Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, 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("3864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.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: | \(30.8541953410\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.17819\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.61186 | 1.16806 | 0.584029 | − | 0.811733i | \(-0.301475\pi\) | ||||
0.584029 | + | 0.811733i | \(0.301475\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.43366 | −1.03529 | −0.517644 | − | 0.855596i | \(-0.673191\pi\) | ||||
−0.517644 | + | 0.855596i | \(0.673191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.821806 | 0.227928 | 0.113964 | − | 0.993485i | \(-0.463645\pi\) | ||||
0.113964 | + | 0.993485i | \(0.463645\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.61186 | 0.674379 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.79005 | −1.40429 | −0.702147 | − | 0.712032i | \(-0.747775\pi\) | ||||
−0.702147 | + | 0.712032i | \(0.747775\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.43366 | −1.70540 | −0.852700 | − | 0.522401i | \(-0.825036\pi\) | ||||
−0.852700 | + | 0.522401i | \(0.825036\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82181 | 0.364361 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.79005 | −1.07519 | −0.537593 | − | 0.843205i | \(-0.680666\pi\) | ||||
−0.537593 | + | 0.843205i | \(0.680666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.07728 | −0.552695 | −0.276348 | − | 0.961058i | \(-0.589124\pi\) | ||||
−0.276348 | + | 0.961058i | \(0.589124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.43366 | −0.597724 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.61186 | −0.441485 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.922724 | −0.151695 | −0.0758474 | − | 0.997119i | \(-0.524166\pi\) | ||||
−0.0758474 | + | 0.997119i | \(0.524166\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.821806 | 0.131594 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.566335 | 0.0884467 | 0.0442234 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442234 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6891 | −1.78258 | −0.891288 | − | 0.453437i | \(-0.850198\pi\) | ||||
−0.891288 | + | 0.453437i | \(0.850198\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.61186 | 0.389353 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.35639 | −0.343715 | −0.171857 | − | 0.985122i | \(-0.554977\pi\) | ||||
−0.171857 | + | 0.985122i | \(0.554977\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.79005 | −0.810770 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.968247 | 0.132999 | 0.0664995 | − | 0.997786i | \(-0.478817\pi\) | ||||
0.0664995 | + | 0.997786i | \(0.478817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.96825 | −1.20928 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.43366 | −0.984613 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.89908 | 0.247239 | 0.123620 | − | 0.992330i | \(-0.460550\pi\) | ||||
0.123620 | + | 0.992330i | \(0.460550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40191 | 0.307533 | 0.153767 | − | 0.988107i | \(-0.450860\pi\) | ||||
0.153767 | + | 0.988107i | \(0.450860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.14644 | 0.266233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.10092 | −0.501007 | −0.250503 | − | 0.968116i | \(-0.580596\pi\) | ||||
−0.250503 | + | 0.968116i | \(0.580596\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.17819 | 0.139826 | 0.0699130 | − | 0.997553i | \(-0.477728\pi\) | ||||
0.0699130 | + | 0.997553i | \(0.477728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.14644 | 0.953469 | 0.476734 | − | 0.879047i | \(-0.341820\pi\) | ||||
0.476734 | + | 0.879047i | \(0.341820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.82181 | 0.210364 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.43366 | 0.391302 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.56634 | −0.288735 | −0.144368 | − | 0.989524i | \(-0.546115\pi\) | ||||
−0.144368 | + | 0.989524i | \(0.546115\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.30099 | −0.691624 | −0.345812 | − | 0.938304i | \(-0.612396\pi\) | ||||
−0.345812 | + | 0.938304i | \(0.612396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.1228 | −1.64030 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.79005 | −0.620759 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.89097 | −0.836441 | −0.418221 | − | 0.908345i | \(-0.637346\pi\) | ||||
−0.418221 | + | 0.908345i | \(0.637346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.821806 | −0.0861487 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.07728 | −0.319099 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.4157 | −1.99201 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.79005 | −0.181752 | −0.0908762 | − | 0.995862i | \(-0.528967\pi\) | ||||
−0.0908762 | + | 0.995862i | \(0.528967\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.43366 | −0.345096 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.12280 | 0.907753 | 0.453876 | − | 0.891065i | \(-0.350041\pi\) | ||||
0.453876 | + | 0.891065i | \(0.350041\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.1602 | 1.88791 | 0.943956 | − | 0.330072i | \(-0.107073\pi\) | ||||
0.943956 | + | 0.330072i | \(0.107073\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.61186 | −0.254891 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.5565 | −1.40723 | −0.703613 | − | 0.710583i | \(-0.748431\pi\) | ||||
−0.703613 | + | 0.710583i | \(0.748431\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0593 | 1.63398 | 0.816992 | − | 0.576649i | \(-0.195640\pi\) | ||||
0.816992 | + | 0.576649i | \(0.195640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.922724 | −0.0875810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.47919 | 0.703583 | 0.351791 | − | 0.936078i | \(-0.385573\pi\) | ||||
0.351791 | + | 0.936078i | \(0.385573\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.61186 | 0.243557 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.821806 | 0.0759760 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.79005 | 0.530773 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.790053 | 0.0718230 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.566335 | 0.0510647 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.30099 | −0.742463 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.4930 | 1.28604 | 0.643021 | − | 0.765849i | \(-0.277681\pi\) | ||||
0.643021 | + | 0.765849i | \(0.277681\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.6891 | −1.02917 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7265 | 1.54878 | 0.774388 | − | 0.632711i | \(-0.218058\pi\) | ||||
0.774388 | + | 0.632711i | \(0.218058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.43366 | 0.644580 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.61186 | 0.224793 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3010 | 0.880073 | 0.440037 | − | 0.897980i | \(-0.354965\pi\) | ||||
0.440037 | + | 0.897980i | \(0.354965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8356 | −1.68243 | −0.841216 | − | 0.540700i | \(-0.818160\pi\) | ||||
−0.841216 | + | 0.540700i | \(0.818160\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.35639 | −0.198444 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.82181 | −0.235971 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.1228 | −1.25588 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0910467 | 0.00745883 | 0.00372942 | − | 0.999993i | \(-0.498813\pi\) | ||||
0.00372942 | + | 0.999993i | \(0.498813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3783 | 0.925951 | 0.462975 | − | 0.886371i | \(-0.346782\pi\) | ||||
0.462975 | + | 0.886371i | \(0.346782\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.79005 | −0.468098 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.03741 | −0.645580 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.22372 | 0.416898 | 0.208449 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208449 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.968247 | 0.0767870 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.10092 | −0.477861 | −0.238930 | − | 0.971037i | \(-0.576797\pi\) | ||||
−0.238930 | + | 0.971037i | \(0.576797\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.96825 | −0.698177 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.30099 | −0.642350 | −0.321175 | − | 0.947020i | \(-0.604078\pi\) | ||||
−0.321175 | + | 0.947020i | \(0.604078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3246 | −0.948049 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.43366 | −0.568467 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.14644 | 0.619362 | 0.309681 | − | 0.950840i | \(-0.399778\pi\) | ||||
0.309681 | + | 0.950840i | \(0.399778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.82181 | −0.137716 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.89908 | 0.142744 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.96825 | 0.670318 | 0.335159 | − | 0.942162i | \(-0.391210\pi\) | ||||
0.335159 | + | 0.942162i | \(0.391210\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.6793 | −1.76007 | −0.880033 | − | 0.474913i | \(-0.842480\pi\) | ||||
−0.880033 | + | 0.474913i | \(0.842480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.40191 | 0.177554 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.41002 | −0.177188 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.8811 | 1.45385 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.09105 | 0.296018 | 0.148009 | − | 0.988986i | \(-0.452714\pi\) | ||||
0.148009 | + | 0.988986i | \(0.452714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.3564 | 0.889432 | 0.444716 | − | 0.895672i | \(-0.353305\pi\) | ||||
0.444716 | + | 0.895672i | \(0.353305\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.14644 | 0.153710 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.24736 | 0.160118 | 0.0800588 | − | 0.996790i | \(-0.474489\pi\) | ||||
0.0800588 | + | 0.996790i | \(0.474489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6810 | −1.53693 | −0.768463 | − | 0.639894i | \(-0.778978\pi\) | ||||
−0.768463 | + | 0.639894i | \(0.778978\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.10092 | −0.289256 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.79005 | 0.406382 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.47919 | 0.103311 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.5247 | 1.76558 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0357 | 1.79237 | 0.896184 | − | 0.443682i | \(-0.146328\pi\) | ||||
0.896184 | + | 0.443682i | \(0.146328\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.17819 | 0.0807285 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.5304 | −2.08215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.07728 | 0.208899 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.14644 | 0.550485 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.75830 | −0.320078 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.8356 | −1.86401 | −0.932004 | − | 0.362448i | \(-0.881941\pi\) | ||||
−0.932004 | + | 0.362448i | \(0.881941\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.82181 | 0.121454 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.32464 | 0.0879191 | 0.0439596 | − | 0.999033i | \(-0.486003\pi\) | ||||
0.0439596 | + | 0.999033i | \(0.486003\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.2138 | 1.79834 | 0.899171 | − | 0.437598i | \(-0.144171\pi\) | ||||
0.899171 | + | 0.437598i | \(0.144171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.43366 | 0.225919 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.1920 | −1.32282 | −0.661410 | − | 0.750025i | \(-0.730042\pi\) | ||||
−0.661410 | + | 0.750025i | \(0.730042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.15455 | −0.401479 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.56634 | −0.166701 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.7721 | 1.40832 | 0.704159 | − | 0.710042i | \(-0.251324\pi\) | ||||
0.704159 | + | 0.710042i | \(0.251324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.6574 | −0.815334 | −0.407667 | − | 0.913131i | \(-0.633658\pi\) | ||||
−0.407667 | + | 0.913131i | \(0.633658\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.61186 | 0.166866 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.10903 | −0.388708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.30099 | −0.399309 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.66549 | 0.546961 | 0.273481 | − | 0.961878i | \(-0.411825\pi\) | ||||
0.273481 | + | 0.961878i | \(0.411825\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.43366 | −0.215873 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.1228 | −0.947026 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.6493 | 1.28807 | 0.644033 | − | 0.764998i | \(-0.277260\pi\) | ||||
0.644033 | + | 0.764998i | \(0.277260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.922724 | 0.0573353 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.79005 | −0.358395 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.1048 | −1.30138 | −0.650689 | − | 0.759344i | \(-0.725520\pi\) | ||||
−0.650689 | + | 0.759344i | \(0.725520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.52892 | 0.155351 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.89097 | −0.482920 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.8493 | −1.14926 | −0.574632 | − | 0.818412i | \(-0.694855\pi\) | ||||
−0.574632 | + | 0.818412i | \(0.694855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.01377 | 0.304565 | 0.152282 | − | 0.988337i | \(-0.451338\pi\) | ||||
0.152282 | + | 0.988337i | \(0.451338\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.821806 | −0.0497380 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.25547 | −0.377219 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.17819 | −0.431296 | −0.215648 | − | 0.976471i | \(-0.569186\pi\) | ||||
−0.215648 | + | 0.976471i | \(0.569186\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.07728 | −0.184232 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.19618 | 0.0713579 | 0.0356790 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356790 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.96825 | −0.414219 | −0.207110 | − | 0.978318i | \(-0.566406\pi\) | ||||
−0.207110 | + | 0.978318i | \(0.566406\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.4157 | −1.15009 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.566335 | −0.0334297 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5247 | 0.972042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.79005 | −0.104935 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.4474 | 1.31139 | 0.655697 | − | 0.755025i | \(-0.272375\pi\) | ||||
0.655697 | + | 0.755025i | \(0.272375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.96013 | 0.288790 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.43366 | −0.199241 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.821806 | 0.0475263 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.6891 | 0.673751 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.12280 | 0.524091 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.27345 | 0.359217 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.6574 | −1.29313 | −0.646563 | − | 0.762861i | \(-0.723794\pi\) | ||||
−0.646563 | + | 0.762861i | \(0.723794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.1602 | 1.08999 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.4238 | 1.32824 | 0.664121 | − | 0.747625i | \(-0.268806\pi\) | ||||
0.664121 | + | 0.747625i | \(0.268806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7622 | −1.00398 | −0.501989 | − | 0.864874i | \(-0.667398\pi\) | ||||
−0.501989 | + | 0.864874i | \(0.667398\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.61186 | −0.147162 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.19196 | 0.460107 | 0.230053 | − | 0.973178i | \(-0.426110\pi\) | ||||
0.230053 | + | 0.973178i | \(0.426110\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.8811 | 1.11313 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.5565 | −0.812463 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 43.0413 | 2.39488 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.49717 | 0.0830481 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.0593 | 0.943381 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.35639 | 0.129912 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.13267 | 0.0622572 | 0.0311286 | − | 0.999515i | \(-0.490090\pi\) | ||||
0.0311286 | + | 0.999515i | \(0.490090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.922724 | −0.0505649 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.7110 | −0.585205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.6475 | −1.45158 | −0.725791 | − | 0.687915i | \(-0.758526\pi\) | ||||
−0.725791 | + | 0.687915i | \(0.758526\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.47919 | 0.406214 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.5663 | 0.572199 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.61186 | 0.140618 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.9030 | −1.33686 | −0.668431 | − | 0.743774i | \(-0.733034\pi\) | ||||
−0.668431 | + | 0.743774i | \(0.733034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4157 | −1.14636 | −0.573178 | − | 0.819431i | \(-0.694289\pi\) | ||||
−0.573178 | + | 0.819431i | \(0.694289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.821806 | 0.0438648 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.2791 | 0.919674 | 0.459837 | − | 0.888003i | \(-0.347908\pi\) | ||||
0.459837 | + | 0.888003i | \(0.347908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.07728 | 0.163325 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.79005 | 0.306442 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.8631 | −1.36500 | −0.682502 | − | 0.730884i | \(-0.739108\pi\) | ||||
−0.682502 | + | 0.730884i | \(0.739108\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.2594 | 1.90839 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.790053 | 0.0414670 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.2774 | 1.11371 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.4930 | −1.59172 | −0.795860 | − | 0.605481i | \(-0.792981\pi\) | ||||
−0.795860 | + | 0.605481i | \(0.792981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.566335 | 0.0294822 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.968247 | −0.0502689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6355 | −0.706019 | −0.353010 | − | 0.935620i | \(-0.614842\pi\) | ||||
−0.353010 | + | 0.935620i | \(0.614842\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.30099 | −0.428661 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.75830 | −0.245065 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.29288 | −0.117777 | −0.0588887 | − | 0.998265i | \(-0.518756\pi\) | ||||
−0.0588887 | + | 0.998265i | \(0.518756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.4930 | 0.742497 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.2791 | −0.780726 | −0.390363 | − | 0.920661i | \(-0.627651\pi\) | ||||
−0.390363 | + | 0.920661i | \(0.627651\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.96825 | 0.457064 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.6891 | −0.594192 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.2318 | −0.670880 | −0.335440 | − | 0.942062i | \(-0.608885\pi\) | ||||
−0.335440 | + | 0.942062i | \(0.608885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.79005 | −0.292816 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7265 | 0.894186 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.70291 | −0.337260 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.1186 | −1.61199 | −0.805993 | − | 0.591925i | \(-0.798368\pi\) | ||||
−0.805993 | + | 0.591925i | \(0.798368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.43366 | 0.372149 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.20995 | −0.310110 | −0.155055 | − | 0.987906i | \(-0.549555\pi\) | ||||
−0.155055 | + | 0.987906i | \(0.549555\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.52892 | −0.125975 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.61186 | 0.129784 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.16832 | 0.157048 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.2594 | −1.24900 | −0.624498 | − | 0.781027i | \(-0.714696\pi\) | ||||
−0.624498 | + | 0.781027i | \(0.714696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.3010 | 0.508111 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.89908 | −0.0934477 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4573 | −0.807857 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.8356 | −0.971352 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.2830 | 1.18630 | 0.593151 | − | 0.805091i | \(-0.297884\pi\) | ||||
0.593151 | + | 0.805091i | \(0.297884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.465418 | 0.0226831 | 0.0113415 | − | 0.999936i | \(-0.496390\pi\) | ||||
0.0113415 | + | 0.999936i | \(0.496390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.35639 | −0.114572 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.5484 | −0.511670 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.40191 | −0.116237 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.82181 | −0.136238 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.78018 | −0.278422 | −0.139211 | − | 0.990263i | \(-0.544457\pi\) | ||||
−0.139211 | + | 0.990263i | \(0.544457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.19618 | 0.441940 | 0.220970 | − | 0.975281i | \(-0.429078\pi\) | ||||
0.220970 | + | 0.975281i | \(0.429078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.1228 | −0.725083 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.43366 | −0.355600 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7901 | −0.753618 | −0.376809 | − | 0.926291i | \(-0.622979\pi\) | ||||
−0.376809 | + | 0.926291i | \(0.622979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.1821 | 1.52902 | 0.764509 | − | 0.644613i | \(-0.222982\pi\) | ||||
0.764509 | + | 0.644613i | \(0.222982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.6101 | −0.977012 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.0910467 | 0.00430636 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.41568 | −0.255582 | −0.127791 | − | 0.991801i | \(-0.540789\pi\) | ||||
−0.127791 | + | 0.991801i | \(0.540789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.94461 | −0.0915679 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3783 | 0.534598 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.14644 | −0.100627 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.8412 | 1.25558 | 0.627790 | − | 0.778383i | \(-0.283960\pi\) | ||||
0.627790 | + | 0.778383i | \(0.283960\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.79005 | −0.270257 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.410023 | 0.0190967 | 0.00954835 | − | 0.999954i | \(-0.496961\pi\) | ||||
0.00954835 | + | 0.999954i | \(0.496961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.6849 | −1.70489 | −0.852446 | − | 0.522815i | \(-0.824882\pi\) | ||||
−0.852446 | + | 0.522815i | \(0.824882\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.03741 | −0.372726 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.7265 | 0.542640 | 0.271320 | − | 0.962489i | \(-0.412540\pi\) | ||||
0.271320 | + | 0.962489i | \(0.412540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.10092 | 0.189363 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.22372 | 0.240696 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.1366 | 1.84548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.5427 | −0.621381 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.968247 | 0.0443330 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0829 | −0.917613 | −0.458806 | − | 0.888536i | \(-0.651723\pi\) | ||||
−0.458806 | + | 0.888536i | \(0.651723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.758300 | −0.0345755 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.67536 | −0.212297 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.51905 | −0.204778 | −0.102389 | − | 0.994744i | \(-0.532649\pi\) | ||||
−0.102389 | + | 0.994744i | \(0.532649\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.10092 | −0.275893 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.26358 | −0.372930 | −0.186465 | − | 0.982462i | \(-0.559703\pi\) | ||||
−0.186465 | + | 0.982462i | \(0.559703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.5247 | 1.50988 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.96825 | −0.403093 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.17819 | −0.0528492 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.9682 | −1.47586 | −0.737931 | − | 0.674876i | \(-0.764197\pi\) | ||||
−0.737931 | + | 0.674876i | \(0.764197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.30099 | −0.370861 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.7029 | −0.833921 | −0.416961 | − | 0.908925i | \(-0.636905\pi\) | ||||
−0.416961 | + | 0.908925i | \(0.636905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.8275 | 1.06031 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3246 | −0.547356 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5109 | −0.820483 | −0.410242 | − | 0.911977i | \(-0.634556\pi\) | ||||
−0.410242 | + | 0.911977i | \(0.634556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.14644 | −0.360377 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.43366 | −0.328204 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 50.0438 | 2.20519 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.09105 | 0.355844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.14644 | 0.357589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.0219 | 1.53434 | 0.767168 | − | 0.641446i | \(-0.221665\pi\) | ||||
0.767168 | + | 0.641446i | \(0.221665\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.3204 | −1.76309 | −0.881544 | − | 0.472101i | \(-0.843496\pi\) | ||||
−0.881544 | + | 0.472101i | \(0.843496\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.82181 | −0.0795101 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.8176 | 0.776147 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.89908 | 0.0824132 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.465418 | 0.0201595 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.0194 | −1.64372 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.96825 | 0.387008 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.43366 | −0.147898 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.2456 | −1.21437 | −0.607187 | − | 0.794559i | \(-0.707702\pi\) | ||||
−0.607187 | + | 0.794559i | \(0.707702\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.6793 | −1.01617 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.5565 | 1.90859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.6810 | −1.09804 | −0.549021 | − | 0.835809i | \(-0.684999\pi\) | ||||
−0.549021 | + | 0.835809i | \(0.684999\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.40191 | 0.102511 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.0413 | 1.83362 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.56634 | 0.109132 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.41002 | −0.102300 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.201835 | 0.00855203 | 0.00427602 | − | 0.999991i | \(-0.498639\pi\) | ||||
0.00427602 | + | 0.999991i | \(0.498639\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.60620 | −0.406299 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.8811 | 0.839381 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 47.4513 | 1.99984 | 0.999918 | − | 0.0128333i | \(-0.00408508\pi\) | ||||
0.999918 | + | 0.0128333i | \(0.00408508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.5346 | 0.821826 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.4199 | −0.604513 | −0.302257 | − | 0.953227i | \(-0.597740\pi\) | ||||
−0.302257 | + | 0.953227i | \(0.597740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4393 | −1.19015 | −0.595074 | − | 0.803671i | \(-0.702877\pi\) | ||||
−0.595074 | + | 0.803671i | \(0.702877\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.09105 | 0.170906 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.82181 | 0.0759746 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7565 | 1.19715 | 0.598575 | − | 0.801067i | \(-0.295734\pi\) | ||||
0.598575 | + | 0.801067i | \(0.295734\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.3564 | 0.513514 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.30099 | 0.261409 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.32464 | −0.137692 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.14644 | 0.0887444 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5783 | 0.890634 | 0.445317 | − | 0.895373i | \(-0.353091\pi\) | ||||
0.445317 | + | 0.895373i | \(0.353091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.8754 | 0.942566 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.24736 | 0.0924440 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.6436 | 0.478146 | 0.239073 | − | 0.971002i | \(-0.423157\pi\) | ||||
0.239073 | + | 0.971002i | \(0.423157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.1228 | 0.619974 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.6810 | −0.887345 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0455 | 0.492167 | 0.246083 | − | 0.969249i | \(-0.420856\pi\) | ||||
0.246083 | + | 0.969249i | \(0.420856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.8137 | 1.01217 | 0.506086 | − | 0.862483i | \(-0.331092\pi\) | ||||
0.506086 | + | 0.862483i | \(0.331092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.10092 | −0.167002 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.06351 | 0.0838935 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.0512 | 1.17915 | 0.589576 | − | 0.807713i | \(-0.299295\pi\) | ||||
0.589576 | + | 0.807713i | \(0.299295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.79005 | 0.234625 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.93649 | −0.0783422 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.300994 | 0.0121570 | 0.00607851 | − | 0.999982i | \(-0.498065\pi\) | ||||
0.00607851 | + | 0.999982i | \(0.498065\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.47919 | 0.0596466 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.8218 | 0.838254 | 0.419127 | − | 0.907928i | \(-0.362336\pi\) | ||||
0.419127 | + | 0.907928i | \(0.362336\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.4076 | 1.02122 | 0.510608 | − | 0.859813i | \(-0.329420\pi\) | ||||
0.510608 | + | 0.859813i | \(0.329420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.89097 | 0.316145 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7901 | −1.23160 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.5247 | 1.01936 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.34262 | 0.213024 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8119 | −0.510035 | −0.255018 | − | 0.966936i | \(-0.582081\pi\) | ||||
−0.255018 | + | 0.966936i | \(0.582081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.0357 | 1.03482 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.8536 | 1.50217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.821806 | 0.0325611 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.17819 | 0.0466086 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.06741 | −0.121155 | −0.0605776 | − | 0.998163i | \(-0.519294\pi\) | ||||
−0.0605776 | + | 0.998163i | \(0.519294\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.15631 | −0.242781 | −0.121391 | − | 0.992605i | \(-0.538735\pi\) | ||||
−0.121391 | + | 0.992605i | \(0.538735\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.5304 | −1.20213 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.4376 | −0.488971 | −0.244486 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244486 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.52081 | −0.255964 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.07728 | 0.120608 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.0536 | −0.393429 | −0.196715 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196715 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.2992 | 1.80906 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.14644 | 0.317823 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.1246 | −0.744987 | −0.372494 | − | 0.928035i | \(-0.621497\pi\) | ||||
−0.372494 | + | 0.928035i | \(0.621497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.7068 | 1.62221 | 0.811103 | − | 0.584903i | \(-0.198867\pi\) | ||||
0.811103 | + | 0.584903i | \(0.198867\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.75830 | −0.184797 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.4157 | 0.752908 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.79005 | −0.224192 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.8356 | −1.07619 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.24736 | −0.318386 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.5247 | −0.598434 | −0.299217 | − | 0.954185i | \(-0.596725\pi\) | ||||
−0.299217 | + | 0.954185i | \(0.596725\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.82181 | 0.0701213 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.24736 | −0.163239 | −0.0816196 | − | 0.996664i | \(-0.526009\pi\) | ||||
−0.0816196 | + | 0.996664i | \(0.526009\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.79005 | 0.0686959 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.32464 | 0.0507601 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.8811 | 1.37295 | 0.686476 | − | 0.727152i | \(-0.259157\pi\) | ||||
0.686476 | + | 0.727152i | \(0.259157\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.9047 | 1.02798 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.2138 | 1.03827 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.795711 | 0.0303142 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.96013 | 0.188692 | 0.0943462 | − | 0.995539i | \(-0.469924\pi\) | ||||
0.0943462 | + | 0.995539i | \(0.469924\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.43366 | 0.130434 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −51.8077 | −1.96518 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.27911 | −0.124205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.1920 | −0.763730 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.2555 | −0.916116 | −0.458058 | − | 0.888922i | \(-0.651455\pi\) | ||||
−0.458058 | + | 0.888922i | \(0.651455\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.85922 | 0.258700 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.15455 | −0.231794 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.12280 | −0.343098 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.21982 | 0.0833670 | 0.0416835 | − | 0.999131i | \(-0.486728\pi\) | ||||
0.0416835 | + | 0.999131i | \(0.486728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.56634 | −0.0962451 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.07728 | −0.115245 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.37016 | −0.275628 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.7721 | 0.813093 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.23183 | −0.0459395 | −0.0229697 | − | 0.999736i | \(-0.507312\pi\) | ||||
−0.0229697 | + | 0.999736i | \(0.507312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.1602 | −0.713564 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.6574 | −0.470733 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.5484 | −0.391756 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.88110 | −0.292294 | −0.146147 | − | 0.989263i | \(-0.546687\pi\) | ||||
−0.146147 | + | 0.989263i | \(0.546687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 67.6807 | 2.50326 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.64927 | 0.245596 | 0.122798 | − | 0.992432i | \(-0.460813\pi\) | ||||
0.122798 | + | 0.992432i | \(0.460813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.61186 | 0.0963399 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.0812 | 0.518687 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.4555 | −0.531756 | −0.265878 | − | 0.964007i | \(-0.585662\pi\) | ||||
−0.265878 | + | 0.964007i | \(0.585662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.10903 | −0.224421 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.63940 | 0.316949 | 0.158474 | − | 0.987363i | \(-0.449342\pi\) | ||||
0.158474 | + | 0.987363i | \(0.449342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.237801 | 0.00871236 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.30099 | −0.230541 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.5565 | 0.531882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.99579 | 0.255280 | 0.127640 | − | 0.991821i | \(-0.459260\pi\) | ||||
0.127640 | + | 0.991821i | \(0.459260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.66549 | 0.315788 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.7184 | 1.08156 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.5304 | 1.10965 | 0.554823 | − | 0.831969i | \(-0.312786\pi\) | ||||
0.554823 | + | 0.831969i | \(0.312786\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.43366 | −0.124634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.867329 | −0.0314407 | −0.0157203 | − | 0.999876i | \(-0.505004\pi\) | ||||
−0.0157203 | + | 0.999876i | \(0.505004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.0593 | −0.617588 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.1228 | −0.546766 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.56068 | 0.0563528 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.5166 | −0.992274 | −0.496137 | − | 0.868244i | \(-0.665249\pi\) | ||||
−0.496137 | + | 0.868244i | \(0.665249\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.6493 | 0.743665 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.58822 | −0.129059 | −0.0645296 | − | 0.997916i | \(-0.520555\pi\) | ||||
−0.0645296 | + | 0.997916i | \(0.520555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.60620 | −0.201381 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.922724 | 0.0331025 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.20995 | −0.150837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.04552 | −0.144760 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.79005 | −0.206920 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.6436 | 0.486961 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.4100 | −1.15529 | −0.577646 | − | 0.816287i | \(-0.696029\pi\) | ||||
−0.577646 | + | 0.816287i | \(0.696029\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.1048 | −0.751351 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.47919 | −0.265929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.97391 | 0.0700954 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.52892 | 0.0896917 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.8038 | −0.736909 | −0.368455 | − | 0.929646i | \(-0.620113\pi\) | ||||
−0.368455 | + | 0.929646i | \(0.620113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6436 | 0.482676 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.89097 | −0.278814 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.9721 | −0.987116 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.61186 | −0.0920559 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.8493 | −0.663528 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.1147 | −0.601720 | −0.300860 | − | 0.953668i | \(-0.597274\pi\) | ||||
−0.300860 | + | 0.953668i | \(0.597274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.4393 | −0.787951 | −0.393976 | − | 0.919121i | \(-0.628901\pi\) | ||||
−0.393976 | + | 0.919121i | \(0.628901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.01377 | 0.175841 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.9347 | −0.558169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 86.8931 | 3.04001 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.821806 | −0.0287162 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.38393 | −0.222801 | −0.111400 | − | 0.993776i | \(-0.535534\pi\) | ||||
−0.111400 | + | 0.993776i | \(0.535534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.8631 | 1.59869 | 0.799344 | − | 0.600874i | \(-0.205181\pi\) | ||||
0.799344 | + | 0.600874i | \(0.205181\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.25547 | −0.217788 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.7029 | −1.69357 | −0.846783 | − | 0.531939i | \(-0.821464\pi\) | ||||
−0.846783 | + | 0.531939i | \(0.821464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.20995 | −0.0767546 | −0.0383773 | − | 0.999263i | \(-0.512219\pi\) | ||||
−0.0383773 | + | 0.999263i | \(0.512219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.17819 | −0.249009 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.79005 | −0.200613 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.6810 | −0.750303 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.07728 | −0.106366 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.4295 | 0.567208 | 0.283604 | − | 0.958942i | \(-0.408470\pi\) | ||||
0.283604 | + | 0.958942i | \(0.408470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.52471 | 0.156025 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.19618 | 0.0411985 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.1902 | −1.10738 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.790053 | −0.0271465 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.96825 | −0.239150 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.922724 | −0.0316306 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.8038 | −0.369916 | −0.184958 | − | 0.982746i | \(-0.559215\pi\) | ||||
−0.184958 | + | 0.982746i | \(0.559215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.4157 | −0.664002 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.90895 | 0.0652086 | 0.0326043 | − | 0.999468i | \(-0.489620\pi\) | ||||
0.0326043 | + | 0.999468i | \(0.489620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.0275 | 1.29748 | 0.648741 | − | 0.761009i | \(-0.275296\pi\) | ||||
0.648741 | + | 0.761009i | \(0.275296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.566335 | −0.0193007 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.2018 | 1.23232 | 0.616162 | − | 0.787619i | \(-0.288686\pi\) | ||||
0.616162 | + | 0.787619i | \(0.288686\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.2774 | 0.723452 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.5247 | 0.561209 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.81193 | 0.298924 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.37016 | −0.114193 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.79005 | −0.0605841 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.30099 | 0.280625 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.86733 | 0.164358 | 0.0821790 | − | 0.996618i | \(-0.473812\pi\) | ||||
0.0821790 | + | 0.996618i | \(0.473812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.4474 | 0.757133 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.9422 | 1.10985 | 0.554925 | − | 0.831901i | \(-0.312747\pi\) | ||||
0.554925 | + | 0.831901i | \(0.312747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.7858 | −0.497583 | −0.248792 | − | 0.968557i | \(-0.580033\pi\) | ||||
−0.248792 | + | 0.968557i | \(0.580033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.96013 | 0.166733 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.8966 | −0.500180 | −0.250090 | − | 0.968223i | \(-0.580460\pi\) | ||||
−0.250090 | + | 0.968223i | \(0.580460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.4930 | −0.486078 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.43366 | −0.115032 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.5166 | 0.586171 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.4238 | 0.782971 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.821806 | 0.0274393 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8176 | 0.594250 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.60620 | −0.186770 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.6891 | 0.388990 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −61.8469 | −2.05586 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.5759 | 1.61294 | 0.806468 | − | 0.591278i | \(-0.201376\pi\) | ||||
0.806468 | + | 0.591278i | \(0.201376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.12280 | 0.302584 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.6436 | 0.584559 | 0.292279 | − | 0.956333i | \(-0.405586\pi\) | ||||
0.292279 | + | 0.956333i | \(0.405586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.6355 | 0.716031 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.27345 | 0.207394 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.7265 | −0.585382 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6630 | −0.384728 | −0.192364 | − | 0.981324i | \(-0.561615\pi\) | ||||
−0.192364 | + | 0.981324i | \(0.561615\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.6574 | −0.746586 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.968247 | 0.0318702 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.68102 | −0.0552717 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.1602 | 0.629304 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.904741 | 0.0296836 | 0.0148418 | − | 0.999890i | \(-0.495276\pi\) | ||||
0.0148418 | + | 0.999890i | \(0.495276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.43366 | −0.243629 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.4238 | 0.766861 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51.9266 | 1.69818 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.4887 | 1.68206 | 0.841032 | − | 0.540985i | \(-0.181949\pi\) | ||||
0.841032 | + | 0.540985i | \(0.181949\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.7622 | −0.579647 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.4693 | 1.54746 | 0.773728 | − | 0.633518i | \(-0.218390\pi\) | ||||
0.773728 | + | 0.633518i | \(0.218390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.566335 | 0.0184424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.61186 | −0.0849638 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.5801 | −1.54615 | −0.773073 | − | 0.634317i | \(-0.781281\pi\) | ||||
−0.773073 | + | 0.634317i | \(0.781281\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.69479 | 0.217322 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.19196 | 0.265643 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −61.6807 | −1.99803 | −0.999017 | − | 0.0443267i | \(-0.985886\pi\) | ||||
−0.999017 | + | 0.0443267i | \(0.985886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.6852 | 0.345766 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.8811 | 0.642665 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.3010 | −0.332636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5304 | −0.694528 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.5565 | −0.469076 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.2731 | 1.03891 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.0275 | −0.579727 | −0.289863 | − | 0.957068i | \(-0.593610\pi\) | ||||
−0.289863 | + | 0.957068i | \(0.593610\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 43.0413 | 1.38269 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.4873 | 0.625377 | 0.312689 | − | 0.949856i | \(-0.398770\pi\) | ||||
0.312689 | + | 0.949856i | \(0.398770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.8356 | 0.635899 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.49717 | 0.0479478 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.1147 | 0.675519 | 0.337759 | − | 0.941232i | \(-0.390331\pi\) | ||||
0.337759 | + | 0.941232i | \(0.390331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0949 | 0.865958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0593 | 0.544661 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.8811 | 1.14443 | 0.572215 | − | 0.820104i | \(-0.306084\pi\) | ||||
0.572215 | + | 0.820104i | \(0.306084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.86978 | 0.187027 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.35639 | 0.0750047 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.6891 | −0.371693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.2417 | 0.484169 | 0.242084 | − | 0.970255i | \(-0.422169\pi\) | ||||
0.242084 | + | 0.970255i | \(0.422169\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.13267 | 0.0359442 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −56.6278 | −1.79522 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.7901 | 1.19682 | 0.598411 | − | 0.801189i | \(-0.295799\pi\) | ||||
0.598411 | + | 0.801189i | \(0.295799\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.922724 | −0.0291937 |
(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 | 3864.2.a.o.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 7728.2.a.bq.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.o.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7728.2.a.bq.1.3 | 3 | 4.3 | odd | 2 |