Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1944.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 9x - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.58423\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.58423 | 1.49200 | 0.746002 | − | 0.665944i | \(-0.231971\pi\) | ||||
0.746002 | + | 0.665944i | \(0.231971\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.67822 | 1.22607 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.67822 | 0.506003 | 0.253001 | − | 0.967466i | \(-0.418582\pi\) | ||||
0.253001 | + | 0.967466i | \(0.418582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.84667 | −1.34422 | −0.672112 | − | 0.740449i | \(-0.734613\pi\) | ||||
−0.672112 | + | 0.740449i | \(0.734613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.84667 | −1.57073 | −0.785367 | − | 0.619030i | \(-0.787526\pi\) | ||||
−0.785367 | + | 0.619030i | \(0.787526\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.26245 | 0.471753 | 0.235876 | − | 0.971783i | \(-0.424204\pi\) | ||||
0.235876 | + | 0.971783i | \(0.424204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.75268 | 0.337303 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.32178 | 0.616839 | 0.308419 | − | 0.951250i | \(-0.400200\pi\) | ||||
0.308419 | + | 0.951250i | \(0.400200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.16845 | −1.64670 | −0.823351 | − | 0.567532i | \(-0.807898\pi\) | ||||
−0.823351 | + | 0.567532i | \(0.807898\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.33690 | 0.754958 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.84667 | 0.467990 | 0.233995 | − | 0.972238i | \(-0.424820\pi\) | ||||
0.233995 | + | 0.972238i | \(0.424820\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.5249 | −2.00559 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.52489 | −1.48754 | −0.743769 | − | 0.668437i | \(-0.766964\pi\) | ||||
−0.743769 | + | 0.668437i | \(0.766964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.58423 | −1.00408 | −0.502042 | − | 0.864843i | \(-0.667418\pi\) | ||||
−0.502042 | + | 0.864843i | \(0.667418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.2031 | −1.78001 | −0.890004 | − | 0.455954i | \(-0.849298\pi\) | ||||
−0.890004 | + | 0.455954i | \(0.849298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.16845 | 0.723728 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.49023 | −1.02886 | −0.514431 | − | 0.857532i | \(-0.671997\pi\) | ||||
−0.514431 | + | 0.857532i | \(0.671997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.6933 | −2.34354 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.49023 | 0.830989 | 0.415494 | − | 0.909596i | \(-0.363609\pi\) | ||||
0.415494 | + | 0.909596i | \(0.363609\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.75268 | 0.702801 | 0.351401 | − | 0.936225i | \(-0.385706\pi\) | ||||
0.351401 | + | 0.936225i | \(0.385706\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.84667 | 0.703857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6933 | −1.36860 | −0.684301 | − | 0.729199i | \(-0.739893\pi\) | ||||
−0.684301 | + | 0.729199i | \(0.739893\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.69334 | 0.640551 | 0.320276 | − | 0.947324i | \(-0.396224\pi\) | ||||
0.320276 | + | 0.947324i | \(0.396224\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.50535 | −0.722817 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5842 | −1.38130 | −0.690649 | − | 0.723190i | \(-0.742675\pi\) | ||||
−0.690649 | + | 0.723190i | \(0.742675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.58423 | 0.920326 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.84667 | 0.619746 | 0.309873 | − | 0.950778i | \(-0.399713\pi\) | ||||
0.309873 | + | 0.950778i | \(0.399713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.6933 | −2.45689 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.17287 | 0.620397 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.0151 | 1.69307 | 0.846534 | − | 0.532335i | \(-0.178685\pi\) | ||||
0.846534 | + | 0.532335i | \(0.178685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.10912 | 0.700482 | 0.350241 | − | 0.936660i | \(-0.386100\pi\) | ||||
0.350241 | + | 0.936660i | \(0.386100\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.75268 | 0.169438 | 0.0847188 | − | 0.996405i | \(-0.473001\pi\) | ||||
0.0847188 | + | 0.996405i | \(0.473001\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.5400 | 1.87159 | 0.935797 | − | 0.352539i | \(-0.114682\pi\) | ||||
0.935797 | + | 0.352539i | \(0.114682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.35644 | 0.698243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.3369 | −0.972414 | −0.486207 | − | 0.873844i | \(-0.661620\pi\) | ||||
−0.486207 | + | 0.873844i | \(0.661620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.8271 | −1.64812 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.18357 | −0.743961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.6145 | −2.21941 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1836 | 1.70227 | 0.851133 | − | 0.524949i | \(-0.175916\pi\) | ||||
0.851133 | + | 0.524949i | \(0.175916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.0151 | −1.49810 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8271 | 1.55756 | 0.778782 | − | 0.627295i | \(-0.215838\pi\) | ||||
0.778782 | + | 0.627295i | \(0.215838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.00000 | −0.341743 | −0.170872 | − | 0.985293i | \(-0.554658\pi\) | ||||
−0.170872 | + | 0.985293i | \(0.554658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.16845 | 0.438382 | 0.219191 | − | 0.975682i | \(-0.429658\pi\) | ||||
0.219191 | + | 0.975682i | \(0.429658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.5356 | −2.65578 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.13379 | −0.680181 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.796886 | 0.0652834 | 0.0326417 | − | 0.999467i | \(-0.489608\pi\) | ||||
0.0326417 | + | 0.999467i | \(0.489608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5249 | −1.34478 | −0.672388 | − | 0.740199i | \(-0.734731\pi\) | ||||
−0.672388 | + | 0.740199i | \(0.734731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.35644 | 0.594733 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.20311 | 0.654680 | 0.327340 | − | 0.944907i | \(-0.393848\pi\) | ||||
0.327340 | + | 0.944907i | \(0.393848\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.3564 | −1.53507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.69334 | −0.289285 | −0.144643 | − | 0.989484i | \(-0.546203\pi\) | ||||
−0.144643 | + | 0.989484i | \(0.546203\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.262447 | −0.0203087 | −0.0101544 | − | 0.999948i | \(-0.503232\pi\) | ||||
−0.0101544 | + | 0.999948i | \(0.503232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4902 | 0.806941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.1836 | −1.92584 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8467 | −1.43289 | −0.716443 | − | 0.697646i | \(-0.754231\pi\) | ||||
−0.716443 | + | 0.697646i | \(0.754231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.6738 | −1.55394 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0151 | −0.898052 | −0.449026 | − | 0.893519i | \(-0.648229\pi\) | ||||
−0.449026 | + | 0.893519i | \(0.648229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.03466 | 0.448553 | 0.224276 | − | 0.974526i | \(-0.427998\pi\) | ||||
0.224276 | + | 0.974526i | \(0.427998\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.7722 | 1.23984 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.35644 | 0.245447 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.83155 | 0.204884 | 0.102442 | − | 0.994739i | \(-0.467334\pi\) | ||||
0.102442 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9805 | −0.934354 | −0.467177 | − | 0.884164i | \(-0.654729\pi\) | ||||
−0.467177 | + | 0.884164i | \(0.654729\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.84667 | 0.345311 | 0.172656 | − | 0.984982i | \(-0.444765\pi\) | ||||
0.172656 | + | 0.984982i | \(0.444765\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3867 | 1.09073 | 0.545367 | − | 0.838198i | \(-0.316390\pi\) | ||||
0.545367 | + | 0.838198i | \(0.316390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8662 | 1.04858 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.32178 | 0.578404 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.4902 | −0.794796 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.18357 | 0.632223 | 0.316112 | − | 0.948722i | \(-0.397623\pi\) | ||||
0.316112 | + | 0.948722i | \(0.397623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −30.2182 | −2.04196 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.69334 | −0.652045 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9805 | −0.869236 | −0.434618 | − | 0.900615i | \(-0.643117\pi\) | ||||
−0.434618 | + | 0.900615i | \(0.643117\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.0302 | −1.46220 | −0.731099 | − | 0.682271i | \(-0.760992\pi\) | ||||
−0.731099 | + | 0.682271i | \(0.760992\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.30666 | −0.284592 | −0.142296 | − | 0.989824i | \(-0.545448\pi\) | ||||
−0.142296 | + | 0.989824i | \(0.545448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.7129 | 0.955705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8618 | 0.702591 | 0.351296 | − | 0.936265i | \(-0.385741\pi\) | ||||
0.351296 | + | 0.936265i | \(0.385741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.203114 | −0.0130837 | −0.00654187 | − | 0.999979i | \(-0.502082\pi\) | ||||
−0.00654187 | + | 0.999979i | \(0.502082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0693 | −1.41575 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.1836 | 2.11142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −32.5205 | −2.06090 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.03466 | −0.317785 | −0.158893 | − | 0.987296i | \(-0.550792\pi\) | ||||
−0.158893 | + | 0.987296i | \(0.550792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.79689 | 0.238708 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.3867 | 1.45882 | 0.729411 | − | 0.684076i | \(-0.239794\pi\) | ||||
0.729411 | + | 0.684076i | \(0.239794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2182 | 0.756290 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.1091 | −1.67162 | −0.835810 | − | 0.549019i | \(-0.815001\pi\) | ||||
−0.835810 | + | 0.549019i | \(0.815001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.1091 | 0.924663 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.49023 | −0.395716 | −0.197858 | − | 0.980231i | \(-0.563399\pi\) | ||||
−0.197858 | + | 0.980231i | \(0.563399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.3867 | 1.42064 | 0.710320 | − | 0.703879i | \(-0.248550\pi\) | ||||
0.710320 | + | 0.703879i | \(0.248550\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.66310 | −0.220094 | −0.110047 | − | 0.993926i | \(-0.535100\pi\) | ||||
−0.110047 | + | 0.993926i | \(0.535100\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −33.7236 | −2.01898 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8965 | 0.828993 | 0.414497 | − | 0.910051i | \(-0.363958\pi\) | ||||
0.414497 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.3369 | −1.20890 | −0.604452 | − | 0.796642i | \(-0.706608\pi\) | ||||
−0.604452 | + | 0.796642i | \(0.706608\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.16845 | −0.302980 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.8467 | 1.10103 | 0.550517 | − | 0.834824i | \(-0.314431\pi\) | ||||
0.550517 | + | 0.834824i | \(0.314431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.94138 | 0.170676 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.9653 | −0.634142 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 43.9709 | 2.52606 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.39623 | −0.136760 | −0.0683802 | − | 0.997659i | \(-0.521783\pi\) | ||||
−0.0683802 | + | 0.997659i | \(0.521783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.3716 | 1.04512 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.66310 | 0.321125 | 0.160562 | − | 0.987026i | \(-0.448669\pi\) | ||||
0.160562 | + | 0.987026i | \(0.448669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.7236 | 1.68008 | 0.840038 | − | 0.542527i | \(-0.182532\pi\) | ||||
0.840038 | + | 0.542527i | \(0.182532\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.0498 | −1.06994 | −0.534971 | − | 0.844870i | \(-0.679678\pi\) | ||||
−0.534971 | + | 0.844870i | \(0.679678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.57468 | 0.312122 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.52931 | 0.252801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.6933 | −0.761918 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 50.4958 | 2.79242 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.32178 | 0.127617 | 0.0638083 | − | 0.997962i | \(-0.479675\pi\) | ||||
0.0638083 | + | 0.997962i | \(0.479675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.4707 | 0.573790 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4062 | 0.893704 | 0.446852 | − | 0.894608i | \(-0.352545\pi\) | ||||
0.446852 | + | 0.894608i | \(0.352545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.7129 | −1.45084 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.3867 | −0.833236 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.58423 | −0.246094 | −0.123047 | − | 0.992401i | \(-0.539267\pi\) | ||||
−0.123047 | + | 0.992401i | \(0.539267\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3716 | −0.662235 | −0.331117 | − | 0.943590i | \(-0.607426\pi\) | ||||
−0.331117 | + | 0.943590i | \(0.607426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.49465 | −0.453411 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.3867 | 1.03185 | 0.515925 | − | 0.856634i | \(-0.327448\pi\) | ||||
0.515925 | + | 0.856634i | \(0.327448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.81201 | −0.517858 | −0.258929 | − | 0.965896i | \(-0.583370\pi\) | ||||
−0.258929 | + | 0.965896i | \(0.583370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.8769 | 1.46721 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.1482 | −1.10999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7180 | −0.663875 | −0.331937 | − | 0.943301i | \(-0.607702\pi\) | ||||
−0.331937 | + | 0.943301i | \(0.607702\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −35.0347 | −1.82383 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4062 | 0.849482 | 0.424741 | − | 0.905315i | \(-0.360365\pi\) | ||||
0.424741 | + | 0.905315i | \(0.360365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.0996 | −0.829170 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4707 | 0.743309 | 0.371655 | − | 0.928371i | \(-0.378791\pi\) | ||||
0.371655 | + | 0.928371i | \(0.378791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49.5747 | 2.53979 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.54956 | −0.181374 | −0.0906871 | − | 0.995879i | \(-0.528906\pi\) | ||||
−0.0906871 | + | 0.995879i | \(0.528906\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.2182 | −1.23108 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.98046 | 0.455327 | 0.227664 | − | 0.973740i | \(-0.426891\pi\) | ||||
0.227664 | + | 0.973740i | \(0.426891\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.52489 | 0.228834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 46.0693 | 2.32389 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.0996 | −1.41028 | −0.705139 | − | 0.709070i | \(-0.749115\pi\) | ||||
−0.705139 | + | 0.709070i | \(0.749115\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.6933 | −1.33300 | −0.666501 | − | 0.745504i | \(-0.732209\pi\) | ||||
−0.666501 | + | 0.745504i | \(0.732209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.4365 | 2.21354 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.77735 | 0.236804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.0649 | −1.38772 | −0.693860 | − | 0.720110i | \(-0.744091\pi\) | ||||
−0.693860 | + | 0.720110i | \(0.744091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.3369 | −0.509882 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.3564 | 0.654068 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8769 | 0.922198 | 0.461099 | − | 0.887349i | \(-0.347455\pi\) | ||||
0.461099 | + | 0.887349i | \(0.347455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.1836 | −1.37358 | −0.686792 | − | 0.726854i | \(-0.740982\pi\) | ||||
−0.686792 | + | 0.726854i | \(0.740982\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −44.8858 | −2.18242 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.0195 | −1.01483 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.83155 | 0.136391 | 0.0681955 | − | 0.997672i | \(-0.478276\pi\) | ||||
0.0681955 | + | 0.997672i | \(0.478276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.33690 | −0.112304 | −0.0561522 | − | 0.998422i | \(-0.517883\pi\) | ||||
−0.0561522 | + | 0.998422i | \(0.517883\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.4902 | −0.740998 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.06933 | 0.289673 | 0.144837 | − | 0.989456i | \(-0.453734\pi\) | ||||
0.144837 | + | 0.989456i | \(0.453734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.6038 | −0.551312 | −0.275656 | − | 0.961256i | \(-0.588895\pi\) | ||||
−0.275656 | + | 0.961256i | \(0.588895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.05933 | 0.0974031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.13821 | 0.195294 | 0.0976470 | − | 0.995221i | \(-0.468868\pi\) | ||||
0.0976470 | + | 0.995221i | \(0.468868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.9849 | −0.752698 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.7040 | −2.00641 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6436 | 0.591441 | 0.295720 | − | 0.955275i | \(-0.404440\pi\) | ||||
0.295720 | + | 0.955275i | \(0.404440\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.50535 | 0.163616 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.7129 | −0.964695 | −0.482348 | − | 0.875980i | \(-0.660216\pi\) | ||||
−0.482348 | + | 0.875980i | \(0.660216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.3811 | 0.761295 | 0.380647 | − | 0.924720i | \(-0.375701\pi\) | ||||
0.380647 | + | 0.924720i | \(0.375701\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.72243 | −0.0797046 | −0.0398523 | − | 0.999206i | \(-0.512689\pi\) | ||||
−0.0398523 | + | 0.999206i | \(0.512689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.1987 | 0.976784 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.0498 | −0.508070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.5507 | −1.26146 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.78176 | 0.0814108 | 0.0407054 | − | 0.999171i | \(-0.487039\pi\) | ||||
0.0407054 | + | 0.999171i | \(0.487039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7969 | −0.629084 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0195 | 0.499343 | 0.249672 | − | 0.968331i | \(-0.419677\pi\) | ||||
0.249672 | + | 0.968331i | \(0.419677\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.54443 | −0.431614 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9311 | −0.944608 | −0.472304 | − | 0.881436i | \(-0.656578\pi\) | ||||
−0.472304 | + | 0.881436i | \(0.656578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.64356 | 0.299211 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.50535 | −0.335986 | −0.167993 | − | 0.985788i | \(-0.553729\pi\) | ||||
−0.167993 | + | 0.985788i | \(0.553729\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.678221 | −0.0303007 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.5842 | 0.917805 | 0.458903 | − | 0.888487i | \(-0.348243\pi\) | ||||
0.458903 | + | 0.888487i | \(0.348243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.1091 | 1.20396 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.6587 | −0.605410 | −0.302705 | − | 0.953084i | \(-0.597890\pi\) | ||||
−0.302705 | + | 0.953084i | \(0.597890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.0000 | −0.529813 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4795 | −0.900688 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.7040 | −2.13787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.1640 | 1.84724 | 0.923620 | − | 0.383310i | \(-0.125216\pi\) | ||||
0.923620 | + | 0.383310i | \(0.125216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6436 | −1.33995 | −0.669975 | − | 0.742384i | \(-0.733695\pi\) | ||||
−0.669975 | + | 0.742384i | \(0.733695\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.3369 | −0.798768 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.8813 | −0.777449 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.4258 | −1.27697 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.1640 | 1.99959 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.0498 | −1.33990 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.6889 | −1.44840 | −0.724200 | − | 0.689590i | \(-0.757791\pi\) | ||||
−0.724200 | + | 0.689590i | \(0.757791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.5949 | 0.669243 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.03979 | 0.129972 | 0.0649861 | − | 0.997886i | \(-0.479300\pi\) | ||||
0.0649861 | + | 0.997886i | \(0.479300\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.8725 | 1.01885 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.7431 | −0.968890 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.1640 | −0.769635 | −0.384817 | − | 0.922993i | \(-0.625736\pi\) | ||||
−0.384817 | + | 0.922993i | \(0.625736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.9116 | 1.34972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.67380 | 0.366208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.9905 | −1.55896 | −0.779481 | − | 0.626426i | \(-0.784517\pi\) | ||||
−0.779481 | + | 0.626426i | \(0.784517\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.6093 | 1.36705 | 0.683527 | − | 0.729925i | \(-0.260445\pi\) | ||||
0.683527 | + | 0.729925i | \(0.260445\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.4365 | 1.69221 | 0.846107 | − | 0.533013i | \(-0.178940\pi\) | ||||
0.846107 | + | 0.533013i | \(0.178940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.31736 | 0.305687 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.0302 | −1.58322 | −0.791610 | − | 0.611027i | \(-0.790757\pi\) | ||||
−0.791610 | + | 0.611027i | \(0.790757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.5444 | −1.39406 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5703 | −0.520607 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.0302 | 1.40458 | 0.702289 | − | 0.711892i | \(-0.252161\pi\) | ||||
0.702289 | + | 0.711892i | \(0.252161\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 62.7734 | 2.58653 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.5249 | 0.515205 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.7236 | −1.38486 | −0.692431 | − | 0.721484i | \(-0.743460\pi\) | ||||
−0.692431 | + | 0.721484i | \(0.743460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.7627 | 1.62738 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.30666 | 0.257683 | 0.128841 | − | 0.991665i | \(-0.458874\pi\) | ||||
0.128841 | + | 0.991665i | \(0.458874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2871 | 0.460411 | 0.230206 | − | 0.973142i | \(-0.426060\pi\) | ||||
0.230206 | + | 0.973142i | \(0.426060\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.1596 | 0.861686 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.4611 | −0.627548 | −0.313774 | − | 0.949498i | \(-0.601594\pi\) | ||||
−0.313774 | + | 0.949498i | \(0.601594\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59.1445 | 2.39273 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.1640 | 0.895197 | 0.447598 | − | 0.894235i | \(-0.352279\pi\) | ||||
0.447598 | + | 0.894235i | \(0.352279\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.9805 | 0.603091 | 0.301545 | − | 0.953452i | \(-0.402498\pi\) | ||||
0.301545 | + | 0.953452i | \(0.402498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.6391 | −0.950137 | −0.475069 | − | 0.879949i | \(-0.657577\pi\) | ||||
−0.475069 | + | 0.879949i | \(0.657577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.96534 | 0.159123 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29.6933 | −1.18584 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.69334 | 0.227008 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7818 | −0.548643 | −0.274322 | − | 0.961638i | \(-0.588453\pi\) | ||||
−0.274322 | + | 0.961638i | \(0.588453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.7324 | 0.943279 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.8618 | 1.73244 | 0.866218 | − | 0.499666i | \(-0.166544\pi\) | ||||
0.866218 | + | 0.499666i | \(0.166544\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.04979 | 0.278016 | 0.139008 | − | 0.990291i | \(-0.455609\pi\) | ||||
0.139008 | + | 0.990291i | \(0.455609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.4807 | −0.962435 | −0.481217 | − | 0.876601i | \(-0.659805\pi\) | ||||
−0.481217 | + | 0.876601i | \(0.659805\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4258 | −0.527008 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.816426 | −0.0319492 | −0.0159746 | − | 0.999872i | \(-0.505085\pi\) | ||||
−0.0159746 | + | 0.999872i | \(0.505085\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −43.0107 | −1.67801 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.2871 | 0.829228 | 0.414614 | − | 0.909997i | \(-0.363917\pi\) | ||||
0.414614 | + | 0.909997i | \(0.363917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.9462 | −1.00919 | −0.504596 | − | 0.863356i | \(-0.668359\pi\) | ||||
−0.504596 | + | 0.863356i | \(0.668359\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.0498 | −0.972853 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.51535 | 0.290995 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.5444 | −1.29690 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8920 | 0.420483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0693 | −0.850710 | −0.425355 | − | 0.905027i | \(-0.639851\pi\) | ||||
−0.425355 | + | 0.905027i | \(0.639851\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.49023 | 0.211007 | 0.105503 | − | 0.994419i | \(-0.466355\pi\) | ||||
0.105503 | + | 0.994419i | \(0.466355\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56.9311 | −2.18161 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.2278 | −0.735731 | −0.367865 | − | 0.929879i | \(-0.619911\pi\) | ||||
−0.367865 | + | 0.929879i | \(0.619911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.1294 | −0.424612 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.3027 | 1.38302 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.2182 | −0.540887 | −0.270444 | − | 0.962736i | \(-0.587170\pi\) | ||||
−0.270444 | + | 0.962736i | \(0.587170\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.0498 | −0.721562 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −46.5161 | −1.75940 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.1533 | 0.534564 | 0.267282 | − | 0.963618i | \(-0.413875\pi\) | ||||
0.267282 | + | 0.963618i | \(0.413875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.4902 | −0.735088 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0454 | 0.640152 | 0.320076 | − | 0.947392i | \(-0.396292\pi\) | ||||
0.320076 | + | 0.947392i | \(0.396292\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.9414 | 0.785363 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.7431 | −0.776836 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.0693 | 1.04827 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5054 | 0.429077 | 0.214539 | − | 0.976716i | \(-0.431175\pi\) | ||||
0.214539 | + | 0.976716i | \(0.431175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.524893 | −0.0195210 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4114 | 0.608664 | 0.304332 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304332 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.5161 | −1.38948 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1685 | −0.487053 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.11425 | −0.336642 | −0.168321 | − | 0.985732i | \(-0.553835\pi\) | ||||
−0.168321 | + | 0.985732i | \(0.553835\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.65426 | 0.355619 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.9956 | −1.28733 | −0.643667 | − | 0.765306i | \(-0.722588\pi\) | ||||
−0.643667 | + | 0.765306i | \(0.722588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 85.7538 | 3.15025 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.5305 | 1.59698 | 0.798489 | − | 0.602009i | \(-0.205633\pi\) | ||||
0.798489 | + | 0.602009i | \(0.205633\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −46.2876 | −1.69357 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.30666 | 0.230133 | 0.115067 | − | 0.993358i | \(-0.463292\pi\) | ||||
0.115067 | + | 0.993358i | \(0.463292\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.0107 | −0.474136 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.3369 | −0.884540 | −0.442270 | − | 0.896882i | \(-0.645827\pi\) | ||||
−0.442270 | + | 0.896882i | \(0.645827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.81201 | 0.356153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.2031 | 1.02236 | 0.511181 | − | 0.859473i | \(-0.329208\pi\) | ||||
0.511181 | + | 0.859473i | \(0.329208\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.7734 | 1.40003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.8965 | 1.51082 | 0.755412 | − | 0.655250i | \(-0.227437\pi\) | ||||
0.755412 | + | 0.655250i | \(0.227437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.4365 | 2.17657 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.8574 | 1.43357 | 0.716785 | − | 0.697294i | \(-0.245613\pi\) | ||||
0.716785 | + | 0.697294i | \(0.245613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 65.2138 | 2.33653 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.82200 | 0.208061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.3274 | 1.25928 | 0.629642 | − | 0.776885i | \(-0.283202\pi\) | ||||
0.629642 | + | 0.776885i | \(0.283202\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −70.0561 | −2.49406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.4560 | −1.11704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.6933 | 1.05179 | 0.525896 | − | 0.850549i | \(-0.323730\pi\) | ||||
0.525896 | + | 0.850549i | \(0.323730\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.4062 | −0.863430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.5054 | 0.759854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.6240 | −0.692517 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.7722 | −0.590410 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.6436 | −0.690631 | −0.345315 | − | 0.938487i | \(-0.612228\pi\) | ||||
−0.345315 | + | 0.938487i | \(0.612228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.252452 | −0.00886479 | −0.00443239 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443239 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 60.4365 | 2.11960 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.0800 | 1.57715 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.7734 | 1.56260 | 0.781301 | − | 0.624155i | \(-0.214556\pi\) | ||||
0.781301 | + | 0.624155i | \(0.214556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.29711 | −0.114930 | −0.0574650 | − | 0.998348i | \(-0.518302\pi\) | ||||
−0.0574650 | + | 0.998348i | \(0.518302\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.41577 | −0.327419 | −0.163709 | − | 0.986509i | \(-0.552346\pi\) | ||||
−0.163709 | + | 0.986509i | \(0.552346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.71288 | 0.163685 | 0.0818426 | − | 0.996645i | \(-0.473920\pi\) | ||||
0.0818426 | + | 0.996645i | \(0.473920\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.46627 | −0.328381 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0693 | −0.555437 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1880 | −0.766015 | −0.383007 | − | 0.923745i | \(-0.625112\pi\) | ||||
−0.383007 | + | 0.923745i | \(0.625112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9658 | −0.619510 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35.9116 | 1.23686 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −52.5551 | −1.80369 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.44044 | 0.220776 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.9267 | 1.36706 | 0.683532 | − | 0.729920i | \(-0.260443\pi\) | ||||
0.683532 | + | 0.729920i | \(0.260443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.62402 | −0.0554754 | −0.0277377 | − | 0.999615i | \(-0.508830\pi\) | ||||
−0.0277377 | + | 0.999615i | \(0.508830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.00000 | −0.272956 | −0.136478 | − | 0.990643i | \(-0.543578\pi\) | ||||
−0.136478 | + | 0.990643i | \(0.543578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.2234 | −0.620331 | −0.310165 | − | 0.950683i | \(-0.600384\pi\) | ||||
−0.310165 | + | 0.950683i | \(0.600384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.5949 | −1.14094 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.55469 | 0.324121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.8813 | −0.944723 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.35644 | −0.248978 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.8769 | 1.71799 | 0.858996 | − | 0.511983i | \(-0.171089\pi\) | ||||
0.858996 | + | 0.511983i | \(0.171089\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 48.7040 | 1.64275 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1187 | 0.644124 | 0.322062 | − | 0.946719i | \(-0.395624\pi\) | ||||
0.322062 | + | 0.946719i | \(0.395624\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.3174 | −1.32313 | −0.661567 | − | 0.749886i | \(-0.730108\pi\) | ||||
−0.661567 | + | 0.749886i | \(0.730108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.0398 | 0.907907 | 0.453954 | − | 0.891025i | \(-0.350013\pi\) | ||||
0.453954 | + | 0.891025i | \(0.350013\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.9174 | −0.365747 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 83.5507 | 2.79592 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.3369 | −0.946142 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.4556 | −1.01575 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.9805 | −0.499071 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.8025 | −1.08919 | −0.544594 | − | 0.838700i | \(-0.683316\pi\) | ||||
−0.544594 | + | 0.838700i | \(0.683316\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 62.5854 | 2.07583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.18799 | 0.205017 | 0.102509 | − | 0.994732i | \(-0.467313\pi\) | ||||
0.102509 | + | 0.994732i | \(0.467313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.1191 | −0.698941 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.7929 | −1.57654 | −0.788271 | − | 0.615328i | \(-0.789024\pi\) | ||||
−0.788271 | + | 0.615328i | \(0.789024\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.19241 | −0.204047 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.1489 | 0.858843 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.8618 | 1.30782 | 0.653912 | − | 0.756571i | \(-0.273127\pi\) | ||||
0.653912 | + | 0.756571i | \(0.273127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.6347 | 0.479119 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.406229 | 0.0132709 | 0.00663546 | − | 0.999978i | \(-0.497888\pi\) | ||||
0.00663546 | + | 0.999978i | \(0.497888\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 76.8125 | 2.50668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.6543 | −1.09710 | −0.548549 | − | 0.836119i | \(-0.684820\pi\) | ||||
−0.548549 | + | 0.836119i | \(0.684820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.5496 | −0.701750 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.84110 | −0.189810 | −0.0949050 | − | 0.995486i | \(-0.530255\pi\) | ||||
−0.0949050 | + | 0.995486i | \(0.530255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.6738 | 1.83971 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49.2289 | −1.59636 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.0605 | −1.03854 | −0.519271 | − | 0.854610i | \(-0.673796\pi\) | ||||
−0.519271 | + | 0.854610i | \(0.673796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.4062 | 0.465687 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.0605 | 1.71163 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.44673 | 0.207743 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0896 | −0.774669 | −0.387334 | − | 0.921939i | \(-0.626604\pi\) | ||||
−0.387334 | + | 0.921939i | \(0.626604\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.3867 | −1.13678 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4707 | −0.592753 | −0.296376 | − | 0.955071i | \(-0.595778\pi\) | ||||
−0.296376 | + | 0.955071i | \(0.595778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.3369 | −0.778606 | −0.389303 | − | 0.921110i | \(-0.627284\pi\) | ||||
−0.389303 | + | 0.921110i | \(0.627284\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.81201 | 0.313593 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 71.8725 | 2.29471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.66868 | 0.276488 | 0.138244 | − | 0.990398i | \(-0.455854\pi\) | ||||
0.138244 | + | 0.990398i | \(0.455854\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.8965 | −0.473680 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.5054 | −1.76319 | −0.881593 | − | 0.472011i | \(-0.843528\pi\) | ||||
−0.881593 | + | 0.472011i | \(0.843528\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.00000 | 0.190404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.1191 | −1.11223 | −0.556117 | − | 0.831104i | \(-0.687709\pi\) | ||||
−0.556117 | + | 0.831104i | \(0.687709\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.98929 | 0.157854 |
(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 | 9800.2.a.cf.1.3 | 3 | ||
5.4 | even | 2 | 1960.2.a.v.1.1 | 3 | |||
7.3 | odd | 6 | 1400.2.q.j.401.3 | 6 | |||
7.5 | odd | 6 | 1400.2.q.j.1201.3 | 6 | |||
7.6 | odd | 2 | 9800.2.a.ce.1.1 | 3 | |||
20.19 | odd | 2 | 3920.2.a.cb.1.3 | 3 | |||
35.3 | even | 12 | 1400.2.bh.i.849.2 | 12 | |||
35.4 | even | 6 | 1960.2.q.w.961.3 | 6 | |||
35.9 | even | 6 | 1960.2.q.w.361.3 | 6 | |||
35.12 | even | 12 | 1400.2.bh.i.249.2 | 12 | |||
35.17 | even | 12 | 1400.2.bh.i.849.5 | 12 | |||
35.19 | odd | 6 | 280.2.q.e.81.1 | ✓ | 6 | ||
35.24 | odd | 6 | 280.2.q.e.121.1 | yes | 6 | ||
35.33 | even | 12 | 1400.2.bh.i.249.5 | 12 | |||
35.34 | odd | 2 | 1960.2.a.w.1.3 | 3 | |||
105.59 | even | 6 | 2520.2.bi.q.1801.1 | 6 | |||
105.89 | even | 6 | 2520.2.bi.q.361.1 | 6 | |||
140.19 | even | 6 | 560.2.q.l.81.3 | 6 | |||
140.59 | even | 6 | 560.2.q.l.401.3 | 6 | |||
140.139 | even | 2 | 3920.2.a.cc.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.e.81.1 | ✓ | 6 | 35.19 | odd | 6 | ||
280.2.q.e.121.1 | yes | 6 | 35.24 | odd | 6 | ||
560.2.q.l.81.3 | 6 | 140.19 | even | 6 | |||
560.2.q.l.401.3 | 6 | 140.59 | even | 6 | |||
1400.2.q.j.401.3 | 6 | 7.3 | odd | 6 | |||
1400.2.q.j.1201.3 | 6 | 7.5 | odd | 6 | |||
1400.2.bh.i.249.2 | 12 | 35.12 | even | 12 | |||
1400.2.bh.i.249.5 | 12 | 35.33 | even | 12 | |||
1400.2.bh.i.849.2 | 12 | 35.3 | even | 12 | |||
1400.2.bh.i.849.5 | 12 | 35.17 | even | 12 | |||
1960.2.a.v.1.1 | 3 | 5.4 | even | 2 | |||
1960.2.a.w.1.3 | 3 | 35.34 | odd | 2 | |||
1960.2.q.w.361.3 | 6 | 35.9 | even | 6 | |||
1960.2.q.w.961.3 | 6 | 35.4 | even | 6 | |||
2520.2.bi.q.361.1 | 6 | 105.89 | even | 6 | |||
2520.2.bi.q.1801.1 | 6 | 105.59 | even | 6 | |||
3920.2.a.cb.1.3 | 3 | 20.19 | odd | 2 | |||
3920.2.a.cc.1.1 | 3 | 140.139 | even | 2 | |||
9800.2.a.ce.1.1 | 3 | 7.6 | odd | 2 | |||
9800.2.a.cf.1.3 | 3 | 1.1 | even | 1 | trivial |