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 | 339.1 | ||
Root | \(0.984564 - 0.175023i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.339 |
Dual form | 2008.1.bd.a.1931.1 |
$q$-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 \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{83}{125}\right)\) | \(-1\) | \(-1\) |
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 | ||||
\(3\) | 0.216489 | − | 0.527330i | 0.216489 | − | 0.527330i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(4\) | 0.968583 | + | 0.248690i | 0.968583 | + | 0.248690i | ||||
\(5\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(6\) | −0.280874 | + | 0.496038i | −0.280874 | + | 0.496038i | ||||
\(7\) | 0 | 0 | 0.514440 | − | 0.857527i | \(-0.328000\pi\) | ||||
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(8\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(9\) | 0.480326 | + | 0.474328i | 0.480326 | + | 0.474328i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.891606 | + | 0.302139i | 0.891606 | + | 0.302139i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(12\) | 0.340829 | − | 0.456924i | 0.340829 | − | 0.456924i | ||||
\(13\) | 0 | 0 | 0.888136 | − | 0.459580i | \(-0.152000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(17\) | −0.562476 | − | 0.256098i | −0.562476 | − | 0.256098i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(18\) | −0.417090 | − | 0.530789i | −0.417090 | − | 0.530789i | ||||
\(19\) | 0.635213 | + | 0.567148i | 0.635213 | + | 0.567148i | 0.920232 | − | 0.391374i | \(-0.128000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.846707 | − | 0.411504i | −0.846707 | − | 0.411504i | ||||
\(23\) | 0 | 0 | 0.979855 | − | 0.199710i | \(-0.0640000\pi\) | ||||
−0.979855 | + | 0.199710i | \(0.936000\pi\) | |||||||
\(24\) | −0.395409 | + | 0.410604i | −0.395409 | + | 0.410604i | ||||
\(25\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.878680 | − | 0.373702i | 0.878680 | − | 0.373702i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.938734 | − | 0.344643i | \(-0.888000\pi\) | ||||
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) | ||||
−0.0125660 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(32\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(33\) | 0.352349 | − | 0.404761i | 0.352349 | − | 0.404761i | ||||
\(34\) | 0.525944 | + | 0.324576i | 0.525944 | + | 0.324576i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.347276 | + | 0.578879i | 0.347276 | + | 0.578879i | ||||
\(37\) | 0 | 0 | −0.162637 | − | 0.986686i | \(-0.552000\pi\) | ||||
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(38\) | −0.559121 | − | 0.642289i | −0.559121 | − | 0.642289i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.618115 | + | 1.15860i | −0.618115 | + | 1.15860i | 0.356412 | + | 0.934329i | \(0.384000\pi\) |
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.35024 | + | 0.0339424i | 1.35024 | + | 0.0339424i | 0.693653 | − | 0.720309i | \(-0.256000\pi\) |
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(44\) | 0.788455 | + | 0.514380i | 0.788455 | + | 0.514380i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(48\) | 0.443754 | − | 0.357808i | 0.443754 | − | 0.357808i | ||||
\(49\) | −0.470704 | − | 0.882291i | −0.470704 | − | 0.882291i | ||||
\(50\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(51\) | −0.256818 | + | 0.241168i | −0.256818 | + | 0.241168i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.332820 | − | 0.942991i | \(-0.608000\pi\) | ||||
0.332820 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(54\) | −0.918589 | + | 0.260627i | −0.918589 | + | 0.260627i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.436590 | − | 0.212185i | 0.436590 | − | 0.212185i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0228729 | + | 0.0104141i | −0.0228729 | + | 0.0104141i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.285019 | − | 0.958522i | \(-0.408000\pi\) | ||||
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.400301 | + | 0.357408i | −0.400301 | + | 0.357408i | ||||
\(67\) | 1.70118 | + | 0.302413i | 1.70118 | + | 0.302413i | 0.938734 | − | 0.344643i | \(-0.112000\pi\) |
0.762443 | + | 0.647056i | \(0.224000\pi\) | |||||||
\(68\) | −0.481116 | − | 0.387935i | −0.481116 | − | 0.387935i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.448383 | − | 0.893841i | \(-0.352000\pi\) | ||||
−0.448383 | + | 0.893841i | \(0.648000\pi\) | |||||||
\(72\) | −0.271984 | − | 0.617839i | −0.271984 | − | 0.617839i | ||||
\(73\) | 0.0886310 | − | 0.364131i | 0.0886310 | − | 0.364131i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.384966 | + | 0.420411i | 0.384966 | + | 0.420411i | ||||
\(76\) | 0.474212 | + | 0.707301i | 0.474212 | + | 0.707301i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.00164310 | + | 0.130746i | 0.00164310 | + | 0.130746i | ||||
\(82\) | 0.758452 | − | 1.07199i | 0.758452 | − | 1.07199i | ||||
\(83\) | −0.520201 | − | 1.92528i | −0.520201 | − | 1.92528i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.33534 | − | 0.202905i | −1.33534 | − | 0.202905i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.717769 | − | 0.609144i | −0.717769 | − | 0.609144i | ||||
\(89\) | −0.00850716 | + | 0.0748988i | −0.00850716 | + | 0.0748988i | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) |
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.485100 | + | 0.299370i | −0.485100 | + | 0.299370i | ||||
\(97\) | −1.54144 | + | 1.00562i | −1.54144 | + | 1.00562i | −0.556876 | + | 0.830596i | \(0.688000\pi\) |
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(98\) | 0.356412 | + | 0.934329i | 0.356412 | + | 0.934329i | ||||
\(99\) | 0.284949 | + | 0.568039i | 0.284949 | + | 0.568039i | ||||
\(100\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(101\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(102\) | 0.285019 | − | 0.207079i | 0.285019 | − | 0.207079i | ||||
\(103\) | 0 | 0 | 0.0878512 | − | 0.996134i | \(-0.472000\pi\) | ||||
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.452605 | − | 1.52211i | −0.452605 | − | 1.52211i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.356412 | − | 0.934329i | \(-0.384000\pi\) | |||||||
\(108\) | 0.944011 | − | 0.143442i | 0.944011 | − | 0.143442i | ||||
\(109\) | 0 | 0 | 0.556876 | − | 0.830596i | \(-0.312000\pi\) | ||||
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.304522 | − | 0.937223i | 0.304522 | − | 0.937223i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
0.979855 | − | 0.199710i | \(-0.0640000\pi\) | |||||||
\(114\) | −0.459742 | + | 0.155793i | −0.459742 | + | 0.155793i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.0239977 | − | 0.00746527i | 0.0239977 | − | 0.00746527i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0903174 | − | 0.0691528i | −0.0903174 | − | 0.0691528i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.477149 | + | 0.576774i | 0.477149 | + | 0.576774i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.260842 | − | 0.965382i | \(-0.416000\pi\) | ||||
−0.260842 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(128\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(129\) | 0.310210 | − | 0.704673i | 0.310210 | − | 0.704673i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.123051 | + | 0.0250798i | 0.123051 | + | 0.0250798i | 0.260842 | − | 0.965382i | \(-0.416000\pi\) |
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(132\) | 0.441940 | − | 0.304418i | 0.441940 | − | 0.304418i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.64986 | − | 0.513242i | −1.64986 | − | 0.513242i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.428701 | + | 0.445175i | 0.428701 | + | 0.445175i | ||||
\(137\) | 0.630426 | − | 0.213633i | 0.630426 | − | 0.213633i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.656200 | − | 0.382531i | 0.656200 | − | 0.382531i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.192404 | + | 0.647056i | 0.192404 | + | 0.647056i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.133570 | + | 0.350152i | −0.133570 | + | 0.350152i | ||||
\(147\) | −0.567160 | + | 0.0572100i | −0.567160 | + | 0.0572100i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(150\) | −0.329239 | − | 0.465345i | −0.329239 | − | 0.465345i | ||||
\(151\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(152\) | −0.381825 | − | 0.761158i | −0.381825 | − | 0.761158i | ||||
\(153\) | −0.148698 | − | 0.389809i | −0.148698 | − | 0.389809i | ||||
\(154\) | 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 | ||||||||
\(162\) | 0.0147567 | − | 0.129921i | 0.0147567 | − | 0.129921i | ||||
\(163\) | 1.43146 | + | 1.21483i | 1.43146 | + | 1.21483i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(164\) | −0.886828 | + | 0.968481i | −0.886828 | + | 0.968481i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.274798 | + | 1.97529i | 0.274798 | + | 1.97529i | ||||
\(167\) | 0 | 0 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
0.379779 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.577573 | − | 0.816339i | 0.577573 | − | 0.816339i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0360951 | + | 0.573715i | 0.0360951 | + | 0.573715i | ||||
\(172\) | 1.29938 | + | 0.368667i | 1.29938 | + | 0.368667i | ||||
\(173\) | 0 | 0 | 0.0376902 | − | 0.999289i | \(-0.488000\pi\) | ||||
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.635764 | + | 0.694301i | 0.635764 | + | 0.694301i | ||||
\(177\) | 0.000539959 | 0.0143161i | 0.000539959 | 0.0143161i | ||||||
\(178\) | 0.0178274 | − | 0.0732420i | 0.0178274 | − | 0.0732420i | ||||
\(179\) | 0.131055 | + | 0.297704i | 0.131055 | + | 0.297704i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.994951 | − | 0.100362i | \(-0.968000\pi\) | ||||
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.424130 | − | 0.398285i | −0.424130 | − | 0.398285i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) | ||||
0.997159 | + | 0.0753268i | \(0.0240000\pi\) | |||||||
\(192\) | 0.518795 | − | 0.236210i | 0.518795 | − | 0.236210i | ||||
\(193\) | −1.02593 | − | 0.530882i | −1.02593 | − | 0.530882i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(194\) | 1.65532 | − | 0.804496i | 1.65532 | − | 0.804496i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.236499 | − | 0.971632i | −0.236499 | − | 0.971632i | ||||
\(197\) | 0 | 0 | 0.962028 | − | 0.272952i | \(-0.0880000\pi\) | ||||
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(198\) | −0.211508 | − | 0.599273i | −0.211508 | − | 0.599273i | ||||
\(199\) | 0 | 0 | 0.974527 | − | 0.224271i | \(-0.0720000\pi\) | ||||
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(200\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(201\) | 0.527757 | − | 0.831612i | 0.527757 | − | 0.831612i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.308726 | + | 0.169723i | −0.308726 | + | 0.169723i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.395002 | + | 0.697595i | 0.395002 | + | 0.697595i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.231551 | − | 1.21383i | −0.231551 | − | 1.21383i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
0.656586 | − | 0.754251i | \(-0.272000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.258265 | + | 1.56684i | 0.258265 | + | 1.56684i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.954545 | + | 0.0239954i | −0.954545 | + | 0.0239954i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.172830 | − | 0.125568i | −0.172830 | − | 0.125568i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.711536 | − | 0.702650i | \(-0.248000\pi\) | ||||
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.633698 | + | 0.232653i | −0.633698 | + | 0.232653i | ||||
\(226\) | −0.419586 | + | 0.891666i | −0.419586 | + | 0.891666i | ||||
\(227\) | −1.28989 | + | 1.33945i | −1.28989 | + | 1.33945i | −0.379779 | + | 0.925077i | \(0.624000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(228\) | 0.475642 | − | 0.0969435i | 0.475642 | − | 0.0969435i | ||||
\(229\) | 0 | 0 | −0.899405 | − | 0.437116i | \(-0.856000\pi\) | ||||
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.139459 | + | 0.177475i | 0.139459 | + | 0.177475i | 0.850994 | − | 0.525175i | \(-0.176000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.0247441 | + | 0.00439869i | −0.0247441 | + | 0.00439869i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.381825 | − | 0.811419i | −0.381825 | − | 0.811419i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
0.617860 | − | 0.786288i | \(-0.288000\pi\) | |||||||
\(242\) | 0.0809381 | + | 0.0799273i | 0.0809381 | + | 0.0799273i | ||||
\(243\) | 0.957096 | + | 0.378941i | 0.957096 | + | 0.378941i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.401098 | − | 0.632029i | −0.401098 | − | 0.632029i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.12787 | − | 0.142484i | −1.12787 | − | 0.142484i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.514440 | − | 0.857527i | −0.514440 | − | 0.857527i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(257\) | −0.933322 | + | 1.64830i | −0.933322 | + | 1.64830i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(258\) | −0.396083 | + | 0.660237i | −0.396083 | + | 0.660237i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.118938 | − | 0.0403044i | −0.118938 | − | 0.0403044i | ||||
\(263\) | 0 | 0 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(264\) | −0.476608 | + | 0.246628i | −0.476608 | + | 0.246628i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0376546 | + | 0.0207008i | 0.0376546 | + | 0.0207008i | ||||
\(268\) | 1.57252 | + | 0.715978i | 1.57252 | + | 0.715978i | ||||
\(269\) | 0 | 0 | −0.617860 | − | 0.786288i | \(-0.712000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | −0.369526 | − | 0.495396i | −0.369526 | − | 0.495396i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.652230 | + | 0.132935i | −0.652230 | + | 0.132935i | ||||
\(275\) | −0.653011 | + | 0.678105i | −0.653011 | + | 0.678105i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(278\) | −0.698970 | + | 0.297271i | −0.698970 | + | 0.297271i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.94659 | + | 0.0979289i | −1.94659 | + | 0.0979289i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.725499 | − | 0.527106i | −0.725499 | − | 0.527106i | 0.162637 | − | 0.986686i | \(-0.448000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.109789 | − | 0.666068i | −0.109789 | − | 0.666068i | ||||
\(289\) | −0.405792 | − | 0.466153i | −0.405792 | − | 0.466153i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.196588 | + | 1.03055i | 0.196588 | + | 1.03055i | ||||
\(292\) | 0.176402 | − | 0.330650i | 0.176402 | − | 0.330650i | ||||
\(293\) | 0 | 0 | −0.492727 | − | 0.870184i | \(-0.664000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(294\) | 0.569859 | + | 0.0143251i | 0.569859 | + | 0.0143251i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.896346 | − | 0.0677113i | 0.896346 | − | 0.0677113i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.268319 | + | 0.502940i | 0.268319 | + | 0.502940i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.283415 | + | 0.803012i | 0.283415 | + | 0.803012i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.0986692 | + | 0.405372i | 0.0986692 | + | 0.405372i | ||||
\(307\) | −1.41034 | + | 1.07985i | −1.41034 | + | 1.07985i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) | ||||
0.997159 | + | 0.0753268i | \(0.0240000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.170270 | + | 1.22393i | −0.170270 | + | 1.22393i | 0.693653 | + | 0.720309i | \(0.256000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.745941 | − | 0.666012i | \(-0.232000\pi\) | ||||
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.900640 | − | 0.0908485i | −0.900640 | − | 0.0908485i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.212046 | − | 0.481684i | −0.212046 | − | 0.481684i | ||||
\(324\) | −0.0309239 | + | 0.127047i | −0.0309239 | + | 0.127047i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.26792 | − | 1.38466i | −1.26792 | − | 1.38466i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.00122 | − | 0.849695i | 1.00122 | − | 0.849695i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0725322 | + | 1.15287i | 0.0725322 | + | 1.15287i | 0.850994 | + | 0.525175i | \(0.176000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(332\) | −0.0250607 | − | 1.99416i | −0.0250607 | − | 1.99416i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.94678 | − | 0.295814i | −1.94678 | − | 0.295814i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(338\) | −0.675333 | + | 0.737513i | −0.675333 | + | 0.737513i | ||||
\(339\) | −0.428300 | − | 0.363482i | −0.428300 | − | 0.363482i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.0360951 | − | 0.573715i | 0.0360951 | − | 0.573715i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.24293 | − | 0.528615i | −1.24293 | − | 0.528615i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.01763 | + | 0.628009i | −1.01763 | + | 0.628009i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.356412 | − | 0.934329i | \(-0.616000\pi\) | ||||
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.543731 | − | 0.768508i | −0.543731 | − | 0.768508i | ||||
\(353\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(354\) | 0.00125858 | − | 0.0142709i | 0.00125858 | − | 0.0142709i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.0268665 | + | 0.0704301i | −0.0268665 | + | 0.0704301i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0927094 | − | 0.311783i | −0.0927094 | − | 0.311783i | ||||
\(359\) | 0 | 0 | 0.988652 | − | 0.150226i | \(-0.0480000\pi\) | ||||
−0.988652 | + | 0.150226i | \(0.952000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0310183 | − | 0.273092i | −0.0310183 | − | 0.273092i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0560190 | + | 0.0326562i | −0.0560190 | + | 0.0326562i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.823533 | − | 0.567269i | \(-0.808000\pi\) | ||||
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.846453 | + | 0.263317i | −0.846453 | + | 0.263317i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.402906 | − | 0.915241i | \(-0.368000\pi\) | ||||
−0.402906 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(374\) | 0.370867 | + | 0.448302i | 0.370867 | + | 0.448302i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.26841 | − | 1.53325i | −1.26841 | − | 1.53325i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
−0.556876 | − | 0.830596i | \(-0.688000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.823533 | − | 0.567269i | \(-0.192000\pi\) | ||||
−0.823533 | + | 0.567269i | \(0.808000\pi\) | |||||||
\(384\) | −0.544310 | + | 0.169325i | −0.544310 | + | 0.169325i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.951300 | + | 0.655278i | 0.951300 | + | 0.655278i | ||||
\(387\) | 0.632456 | + | 0.656760i | 0.632456 | + | 0.656760i | ||||
\(388\) | −1.74310 | + | 0.590685i | −1.74310 | + | 0.590685i | ||||
\(389\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.112856 | + | 0.993611i | 0.112856 | + | 0.993611i | ||||
\(393\) | 0.0398645 | − | 0.0594591i | 0.0398645 | − | 0.0594591i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.134731 | + | 0.621057i | 0.134731 | + | 0.621057i | ||||
\(397\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(401\) | 1.15369 | + | 1.63062i | 1.15369 | + | 1.63062i | 0.617860 | + | 0.786288i | \(0.288000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(402\) | −0.627824 | + | 0.758909i | −0.627824 | + | 0.758909i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.327563 | − | 0.129691i | 0.327563 | − | 0.129691i | ||||
\(409\) | −0.435268 | − | 0.185119i | −0.435268 | − | 0.185119i | 0.162637 | − | 0.986686i | \(-0.448000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0238252 | − | 0.378691i | 0.0238252 | − | 0.378691i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0596601 | − | 0.428847i | −0.0596601 | − | 0.428847i | ||||
\(418\) | −0.304455 | − | 0.741601i | −0.304455 | − | 0.741601i | ||||
\(419\) | −0.123378 | − | 0.456624i | −0.123378 | − | 0.456624i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(422\) | 0.0775915 | + | 1.23328i | 0.0775915 | + | 1.23328i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.471215 | − | 0.399903i | 0.471215 | − | 0.399903i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.0598513 | − | 1.58685i | −0.0598513 | − | 1.58685i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.448383 | − | 0.893841i | \(-0.352000\pi\) | ||||
−0.448383 | + | 0.893841i | \(0.648000\pi\) | |||||||
\(432\) | 0.950025 | + | 0.0958300i | 0.950025 | + | 0.0958300i | ||||
\(433\) | 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 | ||||||||
\(438\) | 0.155729 | + | 0.146239i | 0.155729 | + | 0.146239i | ||||
\(439\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.192404 | − | 0.647056i | 0.192404 | − | 0.647056i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.47258 | − | 0.670474i | 1.47258 | − | 0.670474i | 0.492727 | − | 0.870184i | \(-0.336000\pi\) |
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.566455 | − | 1.60496i | −0.566455 | − | 1.60496i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
0.212007 | − | 0.977268i | \(-0.432000\pi\) | |||||||
\(450\) | 0.657860 | − | 0.151395i | 0.657860 | − | 0.151395i | ||||
\(451\) | −0.901173 | + | 0.846258i | −0.901173 | + | 0.846258i | ||||
\(452\) | 0.528033 | − | 0.832047i | 0.528033 | − | 0.832047i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.44759 | − | 1.16723i | 1.44759 | − | 1.16723i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.484042 | + | 0.0365652i | −0.484042 | + | 0.0365652i | ||||
\(457\) | −0.420671 | + | 1.93912i | −0.420671 | + | 1.93912i | −0.0878512 | + | 0.996134i | \(0.528000\pi\) |
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.589941 | − | 0.0148300i | −0.589941 | − | 0.0148300i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.470704 | − | 0.882291i | \(-0.344000\pi\) | ||||
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.116116 | − | 0.193555i | −0.116116 | − | 0.193555i | ||||
\(467\) | −0.521518 | + | 0.0131099i | −0.521518 | + | 0.0131099i | −0.285019 | − | 0.958522i | \(-0.592000\pi\) |
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0251003 | − | 0.00126274i | 0.0251003 | − | 0.00126274i | ||||
\(473\) | 1.19363 | + | 0.438223i | 1.19363 | + | 0.438223i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.783631 | + | 0.333278i | −0.783631 | + | 0.333278i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.979855 | − | 0.199710i | \(-0.0640000\pi\) | ||||
−0.979855 | + | 0.199710i | \(0.936000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.277116 | + | 0.852876i | 0.277116 | + | 0.852876i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.0702823 | − | 0.0894413i | −0.0702823 | − | 0.0894413i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.902055 | − | 0.495909i | −0.902055 | − | 0.495909i | ||||
\(487\) | 0 | 0 | 0.984564 | − | 0.175023i | \(-0.0560000\pi\) | ||||
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.950509 | − | 0.491856i | 0.950509 | − | 0.491856i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.974450 | + | 0.330212i | 0.974450 | + | 0.330212i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(492\) | 0.318721 | + | 0.677316i | 0.318721 | + | 0.677316i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.10112 | + | 0.282720i | 1.10112 | + | 0.282720i | ||||
\(499\) | −0.161032 | + | 0.392246i | −0.161032 | + | 0.392246i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.402906 | + | 0.915241i | 0.402906 | + | 0.915241i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.305442 | − | 0.481299i | −0.305442 | − | 0.481299i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.514440 | − | 0.857527i | \(-0.328000\pi\) | ||||
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.425779 | − | 0.904827i | −0.425779 | − | 0.904827i | ||||
\(513\) | 0.770093 | + | 0.260962i | 0.770093 | + | 0.260962i | ||||
\(514\) | 1.13255 | − | 1.51833i | 1.13255 | − | 1.51833i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.475710 | − | 0.605388i | 0.475710 | − | 0.605388i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.242636 | − | 0.216637i | −0.242636 | − | 0.216637i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.426201 | − | 0.571376i | −0.426201 | − | 0.571376i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(524\) | 0.112948 | + | 0.0548935i | 0.112948 | + | 0.0548935i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.503761 | − | 0.184949i | 0.503761 | − | 0.184949i | ||||
\(529\) | 0.920232 | − | 0.391374i | 0.920232 | − | 0.391374i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0159261 | − | 0.00584706i | −0.0159261 | − | 0.00584706i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0347632 | − | 0.0252570i | −0.0347632 | − | 0.0252570i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.47039 | − | 0.907421i | −1.47039 | − | 0.907421i | ||||
\(537\) | 0.185360 | − | 0.00465959i | 0.185360 | − | 0.00465959i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.153108 | − | 0.928874i | −0.153108 | − | 0.928874i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.304522 | + | 0.537803i | 0.304522 | + | 0.537803i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0898940 | − | 0.414376i | 0.0898940 | − | 0.414376i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
1.00000 | \(0\) | |||||||||
\(548\) | 0.663748 | − | 0.0501405i | 0.663748 | − | 0.0501405i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.732851 | − | 0.590914i | 0.732851 | − | 0.590914i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.730716 | − | 0.207323i | 0.730716 | − | 0.207323i | ||||
\(557\) | 0 | 0 | −0.236499 | − | 0.971632i | \(-0.576000\pi\) | ||||
0.236499 | + | 0.971632i | \(0.424000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.301847 | + | 0.137432i | −0.301847 | + | 0.137432i | ||||
\(562\) | 1.94352 | + | 0.146816i | 1.94352 | + | 0.146816i | ||||
\(563\) | 0.530008 | − | 1.78242i | 0.530008 | − | 1.78242i | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) |
0.617860 | − | 0.786288i | \(-0.288000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.653715 | + | 0.613879i | 0.653715 | + | 0.613879i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.86496 | + | 0.331528i | 1.86496 | + | 0.331528i | 0.988652 | − | 0.150226i | \(-0.0480000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.337063 | + | 1.76695i | −0.337063 | + | 1.76695i | 0.260842 | + | 0.965382i | \(0.416000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0254430 | + | 0.674576i | 0.0254430 | + | 0.674576i | ||||
\(577\) | −1.34385 | − | 1.46758i | −1.34385 | − | 1.46758i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
−0.597905 | − | 0.801567i | \(-0.704000\pi\) | |||||||
\(578\) | 0.344168 | + | 0.513336i | 0.344168 | + | 0.513336i | ||||
\(579\) | −0.502051 | + | 0.426072i | −0.502051 | + | 0.426072i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.0658757 | − | 1.04706i | −0.0658757 | − | 1.04706i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.216453 | + | 0.305933i | −0.216453 | + | 0.305933i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.265116 | + | 1.90570i | 0.265116 | + | 1.90570i | 0.402906 | + | 0.915241i | \(0.368000\pi\) |
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(588\) | −0.563570 | − | 0.0856344i | −0.563570 | − | 0.0856344i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.0997101 | − | 1.58485i | 0.0997101 | − | 1.58485i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
0.656586 | − | 0.754251i | \(-0.272000\pi\) | |||||||
\(594\) | −0.897765 | − | 0.0451646i | −0.897765 | − | 0.0451646i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.837528 | − | 0.546394i | \(-0.184000\pi\) | ||||
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(600\) | −0.203169 | − | 0.532603i | −0.203169 | − | 0.532603i | ||||
\(601\) | 0.653715 | + | 1.30316i | 0.653715 | + | 1.30316i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.673677 | + | 0.952173i | 0.673677 | + | 0.952173i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(608\) | −0.180536 | − | 0.832201i | −0.180536 | − | 0.832201i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.0470845 | − | 0.414542i | −0.0470845 | − | 0.414542i | ||||
\(613\) | 0 | 0 | −0.974527 | − | 0.224271i | \(-0.928000\pi\) | ||||
0.974527 | + | 0.224271i | \(0.0720000\pi\) | |||||||
\(614\) | 1.53456 | − | 0.894572i | 1.53456 | − | 0.894572i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.32469 | + | 1.37560i | 1.32469 | + | 1.37560i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.215525 | + | 0.0670461i | 0.215525 | + | 0.0670461i | 0.402906 | − | 0.915241i | \(-0.368000\pi\) |
−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 | ||||
\(626\) | 0.322327 | − | 1.19294i | 0.322327 | − | 1.19294i | ||||
\(627\) | 0.453376 | − | 0.0572747i | 0.453376 | − | 0.0572747i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.402906 | − | 0.915241i | \(-0.368000\pi\) | ||||
−0.402906 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.690217 | − | 0.140677i | −0.690217 | − | 0.140677i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.925827 | + | 0.539710i | −0.925827 | + | 0.539710i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(642\) | 0.882152 | + | 0.203012i | 0.882152 | + | 0.203012i | ||||
\(643\) | −0.175709 | − | 1.54698i | −0.175709 | − | 1.54698i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.150003 | + | 0.504462i | 0.150003 | + | 0.504462i | ||||
\(647\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(648\) | 0.0466033 | − | 0.122170i | 0.0466033 | − | 0.122170i | ||||
\(649\) | −0.0235401 | + | 0.00237451i | −0.0235401 | + | 0.00237451i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.08437 | + | 1.53265i | 1.08437 | + | 1.53265i | ||||
\(653\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.09982 | + | 0.717509i | −1.09982 | + | 0.717509i | ||||
\(657\) | 0.215290 | − | 0.132862i | 0.215290 | − | 0.132862i | ||||
\(658\) | 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 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(662\) | 0.0725322 | − | 1.15287i | 0.0725322 | − | 1.15287i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.225071 | + | 1.98158i | −0.225071 | + | 1.98158i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0699330 | − | 1.11155i | −0.0699330 | − | 1.11155i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.793990 | − | 0.607930i | \(-0.208000\pi\) | |||||||
\(674\) | 1.89436 | + | 0.537477i | 1.89436 | + | 0.537477i | ||||
\(675\) | −0.0359883 | + | 0.954168i | −0.0359883 | + | 0.954168i | ||||
\(676\) | 0.762443 | − | 0.647056i | 0.762443 | − | 0.647056i | ||||
\(677\) | 0 | 0 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
0.556876 | + | 0.830596i | \(0.312000\pi\) | |||||||
\(678\) | 0.379366 | + | 0.414296i | 0.379366 | + | 0.414296i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.427088 | + | 0.970171i | 0.427088 | + | 0.970171i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.274189 | − | 0.0276577i | −0.274189 | − | 0.0276577i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(684\) | −0.107716 | + | 0.564668i | −0.107716 | + | 0.564668i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.16687 | + | 0.680227i | 1.16687 | + | 0.680227i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0242101 | − | 0.174026i | 0.0242101 | − | 0.174026i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.08831 | − | 0.495514i | 1.08831 | − | 0.495514i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.644390 | − | 0.493387i | 0.644390 | − | 0.493387i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.123779 | − | 0.0351194i | 0.123779 | − | 0.0351194i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.974527 | − | 0.224271i | \(-0.0720000\pi\) | ||||
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.443124 | + | 0.830596i | 0.443124 | + | 0.830596i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.69755 | − | 0.933237i | 1.69755 | − | 0.933237i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.00303727 | + | 0.0140006i | −0.00303727 | + | 0.0140006i | ||||
\(709\) | 0 | 0 | −0.837528 | − | 0.546394i | \(-0.816000\pi\) | ||||
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.0354818 | − | 0.0665074i | 0.0354818 | − | 0.0665074i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.0529017 | + | 0.320944i | 0.0529017 | + | 0.320944i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.850994 | − | 0.525175i | \(-0.824000\pi\) | ||||
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.00345375 | + | 0.274826i | −0.00345375 | + | 0.274826i | ||||
\(723\) | −0.510546 | + | 0.0256845i | −0.510546 | + | 0.0256845i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0596702 | − | 0.0253777i | 0.0596702 | − | 0.0253777i | ||||
\(727\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.316327 | − | 0.328483i | 0.316327 | − | 0.328483i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.750785 | − | 0.364886i | −0.750785 | − | 0.364886i | ||||
\(732\) | 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 | ||||||||
\(737\) | 1.42541 | + | 0.783625i | 1.42541 | + | 0.783625i | ||||
\(738\) | 0.872781 | − | 0.155152i | 0.872781 | − | 0.155152i | ||||
\(739\) | −0.170270 | + | 0.216686i | −0.170270 | + | 0.216686i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(740\) | 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 | ||||||||
\(747\) | 0.663347 | − | 1.17151i | 0.663347 | − | 1.17151i | ||||
\(748\) | −0.311756 | − | 0.491249i | −0.311756 | − | 0.491249i | ||||
\(749\) | 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 | ||||||||
\(753\) | −0.563570 | + | 0.0856344i | −0.563570 | + | 0.0856344i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(758\) | 1.06624 | + | 1.68013i | 1.06624 | + | 1.68013i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.85427 | + | 0.734157i | 1.85427 | + | 0.734157i | 0.954865 | + | 0.297042i | \(0.0960000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.561240 | − | 0.0997699i | 0.561240 | − | 0.0997699i | ||||
\(769\) | 1.21571 | + | 0.668340i | 1.21571 | + | 0.668340i | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.667143 | + | 0.849007i | 0.667143 | + | 0.849007i | ||||
\(772\) | −0.861670 | − | 0.769341i | −0.861670 | − | 0.769341i | ||||
\(773\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(774\) | −0.545155 | − | 0.730849i | −0.545155 | − | 0.730849i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.80339 | − | 0.367559i | 1.80339 | − | 0.367559i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.04973 | + | 0.385394i | −1.04973 | + | 0.385394i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0125660 | − | 0.999921i | 0.0125660 | − | 0.999921i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.0470024 | + | 0.0539939i | −0.0470024 | + | 0.0539939i | ||||
\(787\) | −1.54899 | − | 0.955929i | −1.54899 | − | 0.955929i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.556876 | − | 0.830596i | \(-0.688000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.0558297 | − | 0.633046i | −0.0558297 | − | 0.633046i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.837528 | − | 0.546394i | \(-0.816000\pi\) | ||||
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(801\) | −0.0396128 | + | 0.0319407i | −0.0396128 | + | 0.0319407i | ||||
\(802\) | −0.940219 | − | 1.76235i | −0.940219 | − | 1.76235i | ||||
\(803\) | 0.189042 | − | 0.297883i | 0.189042 | − | 0.297883i | ||||
\(804\) | 0.717990 | − | 0.674237i | 0.717990 | − | 0.674237i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.10151 | − | 0.843386i | 1.10151 | − | 0.843386i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.66745 | − | 0.862846i | −1.66745 | − | 0.862846i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.675333 | − | 0.737513i | \(-0.736000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.341235 | + | 0.0876142i | −0.341235 | + | 0.0876142i | ||||
\(817\) | 0.838439 | + | 0.787346i | 0.838439 | + | 0.787346i | ||||
\(818\) | 0.408634 | + | 0.238213i | 0.408634 | + | 0.238213i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.778462 | − | 0.627691i | \(-0.784000\pi\) | ||||
0.778462 | + | 0.627691i | \(0.216000\pi\) | |||||||
\(822\) | −0.0711000 | + | 0.372719i | −0.0711000 | + | 0.372719i | ||||
\(823\) | 0 | 0 | −0.994951 | − | 0.100362i | \(-0.968000\pi\) | ||||
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.216215 | + | 0.491154i | 0.216215 | + | 0.491154i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.0196623 | − | 0.521312i | −0.0196623 | − | 0.521312i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.954865 | − | 0.297042i | \(-0.0960000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
0.556876 | + | 0.830596i | \(0.312000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0388067 | + | 0.616814i | 0.0388067 | + | 0.616814i | ||||
\(834\) | 0.00544081 | + | 0.432943i | 0.00544081 | + | 0.432943i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.209107 | + | 0.773912i | 0.209107 | + | 0.773912i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.0651745 | + | 0.468486i | 0.0651745 | + | 0.468486i | ||||
\(839\) | 0 | 0 | −0.988652 | − | 0.150226i | \(-0.952000\pi\) | ||||
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.762443 | + | 0.647056i | 0.762443 | + | 0.647056i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.369774 | + | 1.04770i | −0.369774 | + | 1.04770i | ||||
\(844\) | 0.0775915 | − | 1.23328i | 0.0775915 | − | 1.23328i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.435021 | + | 0.268465i | −0.435021 | + | 0.268465i | ||||
\(850\) | −0.517621 | + | 0.337690i | −0.517621 | + | 0.337690i | ||||
\(851\) | 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 | ||||||||
\(856\) | −0.139506 | + | 1.58184i | −0.139506 | + | 1.58184i | ||||
\(857\) | 1.86799 | − | 0.188426i | 1.86799 | − | 0.188426i | 0.899405 | − | 0.437116i | \(-0.144000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.407913 | − | 1.88032i | −0.407913 | − | 1.88032i | −0.470704 | − | 0.882291i | \(-0.656000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.112856 | − | 0.993611i | \(-0.536000\pi\) | ||||
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(864\) | −0.930524 | − | 0.214144i | −0.930524 | − | 0.214144i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | ||||
\(867\) | −0.333666 | + | 0.113069i | −0.333666 | + | 0.113069i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.21739 | − | 0.248123i | −1.21739 | − | 0.248123i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.136172 | − | 0.164604i | −0.136172 | − | 0.164604i | ||||
\(877\) | 0 | 0 | 0.260842 | − | 0.965382i | \(-0.416000\pi\) | ||||
−0.260842 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.175662 | + | 0.212338i | 0.175662 | + | 0.212338i | 0.850994 | − | 0.525175i | \(-0.176000\pi\) |
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(882\) | −0.271984 | + | 0.617839i | −0.271984 | + | 0.617839i | ||||
\(883\) | −0.297558 | − | 0.227830i | −0.297558 | − | 0.227830i | 0.448383 | − | 0.893841i | \(-0.352000\pi\) |
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.54500 | + | 0.480623i | −1.54500 | + | 0.480623i | ||||
\(887\) | 0 | 0 | −0.954865 | − | 0.297042i | \(-0.904000\pi\) | ||||
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0380386 | + | 0.117071i | −0.0380386 | + | 0.117071i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.360834 | + | 1.66330i | 0.360834 | + | 1.66330i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.671648 | + | 0.0677498i | −0.671648 | + | 0.0677498i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.00013 | − | 0.726638i | 1.00013 | − | 0.726638i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.628152 | + | 0.759306i | −0.628152 | + | 0.759306i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.30397 | − | 0.850695i | 1.30397 | − | 0.850695i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(908\) | −1.58247 | + | 0.976590i | −1.58247 | + | 0.976590i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(912\) | 0.484808 | + | 0.0243897i | 0.484808 | + | 0.0243897i | ||||
\(913\) | 0.117887 | − | 1.87376i | 0.117887 | − | 1.87376i | ||||
\(914\) | 0.660390 | − | 1.87111i | 0.660390 | − | 1.87111i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.583431 | + | 0.0886523i | 0.583431 | + | 0.0886523i | ||||
\(919\) | 0 | 0 | −0.137790 | − | 0.990461i | \(-0.544000\pi\) | ||||
0.137790 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.264113 | + | 0.977491i | 0.264113 | + | 0.977491i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.19958 | + | 1.31002i | 1.19958 | + | 1.31002i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.201393 | − | 0.827401i | 0.201393 | − | 0.827401i | ||||
\(932\) | 0.0909411 | + | 0.206582i | 0.0909411 | + | 0.206582i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.519049 | + | 0.0523570i | 0.519049 | + | 0.0523570i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.271327 | + | 0.0482330i | 0.271327 | + | 0.0482330i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.608554 | + | 0.354756i | 0.608554 | + | 0.354756i | ||||
\(940\) | 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 | ||||||||
\(944\) | −0.0250607 | − | 0.00189312i | −0.0250607 | − | 0.00189312i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.12929 | − | 0.584368i | −1.12929 | − | 0.584368i | ||||
\(947\) | 1.57631 | − | 0.766095i | 1.57631 | − | 0.766095i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.819223 | − | 0.232435i | 0.819223 | − | 0.232435i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.164538 | − | 0.154511i | 0.164538 | − | 0.154511i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
0.762443 | + | 0.647056i | \(0.224000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.999684 | − | 0.0251301i | −0.999684 | − | 0.0251301i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.504583 | − | 0.945795i | 0.504583 | − | 0.945795i | ||||
\(964\) | −0.168037 | − | 0.880882i | −0.168037 | − | 0.880882i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.162637 | − | 0.986686i | \(-0.552000\pi\) | ||||
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(968\) | 0.0585181 | + | 0.0975447i | 0.0585181 | + | 0.0975447i | ||||
\(969\) | −0.299912 | + | 0.00753920i | −0.299912 | + | 0.00753920i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.957261 | − | 1.09965i | 0.957261 | − | 1.09965i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.994951 | − | 0.100362i | \(-0.0320000\pi\) | |||||||
\(972\) | 0.832788 | + | 0.605056i | 0.832788 | + | 0.605056i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.698970 | + | 0.297271i | −0.698970 | + | 0.297271i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(978\) | −1.00466 | + | 0.368847i | −1.00466 | + | 0.368847i | ||||
\(979\) | −0.0302149 | + | 0.0642098i | −0.0302149 | + | 0.0642098i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.925379 | − | 0.449739i | −0.925379 | − | 0.449739i | ||||
\(983\) | 0 | 0 | −0.597905 | − | 0.801567i | \(-0.704000\pi\) | ||||
0.597905 | + | 0.801567i | \(0.296000\pi\) | |||||||
\(984\) | −0.231317 | − | 0.711921i | −0.231317 | − | 0.711921i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.888136 | − | 0.459580i | \(-0.152000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.623643 | + | 0.211334i | 0.623643 | + | 0.211334i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.05701 | − | 0.418498i | −1.05701 | − | 0.418498i | ||||
\(997\) | 0 | 0 | 0.514440 | − | 0.857527i | \(-0.328000\pi\) | ||||
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(998\) | 0.208923 | − | 0.368970i | 0.208923 | − | 0.368970i | ||||
\(999\) | 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.339.1 | ✓ | 100 | |
8.3 | odd | 2 | CM | 2008.1.bd.a.339.1 | ✓ | 100 | |
251.174 | even | 125 | inner | 2008.1.bd.a.1931.1 | yes | 100 | |
2008.1931 | odd | 250 | inner | 2008.1.bd.a.1931.1 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.bd.a.339.1 | ✓ | 100 | 1.1 | even | 1 | trivial | |
2008.1.bd.a.339.1 | ✓ | 100 | 8.3 | odd | 2 | CM | |
2008.1.bd.a.1931.1 | yes | 100 | 251.174 | even | 125 | inner | |
2008.1.bd.a.1931.1 | yes | 100 | 2008.1931 | odd | 250 | inner |