Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(1,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2925.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(23.3562425912\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1821184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 8x^{3} + 13x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.47948\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.47948 | −1.75326 | −0.876630 | − | 0.481165i | \(-0.840214\pi\) | ||||
−0.876630 | + | 0.481165i | \(0.840214\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.14785 | 2.07392 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.949959 | −0.359051 | −0.179525 | − | 0.983753i | \(-0.557456\pi\) | ||||
−0.179525 | + | 0.983753i | \(0.557456\pi\) | |||||||
\(8\) | −5.32555 | −1.88287 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.89611 | −1.17472 | −0.587360 | − | 0.809326i | \(-0.699833\pi\) | ||||
−0.587360 | + | 0.809326i | \(0.699833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 2.35541 | 0.629509 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.90893 | 1.22723 | ||||||||
\(17\) | −5.90893 | −1.43313 | −0.716563 | − | 0.697523i | \(-0.754286\pi\) | ||||
−0.716563 | + | 0.697523i | \(0.754286\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.35541 | 1.45803 | 0.729015 | − | 0.684497i | \(-0.239978\pi\) | ||||
0.729015 | + | 0.684497i | \(0.239978\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.66033 | 2.05959 | ||||||||
\(23\) | 3.30537 | 0.689217 | 0.344608 | − | 0.938747i | \(-0.388012\pi\) | ||||
0.344608 | + | 0.938747i | \(0.388012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.47948 | 0.486267 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.94028 | −0.744643 | ||||||||
\(29\) | 4.29569 | 0.797690 | 0.398845 | − | 0.917018i | \(-0.369411\pi\) | ||||
0.398845 | + | 0.917018i | \(0.369411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.56253 | 1.35827 | 0.679135 | − | 0.734013i | \(-0.262355\pi\) | ||||
0.679135 | + | 0.734013i | \(0.262355\pi\) | |||||||
\(32\) | −1.52052 | −0.268792 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14.6511 | 2.51264 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.30537 | 0.214601 | 0.107301 | − | 0.994227i | \(-0.465779\pi\) | ||||
0.107301 | + | 0.994227i | \(0.465779\pi\) | |||||||
\(38\) | −15.7581 | −2.55631 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.75499 | 1.05495 | 0.527476 | − | 0.849570i | \(-0.323138\pi\) | ||||
0.527476 | + | 0.849570i | \(0.323138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.29569 | −1.26508 | −0.632540 | − | 0.774527i | \(-0.717988\pi\) | ||||
−0.632540 | + | 0.774527i | \(0.717988\pi\) | |||||||
\(44\) | −16.1604 | −2.43628 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.19561 | −1.20838 | ||||||||
\(47\) | 0.0128228 | 0.00187040 | 0.000935200 | − | 1.00000i | \(-0.499702\pi\) | ||||
0.000935200 | 1.00000i | \(0.499702\pi\) | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.09758 | −0.871083 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.14785 | −0.575203 | ||||||||
\(53\) | 2.51249 | 0.345117 | 0.172559 | − | 0.984999i | \(-0.444797\pi\) | ||||
0.172559 | + | 0.984999i | \(0.444797\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.05905 | 0.676044 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.6511 | −1.39856 | ||||||||
\(59\) | 6.30851 | 0.821298 | 0.410649 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410649 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.61324 | 0.206554 | 0.103277 | − | 0.994653i | \(-0.467067\pi\) | ||||
0.103277 | + | 0.994653i | \(0.467067\pi\) | |||||||
\(62\) | −18.7512 | −2.38140 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.04776 | −0.755970 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.66328 | −0.569710 | −0.284855 | − | 0.958571i | \(-0.591945\pi\) | ||||
−0.284855 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(68\) | −24.5093 | −2.97219 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.92175 | −0.940139 | −0.470069 | − | 0.882629i | \(-0.655771\pi\) | ||||
−0.470069 | + | 0.882629i | \(0.655771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.5914 | 1.70779 | 0.853896 | − | 0.520444i | \(-0.174233\pi\) | ||||
0.853896 | + | 0.520444i | \(0.174233\pi\) | |||||||
\(74\) | −3.23664 | −0.376252 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.3612 | 3.02384 | ||||||||
\(77\) | 3.70114 | 0.421784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.6004 | −1.86769 | −0.933845 | − | 0.357678i | \(-0.883569\pi\) | ||||
−0.933845 | + | 0.357678i | \(0.883569\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.7489 | −1.84961 | ||||||||
\(83\) | 12.8044 | 1.40546 | 0.702731 | − | 0.711456i | \(-0.251964\pi\) | ||||
0.702731 | + | 0.711456i | \(0.251964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 20.5690 | 2.21802 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 20.7489 | 2.21184 | ||||||||
\(89\) | −17.6542 | −1.87135 | −0.935673 | − | 0.352868i | \(-0.885206\pi\) | ||||
−0.935673 | + | 0.352868i | \(0.885206\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.949959 | 0.0995827 | ||||||||
\(92\) | 13.7102 | 1.42938 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.0317940 | −0.00327930 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.1226 | −1.84007 | −0.920033 | − | 0.391840i | \(-0.871839\pi\) | ||||
−0.920033 | + | 0.391840i | \(0.871839\pi\) | |||||||
\(98\) | 15.1189 | 1.52723 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6921 | −1.16341 | −0.581705 | − | 0.813400i | \(-0.697614\pi\) | ||||
−0.581705 | + | 0.813400i | \(0.697614\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.52217 | −0.741181 | −0.370591 | − | 0.928796i | \(-0.620845\pi\) | ||||
−0.370591 | + | 0.928796i | \(0.620845\pi\) | |||||||
\(104\) | 5.32555 | 0.522213 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.22968 | −0.605080 | ||||||||
\(107\) | 6.00901 | 0.580913 | 0.290457 | − | 0.956888i | \(-0.406193\pi\) | ||||
0.290457 | + | 0.956888i | \(0.406193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.08139 | 0.103579 | 0.0517894 | − | 0.998658i | \(-0.483508\pi\) | ||||
0.0517894 | + | 0.998658i | \(0.483508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.66328 | −0.440639 | ||||||||
\(113\) | −7.29636 | −0.686383 | −0.343192 | − | 0.939265i | \(-0.611508\pi\) | ||||
−0.343192 | + | 0.939265i | \(0.611508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 17.8179 | 1.65435 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.6419 | −1.43995 | ||||||||
\(119\) | 5.61324 | 0.514565 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.17964 | 0.379967 | ||||||||
\(122\) | −4.00000 | −0.362143 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 31.3682 | 2.81695 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6915 | −0.948714 | −0.474357 | − | 0.880333i | \(-0.657319\pi\) | ||||
−0.474357 | + | 0.880333i | \(0.657319\pi\) | |||||||
\(128\) | 18.0364 | 1.59420 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.225811 | 0.0197292 | 0.00986458 | − | 0.999951i | \(-0.496860\pi\) | ||||
0.00986458 | + | 0.999951i | \(0.496860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.03738 | −0.523507 | ||||||||
\(134\) | 11.5625 | 0.998851 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 31.4683 | 2.69838 | ||||||||
\(137\) | 6.63828 | 0.567146 | 0.283573 | − | 0.958951i | \(-0.408480\pi\) | ||||
0.283573 | + | 0.958951i | \(0.408480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.09758 | 0.262733 | 0.131367 | − | 0.991334i | \(-0.458064\pi\) | ||||
0.131367 | + | 0.991334i | \(0.458064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.6419 | 1.64831 | ||||||||
\(143\) | 3.89611 | 0.325809 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −36.1791 | −2.99420 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.41446 | 0.445066 | ||||||||
\(149\) | −10.9808 | −0.899582 | −0.449791 | − | 0.893134i | \(-0.648502\pi\) | ||||
−0.449791 | + | 0.893134i | \(0.648502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.78901 | −0.226966 | −0.113483 | − | 0.993540i | \(-0.536201\pi\) | ||||
−0.113483 | + | 0.993540i | \(0.536201\pi\) | |||||||
\(152\) | −33.8460 | −2.74528 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.17692 | −0.739497 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3843 | 0.908563 | 0.454281 | − | 0.890858i | \(-0.349896\pi\) | ||||
0.454281 | + | 0.890858i | \(0.349896\pi\) | |||||||
\(158\) | 41.1604 | 3.27455 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.13996 | −0.247464 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.13144 | −0.166947 | −0.0834735 | − | 0.996510i | \(-0.526601\pi\) | ||||
−0.0834735 | + | 0.996510i | \(0.526601\pi\) | |||||||
\(164\) | 28.0187 | 2.18789 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31.7482 | −2.46414 | ||||||||
\(167\) | −3.00587 | −0.232601 | −0.116300 | − | 0.993214i | \(-0.537104\pi\) | ||||
−0.116300 | + | 0.993214i | \(0.537104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −34.4092 | −2.62368 | ||||||||
\(173\) | 0.673441 | 0.0512008 | 0.0256004 | − | 0.999672i | \(-0.491850\pi\) | ||||
0.0256004 | + | 0.999672i | \(0.491850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.1257 | −1.44165 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 43.7734 | 3.28096 | ||||||||
\(179\) | −7.81786 | −0.584334 | −0.292167 | − | 0.956367i | \(-0.594376\pi\) | ||||
−0.292167 | + | 0.956367i | \(0.594376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.53118 | −0.708447 | −0.354223 | − | 0.935161i | \(-0.615255\pi\) | ||||
−0.354223 | + | 0.935161i | \(0.615255\pi\) | |||||||
\(182\) | −2.35541 | −0.174594 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.6029 | −1.29770 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.0218 | 1.68352 | ||||||||
\(188\) | 0.0531870 | 0.00387906 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1073 | 1.16548 | 0.582740 | − | 0.812659i | \(-0.301981\pi\) | ||||
0.582740 | + | 0.812659i | \(0.301981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8967 | 1.00031 | 0.500155 | − | 0.865936i | \(-0.333276\pi\) | ||||
0.500155 | + | 0.865936i | \(0.333276\pi\) | |||||||
\(194\) | 44.9346 | 3.22612 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.2918 | −1.80656 | ||||||||
\(197\) | 11.7647 | 0.838198 | 0.419099 | − | 0.907941i | \(-0.362346\pi\) | ||||
0.419099 | + | 0.907941i | \(0.362346\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.41513 | −0.596533 | −0.298266 | − | 0.954483i | \(-0.596408\pi\) | ||||
−0.298266 | + | 0.954483i | \(0.596408\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 28.9905 | 2.03976 | ||||||||
\(203\) | −4.08073 | −0.286411 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.6511 | 1.29948 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.90893 | −0.340373 | ||||||||
\(209\) | −24.7613 | −1.71278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5402 | 0.794459 | 0.397230 | − | 0.917719i | \(-0.369972\pi\) | ||||
0.397230 | + | 0.917719i | \(0.369972\pi\) | |||||||
\(212\) | 10.4214 | 0.715746 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.8993 | −1.01849 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.18409 | −0.487688 | ||||||||
\(218\) | −2.68130 | −0.181601 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.90893 | 0.397478 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.82173 | −0.523782 | −0.261891 | − | 0.965098i | \(-0.584346\pi\) | ||||
−0.261891 | + | 0.965098i | \(0.584346\pi\) | |||||||
\(224\) | 1.44443 | 0.0965098 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.0912 | 1.20341 | ||||||||
\(227\) | −21.1316 | −1.40255 | −0.701277 | − | 0.712889i | \(-0.747386\pi\) | ||||
−0.701277 | + | 0.712889i | \(0.747386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.5280 | −1.55477 | −0.777387 | − | 0.629022i | \(-0.783455\pi\) | ||||
−0.777387 | + | 0.629022i | \(0.783455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −22.8769 | −1.50194 | ||||||||
\(233\) | −6.40612 | −0.419679 | −0.209839 | − | 0.977736i | \(-0.567294\pi\) | ||||
−0.209839 | + | 0.977736i | \(0.567294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 26.1667 | 1.70331 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.9179 | −0.902166 | ||||||||
\(239\) | 12.6696 | 0.819530 | 0.409765 | − | 0.912191i | \(-0.365611\pi\) | ||||
0.409765 | + | 0.912191i | \(0.365611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.206457 | −0.0132990 | −0.00664952 | − | 0.999978i | \(-0.502117\pi\) | ||||
−0.00664952 | + | 0.999978i | \(0.502117\pi\) | |||||||
\(242\) | −10.3634 | −0.666181 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.69146 | 0.428377 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.35541 | −0.404385 | ||||||||
\(248\) | −40.2746 | −2.55744 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.5028 | −0.978529 | −0.489264 | − | 0.872135i | \(-0.662735\pi\) | ||||
−0.489264 | + | 0.872135i | \(0.662735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8781 | −0.809637 | ||||||||
\(254\) | 26.5093 | 1.66334 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.6254 | −2.03909 | ||||||||
\(257\) | −6.11944 | −0.381720 | −0.190860 | − | 0.981617i | \(-0.561128\pi\) | ||||
−0.190860 | + | 0.981617i | \(0.561128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.24004 | −0.0770526 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.559894 | −0.0345904 | ||||||||
\(263\) | −17.1066 | −1.05484 | −0.527419 | − | 0.849605i | \(-0.676840\pi\) | ||||
−0.527419 | + | 0.849605i | \(0.676840\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.9696 | 0.917844 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −19.3426 | −1.18153 | ||||||||
\(269\) | −27.8981 | −1.70098 | −0.850490 | − | 0.525992i | \(-0.823694\pi\) | ||||
−0.850490 | + | 0.525992i | \(0.823694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.6569 | −1.74079 | −0.870393 | − | 0.492358i | \(-0.836135\pi\) | ||||
−0.870393 | + | 0.492358i | \(0.836135\pi\) | |||||||
\(272\) | −29.0065 | −1.75878 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4595 | −0.994355 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.433599 | 0.0260525 | 0.0130262 | − | 0.999915i | \(-0.495854\pi\) | ||||
0.0130262 | + | 0.999915i | \(0.495854\pi\) | |||||||
\(278\) | −7.68040 | −0.460640 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5747 | 1.10807 | 0.554036 | − | 0.832492i | \(-0.313087\pi\) | ||||
0.554036 | + | 0.832492i | \(0.313087\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.9360 | −1.30396 | −0.651979 | − | 0.758237i | \(-0.726061\pi\) | ||||
−0.651979 | + | 0.758237i | \(0.726061\pi\) | |||||||
\(284\) | −32.8582 | −1.94978 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.66033 | −0.571228 | ||||||||
\(287\) | −6.41696 | −0.378781 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.9154 | 1.05385 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 60.5228 | 3.54183 | ||||||||
\(293\) | −9.26031 | −0.540993 | −0.270497 | − | 0.962721i | \(-0.587188\pi\) | ||||
−0.270497 | + | 0.962721i | \(0.587188\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.95180 | −0.404065 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.2267 | 1.57720 | ||||||||
\(299\) | −3.30537 | −0.191154 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.88056 | 0.454228 | ||||||||
\(302\) | 6.91530 | 0.397931 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 31.1982 | 1.78934 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.15012 | −0.522225 | −0.261113 | − | 0.965308i | \(-0.584089\pi\) | ||||
−0.261113 | + | 0.965308i | \(0.584089\pi\) | |||||||
\(308\) | 15.3518 | 0.874747 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.11488 | −0.460153 | −0.230076 | − | 0.973173i | \(-0.573898\pi\) | ||||
−0.230076 | + | 0.973173i | \(0.573898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.21952 | 0.238501 | 0.119251 | − | 0.992864i | \(-0.461951\pi\) | ||||
0.119251 | + | 0.992864i | \(0.461951\pi\) | |||||||
\(314\) | −28.2271 | −1.59295 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −68.8558 | −3.87344 | ||||||||
\(317\) | −15.4374 | −0.867053 | −0.433527 | − | 0.901141i | \(-0.642731\pi\) | ||||
−0.433527 | + | 0.901141i | \(0.642731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.7365 | −0.937062 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.78549 | 0.433868 | ||||||||
\(323\) | −37.5537 | −2.08954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.28486 | 0.292701 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −35.9740 | −1.98633 | ||||||||
\(329\) | −0.0121811 | −0.000671568 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6619 | 0.805894 | 0.402947 | − | 0.915223i | \(-0.367986\pi\) | ||||
0.402947 | + | 0.915223i | \(0.367986\pi\) | |||||||
\(332\) | 53.1105 | 2.91482 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.45300 | 0.407810 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.6094 | 1.44951 | 0.724753 | − | 0.689009i | \(-0.241954\pi\) | ||||
0.724753 | + | 0.689009i | \(0.241954\pi\) | |||||||
\(338\) | −2.47948 | −0.134866 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.4644 | −1.59559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4422 | 0.671813 | ||||||||
\(344\) | 44.1791 | 2.38198 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.66979 | −0.0897683 | ||||||||
\(347\) | −3.06153 | −0.164352 | −0.0821759 | − | 0.996618i | \(-0.526187\pi\) | ||||
−0.0821759 | + | 0.996618i | \(0.526187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.4273 | −1.20050 | −0.600252 | − | 0.799811i | \(-0.704933\pi\) | ||||
−0.600252 | + | 0.799811i | \(0.704933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.92409 | 0.315755 | ||||||||
\(353\) | −23.7147 | −1.26220 | −0.631102 | − | 0.775700i | \(-0.717397\pi\) | ||||
−0.631102 | + | 0.775700i | \(0.717397\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −73.2271 | −3.88103 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.3843 | 1.02449 | ||||||||
\(359\) | 18.6484 | 0.984227 | 0.492113 | − | 0.870531i | \(-0.336225\pi\) | ||||
0.492113 | + | 0.870531i | \(0.336225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.3912 | 1.12585 | ||||||||
\(362\) | 23.6324 | 1.24209 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.94028 | 0.206527 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7870 | 0.563076 | 0.281538 | − | 0.959550i | \(-0.409155\pi\) | ||||
0.281538 | + | 0.959550i | \(0.409155\pi\) | |||||||
\(368\) | 16.2258 | 0.845829 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.38676 | −0.123914 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0430 | 0.986009 | 0.493005 | − | 0.870027i | \(-0.335899\pi\) | ||||
0.493005 | + | 0.870027i | \(0.335899\pi\) | |||||||
\(374\) | −57.0822 | −2.95165 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0682885 | −0.00352171 | ||||||||
\(377\) | −4.29569 | −0.221239 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.9537 | −0.819489 | −0.409744 | − | 0.912200i | \(-0.634382\pi\) | ||||
−0.409744 | + | 0.912200i | \(0.634382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −39.9377 | −2.04339 | ||||||||
\(383\) | −24.8044 | −1.26744 | −0.633722 | − | 0.773561i | \(-0.718474\pi\) | ||||
−0.633722 | + | 0.773561i | \(0.718474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −34.4568 | −1.75380 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −75.1696 | −3.81616 | ||||||||
\(389\) | 36.2379 | 1.83734 | 0.918668 | − | 0.395030i | \(-0.129266\pi\) | ||||
0.918668 | + | 0.395030i | \(0.129266\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.5312 | −0.987734 | ||||||||
\(392\) | 32.4730 | 1.64013 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.1703 | −1.46958 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.4111 | −0.924025 | −0.462013 | − | 0.886873i | \(-0.652873\pi\) | ||||
−0.462013 | + | 0.886873i | \(0.652873\pi\) | |||||||
\(398\) | 20.8652 | 1.04588 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0667 | −1.20183 | −0.600916 | − | 0.799312i | \(-0.705197\pi\) | ||||
−0.600916 | + | 0.799312i | \(0.705197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.56253 | −0.376717 | ||||||||
\(404\) | −48.4971 | −2.41282 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.1181 | 0.502153 | ||||||||
\(407\) | −5.08585 | −0.252096 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.7102 | 1.76575 | 0.882877 | − | 0.469605i | \(-0.155604\pi\) | ||||
0.882877 | + | 0.469605i | \(0.155604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31.2008 | −1.53715 | ||||||||
\(413\) | −5.99283 | −0.294888 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.52052 | 0.0745494 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 61.3954 | 3.00295 | ||||||||
\(419\) | −21.8241 | −1.06618 | −0.533090 | − | 0.846059i | \(-0.678969\pi\) | ||||
−0.533090 | + | 0.846059i | \(0.678969\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.107706 | −0.00524928 | −0.00262464 | − | 0.999997i | \(-0.500835\pi\) | ||||
−0.00262464 | + | 0.999997i | \(0.500835\pi\) | |||||||
\(422\) | −28.6137 | −1.39289 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.3804 | −0.649809 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.53251 | −0.0741634 | ||||||||
\(428\) | 24.9244 | 1.20477 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.3215 | −1.55687 | −0.778437 | − | 0.627723i | \(-0.783987\pi\) | ||||
−0.778437 | + | 0.627723i | \(0.783987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.5914 | 0.701217 | 0.350608 | − | 0.936522i | \(-0.385975\pi\) | ||||
0.350608 | + | 0.936522i | \(0.385975\pi\) | |||||||
\(434\) | 17.8128 | 0.855044 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.48546 | 0.214814 | ||||||||
\(437\) | 21.0070 | 1.00490 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.4117 | −1.30829 | −0.654146 | − | 0.756369i | \(-0.726972\pi\) | ||||
−0.654146 | + | 0.756369i | \(0.726972\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.6511 | −0.696882 | ||||||||
\(443\) | −7.19811 | −0.341993 | −0.170996 | − | 0.985272i | \(-0.554699\pi\) | ||||
−0.170996 | + | 0.985272i | \(0.554699\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.3939 | 0.918326 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.74513 | 0.271432 | ||||||||
\(449\) | −18.9884 | −0.896119 | −0.448060 | − | 0.894004i | \(-0.647885\pi\) | ||||
−0.448060 | + | 0.894004i | \(0.647885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.3182 | −1.23927 | ||||||||
\(452\) | −30.2642 | −1.42351 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 52.3955 | 2.45904 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.3998 | 1.23493 | 0.617465 | − | 0.786599i | \(-0.288160\pi\) | ||||
0.617465 | + | 0.786599i | \(0.288160\pi\) | |||||||
\(458\) | 58.3373 | 2.72592 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0585 | 1.02737 | 0.513684 | − | 0.857980i | \(-0.328280\pi\) | ||||
0.513684 | + | 0.857980i | \(0.328280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.31425 | −0.0610781 | −0.0305391 | − | 0.999534i | \(-0.509722\pi\) | ||||
−0.0305391 | + | 0.999534i | \(0.509722\pi\) | |||||||
\(464\) | 21.0872 | 0.978950 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.8839 | 0.735806 | ||||||||
\(467\) | 14.8898 | 0.689017 | 0.344509 | − | 0.938783i | \(-0.388046\pi\) | ||||
0.344509 | + | 0.938783i | \(0.388046\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.42992 | 0.204555 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −33.5963 | −1.54639 | ||||||||
\(473\) | 32.3209 | 1.48612 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 23.2828 | 1.06717 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −31.4142 | −1.43685 | ||||||||
\(479\) | −3.03653 | −0.138743 | −0.0693713 | − | 0.997591i | \(-0.522099\pi\) | ||||
−0.0693713 | + | 0.997591i | \(0.522099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.30537 | −0.0595196 | ||||||||
\(482\) | 0.511906 | 0.0233167 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.3365 | 0.788022 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.2584 | −0.736741 | −0.368370 | − | 0.929679i | \(-0.620084\pi\) | ||||
−0.368370 | + | 0.929679i | \(0.620084\pi\) | |||||||
\(488\) | −8.59138 | −0.388914 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5098 | 0.564558 | 0.282279 | − | 0.959332i | \(-0.408910\pi\) | ||||
0.282279 | + | 0.959332i | \(0.408910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.3829 | −1.14319 | ||||||||
\(494\) | 15.7581 | 0.708992 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 37.1239 | 1.66691 | ||||||||
\(497\) | 7.52534 | 0.337557 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.977442 | −0.0437563 | −0.0218782 | − | 0.999761i | \(-0.506965\pi\) | ||||
−0.0218782 | + | 0.999761i | \(0.506965\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 38.4390 | 1.71562 | ||||||||
\(503\) | 22.9051 | 1.02129 | 0.510644 | − | 0.859792i | \(-0.329407\pi\) | ||||
0.510644 | + | 0.859792i | \(0.329407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 31.9310 | 1.41950 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −44.3465 | −1.96756 | ||||||||
\(509\) | 13.2463 | 0.587132 | 0.293566 | − | 0.955939i | \(-0.405158\pi\) | ||||
0.293566 | + | 0.955939i | \(0.405158\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8612 | −0.613184 | ||||||||
\(512\) | 44.8214 | 1.98084 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.1731 | 0.669255 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0499590 | −0.00219720 | ||||||||
\(518\) | 3.07467 | 0.135093 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.70493 | 0.381370 | 0.190685 | − | 0.981651i | \(-0.438929\pi\) | ||||
0.190685 | + | 0.981651i | \(0.438929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4014 | −1.28563 | −0.642817 | − | 0.766020i | \(-0.722234\pi\) | ||||
−0.642817 | + | 0.766020i | \(0.722234\pi\) | |||||||
\(524\) | 0.936627 | 0.0409168 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.4155 | 1.84940 | ||||||||
\(527\) | −44.6865 | −1.94657 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.0745 | −0.524980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25.0421 | −1.08571 | ||||||||
\(533\) | −6.75499 | −0.292591 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.8345 | 1.07269 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 69.1730 | 2.98226 | ||||||||
\(539\) | 23.7568 | 1.02328 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.40100 | −0.0602335 | −0.0301168 | − | 0.999546i | \(-0.509588\pi\) | ||||
−0.0301168 | + | 0.999546i | \(0.509588\pi\) | |||||||
\(542\) | 71.0544 | 3.05205 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.98462 | 0.385212 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.42904 | 0.103858 | 0.0519292 | − | 0.998651i | \(-0.483463\pi\) | ||||
0.0519292 | + | 0.998651i | \(0.483463\pi\) | |||||||
\(548\) | 27.5345 | 1.17622 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.3009 | 1.16306 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.7697 | 0.670595 | ||||||||
\(554\) | −1.07510 | −0.0456767 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.8483 | 0.544888 | ||||||||
\(557\) | −14.2429 | −0.603491 | −0.301746 | − | 0.953388i | \(-0.597569\pi\) | ||||
−0.301746 | + | 0.953388i | \(0.597569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.29569 | 0.350870 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −46.0557 | −1.94274 | ||||||||
\(563\) | −38.1924 | −1.60962 | −0.804810 | − | 0.593533i | \(-0.797733\pi\) | ||||
−0.804810 | + | 0.593533i | \(0.797733\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 54.3899 | 2.28618 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.1877 | 1.77016 | ||||||||
\(569\) | 22.1387 | 0.928104 | 0.464052 | − | 0.885808i | \(-0.346395\pi\) | ||||
0.464052 | + | 0.885808i | \(0.346395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.8956 | −1.87882 | −0.939412 | − | 0.342791i | \(-0.888628\pi\) | ||||
−0.939412 | + | 0.342791i | \(0.888628\pi\) | |||||||
\(572\) | 16.1604 | 0.675702 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.9108 | 0.664103 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.07248 | 0.169540 | 0.0847698 | − | 0.996401i | \(-0.472984\pi\) | ||||
0.0847698 | + | 0.996401i | \(0.472984\pi\) | |||||||
\(578\) | −44.4210 | −1.84767 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.1636 | −0.504632 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.78893 | −0.405416 | ||||||||
\(584\) | −77.7071 | −3.21554 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.9608 | 0.948502 | ||||||||
\(587\) | 24.5786 | 1.01447 | 0.507233 | − | 0.861809i | \(-0.330668\pi\) | ||||
0.507233 | + | 0.861809i | \(0.330668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.0630 | 1.98040 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.40795 | 0.263365 | ||||||||
\(593\) | 0.191663 | 0.00787065 | 0.00393532 | − | 0.999992i | \(-0.498747\pi\) | ||||
0.00393532 | + | 0.999992i | \(0.498747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −45.5467 | −1.86566 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.19561 | 0.335143 | ||||||||
\(599\) | −22.5977 | −0.923316 | −0.461658 | − | 0.887058i | \(-0.652745\pi\) | ||||
−0.461658 | + | 0.887058i | \(0.652745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0155 | 0.694077 | 0.347039 | − | 0.937851i | \(-0.387187\pi\) | ||||
0.347039 | + | 0.937851i | \(0.387187\pi\) | |||||||
\(602\) | −19.5397 | −0.796380 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.5684 | −0.470710 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.4651 | 1.39889 | 0.699447 | − | 0.714684i | \(-0.253430\pi\) | ||||
0.699447 | + | 0.714684i | \(0.253430\pi\) | |||||||
\(608\) | −9.66349 | −0.391906 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0128228 | −0.000518755 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.02682 | 0.283810 | 0.141905 | − | 0.989880i | \(-0.454677\pi\) | ||||
0.141905 | + | 0.989880i | \(0.454677\pi\) | |||||||
\(614\) | 22.6876 | 0.915597 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.7106 | −0.794163 | ||||||||
\(617\) | 12.1122 | 0.487620 | 0.243810 | − | 0.969823i | \(-0.421603\pi\) | ||||
0.243810 | + | 0.969823i | \(0.421603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.8710 | 1.24081 | 0.620406 | − | 0.784281i | \(-0.286968\pi\) | ||||
0.620406 | + | 0.784281i | \(0.286968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.1207 | 0.806767 | ||||||||
\(623\) | 16.7708 | 0.671908 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.4622 | −0.418155 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 47.2201 | 1.88429 | ||||||||
\(629\) | −7.71332 | −0.307550 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.48047 | 0.377412 | 0.188706 | − | 0.982034i | \(-0.439571\pi\) | ||||
0.188706 | + | 0.982034i | \(0.439571\pi\) | |||||||
\(632\) | 88.4062 | 3.51661 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 38.2769 | 1.52017 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.09758 | 0.241595 | ||||||||
\(638\) | 41.4978 | 1.64291 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.3964 | −0.687118 | −0.343559 | − | 0.939131i | \(-0.611633\pi\) | ||||
−0.343559 | + | 0.939131i | \(0.611633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.9506 | 1.33888 | 0.669440 | − | 0.742866i | \(-0.266534\pi\) | ||||
0.669440 | + | 0.742866i | \(0.266534\pi\) | |||||||
\(644\) | −13.0241 | −0.513221 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 93.1137 | 3.66351 | ||||||||
\(647\) | 9.18548 | 0.361118 | 0.180559 | − | 0.983564i | \(-0.442209\pi\) | ||||
0.180559 | + | 0.983564i | \(0.442209\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.5786 | −0.964796 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.84087 | −0.346235 | ||||||||
\(653\) | −3.54781 | −0.138837 | −0.0694183 | − | 0.997588i | \(-0.522114\pi\) | ||||
−0.0694183 | + | 0.997588i | \(0.522114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 33.1598 | 1.29467 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.0302030 | 0.00117743 | ||||||||
\(659\) | 15.5339 | 0.605115 | 0.302557 | − | 0.953131i | \(-0.402160\pi\) | ||||
0.302557 | + | 0.953131i | \(0.402160\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.60878 | 0.0625745 | 0.0312872 | − | 0.999510i | \(-0.490039\pi\) | ||||
0.0312872 | + | 0.999510i | \(0.490039\pi\) | |||||||
\(662\) | −36.3541 | −1.41294 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −68.1903 | −2.64630 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1988 | 0.549781 | ||||||||
\(668\) | −12.4679 | −0.482396 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.28535 | −0.242643 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.18214 | 0.315398 | 0.157699 | − | 0.987487i | \(-0.449592\pi\) | ||||
0.157699 | + | 0.987487i | \(0.449592\pi\) | |||||||
\(674\) | −65.9776 | −2.54136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.14785 | 0.159533 | ||||||||
\(677\) | −42.7063 | −1.64134 | −0.820668 | − | 0.571405i | \(-0.806399\pi\) | ||||
−0.820668 | + | 0.571405i | \(0.806399\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.2157 | 0.660677 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 73.0566 | 2.79748 | ||||||||
\(683\) | 9.14962 | 0.350100 | 0.175050 | − | 0.984560i | \(-0.443991\pi\) | ||||
0.175050 | + | 0.984560i | \(0.443991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −30.8501 | −1.17786 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −40.7229 | −1.55255 | ||||||||
\(689\) | −2.51249 | −0.0957182 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9918 | −0.646398 | −0.323199 | − | 0.946331i | \(-0.604758\pi\) | ||||
−0.323199 | + | 0.946331i | \(0.604758\pi\) | |||||||
\(692\) | 2.79333 | 0.106186 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.59103 | 0.288152 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.9148 | −1.51188 | ||||||||
\(698\) | 55.6080 | 2.10480 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8320 | 1.54220 | 0.771101 | − | 0.636712i | \(-0.219706\pi\) | ||||
0.771101 | + | 0.636712i | \(0.219706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.29614 | 0.312895 | ||||||||
\(704\) | 23.5627 | 0.888053 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 58.8001 | 2.21297 | ||||||||
\(707\) | 11.1070 | 0.417723 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0193 | −1.42784 | −0.713922 | − | 0.700225i | \(-0.753083\pi\) | ||||
−0.713922 | + | 0.700225i | \(0.753083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 94.0185 | 3.52349 | ||||||||
\(713\) | 24.9969 | 0.936143 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −32.4273 | −1.21186 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −46.2385 | −1.72561 | ||||||||
\(719\) | −27.9175 | −1.04115 | −0.520573 | − | 0.853817i | \(-0.674282\pi\) | ||||
−0.520573 | + | 0.853817i | \(0.674282\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.14575 | 0.266122 | ||||||||
\(722\) | −53.0392 | −1.97391 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −39.5338 | −1.46926 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.31960 | 0.160205 | 0.0801026 | − | 0.996787i | \(-0.474475\pi\) | ||||
0.0801026 | + | 0.996787i | \(0.474475\pi\) | |||||||
\(728\) | −5.05905 | −0.187501 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.0186 | 1.81302 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.1669 | 0.486330 | 0.243165 | − | 0.969985i | \(-0.421814\pi\) | ||||
0.243165 | + | 0.969985i | \(0.421814\pi\) | |||||||
\(734\) | −26.7462 | −0.987219 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.02586 | −0.185256 | ||||||||
\(737\) | 18.1686 | 0.669250 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.14218 | 0.0788014 | 0.0394007 | − | 0.999223i | \(-0.487455\pi\) | ||||
0.0394007 | + | 0.999223i | \(0.487455\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.91794 | 0.217254 | ||||||||
\(743\) | −24.4771 | −0.897979 | −0.448990 | − | 0.893537i | \(-0.648216\pi\) | ||||
−0.448990 | + | 0.893537i | \(0.648216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −47.2168 | −1.72873 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 95.4909 | 3.49149 | ||||||||
\(749\) | −5.70831 | −0.208577 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0058 | −0.438097 | −0.219049 | − | 0.975714i | \(-0.570295\pi\) | ||||
−0.219049 | + | 0.975714i | \(0.570295\pi\) | |||||||
\(752\) | 0.0629463 | 0.00229541 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.6511 | 0.387890 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.8442 | −0.612212 | −0.306106 | − | 0.951997i | \(-0.599026\pi\) | ||||
−0.306106 | + | 0.951997i | \(0.599026\pi\) | |||||||
\(758\) | 39.5571 | 1.43678 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.97932 | −0.144250 | −0.0721251 | − | 0.997396i | \(-0.522978\pi\) | ||||
−0.0721251 | + | 0.997396i | \(0.522978\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.02728 | −0.0371900 | ||||||||
\(764\) | 66.8104 | 2.41712 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 61.5021 | 2.22216 | ||||||||
\(767\) | −6.30851 | −0.227787 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5176 | 0.559579 | 0.279790 | − | 0.960061i | \(-0.409735\pi\) | ||||
0.279790 | + | 0.960061i | \(0.409735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 57.6416 | 2.07456 | ||||||||
\(773\) | 44.4624 | 1.59920 | 0.799601 | − | 0.600531i | \(-0.205044\pi\) | ||||
0.799601 | + | 0.600531i | \(0.205044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 96.5126 | 3.46460 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −89.8514 | −3.22133 | ||||||||
\(779\) | 42.9307 | 1.53815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.8640 | 1.10440 | ||||||||
\(782\) | 48.4273 | 1.73176 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −29.9326 | −1.06902 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.0619 | −1.14288 | −0.571441 | − | 0.820643i | \(-0.693616\pi\) | ||||
−0.571441 | + | 0.820643i | \(0.693616\pi\) | |||||||
\(788\) | 48.7980 | 1.73836 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.93124 | 0.246446 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.61324 | −0.0572878 | ||||||||
\(794\) | 45.6500 | 1.62006 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.9046 | −1.23716 | ||||||||
\(797\) | 24.7378 | 0.876260 | 0.438130 | − | 0.898912i | \(-0.355641\pi\) | ||||
0.438130 | + | 0.898912i | \(0.355641\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0757691 | −0.00268052 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 59.6729 | 2.10712 | ||||||||
\(803\) | −56.8496 | −2.00618 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.7512 | 0.660482 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 62.2670 | 2.19055 | ||||||||
\(809\) | −11.3400 | −0.398694 | −0.199347 | − | 0.979929i | \(-0.563882\pi\) | ||||
−0.199347 | + | 0.979929i | \(0.563882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.96070 | 0.314653 | 0.157326 | − | 0.987547i | \(-0.449713\pi\) | ||||
0.157326 | + | 0.987547i | \(0.449713\pi\) | |||||||
\(812\) | −16.9262 | −0.593994 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.6103 | 0.441990 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.7225 | −1.84453 | ||||||||
\(818\) | −88.5428 | −3.09583 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.28500 | −0.184448 | −0.0922239 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922239 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.2463 | 0.392023 | 0.196012 | − | 0.980602i | \(-0.437201\pi\) | ||||
0.196012 | + | 0.980602i | \(0.437201\pi\) | |||||||
\(824\) | 40.0597 | 1.39554 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.8591 | 0.517015 | ||||||||
\(827\) | −42.9625 | −1.49395 | −0.746976 | − | 0.664851i | \(-0.768495\pi\) | ||||
−0.746976 | + | 0.664851i | \(0.768495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.1444 | 0.734376 | 0.367188 | − | 0.930147i | \(-0.380321\pi\) | ||||
0.367188 | + | 0.930147i | \(0.380321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.04776 | 0.209668 | ||||||||
\(833\) | 36.0302 | 1.24837 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −102.706 | −3.55217 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 54.1126 | 1.86929 | ||||||||
\(839\) | 26.3671 | 0.910293 | 0.455146 | − | 0.890417i | \(-0.349587\pi\) | ||||
0.455146 | + | 0.890417i | \(0.349587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5470 | −0.363691 | ||||||||
\(842\) | 0.267056 | 0.00920336 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 47.8669 | 1.64765 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.97048 | −0.136427 | ||||||||
\(848\) | 12.3336 | 0.423539 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.31472 | 0.147907 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.4061 | −1.79435 | −0.897175 | − | 0.441676i | \(-0.854384\pi\) | ||||
−0.897175 | + | 0.441676i | \(0.854384\pi\) | |||||||
\(854\) | 3.79984 | 0.130028 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −32.0013 | −1.09378 | ||||||||
\(857\) | 24.6382 | 0.841625 | 0.420813 | − | 0.907148i | \(-0.361745\pi\) | ||||
0.420813 | + | 0.907148i | \(0.361745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.0110 | −1.60399 | −0.801997 | − | 0.597329i | \(-0.796229\pi\) | ||||
−0.801997 | + | 0.597329i | \(0.796229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 80.1407 | 2.72960 | ||||||||
\(863\) | −14.9378 | −0.508490 | −0.254245 | − | 0.967140i | \(-0.581827\pi\) | ||||
−0.254245 | + | 0.967140i | \(0.581827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −36.1791 | −1.22942 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −29.7985 | −1.01143 | ||||||||
\(869\) | 64.6769 | 2.19401 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.66328 | 0.158009 | ||||||||
\(872\) | −5.75902 | −0.195025 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −52.0864 | −1.76185 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.3418 | 0.990801 | 0.495400 | − | 0.868665i | \(-0.335021\pi\) | ||||
0.495400 | + | 0.868665i | \(0.335021\pi\) | |||||||
\(878\) | 67.9670 | 2.29378 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1590 | −0.409647 | −0.204824 | − | 0.978799i | \(-0.565662\pi\) | ||||
−0.204824 | + | 0.978799i | \(0.565662\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.1431 | −1.04805 | −0.524024 | − | 0.851703i | \(-0.675570\pi\) | ||||
−0.524024 | + | 0.851703i | \(0.675570\pi\) | |||||||
\(884\) | 24.5093 | 0.824338 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.8476 | 0.599602 | ||||||||
\(887\) | −2.56117 | −0.0859955 | −0.0429978 | − | 0.999075i | \(-0.513691\pi\) | ||||
−0.0429978 | + | 0.999075i | \(0.513691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1564 | 0.340636 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −32.4433 | −1.08628 | ||||||||
\(893\) | 0.0814942 | 0.00272710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17.1338 | −0.572400 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 47.0815 | 1.57113 | ||||||||
\(899\) | 32.4863 | 1.08348 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.8461 | −0.494596 | ||||||||
\(902\) | 65.2555 | 2.17277 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.8571 | 1.29237 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.5273 | −1.14646 | −0.573231 | − | 0.819394i | \(-0.694310\pi\) | ||||
−0.573231 | + | 0.819394i | \(0.694310\pi\) | |||||||
\(908\) | −87.6506 | −2.90879 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.4985 | 0.546619 | 0.273309 | − | 0.961926i | \(-0.411882\pi\) | ||||
0.273309 | + | 0.961926i | \(0.411882\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.8872 | −1.65102 | ||||||||
\(914\) | −65.4578 | −2.16515 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −97.5905 | −3.22448 | ||||||||
\(917\) | −0.214511 | −0.00708377 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.8399 | 0.984327 | 0.492163 | − | 0.870503i | \(-0.336206\pi\) | ||||
0.492163 | + | 0.870503i | \(0.336206\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −54.6938 | −1.80124 | ||||||||
\(923\) | 7.92175 | 0.260748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.25865 | 0.107086 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.53166 | −0.214412 | ||||||||
\(929\) | −29.9391 | −0.982270 | −0.491135 | − | 0.871084i | \(-0.663418\pi\) | ||||
−0.491135 | + | 0.871084i | \(0.663418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.7526 | −1.27007 | ||||||||
\(932\) | −26.5716 | −0.870381 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.9190 | −1.20803 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7542 | 1.07003 | 0.535016 | − | 0.844842i | \(-0.320306\pi\) | ||||
0.535016 | + | 0.844842i | \(0.320306\pi\) | |||||||
\(938\) | −10.9839 | −0.358638 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.6679 | 0.869349 | 0.434675 | − | 0.900588i | \(-0.356863\pi\) | ||||
0.434675 | + | 0.900588i | \(0.356863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.3277 | 0.727091 | ||||||||
\(944\) | 30.9680 | 1.00792 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −80.1391 | −2.60555 | ||||||||
\(947\) | −16.9685 | −0.551402 | −0.275701 | − | 0.961243i | \(-0.588910\pi\) | ||||
−0.275701 | + | 0.961243i | \(0.588910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.5914 | −0.473656 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29.8936 | −0.968856 | ||||||||
\(953\) | −45.6056 | −1.47731 | −0.738655 | − | 0.674084i | \(-0.764539\pi\) | ||||
−0.738655 | + | 0.674084i | \(0.764539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 52.5517 | 1.69964 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.52903 | 0.243252 | ||||||||
\(959\) | −6.30609 | −0.203634 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.1919 | 0.844899 | ||||||||
\(962\) | 3.23664 | 0.104353 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.856350 | −0.0275812 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.77794 | −0.250122 | −0.125061 | − | 0.992149i | \(-0.539913\pi\) | ||||
−0.125061 | + | 0.992149i | \(0.539913\pi\) | |||||||
\(968\) | −22.2589 | −0.715427 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1572 | −0.454327 | −0.227163 | − | 0.973857i | \(-0.572945\pi\) | ||||
−0.227163 | + | 0.973857i | \(0.572945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.94257 | −0.0943345 | ||||||||
\(974\) | 40.3126 | 1.29170 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.91927 | 0.253490 | ||||||||
\(977\) | −13.0985 | −0.419058 | −0.209529 | − | 0.977802i | \(-0.567193\pi\) | ||||
−0.209529 | + | 0.977802i | \(0.567193\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.7828 | 2.19831 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.0178 | −0.989817 | ||||||||
\(983\) | 49.1176 | 1.56661 | 0.783305 | − | 0.621638i | \(-0.213533\pi\) | ||||
0.783305 | + | 0.621638i | \(0.213533\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 62.9366 | 2.00431 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −26.3612 | −0.838663 | ||||||||
\(989\) | −27.4203 | −0.871915 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.0358 | 0.541161 | 0.270581 | − | 0.962697i | \(-0.412784\pi\) | ||||
0.270581 | + | 0.962697i | \(0.412784\pi\) | |||||||
\(992\) | −11.4989 | −0.365092 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.6590 | −0.591826 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.01802 | 0.253933 | 0.126967 | − | 0.991907i | \(-0.459476\pi\) | ||||
0.126967 | + | 0.991907i | \(0.459476\pi\) | |||||||
\(998\) | 2.42355 | 0.0767162 | ||||||||
\(999\) | 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 | 2925.2.a.bl.1.1 | 5 | ||
3.2 | odd | 2 | 975.2.a.r.1.5 | 5 | |||
5.2 | odd | 4 | 585.2.c.c.469.1 | 10 | |||
5.3 | odd | 4 | 585.2.c.c.469.10 | 10 | |||
5.4 | even | 2 | 2925.2.a.bm.1.5 | 5 | |||
15.2 | even | 4 | 195.2.c.b.79.10 | yes | 10 | ||
15.8 | even | 4 | 195.2.c.b.79.1 | ✓ | 10 | ||
15.14 | odd | 2 | 975.2.a.s.1.1 | 5 | |||
60.23 | odd | 4 | 3120.2.l.p.1249.7 | 10 | |||
60.47 | odd | 4 | 3120.2.l.p.1249.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.c.b.79.1 | ✓ | 10 | 15.8 | even | 4 | ||
195.2.c.b.79.10 | yes | 10 | 15.2 | even | 4 | ||
585.2.c.c.469.1 | 10 | 5.2 | odd | 4 | |||
585.2.c.c.469.10 | 10 | 5.3 | odd | 4 | |||
975.2.a.r.1.5 | 5 | 3.2 | odd | 2 | |||
975.2.a.s.1.1 | 5 | 15.14 | odd | 2 | |||
2925.2.a.bl.1.1 | 5 | 1.1 | even | 1 | trivial | ||
2925.2.a.bm.1.5 | 5 | 5.4 | even | 2 | |||
3120.2.l.p.1249.2 | 10 | 60.47 | odd | 4 | |||
3120.2.l.p.1249.7 | 10 | 60.23 | odd | 4 |