Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7280,2,Mod(1,7280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7280, 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("7280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7280.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: | \(58.1310926715\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3640) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7280.1 |
$q$-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 | ||||||||
\(3\) | −1.30278 | −0.752158 | −0.376079 | − | 0.926588i | \(-0.622728\pi\) | ||||
−0.376079 | + | 0.926588i | \(0.622728\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.30278 | −0.434259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.60555 | 1.38863 | 0.694313 | − | 0.719673i | \(-0.255708\pi\) | ||||
0.694313 | + | 0.719673i | \(0.255708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.30278 | −0.336375 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.30278 | 1.52865 | 0.764324 | − | 0.644833i | \(-0.223073\pi\) | ||||
0.764324 | + | 0.644833i | \(0.223073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.30278 | 1.44596 | 0.722978 | − | 0.690871i | \(-0.242773\pi\) | ||||
0.722978 | + | 0.690871i | \(0.242773\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30278 | 0.284289 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.60555 | 1.07879 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.90833 | 0.354367 | 0.177184 | − | 0.984178i | \(-0.443301\pi\) | ||||
0.177184 | + | 0.984178i | \(0.443301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.697224 | 0.125225 | 0.0626126 | − | 0.998038i | \(-0.480057\pi\) | ||||
0.0626126 | + | 0.998038i | \(0.480057\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00000 | −1.04447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.90833 | −0.642525 | −0.321262 | − | 0.946990i | \(-0.604107\pi\) | ||||
−0.321262 | + | 0.946990i | \(0.604107\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.30278 | 0.208611 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.30278 | −0.671981 | −0.335990 | − | 0.941865i | \(-0.609071\pi\) | ||||
−0.335990 | + | 0.941865i | \(0.609071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.30278 | −0.194206 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.60555 | 0.671789 | 0.335894 | − | 0.941900i | \(-0.390961\pi\) | ||||
0.335894 | + | 0.941900i | \(0.390961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.21110 | −1.14978 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.60555 | −0.357900 | −0.178950 | − | 0.983858i | \(-0.557270\pi\) | ||||
−0.178950 | + | 0.983858i | \(0.557270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.60555 | 0.621012 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.21110 | −1.08759 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.1194 | −1.44763 | −0.723813 | − | 0.689996i | \(-0.757612\pi\) | ||||
−0.723813 | + | 0.689996i | \(0.757612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.21110 | −0.155066 | −0.0775329 | − | 0.996990i | \(-0.524704\pi\) | ||||
−0.0775329 | + | 0.996990i | \(0.524704\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.30278 | 0.164134 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.90833 | −1.08833 | −0.544163 | − | 0.838980i | \(-0.683153\pi\) | ||||
−0.544163 | + | 0.838980i | \(0.683153\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.4222 | −1.25469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.60555 | 0.309222 | 0.154611 | − | 0.987975i | \(-0.450588\pi\) | ||||
0.154611 | + | 0.987975i | \(0.450588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.60555 | −1.00720 | −0.503602 | − | 0.863936i | \(-0.667992\pi\) | ||||
−0.503602 | + | 0.863936i | \(0.667992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.30278 | −0.150432 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.60555 | −0.524851 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.51388 | −0.395342 | −0.197671 | − | 0.980268i | \(-0.563338\pi\) | ||||
−0.197671 | + | 0.980268i | \(0.563338\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8167 | 1.29705 | 0.648523 | − | 0.761195i | \(-0.275387\pi\) | ||||
0.648523 | + | 0.761195i | \(0.275387\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.30278 | 0.683632 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.48612 | −0.266540 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.30278 | −0.774093 | −0.387046 | − | 0.922060i | \(-0.626505\pi\) | ||||
−0.387046 | + | 0.922060i | \(0.626505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.908327 | −0.0941891 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.30278 | 0.646651 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2111 | −1.34138 | −0.670692 | − | 0.741736i | \(-0.734003\pi\) | ||||
−0.670692 | + | 0.741736i | \(0.734003\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.90833 | 0.877764 | 0.438882 | − | 0.898545i | \(-0.355375\pi\) | ||||
0.438882 | + | 0.898545i | \(0.355375\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30278 | 0.127138 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.09167 | 0.483280 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.81665 | 0.735329 | 0.367664 | − | 0.929959i | \(-0.380157\pi\) | ||||
0.367664 | + | 0.929959i | \(0.380157\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.30278 | 0.120442 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.30278 | −0.577774 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2111 | 0.928282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.60555 | 0.505436 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.60555 | 0.763619 | 0.381810 | − | 0.924241i | \(-0.375301\pi\) | ||||
0.381810 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.60555 | −0.229406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.30278 | −0.546520 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.60555 | 0.482449 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.69722 | 0.230439 | 0.115220 | − | 0.993340i | \(-0.463243\pi\) | ||||
0.115220 | + | 0.993340i | \(0.463243\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4222 | −1.39291 | −0.696457 | − | 0.717599i | \(-0.745241\pi\) | ||||
−0.696457 | + | 0.717599i | \(0.745241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.60555 | −0.385136 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.90833 | 0.158478 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.30278 | −0.107451 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.00000 | 0.655386 | 0.327693 | − | 0.944784i | \(-0.393729\pi\) | ||||
0.327693 | + | 0.944784i | \(0.393729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.21110 | −0.663828 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.697224 | 0.0560024 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5139 | 0.839099 | 0.419549 | − | 0.907732i | \(-0.362188\pi\) | ||||
0.419549 | + | 0.907732i | \(0.362188\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.39445 | 0.269197 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25.1194 | −1.96751 | −0.983753 | − | 0.179528i | \(-0.942543\pi\) | ||||
−0.983753 | + | 0.179528i | \(0.942543\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | −0.467099 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.2111 | 1.79613 | 0.898065 | − | 0.439864i | \(-0.144973\pi\) | ||||
0.898065 | + | 0.439864i | \(0.144973\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.21110 | −0.627919 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6972 | 1.42152 | 0.710762 | − | 0.703433i | \(-0.248350\pi\) | ||||
0.710762 | + | 0.703433i | \(0.248350\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.4861 | 1.08884 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.09167 | 0.679544 | 0.339772 | − | 0.940508i | \(-0.389650\pi\) | ||||
0.339772 | + | 0.940508i | \(0.389650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.81665 | 0.729666 | 0.364833 | − | 0.931073i | \(-0.381126\pi\) | ||||
0.364833 | + | 0.931073i | \(0.381126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.57779 | 0.116634 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.90833 | −0.287346 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.0278 | 2.12272 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.60555 | −0.407744 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5139 | 1.19490 | 0.597451 | − | 0.801905i | \(-0.296180\pi\) | ||||
0.597451 | + | 0.801905i | \(0.296180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9083 | 0.785199 | 0.392599 | − | 0.919710i | \(-0.371576\pi\) | ||||
0.392599 | + | 0.919710i | \(0.371576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.30278 | 0.0932937 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1194 | 0.934721 | 0.467360 | − | 0.884067i | \(-0.345205\pi\) | ||||
0.467360 | + | 0.884067i | \(0.345205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.21110 | −0.0858528 | −0.0429264 | − | 0.999078i | \(-0.513668\pi\) | ||||
−0.0429264 | + | 0.999078i | \(0.513668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6056 | 0.818592 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.90833 | −0.133938 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.30278 | −0.300519 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.4222 | −0.724393 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.0278 | 2.00789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5139 | −0.792648 | −0.396324 | − | 0.918111i | \(-0.629714\pi\) | ||||
−0.396324 | + | 0.918111i | \(0.629714\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.39445 | −0.232584 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.697224 | −0.0473307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.2111 | 0.757576 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.30278 | −0.423971 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2111 | −0.884681 | −0.442340 | − | 0.896847i | \(-0.645852\pi\) | ||||
−0.442340 | + | 0.896847i | \(0.645852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.30278 | −0.0868517 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.8167 | 1.31528 | 0.657639 | − | 0.753333i | \(-0.271555\pi\) | ||||
0.657639 | + | 0.753333i | \(0.271555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.302776 | −0.0200080 | −0.0100040 | − | 0.999950i | \(-0.503184\pi\) | ||||
−0.0100040 | + | 0.999950i | \(0.503184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.81665 | −0.119013 | −0.0595065 | − | 0.998228i | \(-0.518953\pi\) | ||||
−0.0595065 | + | 0.998228i | \(0.518953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.60555 | 0.300433 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.57779 | 0.297360 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.6333 | −1.39934 | −0.699671 | − | 0.714465i | \(-0.746670\pi\) | ||||
−0.699671 | + | 0.714465i | \(0.746670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9083 | −1.08916 | −0.544581 | − | 0.838709i | \(-0.683311\pi\) | ||||
−0.544581 | + | 0.838709i | \(0.683311\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.3944 | −0.795104 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.30278 | −0.401036 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.3944 | −0.975584 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.6333 | 1.74420 | 0.872099 | − | 0.489329i | \(-0.162758\pi\) | ||||
0.872099 | + | 0.489329i | \(0.162758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.8444 | 2.31639 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.21110 | −0.514199 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.6333 | 1.34945 | 0.674724 | − | 0.738070i | \(-0.264263\pi\) | ||||
0.674724 | + | 0.738070i | \(0.264263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.90833 | 0.242852 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.48612 | −0.153887 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.6333 | −0.963991 | −0.481996 | − | 0.876174i | \(-0.660088\pi\) | ||||
−0.481996 | + | 0.876174i | \(0.660088\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.60555 | −0.160058 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.51388 | 0.582240 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8167 | −1.08630 | −0.543150 | − | 0.839636i | \(-0.682769\pi\) | ||||
−0.543150 | + | 0.839636i | \(0.682769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.30278 | −0.0788476 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.60555 | 0.277725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.21110 | 0.0727681 | 0.0363840 | − | 0.999338i | \(-0.488416\pi\) | ||||
0.0363840 | + | 0.999338i | \(0.488416\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.908327 | −0.0543801 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.0000 | −1.90896 | −0.954480 | − | 0.298275i | \(-0.903589\pi\) | ||||
−0.954480 | + | 0.298275i | \(0.903589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0917 | 0.897107 | 0.448553 | − | 0.893756i | \(-0.351939\pi\) | ||||
0.448553 | + | 0.893756i | \(0.351939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.21110 | −0.486384 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.30278 | 0.253985 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.7250 | 1.33676 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.2111 | 1.00893 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.42221 | 0.141507 | 0.0707534 | − | 0.997494i | \(-0.477460\pi\) | ||||
0.0707534 | + | 0.997494i | \(0.477460\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.1194 | −0.647398 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.8167 | 1.49803 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | −0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.81665 | −0.449055 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.21110 | −0.0693475 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.39445 | −0.422023 | −0.211012 | − | 0.977484i | \(-0.567676\pi\) | ||||
−0.211012 | + | 0.977484i | \(0.567676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6056 | −0.660217 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.0278 | 1.30578 | 0.652892 | − | 0.757451i | \(-0.273555\pi\) | ||||
0.652892 | + | 0.757451i | \(0.273555\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.3305 | −1.71438 | −0.857192 | − | 0.514998i | \(-0.827793\pi\) | ||||
−0.857192 | + | 0.514998i | \(0.827793\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.30278 | 0.0734031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.4222 | −0.922363 | −0.461181 | − | 0.887306i | \(-0.652574\pi\) | ||||
−0.461181 | + | 0.887306i | \(0.652574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.78890 | 0.492084 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.81665 | −0.436283 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.7250 | 2.21036 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.21110 | 0.288175 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.60555 | −0.253912 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0000 | −0.989369 | −0.494685 | − | 0.869072i | \(-0.664716\pi\) | ||||
−0.494685 | + | 0.869072i | \(0.664716\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.09167 | 0.279022 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.90833 | −0.486714 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.4222 | −1.33036 | −0.665181 | − | 0.746682i | \(-0.731646\pi\) | ||||
−0.665181 | + | 0.746682i | \(0.731646\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.1833 | −0.553083 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.21110 | 0.173891 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.4222 | −0.561113 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.8167 | 1.60064 | 0.800321 | − | 0.599572i | \(-0.204662\pi\) | ||||
0.800321 | + | 0.599572i | \(0.204662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9361 | −1.22774 | −0.613870 | − | 0.789407i | \(-0.710388\pi\) | ||||
−0.613870 | + | 0.789407i | \(0.710388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.60555 | −0.299202 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.6333 | 0.938526 | 0.469263 | − | 0.883058i | \(-0.344520\pi\) | ||||
0.469263 | + | 0.883058i | \(0.344520\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.60555 | 0.138288 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.21110 | 0.434578 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.0278 | −1.32091 | −0.660457 | − | 0.750864i | \(-0.729638\pi\) | ||||
−0.660457 | + | 0.750864i | \(0.729638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7250 | 1.09079 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.3028 | −0.698215 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.60555 | −0.450435 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.4222 | −1.58803 | −0.794013 | − | 0.607901i | \(-0.792012\pi\) | ||||
−0.794013 | + | 0.607901i | \(0.792012\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.60555 | 0.291813 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.60555 | 0.135273 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0000 | −0.724893 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.30278 | −0.0672750 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.90833 | −0.0982838 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6333 | 1.52216 | 0.761080 | − | 0.648658i | \(-0.224669\pi\) | ||||
0.761080 | + | 0.648658i | \(0.224669\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.2111 | −0.574362 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.2389 | 1.23855 | 0.619274 | − | 0.785175i | \(-0.287427\pi\) | ||||
0.619274 | + | 0.785175i | \(0.287427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.60555 | −0.234721 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.60555 | −0.132448 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.51388 | 0.482373 | 0.241186 | − | 0.970479i | \(-0.422463\pi\) | ||||
0.241186 | + | 0.970479i | \(0.422463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.4222 | 2.54996 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.51388 | −0.176802 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.8167 | 1.49645 | 0.748227 | − | 0.663442i | \(-0.230905\pi\) | ||||
0.748227 | + | 0.663442i | \(0.230905\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.21110 | 0.411069 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0000 | −1.19850 | −0.599251 | − | 0.800561i | \(-0.704535\pi\) | ||||
−0.599251 | + | 0.800561i | \(0.704535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.697224 | −0.0347312 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.39445 | −0.168672 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.0000 | −0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | −0.0988936 | −0.0494468 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494468 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.51388 | −0.173327 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.1194 | 0.547151 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.8167 | 0.580057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.3944 | 1.04769 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.6333 | −1.34998 | −0.674988 | − | 0.737829i | \(-0.735851\pi\) | ||||
−0.674988 | + | 0.737829i | \(0.735851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4222 | 0.800369 | 0.400185 | − | 0.916435i | \(-0.368946\pi\) | ||||
0.400185 | + | 0.916435i | \(0.368946\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.30278 | 0.305730 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.21110 | 0.0586094 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00000 | 0.289683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.0000 | 1.63772 | 0.818861 | − | 0.573992i | \(-0.194606\pi\) | ||||
0.818861 | + | 0.573992i | \(0.194606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.9361 | 1.05418 | 0.527090 | − | 0.849809i | \(-0.323283\pi\) | ||||
0.527090 | + | 0.849809i | \(0.323283\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.48612 | −0.119200 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 50.4222 | 2.41202 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.78890 | −0.228562 | −0.114281 | − | 0.993448i | \(-0.536456\pi\) | ||||
−0.114281 | + | 0.993448i | \(0.536456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.30278 | −0.0620369 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.39445 | −0.446344 | −0.223172 | − | 0.974779i | \(-0.571641\pi\) | ||||
−0.223172 | + | 0.974779i | \(0.571641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.30278 | −0.346185 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.4222 | −0.492953 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.02776 | 0.0485028 | 0.0242514 | − | 0.999706i | \(-0.492280\pi\) | ||||
0.0242514 | + | 0.999706i | \(0.492280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.8167 | −0.933130 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.0278 | −0.612097 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.48612 | 0.443742 | 0.221871 | − | 0.975076i | \(-0.428784\pi\) | ||||
0.221871 | + | 0.975076i | \(0.428784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.3305 | 1.64909 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0917 | 0.656315 | 0.328157 | − | 0.944623i | \(-0.393572\pi\) | ||||
0.328157 | + | 0.944623i | \(0.393572\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.7250 | 1.24202 | 0.621008 | − | 0.783805i | \(-0.286724\pi\) | ||||
0.621008 | + | 0.783805i | \(0.286724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.908327 | −0.0421227 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.5139 | 1.73594 | 0.867968 | − | 0.496621i | \(-0.165426\pi\) | ||||
0.867968 | + | 0.496621i | \(0.165426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.90833 | 0.411348 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.6972 | −0.631135 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.21110 | 0.423527 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.30278 | 0.289191 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.39445 | 0.155421 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0917 | −1.37492 | −0.687462 | − | 0.726221i | \(-0.741275\pi\) | ||||
−0.687462 | + | 0.726221i | \(0.741275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.90833 | 0.178204 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.4222 | 0.474227 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.2111 | −0.599885 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.6972 | −1.20977 | −0.604883 | − | 0.796314i | \(-0.706780\pi\) | ||||
−0.604883 | + | 0.796314i | \(0.706780\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.7250 | 1.47987 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.57779 | 0.0712049 | 0.0356024 | − | 0.999366i | \(-0.488665\pi\) | ||||
0.0356024 | + | 0.999366i | \(0.488665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0278 | 0.541703 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | −0.269680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.60555 | −0.116875 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.0000 | −1.16392 | −0.581960 | − | 0.813217i | \(-0.697714\pi\) | ||||
−0.581960 | + | 0.813217i | \(0.697714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.2389 | −1.35097 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6333 | −0.697055 | −0.348527 | − | 0.937299i | \(-0.613318\pi\) | ||||
−0.348527 | + | 0.937299i | \(0.613318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.30278 | −0.0578583 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.3305 | 0.679514 | 0.339757 | − | 0.940513i | \(-0.389655\pi\) | ||||
0.339757 | + | 0.940513i | \(0.389655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.60555 | 0.380687 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.3305 | 1.55988 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.90833 | 0.392548 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.2111 | 0.932863 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.3583 | −1.06921 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.2389 | 1.23717 | 0.618583 | − | 0.785719i | \(-0.287707\pi\) | ||||
0.618583 | + | 0.785719i | \(0.287707\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.57779 | −0.243900 | −0.121950 | − | 0.992536i | \(-0.538915\pi\) | ||||
−0.121950 | + | 0.992536i | \(0.538915\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.30278 | 0.0568578 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.39445 | 0.191425 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.4861 | 0.628644 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.30278 | 0.186374 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.8444 | −0.511124 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.60555 | 0.198375 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0555 | −1.46416 | −0.732080 | − | 0.681218i | \(-0.761450\pi\) | ||||
−0.732080 | + | 0.681218i | \(0.761450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.7889 | −0.548824 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.63331 | −0.240863 | −0.120431 | − | 0.992722i | \(-0.538428\pi\) | ||||
−0.120431 | + | 0.992722i | \(0.538428\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.57779 | 0.0673386 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0278 | 0.512400 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.51388 | 0.149425 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.09167 | 0.216129 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.9083 | 0.631686 | 0.315843 | − | 0.948811i | \(-0.397713\pi\) | ||||
0.315843 | + | 0.948811i | \(0.397713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.8167 | −1.59662 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.5416 | 0.528567 | 0.264283 | − | 0.964445i | \(-0.414865\pi\) | ||||
0.264283 | + | 0.964445i | \(0.414865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.81665 | 0.328849 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.39445 | 0.142553 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.7527 | −0.953844 | −0.476922 | − | 0.878946i | \(-0.658248\pi\) | ||||
−0.476922 | + | 0.878946i | \(0.658248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7250 | −0.909162 | −0.454581 | − | 0.890705i | \(-0.650211\pi\) | ||||
−0.454581 | + | 0.890705i | \(0.650211\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.5139 | −0.898755 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.39445 | −0.307835 | −0.153917 | − | 0.988084i | \(-0.549189\pi\) | ||||
−0.153917 | + | 0.988084i | \(0.549189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.2111 | −0.590593 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8167 | −0.490237 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | −0.496989 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.30278 | 0.0538631 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.8167 | 0.817921 | 0.408960 | − | 0.912552i | \(-0.365891\pi\) | ||||
0.408960 | + | 0.912552i | \(0.365891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.39445 | 0.181070 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.0917 | −0.703057 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.8167 | −1.79933 | −0.899667 | − | 0.436576i | \(-0.856191\pi\) | ||||
−0.899667 | + | 0.436576i | \(0.856191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.30278 | −0.258389 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.57779 | 0.0645748 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4222 | 0.425840 | 0.212920 | − | 0.977070i | \(-0.431703\pi\) | ||||
0.212920 | + | 0.977070i | \(0.431703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.7889 | 0.929579 | 0.464789 | − | 0.885421i | \(-0.346130\pi\) | ||||
0.464789 | + | 0.885421i | \(0.346130\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.6056 | 0.472615 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2111 | 0.415140 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.51388 | −0.264390 | −0.132195 | − | 0.991224i | \(-0.542203\pi\) | ||||
−0.132195 | + | 0.991224i | \(0.542203\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.48612 | 0.100743 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.60555 | −0.186321 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.8444 | 1.56891 | 0.784455 | − | 0.620185i | \(-0.212943\pi\) | ||||
0.784455 | + | 0.620185i | \(0.212943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.60555 | 0.226038 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.90833 | −0.278119 | −0.139059 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139059 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.7250 | 0.873201 | 0.436600 | − | 0.899656i | \(-0.356182\pi\) | ||||
0.436600 | + | 0.899656i | \(0.356182\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.8444 | 1.79954 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.30278 | 0.292580 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −37.8167 | −1.51025 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.6333 | −0.982194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.8167 | 0.629651 | 0.314826 | − | 0.949150i | \(-0.398054\pi\) | ||||
0.314826 | + | 0.949150i | \(0.398054\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.0000 | 0.596196 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.60555 | 0.341501 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.39445 | −0.134282 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.27502 | −0.247848 | −0.123924 | − | 0.992292i | \(-0.539548\pi\) | ||||
−0.123924 | + | 0.992292i | \(0.539548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8444 | 0.585406 | 0.292703 | − | 0.956203i | \(-0.405445\pi\) | ||||
0.292703 | + | 0.956203i | \(0.405445\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.60555 | −0.102593 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.5139 | −0.727856 | −0.363928 | − | 0.931427i | \(-0.618565\pi\) | ||||
−0.363928 | + | 0.931427i | \(0.618565\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.2111 | −2.01021 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.908327 | 0.0356001 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.4222 | −1.03398 | −0.516990 | − | 0.855991i | \(-0.672948\pi\) | ||||
−0.516990 | + | 0.855991i | \(0.672948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.2111 | 0.437387 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1472 | −1.21332 | −0.606661 | − | 0.794961i | \(-0.707491\pi\) | ||||
−0.606661 | + | 0.794961i | \(0.707491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.5139 | 1.30354 | 0.651769 | − | 0.758417i | \(-0.274027\pi\) | ||||
0.651769 | + | 0.758417i | \(0.274027\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.21110 | 0.318893 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.30278 | −0.244411 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.2666 | 0.591126 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.2111 | 0.665420 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.57779 | −0.215328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.8167 | −0.532593 | −0.266296 | − | 0.963891i | \(-0.585800\pi\) | ||||
−0.266296 | + | 0.963891i | \(0.585800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.60555 | 0.215758 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.4222 | 0.784889 | 0.392445 | − | 0.919776i | \(-0.371629\pi\) | ||||
0.392445 | + | 0.919776i | \(0.371629\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.2111 | 0.506996 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.8167 | −0.989296 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.9361 | 1.68117 | 0.840584 | − | 0.541682i | \(-0.182212\pi\) | ||||
0.840584 | + | 0.541682i | \(0.182212\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.69722 | 0.103056 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.394449 | 0.0150492 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.60555 | 0.0992636 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.9083 | 0.529098 | 0.264549 | − | 0.964372i | \(-0.414777\pi\) | ||||
0.264549 | + | 0.964372i | \(0.414777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.00000 | 0.227921 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.4222 | −0.622930 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.1194 | −1.02722 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.36669 | 0.0895165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.88057 | −0.373184 | −0.186592 | − | 0.982437i | \(-0.559744\pi\) | ||||
−0.186592 | + | 0.982437i | \(0.559744\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.6333 | −0.929063 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7889 | 0.555409 | 0.277704 | − | 0.960667i | \(-0.410426\pi\) | ||||
0.277704 | + | 0.960667i | \(0.410426\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.57779 | 0.171681 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.57779 | 0.208890 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.60555 | −0.172238 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.1833 | 1.05253 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.4222 | −0.985382 | −0.492691 | − | 0.870204i | \(-0.663987\pi\) | ||||
−0.492691 | + | 0.870204i | \(0.663987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.90833 | −0.331763 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.0278 | 0.819221 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.90833 | 0.0708735 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.3028 | 1.08678 | 0.543390 | − | 0.839480i | \(-0.317141\pi\) | ||||
0.543390 | + | 0.839480i | \(0.317141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.3305 | 0.975205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.6056 | 0.466233 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0000 | 0.443230 | 0.221615 | − | 0.975134i | \(-0.428867\pi\) | ||||
0.221615 | + | 0.975134i | \(0.428867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.30278 | −0.0480536 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.0278 | −1.51128 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.0555 | 0.958468 | 0.479234 | − | 0.877687i | \(-0.340915\pi\) | ||||
0.479234 | + | 0.877687i | \(0.340915\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.21110 | 0.301642 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.9083 | −1.35404 | −0.677018 | − | 0.735967i | \(-0.736728\pi\) | ||||
−0.677018 | + | 0.735967i | \(0.736728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | 0.293097 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.3944 | −0.563253 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5139 | −0.456638 | −0.228319 | − | 0.973586i | \(-0.573323\pi\) | ||||
−0.228319 | + | 0.973586i | \(0.573323\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.0000 | −1.31191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0000 | 0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.8167 | 1.66523 | 0.832617 | − | 0.553849i | \(-0.186841\pi\) | ||||
0.832617 | + | 0.553849i | \(0.186841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −48.0000 | −1.74229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.5139 | −0.888627 | −0.444314 | − | 0.895871i | \(-0.646552\pi\) | ||||
−0.444314 | + | 0.895871i | \(0.646552\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00000 | 0.144810 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.21110 | −0.296873 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1194 | 0.401499 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5778 | −0.561750 | −0.280875 | − | 0.959744i | \(-0.590625\pi\) | ||||
−0.280875 | + | 0.959744i | \(0.590625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.1833 | −1.01500 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.1833 | 0.582075 | 0.291037 | − | 0.956712i | \(-0.406000\pi\) | ||||
0.291037 | + | 0.956712i | \(0.406000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.697224 | 0.0250450 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.09167 | −0.182663 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.1194 | −0.971654 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | 0.429394 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.6972 | 0.382288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.5139 | 0.375256 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4222 | 0.514096 | 0.257048 | − | 0.966399i | \(-0.417250\pi\) | ||||
0.257048 | + | 0.966399i | \(0.417250\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.3667 | 0.725073 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.81665 | −0.277928 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.21110 | 0.0430075 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.39445 | 0.120389 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.5416 | −1.54232 | −0.771162 | − | 0.636639i | \(-0.780324\pi\) | ||||
−0.771162 | + | 0.636639i | \(0.780324\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.0278 | 1.02693 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.51388 | 0.336156 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39.6333 | −1.39863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | −0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.2111 | 0.817070 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.5139 | −0.756388 | −0.378194 | − | 0.925726i | \(-0.623455\pi\) | ||||
−0.378194 | + | 0.925726i | \(0.623455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.6333 | 1.11080 | 0.555398 | − | 0.831585i | \(-0.312566\pi\) | ||||
0.555398 | + | 0.831585i | \(0.312566\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.1194 | −0.879895 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.6056 | 0.441012 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.30278 | −0.0455227 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.4777 | 1.62208 | 0.811042 | − | 0.584988i | \(-0.198901\pi\) | ||||
0.811042 | + | 0.584988i | \(0.198901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.02776 | 0.105541 | 0.0527705 | − | 0.998607i | \(-0.483195\pi\) | ||||
0.0527705 | + | 0.998607i | \(0.483195\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.63331 | 0.126342 | 0.0631712 | − | 0.998003i | \(-0.479879\pi\) | ||||
0.0631712 | + | 0.998003i | \(0.479879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.21110 | 0.319915 | 0.159957 | − | 0.987124i | \(-0.448864\pi\) | ||||
0.159957 | + | 0.987124i | \(0.448864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.57779 | −0.0547331 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.30278 | 0.218378 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.2111 | 0.803253 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.90833 | 0.135092 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.8444 | 1.27201 | 0.636005 | − | 0.771685i | \(-0.280586\pi\) | ||||
0.636005 | + | 0.771685i | \(0.280586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3583 | −0.874424 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 41.6888 | 1.43584 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.2111 | −0.350858 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.6611 | −0.674766 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.2666 | −1.07181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.1833 | 0.828022 | 0.414011 | − | 0.910272i | \(-0.364128\pi\) | ||||
0.414011 | + | 0.910272i | \(0.364128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.21110 | −0.280814 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.3028 | 1.68415 | 0.842075 | − | 0.539360i | \(-0.181334\pi\) | ||||
0.842075 | + | 0.539360i | \(0.181334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.4222 | −0.628558 | −0.314279 | − | 0.949331i | \(-0.601763\pi\) | ||||
−0.314279 | + | 0.949331i | \(0.601763\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.60555 | −0.191037 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.7250 | −1.72670 | −0.863349 | − | 0.504607i | \(-0.831637\pi\) | ||||
−0.863349 | + | 0.504607i | \(0.831637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.6972 | 0.635725 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.6056 | −1.00546 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.1833 | −0.548982 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.90833 | 0.301847 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.2111 | 0.582508 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.0917 | 0.712215 | 0.356108 | − | 0.934445i | \(-0.384104\pi\) | ||||
0.356108 | + | 0.934445i | \(0.384104\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.15559 | −0.106435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.4500 | 0.992194 | 0.496097 | − | 0.868267i | \(-0.334766\pi\) | ||||
0.496097 | + | 0.868267i | \(0.334766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.6056 | −0.962653 | −0.481327 | − | 0.876541i | \(-0.659845\pi\) | ||||
−0.481327 | + | 0.876541i | \(0.659845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.4861 | 0.486946 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.1472 | −0.877937 | −0.438968 | − | 0.898503i | \(-0.644656\pi\) | ||||
−0.438968 | + | 0.898503i | \(0.644656\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.60555 | −0.288621 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.6333 | −0.523736 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.0278 | 0.971377 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.09167 | 0.303901 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4222 | 0.347987 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.33053 | 0.0443757 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.4222 | −0.547103 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.60555 | 0.0867073 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.81665 | 0.326317 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.60555 | −0.0865159 | −0.0432580 | − | 0.999064i | \(-0.513774\pi\) | ||||
−0.0432580 | + | 0.999064i | \(0.513774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.81665 | −0.259262 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.0917 | 0.433746 | 0.216873 | − | 0.976200i | \(-0.430414\pi\) | ||||
0.216873 | + | 0.976200i | \(0.430414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.4222 | 1.80111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.57779 | 0.0521603 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5416 | −0.710593 | −0.355296 | − | 0.934754i | \(-0.615620\pi\) | ||||
−0.355296 | + | 0.934754i | \(0.615620\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.63331 | 0.317428 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.60555 | −0.0857628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.90833 | −0.128505 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.6056 | −0.381176 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.7527 | 1.14020 | 0.570100 | − | 0.821575i | \(-0.306904\pi\) | ||||
0.570100 | + | 0.821575i | \(0.306904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.30278 | 0.206565 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.0000 | −0.982156 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.0278 | 0.949309 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.6972 | −1.10084 | −0.550420 | − | 0.834888i | \(-0.685532\pi\) | ||||
−0.550420 | + | 0.834888i | \(0.685532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39.5139 | 1.28949 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.88057 | −0.0613048 | −0.0306524 | − | 0.999530i | \(-0.509758\pi\) | ||||
−0.0306524 | + | 0.999530i | \(0.509758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.4222 | −1.12094 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.60555 | −0.182349 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.14719 | −0.167261 | −0.0836305 | − | 0.996497i | \(-0.526652\pi\) | ||||
−0.0836305 | + | 0.996497i | \(0.526652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.60555 | 0.279348 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.3944 | 0.693763 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.0278 | −0.810729 | −0.405364 | − | 0.914155i | \(-0.632855\pi\) | ||||
−0.405364 | + | 0.914155i | \(0.632855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.5139 | 0.534377 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.4500 | −0.370125 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.69722 | −0.0870979 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5139 | −0.984319 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.81665 | −0.251888 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.9083 | 0.351151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.5139 | −0.981260 | −0.490630 | − | 0.871368i | \(-0.663233\pi\) | ||||
−0.490630 | + | 0.871368i | \(0.663233\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −51.7527 | −1.66254 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9722 | −0.416299 | −0.208150 | − | 0.978097i | \(-0.566744\pi\) | ||||
−0.208150 | + | 0.978097i | \(0.566744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.4222 | 0.526472 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.30278 | 0.0417222 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.90833 | 0.0930456 | 0.0465228 | − | 0.998917i | \(-0.485186\pi\) | ||||
0.0465228 | + | 0.998917i | \(0.485186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.6333 | −1.07493 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.21110 | 0.166378 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.4500 | −0.365197 | −0.182599 | − | 0.983188i | \(-0.558451\pi\) | ||||
−0.182599 | + | 0.983188i | \(0.558451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1194 | 0.418020 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | 0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.1472 | −0.862359 | −0.431179 | − | 0.902266i | \(-0.641902\pi\) | ||||
−0.431179 | + | 0.902266i | \(0.641902\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.4500 | 0.744162 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.21110 | −0.0383945 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.1472 | 1.74653 | 0.873264 | − | 0.487247i | \(-0.161999\pi\) | ||||
0.873264 | + | 0.487247i | \(0.161999\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.9083 | −0.693149 |
(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 | 7280.2.a.bh.1.1 | 2 | ||
4.3 | odd | 2 | 3640.2.a.l.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.l.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
7280.2.a.bh.1.1 | 2 | 1.1 | even | 1 | trivial |