Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9576,2,Mod(1,9576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9576.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: | \(76.4647449756\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.401584.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 8x^{2} + 12x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 3192) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.86937\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9576.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.93275 | 1.31157 | 0.655784 | − | 0.754949i | \(-0.272338\pi\) | ||||
0.655784 | + | 0.754949i | \(0.272338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.73874 | −1.73029 | −0.865147 | − | 0.501518i | \(-0.832775\pi\) | ||||
−0.865147 | + | 0.501518i | \(0.832775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.54964 | 0.707144 | 0.353572 | − | 0.935407i | \(-0.384967\pi\) | ||||
0.353572 | + | 0.935407i | \(0.384967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.34470 | 0.568674 | 0.284337 | − | 0.958724i | \(-0.408227\pi\) | ||||
0.284337 | + | 0.958724i | \(0.408227\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.32679 | 0.485169 | 0.242584 | − | 0.970130i | \(-0.422005\pi\) | ||||
0.242584 | + | 0.970130i | \(0.422005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.60104 | 0.720208 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.47147 | −1.20172 | −0.600861 | − | 0.799353i | \(-0.705176\pi\) | ||||
−0.600861 | + | 0.799353i | \(0.705176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.87850 | −1.77423 | −0.887115 | − | 0.461548i | \(-0.847294\pi\) | ||||
−0.887115 | + | 0.461548i | \(0.847294\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.93275 | 0.495726 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.68734 | −0.606195 | −0.303097 | − | 0.952960i | \(-0.598021\pi\) | ||||
−0.303097 | + | 0.952960i | \(0.598021\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6536 | −1.66381 | −0.831905 | − | 0.554919i | \(-0.812749\pi\) | ||||
−0.831905 | + | 0.554919i | \(0.812749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.08836 | −0.623469 | −0.311735 | − | 0.950169i | \(-0.600910\pi\) | ||||
−0.311735 | + | 0.950169i | \(0.600910\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.29330 | −0.626242 | −0.313121 | − | 0.949713i | \(-0.601375\pi\) | ||||
−0.313121 | + | 0.949713i | \(0.601375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.47147 | −0.888925 | −0.444462 | − | 0.895797i | \(-0.646605\pi\) | ||||
−0.444462 | + | 0.895797i | \(0.646605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.8303 | −2.26940 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.07744 | −0.921404 | −0.460702 | − | 0.887555i | \(-0.652402\pi\) | ||||
−0.460702 | + | 0.887555i | \(0.652402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.47747 | 0.927466 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.95067 | 0.360481 | 0.180241 | − | 0.983623i | \(-0.442312\pi\) | ||||
0.180241 | + | 0.983623i | \(0.442312\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.98415 | −1.06622 | −0.533111 | − | 0.846045i | \(-0.678977\pi\) | ||||
−0.533111 | + | 0.846045i | \(0.678977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.86551 | 0.920588 | 0.460294 | − | 0.887767i | \(-0.347744\pi\) | ||||
0.460294 | + | 0.887767i | \(0.347744\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.73874 | −0.653990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.32679 | −0.261784 | −0.130892 | − | 0.991397i | \(-0.541784\pi\) | ||||
−0.130892 | + | 0.991397i | \(0.541784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.29537 | 0.361714 | 0.180857 | − | 0.983509i | \(-0.442113\pi\) | ||||
0.180857 | + | 0.983509i | \(0.442113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.87643 | 0.745854 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.7529 | 1.24580 | 0.622900 | − | 0.782301i | \(-0.285954\pi\) | ||||
0.622900 | + | 0.782301i | \(0.285954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.54964 | 0.267275 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.93275 | 0.300894 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.46335 | −0.148580 | −0.0742902 | − | 0.997237i | \(-0.523669\pi\) | ||||
−0.0742902 | + | 0.997237i | \(0.523669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9011 | 1.28370 | 0.641852 | − | 0.766829i | \(-0.278166\pi\) | ||||
0.641852 | + | 0.766829i | \(0.278166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.41195 | −0.336189 | −0.168095 | − | 0.985771i | \(-0.553761\pi\) | ||||
−0.168095 | + | 0.985771i | \(0.553761\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.8715 | −1.63103 | −0.815515 | − | 0.578736i | \(-0.803546\pi\) | ||||
−0.815515 | + | 0.578736i | \(0.803546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.47541 | 0.237101 | 0.118551 | − | 0.992948i | \(-0.462175\pi\) | ||||
0.118551 | + | 0.992948i | \(0.462175\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.1250 | −1.42284 | −0.711422 | − | 0.702765i | \(-0.751949\pi\) | ||||
−0.711422 | + | 0.702765i | \(0.751949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.82390 | 0.636332 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.34470 | 0.214938 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.9331 | 1.99392 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.10280 | −0.366965 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2916 | 1.17944 | 0.589719 | − | 0.807609i | \(-0.299239\pi\) | ||||
0.589719 | + | 0.807609i | \(0.299239\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.39404 | −0.471279 | −0.235640 | − | 0.971841i | \(-0.575718\pi\) | ||||
−0.235640 | + | 0.971841i | \(0.575718\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.07744 | −0.775538 | −0.387769 | − | 0.921757i | \(-0.626754\pi\) | ||||
−0.387769 | + | 0.921757i | \(0.626754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.51330 | 0.637270 | 0.318635 | − | 0.947878i | \(-0.396776\pi\) | ||||
0.318635 | + | 0.947878i | \(0.396776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.6317 | −1.22357 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.9792 | −1.57614 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.200018 | −0.0163861 | −0.00819307 | − | 0.999966i | \(-0.502608\pi\) | ||||
−0.00819307 | + | 0.999966i | \(0.502608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2697 | −1.56815 | −0.784074 | − | 0.620667i | \(-0.786862\pi\) | ||||
−0.784074 | + | 0.620667i | \(0.786862\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −28.9712 | −2.32702 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6542 | 1.40896 | 0.704479 | − | 0.709725i | \(-0.251181\pi\) | ||||
0.704479 | + | 0.709725i | \(0.251181\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.32679 | 0.183377 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5658 | −0.905906 | −0.452953 | − | 0.891534i | \(-0.649629\pi\) | ||||
−0.452953 | + | 0.891534i | \(0.649629\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.4204 | −1.88971 | −0.944854 | − | 0.327491i | \(-0.893797\pi\) | ||||
−0.944854 | + | 0.327491i | \(0.893797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.49932 | −0.499948 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.5549 | 1.56276 | 0.781380 | − | 0.624055i | \(-0.214516\pi\) | ||||
0.781380 | + | 0.624055i | \(0.214516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.60104 | 0.272213 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.59612 | 0.194043 | 0.0970215 | − | 0.995282i | \(-0.469068\pi\) | ||||
0.0970215 | + | 0.995282i | \(0.469068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7056 | 1.31605 | 0.658023 | − | 0.752998i | \(-0.271393\pi\) | ||||
0.658023 | + | 0.752998i | \(0.271393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8141 | −0.795065 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4556 | −0.983973 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.69506 | −0.556795 | −0.278398 | − | 0.960466i | \(-0.589803\pi\) | ||||
−0.278398 | + | 0.960466i | \(0.589803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.1092 | 1.73542 | 0.867709 | − | 0.497072i | \(-0.165592\pi\) | ||||
0.867709 | + | 0.497072i | \(0.165592\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.3450 | −1.30703 | −0.653515 | − | 0.756913i | \(-0.726706\pi\) | ||||
−0.653515 | + | 0.756913i | \(0.726706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4198 | 1.23486 | 0.617428 | − | 0.786627i | \(-0.288175\pi\) | ||||
0.617428 | + | 0.786627i | \(0.288175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.47147 | −0.454208 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.2443 | −2.18220 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.73874 | −0.396957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0951 | 0.970345 | 0.485173 | − | 0.874418i | \(-0.338757\pi\) | ||||
0.485173 | + | 0.874418i | \(0.338757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.9902 | −0.817722 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.87850 | −0.670596 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.97815 | 0.402134 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.95532 | −0.130938 | −0.0654688 | − | 0.997855i | \(-0.520854\pi\) | ||||
−0.0654688 | + | 0.997855i | \(0.520854\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.512681 | −0.0340278 | −0.0170139 | − | 0.999855i | \(-0.505416\pi\) | ||||
−0.0170139 | + | 0.999855i | \(0.505416\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.1409 | −1.46311 | −0.731556 | − | 0.681782i | \(-0.761205\pi\) | ||||
−0.731556 | + | 0.681782i | \(0.761205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.2402 | −0.998417 | −0.499209 | − | 0.866482i | \(-0.666376\pi\) | ||||
−0.499209 | + | 0.866482i | \(0.666376\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.5912 | −0.821359 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3176 | 1.37892 | 0.689459 | − | 0.724325i | \(-0.257848\pi\) | ||||
0.689459 | + | 0.724325i | \(0.257848\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.0459 | −1.35568 | −0.677842 | − | 0.735207i | \(-0.737085\pi\) | ||||
−0.677842 | + | 0.735207i | \(0.737085\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.93275 | 0.187367 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.54964 | 0.162230 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3271 | 0.651843 | 0.325921 | − | 0.945397i | \(-0.394326\pi\) | ||||
0.325921 | + | 0.945397i | \(0.394326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.3528 | −0.839485 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.8661 | 1.42635 | 0.713175 | − | 0.700986i | \(-0.247257\pi\) | ||||
0.713175 | + | 0.700986i | \(0.247257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.68734 | −0.229120 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.45777 | 0.0898899 | 0.0449449 | − | 0.998989i | \(-0.485689\pi\) | ||||
0.0449449 | + | 0.998989i | \(0.485689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.9792 | −1.16588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.7177 | 1.62900 | 0.814502 | − | 0.580161i | \(-0.197010\pi\) | ||||
0.814502 | + | 0.580161i | \(0.197010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.70916 | 0.589790 | 0.294895 | − | 0.955530i | \(-0.404715\pi\) | ||||
0.294895 | + | 0.955530i | \(0.404715\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.6654 | −1.24617 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2552 | −1.09685 | −0.548425 | − | 0.836199i | \(-0.684773\pi\) | ||||
−0.548425 | + | 0.836199i | \(0.684773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.1117 | −1.19976 | −0.599881 | − | 0.800089i | \(-0.704786\pi\) | ||||
−0.599881 | + | 0.800089i | \(0.704786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4416 | 0.917911 | 0.458955 | − | 0.888459i | \(-0.348224\pi\) | ||||
0.458955 | + | 0.888459i | \(0.348224\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6536 | −0.628861 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.5024 | −0.676610 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.0382 | 1.81327 | 0.906635 | − | 0.421917i | \(-0.138643\pi\) | ||||
0.906635 | + | 0.421917i | \(0.138643\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.7564 | −1.20848 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.93248 | 0.343084 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.08836 | −0.235649 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.86551 | −0.335858 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.9222 | −1.13702 | −0.568509 | − | 0.822677i | \(-0.692480\pi\) | ||||
−0.568509 | + | 0.822677i | \(0.692480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.8800 | 1.24070 | 0.620350 | − | 0.784325i | \(-0.286991\pi\) | ||||
0.620350 | + | 0.784325i | \(0.286991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0577 | 0.738067 | 0.369034 | − | 0.929416i | \(-0.379689\pi\) | ||||
0.369034 | + | 0.929416i | \(0.379689\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.05746 | 0.452552 | 0.226276 | − | 0.974063i | \(-0.427345\pi\) | ||||
0.226276 | + | 0.974063i | \(0.427345\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.1381 | 2.07933 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.34470 | 0.130463 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.18137 | 0.509291 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.29330 | −0.236697 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0776 | −0.718809 | −0.359405 | − | 0.933182i | \(-0.617020\pi\) | ||||
−0.359405 | + | 0.933182i | \(0.617020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.65358 | 0.472795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.9966 | −1.30718 | −0.653588 | − | 0.756851i | \(-0.726737\pi\) | ||||
−0.653588 | + | 0.756851i | \(0.726737\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 56.6901 | 3.06994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.1373 | −1.72522 | −0.862610 | − | 0.505869i | \(-0.831172\pi\) | ||||
−0.862610 | + | 0.505869i | \(0.831172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.8795 | −0.742952 | −0.371476 | − | 0.928443i | \(-0.621148\pi\) | ||||
−0.371476 | + | 0.928443i | \(0.621148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.24190 | −0.332223 | −0.166111 | − | 0.986107i | \(-0.553121\pi\) | ||||
−0.166111 | + | 0.986107i | \(0.553121\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.3483 | −1.39842 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5964 | −0.717590 | −0.358795 | − | 0.933416i | \(-0.616812\pi\) | ||||
−0.358795 | + | 0.933416i | \(0.616812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.0676 | 1.20741 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6958 | 1.18471 | 0.592356 | − | 0.805677i | \(-0.298198\pi\) | ||||
0.592356 | + | 0.805677i | \(0.298198\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.47147 | −0.335982 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.23523 | −0.0639576 | −0.0319788 | − | 0.999489i | \(-0.510181\pi\) | ||||
−0.0319788 | + | 0.999489i | \(0.510181\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.4999 | −0.849790 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.2064 | 0.678365 | 0.339183 | − | 0.940721i | \(-0.389850\pi\) | ||||
0.339183 | + | 0.940721i | \(0.389850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1450 | −0.927168 | −0.463584 | − | 0.886053i | \(-0.653437\pi\) | ||||
−0.463584 | + | 0.886053i | \(0.653437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.8303 | −0.857751 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.4085 | 1.38967 | 0.694833 | − | 0.719171i | \(-0.255478\pi\) | ||||
0.694833 | + | 0.719171i | \(0.255478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.45562 | 0.275903 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.82390 | −0.343347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.8972 | −0.898235 | −0.449117 | − | 0.893473i | \(-0.648262\pi\) | ||||
−0.449117 | + | 0.893473i | \(0.648262\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.9749 | −1.29713 | −0.648563 | − | 0.761161i | \(-0.724630\pi\) | ||||
−0.648563 | + | 0.761161i | \(0.724630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.1866 | −1.25464 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.1607 | 1.04889 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.9223 | 1.18288 | 0.591441 | − | 0.806348i | \(-0.298559\pi\) | ||||
0.591441 | + | 0.806348i | \(0.298559\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.07744 | −0.348258 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.66450 | 0.474412 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.2925 | 1.77301 | 0.886503 | − | 0.462722i | \(-0.153127\pi\) | ||||
0.886503 | + | 0.462722i | \(0.153127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.93103 | −0.386535 | −0.193267 | − | 0.981146i | \(-0.561908\pi\) | ||||
−0.193267 | + | 0.981146i | \(0.561908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.44337 | 0.409564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3012 | −1.07421 | −0.537104 | − | 0.843516i | \(-0.680482\pi\) | ||||
−0.537104 | + | 0.843516i | \(0.680482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.27960 | −0.157607 | −0.0788037 | − | 0.996890i | \(-0.525110\pi\) | ||||
−0.0788037 | + | 0.996890i | \(0.525110\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.32679 | 0.111305 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.94540 | −0.236031 | −0.118016 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118016 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3809 | 0.540724 | 0.270362 | − | 0.962759i | \(-0.412857\pi\) | ||||
0.270362 | + | 0.962759i | \(0.412857\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.4682 | 1.63395 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.8363 | 1.21929 | 0.609645 | − | 0.792674i | \(-0.291312\pi\) | ||||
0.609645 | + | 0.792674i | \(0.291312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 61.1381 | 2.87888 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.47747 | 0.350549 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.47701 | 0.349760 | 0.174880 | − | 0.984590i | \(-0.444046\pi\) | ||||
0.174880 | + | 0.984590i | \(0.444046\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.7174 | −0.918330 | −0.459165 | − | 0.888351i | \(-0.651851\pi\) | ||||
−0.459165 | + | 0.888351i | \(0.651851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9112 | 0.507089 | 0.253544 | − | 0.967324i | \(-0.418404\pi\) | ||||
0.253544 | + | 0.967324i | \(0.418404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.9693 | 1.10917 | 0.554584 | − | 0.832128i | \(-0.312877\pi\) | ||||
0.554584 | + | 0.832128i | \(0.312877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.95067 | 0.136249 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.4620 | 1.07879 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.60104 | 0.165227 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.8806 | 1.31959 | 0.659794 | − | 0.751447i | \(-0.270644\pi\) | ||||
0.659794 | + | 0.751447i | \(0.270644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.40139 | −0.428667 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.29164 | −0.194873 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0028 | −1.45019 | −0.725093 | − | 0.688651i | \(-0.758203\pi\) | ||||
−0.725093 | + | 0.688651i | \(0.758203\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9050 | 0.853170 | 0.426585 | − | 0.904447i | \(-0.359716\pi\) | ||||
0.426585 | + | 0.904447i | \(0.359716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.1737 | −0.683388 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.98415 | −0.402994 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.5809 | −0.831795 | −0.415897 | − | 0.909412i | \(-0.636532\pi\) | ||||
−0.415897 | + | 0.909412i | \(0.636532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.0878 | −1.65366 | −0.826831 | − | 0.562450i | \(-0.809859\pi\) | ||||
−0.826831 | + | 0.562450i | \(0.809859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.8356 | 1.68366 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.7881 | 1.27601 | 0.638004 | − | 0.770033i | \(-0.279760\pi\) | ||||
0.638004 | + | 0.770033i | \(0.279760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.86551 | 0.347950 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0064 | −0.440935 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.6381 | 1.08358 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1197 | 0.662405 | 0.331202 | − | 0.943560i | \(-0.392546\pi\) | ||||
0.331202 | + | 0.943560i | \(0.392546\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.72009 | 0.118941 | 0.0594706 | − | 0.998230i | \(-0.481059\pi\) | ||||
0.0594706 | + | 0.998230i | \(0.481059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.1621 | −1.00896 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5861 | −0.764611 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.1628 | −1.17655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49.4800 | −2.13921 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.73874 | −0.247185 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.6606 | 1.18922 | 0.594611 | − | 0.804014i | \(-0.297306\pi\) | ||||
0.594611 | + | 0.804014i | \(0.297306\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.25976 | 0.310974 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6619 | −0.926197 | −0.463098 | − | 0.886307i | \(-0.653262\pi\) | ||||
−0.463098 | + | 0.886307i | \(0.653262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.47147 | −0.275694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.32679 | −0.0989451 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.2006 | 0.813557 | 0.406779 | − | 0.913527i | \(-0.366652\pi\) | ||||
0.406779 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.4239 | −0.440882 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.4429 | −1.24087 | −0.620435 | − | 0.784258i | \(-0.713044\pi\) | ||||
−0.620435 | + | 0.784258i | \(0.713044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −44.3580 | −1.86616 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2954 | 0.557371 | 0.278685 | − | 0.960382i | \(-0.410101\pi\) | ||||
0.278685 | + | 0.960382i | \(0.410101\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.34704 | −0.0982206 | −0.0491103 | − | 0.998793i | \(-0.515639\pi\) | ||||
−0.0491103 | + | 0.998793i | \(0.515639\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.37886 | 0.349423 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.17672 | −0.257140 | −0.128570 | − | 0.991700i | \(-0.541039\pi\) | ||||
−0.128570 | + | 0.991700i | \(0.541039\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.29537 | 0.136715 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.1381 | 1.53810 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.9953 | −1.65078 | −0.825391 | − | 0.564561i | \(-0.809046\pi\) | ||||
−0.825391 | + | 0.564561i | \(0.809046\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.87850 | −0.407036 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.9130 | −0.489207 | −0.244604 | − | 0.969623i | \(-0.578658\pi\) | ||||
−0.244604 | + | 0.969623i | \(0.578658\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.87643 | 0.281906 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.21793 | 0.335776 | 0.167888 | − | 0.985806i | \(-0.446305\pi\) | ||||
0.167888 | + | 0.985806i | \(0.446305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.8380 | −1.17633 | −0.588164 | − | 0.808742i | \(-0.700149\pi\) | ||||
−0.588164 | + | 0.808742i | \(0.700149\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 64.3244 | 2.61516 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.77960 | −0.0722318 | −0.0361159 | − | 0.999348i | \(-0.511499\pi\) | ||||
−0.0361159 | + | 0.999348i | \(0.511499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.9464 | −0.442843 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.09623 | −0.246225 | −0.123112 | − | 0.992393i | \(-0.539288\pi\) | ||||
−0.123112 | + | 0.992393i | \(0.539288\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.4740 | 0.421666 | 0.210833 | − | 0.977522i | \(-0.432382\pi\) | ||||
0.210833 | + | 0.977522i | \(0.432382\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0428 | 1.00656 | 0.503278 | − | 0.864124i | \(-0.332127\pi\) | ||||
0.503278 | + | 0.864124i | \(0.332127\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.7529 | 0.470868 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0377 | −1.20151 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.64571 | −0.344727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.9174 | −0.434616 | −0.217308 | − | 0.976103i | \(-0.569728\pi\) | ||||
−0.217308 | + | 0.976103i | \(0.569728\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.9809 | 1.54691 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.54964 | 0.101021 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.0870 | −0.595899 | −0.297949 | − | 0.954582i | \(-0.596303\pi\) | ||||
−0.297949 | + | 0.954582i | \(0.596303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.6029 | −1.56179 | −0.780893 | − | 0.624664i | \(-0.785236\pi\) | ||||
−0.780893 | + | 0.624664i | \(0.785236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.6834 | −0.459323 | −0.229661 | − | 0.973271i | \(-0.573762\pi\) | ||||
−0.229661 | + | 0.973271i | \(0.573762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.6155 | 1.59430 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.3127 | 0.638364 | 0.319182 | − | 0.947693i | \(-0.396592\pi\) | ||||
0.319182 | + | 0.947693i | \(0.396592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.8194 | −0.618114 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.8573 | −1.51367 | −0.756833 | − | 0.653609i | \(-0.773254\pi\) | ||||
−0.756833 | + | 0.653609i | \(0.773254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.17497 | −0.123492 | −0.0617460 | − | 0.998092i | \(-0.519667\pi\) | ||||
−0.0617460 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.93275 | 0.113727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0577 | −0.583038 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4775 | 0.443083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.9444 | 0.498970 | 0.249485 | − | 0.968379i | \(-0.419739\pi\) | ||||
0.249485 | + | 0.968379i | \(0.419739\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.3085 | −1.77978 | −0.889889 | − | 0.456176i | \(-0.849219\pi\) | ||||
−0.889889 | + | 0.456176i | \(0.849219\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.46335 | −0.0561581 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.2482 | 0.774774 | 0.387387 | − | 0.921917i | \(-0.373378\pi\) | ||||
0.387387 | + | 0.921917i | \(0.373378\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.6219 | −1.01717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.4999 | −0.628598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.445709 | −0.0169556 | −0.00847778 | − | 0.999964i | \(-0.502699\pi\) | ||||
−0.00847778 | + | 0.999964i | \(0.502699\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.0347 | 0.835822 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.9795 | −0.946164 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.220398 | −0.00832432 | −0.00416216 | − | 0.999991i | \(-0.501325\pi\) | ||||
−0.00416216 | + | 0.999991i | \(0.501325\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.68734 | −0.139071 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.9011 | 0.485194 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.2765 | −1.24972 | −0.624862 | − | 0.780735i | \(-0.714845\pi\) | ||||
−0.624862 | + | 0.780735i | \(0.714845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.9852 | −0.860801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.9112 | −1.60479 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.2060 | 0.940026 | 0.470013 | − | 0.882660i | \(-0.344249\pi\) | ||||
0.470013 | + | 0.882660i | \(0.344249\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.41195 | −0.127068 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.3040 | −0.865490 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.202702 | 0.00751781 | 0.00375891 | − | 0.999993i | \(-0.498803\pi\) | ||||
0.00375891 | + | 0.999993i | \(0.498803\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.58599 | −0.354551 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0647 | 0.630299 | 0.315149 | − | 0.949042i | \(-0.397945\pi\) | ||||
0.315149 | + | 0.949042i | \(0.397945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.9331 | −0.623739 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.0167085 | −0.000614633 0 | −0.000307316 | − | 1.00000i | \(-0.500098\pi\) | ||||
−0.000307316 | 1.00000i | \(0.500098\pi\) | ||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.12849 | 0.114773 | 0.0573866 | − | 0.998352i | \(-0.481723\pi\) | ||||
0.0573866 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.586604 | −0.0214915 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.8715 | −0.616471 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2459 | 0.775274 | 0.387637 | − | 0.921812i | \(-0.373291\pi\) | ||||
0.387637 | + | 0.921812i | \(0.373291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −56.5134 | −2.05673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.6879 | −0.606533 | −0.303267 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303267 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.0440 | −0.726595 | −0.363298 | − | 0.931673i | \(-0.618349\pi\) | ||||
−0.363298 | + | 0.931673i | \(0.618349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.47541 | 0.0896158 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.0449 | −0.651565 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.4537 | −0.557273 | −0.278636 | − | 0.960397i | \(-0.589882\pi\) | ||||
−0.278636 | + | 0.960397i | \(0.589882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.39591 | −0.158110 | −0.0790549 | − | 0.996870i | \(-0.525190\pi\) | ||||
−0.0790549 | + | 0.996870i | \(0.525190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.5729 | −1.27782 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.6536 | −0.381704 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.5577 | 1.84488 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 51.7754 | 1.84794 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.6744 | 0.950840 | 0.475420 | − | 0.879759i | \(-0.342296\pi\) | ||||
0.475420 | + | 0.879759i | \(0.342296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.1250 | −0.537785 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.09929 | −0.181081 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.2641 | −0.363572 | −0.181786 | − | 0.983338i | \(-0.558188\pi\) | ||||
−0.181786 | + | 0.983338i | \(0.558188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0665 | −0.356128 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45.1381 | −1.59289 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.82390 | 0.240511 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.44158 | −0.296790 | −0.148395 | − | 0.988928i | \(-0.547411\pi\) | ||||
−0.148395 | + | 0.988928i | \(0.547411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.1040 | −1.19755 | −0.598777 | − | 0.800916i | \(-0.704347\pi\) | ||||
−0.598777 | + | 0.800916i | \(0.704347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.9197 | −1.18816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.08836 | −0.143034 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.9352 | −0.905143 | −0.452572 | − | 0.891728i | \(-0.649493\pi\) | ||||
−0.452572 | + | 0.891728i | \(0.649493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.9116 | −0.415214 | −0.207607 | − | 0.978212i | \(-0.566567\pi\) | ||||
−0.207607 | + | 0.978212i | \(0.566567\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.2404 | 1.43407 | 0.717035 | − | 0.697038i | \(-0.245499\pi\) | ||||
0.717035 | + | 0.697038i | \(0.245499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.6796 | −1.58652 | −0.793259 | − | 0.608884i | \(-0.791617\pi\) | ||||
−0.793259 | + | 0.608884i | \(0.791617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.34470 | 0.0812391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −71.6191 | −2.47848 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0536 | −0.450661 | −0.225330 | − | 0.974282i | \(-0.572346\pi\) | ||||
−0.225330 | + | 0.974282i | \(0.572346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8799 | 0.444136 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.0609 | −0.655715 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.9331 | 0.753630 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.57965 | −0.294107 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.82451 | −0.267906 | −0.133953 | − | 0.990988i | \(-0.542767\pi\) | ||||
−0.133953 | + | 0.990988i | \(0.542767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.423860 | 0.0144788 | 0.00723939 | − | 0.999974i | \(-0.497696\pi\) | ||||
0.00723939 | + | 0.999974i | \(0.497696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8297 | −0.744819 | −0.372410 | − | 0.928068i | \(-0.621468\pi\) | ||||
−0.372410 | + | 0.928068i | \(0.621468\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.2885 | 1.20123 | 0.600617 | − | 0.799537i | \(-0.294922\pi\) | ||||
0.600617 | + | 0.799537i | \(0.294922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 60.2825 | 2.04967 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3528 | 0.452964 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.52315 | 0.254912 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.10280 | −0.138700 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.8267 | 1.47992 | 0.739960 | − | 0.672650i | \(-0.234844\pi\) | ||||
0.739960 | + | 0.672650i | \(0.234844\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7975 | 1.50927 | 0.754633 | − | 0.656147i | \(-0.227815\pi\) | ||||
0.754633 | + | 0.656147i | \(0.227815\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.0176 | 1.91879 | 0.959397 | − | 0.282060i | \(-0.0910178\pi\) | ||||
0.959397 | + | 0.282060i | \(0.0910178\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.5669 | −0.556262 | −0.278131 | − | 0.960543i | \(-0.589715\pi\) | ||||
−0.278131 | + | 0.960543i | \(0.589715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.2916 | 0.445785 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.29330 | −0.143670 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.61378 | 0.254500 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 63.9284 | 2.13213 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.1737 | −0.505508 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.9261 | 1.72608 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.4212 | −1.10973 | −0.554866 | − | 0.831940i | \(-0.687231\pi\) | ||||
−0.554866 | + | 0.831940i | \(0.687231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.98292 | 0.0988284 | 0.0494142 | − | 0.998778i | \(-0.484265\pi\) | ||||
0.0494142 | + | 0.998778i | \(0.484265\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.9112 | −0.625871 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.39404 | −0.178127 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.91125 | 0.0960332 | 0.0480166 | − | 0.998847i | \(-0.484710\pi\) | ||||
0.0480166 | + | 0.998847i | \(0.484710\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.9064 | −0.753973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.2783 | −0.436586 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.2708 | −1.25563 | −0.627813 | − | 0.778364i | \(-0.716050\pi\) | ||||
−0.627813 | + | 0.778364i | \(0.716050\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39.4620 | −1.29055 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.33313 | 0.239563 | 0.119782 | − | 0.992800i | \(-0.461781\pi\) | ||||
0.119782 | + | 0.992800i | \(0.461781\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5846 | 0.736238 | 0.368119 | − | 0.929779i | \(-0.380002\pi\) | ||||
0.368119 | + | 0.929779i | \(0.380002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.7886 | −0.807228 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.6943 | 1.41987 | 0.709937 | − | 0.704265i | \(-0.248723\pi\) | ||||
0.709937 | + | 0.704265i | \(0.248723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.0542 | 0.650988 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.9131 | 0.450690 | 0.225345 | − | 0.974279i | \(-0.427649\pi\) | ||||
0.225345 | + | 0.974279i | \(0.427649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.5677 | −0.730274 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.07744 | −0.293126 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.5847 | 2.14789 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 70.7063 | 2.27612 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.4995 | −1.65611 | −0.828057 | − | 0.560644i | \(-0.810554\pi\) | ||||
−0.828057 | + | 0.560644i | \(0.810554\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0536 | −0.547276 | −0.273638 | − | 0.961833i | \(-0.588227\pi\) | ||||
−0.273638 | + | 0.961833i | \(0.588227\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.51330 | 0.240865 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.1469 | −1.44438 | −0.722189 | − | 0.691696i | \(-0.756864\pi\) | ||||
−0.722189 | + | 0.691696i | \(0.756864\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.4466 | −2.15560 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.9655 | 0.732485 | 0.366243 | − | 0.930519i | \(-0.380644\pi\) | ||||
0.366243 | + | 0.930519i | \(0.380644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53.8015 | −1.71426 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.51275 | −0.302488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.2776 | −0.358245 | −0.179122 | − | 0.983827i | \(-0.557326\pi\) | ||||
−0.179122 | + | 0.983827i | \(0.557326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51.0880 | 1.61960 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.65420 | −0.179070 | −0.0895351 | − | 0.995984i | \(-0.528538\pi\) | ||||
−0.0895351 | + | 0.995984i | \(0.528538\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 9576.2.a.cn.1.5 | 5 | ||
3.2 | odd | 2 | 3192.2.a.bb.1.1 | ✓ | 5 | ||
12.11 | even | 2 | 6384.2.a.cd.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.2.a.bb.1.1 | ✓ | 5 | 3.2 | odd | 2 | ||
6384.2.a.cd.1.1 | 5 | 12.11 | even | 2 | |||
9576.2.a.cn.1.5 | 5 | 1.1 | even | 1 | trivial |