Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2008,1,Mod(3,2008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2008, base_ring=CyclotomicField(250))
chi = DirichletCharacter(H, H._module([125, 125, 16]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2008.3");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2008 = 2^{3} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2008.bd (of order \(250\), degree \(100\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.00212254537\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Coefficient field: | \(\Q(\zeta_{250})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{100} - x^{75} + x^{50} - x^{25} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{125}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{125} - \cdots)\) |
Embedding invariants
Embedding label | 155.1 | ||
Root | \(0.137790 - 0.990461i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.155 |
Dual form | 2008.1.bd.a.1723.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{33}{125}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(3\) | −0.507512 | − | 0.430706i | −0.507512 | − | 0.430706i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(4\) | 0.968583 | + | 0.248690i | 0.968583 | + | 0.248690i | ||||
\(5\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(6\) | 0.449528 | + | 0.490918i | 0.449528 | + | 0.490918i | ||||
\(7\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(8\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(9\) | −0.0905766 | − | 0.549510i | −0.0905766 | − | 0.549510i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17735 | − | 1.57839i | 1.17735 | − | 1.57839i | 0.448383 | − | 0.893841i | \(-0.352000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(12\) | −0.384455 | − | 0.543387i | −0.384455 | − | 0.543387i | ||||
\(13\) | 0 | 0 | −0.988652 | − | 0.150226i | \(-0.952000\pi\) | ||||
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(17\) | 0.0697491 | − | 0.614086i | 0.0697491 | − | 0.614086i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
0.979855 | − | 0.199710i | \(-0.0640000\pi\) | |||||||
\(18\) | 0.0209906 | + | 0.556529i | 0.0209906 | + | 0.556529i | ||||
\(19\) | −0.847259 | − | 0.0854639i | −0.847259 | − | 0.0854639i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.36589 | + | 1.41838i | −1.36589 | + | 1.41838i | ||||
\(23\) | 0 | 0 | −0.492727 | − | 0.870184i | \(-0.664000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(24\) | 0.313319 | + | 0.587288i | 0.313319 | + | 0.587288i | ||||
\(25\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.533139 | + | 0.888698i | −0.533139 | + | 0.888698i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.962028 | − | 0.272952i | \(-0.0880000\pi\) | ||||
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.947098 | − | 0.320944i | \(-0.896000\pi\) | ||||
0.947098 | + | 0.320944i | \(0.104000\pi\) | |||||||
\(32\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(33\) | −1.27734 | + | 0.293958i | −1.27734 | + | 0.293958i | ||||
\(34\) | −0.146164 | + | 0.600501i | −0.146164 | + | 0.600501i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0489265 | − | 0.554771i | 0.0489265 | − | 0.554771i | ||||
\(37\) | 0 | 0 | 0.448383 | − | 0.893841i | \(-0.352000\pi\) | ||||
−0.448383 | + | 0.893841i | \(0.648000\pi\) | |||||||
\(38\) | 0.829867 | + | 0.190980i | 0.829867 | + | 0.190980i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.91897 | + | 0.341129i | 1.91897 | + | 0.341129i | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) |
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.44523 | − | 1.10656i | −1.44523 | − | 1.10656i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
−0.470704 | − | 0.882291i | \(-0.656000\pi\) | |||||||
\(44\) | 1.53289 | − | 1.23601i | 1.53289 | − | 1.23601i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(48\) | −0.237242 | − | 0.621926i | −0.237242 | − | 0.621926i | ||||
\(49\) | −0.984564 | + | 0.175023i | −0.984564 | + | 0.175023i | ||||
\(50\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(51\) | −0.299889 | + | 0.281614i | −0.299889 | + | 0.281614i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.823533 | − | 0.567269i | \(-0.808000\pi\) | ||||
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(54\) | 0.640319 | − | 0.814870i | 0.640319 | − | 0.814870i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.393184 | + | 0.408293i | 0.393184 | + | 0.408293i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.213772 | − | 1.88210i | −0.213772 | − | 1.88210i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.212007 | − | 0.977268i | \(-0.432000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.332820 | − | 0.942991i | \(-0.608000\pi\) | ||||
0.332820 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.30411 | − | 0.131547i | 1.30411 | − | 0.131547i | ||||
\(67\) | −0.111033 | − | 0.798127i | −0.111033 | − | 0.798127i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
0.850994 | − | 0.525175i | \(-0.176000\pi\) | |||||||
\(68\) | 0.220275 | − | 0.577447i | 0.220275 | − | 0.577447i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.888136 | − | 0.459580i | \(-0.152000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(72\) | −0.118072 | + | 0.544265i | −0.118072 | + | 0.544265i | ||||
\(73\) | 0.373698 | − | 0.0282297i | 0.373698 | − | 0.0282297i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.605802 | − | 0.275825i | 0.605802 | − | 0.275825i | ||||
\(76\) | −0.799387 | − | 0.293484i | −0.799387 | − | 0.293484i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.617860 | − | 0.786288i | \(-0.712000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.125879 | − | 0.0426567i | 0.125879 | − | 0.0426567i | ||||
\(82\) | −1.86108 | − | 0.578950i | −1.86108 | − | 0.578950i | ||||
\(83\) | 0.636151 | − | 0.415018i | 0.636151 | − | 0.415018i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.29515 | + | 1.27897i | 1.29515 | + | 1.27897i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.67572 | + | 1.03414i | −1.67572 | + | 1.03414i | ||||
\(89\) | −1.09131 | + | 0.222427i | −1.09131 | + | 0.222427i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.157423 | + | 0.646756i | 0.157423 | + | 0.646756i | ||||
\(97\) | 0.800944 | + | 0.645819i | 0.800944 | + | 0.645819i | 0.938734 | − | 0.344643i | \(-0.112000\pi\) |
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(98\) | 0.998737 | − | 0.0502443i | 0.998737 | − | 0.0502443i | ||||
\(99\) | −0.973980 | − | 0.504001i | −0.973980 | − | 0.504001i | ||||
\(100\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(101\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(102\) | 0.332820 | − | 0.241808i | 0.332820 | − | 0.241808i | ||||
\(103\) | 0 | 0 | 0.656586 | − | 0.754251i | \(-0.272000\pi\) | ||||
−0.656586 | + | 0.754251i | \(0.728000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.189720 | − | 0.537541i | 0.189720 | − | 0.537541i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(108\) | −0.737400 | + | 0.728191i | −0.737400 | + | 0.728191i | ||||
\(109\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.417379 | + | 1.28456i | −0.417379 | + | 1.28456i | 0.492727 | + | 0.870184i | \(0.336000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(114\) | −0.338911 | − | 0.454353i | −0.338911 | − | 0.454353i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0238026 | + | 1.89405i | −0.0238026 | + | 1.89405i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.820134 | − | 2.75812i | −0.820134 | − | 2.75812i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.826972 | − | 0.999638i | −0.826972 | − | 0.999638i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.837528 | − | 0.546394i | \(-0.816000\pi\) | ||||
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(128\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(129\) | 0.256869 | + | 1.18406i | 0.256869 | + | 1.18406i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0618772 | − | 0.109279i | 0.0618772 | − | 0.109279i | −0.837528 | − | 0.546394i | \(-0.816000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(132\) | −1.31032 | − | 0.0329387i | −1.31032 | − | 0.0329387i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.0101259 | + | 0.805749i | 0.0101259 | + | 0.805749i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.290911 | + | 0.545286i | −0.290911 | + | 0.545286i | ||||
\(137\) | −0.984788 | − | 1.32023i | −0.984788 | − | 1.32023i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.0376902 | − | 0.999289i | \(-0.512000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.614386 | − | 1.39564i | 0.614386 | − | 1.39564i | −0.285019 | − | 0.958522i | \(-0.592000\pi\) |
0.899405 | − | 0.437116i | \(-0.144000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.185355 | − | 0.525175i | 0.185355 | − | 0.525175i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.374289 | − | 0.0188297i | −0.374289 | − | 0.0188297i | ||||
\(147\) | 0.575061 | + | 0.335231i | 0.575061 | + | 0.335231i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(150\) | −0.635595 | + | 0.197722i | −0.635595 | + | 0.197722i | ||||
\(151\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(152\) | 0.756300 | + | 0.391359i | 0.756300 | + | 0.391359i | ||||
\(153\) | −0.343764 | + | 0.0172940i | −0.343764 | + | 0.0172940i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.130233 | + | 0.0265435i | −0.130233 | + | 0.0265435i | ||||
\(163\) | −1.63736 | + | 1.01047i | −1.63736 | + | 1.01047i | −0.675333 | + | 0.737513i | \(0.736000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(164\) | 1.77385 | + | 0.807640i | 1.77385 | + | 0.807640i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.683151 | + | 0.332015i | −0.683151 | + | 0.332015i | ||||
\(167\) | 0 | 0 | 0.762443 | − | 0.647056i | \(-0.224000\pi\) | ||||
−0.762443 | + | 0.647056i | \(0.776000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.954865 | + | 0.297042i | 0.954865 | + | 0.297042i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0297787 | + | 0.473318i | 0.0297787 | + | 0.473318i | ||||
\(172\) | −1.12464 | − | 1.43121i | −1.12464 | − | 1.43121i | ||||
\(173\) | 0 | 0 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
0.556876 | + | 0.830596i | \(0.312000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.79212 | − | 0.815959i | 1.79212 | − | 0.815959i | ||||
\(177\) | −0.702137 | + | 1.04726i | −0.702137 | + | 1.04726i | ||||
\(178\) | 1.11059 | − | 0.0838953i | 1.11059 | − | 0.0838953i | ||||
\(179\) | 0.190121 | − | 0.876381i | 0.190121 | − | 0.876381i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.863923 | − | 0.503623i | \(-0.168000\pi\) | ||||
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.887146 | − | 0.833086i | −0.887146 | − | 0.833086i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.379779 | − | 0.925077i | \(-0.376000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(192\) | −0.0751216 | − | 0.661387i | −0.0751216 | − | 0.661387i | ||||
\(193\) | 1.88806 | − | 0.286890i | 1.88806 | − | 0.286890i | 0.899405 | − | 0.437116i | \(-0.144000\pi\) |
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(194\) | −0.713685 | − | 0.741111i | −0.713685 | − | 0.741111i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.997159 | − | 0.0753268i | −0.997159 | − | 0.0753268i | ||||
\(197\) | 0 | 0 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
−0.617860 | + | 0.786288i | \(0.712000\pi\) | |||||||
\(198\) | 0.903132 | + | 0.622099i | 0.903132 | + | 0.622099i | ||||
\(199\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(200\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(201\) | −0.287407 | + | 0.452881i | −0.287407 | + | 0.452881i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.360502 | + | 0.198187i | −0.360502 | + | 0.198187i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.13242 | + | 1.23668i | −1.13242 | + | 1.23668i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0141249 | + | 0.0740452i | 0.0141249 | + | 0.0740452i | 0.988652 | − | 0.150226i | \(-0.0480000\pi\) |
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.255596 | + | 0.509524i | −0.255596 | + | 0.509524i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.822852 | − | 0.630028i | 0.822852 | − | 0.630028i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.201815 | − | 0.146627i | −0.201815 | − | 0.146627i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.162637 | − | 0.986686i | \(-0.448000\pi\) | ||||
−0.162637 | + | 0.986686i | \(0.552000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.535777 | + | 0.152014i | 0.535777 | + | 0.152014i | ||||
\(226\) | 0.575085 | − | 1.22212i | 0.575085 | − | 1.22212i | ||||
\(227\) | 0.875299 | + | 1.64067i | 0.875299 | + | 1.64067i | 0.762443 | + | 0.647056i | \(0.224000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(228\) | 0.279293 | + | 0.493247i | 0.279293 | + | 0.493247i | ||||
\(229\) | 0 | 0 | 0.693653 | − | 0.720309i | \(-0.256000\pi\) | ||||
−0.693653 | + | 0.720309i | \(0.744000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.0738618 | − | 1.95832i | −0.0738618 | − | 1.95832i | −0.236499 | − | 0.971632i | \(-0.576000\pi\) |
0.162637 | − | 0.986686i | \(-0.448000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.261002 | − | 1.87613i | 0.261002 | − | 1.87613i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.756300 | + | 1.60722i | 0.756300 | + | 1.60722i | 0.793990 | + | 0.607930i | \(0.208000\pi\) |
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(242\) | 0.467983 | + | 2.83916i | 0.467983 | + | 2.83916i | ||||
\(243\) | 0.881316 | + | 0.348938i | 0.881316 | + | 0.348938i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.695164 | + | 1.09540i | 0.695164 | + | 1.09540i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.501605 | − | 0.0633674i | −0.501605 | − | 0.0633674i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.0878512 | + | 0.996134i | −0.0878512 | + | 0.996134i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(257\) | 0.807570 | + | 0.881926i | 0.807570 | + | 0.881926i | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(258\) | −0.106441 | − | 1.20692i | −0.106441 | − | 1.20692i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.0750855 | + | 0.100662i | −0.0750855 | + | 0.100662i | ||||
\(263\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(264\) | 1.29585 | + | 0.196905i | 1.29585 | + | 0.196905i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.649656 | + | 0.357151i | 0.649656 | + | 0.357151i | ||||
\(268\) | 0.0909411 | − | 0.800665i | 0.0909411 | − | 0.800665i | ||||
\(269\) | 0 | 0 | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) | ||||
0.0376902 | + | 0.999289i | \(0.488000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | 0.356960 | − | 0.504525i | 0.356960 | − | 0.504525i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.811554 | + | 1.43325i | 0.811554 | + | 1.43325i | ||||
\(275\) | 0.926877 | + | 1.73734i | 0.926877 | + | 1.73734i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(278\) | −0.784461 | + | 1.30763i | −0.784461 | + | 1.30763i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.480069 | − | 1.77675i | 0.480069 | − | 1.77675i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
0.617860 | − | 0.786288i | \(-0.288000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.43703 | + | 1.04407i | 1.43703 | + | 1.04407i | 0.988652 | + | 0.150226i | \(0.0480000\pi\) |
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.249716 | + | 0.497802i | −0.249716 | + | 0.497802i | ||||
\(289\) | 0.602291 | + | 0.138607i | 0.602291 | + | 0.138607i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.128330 | − | 0.672731i | −0.128330 | − | 0.672731i | ||||
\(292\) | 0.368978 | + | 0.0655921i | 0.368978 | + | 0.0655921i | ||||
\(293\) | 0 | 0 | 0.675333 | − | 0.737513i | \(-0.264000\pi\) | ||||
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(294\) | −0.528511 | − | 0.404662i | −0.528511 | − | 0.404662i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.775018 | + | 1.88781i | 0.775018 | + | 1.88781i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.655365 | − | 0.116502i | 0.655365 | − | 0.116502i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.701286 | − | 0.483063i | −0.701286 | − | 0.483063i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.343220 | + | 0.0259274i | 0.343220 | + | 0.0259274i | ||||
\(307\) | −0.563570 | + | 1.89529i | −0.563570 | + | 1.89529i | −0.137790 | + | 0.990461i | \(0.544000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.379779 | − | 0.925077i | \(-0.376000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.0677975 | − | 0.0329499i | −0.0677975 | − | 0.0329499i | 0.402906 | − | 0.915241i | \(-0.368000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) | ||||
−0.994951 | + | 0.100362i | \(0.968000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.327807 | + | 0.191095i | −0.327807 | + | 0.191095i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.111578 | + | 0.514329i | −0.111578 | + | 0.514329i | ||||
\(324\) | 0.132533 | − | 0.0100117i | 0.132533 | − | 0.0100117i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.75109 | − | 0.797282i | 1.75109 | − | 0.797282i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.65863 | − | 1.02359i | −1.65863 | − | 1.02359i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.119913 | + | 1.90596i | 0.119913 | + | 1.90596i | 0.356412 | + | 0.934329i | \(0.384000\pi\) |
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(332\) | 0.719376 | − | 0.243775i | 0.719376 | − | 0.243775i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.196085 | + | 0.193637i | 0.196085 | + | 0.193637i | 0.793990 | − | 0.607930i | \(-0.208000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(338\) | −0.910106 | − | 0.414376i | −0.910106 | − | 0.414376i | ||||
\(339\) | 0.765092 | − | 0.472161i | 0.765092 | − | 0.472161i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.0297787 | − | 0.473318i | 0.0297787 | − | 0.473318i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.936389 | + | 1.56088i | 0.936389 | + | 1.56088i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.273191 | − | 1.12238i | −0.273191 | − | 1.12238i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.656586 | − | 0.754251i | \(-0.272000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | ||||
−0.998737 | + | 0.0502443i | \(0.984000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.88025 | + | 0.584913i | −1.88025 | + | 0.584913i | ||||
\(353\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(354\) | 0.827857 | − | 0.950999i | 0.827857 | − | 0.950999i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.11234 | − | 0.0559597i | −1.11234 | − | 0.0559597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.298461 | + | 0.845642i | −0.298461 | + | 0.845642i | ||||
\(359\) | 0 | 0 | 0.711536 | − | 0.702650i | \(-0.248000\pi\) | ||||
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.269311 | − | 0.0548899i | −0.269311 | − | 0.0548899i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.771709 | + | 1.75301i | −0.771709 | + | 1.75301i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.999684 | − | 0.0251301i | \(-0.00800000\pi\) | ||||
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0136401 | − | 1.08539i | 0.0136401 | − | 1.08539i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(374\) | 0.775738 | + | 0.937706i | 0.775738 | + | 0.937706i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.10137 | + | 1.33133i | 1.10137 | + | 1.33133i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) | ||||
0.999684 | + | 0.0251301i | \(0.00800000\pi\) | |||||||
\(384\) | −0.00836445 | + | 0.665587i | −0.00836445 | + | 0.665587i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.90913 | + | 0.0479917i | −1.90913 | + | 0.0479917i | ||||
\(387\) | −0.477162 | + | 0.894397i | −0.477162 | + | 0.894397i | ||||
\(388\) | 0.615172 | + | 0.824715i | 0.615172 | + | 0.824715i | ||||
\(389\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.979855 | + | 0.199710i | 0.979855 | + | 0.199710i | ||||
\(393\) | −0.0784703 | + | 0.0288093i | −0.0784703 | + | 0.0288093i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.818041 | − | 0.730386i | −0.818041 | − | 0.730386i | ||||
\(397\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(401\) | 0.498137 | − | 0.154962i | 0.498137 | − | 0.154962i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(402\) | 0.341902 | − | 0.413288i | 0.341902 | − | 0.413288i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.382498 | − | 0.151442i | 0.382498 | − | 0.151442i | ||||
\(409\) | 1.02596 | + | 1.71018i | 1.02596 | + | 1.71018i | 0.577573 | + | 0.816339i | \(0.304000\pi\) |
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0688404 | + | 1.09419i | −0.0688404 | + | 1.09419i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.912917 | + | 0.443683i | −0.912917 | + | 0.443683i | ||||
\(418\) | 1.27849 | − | 1.08500i | 1.27849 | − | 1.08500i | ||||
\(419\) | 1.67030 | − | 1.08968i | 1.67030 | − | 1.08968i | 0.793990 | − | 0.607930i | \(-0.208000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.947098 | − | 0.320944i | \(-0.104000\pi\) | ||||
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(422\) | −0.00473317 | − | 0.0752316i | −0.00473317 | − | 0.0752316i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.525944 | + | 0.324576i | 0.525944 | + | 0.324576i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.317441 | − | 0.473472i | 0.317441 | − | 0.473472i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.888136 | − | 0.459580i | \(-0.152000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(432\) | −0.895327 | + | 0.521930i | −0.895327 | + | 0.521930i | ||||
\(433\) | 0.238883 | − | 1.25227i | 0.238883 | − | 1.25227i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.181846 | + | 0.170765i | 0.181846 | + | 0.170765i | ||||
\(439\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.185355 | + | 0.525175i | 0.185355 | + | 0.525175i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.182605 | − | 1.60770i | −0.182605 | − | 1.60770i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
0.492727 | − | 0.870184i | \(-0.336000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.389529 | − | 0.268317i | −0.389529 | − | 0.268317i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(450\) | −0.512500 | − | 0.217966i | −0.512500 | − | 0.217966i | ||||
\(451\) | 2.79774 | − | 2.62725i | 2.79774 | − | 2.62725i | ||||
\(452\) | −0.723723 | + | 1.14040i | −0.723723 | + | 1.14040i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.662767 | − | 1.73743i | −0.662767 | − | 1.73743i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.215270 | − | 0.524362i | −0.215270 | − | 0.524362i | ||||
\(457\) | 1.48012 | − | 1.32152i | 1.48012 | − | 1.32152i | 0.656586 | − | 0.754251i | \(-0.272000\pi\) |
0.823533 | − | 0.567269i | \(-0.192000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.508550 | + | 0.389379i | 0.508550 | + | 0.389379i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.984564 | − | 0.175023i | \(-0.944000\pi\) | ||||
0.984564 | + | 0.175023i | \(0.0560000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.656586 | − | 0.754251i | \(-0.728000\pi\) | ||||
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.172163 | + | 1.95213i | −0.172163 | + | 1.95213i | ||||
\(467\) | −1.32998 | + | 1.01832i | −1.32998 | + | 1.01832i | −0.332820 | + | 0.942991i | \(0.608000\pi\) |
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.494085 | + | 1.82862i | −0.494085 | + | 1.82862i | ||||
\(473\) | −3.44813 | + | 0.978323i | −3.44813 | + | 0.978323i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.438075 | − | 0.730234i | 0.438075 | − | 0.730234i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.492727 | − | 0.870184i | \(-0.664000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.548899 | − | 1.68934i | −0.548899 | − | 1.68934i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.108452 | − | 2.87542i | −0.108452 | − | 2.87542i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.830633 | − | 0.456644i | −0.830633 | − | 0.456644i | ||||
\(487\) | 0 | 0 | 0.137790 | − | 0.990461i | \(-0.456000\pi\) | ||||
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.26619 | + | 0.192398i | 1.26619 | + | 0.192398i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.105053 | − | 0.140837i | 0.105053 | − | 0.140837i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(492\) | −0.552392 | − | 1.17389i | −0.552392 | − | 1.17389i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.489708 | + | 0.125736i | 0.489708 | + | 0.125736i | ||||
\(499\) | −1.13747 | − | 0.965331i | −1.13747 | − | 0.965331i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.212007 | − | 0.977268i | 0.212007 | − | 0.977268i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.356667 | − | 0.562018i | −0.356667 | − | 0.562018i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.425779 | − | 0.904827i | −0.425779 | − | 0.904827i | ||||
\(513\) | 0.527659 | − | 0.707393i | 0.527659 | − | 0.707393i | ||||
\(514\) | −0.690667 | − | 0.976187i | −0.690667 | − | 0.976187i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.0456656 | + | 1.21074i | −0.0456656 | + | 1.21074i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.892239 | + | 0.0900010i | 0.892239 | + | 0.0900010i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.15369 | − | 1.63062i | 1.15369 | − | 1.63062i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.617860 | − | 0.786288i | \(-0.288000\pi\) | |||||||
\(524\) | 0.0871097 | − | 0.0904572i | 0.0871097 | − | 0.0904572i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.26096 | − | 0.357766i | −1.26096 | − | 0.357766i | ||||
\(529\) | −0.514440 | + | 0.857527i | −0.514440 | + | 0.857527i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.01487 | + | 0.287944i | −1.01487 | + | 0.287944i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.599770 | − | 0.435758i | −0.599770 | − | 0.435758i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.190574 | + | 0.782953i | −0.190574 | + | 0.782953i | ||||
\(537\) | −0.473951 | + | 0.362887i | −0.473951 | + | 0.362887i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.882924 | + | 1.76009i | −0.882924 | + | 1.76009i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.656586 | − | 0.754251i | \(-0.728000\pi\) | ||||
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.417379 | + | 0.455808i | −0.417379 | + | 0.455808i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.11286 | − | 0.993611i | 1.11286 | − | 0.993611i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
1.00000 | \(0\) | |||||||||
\(548\) | −0.625521 | − | 1.52366i | −0.625521 | − | 1.52366i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.701821 | − | 1.83981i | −0.701821 | − | 1.83981i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.942165 | − | 1.19900i | 0.942165 | − | 1.19900i | ||||
\(557\) | 0 | 0 | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) | ||||
0.997159 | + | 0.0753268i | \(0.0240000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0914221 | + | 0.804900i | 0.0914221 | + | 0.804900i | ||||
\(562\) | −0.698970 | + | 1.70257i | −0.698970 | + | 1.70257i | ||||
\(563\) | 0.618896 | + | 1.75354i | 0.618896 | + | 1.75354i | 0.656586 | + | 0.754251i | \(0.272000\pi\) |
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.29485 | − | 1.21594i | −1.29485 | − | 1.21594i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.164771 | + | 1.18440i | 0.164771 | + | 1.18440i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.259955 | + | 1.36273i | −0.259955 | + | 1.36273i | 0.577573 | + | 0.816339i | \(0.304000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.310138 | − | 0.462579i | 0.310138 | − | 0.462579i | ||||
\(577\) | 1.57252 | − | 0.715978i | 1.57252 | − | 0.715978i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(578\) | −0.580169 | − | 0.213001i | −0.580169 | − | 0.213001i | ||||
\(579\) | −1.08178 | − | 0.667597i | −1.08178 | − | 0.667597i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.0430028 | + | 0.683511i | 0.0430028 | + | 0.683511i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.357848 | − | 0.111320i | −0.357848 | − | 0.111320i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.11141 | − | 0.540152i | 1.11141 | − | 0.540152i | 0.212007 | − | 0.977268i | \(-0.432000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(588\) | 0.473626 | + | 0.467711i | 0.473626 | + | 0.467711i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.0357930 | + | 0.568914i | −0.0357930 | + | 0.568914i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(594\) | −0.532301 | − | 1.97006i | −0.532301 | − | 1.97006i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.778462 | − | 0.627691i | \(-0.784000\pi\) | ||||
0.778462 | + | 0.627691i | \(0.216000\pi\) | |||||||
\(600\) | −0.664798 | + | 0.0334446i | −0.664798 | + | 0.0334446i | ||||
\(601\) | −1.29485 | − | 0.670039i | −1.29485 | − | 0.670039i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.428521 | + | 0.133305i | −0.428521 | + | 0.133305i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(608\) | 0.635213 | + | 0.567148i | 0.635213 | + | 0.567148i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.337264 | − | 0.0687398i | −0.337264 | − | 0.0687398i | ||||
\(613\) | 0 | 0 | 0.920232 | − | 0.391374i | \(-0.128000\pi\) | ||||
−0.920232 | + | 0.391374i | \(0.872000\pi\) | |||||||
\(614\) | 0.796668 | − | 1.80971i | 0.796668 | − | 1.80971i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.0118298 | + | 0.0221738i | −0.0118298 | + | 0.0221738i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0246258 | + | 1.95956i | 0.0246258 | + | 1.95956i | 0.212007 | + | 0.977268i | \(0.432000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(626\) | 0.0631332 | + | 0.0411874i | 0.0631332 | + | 0.0411874i | ||||
\(627\) | 1.10736 | − | 0.139892i | 1.10736 | − | 0.139892i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0247231 | − | 0.0436624i | 0.0247231 | − | 0.0436624i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.431776 | − | 0.980821i | 0.431776 | − | 0.980821i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
0.988652 | − | 0.150226i | \(-0.0480000\pi\) | |||||||
\(642\) | 0.349173 | − | 0.148503i | 0.349173 | − | 0.148503i | ||||
\(643\) | 0.698464 | + | 0.142358i | 0.698464 | + | 0.142358i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.175160 | − | 0.496289i | 0.175160 | − | 0.496289i | ||||
\(647\) | 0 | 0 | −0.745941 | − | 0.666012i | \(-0.768000\pi\) | ||||
0.745941 | + | 0.666012i | \(0.232000\pi\) | |||||||
\(648\) | −0.132743 | − | 0.00667799i | −0.132743 | − | 0.00667799i | ||||
\(649\) | −3.22236 | − | 1.87847i | −3.22236 | − | 1.87847i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.83721 | + | 0.571524i | −1.83721 | + | 0.571524i | ||||
\(653\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.51726 | + | 1.22340i | 1.51726 | + | 1.22340i | ||||
\(657\) | −0.0493608 | − | 0.202794i | −0.0493608 | − | 0.202794i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.116762 | + | 0.0462295i | −0.116762 | + | 0.0462295i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.260842 | − | 0.965382i | \(-0.584000\pi\) | ||||
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(662\) | 0.119913 | − | 1.90596i | 0.119913 | − | 1.90596i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.744257 | + | 0.151691i | −0.744257 | + | 0.151691i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.117887 | + | 1.87376i | 0.117887 | + | 1.87376i | 0.402906 | + | 0.915241i | \(0.368000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(674\) | −0.170270 | − | 0.216686i | −0.170270 | − | 0.216686i | ||||
\(675\) | −0.577118 | − | 0.860788i | −0.577118 | − | 0.860788i | ||||
\(676\) | 0.850994 | + | 0.525175i | 0.850994 | + | 0.525175i | ||||
\(677\) | 0 | 0 | −0.938734 | − | 0.344643i | \(-0.888000\pi\) | ||||
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(678\) | −0.818236 | + | 0.372547i | −0.818236 | + | 0.372547i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.262421 | − | 1.20965i | 0.262421 | − | 1.20965i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.55403 | + | 0.905923i | −1.55403 | + | 0.905923i | −0.556876 | + | 0.830596i | \(0.688000\pi\) |
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(684\) | −0.0888663 | + | 0.465854i | −0.0888663 | + | 0.465854i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.733375 | − | 1.66593i | −0.733375 | − | 1.66593i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18107 | + | 0.574008i | 1.18107 | + | 0.574008i | 0.920232 | − | 0.391374i | \(-0.128000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.130366 | + | 1.14777i | 0.130366 | + | 1.14777i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.343329 | − | 1.15462i | 0.343329 | − | 1.15462i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.805973 | + | 1.02568i | −0.805973 | + | 1.02568i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.93873 | − | 0.344643i | 1.93873 | − | 0.344643i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.69755 | − | 0.933237i | 1.69755 | − | 0.933237i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.940521 | + | 0.839742i | −0.940521 | + | 0.839742i | ||||
\(709\) | 0 | 0 | 0.778462 | − | 0.627691i | \(-0.216000\pi\) | ||||
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.09656 | + | 0.194932i | 1.09656 | + | 0.194932i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.402095 | − | 0.801567i | 0.402095 | − | 0.801567i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.236499 | − | 0.971632i | \(-0.424000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.260308 | + | 0.0882107i | 0.260308 | + | 0.0882107i | ||||
\(723\) | 0.308408 | − | 1.14143i | 0.308408 | − | 1.14143i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.985334 | − | 1.64247i | 0.985334 | − | 1.64247i | ||||
\(727\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.359550 | − | 0.673943i | −0.359550 | − | 0.673943i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.780327 | + | 0.810314i | −0.780327 | + | 0.810314i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.39048 | − | 0.764422i | −1.39048 | − | 0.764422i | ||||
\(738\) | −0.149568 | + | 1.07512i | −0.149568 | + | 1.07512i | ||||
\(739\) | −0.0677975 | + | 1.79753i | −0.0677975 | + | 1.79753i | 0.402906 | + | 0.915241i | \(0.368000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.285677 | − | 0.311980i | −0.285677 | − | 0.311980i | ||||
\(748\) | −0.652095 | − | 1.02754i | −0.652095 | − | 1.02754i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.473626 | − | 0.467711i | 0.473626 | − | 0.467711i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(758\) | −0.925827 | − | 1.45887i | −0.925827 | − | 1.45887i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.706219 | + | 0.279612i | 0.706219 | + | 0.279612i | 0.693653 | − | 0.720309i | \(-0.256000\pi\) |
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.0917186 | − | 0.659290i | 0.0917186 | − | 0.659290i | ||||
\(769\) | −0.824962 | − | 0.453527i | −0.824962 | − | 0.453527i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0300006 | − | 0.795412i | −0.0300006 | − | 0.795412i | ||||
\(772\) | 1.90009 | + | 0.191664i | 1.90009 | + | 0.191664i | ||||
\(773\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(774\) | 0.585497 | − | 0.827540i | 0.585497 | − | 0.827540i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.506957 | − | 0.895314i | −0.506957 | − | 0.895314i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.59671 | − | 0.453027i | −1.59671 | − | 0.453027i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.947098 | − | 0.320944i | −0.947098 | − | 0.320944i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0814623 | − | 0.0187472i | 0.0814623 | − | 0.0187472i | ||||
\(787\) | −0.0533808 | + | 0.219310i | −0.0533808 | + | 0.219310i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.720049 | + | 0.827154i | 0.720049 | + | 0.827154i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.778462 | − | 0.627691i | \(-0.216000\pi\) | ||||
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(801\) | 0.221074 | + | 0.579541i | 0.221074 | + | 0.579541i | ||||
\(802\) | −0.513630 | + | 0.0913066i | −0.513630 | + | 0.0913066i | ||||
\(803\) | 0.395417 | − | 0.623077i | 0.395417 | − | 0.623077i | ||||
\(804\) | −0.391005 | + | 0.367178i | −0.391005 | + | 0.367178i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.268319 | − | 0.902360i | 0.268319 | − | 0.902360i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
0.979855 | − | 0.199710i | \(-0.0640000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.90222 | + | 0.289042i | −1.90222 | + | 0.289042i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.398463 | + | 0.102308i | −0.398463 | + | 0.102308i | ||||
\(817\) | 1.12991 | + | 1.06106i | 1.12991 | + | 1.06106i | ||||
\(818\) | −0.803523 | − | 1.82528i | −0.803523 | − | 1.82528i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(822\) | 0.205436 | − | 1.07693i | 0.205436 | − | 1.07693i | ||||
\(823\) | 0 | 0 | 0.863923 | − | 0.503623i | \(-0.168000\pi\) | ||||
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.277884 | − | 1.28093i | 0.277884 | − | 1.28093i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.932798 | − | 1.39129i | 0.932798 | − | 1.39129i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
0.920232 | − | 0.391374i | \(-0.128000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.938734 | − | 0.344643i | \(-0.888000\pi\) | ||||
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0388067 | + | 0.616814i | 0.0388067 | + | 0.616814i | ||||
\(834\) | 0.961327 | − | 0.325765i | 0.961327 | − | 0.325765i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.40439 | + | 0.916210i | −1.40439 | + | 0.916210i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.79370 | + | 0.871748i | −1.79370 | + | 0.871748i | ||||
\(839\) | 0 | 0 | −0.711536 | − | 0.702650i | \(-0.752000\pi\) | ||||
0.711536 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.850994 | − | 0.525175i | 0.850994 | − | 0.525175i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.00890 | + | 0.694952i | −1.00890 | + | 0.694952i | ||||
\(844\) | −0.00473317 | + | 0.0752316i | −0.00473317 | + | 0.0752316i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.279626 | − | 1.14882i | −0.279626 | − | 1.14882i | ||||
\(850\) | −0.481116 | − | 0.387935i | −0.481116 | − | 0.387935i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.374279 | + | 0.429952i | −0.374279 | + | 0.429952i | ||||
\(857\) | 1.66224 | + | 0.968999i | 1.66224 | + | 0.968999i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.921774 | − | 0.823004i | −0.921774 | − | 0.823004i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.979855 | − | 0.199710i | \(-0.936000\pi\) | ||||
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(864\) | 0.953682 | − | 0.405600i | 0.953682 | − | 0.405600i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | ||||
\(867\) | −0.245971 | − | 0.329755i | −0.245971 | − | 0.329755i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.282337 | − | 0.498622i | 0.282337 | − | 0.498622i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.159010 | − | 0.192210i | −0.159010 | − | 0.192210i | ||||
\(877\) | 0 | 0 | −0.837528 | − | 0.546394i | \(-0.816000\pi\) | ||||
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.14660 | − | 1.38601i | −1.14660 | − | 1.38601i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
−0.236499 | − | 0.971632i | \(-0.576000\pi\) | |||||||
\(882\) | −0.118072 | − | 0.544265i | −0.118072 | − | 0.544265i | ||||
\(883\) | 0.106815 | + | 0.359218i | 0.106815 | + | 0.359218i | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0203323 | + | 1.61791i | −0.0203323 | + | 1.61791i | ||||
\(887\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0808752 | − | 0.248908i | 0.0808752 | − | 0.248908i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.352829 | + | 0.315022i | 0.352829 | + | 0.315022i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.481140 | + | 0.280480i | 0.481140 | + | 0.280480i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3.10496 | + | 2.25588i | −3.10496 | + | 2.25588i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.860947 | − | 1.04071i | 0.860947 | − | 1.04071i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.554906 | − | 0.447433i | −0.554906 | − | 0.447433i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(908\) | 0.439782 | + | 1.80680i | 0.439782 | + | 1.80680i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.514440 | − | 0.857527i | \(-0.672000\pi\) | ||||
0.514440 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(912\) | 0.147853 | + | 0.547208i | 0.147853 | + | 0.547208i | ||||
\(913\) | 0.0939138 | − | 1.49272i | 0.0939138 | − | 1.49272i | ||||
\(914\) | −1.63408 | + | 1.12559i | −1.63408 | + | 1.12559i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.455738 | − | 0.450047i | −0.455738 | − | 0.450047i | ||||
\(919\) | 0 | 0 | 0.899405 | − | 0.437116i | \(-0.144000\pi\) | ||||
−0.899405 | + | 0.437116i | \(0.856000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.10233 | − | 0.719148i | 1.10233 | − | 0.719148i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.79956 | + | 0.819346i | −1.79956 | + | 0.819346i | −0.837528 | + | 0.546394i | \(0.816000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.849139 | − | 0.0641452i | 0.849139 | − | 0.0641452i | ||||
\(932\) | 0.415472 | − | 1.91516i | 0.415472 | − | 1.91516i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.44712 | − | 0.843597i | 1.44712 | − | 0.843597i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.247859 | − | 1.78165i | −0.247859 | − | 1.78165i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.0202163 | + | 0.0459232i | 0.0202163 | + | 0.0459232i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.719376 | − | 1.75228i | 0.719376 | − | 1.75228i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.54356 | − | 0.538443i | 3.54356 | − | 0.538443i | ||||
\(947\) | 1.21571 | + | 1.26242i | 1.21571 | + | 1.26242i | 0.954865 | + | 0.297042i | \(0.0960000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.526144 | + | 0.669571i | −0.526144 | + | 0.669571i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.42857 | − | 1.34151i | 1.42857 | − | 1.34151i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
0.850994 | − | 0.525175i | \(-0.176000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.793990 | + | 0.607930i | 0.793990 | + | 0.607930i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.312568 | − | 0.0555643i | −0.312568 | − | 0.0555643i | ||||
\(964\) | 0.332840 | + | 1.74481i | 0.332840 | + | 1.74481i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.448383 | − | 0.893841i | \(-0.352000\pi\) | ||||
−0.448383 | + | 0.893841i | \(0.648000\pi\) | |||||||
\(968\) | −0.252789 | + | 2.86634i | −0.252789 | + | 2.86634i | ||||
\(969\) | 0.278151 | − | 0.212971i | 0.278151 | − | 0.212971i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.42080 | + | 0.326973i | −1.42080 | + | 0.326973i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(972\) | 0.766851 | + | 0.557150i | 0.766851 | + | 0.557150i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.784461 | + | 1.30763i | −0.784461 | + | 1.30763i | 0.162637 | + | 0.986686i | \(0.448000\pi\) |
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(978\) | −1.23209 | − | 0.349577i | −1.23209 | − | 0.349577i | ||||
\(979\) | −0.933785 | + | 1.98439i | −0.933785 | + | 1.98439i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.121877 | + | 0.126560i | −0.121877 | + | 0.126560i | ||||
\(983\) | 0 | 0 | 0.577573 | − | 0.816339i | \(-0.304000\pi\) | ||||
−0.577573 | + | 0.816339i | \(0.696000\pi\) | |||||||
\(984\) | 0.400908 | + | 1.23387i | 0.400908 | + | 1.23387i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.988652 | − | 0.150226i | \(-0.952000\pi\) | ||||
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.760051 | − | 1.01894i | 0.760051 | − | 1.01894i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.470087 | − | 0.186121i | −0.470087 | − | 0.186121i | ||||
\(997\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(998\) | 1.00752 | + | 1.10028i | 1.00752 | + | 1.10028i | ||||
\(999\) | 0 | 0 |
(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 | 2008.1.bd.a.155.1 | ✓ | 100 | |
8.3 | odd | 2 | CM | 2008.1.bd.a.155.1 | ✓ | 100 | |
251.217 | even | 125 | inner | 2008.1.bd.a.1723.1 | yes | 100 | |
2008.1723 | odd | 250 | inner | 2008.1.bd.a.1723.1 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.bd.a.155.1 | ✓ | 100 | 1.1 | even | 1 | trivial | |
2008.1.bd.a.155.1 | ✓ | 100 | 8.3 | odd | 2 | CM | |
2008.1.bd.a.1723.1 | yes | 100 | 251.217 | even | 125 | inner | |
2008.1.bd.a.1723.1 | yes | 100 | 2008.1723 | odd | 250 | inner |