Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.978400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 2x^{4} - 7x^{3} + 6x^{2} + 14x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.154912\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.66618 | 1.53932 | 0.769659 | − | 0.638455i | \(-0.220426\pi\) | ||||
0.769659 | + | 0.638455i | \(0.220426\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.70044 | 0.760460 | 0.380230 | − | 0.924892i | \(-0.375845\pi\) | ||||
0.380230 | + | 0.924892i | \(0.375845\pi\) | |||||||
\(6\) | −2.66618 | −1.08846 | ||||||||
\(7\) | −0.855351 | −0.323292 | −0.161646 | − | 0.986849i | \(-0.551680\pi\) | ||||
−0.161646 | + | 0.986849i | \(0.551680\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.10851 | 1.36950 | ||||||||
\(10\) | −1.70044 | −0.537726 | ||||||||
\(11\) | 5.83135 | 1.75822 | 0.879110 | − | 0.476620i | \(-0.158138\pi\) | ||||
0.879110 | + | 0.476620i | \(0.158138\pi\) | |||||||
\(12\) | 2.66618 | 0.769659 | ||||||||
\(13\) | 3.52153 | 0.976697 | 0.488348 | − | 0.872649i | \(-0.337600\pi\) | ||||
0.488348 | + | 0.872649i | \(0.337600\pi\) | |||||||
\(14\) | 0.855351 | 0.228602 | ||||||||
\(15\) | 4.53367 | 1.17059 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.68859 | −1.37968 | −0.689842 | − | 0.723960i | \(-0.742320\pi\) | ||||
−0.689842 | + | 0.723960i | \(0.742320\pi\) | |||||||
\(18\) | −4.10851 | −0.968384 | ||||||||
\(19\) | 3.55767 | 0.816186 | 0.408093 | − | 0.912940i | \(-0.366194\pi\) | ||||
0.408093 | + | 0.912940i | \(0.366194\pi\) | |||||||
\(20\) | 1.70044 | 0.380230 | ||||||||
\(21\) | −2.28052 | −0.497650 | ||||||||
\(22\) | −5.83135 | −1.24325 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.66618 | −0.544231 | ||||||||
\(25\) | −2.10851 | −0.421701 | ||||||||
\(26\) | −3.52153 | −0.690629 | ||||||||
\(27\) | 2.95548 | 0.568782 | ||||||||
\(28\) | −0.855351 | −0.161646 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −4.53367 | −0.827732 | ||||||||
\(31\) | −3.83135 | −0.688131 | −0.344066 | − | 0.938946i | \(-0.611804\pi\) | ||||
−0.344066 | + | 0.938946i | \(0.611804\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 15.5474 | 2.70646 | ||||||||
\(34\) | 5.68859 | 0.975584 | ||||||||
\(35\) | −1.45447 | −0.245851 | ||||||||
\(36\) | 4.10851 | 0.684751 | ||||||||
\(37\) | −9.92270 | −1.63128 | −0.815641 | − | 0.578559i | \(-0.803615\pi\) | ||||
−0.815641 | + | 0.578559i | \(0.803615\pi\) | |||||||
\(38\) | −3.55767 | −0.577131 | ||||||||
\(39\) | 9.38903 | 1.50345 | ||||||||
\(40\) | −1.70044 | −0.268863 | ||||||||
\(41\) | −6.21200 | −0.970151 | −0.485075 | − | 0.874472i | \(-0.661208\pi\) | ||||
−0.485075 | + | 0.874472i | \(0.661208\pi\) | |||||||
\(42\) | 2.28052 | 0.351892 | ||||||||
\(43\) | 4.94670 | 0.754364 | 0.377182 | − | 0.926139i | \(-0.376893\pi\) | ||||
0.377182 | + | 0.926139i | \(0.376893\pi\) | |||||||
\(44\) | 5.83135 | 0.879110 | ||||||||
\(45\) | 6.98627 | 1.04145 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 6.34758 | 0.925889 | 0.462945 | − | 0.886387i | \(-0.346793\pi\) | ||||
0.462945 | + | 0.886387i | \(0.346793\pi\) | |||||||
\(48\) | 2.66618 | 0.384830 | ||||||||
\(49\) | −6.26837 | −0.895482 | ||||||||
\(50\) | 2.10851 | 0.298188 | ||||||||
\(51\) | −15.1668 | −2.12377 | ||||||||
\(52\) | 3.52153 | 0.488348 | ||||||||
\(53\) | 4.81578 | 0.661499 | 0.330749 | − | 0.943719i | \(-0.392699\pi\) | ||||
0.330749 | + | 0.943719i | \(0.392699\pi\) | |||||||
\(54\) | −2.95548 | −0.402189 | ||||||||
\(55\) | 9.91586 | 1.33705 | ||||||||
\(56\) | 0.855351 | 0.114301 | ||||||||
\(57\) | 9.48539 | 1.25637 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 4.24130 | 0.552170 | 0.276085 | − | 0.961133i | \(-0.410963\pi\) | ||||
0.276085 | + | 0.961133i | \(0.410963\pi\) | |||||||
\(60\) | 4.53367 | 0.585295 | ||||||||
\(61\) | 14.2805 | 1.82843 | 0.914217 | − | 0.405226i | \(-0.132807\pi\) | ||||
0.914217 | + | 0.405226i | \(0.132807\pi\) | |||||||
\(62\) | 3.83135 | 0.486582 | ||||||||
\(63\) | −3.51422 | −0.442750 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.98815 | 0.742738 | ||||||||
\(66\) | −15.5474 | −1.91376 | ||||||||
\(67\) | 0.621238 | 0.0758963 | 0.0379481 | − | 0.999280i | \(-0.487918\pi\) | ||||
0.0379481 | + | 0.999280i | \(0.487918\pi\) | |||||||
\(68\) | −5.68859 | −0.689842 | ||||||||
\(69\) | 2.66618 | 0.320970 | ||||||||
\(70\) | 1.45447 | 0.173843 | ||||||||
\(71\) | −6.73323 | −0.799088 | −0.399544 | − | 0.916714i | \(-0.630832\pi\) | ||||
−0.399544 | + | 0.916714i | \(0.630832\pi\) | |||||||
\(72\) | −4.10851 | −0.484192 | ||||||||
\(73\) | 3.71948 | 0.435332 | 0.217666 | − | 0.976023i | \(-0.430156\pi\) | ||||
0.217666 | + | 0.976023i | \(0.430156\pi\) | |||||||
\(74\) | 9.92270 | 1.15349 | ||||||||
\(75\) | −5.62165 | −0.649133 | ||||||||
\(76\) | 3.55767 | 0.408093 | ||||||||
\(77\) | −4.98786 | −0.568419 | ||||||||
\(78\) | −9.38903 | −1.06310 | ||||||||
\(79\) | 7.65244 | 0.860967 | 0.430484 | − | 0.902598i | \(-0.358343\pi\) | ||||
0.430484 | + | 0.902598i | \(0.358343\pi\) | |||||||
\(80\) | 1.70044 | 0.190115 | ||||||||
\(81\) | −4.44569 | −0.493966 | ||||||||
\(82\) | 6.21200 | 0.686000 | ||||||||
\(83\) | −15.4097 | −1.69143 | −0.845716 | − | 0.533633i | \(-0.820826\pi\) | ||||
−0.845716 | + | 0.533633i | \(0.820826\pi\) | |||||||
\(84\) | −2.28052 | −0.248825 | ||||||||
\(85\) | −9.67309 | −1.04919 | ||||||||
\(86\) | −4.94670 | −0.533416 | ||||||||
\(87\) | −2.66618 | −0.285844 | ||||||||
\(88\) | −5.83135 | −0.621624 | ||||||||
\(89\) | −8.61831 | −0.913539 | −0.456769 | − | 0.889585i | \(-0.650994\pi\) | ||||
−0.456769 | + | 0.889585i | \(0.650994\pi\) | |||||||
\(90\) | −6.98627 | −0.736417 | ||||||||
\(91\) | −3.01214 | −0.315759 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −10.2151 | −1.05925 | ||||||||
\(94\) | −6.34758 | −0.654702 | ||||||||
\(95\) | 6.04960 | 0.620676 | ||||||||
\(96\) | −2.66618 | −0.272116 | ||||||||
\(97\) | −16.7420 | −1.69990 | −0.849948 | − | 0.526867i | \(-0.823367\pi\) | ||||
−0.849948 | + | 0.526867i | \(0.823367\pi\) | |||||||
\(98\) | 6.26837 | 0.633201 | ||||||||
\(99\) | 23.9582 | 2.40789 | ||||||||
\(100\) | −2.10851 | −0.210851 | ||||||||
\(101\) | 16.4335 | 1.63520 | 0.817600 | − | 0.575787i | \(-0.195304\pi\) | ||||
0.817600 | + | 0.575787i | \(0.195304\pi\) | |||||||
\(102\) | 15.1668 | 1.50174 | ||||||||
\(103\) | −9.55928 | −0.941904 | −0.470952 | − | 0.882159i | \(-0.656089\pi\) | ||||
−0.470952 | + | 0.882159i | \(0.656089\pi\) | |||||||
\(104\) | −3.52153 | −0.345314 | ||||||||
\(105\) | −3.87788 | −0.378443 | ||||||||
\(106\) | −4.81578 | −0.467750 | ||||||||
\(107\) | −10.6764 | −1.03213 | −0.516065 | − | 0.856549i | \(-0.672604\pi\) | ||||
−0.516065 | + | 0.856549i | \(0.672604\pi\) | |||||||
\(108\) | 2.95548 | 0.284391 | ||||||||
\(109\) | 19.4128 | 1.85940 | 0.929702 | − | 0.368312i | \(-0.120064\pi\) | ||||
0.929702 | + | 0.368312i | \(0.120064\pi\) | |||||||
\(110\) | −9.91586 | −0.945440 | ||||||||
\(111\) | −26.4557 | −2.51106 | ||||||||
\(112\) | −0.855351 | −0.0808231 | ||||||||
\(113\) | 1.83602 | 0.172718 | 0.0863590 | − | 0.996264i | \(-0.472477\pi\) | ||||
0.0863590 | + | 0.996264i | \(0.472477\pi\) | |||||||
\(114\) | −9.48539 | −0.888388 | ||||||||
\(115\) | 1.70044 | 0.158567 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 14.4682 | 1.33759 | ||||||||
\(118\) | −4.24130 | −0.390444 | ||||||||
\(119\) | 4.86574 | 0.446042 | ||||||||
\(120\) | −4.53367 | −0.413866 | ||||||||
\(121\) | 23.0047 | 2.09133 | ||||||||
\(122\) | −14.2805 | −1.29290 | ||||||||
\(123\) | −16.5623 | −1.49337 | ||||||||
\(124\) | −3.83135 | −0.344066 | ||||||||
\(125\) | −12.0876 | −1.08115 | ||||||||
\(126\) | 3.51422 | 0.313071 | ||||||||
\(127\) | −1.91710 | −0.170115 | −0.0850576 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850576 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 13.1888 | 1.16121 | ||||||||
\(130\) | −5.98815 | −0.525195 | ||||||||
\(131\) | −0.359429 | −0.0314034 | −0.0157017 | − | 0.999877i | \(-0.504998\pi\) | ||||
−0.0157017 | + | 0.999877i | \(0.504998\pi\) | |||||||
\(132\) | 15.5474 | 1.35323 | ||||||||
\(133\) | −3.04306 | −0.263867 | ||||||||
\(134\) | −0.621238 | −0.0536668 | ||||||||
\(135\) | 5.02561 | 0.432535 | ||||||||
\(136\) | 5.68859 | 0.487792 | ||||||||
\(137\) | 16.4666 | 1.40684 | 0.703420 | − | 0.710775i | \(-0.251655\pi\) | ||||
0.703420 | + | 0.710775i | \(0.251655\pi\) | |||||||
\(138\) | −2.66618 | −0.226960 | ||||||||
\(139\) | 9.77421 | 0.829038 | 0.414519 | − | 0.910041i | \(-0.363950\pi\) | ||||
0.414519 | + | 0.910041i | \(0.363950\pi\) | |||||||
\(140\) | −1.45447 | −0.122925 | ||||||||
\(141\) | 16.9238 | 1.42524 | ||||||||
\(142\) | 6.73323 | 0.565041 | ||||||||
\(143\) | 20.5353 | 1.71725 | ||||||||
\(144\) | 4.10851 | 0.342376 | ||||||||
\(145\) | −1.70044 | −0.141214 | ||||||||
\(146\) | −3.71948 | −0.307826 | ||||||||
\(147\) | −16.7126 | −1.37843 | ||||||||
\(148\) | −9.92270 | −0.815641 | ||||||||
\(149\) | −14.1687 | −1.16074 | −0.580371 | − | 0.814352i | \(-0.697093\pi\) | ||||
−0.580371 | + | 0.814352i | \(0.697093\pi\) | |||||||
\(150\) | 5.62165 | 0.459006 | ||||||||
\(151\) | 15.2844 | 1.24382 | 0.621912 | − | 0.783087i | \(-0.286356\pi\) | ||||
0.621912 | + | 0.783087i | \(0.286356\pi\) | |||||||
\(152\) | −3.55767 | −0.288565 | ||||||||
\(153\) | −23.3716 | −1.88948 | ||||||||
\(154\) | 4.98786 | 0.401933 | ||||||||
\(155\) | −6.51498 | −0.523296 | ||||||||
\(156\) | 9.38903 | 0.751724 | ||||||||
\(157\) | −22.8829 | −1.82625 | −0.913125 | − | 0.407679i | \(-0.866338\pi\) | ||||
−0.913125 | + | 0.407679i | \(0.866338\pi\) | |||||||
\(158\) | −7.65244 | −0.608796 | ||||||||
\(159\) | 12.8397 | 1.01826 | ||||||||
\(160\) | −1.70044 | −0.134432 | ||||||||
\(161\) | −0.855351 | −0.0674111 | ||||||||
\(162\) | 4.44569 | 0.349287 | ||||||||
\(163\) | 0.931187 | 0.0729362 | 0.0364681 | − | 0.999335i | \(-0.488389\pi\) | ||||
0.0364681 | + | 0.999335i | \(0.488389\pi\) | |||||||
\(164\) | −6.21200 | −0.485075 | ||||||||
\(165\) | 26.4375 | 2.05815 | ||||||||
\(166\) | 15.4097 | 1.19602 | ||||||||
\(167\) | 7.28436 | 0.563681 | 0.281840 | − | 0.959461i | \(-0.409055\pi\) | ||||
0.281840 | + | 0.959461i | \(0.409055\pi\) | |||||||
\(168\) | 2.28052 | 0.175946 | ||||||||
\(169\) | −0.598830 | −0.0460639 | ||||||||
\(170\) | 9.67309 | 0.741893 | ||||||||
\(171\) | 14.6167 | 1.11777 | ||||||||
\(172\) | 4.94670 | 0.377182 | ||||||||
\(173\) | 19.9725 | 1.51848 | 0.759242 | − | 0.650809i | \(-0.225570\pi\) | ||||
0.759242 | + | 0.650809i | \(0.225570\pi\) | |||||||
\(174\) | 2.66618 | 0.202122 | ||||||||
\(175\) | 1.80351 | 0.136333 | ||||||||
\(176\) | 5.83135 | 0.439555 | ||||||||
\(177\) | 11.3081 | 0.849966 | ||||||||
\(178\) | 8.61831 | 0.645969 | ||||||||
\(179\) | −16.7730 | −1.25368 | −0.626838 | − | 0.779150i | \(-0.715651\pi\) | ||||
−0.626838 | + | 0.779150i | \(0.715651\pi\) | |||||||
\(180\) | 6.98627 | 0.520725 | ||||||||
\(181\) | −4.47713 | −0.332782 | −0.166391 | − | 0.986060i | \(-0.553211\pi\) | ||||
−0.166391 | + | 0.986060i | \(0.553211\pi\) | |||||||
\(182\) | 3.01214 | 0.223275 | ||||||||
\(183\) | 38.0744 | 2.81454 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −16.8729 | −1.24052 | ||||||||
\(186\) | 10.2151 | 0.749005 | ||||||||
\(187\) | −33.1722 | −2.42579 | ||||||||
\(188\) | 6.34758 | 0.462945 | ||||||||
\(189\) | −2.52797 | −0.183883 | ||||||||
\(190\) | −6.04960 | −0.438884 | ||||||||
\(191\) | −21.7201 | −1.57161 | −0.785805 | − | 0.618474i | \(-0.787751\pi\) | ||||
−0.785805 | + | 0.618474i | \(0.787751\pi\) | |||||||
\(192\) | 2.66618 | 0.192415 | ||||||||
\(193\) | 10.3549 | 0.745361 | 0.372681 | − | 0.927960i | \(-0.378439\pi\) | ||||
0.372681 | + | 0.927960i | \(0.378439\pi\) | |||||||
\(194\) | 16.7420 | 1.20201 | ||||||||
\(195\) | 15.9655 | 1.14331 | ||||||||
\(196\) | −6.26837 | −0.447741 | ||||||||
\(197\) | −8.55113 | −0.609243 | −0.304621 | − | 0.952474i | \(-0.598530\pi\) | ||||
−0.304621 | + | 0.952474i | \(0.598530\pi\) | |||||||
\(198\) | −23.9582 | −1.70263 | ||||||||
\(199\) | 11.1801 | 0.792536 | 0.396268 | − | 0.918135i | \(-0.370305\pi\) | ||||
0.396268 | + | 0.918135i | \(0.370305\pi\) | |||||||
\(200\) | 2.10851 | 0.149094 | ||||||||
\(201\) | 1.65633 | 0.116829 | ||||||||
\(202\) | −16.4335 | −1.15626 | ||||||||
\(203\) | 0.855351 | 0.0600339 | ||||||||
\(204\) | −15.1668 | −1.06189 | ||||||||
\(205\) | −10.5631 | −0.737761 | ||||||||
\(206\) | 9.55928 | 0.666027 | ||||||||
\(207\) | 4.10851 | 0.285561 | ||||||||
\(208\) | 3.52153 | 0.244174 | ||||||||
\(209\) | 20.7460 | 1.43503 | ||||||||
\(210\) | 3.87788 | 0.267599 | ||||||||
\(211\) | −4.68294 | −0.322387 | −0.161194 | − | 0.986923i | \(-0.551534\pi\) | ||||
−0.161194 | + | 0.986923i | \(0.551534\pi\) | |||||||
\(212\) | 4.81578 | 0.330749 | ||||||||
\(213\) | −17.9520 | −1.23005 | ||||||||
\(214\) | 10.6764 | 0.729827 | ||||||||
\(215\) | 8.41156 | 0.573663 | ||||||||
\(216\) | −2.95548 | −0.201095 | ||||||||
\(217\) | 3.27715 | 0.222468 | ||||||||
\(218\) | −19.4128 | −1.31480 | ||||||||
\(219\) | 9.91680 | 0.670115 | ||||||||
\(220\) | 9.91586 | 0.668527 | ||||||||
\(221\) | −20.0325 | −1.34753 | ||||||||
\(222\) | 26.4557 | 1.77559 | ||||||||
\(223\) | 15.8006 | 1.05809 | 0.529043 | − | 0.848595i | \(-0.322551\pi\) | ||||
0.529043 | + | 0.848595i | \(0.322551\pi\) | |||||||
\(224\) | 0.855351 | 0.0571506 | ||||||||
\(225\) | −8.66281 | −0.577521 | ||||||||
\(226\) | −1.83602 | −0.122130 | ||||||||
\(227\) | −25.1513 | −1.66935 | −0.834675 | − | 0.550743i | \(-0.814345\pi\) | ||||
−0.834675 | + | 0.550743i | \(0.814345\pi\) | |||||||
\(228\) | 9.48539 | 0.628185 | ||||||||
\(229\) | −0.762291 | −0.0503736 | −0.0251868 | − | 0.999683i | \(-0.508018\pi\) | ||||
−0.0251868 | + | 0.999683i | \(0.508018\pi\) | |||||||
\(230\) | −1.70044 | −0.112124 | ||||||||
\(231\) | −13.2985 | −0.874978 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −0.137732 | −0.00902313 | −0.00451157 | − | 0.999990i | \(-0.501436\pi\) | ||||
−0.00451157 | + | 0.999990i | \(0.501436\pi\) | |||||||
\(234\) | −14.4682 | −0.945818 | ||||||||
\(235\) | 10.7937 | 0.704101 | ||||||||
\(236\) | 4.24130 | 0.276085 | ||||||||
\(237\) | 20.4028 | 1.32530 | ||||||||
\(238\) | −4.86574 | −0.315399 | ||||||||
\(239\) | −7.59313 | −0.491158 | −0.245579 | − | 0.969377i | \(-0.578978\pi\) | ||||
−0.245579 | + | 0.969377i | \(0.578978\pi\) | |||||||
\(240\) | 4.53367 | 0.292647 | ||||||||
\(241\) | 22.2852 | 1.43552 | 0.717758 | − | 0.696293i | \(-0.245168\pi\) | ||||
0.717758 | + | 0.696293i | \(0.245168\pi\) | |||||||
\(242\) | −23.0047 | −1.47880 | ||||||||
\(243\) | −20.7194 | −1.32915 | ||||||||
\(244\) | 14.2805 | 0.914217 | ||||||||
\(245\) | −10.6590 | −0.680978 | ||||||||
\(246\) | 16.5623 | 1.05597 | ||||||||
\(247\) | 12.5284 | 0.797166 | ||||||||
\(248\) | 3.83135 | 0.243291 | ||||||||
\(249\) | −41.0849 | −2.60365 | ||||||||
\(250\) | 12.0876 | 0.764486 | ||||||||
\(251\) | −18.2510 | −1.15199 | −0.575997 | − | 0.817452i | \(-0.695386\pi\) | ||||
−0.575997 | + | 0.817452i | \(0.695386\pi\) | |||||||
\(252\) | −3.51422 | −0.221375 | ||||||||
\(253\) | 5.83135 | 0.366614 | ||||||||
\(254\) | 1.91710 | 0.120290 | ||||||||
\(255\) | −25.7902 | −1.61504 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.607568 | 0.0378990 | 0.0189495 | − | 0.999820i | \(-0.493968\pi\) | ||||
0.0189495 | + | 0.999820i | \(0.493968\pi\) | |||||||
\(258\) | −13.1888 | −0.821097 | ||||||||
\(259\) | 8.48739 | 0.527381 | ||||||||
\(260\) | 5.98815 | 0.371369 | ||||||||
\(261\) | −4.10851 | −0.254310 | ||||||||
\(262\) | 0.359429 | 0.0222056 | ||||||||
\(263\) | −11.9175 | −0.734862 | −0.367431 | − | 0.930051i | \(-0.619763\pi\) | ||||
−0.367431 | + | 0.930051i | \(0.619763\pi\) | |||||||
\(264\) | −15.5474 | −0.956878 | ||||||||
\(265\) | 8.18895 | 0.503043 | ||||||||
\(266\) | 3.04306 | 0.186582 | ||||||||
\(267\) | −22.9779 | −1.40623 | ||||||||
\(268\) | 0.621238 | 0.0379481 | ||||||||
\(269\) | 2.13434 | 0.130133 | 0.0650665 | − | 0.997881i | \(-0.479274\pi\) | ||||
0.0650665 | + | 0.997881i | \(0.479274\pi\) | |||||||
\(270\) | −5.02561 | −0.305849 | ||||||||
\(271\) | −11.9244 | −0.724357 | −0.362178 | − | 0.932109i | \(-0.617967\pi\) | ||||
−0.362178 | + | 0.932109i | \(0.617967\pi\) | |||||||
\(272\) | −5.68859 | −0.344921 | ||||||||
\(273\) | −8.03091 | −0.486053 | ||||||||
\(274\) | −16.4666 | −0.994786 | ||||||||
\(275\) | −12.2954 | −0.741443 | ||||||||
\(276\) | 2.66618 | 0.160485 | ||||||||
\(277\) | −7.68861 | −0.461964 | −0.230982 | − | 0.972958i | \(-0.574194\pi\) | ||||
−0.230982 | + | 0.972958i | \(0.574194\pi\) | |||||||
\(278\) | −9.77421 | −0.586218 | ||||||||
\(279\) | −15.7411 | −0.942397 | ||||||||
\(280\) | 1.45447 | 0.0869214 | ||||||||
\(281\) | −16.8021 | −1.00233 | −0.501165 | − | 0.865351i | \(-0.667095\pi\) | ||||
−0.501165 | + | 0.865351i | \(0.667095\pi\) | |||||||
\(282\) | −16.9238 | −1.00780 | ||||||||
\(283\) | 16.8892 | 1.00396 | 0.501980 | − | 0.864879i | \(-0.332605\pi\) | ||||
0.501980 | + | 0.864879i | \(0.332605\pi\) | |||||||
\(284\) | −6.73323 | −0.399544 | ||||||||
\(285\) | 16.1293 | 0.955419 | ||||||||
\(286\) | −20.5353 | −1.21428 | ||||||||
\(287\) | 5.31344 | 0.313642 | ||||||||
\(288\) | −4.10851 | −0.242096 | ||||||||
\(289\) | 15.3600 | 0.903530 | ||||||||
\(290\) | 1.70044 | 0.0998532 | ||||||||
\(291\) | −44.6372 | −2.61668 | ||||||||
\(292\) | 3.71948 | 0.217666 | ||||||||
\(293\) | −0.421325 | −0.0246141 | −0.0123070 | − | 0.999924i | \(-0.503918\pi\) | ||||
−0.0123070 | + | 0.999924i | \(0.503918\pi\) | |||||||
\(294\) | 16.7126 | 0.974699 | ||||||||
\(295\) | 7.21208 | 0.419903 | ||||||||
\(296\) | 9.92270 | 0.576745 | ||||||||
\(297\) | 17.2344 | 1.00004 | ||||||||
\(298\) | 14.1687 | 0.820769 | ||||||||
\(299\) | 3.52153 | 0.203655 | ||||||||
\(300\) | −5.62165 | −0.324566 | ||||||||
\(301\) | −4.23116 | −0.243880 | ||||||||
\(302\) | −15.2844 | −0.879516 | ||||||||
\(303\) | 43.8148 | 2.51709 | ||||||||
\(304\) | 3.55767 | 0.204046 | ||||||||
\(305\) | 24.2832 | 1.39045 | ||||||||
\(306\) | 23.3716 | 1.33607 | ||||||||
\(307\) | 30.0457 | 1.71480 | 0.857400 | − | 0.514650i | \(-0.172078\pi\) | ||||
0.857400 | + | 0.514650i | \(0.172078\pi\) | |||||||
\(308\) | −4.98786 | −0.284209 | ||||||||
\(309\) | −25.4867 | −1.44989 | ||||||||
\(310\) | 6.51498 | 0.370026 | ||||||||
\(311\) | 4.44745 | 0.252192 | 0.126096 | − | 0.992018i | \(-0.459755\pi\) | ||||
0.126096 | + | 0.992018i | \(0.459755\pi\) | |||||||
\(312\) | −9.38903 | −0.531549 | ||||||||
\(313\) | −20.3620 | −1.15093 | −0.575463 | − | 0.817828i | \(-0.695178\pi\) | ||||
−0.575463 | + | 0.817828i | \(0.695178\pi\) | |||||||
\(314\) | 22.8829 | 1.29135 | ||||||||
\(315\) | −5.97571 | −0.336693 | ||||||||
\(316\) | 7.65244 | 0.430484 | ||||||||
\(317\) | 16.8713 | 0.947589 | 0.473794 | − | 0.880636i | \(-0.342884\pi\) | ||||
0.473794 | + | 0.880636i | \(0.342884\pi\) | |||||||
\(318\) | −12.8397 | −0.720017 | ||||||||
\(319\) | −5.83135 | −0.326493 | ||||||||
\(320\) | 1.70044 | 0.0950574 | ||||||||
\(321\) | −28.4653 | −1.58878 | ||||||||
\(322\) | 0.855351 | 0.0476669 | ||||||||
\(323\) | −20.2381 | −1.12608 | ||||||||
\(324\) | −4.44569 | −0.246983 | ||||||||
\(325\) | −7.42517 | −0.411874 | ||||||||
\(326\) | −0.931187 | −0.0515737 | ||||||||
\(327\) | 51.7579 | 2.86222 | ||||||||
\(328\) | 6.21200 | 0.343000 | ||||||||
\(329\) | −5.42941 | −0.299333 | ||||||||
\(330\) | −26.4375 | −1.45533 | ||||||||
\(331\) | 10.5710 | 0.581033 | 0.290516 | − | 0.956870i | \(-0.406173\pi\) | ||||
0.290516 | + | 0.956870i | \(0.406173\pi\) | |||||||
\(332\) | −15.4097 | −0.845716 | ||||||||
\(333\) | −40.7675 | −2.23404 | ||||||||
\(334\) | −7.28436 | −0.398583 | ||||||||
\(335\) | 1.05638 | 0.0577161 | ||||||||
\(336\) | −2.28052 | −0.124413 | ||||||||
\(337\) | −19.8437 | −1.08096 | −0.540478 | − | 0.841358i | \(-0.681756\pi\) | ||||
−0.540478 | + | 0.841358i | \(0.681756\pi\) | |||||||
\(338\) | 0.598830 | 0.0325721 | ||||||||
\(339\) | 4.89515 | 0.265868 | ||||||||
\(340\) | −9.67309 | −0.524597 | ||||||||
\(341\) | −22.3420 | −1.20989 | ||||||||
\(342\) | −14.6167 | −0.790382 | ||||||||
\(343\) | 11.3491 | 0.612795 | ||||||||
\(344\) | −4.94670 | −0.266708 | ||||||||
\(345\) | 4.53367 | 0.244085 | ||||||||
\(346\) | −19.9725 | −1.07373 | ||||||||
\(347\) | −18.6615 | −1.00180 | −0.500902 | − | 0.865504i | \(-0.666998\pi\) | ||||
−0.500902 | + | 0.865504i | \(0.666998\pi\) | |||||||
\(348\) | −2.66618 | −0.142922 | ||||||||
\(349\) | −24.8689 | −1.33120 | −0.665601 | − | 0.746307i | \(-0.731825\pi\) | ||||
−0.665601 | + | 0.746307i | \(0.731825\pi\) | |||||||
\(350\) | −1.80351 | −0.0964019 | ||||||||
\(351\) | 10.4078 | 0.555527 | ||||||||
\(352\) | −5.83135 | −0.310812 | ||||||||
\(353\) | −36.7896 | −1.95811 | −0.979056 | − | 0.203593i | \(-0.934738\pi\) | ||||
−0.979056 | + | 0.203593i | \(0.934738\pi\) | |||||||
\(354\) | −11.3081 | −0.601017 | ||||||||
\(355\) | −11.4495 | −0.607674 | ||||||||
\(356\) | −8.61831 | −0.456769 | ||||||||
\(357\) | 12.9729 | 0.686600 | ||||||||
\(358\) | 16.7730 | 0.886482 | ||||||||
\(359\) | −21.0450 | −1.11071 | −0.555357 | − | 0.831612i | \(-0.687418\pi\) | ||||
−0.555357 | + | 0.831612i | \(0.687418\pi\) | |||||||
\(360\) | −6.98627 | −0.368209 | ||||||||
\(361\) | −6.34297 | −0.333841 | ||||||||
\(362\) | 4.47713 | 0.235313 | ||||||||
\(363\) | 61.3346 | 3.21923 | ||||||||
\(364\) | −3.01214 | −0.157879 | ||||||||
\(365\) | 6.32475 | 0.331053 | ||||||||
\(366\) | −38.0744 | −1.99018 | ||||||||
\(367\) | 9.65552 | 0.504014 | 0.252007 | − | 0.967725i | \(-0.418909\pi\) | ||||
0.252007 | + | 0.967725i | \(0.418909\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −25.5220 | −1.32862 | ||||||||
\(370\) | 16.8729 | 0.877183 | ||||||||
\(371\) | −4.11919 | −0.213857 | ||||||||
\(372\) | −10.2151 | −0.529627 | ||||||||
\(373\) | −3.19789 | −0.165581 | −0.0827903 | − | 0.996567i | \(-0.526383\pi\) | ||||
−0.0827903 | + | 0.996567i | \(0.526383\pi\) | |||||||
\(374\) | 33.1722 | 1.71529 | ||||||||
\(375\) | −32.2277 | −1.66423 | ||||||||
\(376\) | −6.34758 | −0.327351 | ||||||||
\(377\) | −3.52153 | −0.181368 | ||||||||
\(378\) | 2.52797 | 0.130025 | ||||||||
\(379\) | 20.3440 | 1.04500 | 0.522501 | − | 0.852639i | \(-0.324999\pi\) | ||||
0.522501 | + | 0.852639i | \(0.324999\pi\) | |||||||
\(380\) | 6.04960 | 0.310338 | ||||||||
\(381\) | −5.11133 | −0.261861 | ||||||||
\(382\) | 21.7201 | 1.11130 | ||||||||
\(383\) | −15.0076 | −0.766853 | −0.383426 | − | 0.923571i | \(-0.625256\pi\) | ||||
−0.383426 | + | 0.923571i | \(0.625256\pi\) | |||||||
\(384\) | −2.66618 | −0.136058 | ||||||||
\(385\) | −8.48154 | −0.432260 | ||||||||
\(386\) | −10.3549 | −0.527050 | ||||||||
\(387\) | 20.3235 | 1.03310 | ||||||||
\(388\) | −16.7420 | −0.849948 | ||||||||
\(389\) | −14.8574 | −0.753302 | −0.376651 | − | 0.926355i | \(-0.622924\pi\) | ||||
−0.376651 | + | 0.926355i | \(0.622924\pi\) | |||||||
\(390\) | −15.9655 | −0.808443 | ||||||||
\(391\) | −5.68859 | −0.287684 | ||||||||
\(392\) | 6.26837 | 0.316601 | ||||||||
\(393\) | −0.958301 | −0.0483399 | ||||||||
\(394\) | 8.55113 | 0.430800 | ||||||||
\(395\) | 13.0125 | 0.654731 | ||||||||
\(396\) | 23.9582 | 1.20394 | ||||||||
\(397\) | 5.85052 | 0.293629 | 0.146815 | − | 0.989164i | \(-0.453098\pi\) | ||||
0.146815 | + | 0.989164i | \(0.453098\pi\) | |||||||
\(398\) | −11.1801 | −0.560408 | ||||||||
\(399\) | −8.11334 | −0.406175 | ||||||||
\(400\) | −2.10851 | −0.105425 | ||||||||
\(401\) | 5.32050 | 0.265693 | 0.132847 | − | 0.991137i | \(-0.457588\pi\) | ||||
0.132847 | + | 0.991137i | \(0.457588\pi\) | |||||||
\(402\) | −1.65633 | −0.0826103 | ||||||||
\(403\) | −13.4922 | −0.672096 | ||||||||
\(404\) | 16.4335 | 0.817600 | ||||||||
\(405\) | −7.55963 | −0.375641 | ||||||||
\(406\) | −0.855351 | −0.0424504 | ||||||||
\(407\) | −57.8628 | −2.86815 | ||||||||
\(408\) | 15.1668 | 0.750868 | ||||||||
\(409\) | −2.27676 | −0.112578 | −0.0562892 | − | 0.998415i | \(-0.517927\pi\) | ||||
−0.0562892 | + | 0.998415i | \(0.517927\pi\) | |||||||
\(410\) | 10.5631 | 0.521675 | ||||||||
\(411\) | 43.9030 | 2.16557 | ||||||||
\(412\) | −9.55928 | −0.470952 | ||||||||
\(413\) | −3.62780 | −0.178513 | ||||||||
\(414\) | −4.10851 | −0.201922 | ||||||||
\(415\) | −26.2032 | −1.28627 | ||||||||
\(416\) | −3.52153 | −0.172657 | ||||||||
\(417\) | 26.0598 | 1.27615 | ||||||||
\(418\) | −20.7460 | −1.01472 | ||||||||
\(419\) | 32.6799 | 1.59652 | 0.798258 | − | 0.602315i | \(-0.205755\pi\) | ||||
0.798258 | + | 0.602315i | \(0.205755\pi\) | |||||||
\(420\) | −3.87788 | −0.189221 | ||||||||
\(421\) | 22.6645 | 1.10460 | 0.552299 | − | 0.833646i | \(-0.313751\pi\) | ||||
0.552299 | + | 0.833646i | \(0.313751\pi\) | |||||||
\(422\) | 4.68294 | 0.227962 | ||||||||
\(423\) | 26.0791 | 1.26801 | ||||||||
\(424\) | −4.81578 | −0.233875 | ||||||||
\(425\) | 11.9944 | 0.581815 | ||||||||
\(426\) | 17.9520 | 0.869777 | ||||||||
\(427\) | −12.2149 | −0.591118 | ||||||||
\(428\) | −10.6764 | −0.516065 | ||||||||
\(429\) | 54.7507 | 2.64339 | ||||||||
\(430\) | −8.41156 | −0.405641 | ||||||||
\(431\) | −8.70338 | −0.419227 | −0.209614 | − | 0.977784i | \(-0.567221\pi\) | ||||
−0.209614 | + | 0.977784i | \(0.567221\pi\) | |||||||
\(432\) | 2.95548 | 0.142195 | ||||||||
\(433\) | 38.4043 | 1.84559 | 0.922796 | − | 0.385290i | \(-0.125899\pi\) | ||||
0.922796 | + | 0.385290i | \(0.125899\pi\) | |||||||
\(434\) | −3.27715 | −0.157308 | ||||||||
\(435\) | −4.53367 | −0.217373 | ||||||||
\(436\) | 19.4128 | 0.929702 | ||||||||
\(437\) | 3.55767 | 0.170187 | ||||||||
\(438\) | −9.91680 | −0.473843 | ||||||||
\(439\) | 4.34450 | 0.207352 | 0.103676 | − | 0.994611i | \(-0.466940\pi\) | ||||
0.103676 | + | 0.994611i | \(0.466940\pi\) | |||||||
\(440\) | −9.91586 | −0.472720 | ||||||||
\(441\) | −25.7537 | −1.22636 | ||||||||
\(442\) | 20.0325 | 0.952850 | ||||||||
\(443\) | −36.8543 | −1.75100 | −0.875501 | − | 0.483216i | \(-0.839468\pi\) | ||||
−0.875501 | + | 0.483216i | \(0.839468\pi\) | |||||||
\(444\) | −26.4557 | −1.25553 | ||||||||
\(445\) | −14.6549 | −0.694709 | ||||||||
\(446\) | −15.8006 | −0.748179 | ||||||||
\(447\) | −37.7762 | −1.78675 | ||||||||
\(448\) | −0.855351 | −0.0404115 | ||||||||
\(449\) | 22.7892 | 1.07549 | 0.537745 | − | 0.843108i | \(-0.319276\pi\) | ||||
0.537745 | + | 0.843108i | \(0.319276\pi\) | |||||||
\(450\) | 8.66281 | 0.408369 | ||||||||
\(451\) | −36.2243 | −1.70574 | ||||||||
\(452\) | 1.83602 | 0.0863590 | ||||||||
\(453\) | 40.7508 | 1.91464 | ||||||||
\(454\) | 25.1513 | 1.18041 | ||||||||
\(455\) | −5.12197 | −0.240122 | ||||||||
\(456\) | −9.48539 | −0.444194 | ||||||||
\(457\) | 12.5719 | 0.588089 | 0.294044 | − | 0.955792i | \(-0.404999\pi\) | ||||
0.294044 | + | 0.955792i | \(0.404999\pi\) | |||||||
\(458\) | 0.762291 | 0.0356195 | ||||||||
\(459\) | −16.8125 | −0.784739 | ||||||||
\(460\) | 1.70044 | 0.0792834 | ||||||||
\(461\) | −13.4971 | −0.628624 | −0.314312 | − | 0.949320i | \(-0.601774\pi\) | ||||
−0.314312 | + | 0.949320i | \(0.601774\pi\) | |||||||
\(462\) | 13.2985 | 0.618703 | ||||||||
\(463\) | 19.1228 | 0.888711 | 0.444355 | − | 0.895851i | \(-0.353433\pi\) | ||||
0.444355 | + | 0.895851i | \(0.353433\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −17.3701 | −0.805519 | ||||||||
\(466\) | 0.137732 | 0.00638032 | ||||||||
\(467\) | −0.400694 | −0.0185419 | −0.00927094 | − | 0.999957i | \(-0.502951\pi\) | ||||
−0.00927094 | + | 0.999957i | \(0.502951\pi\) | |||||||
\(468\) | 14.4682 | 0.668794 | ||||||||
\(469\) | −0.531377 | −0.0245367 | ||||||||
\(470\) | −10.7937 | −0.497875 | ||||||||
\(471\) | −61.0098 | −2.81118 | ||||||||
\(472\) | −4.24130 | −0.195222 | ||||||||
\(473\) | 28.8459 | 1.32634 | ||||||||
\(474\) | −20.4028 | −0.937131 | ||||||||
\(475\) | −7.50137 | −0.344187 | ||||||||
\(476\) | 4.86574 | 0.223021 | ||||||||
\(477\) | 19.7857 | 0.905924 | ||||||||
\(478\) | 7.59313 | 0.347301 | ||||||||
\(479\) | 2.95436 | 0.134988 | 0.0674941 | − | 0.997720i | \(-0.478500\pi\) | ||||
0.0674941 | + | 0.997720i | \(0.478500\pi\) | |||||||
\(480\) | −4.53367 | −0.206933 | ||||||||
\(481\) | −34.9431 | −1.59327 | ||||||||
\(482\) | −22.2852 | −1.01506 | ||||||||
\(483\) | −2.28052 | −0.103767 | ||||||||
\(484\) | 23.0047 | 1.04567 | ||||||||
\(485\) | −28.4688 | −1.29270 | ||||||||
\(486\) | 20.7194 | 0.939853 | ||||||||
\(487\) | 39.8315 | 1.80494 | 0.902469 | − | 0.430755i | \(-0.141753\pi\) | ||||
0.902469 | + | 0.430755i | \(0.141753\pi\) | |||||||
\(488\) | −14.2805 | −0.646449 | ||||||||
\(489\) | 2.48271 | 0.112272 | ||||||||
\(490\) | 10.6590 | 0.481524 | ||||||||
\(491\) | −12.5185 | −0.564953 | −0.282476 | − | 0.959274i | \(-0.591156\pi\) | ||||
−0.282476 | + | 0.959274i | \(0.591156\pi\) | |||||||
\(492\) | −16.5623 | −0.746686 | ||||||||
\(493\) | 5.68859 | 0.256201 | ||||||||
\(494\) | −12.5284 | −0.563681 | ||||||||
\(495\) | 40.7394 | 1.83110 | ||||||||
\(496\) | −3.83135 | −0.172033 | ||||||||
\(497\) | 5.75928 | 0.258339 | ||||||||
\(498\) | 41.0849 | 1.84106 | ||||||||
\(499\) | −28.3237 | −1.26794 | −0.633971 | − | 0.773357i | \(-0.718576\pi\) | ||||
−0.633971 | + | 0.773357i | \(0.718576\pi\) | |||||||
\(500\) | −12.0876 | −0.540573 | ||||||||
\(501\) | 19.4214 | 0.867684 | ||||||||
\(502\) | 18.2510 | 0.814582 | ||||||||
\(503\) | −14.1559 | −0.631180 | −0.315590 | − | 0.948896i | \(-0.602202\pi\) | ||||
−0.315590 | + | 0.948896i | \(0.602202\pi\) | |||||||
\(504\) | 3.51422 | 0.156536 | ||||||||
\(505\) | 27.9443 | 1.24350 | ||||||||
\(506\) | −5.83135 | −0.259235 | ||||||||
\(507\) | −1.59659 | −0.0709070 | ||||||||
\(508\) | −1.91710 | −0.0850576 | ||||||||
\(509\) | 40.3757 | 1.78962 | 0.894810 | − | 0.446447i | \(-0.147311\pi\) | ||||
0.894810 | + | 0.446447i | \(0.147311\pi\) | |||||||
\(510\) | 25.7902 | 1.14201 | ||||||||
\(511\) | −3.18146 | −0.140740 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 10.5146 | 0.464231 | ||||||||
\(514\) | −0.607568 | −0.0267987 | ||||||||
\(515\) | −16.2550 | −0.716280 | ||||||||
\(516\) | 13.1888 | 0.580603 | ||||||||
\(517\) | 37.0150 | 1.62792 | ||||||||
\(518\) | −8.48739 | −0.372915 | ||||||||
\(519\) | 53.2503 | 2.33743 | ||||||||
\(520\) | −5.98815 | −0.262598 | ||||||||
\(521\) | 0.967224 | 0.0423748 | 0.0211874 | − | 0.999776i | \(-0.493255\pi\) | ||||
0.0211874 | + | 0.999776i | \(0.493255\pi\) | |||||||
\(522\) | 4.10851 | 0.179824 | ||||||||
\(523\) | −6.38476 | −0.279186 | −0.139593 | − | 0.990209i | \(-0.544579\pi\) | ||||
−0.139593 | + | 0.990209i | \(0.544579\pi\) | |||||||
\(524\) | −0.359429 | −0.0157017 | ||||||||
\(525\) | 4.80849 | 0.209860 | ||||||||
\(526\) | 11.9175 | 0.519626 | ||||||||
\(527\) | 21.7950 | 0.949404 | ||||||||
\(528\) | 15.5474 | 0.676615 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −8.18895 | −0.355705 | ||||||||
\(531\) | 17.4254 | 0.756199 | ||||||||
\(532\) | −3.04306 | −0.131933 | ||||||||
\(533\) | −21.8757 | −0.947543 | ||||||||
\(534\) | 22.9779 | 0.994353 | ||||||||
\(535\) | −18.1546 | −0.784894 | ||||||||
\(536\) | −0.621238 | −0.0268334 | ||||||||
\(537\) | −44.7199 | −1.92981 | ||||||||
\(538\) | −2.13434 | −0.0920179 | ||||||||
\(539\) | −36.5531 | −1.57445 | ||||||||
\(540\) | 5.02561 | 0.216268 | ||||||||
\(541\) | 12.3003 | 0.528830 | 0.264415 | − | 0.964409i | \(-0.414821\pi\) | ||||
0.264415 | + | 0.964409i | \(0.414821\pi\) | |||||||
\(542\) | 11.9244 | 0.512197 | ||||||||
\(543\) | −11.9368 | −0.512258 | ||||||||
\(544\) | 5.68859 | 0.243896 | ||||||||
\(545\) | 33.0102 | 1.41400 | ||||||||
\(546\) | 8.03091 | 0.343691 | ||||||||
\(547\) | −19.9534 | −0.853145 | −0.426573 | − | 0.904453i | \(-0.640279\pi\) | ||||
−0.426573 | + | 0.904453i | \(0.640279\pi\) | |||||||
\(548\) | 16.4666 | 0.703420 | ||||||||
\(549\) | 58.6716 | 2.50404 | ||||||||
\(550\) | 12.2954 | 0.524280 | ||||||||
\(551\) | −3.55767 | −0.151562 | ||||||||
\(552\) | −2.66618 | −0.113480 | ||||||||
\(553\) | −6.54553 | −0.278344 | ||||||||
\(554\) | 7.68861 | 0.326658 | ||||||||
\(555\) | −44.9863 | −1.90956 | ||||||||
\(556\) | 9.77421 | 0.414519 | ||||||||
\(557\) | 4.95719 | 0.210043 | 0.105021 | − | 0.994470i | \(-0.466509\pi\) | ||||
0.105021 | + | 0.994470i | \(0.466509\pi\) | |||||||
\(558\) | 15.7411 | 0.666376 | ||||||||
\(559\) | 17.4199 | 0.736785 | ||||||||
\(560\) | −1.45447 | −0.0614627 | ||||||||
\(561\) | −88.4429 | −3.73406 | ||||||||
\(562\) | 16.8021 | 0.708755 | ||||||||
\(563\) | −20.8402 | −0.878310 | −0.439155 | − | 0.898411i | \(-0.644722\pi\) | ||||
−0.439155 | + | 0.898411i | \(0.644722\pi\) | |||||||
\(564\) | 16.9238 | 0.712619 | ||||||||
\(565\) | 3.12204 | 0.131345 | ||||||||
\(566\) | −16.8892 | −0.709907 | ||||||||
\(567\) | 3.80263 | 0.159695 | ||||||||
\(568\) | 6.73323 | 0.282520 | ||||||||
\(569\) | 35.6966 | 1.49648 | 0.748240 | − | 0.663428i | \(-0.230899\pi\) | ||||
0.748240 | + | 0.663428i | \(0.230899\pi\) | |||||||
\(570\) | −16.1293 | −0.675583 | ||||||||
\(571\) | −27.2489 | −1.14033 | −0.570166 | − | 0.821529i | \(-0.693121\pi\) | ||||
−0.570166 | + | 0.821529i | \(0.693121\pi\) | |||||||
\(572\) | 20.5353 | 0.858623 | ||||||||
\(573\) | −57.9096 | −2.41921 | ||||||||
\(574\) | −5.31344 | −0.221779 | ||||||||
\(575\) | −2.10851 | −0.0879308 | ||||||||
\(576\) | 4.10851 | 0.171188 | ||||||||
\(577\) | −5.69519 | −0.237094 | −0.118547 | − | 0.992948i | \(-0.537824\pi\) | ||||
−0.118547 | + | 0.992948i | \(0.537824\pi\) | |||||||
\(578\) | −15.3600 | −0.638892 | ||||||||
\(579\) | 27.6080 | 1.14735 | ||||||||
\(580\) | −1.70044 | −0.0706069 | ||||||||
\(581\) | 13.1807 | 0.546827 | ||||||||
\(582\) | 44.6372 | 1.85027 | ||||||||
\(583\) | 28.0825 | 1.16306 | ||||||||
\(584\) | −3.71948 | −0.153913 | ||||||||
\(585\) | 24.6023 | 1.01718 | ||||||||
\(586\) | 0.421325 | 0.0174048 | ||||||||
\(587\) | 13.9718 | 0.576679 | 0.288340 | − | 0.957528i | \(-0.406897\pi\) | ||||
0.288340 | + | 0.957528i | \(0.406897\pi\) | |||||||
\(588\) | −16.7126 | −0.689216 | ||||||||
\(589\) | −13.6307 | −0.561643 | ||||||||
\(590\) | −7.21208 | −0.296916 | ||||||||
\(591\) | −22.7988 | −0.937818 | ||||||||
\(592\) | −9.92270 | −0.407820 | ||||||||
\(593\) | 5.84013 | 0.239825 | 0.119913 | − | 0.992784i | \(-0.461739\pi\) | ||||
0.119913 | + | 0.992784i | \(0.461739\pi\) | |||||||
\(594\) | −17.2344 | −0.707137 | ||||||||
\(595\) | 8.27389 | 0.339197 | ||||||||
\(596\) | −14.1687 | −0.580371 | ||||||||
\(597\) | 29.8081 | 1.21997 | ||||||||
\(598\) | −3.52153 | −0.144006 | ||||||||
\(599\) | 23.3189 | 0.952786 | 0.476393 | − | 0.879233i | \(-0.341944\pi\) | ||||
0.476393 | + | 0.879233i | \(0.341944\pi\) | |||||||
\(600\) | 5.62165 | 0.229503 | ||||||||
\(601\) | 37.7353 | 1.53925 | 0.769627 | − | 0.638494i | \(-0.220442\pi\) | ||||
0.769627 | + | 0.638494i | \(0.220442\pi\) | |||||||
\(602\) | 4.23116 | 0.172449 | ||||||||
\(603\) | 2.55236 | 0.103940 | ||||||||
\(604\) | 15.2844 | 0.621912 | ||||||||
\(605\) | 39.1181 | 1.59038 | ||||||||
\(606\) | −43.8148 | −1.77985 | ||||||||
\(607\) | −35.2763 | −1.43182 | −0.715911 | − | 0.698192i | \(-0.753988\pi\) | ||||
−0.715911 | + | 0.698192i | \(0.753988\pi\) | |||||||
\(608\) | −3.55767 | −0.144283 | ||||||||
\(609\) | 2.28052 | 0.0924113 | ||||||||
\(610\) | −24.2832 | −0.983196 | ||||||||
\(611\) | 22.3532 | 0.904313 | ||||||||
\(612\) | −23.3716 | −0.944741 | ||||||||
\(613\) | −34.1983 | −1.38126 | −0.690629 | − | 0.723210i | \(-0.742666\pi\) | ||||
−0.690629 | + | 0.723210i | \(0.742666\pi\) | |||||||
\(614\) | −30.0457 | −1.21255 | ||||||||
\(615\) | −28.1632 | −1.13565 | ||||||||
\(616\) | 4.98786 | 0.200966 | ||||||||
\(617\) | −7.38230 | −0.297200 | −0.148600 | − | 0.988897i | \(-0.547477\pi\) | ||||
−0.148600 | + | 0.988897i | \(0.547477\pi\) | |||||||
\(618\) | 25.4867 | 1.02523 | ||||||||
\(619\) | −45.2476 | −1.81865 | −0.909326 | − | 0.416084i | \(-0.863402\pi\) | ||||
−0.909326 | + | 0.416084i | \(0.863402\pi\) | |||||||
\(620\) | −6.51498 | −0.261648 | ||||||||
\(621\) | 2.95548 | 0.118599 | ||||||||
\(622\) | −4.44745 | −0.178327 | ||||||||
\(623\) | 7.37168 | 0.295340 | ||||||||
\(624\) | 9.38903 | 0.375862 | ||||||||
\(625\) | −10.0117 | −0.400467 | ||||||||
\(626\) | 20.3620 | 0.813827 | ||||||||
\(627\) | 55.3126 | 2.20897 | ||||||||
\(628\) | −22.8829 | −0.913125 | ||||||||
\(629\) | 56.4461 | 2.25065 | ||||||||
\(630\) | 5.97571 | 0.238078 | ||||||||
\(631\) | 5.27078 | 0.209826 | 0.104913 | − | 0.994481i | \(-0.466544\pi\) | ||||
0.104913 | + | 0.994481i | \(0.466544\pi\) | |||||||
\(632\) | −7.65244 | −0.304398 | ||||||||
\(633\) | −12.4856 | −0.496256 | ||||||||
\(634\) | −16.8713 | −0.670046 | ||||||||
\(635\) | −3.25991 | −0.129366 | ||||||||
\(636\) | 12.8397 | 0.509129 | ||||||||
\(637\) | −22.0743 | −0.874614 | ||||||||
\(638\) | 5.83135 | 0.230865 | ||||||||
\(639\) | −27.6635 | −1.09435 | ||||||||
\(640\) | −1.70044 | −0.0672158 | ||||||||
\(641\) | 24.3500 | 0.961768 | 0.480884 | − | 0.876784i | \(-0.340316\pi\) | ||||
0.480884 | + | 0.876784i | \(0.340316\pi\) | |||||||
\(642\) | 28.4653 | 1.12344 | ||||||||
\(643\) | −21.6256 | −0.852832 | −0.426416 | − | 0.904527i | \(-0.640224\pi\) | ||||
−0.426416 | + | 0.904527i | \(0.640224\pi\) | |||||||
\(644\) | −0.855351 | −0.0337056 | ||||||||
\(645\) | 22.4267 | 0.883051 | ||||||||
\(646\) | 20.2381 | 0.796258 | ||||||||
\(647\) | −26.1922 | −1.02972 | −0.514862 | − | 0.857273i | \(-0.672157\pi\) | ||||
−0.514862 | + | 0.857273i | \(0.672157\pi\) | |||||||
\(648\) | 4.44569 | 0.174643 | ||||||||
\(649\) | 24.7325 | 0.970837 | ||||||||
\(650\) | 7.42517 | 0.291239 | ||||||||
\(651\) | 8.73747 | 0.342449 | ||||||||
\(652\) | 0.931187 | 0.0364681 | ||||||||
\(653\) | 21.3985 | 0.837389 | 0.418695 | − | 0.908127i | \(-0.362488\pi\) | ||||
0.418695 | + | 0.908127i | \(0.362488\pi\) | |||||||
\(654\) | −51.7579 | −2.02389 | ||||||||
\(655\) | −0.611187 | −0.0238810 | ||||||||
\(656\) | −6.21200 | −0.242538 | ||||||||
\(657\) | 15.2815 | 0.596189 | ||||||||
\(658\) | 5.42941 | 0.211660 | ||||||||
\(659\) | −32.0676 | −1.24918 | −0.624588 | − | 0.780955i | \(-0.714733\pi\) | ||||
−0.624588 | + | 0.780955i | \(0.714733\pi\) | |||||||
\(660\) | 26.4375 | 1.02908 | ||||||||
\(661\) | 11.8565 | 0.461166 | 0.230583 | − | 0.973053i | \(-0.425937\pi\) | ||||
0.230583 | + | 0.973053i | \(0.425937\pi\) | |||||||
\(662\) | −10.5710 | −0.410852 | ||||||||
\(663\) | −53.4103 | −2.07428 | ||||||||
\(664\) | 15.4097 | 0.598011 | ||||||||
\(665\) | −5.17454 | −0.200660 | ||||||||
\(666\) | 40.7675 | 1.57971 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 7.28436 | 0.281840 | ||||||||
\(669\) | 42.1272 | 1.62873 | ||||||||
\(670\) | −1.05638 | −0.0408114 | ||||||||
\(671\) | 83.2748 | 3.21479 | ||||||||
\(672\) | 2.28052 | 0.0879729 | ||||||||
\(673\) | −0.182214 | −0.00702384 | −0.00351192 | − | 0.999994i | \(-0.501118\pi\) | ||||
−0.00351192 | + | 0.999994i | \(0.501118\pi\) | |||||||
\(674\) | 19.8437 | 0.764351 | ||||||||
\(675\) | −6.23164 | −0.239856 | ||||||||
\(676\) | −0.598830 | −0.0230319 | ||||||||
\(677\) | 30.5773 | 1.17518 | 0.587590 | − | 0.809159i | \(-0.300077\pi\) | ||||
0.587590 | + | 0.809159i | \(0.300077\pi\) | |||||||
\(678\) | −4.89515 | −0.187997 | ||||||||
\(679\) | 14.3203 | 0.549563 | ||||||||
\(680\) | 9.67309 | 0.370946 | ||||||||
\(681\) | −67.0578 | −2.56966 | ||||||||
\(682\) | 22.3420 | 0.855519 | ||||||||
\(683\) | −3.92478 | −0.150178 | −0.0750889 | − | 0.997177i | \(-0.523924\pi\) | ||||
−0.0750889 | + | 0.997177i | \(0.523924\pi\) | |||||||
\(684\) | 14.6167 | 0.558884 | ||||||||
\(685\) | 28.0005 | 1.06984 | ||||||||
\(686\) | −11.3491 | −0.433311 | ||||||||
\(687\) | −2.03240 | −0.0775410 | ||||||||
\(688\) | 4.94670 | 0.188591 | ||||||||
\(689\) | 16.9589 | 0.646083 | ||||||||
\(690\) | −4.53367 | −0.172594 | ||||||||
\(691\) | 21.0485 | 0.800724 | 0.400362 | − | 0.916357i | \(-0.368884\pi\) | ||||
0.400362 | + | 0.916357i | \(0.368884\pi\) | |||||||
\(692\) | 19.9725 | 0.759242 | ||||||||
\(693\) | −20.4926 | −0.778451 | ||||||||
\(694\) | 18.6615 | 0.708382 | ||||||||
\(695\) | 16.6204 | 0.630450 | ||||||||
\(696\) | 2.66618 | 0.101061 | ||||||||
\(697\) | 35.3375 | 1.33850 | ||||||||
\(698\) | 24.8689 | 0.941303 | ||||||||
\(699\) | −0.367218 | −0.0138895 | ||||||||
\(700\) | 1.80351 | 0.0681664 | ||||||||
\(701\) | −6.32855 | −0.239026 | −0.119513 | − | 0.992833i | \(-0.538133\pi\) | ||||
−0.119513 | + | 0.992833i | \(0.538133\pi\) | |||||||
\(702\) | −10.4078 | −0.392817 | ||||||||
\(703\) | −35.3017 | −1.33143 | ||||||||
\(704\) | 5.83135 | 0.219777 | ||||||||
\(705\) | 28.7778 | 1.08384 | ||||||||
\(706\) | 36.7896 | 1.38459 | ||||||||
\(707\) | −14.0565 | −0.528647 | ||||||||
\(708\) | 11.3081 | 0.424983 | ||||||||
\(709\) | −17.8754 | −0.671323 | −0.335662 | − | 0.941983i | \(-0.608960\pi\) | ||||
−0.335662 | + | 0.941983i | \(0.608960\pi\) | |||||||
\(710\) | 11.4495 | 0.429690 | ||||||||
\(711\) | 31.4401 | 1.17910 | ||||||||
\(712\) | 8.61831 | 0.322985 | ||||||||
\(713\) | −3.83135 | −0.143485 | ||||||||
\(714\) | −12.9729 | −0.485500 | ||||||||
\(715\) | 34.9190 | 1.30590 | ||||||||
\(716\) | −16.7730 | −0.626838 | ||||||||
\(717\) | −20.2446 | −0.756049 | ||||||||
\(718\) | 21.0450 | 0.785393 | ||||||||
\(719\) | 29.6529 | 1.10587 | 0.552934 | − | 0.833225i | \(-0.313508\pi\) | ||||
0.552934 | + | 0.833225i | \(0.313508\pi\) | |||||||
\(720\) | 6.98627 | 0.260363 | ||||||||
\(721\) | 8.17654 | 0.304510 | ||||||||
\(722\) | 6.34297 | 0.236061 | ||||||||
\(723\) | 59.4163 | 2.20972 | ||||||||
\(724\) | −4.47713 | −0.166391 | ||||||||
\(725\) | 2.10851 | 0.0783080 | ||||||||
\(726\) | −61.3346 | −2.27634 | ||||||||
\(727\) | 10.7183 | 0.397519 | 0.198759 | − | 0.980048i | \(-0.436309\pi\) | ||||
0.198759 | + | 0.980048i | \(0.436309\pi\) | |||||||
\(728\) | 3.01214 | 0.111638 | ||||||||
\(729\) | −41.9046 | −1.55202 | ||||||||
\(730\) | −6.32475 | −0.234090 | ||||||||
\(731\) | −28.1397 | −1.04078 | ||||||||
\(732\) | 38.0744 | 1.40727 | ||||||||
\(733\) | 15.0377 | 0.555430 | 0.277715 | − | 0.960663i | \(-0.410423\pi\) | ||||
0.277715 | + | 0.960663i | \(0.410423\pi\) | |||||||
\(734\) | −9.65552 | −0.356392 | ||||||||
\(735\) | −28.4188 | −1.04824 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 3.62266 | 0.133442 | ||||||||
\(738\) | 25.5220 | 0.939479 | ||||||||
\(739\) | −12.6539 | −0.465480 | −0.232740 | − | 0.972539i | \(-0.574769\pi\) | ||||
−0.232740 | + | 0.972539i | \(0.574769\pi\) | |||||||
\(740\) | −16.8729 | −0.620262 | ||||||||
\(741\) | 33.4031 | 1.22709 | ||||||||
\(742\) | 4.11919 | 0.151220 | ||||||||
\(743\) | −13.6380 | −0.500328 | −0.250164 | − | 0.968203i | \(-0.580485\pi\) | ||||
−0.250164 | + | 0.968203i | \(0.580485\pi\) | |||||||
\(744\) | 10.2151 | 0.374503 | ||||||||
\(745\) | −24.0930 | −0.882698 | ||||||||
\(746\) | 3.19789 | 0.117083 | ||||||||
\(747\) | −63.3108 | −2.31642 | ||||||||
\(748\) | −33.1722 | −1.21289 | ||||||||
\(749\) | 9.13211 | 0.333680 | ||||||||
\(750\) | 32.2277 | 1.17679 | ||||||||
\(751\) | 28.7725 | 1.04992 | 0.524961 | − | 0.851126i | \(-0.324080\pi\) | ||||
0.524961 | + | 0.851126i | \(0.324080\pi\) | |||||||
\(752\) | 6.34758 | 0.231472 | ||||||||
\(753\) | −48.6604 | −1.77328 | ||||||||
\(754\) | 3.52153 | 0.128247 | ||||||||
\(755\) | 25.9901 | 0.945878 | ||||||||
\(756\) | −2.52797 | −0.0919414 | ||||||||
\(757\) | 44.9191 | 1.63261 | 0.816307 | − | 0.577618i | \(-0.196018\pi\) | ||||
0.816307 | + | 0.577618i | \(0.196018\pi\) | |||||||
\(758\) | −20.3440 | −0.738928 | ||||||||
\(759\) | 15.5474 | 0.564336 | ||||||||
\(760\) | −6.04960 | −0.219442 | ||||||||
\(761\) | 2.74546 | 0.0995228 | 0.0497614 | − | 0.998761i | \(-0.484154\pi\) | ||||
0.0497614 | + | 0.998761i | \(0.484154\pi\) | |||||||
\(762\) | 5.11133 | 0.185164 | ||||||||
\(763\) | −16.6047 | −0.601131 | ||||||||
\(764\) | −21.7201 | −0.785805 | ||||||||
\(765\) | −39.7420 | −1.43687 | ||||||||
\(766\) | 15.0076 | 0.542247 | ||||||||
\(767\) | 14.9359 | 0.539303 | ||||||||
\(768\) | 2.66618 | 0.0962074 | ||||||||
\(769\) | 31.1169 | 1.12210 | 0.561051 | − | 0.827781i | \(-0.310397\pi\) | ||||
0.561051 | + | 0.827781i | \(0.310397\pi\) | |||||||
\(770\) | 8.48154 | 0.305654 | ||||||||
\(771\) | 1.61988 | 0.0583387 | ||||||||
\(772\) | 10.3549 | 0.372681 | ||||||||
\(773\) | 51.5614 | 1.85453 | 0.927267 | − | 0.374400i | \(-0.122151\pi\) | ||||
0.927267 | + | 0.374400i | \(0.122151\pi\) | |||||||
\(774\) | −20.3235 | −0.730514 | ||||||||
\(775\) | 8.07843 | 0.290186 | ||||||||
\(776\) | 16.7420 | 0.601004 | ||||||||
\(777\) | 22.6289 | 0.811807 | ||||||||
\(778\) | 14.8574 | 0.532665 | ||||||||
\(779\) | −22.1002 | −0.791823 | ||||||||
\(780\) | 15.9655 | 0.571655 | ||||||||
\(781\) | −39.2639 | −1.40497 | ||||||||
\(782\) | 5.68859 | 0.203423 | ||||||||
\(783\) | −2.95548 | −0.105620 | ||||||||
\(784\) | −6.26837 | −0.223871 | ||||||||
\(785\) | −38.9109 | −1.38879 | ||||||||
\(786\) | 0.958301 | 0.0341815 | ||||||||
\(787\) | −36.3326 | −1.29512 | −0.647558 | − | 0.762016i | \(-0.724210\pi\) | ||||
−0.647558 | + | 0.762016i | \(0.724210\pi\) | |||||||
\(788\) | −8.55113 | −0.304621 | ||||||||
\(789\) | −31.7741 | −1.13119 | ||||||||
\(790\) | −13.0125 | −0.462965 | ||||||||
\(791\) | −1.57044 | −0.0558384 | ||||||||
\(792\) | −23.9582 | −0.851316 | ||||||||
\(793\) | 50.2893 | 1.78582 | ||||||||
\(794\) | −5.85052 | −0.207627 | ||||||||
\(795\) | 21.8332 | 0.774343 | ||||||||
\(796\) | 11.1801 | 0.396268 | ||||||||
\(797\) | −3.32566 | −0.117801 | −0.0589005 | − | 0.998264i | \(-0.518759\pi\) | ||||
−0.0589005 | + | 0.998264i | \(0.518759\pi\) | |||||||
\(798\) | 8.11334 | 0.287209 | ||||||||
\(799\) | −36.1087 | −1.27744 | ||||||||
\(800\) | 2.10851 | 0.0745470 | ||||||||
\(801\) | −35.4084 | −1.25109 | ||||||||
\(802\) | −5.32050 | −0.187874 | ||||||||
\(803\) | 21.6896 | 0.765410 | ||||||||
\(804\) | 1.65633 | 0.0584143 | ||||||||
\(805\) | −1.45447 | −0.0512634 | ||||||||
\(806\) | 13.4922 | 0.475243 | ||||||||
\(807\) | 5.69053 | 0.200316 | ||||||||
\(808\) | −16.4335 | −0.578130 | ||||||||
\(809\) | −7.08203 | −0.248991 | −0.124495 | − | 0.992220i | \(-0.539731\pi\) | ||||
−0.124495 | + | 0.992220i | \(0.539731\pi\) | |||||||
\(810\) | 7.55963 | 0.265618 | ||||||||
\(811\) | 5.69088 | 0.199834 | 0.0999169 | − | 0.994996i | \(-0.468142\pi\) | ||||
0.0999169 | + | 0.994996i | \(0.468142\pi\) | |||||||
\(812\) | 0.855351 | 0.0300169 | ||||||||
\(813\) | −31.7926 | −1.11502 | ||||||||
\(814\) | 57.8628 | 2.02809 | ||||||||
\(815\) | 1.58343 | 0.0554650 | ||||||||
\(816\) | −15.1668 | −0.530944 | ||||||||
\(817\) | 17.5987 | 0.615701 | ||||||||
\(818\) | 2.27676 | 0.0796049 | ||||||||
\(819\) | −12.3754 | −0.432432 | ||||||||
\(820\) | −10.5631 | −0.368880 | ||||||||
\(821\) | 37.9023 | 1.32280 | 0.661400 | − | 0.750033i | \(-0.269963\pi\) | ||||
0.661400 | + | 0.750033i | \(0.269963\pi\) | |||||||
\(822\) | −43.9030 | −1.53129 | ||||||||
\(823\) | 7.88827 | 0.274968 | 0.137484 | − | 0.990504i | \(-0.456098\pi\) | ||||
0.137484 | + | 0.990504i | \(0.456098\pi\) | |||||||
\(824\) | 9.55928 | 0.333013 | ||||||||
\(825\) | −32.7819 | −1.14132 | ||||||||
\(826\) | 3.62780 | 0.126227 | ||||||||
\(827\) | −16.5985 | −0.577185 | −0.288593 | − | 0.957452i | \(-0.593187\pi\) | ||||
−0.288593 | + | 0.957452i | \(0.593187\pi\) | |||||||
\(828\) | 4.10851 | 0.142780 | ||||||||
\(829\) | −21.8176 | −0.757756 | −0.378878 | − | 0.925447i | \(-0.623690\pi\) | ||||
−0.378878 | + | 0.925447i | \(0.623690\pi\) | |||||||
\(830\) | 26.2032 | 0.909527 | ||||||||
\(831\) | −20.4992 | −0.711109 | ||||||||
\(832\) | 3.52153 | 0.122087 | ||||||||
\(833\) | 35.6582 | 1.23548 | ||||||||
\(834\) | −26.0598 | −0.902376 | ||||||||
\(835\) | 12.3866 | 0.428656 | ||||||||
\(836\) | 20.7460 | 0.717517 | ||||||||
\(837\) | −11.3235 | −0.391396 | ||||||||
\(838\) | −32.6799 | −1.12891 | ||||||||
\(839\) | 34.2556 | 1.18264 | 0.591318 | − | 0.806439i | \(-0.298608\pi\) | ||||
0.591318 | + | 0.806439i | \(0.298608\pi\) | |||||||
\(840\) | 3.87788 | 0.133800 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −22.6645 | −0.781069 | ||||||||
\(843\) | −44.7975 | −1.54291 | ||||||||
\(844\) | −4.68294 | −0.161194 | ||||||||
\(845\) | −1.01827 | −0.0350297 | ||||||||
\(846\) | −26.0791 | −0.896616 | ||||||||
\(847\) | −19.6771 | −0.676113 | ||||||||
\(848\) | 4.81578 | 0.165375 | ||||||||
\(849\) | 45.0297 | 1.54541 | ||||||||
\(850\) | −11.9944 | −0.411405 | ||||||||
\(851\) | −9.92270 | −0.340146 | ||||||||
\(852\) | −17.9520 | −0.615026 | ||||||||
\(853\) | 38.5831 | 1.32106 | 0.660530 | − | 0.750800i | \(-0.270332\pi\) | ||||
0.660530 | + | 0.750800i | \(0.270332\pi\) | |||||||
\(854\) | 12.2149 | 0.417984 | ||||||||
\(855\) | 24.8548 | 0.850018 | ||||||||
\(856\) | 10.6764 | 0.364913 | ||||||||
\(857\) | 14.3892 | 0.491526 | 0.245763 | − | 0.969330i | \(-0.420962\pi\) | ||||
0.245763 | + | 0.969330i | \(0.420962\pi\) | |||||||
\(858\) | −54.7507 | −1.86916 | ||||||||
\(859\) | 2.56173 | 0.0874050 | 0.0437025 | − | 0.999045i | \(-0.486085\pi\) | ||||
0.0437025 | + | 0.999045i | \(0.486085\pi\) | |||||||
\(860\) | 8.41156 | 0.286832 | ||||||||
\(861\) | 14.1666 | 0.482796 | ||||||||
\(862\) | 8.70338 | 0.296438 | ||||||||
\(863\) | 16.9392 | 0.576616 | 0.288308 | − | 0.957538i | \(-0.406907\pi\) | ||||
0.288308 | + | 0.957538i | \(0.406907\pi\) | |||||||
\(864\) | −2.95548 | −0.100547 | ||||||||
\(865\) | 33.9621 | 1.15475 | ||||||||
\(866\) | −38.4043 | −1.30503 | ||||||||
\(867\) | 40.9525 | 1.39082 | ||||||||
\(868\) | 3.27715 | 0.111234 | ||||||||
\(869\) | 44.6241 | 1.51377 | ||||||||
\(870\) | 4.53367 | 0.153706 | ||||||||
\(871\) | 2.18771 | 0.0741276 | ||||||||
\(872\) | −19.4128 | −0.657399 | ||||||||
\(873\) | −68.7848 | −2.32801 | ||||||||
\(874\) | −3.55767 | −0.120340 | ||||||||
\(875\) | 10.3391 | 0.349526 | ||||||||
\(876\) | 9.91680 | 0.335058 | ||||||||
\(877\) | −41.9655 | −1.41707 | −0.708537 | − | 0.705674i | \(-0.750644\pi\) | ||||
−0.708537 | + | 0.705674i | \(0.750644\pi\) | |||||||
\(878\) | −4.34450 | −0.146620 | ||||||||
\(879\) | −1.12333 | −0.0378889 | ||||||||
\(880\) | 9.91586 | 0.334264 | ||||||||
\(881\) | −51.7200 | −1.74249 | −0.871246 | − | 0.490847i | \(-0.836687\pi\) | ||||
−0.871246 | + | 0.490847i | \(0.836687\pi\) | |||||||
\(882\) | 25.7537 | 0.867171 | ||||||||
\(883\) | 19.4048 | 0.653024 | 0.326512 | − | 0.945193i | \(-0.394127\pi\) | ||||
0.326512 | + | 0.945193i | \(0.394127\pi\) | |||||||
\(884\) | −20.0325 | −0.673767 | ||||||||
\(885\) | 19.2287 | 0.646365 | ||||||||
\(886\) | 36.8543 | 1.23815 | ||||||||
\(887\) | 27.7780 | 0.932693 | 0.466347 | − | 0.884602i | \(-0.345570\pi\) | ||||
0.466347 | + | 0.884602i | \(0.345570\pi\) | |||||||
\(888\) | 26.4557 | 0.887795 | ||||||||
\(889\) | 1.63979 | 0.0549969 | ||||||||
\(890\) | 14.6549 | 0.491234 | ||||||||
\(891\) | −25.9244 | −0.868501 | ||||||||
\(892\) | 15.8006 | 0.529043 | ||||||||
\(893\) | 22.5826 | 0.755698 | ||||||||
\(894\) | 37.7762 | 1.26342 | ||||||||
\(895\) | −28.5215 | −0.953369 | ||||||||
\(896\) | 0.855351 | 0.0285753 | ||||||||
\(897\) | 9.38903 | 0.313490 | ||||||||
\(898\) | −22.7892 | −0.760486 | ||||||||
\(899\) | 3.83135 | 0.127783 | ||||||||
\(900\) | −8.66281 | −0.288760 | ||||||||
\(901\) | −27.3950 | −0.912660 | ||||||||
\(902\) | 36.2243 | 1.20614 | ||||||||
\(903\) | −11.2810 | −0.375409 | ||||||||
\(904\) | −1.83602 | −0.0610650 | ||||||||
\(905\) | −7.61309 | −0.253068 | ||||||||
\(906\) | −40.7508 | −1.35386 | ||||||||
\(907\) | −5.19013 | −0.172336 | −0.0861678 | − | 0.996281i | \(-0.527462\pi\) | ||||
−0.0861678 | + | 0.996281i | \(0.527462\pi\) | |||||||
\(908\) | −25.1513 | −0.834675 | ||||||||
\(909\) | 67.5173 | 2.23941 | ||||||||
\(910\) | 5.12197 | 0.169792 | ||||||||
\(911\) | 3.78632 | 0.125447 | 0.0627233 | − | 0.998031i | \(-0.480021\pi\) | ||||
0.0627233 | + | 0.998031i | \(0.480021\pi\) | |||||||
\(912\) | 9.48539 | 0.314093 | ||||||||
\(913\) | −89.8593 | −2.97391 | ||||||||
\(914\) | −12.5719 | −0.415842 | ||||||||
\(915\) | 64.7432 | 2.14034 | ||||||||
\(916\) | −0.762291 | −0.0251868 | ||||||||
\(917\) | 0.307438 | 0.0101525 | ||||||||
\(918\) | 16.8125 | 0.554894 | ||||||||
\(919\) | −45.8918 | −1.51383 | −0.756915 | − | 0.653514i | \(-0.773294\pi\) | ||||
−0.756915 | + | 0.653514i | \(0.773294\pi\) | |||||||
\(920\) | −1.70044 | −0.0560618 | ||||||||
\(921\) | 80.1073 | 2.63962 | ||||||||
\(922\) | 13.4971 | 0.444504 | ||||||||
\(923\) | −23.7113 | −0.780466 | ||||||||
\(924\) | −13.2985 | −0.437489 | ||||||||
\(925\) | 20.9221 | 0.687914 | ||||||||
\(926\) | −19.1228 | −0.628413 | ||||||||
\(927\) | −39.2744 | −1.28994 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −48.9309 | −1.60537 | −0.802685 | − | 0.596403i | \(-0.796596\pi\) | ||||
−0.802685 | + | 0.596403i | \(0.796596\pi\) | |||||||
\(930\) | 17.3701 | 0.569588 | ||||||||
\(931\) | −22.3008 | −0.730880 | ||||||||
\(932\) | −0.137732 | −0.00451157 | ||||||||
\(933\) | 11.8577 | 0.388204 | ||||||||
\(934\) | 0.400694 | 0.0131111 | ||||||||
\(935\) | −56.4072 | −1.84471 | ||||||||
\(936\) | −14.4682 | −0.472909 | ||||||||
\(937\) | 53.9467 | 1.76236 | 0.881181 | − | 0.472778i | \(-0.156749\pi\) | ||||
0.881181 | + | 0.472778i | \(0.156749\pi\) | |||||||
\(938\) | 0.531377 | 0.0173501 | ||||||||
\(939\) | −54.2886 | −1.77164 | ||||||||
\(940\) | 10.7937 | 0.352051 | ||||||||
\(941\) | −41.5313 | −1.35388 | −0.676940 | − | 0.736038i | \(-0.736694\pi\) | ||||
−0.676940 | + | 0.736038i | \(0.736694\pi\) | |||||||
\(942\) | 61.0098 | 1.98781 | ||||||||
\(943\) | −6.21200 | −0.202290 | ||||||||
\(944\) | 4.24130 | 0.138043 | ||||||||
\(945\) | −4.29866 | −0.139835 | ||||||||
\(946\) | −28.8459 | −0.937862 | ||||||||
\(947\) | 55.6668 | 1.80893 | 0.904464 | − | 0.426551i | \(-0.140272\pi\) | ||||
0.904464 | + | 0.426551i | \(0.140272\pi\) | |||||||
\(948\) | 20.4028 | 0.662651 | ||||||||
\(949\) | 13.0983 | 0.425188 | ||||||||
\(950\) | 7.50137 | 0.243377 | ||||||||
\(951\) | 44.9820 | 1.45864 | ||||||||
\(952\) | −4.86574 | −0.157700 | ||||||||
\(953\) | −21.9874 | −0.712240 | −0.356120 | − | 0.934440i | \(-0.615901\pi\) | ||||
−0.356120 | + | 0.934440i | \(0.615901\pi\) | |||||||
\(954\) | −19.7857 | −0.640585 | ||||||||
\(955\) | −36.9337 | −1.19515 | ||||||||
\(956\) | −7.59313 | −0.245579 | ||||||||
\(957\) | −15.5474 | −0.502577 | ||||||||
\(958\) | −2.95436 | −0.0954511 | ||||||||
\(959\) | −14.0848 | −0.454821 | ||||||||
\(960\) | 4.53367 | 0.146324 | ||||||||
\(961\) | −16.3207 | −0.526475 | ||||||||
\(962\) | 34.9431 | 1.12661 | ||||||||
\(963\) | −43.8642 | −1.41351 | ||||||||
\(964\) | 22.2852 | 0.717758 | ||||||||
\(965\) | 17.6079 | 0.566817 | ||||||||
\(966\) | 2.28052 | 0.0733745 | ||||||||
\(967\) | 39.1360 | 1.25853 | 0.629265 | − | 0.777191i | \(-0.283356\pi\) | ||||
0.629265 | + | 0.777191i | \(0.283356\pi\) | |||||||
\(968\) | −23.0047 | −0.739399 | ||||||||
\(969\) | −53.9584 | −1.73339 | ||||||||
\(970\) | 28.4688 | 0.914078 | ||||||||
\(971\) | −6.74691 | −0.216519 | −0.108259 | − | 0.994123i | \(-0.534528\pi\) | ||||
−0.108259 | + | 0.994123i | \(0.534528\pi\) | |||||||
\(972\) | −20.7194 | −0.664576 | ||||||||
\(973\) | −8.36038 | −0.268022 | ||||||||
\(974\) | −39.8315 | −1.27628 | ||||||||
\(975\) | −19.7968 | −0.634006 | ||||||||
\(976\) | 14.2805 | 0.457108 | ||||||||
\(977\) | 9.54652 | 0.305420 | 0.152710 | − | 0.988271i | \(-0.451200\pi\) | ||||
0.152710 | + | 0.988271i | \(0.451200\pi\) | |||||||
\(978\) | −2.48271 | −0.0793883 | ||||||||
\(979\) | −50.2564 | −1.60620 | ||||||||
\(980\) | −10.6590 | −0.340489 | ||||||||
\(981\) | 79.7574 | 2.54646 | ||||||||
\(982\) | 12.5185 | 0.399482 | ||||||||
\(983\) | −45.9130 | −1.46440 | −0.732199 | − | 0.681090i | \(-0.761506\pi\) | ||||
−0.732199 | + | 0.681090i | \(0.761506\pi\) | |||||||
\(984\) | 16.5623 | 0.527987 | ||||||||
\(985\) | −14.5407 | −0.463304 | ||||||||
\(986\) | −5.68859 | −0.181161 | ||||||||
\(987\) | −14.4758 | −0.460769 | ||||||||
\(988\) | 12.5284 | 0.398583 | ||||||||
\(989\) | 4.94670 | 0.157296 | ||||||||
\(990\) | −40.7394 | −1.29478 | ||||||||
\(991\) | −41.4321 | −1.31613 | −0.658067 | − | 0.752960i | \(-0.728626\pi\) | ||||
−0.658067 | + | 0.752960i | \(0.728626\pi\) | |||||||
\(992\) | 3.83135 | 0.121646 | ||||||||
\(993\) | 28.1841 | 0.894395 | ||||||||
\(994\) | −5.75928 | −0.182673 | ||||||||
\(995\) | 19.0111 | 0.602692 | ||||||||
\(996\) | −41.0849 | −1.30183 | ||||||||
\(997\) | −21.7210 | −0.687910 | −0.343955 | − | 0.938986i | \(-0.611767\pi\) | ||||
−0.343955 | + | 0.938986i | \(0.611767\pi\) | |||||||
\(998\) | 28.3237 | 0.896570 | ||||||||
\(999\) | −29.3263 | −0.927843 |
(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 | 1334.2.a.g.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.g.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial |