||||||
\(103\) | 0.944272 | 0.0930419 | 0.0465209 | − | 0.998917i | \(-0.485187\pi\) | ||||
0.0465209 | + | 0.998917i | \(0.485187\pi\) | |||||||
\(104\) | 11.7082 | 1.14808 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.14590 | 0.596942 | ||||||||
\(107\) | 14.2361 | 1.37625 | 0.688126 | − | 0.725591i | \(-0.258433\pi\) | ||||
0.688126 | + | 0.725591i | \(0.258433\pi\) | |||||||
\(108\) | −1.61803 | −0.155695 | ||||||||
\(109\) | −14.9443 | −1.43140 | −0.715701 | − | 0.698407i | \(-0.753893\pi\) | ||||
−0.715701 | + | 0.698407i | \(0.753893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.763932 | −0.0725092 | ||||||||
\(112\) | 6.00000 | 0.566947 | ||||||||
\(113\) | 12.4164 | 1.16804 | 0.584019 | − | 0.811740i | \(-0.301479\pi\) | ||||
0.584019 | + | 0.811740i | \(0.301479\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 5.23607 | 0.484075 | ||||||||
\(118\) | −7.23607 | −0.666134 | ||||||||
\(119\) | −17.7082 | −1.62331 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −0.909830 | −0.0823721 | ||||||||
\(123\) | −3.52786 | −0.318097 | ||||||||
\(124\) | 10.8541 | 0.974727 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 3.70820 | 0.329050 | 0.164525 | − | 0.986373i | \(-0.447391\pi\) | ||||
0.164525 | + | 0.986373i | \(0.447391\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | −5.23607 | −0.461010 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.472136 | 0.0412507 | 0.0206254 | − | 0.999787i | \(-0.493434\pi\) | ||||
0.0206254 | + | 0.999787i | \(0.493434\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.9443 | −1.81610 | ||||||||
\(134\) | 6.94427 | 0.599894 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.2361 | −1.04923 | ||||||||
\(137\) | −17.4721 | −1.49275 | −0.746373 | − | 0.665528i | \(-0.768206\pi\) | ||||
−0.746373 | + | 0.665528i | \(0.768206\pi\) | |||||||
\(138\) | −2.90983 | −0.247701 | ||||||||
\(139\) | 7.29180 | 0.618482 | 0.309241 | − | 0.950984i | \(-0.399925\pi\) | ||||
0.309241 | + | 0.950984i | \(0.399925\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.70820 | −0.733363 | ||||||||
\(142\) | 8.94427 | 0.750587 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.47214 | 0.535638 | ||||||||
\(147\) | 3.47214 | 0.286377 | ||||||||
\(148\) | 1.23607 | 0.101604 | ||||||||
\(149\) | 4.29180 | 0.351598 | 0.175799 | − | 0.984426i | \(-0.443749\pi\) | ||||
0.175799 | + | 0.984426i | \(0.443749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.29180 | −0.593398 | −0.296699 | − | 0.954971i | \(-0.595886\pi\) | ||||
−0.296699 | + | 0.954971i | \(0.595886\pi\) | |||||||
\(152\) | −14.4721 | −1.17385 | ||||||||
\(153\) | −5.47214 | −0.442396 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.47214 | −0.678314 | ||||||||
\(157\) | −2.29180 | −0.182905 | −0.0914526 | − | 0.995809i | \(-0.529151\pi\) | ||||
−0.0914526 | + | 0.995809i | \(0.529151\pi\) | |||||||
\(158\) | 7.85410 | 0.624839 | ||||||||
\(159\) | −9.94427 | −0.788632 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2361 | 1.20077 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | −6.18034 | −0.484082 | −0.242041 | − | 0.970266i | \(-0.577817\pi\) | ||||
−0.242041 | + | 0.970266i | \(0.577817\pi\) | |||||||
\(164\) | 5.70820 | 0.445736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.47214 | 0.191875 | ||||||||
\(167\) | 3.18034 | 0.246102 | 0.123051 | − | 0.992400i | \(-0.460732\pi\) | ||||
0.123051 | + | 0.992400i | \(0.460732\pi\) | |||||||
\(168\) | 7.23607 | 0.558275 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.47214 | −0.494937 | ||||||||
\(172\) | 8.47214 | 0.645994 | ||||||||
\(173\) | 2.94427 | 0.223849 | 0.111924 | − | 0.993717i | \(-0.464299\pi\) | ||||
0.111924 | + | 0.993717i | \(0.464299\pi\) | |||||||
\(174\) | −0.763932 | −0.0579135 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.7082 | 0.880042 | ||||||||
\(178\) | −2.94427 | −0.220683 | ||||||||
\(179\) | −20.1803 | −1.50835 | −0.754175 | − | 0.656674i | \(-0.771963\pi\) | ||||
−0.754175 | + | 0.656674i | \(0.771963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4164 | −1.59187 | −0.795935 | − | 0.605383i | \(-0.793020\pi\) | ||||
−0.795935 | + | 0.605383i | \(0.793020\pi\) | |||||||
\(182\) | −10.4721 | −0.776246 | ||||||||
\(183\) | 1.47214 | 0.108823 | ||||||||
\(184\) | 10.5279 | 0.776124 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.14590 | 0.303992 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 14.0902 | 1.02763 | ||||||||
\(189\) | 3.23607 | 0.235389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 27.5967 | 1.99683 | 0.998415 | − | 0.0562752i | \(-0.0179224\pi\) | ||||
0.998415 | + | 0.0562752i | \(0.0179224\pi\) | |||||||
\(192\) | −0.236068 | −0.0170367 | ||||||||
\(193\) | 16.1803 | 1.16469 | 0.582343 | − | 0.812943i | \(-0.302136\pi\) | ||||
0.582343 | + | 0.812943i | \(0.302136\pi\) | |||||||
\(194\) | 7.88854 | 0.566364 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.61803 | −0.401288 | ||||||||
\(197\) | −1.41641 | −0.100915 | −0.0504574 | − | 0.998726i | \(-0.516068\pi\) | ||||
−0.0504574 | + | 0.998726i | \(0.516068\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2361 | 1.15094 | 0.575472 | − | 0.817821i | \(-0.304818\pi\) | ||||
0.575472 | + | 0.817821i | \(0.304818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.2361 | −0.792531 | ||||||||
\(202\) | −3.41641 | −0.240378 | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 8.85410 | 0.619911 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.583592 | −0.0406608 | ||||||||
\(207\) | 4.70820 | 0.327243 | ||||||||
\(208\) | 9.70820 | 0.673143 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.76393 | −0.121434 | −0.0607170 | − | 0.998155i | \(-0.519339\pi\) | ||||
−0.0607170 | + | 0.998155i | \(0.519339\pi\) | |||||||
\(212\) | 16.0902 | 1.10508 | ||||||||
\(213\) | −14.4721 | −0.991614 | ||||||||
\(214\) | −8.79837 | −0.601444 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −21.7082 | −1.47365 | ||||||||
\(218\) | 9.23607 | 0.625545 | ||||||||
\(219\) | −10.4721 | −0.707641 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.6525 | −1.92737 | ||||||||
\(222\) | 0.472136 | 0.0316877 | ||||||||
\(223\) | −9.05573 | −0.606416 | −0.303208 | − | 0.952924i | \(-0.598058\pi\) | ||||
−0.303208 | + | 0.952924i | \(0.598058\pi\) | |||||||
\(224\) | −18.1803 | −1.21473 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.67376 | −0.510451 | ||||||||
\(227\) | 16.7082 | 1.10896 | 0.554481 | − | 0.832196i | \(-0.312917\pi\) | ||||
0.554481 | + | 0.832196i | \(0.312917\pi\) | |||||||
\(228\) | 10.4721 | 0.693534 | ||||||||
\(229\) | 7.00000 | 0.462573 | 0.231287 | − | 0.972886i | \(-0.425707\pi\) | ||||
0.231287 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.76393 | 0.181461 | ||||||||
\(233\) | 10.8885 | 0.713332 | 0.356666 | − | 0.934232i | \(-0.383913\pi\) | ||||
0.356666 | + | 0.934232i | \(0.383913\pi\) | |||||||
\(234\) | −3.23607 | −0.211548 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −18.9443 | −1.23317 | ||||||||
\(237\) | −12.7082 | −0.825487 | ||||||||
\(238\) | 10.9443 | 0.709412 | ||||||||
\(239\) | 24.6525 | 1.59464 | 0.797318 | − | 0.603559i | \(-0.206251\pi\) | ||||
0.797318 | + | 0.603559i | \(0.206251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9443 | 1.15589 | 0.577946 | − | 0.816075i | \(-0.303854\pi\) | ||||
0.577946 | + | 0.816075i | \(0.303854\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.38197 | −0.152490 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.18034 | 0.139013 | ||||||||
\(247\) | −33.8885 | −2.15628 | ||||||||
\(248\) | −15.0000 | −0.952501 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7082 | −1.49645 | −0.748224 | − | 0.663446i | \(-0.769093\pi\) | ||||
−0.748224 | + | 0.663446i | \(0.769093\pi\) | |||||||
\(252\) | −5.23607 | −0.329841 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.29180 | −0.143800 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −28.8885 | −1.80202 | −0.901009 | − | 0.433801i | \(-0.857172\pi\) | ||||
−0.901009 | + | 0.433801i | \(0.857172\pi\) | |||||||
\(258\) | 3.23607 | 0.201469 | ||||||||
\(259\) | −2.47214 | −0.153611 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.23607 | 0.0765107 | ||||||||
\(262\) | −0.291796 | −0.0180272 | ||||||||
\(263\) | 20.1246 | 1.24094 | 0.620468 | − | 0.784231i | \(-0.286943\pi\) | ||||
0.620468 | + | 0.784231i | \(0.286943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.9443 | 0.793664 | ||||||||
\(267\) | 4.76393 | 0.291548 | ||||||||
\(268\) | 18.1803 | 1.11054 | ||||||||
\(269\) | 7.05573 | 0.430195 | 0.215098 | − | 0.976593i | \(-0.430993\pi\) | ||||
0.215098 | + | 0.976593i | \(0.430993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.2361 | 1.47224 | 0.736118 | − | 0.676853i | \(-0.236657\pi\) | ||||
0.736118 | + | 0.676853i | \(0.236657\pi\) | |||||||
\(272\) | −10.1459 | −0.615185 | ||||||||
\(273\) | 16.9443 | 1.02551 | ||||||||
\(274\) | 10.7984 | 0.652354 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.61803 | −0.458552 | ||||||||
\(277\) | −4.94427 | −0.297073 | −0.148536 | − | 0.988907i | \(-0.547456\pi\) | ||||
−0.148536 | + | 0.988907i | \(0.547456\pi\) | |||||||
\(278\) | −4.50658 | −0.270287 | ||||||||
\(279\) | −6.70820 | −0.401610 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.2361 | −0.908908 | −0.454454 | − | 0.890770i | \(-0.650166\pi\) | ||||
−0.454454 | + | 0.890770i | \(0.650166\pi\) | |||||||
\(282\) | 5.38197 | 0.320491 | ||||||||
\(283\) | 11.8885 | 0.706701 | 0.353350 | − | 0.935491i | \(-0.385042\pi\) | ||||
0.353350 | + | 0.935491i | \(0.385042\pi\) | |||||||
\(284\) | 23.4164 | 1.38951 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4164 | −0.673889 | ||||||||
\(288\) | −5.61803 | −0.331046 | ||||||||
\(289\) | 12.9443 | 0.761428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.7639 | −0.748235 | ||||||||
\(292\) | 16.9443 | 0.991589 | ||||||||
\(293\) | 21.4721 | 1.25442 | 0.627208 | − | 0.778852i | \(-0.284198\pi\) | ||||
0.627208 | + | 0.778852i | \(0.284198\pi\) | |||||||
\(294\) | −2.14590 | −0.125151 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.70820 | −0.0992873 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.65248 | −0.153654 | ||||||||
\(299\) | 24.6525 | 1.42569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.9443 | −0.976652 | ||||||||
\(302\) | 4.50658 | 0.259324 | ||||||||
\(303\) | 5.52786 | 0.317567 | ||||||||
\(304\) | −12.0000 | −0.688247 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.38197 | 0.193334 | ||||||||
\(307\) | −11.8885 | −0.678515 | −0.339258 | − | 0.940694i | \(-0.610176\pi\) | ||||
−0.339258 | + | 0.940694i | \(0.610176\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.944272 | 0.0537178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.23607 | −0.183501 | −0.0917503 | − | 0.995782i | \(-0.529246\pi\) | ||||
−0.0917503 | + | 0.995782i | \(0.529246\pi\) | |||||||
\(312\) | 11.7082 | 0.662847 | ||||||||
\(313\) | −22.7639 | −1.28669 | −0.643347 | − | 0.765575i | \(-0.722455\pi\) | ||||
−0.643347 | + | 0.765575i | \(0.722455\pi\) | |||||||
\(314\) | 1.41641 | 0.0799325 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.5623 | 1.15672 | ||||||||
\(317\) | 3.94427 | 0.221532 | 0.110766 | − | 0.993846i | \(-0.464670\pi\) | ||||
0.110766 | + | 0.993846i | \(0.464670\pi\) | |||||||
\(318\) | 6.14590 | 0.344645 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.2361 | 0.794580 | ||||||||
\(322\) | −9.41641 | −0.524756 | ||||||||
\(323\) | 35.4164 | 1.97062 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.81966 | 0.211551 | ||||||||
\(327\) | −14.9443 | −0.826420 | ||||||||
\(328\) | −7.88854 | −0.435572 | ||||||||
\(329\) | −28.1803 | −1.55363 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1803 | −0.944317 | −0.472158 | − | 0.881514i | \(-0.656525\pi\) | ||||
−0.472158 | + | 0.881514i | \(0.656525\pi\) | |||||||
\(332\) | 6.47214 | 0.355205 | ||||||||
\(333\) | −0.763932 | −0.0418632 | ||||||||
\(334\) | −1.96556 | −0.107551 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.00000 | 0.327327 | ||||||||
\(337\) | −7.88854 | −0.429716 | −0.214858 | − | 0.976645i | \(-0.568929\pi\) | ||||
−0.214858 | + | 0.976645i | \(0.568929\pi\) | |||||||
\(338\) | −8.90983 | −0.484631 | ||||||||
\(339\) | 12.4164 | 0.674367 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | −11.7082 | −0.631264 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.81966 | −0.0978255 | ||||||||
\(347\) | −14.2361 | −0.764232 | −0.382116 | − | 0.924114i | \(-0.624805\pi\) | ||||
−0.382116 | + | 0.924114i | \(0.624805\pi\) | |||||||
\(348\) | −2.00000 | −0.107211 | ||||||||
\(349\) | 15.0000 | 0.802932 | 0.401466 | − | 0.915874i | \(-0.368501\pi\) | ||||
0.401466 | + | 0.915874i | \(0.368501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.23607 | 0.279481 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.00000 | 0.372572 | 0.186286 | − | 0.982496i | \(-0.440355\pi\) | ||||
0.186286 | + | 0.982496i | \(0.440355\pi\) | |||||||
\(354\) | −7.23607 | −0.384593 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.70820 | −0.408534 | ||||||||
\(357\) | −17.7082 | −0.937218 | ||||||||
\(358\) | 12.4721 | 0.659173 | ||||||||
\(359\) | −7.41641 | −0.391423 | −0.195712 | − | 0.980662i | \(-0.562702\pi\) | ||||
−0.195712 | + | 0.980662i | \(0.562702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 13.2361 | 0.695672 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −27.4164 | −1.43701 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.909830 | −0.0475576 | ||||||||
\(367\) | −4.76393 | −0.248675 | −0.124338 | − | 0.992240i | \(-0.539681\pi\) | ||||
−0.124338 | + | 0.992240i | \(0.539681\pi\) | |||||||
\(368\) | 8.72949 | 0.455056 | ||||||||
\(369\) | −3.52786 | −0.183653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.1803 | −1.67072 | ||||||||
\(372\) | 10.8541 | 0.562759 | ||||||||
\(373\) | 29.8885 | 1.54757 | 0.773785 | − | 0.633448i | \(-0.218361\pi\) | ||||
0.773785 | + | 0.633448i | \(0.218361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.4721 | −1.00420 | ||||||||
\(377\) | 6.47214 | 0.333332 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 30.5967 | 1.57165 | 0.785825 | − | 0.618449i | \(-0.212239\pi\) | ||||
0.785825 | + | 0.618449i | \(0.212239\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.70820 | 0.189977 | ||||||||
\(382\) | −17.0557 | −0.872647 | ||||||||
\(383\) | −16.0000 | −0.817562 | −0.408781 | − | 0.912633i | \(-0.634046\pi\) | ||||
−0.408781 | + | 0.912633i | \(0.634046\pi\) | |||||||
\(384\) | 11.3820 | 0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | −5.23607 | −0.266164 | ||||||||
\(388\) | 20.6525 | 1.04847 | ||||||||
\(389\) | −21.5967 | −1.09500 | −0.547499 | − | 0.836806i | \(-0.684420\pi\) | ||||
−0.547499 | + | 0.836806i | \(0.684420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.7639 | −1.30294 | ||||||||
\(392\) | 7.76393 | 0.392138 | ||||||||
\(393\) | 0.472136 | 0.0238161 | ||||||||
\(394\) | 0.875388 | 0.0441014 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.4164 | 0.874104 | 0.437052 | − | 0.899436i | \(-0.356022\pi\) | ||||
0.437052 | + | 0.899436i | \(0.356022\pi\) | |||||||
\(398\) | −10.0344 | −0.502981 | ||||||||
\(399\) | −20.9443 | −1.04853 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.9443 | 1.04591 | 0.522954 | − | 0.852361i | \(-0.324830\pi\) | ||||
0.522954 | + | 0.852361i | \(0.324830\pi\) | |||||||
\(402\) | 6.94427 | 0.346349 | ||||||||
\(403\) | −35.1246 | −1.74968 | ||||||||
\(404\) | −8.94427 | −0.444994 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.47214 | −0.122690 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −12.2361 | −0.605776 | ||||||||
\(409\) | −36.7771 | −1.81851 | −0.909255 | − | 0.416240i | \(-0.863348\pi\) | ||||
−0.909255 | + | 0.416240i | \(0.863348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.4721 | −0.861837 | ||||||||
\(412\) | −1.52786 | −0.0752725 | ||||||||
\(413\) | 37.8885 | 1.86437 | ||||||||
\(414\) | −2.90983 | −0.143010 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −29.4164 | −1.44226 | ||||||||
\(417\) | 7.29180 | 0.357081 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0000 | −0.683945 | −0.341972 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341972 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8328 | 1.45396 | 0.726981 | − | 0.686657i | \(-0.240923\pi\) | ||||
0.726981 | + | 0.686657i | \(0.240923\pi\) | |||||||
\(422\) | 1.09017 | 0.0530686 | ||||||||
\(423\) | −8.70820 | −0.423407 | ||||||||
\(424\) | −22.2361 | −1.07988 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.94427 | 0.433351 | ||||||||
\(427\) | 4.76393 | 0.230543 | ||||||||
\(428\) | −23.0344 | −1.11341 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.81966 | 0.280323 | 0.140162 | − | 0.990129i | \(-0.455238\pi\) | ||||
0.140162 | + | 0.990129i | \(0.455238\pi\) | |||||||
\(432\) | 1.85410 | 0.0892055 | ||||||||
\(433\) | −25.2361 | −1.21277 | −0.606384 | − | 0.795172i | \(-0.707381\pi\) | ||||
−0.606384 | + | 0.795172i | \(0.707381\pi\) | |||||||
\(434\) | 13.4164 | 0.644008 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.1803 | 1.15803 | ||||||||
\(437\) | −30.4721 | −1.45768 | ||||||||
\(438\) | 6.47214 | 0.309251 | ||||||||
\(439\) | 8.12461 | 0.387767 | 0.193883 | − | 0.981025i | \(-0.437892\pi\) | ||||
0.193883 | + | 0.981025i | \(0.437892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | 17.7082 | 0.842293 | ||||||||
\(443\) | −7.41641 | −0.352364 | −0.176182 | − | 0.984358i | \(-0.556375\pi\) | ||||
−0.176182 | + | 0.984358i | \(0.556375\pi\) | |||||||
\(444\) | 1.23607 | 0.0586612 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.59675 | 0.265014 | ||||||||
\(447\) | 4.29180 | 0.202995 | ||||||||
\(448\) | −0.763932 | −0.0360924 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −20.0902 | −0.944962 | ||||||||
\(453\) | −7.29180 | −0.342598 | ||||||||
\(454\) | −10.3262 | −0.484634 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.4721 | −0.677720 | ||||||||
\(457\) | −34.3607 | −1.60732 | −0.803662 | − | 0.595085i | \(-0.797118\pi\) | ||||
−0.803662 | + | 0.595085i | \(0.797118\pi\) | |||||||
\(458\) | −4.32624 | −0.202152 | ||||||||
\(459\) | −5.47214 | −0.255417 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.1803 | −1.40564 | −0.702819 | − | 0.711368i | \(-0.748076\pi\) | ||||
−0.702819 | + | 0.711368i | \(0.748076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.00000 | −0.278844 | −0.139422 | − | 0.990233i | \(-0.544524\pi\) | ||||
−0.139422 | + | 0.990233i | \(0.544524\pi\) | |||||||
\(464\) | 2.29180 | 0.106394 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.72949 | −0.311738 | ||||||||
\(467\) | 3.76393 | 0.174174 | 0.0870870 | − | 0.996201i | \(-0.472244\pi\) | ||||
0.0870870 | + | 0.996201i | \(0.472244\pi\) | |||||||
\(468\) | −8.47214 | −0.391625 | ||||||||
\(469\) | −36.3607 | −1.67898 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.29180 | −0.105600 | ||||||||
\(472\) | 26.1803 | 1.20505 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 7.85410 | 0.360751 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 28.6525 | 1.31328 | ||||||||
\(477\) | −9.94427 | −0.455317 | ||||||||
\(478\) | −15.2361 | −0.696882 | ||||||||
\(479\) | 0.291796 | 0.0133325 | 0.00666625 | − | 0.999978i | \(-0.497878\pi\) | ||||
0.00666625 | + | 0.999978i | \(0.497878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | −11.0902 | −0.505143 | ||||||||
\(483\) | 15.2361 | 0.693265 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.618034 | −0.0280346 | ||||||||
\(487\) | 11.7082 | 0.530549 | 0.265275 | − | 0.964173i | \(-0.414537\pi\) | ||||
0.265275 | + | 0.964173i | \(0.414537\pi\) | |||||||
\(488\) | 3.29180 | 0.149013 | ||||||||
\(489\) | −6.18034 | −0.279485 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4721 | 1.73622 | 0.868112 | − | 0.496369i | \(-0.165334\pi\) | ||||
0.868112 | + | 0.496369i | \(0.165334\pi\) | |||||||
\(492\) | 5.70820 | 0.257346 | ||||||||
\(493\) | −6.76393 | −0.304632 | ||||||||
\(494\) | 20.9443 | 0.942327 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.4377 | −0.558469 | ||||||||
\(497\) | −46.8328 | −2.10074 | ||||||||
\(498\) | 2.47214 | 0.110779 | ||||||||
\(499\) | −0.944272 | −0.0422714 | −0.0211357 | − | 0.999777i | \(-0.506728\pi\) | ||||
−0.0211357 | + | 0.999777i | \(0.506728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.18034 | 0.142087 | ||||||||
\(502\) | 14.6525 | 0.653972 | ||||||||
\(503\) | −23.1803 | −1.03356 | −0.516780 | − | 0.856118i | \(-0.672870\pi\) | ||||
−0.516780 | + | 0.856118i | \(0.672870\pi\) | |||||||
\(504\) | 7.23607 | 0.322320 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.4164 | 0.640255 | ||||||||
\(508\) | −6.00000 | −0.266207 | ||||||||
\(509\) | 15.5967 | 0.691314 | 0.345657 | − | 0.938361i | \(-0.387656\pi\) | ||||
0.345657 | + | 0.938361i | \(0.387656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.8885 | −1.49914 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | −6.47214 | −0.285752 | ||||||||
\(514\) | 17.8541 | 0.787511 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.47214 | 0.372965 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.52786 | 0.0671305 | ||||||||
\(519\) | 2.94427 | 0.129239 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8197 | 0.780693 | 0.390347 | − | 0.920668i | \(-0.372355\pi\) | ||||
0.390347 | + | 0.920668i | \(0.372355\pi\) | |||||||
\(522\) | −0.763932 | −0.0334364 | ||||||||
\(523\) | −24.5410 | −1.07310 | −0.536552 | − | 0.843867i | \(-0.680273\pi\) | ||||
−0.536552 | + | 0.843867i | \(0.680273\pi\) | |||||||
\(524\) | −0.763932 | −0.0333725 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.4377 | −0.542309 | ||||||||
\(527\) | 36.7082 | 1.59903 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.832816 | −0.0362094 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.7082 | 0.508093 | ||||||||
\(532\) | 33.8885 | 1.46925 | ||||||||
\(533\) | −18.4721 | −0.800117 | ||||||||
\(534\) | −2.94427 | −0.127411 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.1246 | −1.08522 | ||||||||
\(537\) | −20.1803 | −0.870846 | ||||||||
\(538\) | −4.36068 | −0.188002 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.3050 | 1.86183 | 0.930913 | − | 0.365242i | \(-0.119014\pi\) | ||||
0.930913 | + | 0.365242i | \(0.119014\pi\) | |||||||
\(542\) | −14.9787 | −0.643391 | ||||||||
\(543\) | −21.4164 | −0.919066 | ||||||||
\(544\) | 30.7426 | 1.31808 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.4721 | −0.448166 | ||||||||
\(547\) | −9.59675 | −0.410327 | −0.205164 | − | 0.978728i | \(-0.565773\pi\) | ||||
−0.205164 | + | 0.978728i | \(0.565773\pi\) | |||||||
\(548\) | 28.2705 | 1.20766 | ||||||||
\(549\) | 1.47214 | 0.0628292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.00000 | −0.340811 | ||||||||
\(552\) | 10.5279 | 0.448096 | ||||||||
\(553\) | −41.1246 | −1.74880 | ||||||||
\(554\) | 3.05573 | 0.129825 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.7984 | −0.500363 | ||||||||
\(557\) | −8.52786 | −0.361337 | −0.180669 | − | 0.983544i | \(-0.557826\pi\) | ||||
−0.180669 | + | 0.983544i | \(0.557826\pi\) | |||||||
\(558\) | 4.14590 | 0.175510 | ||||||||
\(559\) | −27.4164 | −1.15959 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.41641 | 0.397207 | ||||||||
\(563\) | −0.944272 | −0.0397963 | −0.0198982 | − | 0.999802i | \(-0.506334\pi\) | ||||
−0.0198982 | + | 0.999802i | \(0.506334\pi\) | |||||||
\(564\) | 14.0902 | 0.593303 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.34752 | −0.308839 | ||||||||
\(567\) | 3.23607 | 0.135902 | ||||||||
\(568\) | −32.3607 | −1.35782 | ||||||||
\(569\) | 19.7082 | 0.826211 | 0.413105 | − | 0.910683i | \(-0.364444\pi\) | ||||
0.413105 | + | 0.910683i | \(0.364444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.124612 | −0.00521484 | −0.00260742 | − | 0.999997i | \(-0.500830\pi\) | ||||
−0.00260742 | + | 0.999997i | \(0.500830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.5967 | 1.15287 | ||||||||
\(574\) | 7.05573 | 0.294500 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.236068 | −0.00983617 | ||||||||
\(577\) | −20.0000 | −0.832611 | −0.416305 | − | 0.909225i | \(-0.636675\pi\) | ||||
−0.416305 | + | 0.909225i | \(0.636675\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | 16.1803 | 0.672432 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.9443 | −0.537019 | ||||||||
\(582\) | 7.88854 | 0.326991 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −23.4164 | −0.968978 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.2705 | −0.548200 | ||||||||
\(587\) | 11.6525 | 0.480949 | 0.240475 | − | 0.970655i | \(-0.422697\pi\) | ||||
0.240475 | + | 0.970655i | \(0.422697\pi\) | |||||||
\(588\) | −5.61803 | −0.231684 | ||||||||
\(589\) | 43.4164 | 1.78894 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.41641 | −0.0582632 | ||||||||
\(592\) | −1.41641 | −0.0582140 | ||||||||
\(593\) | −34.9443 | −1.43499 | −0.717495 | − | 0.696564i | \(-0.754711\pi\) | ||||
−0.717495 | + | 0.696564i | \(0.754711\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.94427 | −0.284448 | ||||||||
\(597\) | 16.2361 | 0.664498 | ||||||||
\(598\) | −15.2361 | −0.623049 | ||||||||
\(599\) | −31.0132 | −1.26716 | −0.633582 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633582 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.4721 | −1.16140 | −0.580701 | − | 0.814117i | \(-0.697222\pi\) | ||||
−0.580701 | + | 0.814117i | \(0.697222\pi\) | |||||||
\(602\) | 10.4721 | 0.426812 | ||||||||
\(603\) | −11.2361 | −0.457568 | ||||||||
\(604\) | 11.7984 | 0.480069 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.41641 | −0.138782 | ||||||||
\(607\) | 6.29180 | 0.255376 | 0.127688 | − | 0.991814i | \(-0.459244\pi\) | ||||
0.127688 | + | 0.991814i | \(0.459244\pi\) | |||||||
\(608\) | 36.3607 | 1.47462 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.5967 | −1.84465 | ||||||||
\(612\) | 8.85410 | 0.357906 | ||||||||
\(613\) | −14.8328 | −0.599092 | −0.299546 | − | 0.954082i | \(-0.596835\pi\) | ||||
−0.299546 | + | 0.954082i | \(0.596835\pi\) | |||||||
\(614\) | 7.34752 | 0.296522 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.7771 | −1.68188 | −0.840941 | − | 0.541127i | \(-0.817998\pi\) | ||||
−0.840941 | + | 0.541127i | \(0.817998\pi\) | |||||||
\(618\) | −0.583592 | −0.0234755 | ||||||||
\(619\) | −9.52786 | −0.382957 | −0.191479 | − | 0.981497i | \(-0.561328\pi\) | ||||
−0.191479 | + | 0.981497i | \(0.561328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.70820 | 0.188934 | ||||||||
\(622\) | 2.00000 | 0.0801927 | ||||||||
\(623\) | 15.4164 | 0.617645 | ||||||||
\(624\) | 9.70820 | 0.388639 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.0689 | 0.562306 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.70820 | 0.147973 | ||||||||
\(629\) | 4.18034 | 0.166681 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.18034 | 0.365464 | 0.182732 | − | 0.983163i | \(-0.441506\pi\) | ||||
0.182732 | + | 0.983163i | \(0.441506\pi\) | |||||||
\(632\) | −28.4164 | −1.13034 | ||||||||
\(633\) | −1.76393 | −0.0701100 | ||||||||
\(634\) | −2.43769 | −0.0968132 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.0902 | 0.638017 | ||||||||
\(637\) | 18.1803 | 0.720331 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.4721 | −0.572509 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.12461 | −0.360400 | −0.180200 | − | 0.983630i | \(-0.557675\pi\) | ||||
−0.180200 | + | 0.983630i | \(0.557675\pi\) | |||||||
\(642\) | −8.79837 | −0.347244 | ||||||||
\(643\) | 28.8328 | 1.13706 | 0.568528 | − | 0.822664i | \(-0.307513\pi\) | ||||
0.568528 | + | 0.822664i | \(0.307513\pi\) | |||||||
\(644\) | −24.6525 | −0.971444 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.8885 | −0.861193 | ||||||||
\(647\) | 16.2361 | 0.638306 | 0.319153 | − | 0.947703i | \(-0.396602\pi\) | ||||
0.319153 | + | 0.947703i | \(0.396602\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.7082 | −0.850812 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | −16.8328 | −0.658719 | −0.329359 | − | 0.944205i | \(-0.606833\pi\) | ||||
−0.329359 | + | 0.944205i | \(0.606833\pi\) | |||||||
\(654\) | 9.23607 | 0.361159 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.54102 | −0.255384 | ||||||||
\(657\) | −10.4721 | −0.408557 | ||||||||
\(658\) | 17.4164 | 0.678962 | ||||||||
\(659\) | −35.5967 | −1.38665 | −0.693326 | − | 0.720624i | \(-0.743855\pi\) | ||||
−0.693326 | + | 0.720624i | \(0.743855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.7771 | 1.78052 | 0.890261 | − | 0.455450i | \(-0.150522\pi\) | ||||
0.890261 | + | 0.455450i | \(0.150522\pi\) | |||||||
\(662\) | 10.6180 | 0.412682 | ||||||||
\(663\) | −28.6525 | −1.11277 | ||||||||
\(664\) | −8.94427 | −0.347105 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.472136 | 0.0182949 | ||||||||
\(667\) | 5.81966 | 0.225338 | ||||||||
\(668\) | −5.14590 | −0.199101 | ||||||||
\(669\) | −9.05573 | −0.350115 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −18.1803 | −0.701322 | ||||||||
\(673\) | −27.5967 | −1.06378 | −0.531888 | − | 0.846815i | \(-0.678517\pi\) | ||||
−0.531888 | + | 0.846815i | \(0.678517\pi\) | |||||||
\(674\) | 4.87539 | 0.187793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.3262 | −0.897163 | ||||||||
\(677\) | 5.41641 | 0.208169 | 0.104085 | − | 0.994568i | \(-0.466809\pi\) | ||||
0.104085 | + | 0.994568i | \(0.466809\pi\) | |||||||
\(678\) | −7.67376 | −0.294709 | ||||||||
\(679\) | −41.3050 | −1.58514 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.7082 | 0.640260 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0000 | 0.918334 | 0.459167 | − | 0.888350i | \(-0.348148\pi\) | ||||
0.459167 | + | 0.888350i | \(0.348148\pi\) | |||||||
\(684\) | 10.4721 | 0.400412 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.05573 | 0.269389 | ||||||||
\(687\) | 7.00000 | 0.267067 | ||||||||
\(688\) | −9.70820 | −0.370122 | ||||||||
\(689\) | −52.0689 | −1.98367 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5410 | −1.42813 | −0.714064 | − | 0.700081i | \(-0.753147\pi\) | ||||
−0.714064 | + | 0.700081i | \(0.753147\pi\) | |||||||
\(692\) | −4.76393 | −0.181098 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.79837 | 0.333982 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.76393 | 0.104767 | ||||||||
\(697\) | 19.3050 | 0.731227 | ||||||||
\(698\) | −9.27051 | −0.350894 | ||||||||
\(699\) | 10.8885 | 0.411843 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.1803 | −1.36651 | −0.683256 | − | 0.730179i | \(-0.739437\pi\) | ||||
−0.683256 | + | 0.730179i | \(0.739437\pi\) | |||||||
\(702\) | −3.23607 | −0.122138 | ||||||||
\(703\) | 4.94427 | 0.186477 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.32624 | −0.162820 | ||||||||
\(707\) | 17.8885 | 0.672768 | ||||||||
\(708\) | −18.9443 | −0.711969 | ||||||||
\(709\) | −17.9443 | −0.673911 | −0.336956 | − | 0.941521i | \(-0.609397\pi\) | ||||
−0.336956 | + | 0.941521i | \(0.609397\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.7082 | −0.476595 | ||||||||
\(712\) | 10.6525 | 0.399218 | ||||||||
\(713\) | −31.5836 | −1.18281 | ||||||||
\(714\) | 10.9443 | 0.409579 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.6525 | 1.22028 | ||||||||
\(717\) | 24.6525 | 0.920664 | ||||||||
\(718\) | 4.58359 | 0.171058 | ||||||||
\(719\) | 26.3607 | 0.983087 | 0.491544 | − | 0.870853i | \(-0.336433\pi\) | ||||
0.491544 | + | 0.870853i | \(0.336433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.05573 | 0.113801 | ||||||||
\(722\) | −14.1459 | −0.526456 | ||||||||
\(723\) | 17.9443 | 0.667355 | ||||||||
\(724\) | 34.6525 | 1.28785 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.8328 | −1.66276 | −0.831379 | − | 0.555706i | \(-0.812448\pi\) | ||||
−0.831379 | + | 0.555706i | \(0.812448\pi\) | |||||||
\(728\) | 37.8885 | 1.40424 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.6525 | 1.05975 | ||||||||
\(732\) | −2.38197 | −0.0880400 | ||||||||
\(733\) | 47.8885 | 1.76880 | 0.884402 | − | 0.466726i | \(-0.154567\pi\) | ||||
0.884402 | + | 0.466726i | \(0.154567\pi\) | |||||||
\(734\) | 2.94427 | 0.108675 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.4508 | −0.974991 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.18034 | 0.0802594 | ||||||||
\(739\) | −1.65248 | −0.0607873 | −0.0303937 | − | 0.999538i | \(-0.509676\pi\) | ||||
−0.0303937 | + | 0.999538i | \(0.509676\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.8885 | −1.24493 | ||||||||
\(742\) | 19.8885 | 0.730131 | ||||||||
\(743\) | 2.23607 | 0.0820334 | 0.0410167 | − | 0.999158i | \(-0.486940\pi\) | ||||
0.0410167 | + | 0.999158i | \(0.486940\pi\) | |||||||
\(744\) | −15.0000 | −0.549927 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18.4721 | −0.676313 | ||||||||
\(747\) | −4.00000 | −0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.0689 | 1.68332 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.0132 | −1.24116 | −0.620579 | − | 0.784144i | \(-0.713102\pi\) | ||||
−0.620579 | + | 0.784144i | \(0.713102\pi\) | |||||||
\(752\) | −16.1459 | −0.588780 | ||||||||
\(753\) | −23.7082 | −0.863975 | ||||||||
\(754\) | −4.00000 | −0.145671 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.23607 | −0.190434 | ||||||||
\(757\) | −18.9443 | −0.688541 | −0.344271 | − | 0.938870i | \(-0.611874\pi\) | ||||
−0.344271 | + | 0.938870i | \(0.611874\pi\) | |||||||
\(758\) | −18.9098 | −0.686836 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.6525 | 1.61865 | 0.809325 | − | 0.587360i | \(-0.199833\pi\) | ||||
0.809325 | + | 0.587360i | \(0.199833\pi\) | |||||||
\(762\) | −2.29180 | −0.0830230 | ||||||||
\(763\) | −48.3607 | −1.75077 | ||||||||
\(764\) | −44.6525 | −1.61547 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.88854 | 0.357288 | ||||||||
\(767\) | 61.3050 | 2.21359 | ||||||||
\(768\) | −6.56231 | −0.236797 | ||||||||
\(769\) | 24.5279 | 0.884497 | 0.442249 | − | 0.896892i | \(-0.354181\pi\) | ||||
0.442249 | + | 0.896892i | \(0.354181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.8885 | −1.04040 | ||||||||
\(772\) | −26.1803 | −0.942251 | ||||||||
\(773\) | 7.94427 | 0.285736 | 0.142868 | − | 0.989742i | \(-0.454368\pi\) | ||||
0.142868 | + | 0.989742i | \(0.454368\pi\) | |||||||
\(774\) | 3.23607 | 0.116318 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −28.5410 | −1.02456 | ||||||||
\(777\) | −2.47214 | −0.0886874 | ||||||||
\(778\) | 13.3475 | 0.478532 | ||||||||
\(779\) | 22.8328 | 0.818071 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 15.9230 | 0.569405 | ||||||||
\(783\) | 1.23607 | 0.0441735 | ||||||||
\(784\) | 6.43769 | 0.229918 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.291796 | −0.0104080 | ||||||||
\(787\) | −27.0557 | −0.964433 | −0.482216 | − | 0.876052i | \(-0.660168\pi\) | ||||
−0.482216 | + | 0.876052i | \(0.660168\pi\) | |||||||
\(788\) | 2.29180 | 0.0816419 | ||||||||
\(789\) | 20.1246 | 0.716455 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.1803 | 1.42865 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.70820 | 0.273726 | ||||||||
\(794\) | −10.7639 | −0.381998 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.2705 | −0.931134 | ||||||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 12.9443 | 0.458222 | ||||||||
\(799\) | 47.6525 | 1.68582 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.76393 | 0.168325 | ||||||||
\(802\) | −12.9443 | −0.457078 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 18.1803 | 0.641171 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.7082 | 0.764639 | ||||||||
\(807\) | 7.05573 | 0.248373 | ||||||||
\(808\) | 12.3607 | 0.434847 | ||||||||
\(809\) | 8.00000 | 0.281265 | 0.140633 | − | 0.990062i | \(-0.455086\pi\) | ||||
0.140633 | + | 0.990062i | \(0.455086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.87539 | −0.276542 | −0.138271 | − | 0.990394i | \(-0.544155\pi\) | ||||
−0.138271 | + | 0.990394i | \(0.544155\pi\) | |||||||
\(812\) | −6.47214 | −0.227127 | ||||||||
\(813\) | 24.2361 | 0.849996 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.1459 | −0.355177 | ||||||||
\(817\) | 33.8885 | 1.18561 | ||||||||
\(818\) | 22.7295 | 0.794718 | ||||||||
\(819\) | 16.9443 | 0.592081 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.7771 | 1.17883 | 0.589414 | − | 0.807831i | \(-0.299359\pi\) | ||||
0.589414 | + | 0.807831i | \(0.299359\pi\) | |||||||
\(822\) | 10.7984 | 0.376637 | ||||||||
\(823\) | −38.2492 | −1.33328 | −0.666642 | − | 0.745378i | \(-0.732269\pi\) | ||||
−0.666642 | + | 0.745378i | \(0.732269\pi\) | |||||||
\(824\) | 2.11146 | 0.0735561 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.4164 | −0.814761 | ||||||||
\(827\) | 8.94427 | 0.311023 | 0.155511 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155511 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(828\) | −7.61803 | −0.264745 | ||||||||
\(829\) | −11.0000 | −0.382046 | −0.191023 | − | 0.981586i | \(-0.561180\pi\) | ||||
−0.191023 | + | 0.981586i | \(0.561180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.94427 | −0.171515 | ||||||||
\(832\) | −1.23607 | −0.0428529 | ||||||||
\(833\) | −19.0000 | −0.658311 | ||||||||
\(834\) | −4.50658 | −0.156050 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.70820 | −0.231869 | ||||||||
\(838\) | 8.65248 | 0.298895 | ||||||||
\(839\) | 28.3607 | 0.979119 | 0.489560 | − | 0.871970i | \(-0.337158\pi\) | ||||
0.489560 | + | 0.871970i | \(0.337158\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4721 | −0.947315 | ||||||||
\(842\) | −18.4377 | −0.635405 | ||||||||
\(843\) | −15.2361 | −0.524758 | ||||||||
\(844\) | 2.85410 | 0.0982422 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.38197 | 0.185036 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.4377 | −0.633153 | ||||||||
\(849\) | 11.8885 | 0.408014 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.59675 | −0.123295 | ||||||||
\(852\) | 23.4164 | 0.802233 | ||||||||
\(853\) | −31.8885 | −1.09184 | −0.545921 | − | 0.837836i | \(-0.683820\pi\) | ||||
−0.545921 | + | 0.837836i | \(0.683820\pi\) | |||||||
\(854\) | −2.94427 | −0.100751 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.8328 | 1.08802 | ||||||||
\(857\) | 1.00000 | 0.0341593 | 0.0170797 | − | 0.999854i | \(-0.494563\pi\) | ||||
0.0170797 | + | 0.999854i | \(0.494563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.8328 | −0.915524 | −0.457762 | − | 0.889075i | \(-0.651349\pi\) | ||||
−0.457762 | + | 0.889075i | \(0.651349\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.4164 | −0.389070 | ||||||||
\(862\) | −3.59675 | −0.122506 | ||||||||
\(863\) | 37.8885 | 1.28974 | 0.644871 | − | 0.764292i | \(-0.276911\pi\) | ||||
0.644871 | + | 0.764292i | \(0.276911\pi\) | |||||||
\(864\) | −5.61803 | −0.191129 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.5967 | 0.529999 | ||||||||
\(867\) | 12.9443 | 0.439611 | ||||||||
\(868\) | 35.1246 | 1.19221 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −58.8328 | −1.99347 | ||||||||
\(872\) | −33.4164 | −1.13162 | ||||||||
\(873\) | −12.7639 | −0.431994 | ||||||||
\(874\) | 18.8328 | 0.637029 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.9443 | 0.572494 | ||||||||
\(877\) | 11.3050 | 0.381741 | 0.190871 | − | 0.981615i | \(-0.438869\pi\) | ||||
0.190871 | + | 0.981615i | \(0.438869\pi\) | |||||||
\(878\) | −5.02129 | −0.169460 | ||||||||
\(879\) | 21.4721 | 0.724237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.8328 | 1.30831 | 0.654155 | − | 0.756360i | \(-0.273024\pi\) | ||||
0.654155 | + | 0.756360i | \(0.273024\pi\) | |||||||
\(882\) | −2.14590 | −0.0722561 | ||||||||
\(883\) | −10.1803 | −0.342596 | −0.171298 | − | 0.985219i | \(-0.554796\pi\) | ||||
−0.171298 | + | 0.985219i | \(0.554796\pi\) | |||||||
\(884\) | 46.3607 | 1.55928 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.58359 | 0.153989 | ||||||||
\(887\) | 16.9443 | 0.568933 | 0.284466 | − | 0.958686i | \(-0.408184\pi\) | ||||
0.284466 | + | 0.958686i | \(0.408184\pi\) | |||||||
\(888\) | −1.70820 | −0.0573236 | ||||||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.6525 | 0.490601 | ||||||||
\(893\) | 56.3607 | 1.88604 | ||||||||
\(894\) | −2.65248 | −0.0887121 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 36.8328 | 1.23050 | ||||||||
\(897\) | 24.6525 | 0.823122 | ||||||||
\(898\) | 6.18034 | 0.206241 | ||||||||
\(899\) | −8.29180 | −0.276547 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.4164 | 1.81287 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.9443 | −0.563870 | ||||||||
\(904\) | 27.7639 | 0.923415 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.50658 | 0.149721 | ||||||||
\(907\) | 42.0000 | 1.39459 | 0.697294 | − | 0.716786i | \(-0.254387\pi\) | ||||
0.697294 | + | 0.716786i | \(0.254387\pi\) | |||||||
\(908\) | −27.0344 | −0.897169 | ||||||||
\(909\) | 5.52786 | 0.183348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.9574 | 1.58890 | 0.794450 | − | 0.607329i | \(-0.207759\pi\) | ||||
0.794450 | + | 0.607329i | \(0.207759\pi\) | |||||||
\(912\) | −12.0000 | −0.397360 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 21.2361 | 0.702427 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.3262 | −0.374229 | ||||||||
\(917\) | 1.52786 | 0.0504545 | ||||||||
\(918\) | 3.38197 | 0.111622 | ||||||||
\(919\) | −3.41641 | −0.112697 | −0.0563484 | − | 0.998411i | \(-0.517946\pi\) | ||||
−0.0563484 | + | 0.998411i | \(0.517946\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.8885 | −0.391741 | ||||||||
\(922\) | 18.6525 | 0.614287 | ||||||||
\(923\) | −75.7771 | −2.49423 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.70820 | 0.121859 | ||||||||
\(927\) | 0.944272 | 0.0310140 | ||||||||
\(928\) | −6.94427 | −0.227957 | ||||||||
\(929\) | 50.9443 | 1.67143 | 0.835714 | − | 0.549165i | \(-0.185054\pi\) | ||||
0.835714 | + | 0.549165i | \(0.185054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.4721 | −0.736495 | ||||||||
\(932\) | −17.6180 | −0.577098 | ||||||||
\(933\) | −3.23607 | −0.105944 | ||||||||
\(934\) | −2.32624 | −0.0761168 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.7082 | 0.382695 | ||||||||
\(937\) | 33.1246 | 1.08213 | 0.541067 | − | 0.840980i | \(-0.318021\pi\) | ||||
0.541067 | + | 0.840980i | \(0.318021\pi\) | |||||||
\(938\) | 22.4721 | 0.733741 | ||||||||
\(939\) | −22.7639 | −0.742873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.2361 | 1.47465 | 0.737327 | − | 0.675536i | \(-0.236088\pi\) | ||||
0.737327 | + | 0.675536i | \(0.236088\pi\) | |||||||
\(942\) | 1.41641 | 0.0461491 | ||||||||
\(943\) | −16.6099 | −0.540893 | ||||||||
\(944\) | 21.7082 | 0.706542 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.2361 | 0.592593 | 0.296296 | − | 0.955096i | \(-0.404248\pi\) | ||||
0.296296 | + | 0.955096i | \(0.404248\pi\) | |||||||
\(948\) | 20.5623 | 0.667833 | ||||||||
\(949\) | −54.8328 | −1.77995 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.94427 | 0.127902 | ||||||||
\(952\) | −39.5967 | −1.28334 | ||||||||
\(953\) | 31.8885 | 1.03297 | 0.516486 | − | 0.856296i | \(-0.327240\pi\) | ||||
0.516486 | + | 0.856296i | \(0.327240\pi\) | |||||||
\(954\) | 6.14590 | 0.198981 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −39.8885 | −1.29009 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.180340 | −0.00582652 | ||||||||
\(959\) | −56.5410 | −1.82580 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | 2.47214 | 0.0797049 | ||||||||
\(963\) | 14.2361 | 0.458751 | ||||||||
\(964\) | −29.0344 | −0.935136 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.41641 | −0.302968 | ||||||||
\(967\) | −32.0000 | −1.02905 | −0.514525 | − | 0.857475i | \(-0.672032\pi\) | ||||
−0.514525 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.4164 | 1.13774 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.2361 | 0.938230 | 0.469115 | − | 0.883137i | \(-0.344573\pi\) | ||||
0.469115 | + | 0.883137i | \(0.344573\pi\) | |||||||
\(972\) | −1.61803 | −0.0518985 | ||||||||
\(973\) | 23.5967 | 0.756477 | ||||||||
\(974\) | −7.23607 | −0.231859 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.72949 | 0.0873689 | ||||||||
\(977\) | 15.9443 | 0.510102 | 0.255051 | − | 0.966928i | \(-0.417908\pi\) | ||||
0.255051 | + | 0.966928i | \(0.417908\pi\) | |||||||
\(978\) | 3.81966 | 0.122139 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9443 | −0.477134 | ||||||||
\(982\) | −23.7771 | −0.758757 | ||||||||
\(983\) | 55.1803 | 1.75998 | 0.879990 | − | 0.474993i | \(-0.157549\pi\) | ||||
0.879990 | + | 0.474993i | \(0.157549\pi\) | |||||||
\(984\) | −7.88854 | −0.251478 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.18034 | 0.133129 | ||||||||
\(987\) | −28.1803 | −0.896990 | ||||||||
\(988\) | 54.8328 | 1.74446 | ||||||||
\(989\) | −24.6525 | −0.783903 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.23607 | 0.198095 | 0.0990476 | − | 0.995083i | \(-0.468420\pi\) | ||||
0.0990476 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(992\) | 37.6869 | 1.19656 | ||||||||
\(993\) | −17.1803 | −0.545202 | ||||||||
\(994\) | 28.9443 | 0.918057 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.47214 | 0.205077 | ||||||||
\(997\) | 38.7639 | 1.22767 | 0.613833 | − | 0.789436i | \(-0.289627\pi\) | ||||
0.613833 | + | 0.789436i | \(0.289627\pi\) | |||||||
\(998\) | 0.583592 | 0.0184733 | ||||||||
\(999\) | −0.763932 | −0.0241697 |
(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 | 9075.2.a.bx.1.1 | 2 | ||
5.4 | even | 2 | 1815.2.a.f.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 9075.2.a.bd.1.2 | 2 | |||
15.14 | odd | 2 | 5445.2.a.x.1.1 | 2 | |||
55.54 | odd | 2 | 1815.2.a.j.1.1 | yes | 2 | ||
165.164 | even | 2 | 5445.2.a.o.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.f.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
1815.2.a.j.1.1 | yes | 2 | 55.54 | odd | 2 | ||
5445.2.a.o.1.2 | 2 | 165.164 | even | 2 | |||
5445.2.a.x.1.1 | 2 | 15.14 | odd | 2 | |||
9075.2.a.bd.1.2 | 2 | 11.10 | odd | 2 | |||
9075.2.a.bx.1.1 | 2 | 1.1 | even | 1 | trivial |