Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1472,2,Mod(1,1472)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1472, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1472.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1472 = 2^{6} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1472.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: | \(11.7539791775\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 184) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1472.1 |
$q$-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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.12311 | 0.941652 | 0.470826 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.438447 | −0.121603 | −0.0608017 | − | 0.998150i | \(-0.519366\pi\) | ||||
−0.0608017 | + | 0.998150i | \(0.519366\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.12311 | 0.806382 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.12311 | 1.24254 | 0.621268 | − | 0.783598i | \(-0.286618\pi\) | ||||
0.621268 | + | 0.783598i | \(0.286618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12311 | 0.716490 | 0.358245 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358245 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.56155 | −0.661364 | −0.330682 | − | 0.943742i | \(-0.607279\pi\) | ||||
−0.330682 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43845 | −0.437958 | −0.218979 | − | 0.975730i | \(-0.570273\pi\) | ||||
−0.218979 | + | 0.975730i | \(0.570273\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.87689 | −0.848958 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.24621 | −1.35567 | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||||
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.684658 | 0.109633 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.80776 | −1.53172 | −0.765858 | − | 0.643010i | \(-0.777685\pi\) | ||||
−0.765858 | + | 0.643010i | \(0.777685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.12311 | 0.167423 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.684658 | −0.0998677 | −0.0499338 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499338 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.00000 | −1.12022 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.24621 | −0.842239 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.87689 | −0.645960 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2462 | −1.33394 | −0.666972 | − | 0.745083i | \(-0.732410\pi\) | ||||
−0.666972 | + | 0.745083i | \(0.732410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.24621 | 0.543672 | 0.271836 | − | 0.962344i | \(-0.412369\pi\) | ||||
0.271836 | + | 0.962344i | \(0.412369\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.876894 | 0.108765 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.12311 | −0.381548 | −0.190774 | − | 0.981634i | \(-0.561100\pi\) | ||||
−0.190774 | + | 0.981634i | \(0.561100\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.56155 | 0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5616 | 1.60946 | 0.804730 | − | 0.593641i | \(-0.202310\pi\) | ||||
0.804730 | + | 0.593641i | \(0.202310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6847 | −1.71871 | −0.859355 | − | 0.511380i | \(-0.829134\pi\) | ||||
−0.859355 | + | 0.511380i | \(0.829134\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.56155 | 0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.12311 | 0.351377 | 0.175688 | − | 0.984446i | \(-0.443785\pi\) | ||||
0.175688 | + | 0.984446i | \(0.443785\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.2462 | −1.56372 | −0.781862 | − | 0.623451i | \(-0.785730\pi\) | ||||
−0.781862 | + | 0.623451i | \(0.785730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.2462 | −1.11136 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.56155 | 0.596261 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3693 | 1.20515 | 0.602573 | − | 0.798064i | \(-0.294142\pi\) | ||||
0.602573 | + | 0.798064i | \(0.294142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.80776 | 0.394847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.24621 | −0.640848 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3693 | 1.15438 | 0.577190 | − | 0.816610i | \(-0.304149\pi\) | ||||
0.577190 | + | 0.816610i | \(0.304149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.75379 | −0.176262 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2462 | −1.21854 | −0.609272 | − | 0.792961i | \(-0.708538\pi\) | ||||
−0.609272 | + | 0.792961i | \(0.708538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.2462 | −1.40372 | −0.701860 | − | 0.712314i | \(-0.747647\pi\) | ||||
−0.701860 | + | 0.712314i | \(0.747647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.1231 | −1.07531 | −0.537656 | − | 0.843165i | \(-0.680690\pi\) | ||||
−0.537656 | + | 0.843165i | \(0.680690\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1231 | −1.25697 | −0.628483 | − | 0.777824i | \(-0.716324\pi\) | ||||
−0.628483 | + | 0.777824i | \(0.716324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8769 | 1.22222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.87689 | −0.270635 | −0.135318 | − | 0.990802i | \(-0.543206\pi\) | ||||
−0.135318 | + | 0.990802i | \(0.543206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.246211 | 0.0227622 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24621 | −0.113292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.3153 | 1.38094 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.684658 | 0.0607536 | 0.0303768 | − | 0.999539i | \(-0.490329\pi\) | ||||
0.0303768 | + | 0.999539i | \(0.490329\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.4924 | −1.09990 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.31534 | −0.289663 | −0.144831 | − | 0.989456i | \(-0.546264\pi\) | ||||
−0.144831 | + | 0.989456i | \(0.546264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.1231 | −0.957325 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.87689 | 0.587533 | 0.293766 | − | 0.955877i | \(-0.405091\pi\) | ||||
0.293766 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31534 | 0.281204 | 0.140602 | − | 0.990066i | \(-0.455096\pi\) | ||||
0.140602 | + | 0.990066i | \(0.455096\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.06913 | 0.0900370 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.36932 | −0.114508 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.12311 | 0.591542 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9309 | 0.901563 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.2462 | 1.65863 | 0.829317 | − | 0.558778i | \(-0.188730\pi\) | ||||
0.829317 | + | 0.558778i | \(0.188730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4384 | −0.849469 | −0.424734 | − | 0.905318i | \(-0.639633\pi\) | ||||
−0.424734 | + | 0.905318i | \(0.639633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.87689 | −0.232583 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.87689 | 0.391722 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.1231 | −1.68581 | −0.842904 | − | 0.538064i | \(-0.819156\pi\) | ||||
−0.842904 | + | 0.538064i | \(0.819156\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.12311 | 0.247678 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.9309 | −1.48278 | −0.741390 | − | 0.671074i | \(-0.765833\pi\) | ||||
−0.741390 | + | 0.671074i | \(0.765833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.75379 | 0.759331 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8078 | −0.985213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.75379 | −0.134116 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0000 | 0.760286 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | 1.20263 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.31534 | 0.247800 | 0.123900 | − | 0.992295i | \(-0.460460\pi\) | ||||
0.123900 | + | 0.992295i | \(0.460460\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.75379 | −0.279017 | −0.139508 | − | 0.990221i | \(-0.544552\pi\) | ||||
−0.139508 | + | 0.990221i | \(0.544552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.63068 | −0.490154 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.4924 | 1.21255 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0000 | 1.17004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3693 | 1.83566 | 0.917830 | − | 0.396974i | \(-0.129940\pi\) | ||||
0.917830 | + | 0.396974i | \(0.129940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.438447 | −0.0315601 | −0.0157801 | − | 0.999875i | \(-0.505023\pi\) | ||||
−0.0157801 | + | 0.999875i | \(0.505023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.36932 | −0.0980588 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9309 | 1.20627 | 0.603137 | − | 0.797637i | \(-0.293917\pi\) | ||||
0.603137 | + | 0.797637i | \(0.293917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1231 | 0.788496 | 0.394248 | − | 0.919004i | \(-0.371005\pi\) | ||||
0.394248 | + | 0.919004i | \(0.371005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.87689 | 0.343990 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.6155 | 1.37001 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.561553 | 0.0390306 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.75379 | 0.674684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.1771 | −1.45103 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0000 | −1.09119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.9309 | 1.54952 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.24621 | −0.151097 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.4924 | −1.90799 | −0.953997 | − | 0.299817i | \(-0.903075\pi\) | ||||
−0.953997 | + | 0.299817i | \(0.903075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.561553 | 0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.24621 | 0.414576 | 0.207288 | − | 0.978280i | \(-0.433536\pi\) | ||||
0.207288 | + | 0.978280i | \(0.433536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.8769 | −0.983093 | −0.491546 | − | 0.870851i | \(-0.663568\pi\) | ||||
−0.491546 | + | 0.870851i | \(0.663568\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.0540 | −1.05173 | −0.525865 | − | 0.850568i | \(-0.676258\pi\) | ||||
−0.525865 | + | 0.850568i | \(0.676258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.36932 | 0.0893244 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.87689 | −0.316788 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0540 | 1.68529 | 0.842646 | − | 0.538468i | \(-0.180997\pi\) | ||||
0.842646 | + | 0.538468i | \(0.180997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.49242 | 0.418214 | 0.209107 | − | 0.977893i | \(-0.432944\pi\) | ||||
0.209107 | + | 0.977893i | \(0.432944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.0000 | 0.894427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.36932 | −0.0871275 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.2462 | 1.40980 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.24621 | 0.394257 | 0.197129 | − | 0.980378i | \(-0.436838\pi\) | ||||
0.197129 | + | 0.980378i | \(0.436838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.12311 | −0.196348 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.0000 | 1.00196 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.31534 | −0.331562 | −0.165781 | − | 0.986163i | \(-0.553014\pi\) | ||||
−0.165781 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.1231 | −1.17918 | −0.589591 | − | 0.807702i | \(-0.700711\pi\) | ||||
−0.589591 | + | 0.807702i | \(0.700711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.7538 | −1.08651 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3153 | −0.811851 | −0.405925 | − | 0.913906i | \(-0.633051\pi\) | ||||
−0.405925 | + | 0.913906i | \(0.633051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.12311 | −0.188330 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8078 | −1.06996 | −0.534982 | − | 0.844863i | \(-0.679682\pi\) | ||||
−0.534982 | + | 0.844863i | \(0.679682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.36932 | 0.0819789 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.12311 | 0.305619 | 0.152809 | − | 0.988256i | \(-0.451168\pi\) | ||||
0.152809 | + | 0.988256i | \(0.451168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.12311 | −0.185649 | −0.0928247 | − | 0.995682i | \(-0.529590\pi\) | ||||
−0.0928247 | + | 0.995682i | \(0.529590\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.75379 | 0.577765 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.24621 | 0.543895 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.7538 | −1.04075 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.3693 | 0.897885 | 0.448943 | − | 0.893561i | \(-0.351801\pi\) | ||||
0.448943 | + | 0.893561i | \(0.351801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.4924 | 1.19311 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.3693 | 1.00787 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.438447 | 0.0253561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.1231 | 1.09859 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.49242 | −0.486275 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.2462 | 1.04137 | 0.520683 | − | 0.853750i | \(-0.325677\pi\) | ||||
0.520683 | + | 0.853750i | \(0.325677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.2462 | 1.26554 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.56155 | 0.315367 | 0.157683 | − | 0.987490i | \(-0.449597\pi\) | ||||
0.157683 | + | 0.987490i | \(0.449597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.3693 | −0.868725 | −0.434363 | − | 0.900738i | \(-0.643026\pi\) | ||||
−0.434363 | + | 0.900738i | \(0.643026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.75379 | 0.210834 | 0.105417 | − | 0.994428i | \(-0.466382\pi\) | ||||
0.105417 | + | 0.994428i | \(0.466382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.1231 | −0.622774 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.3693 | 0.969461 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000 | 0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.438447 | 0.0243207 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.4924 | 1.13323 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.4233 | −1.72718 | −0.863590 | − | 0.504194i | \(-0.831789\pi\) | ||||
−0.863590 | + | 0.504194i | \(0.831789\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.63068 | 0.253760 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.24621 | 0.341267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.6155 | −1.17747 | −0.588736 | − | 0.808325i | \(-0.700374\pi\) | ||||
−0.588736 | + | 0.808325i | \(0.700374\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.49242 | 0.243995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.61553 | −0.412404 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.12311 | −0.168142 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4924 | 0.885360 | 0.442680 | − | 0.896680i | \(-0.354028\pi\) | ||||
0.442680 | + | 0.896680i | \(0.354028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.6847 | 1.85663 | 0.928314 | − | 0.371798i | \(-0.121259\pi\) | ||||
0.928314 | + | 0.371798i | \(0.121259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.43845 | −0.130155 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5616 | 0.828258 | 0.414129 | − | 0.910218i | \(-0.364086\pi\) | ||||
0.414129 | + | 0.910218i | \(0.364086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.1231 | −1.43954 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.6155 | −1.24638 | −0.623190 | − | 0.782071i | \(-0.714164\pi\) | ||||
−0.623190 | + | 0.782071i | \(0.714164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94602 | 0.102140 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.3693 | 1.53726 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.2462 | −0.743646 | −0.371823 | − | 0.928304i | \(-0.621267\pi\) | ||||
−0.371823 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.50758 | 0.286713 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4924 | 0.543277 | 0.271639 | − | 0.962399i | \(-0.412434\pi\) | ||||
0.271639 | + | 0.962399i | \(0.412434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.7386 | −0.967659 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.56155 | 0.0804241 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4924 | 0.641693 | 0.320846 | − | 0.947131i | \(-0.396033\pi\) | ||||
0.320846 | + | 0.947131i | \(0.396033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06913 | −0.0547732 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.75379 | 0.498395 | 0.249198 | − | 0.968453i | \(-0.419833\pi\) | ||||
0.249198 | + | 0.968453i | \(0.419833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.49242 | −0.228363 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.3693 | 1.18487 | 0.592436 | − | 0.805618i | \(-0.298166\pi\) | ||||
0.592436 | + | 0.805618i | \(0.298166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.12311 | −0.259087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.17708 | 0.261149 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.24621 | −0.314281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.4384 | −0.825022 | −0.412511 | − | 0.910953i | \(-0.635348\pi\) | ||||
−0.412511 | + | 0.910953i | \(0.635348\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.2462 | −1.41055 | −0.705274 | − | 0.708935i | \(-0.749176\pi\) | ||||
−0.705274 | + | 0.708935i | \(0.749176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.06913 | 0.0532572 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.0000 | 0.695666 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.7538 | −1.27657 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3002 | 1.30046 | 0.650230 | − | 0.759737i | \(-0.274672\pi\) | ||||
0.650230 | + | 0.759737i | \(0.274672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7386 | −0.529698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.4924 | 1.39864 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.17708 | −0.253523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.4924 | −1.00112 | −0.500560 | − | 0.865702i | \(-0.666873\pi\) | ||||
−0.500560 | + | 0.865702i | \(0.666873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8769 | 0.920004 | 0.460002 | − | 0.887918i | \(-0.347849\pi\) | ||||
0.460002 | + | 0.887918i | \(0.347849\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.384472 | 0.0186937 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.12311 | −0.248507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.13826 | 0.103236 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.49242 | 0.216392 | 0.108196 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108196 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7386 | −1.18886 | −0.594431 | − | 0.804146i | \(-0.702623\pi\) | ||||
−0.594431 | + | 0.804146i | \(0.702623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.1231 | −0.533312 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.12311 | −0.149398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.0540 | −1.24349 | −0.621744 | − | 0.783220i | \(-0.713576\pi\) | ||||
−0.621744 | + | 0.783220i | \(0.713576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.93087 | 0.187184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.9309 | 1.65962 | 0.829808 | − | 0.558049i | \(-0.188450\pi\) | ||||
0.829808 | + | 0.558049i | \(0.188450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.7386 | −1.07791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.6155 | −1.49536 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.24621 | 0.389163 | 0.194581 | − | 0.980886i | \(-0.437665\pi\) | ||||
0.194581 | + | 0.980886i | \(0.437665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.6307 | −1.44234 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.3002 | 0.765850 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3693 | 0.906058 | 0.453029 | − | 0.891496i | \(-0.350343\pi\) | ||||
0.453029 | + | 0.891496i | \(0.350343\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.4924 | 1.32991 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.80776 | −0.456793 | −0.228397 | − | 0.973568i | \(-0.573348\pi\) | ||||
−0.228397 | + | 0.973568i | \(0.573348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4924 | −0.952364 | −0.476182 | − | 0.879347i | \(-0.657980\pi\) | ||||
−0.476182 | + | 0.879347i | \(0.657980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.61553 | −0.353162 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.36932 | −0.433560 | −0.216780 | − | 0.976220i | \(-0.569555\pi\) | ||||
−0.216780 | + | 0.976220i | \(0.569555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.9848 | 1.51986 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.9848 | 1.14880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.12311 | −0.143298 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.12311 | 0.0514235 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.24621 | −0.285397 | −0.142698 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142698 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.61553 | 0.164854 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.7386 | −1.03251 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.6847 | 1.11857 | 0.559284 | − | 0.828976i | \(-0.311076\pi\) | ||||
0.559284 | + | 0.828976i | \(0.311076\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.5616 | 1.33682 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.80776 | 0.352359 | 0.176180 | − | 0.984358i | \(-0.443626\pi\) | ||||
0.176180 | + | 0.984358i | \(0.443626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.2462 | −0.821768 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.50758 | 0.157654 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0540 | −0.629142 | −0.314571 | − | 0.949234i | \(-0.601861\pi\) | ||||
−0.314571 | + | 0.949234i | \(0.601861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.9848 | 1.11624 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.3693 | −0.774460 | −0.387230 | − | 0.921983i | \(-0.626568\pi\) | ||||
−0.387230 | + | 0.921983i | \(0.626568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.4924 | 1.08990 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.0000 | 0.888231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.3002 | −1.69763 | −0.848813 | − | 0.528693i | \(-0.822682\pi\) | ||||
−0.848813 | + | 0.528693i | \(0.822682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.3693 | 0.766874 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.4924 | 1.25553 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.13826 | −0.0940406 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.6155 | −0.685446 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.6155 | −0.946993 | −0.473497 | − | 0.880796i | \(-0.657008\pi\) | ||||
−0.473497 | + | 0.880796i | \(0.657008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2462 | −0.972759 | −0.486379 | − | 0.873748i | \(-0.661683\pi\) | ||||
−0.486379 | + | 0.873748i | \(0.661683\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.4924 | −0.544178 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.75379 | 0.249693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.30019 | 0.186262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.2462 | 0.961788 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.17708 | −0.223408 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.8617 | −0.941652 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.06913 | −0.303926 | −0.151963 | − | 0.988386i | \(-0.548559\pi\) | ||||
−0.151963 | + | 0.988386i | \(0.548559\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.86174 | 0.251551 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.2462 | 1.12426 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.5464 | 1.13504 | 0.567521 | − | 0.823359i | \(-0.307903\pi\) | ||||
0.567521 | + | 0.823359i | \(0.307903\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.38447 | −0.101767 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.1231 | −0.473860 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.7538 | −1.09319 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.12311 | 0.386558 | 0.193279 | − | 0.981144i | \(-0.438088\pi\) | ||||
0.193279 | + | 0.981144i | \(0.438088\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.50758 | −0.148355 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.9848 | −1.05486 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.2462 | −0.937566 | −0.468783 | − | 0.883313i | \(-0.655307\pi\) | ||||
−0.468783 | + | 0.883313i | \(0.655307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.75379 | 0.242064 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.24621 | 0.345699 | 0.172850 | − | 0.984948i | \(-0.444703\pi\) | ||||
0.172850 | + | 0.984948i | \(0.444703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.4924 | 1.86195 | 0.930975 | − | 0.365083i | \(-0.118959\pi\) | ||||
0.930975 | + | 0.365083i | \(0.118959\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.6155 | −1.65496 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.9309 | −0.538319 | −0.269160 | − | 0.963096i | \(-0.586746\pi\) | ||||
−0.269160 | + | 0.963096i | \(0.586746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.684658 | 0.0284534 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.24621 | −0.258692 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.492423 | −0.0203592 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0540 | −0.580070 | −0.290035 | − | 0.957016i | \(-0.593667\pi\) | ||||
−0.290035 | + | 0.957016i | \(0.593667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.61553 | −0.313792 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.4384 | −1.08753 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.73863 | 0.194592 | 0.0972962 | − | 0.995255i | \(-0.468981\pi\) | ||||
0.0972962 | + | 0.995255i | \(0.468981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.3693 | −0.710879 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.1922 | −0.742077 | −0.371038 | − | 0.928618i | \(-0.620998\pi\) | ||||
−0.371038 | + | 0.928618i | \(0.620998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.75379 | 0.0714198 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.49242 | 0.101331 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7386 | 1.41000 | 0.704999 | − | 0.709208i | \(-0.250948\pi\) | ||||
0.704999 | + | 0.709208i | \(0.250948\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.300187 | 0.0121442 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.1080 | −1.86228 | −0.931141 | − | 0.364659i | \(-0.881186\pi\) | ||||
−0.931141 | + | 0.364659i | \(0.881186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −30.6307 | −1.23515 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9848 | −1.24740 | −0.623701 | − | 0.781663i | \(-0.714372\pi\) | ||||
−0.623701 | + | 0.781663i | \(0.714372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.49242 | 0.180566 | 0.0902829 | − | 0.995916i | \(-0.471223\pi\) | ||||
0.0902829 | + | 0.995916i | \(0.471223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.56155 | −0.223177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.2311 | −0.608270 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.2462 | −1.68447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.7386 | 1.70140 | 0.850699 | − | 0.525653i | \(-0.176179\pi\) | ||||
0.850699 | + | 0.525653i | \(0.176179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.24621 | −0.248265 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.36932 | −0.0543397 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.06913 | 0.121603 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.61553 | −0.301266 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3693 | 0.449061 | 0.224531 | − | 0.974467i | \(-0.427915\pi\) | ||||
0.224531 | + | 0.974467i | \(0.427915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.36932 | −0.0540006 | −0.0270003 | − | 0.999635i | \(-0.508596\pi\) | ||||
−0.0270003 | + | 0.999635i | \(0.508596\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.9848 | 0.983777 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.3002 | 0.955339 | 0.477669 | − | 0.878540i | \(-0.341482\pi\) | ||||
0.477669 | + | 0.878540i | \(0.341482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0540 | 0.471709 | 0.235854 | − | 0.971788i | \(-0.424211\pi\) | ||||
0.235854 | + | 0.971788i | \(0.424211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.63068 | 0.259082 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.24621 | 0.321715 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.2462 | 0.554954 | 0.277477 | − | 0.960732i | \(-0.410502\pi\) | ||||
0.277477 | + | 0.960732i | \(0.410502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2462 | −0.631904 | −0.315952 | − | 0.948775i | \(-0.602324\pi\) | ||||
−0.315952 | + | 0.948775i | \(0.602324\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.50758 | 0.136223 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.56155 | 0.137904 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 44.4924 | 1.72018 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.2614 | 0.511949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0540 | −1.54397 | −0.771984 | − | 0.635642i | \(-0.780735\pi\) | ||||
−0.771984 | + | 0.635642i | \(0.780735\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.56155 | −0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.9848 | −1.03711 | −0.518556 | − | 0.855044i | \(-0.673530\pi\) | ||||
−0.518556 | + | 0.855044i | \(0.673530\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.75379 | −0.373766 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.6847 | −1.09759 | −0.548794 | − | 0.835958i | \(-0.684913\pi\) | ||||
−0.548794 | + | 0.835958i | \(0.684913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.7538 | −0.525505 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.2311 | 0.886320 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.876894 | 0.0334070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.9848 | 1.71130 | 0.855652 | − | 0.517551i | \(-0.173156\pi\) | ||||
0.855652 | + | 0.517551i | \(0.173156\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.63068 | −0.251516 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.2462 | −1.90321 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.0691 | 0.948202 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.8617 | 1.05232 | 0.526162 | − | 0.850385i | \(-0.323631\pi\) | ||||
0.526162 | + | 0.850385i | \(0.323631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.7538 | −0.971323 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.13826 | −0.0805316 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6307 | 0.474355 | 0.237178 | − | 0.971466i | \(-0.423778\pi\) | ||||
0.237178 | + | 0.971466i | \(0.423778\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75379 | −0.0657722 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.43845 | 0.0913206 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.73863 | 0.102419 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.6847 | −1.51940 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.4924 | −1.06259 | −0.531294 | − | 0.847187i | \(-0.678294\pi\) | ||||
−0.531294 | + | 0.847187i | \(0.678294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.1383 | −0.377046 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.56155 | 0.132273 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.6307 | −0.542622 | −0.271311 | − | 0.962492i | \(-0.587457\pi\) | ||||
−0.271311 | + | 0.962492i | \(0.587457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.9848 | 1.51588 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.6307 | −0.909755 | −0.454878 | − | 0.890554i | \(-0.650317\pi\) | ||||
−0.454878 | + | 0.890554i | \(0.650317\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.8617 | −0.806382 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.75379 | −0.359285 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.6847 | −0.466613 | −0.233306 | − | 0.972403i | \(-0.574954\pi\) | ||||
−0.233306 | + | 0.972403i | \(0.574954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.13826 | 0.0785510 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.7538 | 0.651323 | 0.325662 | − | 0.945486i | \(-0.394413\pi\) | ||||
0.325662 | + | 0.945486i | \(0.394413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.4924 | −1.48353 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.00000 | 0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.9848 | −0.911710 | −0.455855 | − | 0.890054i | \(-0.650666\pi\) | ||||
−0.455855 | + | 0.890054i | \(0.650666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.75379 | −0.355448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.8769 | 0.759788 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4924 | 1.25365 | 0.626824 | − | 0.779161i | \(-0.284354\pi\) | ||||
0.626824 | + | 0.779161i | \(0.284354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.87689 | 0.177020 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.6847 | −1.11232 | −0.556159 | − | 0.831076i | \(-0.687725\pi\) | ||||
−0.556159 | + | 0.831076i | \(0.687725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.75379 | 0.208029 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.49242 | 0.162212 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.00000 | −0.216366 | −0.108183 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108183 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.30019 | 0.298924 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.3693 | −0.984406 | −0.492203 | − | 0.870480i | \(-0.663808\pi\) | ||||
−0.492203 | + | 0.870480i | \(0.663808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.43845 | 0.0875916 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.6307 | −1.09746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.3542 | 1.51555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.8078 | −0.707872 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.2462 | 1.50783 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.75379 | 0.347685 | 0.173843 | − | 0.984773i | \(-0.444382\pi\) | ||||
0.173843 | + | 0.984773i | \(0.444382\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.8617 | 1.06311 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.86174 | −0.0661123 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.24621 | −0.221530 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.24621 | 0.150409 | 0.0752043 | − | 0.997168i | \(-0.476039\pi\) | ||||
0.0752043 | + | 0.997168i | \(0.476039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.50758 | −0.124089 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.38447 | −0.225584 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45.8617 | −1.61843 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.7926 | 0.731935 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.0000 | 0.914111 | 0.457056 | − | 0.889438i | \(-0.348904\pi\) | ||||
0.457056 | + | 0.889438i | \(0.348904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.06913 | −0.178001 | −0.0890006 | − | 0.996032i | \(-0.528367\pi\) | ||||
−0.0890006 | + | 0.996032i | \(0.528367\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.4773 | −1.31439 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.8617 | 1.32624 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.9848 | 0.874109 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.7386 | −0.863384 | −0.431692 | − | 0.902021i | \(-0.642083\pi\) | ||||
−0.431692 | + | 0.902021i | \(0.642083\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 53.5616 | 1.86704 | 0.933519 | − | 0.358527i | \(-0.116721\pi\) | ||||
0.933519 | + | 0.358527i | \(0.116721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.87689 | 0.169792 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.4924 | 0.990779 | 0.495389 | − | 0.868671i | \(-0.335025\pi\) | ||||
0.495389 | + | 0.868671i | \(0.335025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.75379 | 0.130374 | 0.0651872 | − | 0.997873i | \(-0.479236\pi\) | ||||
0.0651872 | + | 0.997873i | \(0.479236\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.8078 | 0.964641 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.8617 | −1.24254 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0000 | 1.10741 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5616 | −0.468756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.7538 | 1.16531 | 0.582655 | − | 0.812720i | \(-0.302014\pi\) | ||||
0.582655 | + | 0.812720i | \(0.302014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3153 | −0.562598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.00000 | −0.275535 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.6155 | 0.881201 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.87689 | 0.167375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.24621 | 0.282676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.9848 | −1.06090 | −0.530450 | − | 0.847716i | \(-0.677977\pi\) | ||||
−0.530450 | + | 0.847716i | \(0.677977\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.50758 | 0.119957 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4384 | 0.424889 | 0.212445 | − | 0.977173i | \(-0.431857\pi\) | ||||
0.212445 | + | 0.977173i | \(0.431857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.0540 | −1.84430 | −0.922149 | − | 0.386835i | \(-0.873568\pi\) | ||||
−0.922149 | + | 0.386835i | \(0.873568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1771 | 1.26552 | 0.632761 | − | 0.774347i | \(-0.281921\pi\) | ||||
0.632761 | + | 0.774347i | \(0.281921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.0000 | −0.680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.4384 | −0.490355 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.75379 | 0.330875 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.36932 | 0.0463975 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.38447 | −0.216082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.9848 | 1.18135 | 0.590677 | − | 0.806908i | \(-0.298861\pi\) | ||||
0.590677 | + | 0.806908i | \(0.298861\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.0000 | −0.809500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.1231 | 0.442129 | 0.221064 | − | 0.975259i | \(-0.429047\pi\) | ||||
0.221064 | + | 0.975259i | \(0.429047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9848 | 0.975418 | 0.487709 | − | 0.873006i | \(-0.337833\pi\) | ||||
0.487709 | + | 0.873006i | \(0.337833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32.0000 | −1.07567 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.31534 | 0.245625 | 0.122813 | − | 0.992430i | \(-0.460809\pi\) | ||||
0.122813 | + | 0.992430i | \(0.460809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.8617 | −0.732396 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.13826 | −0.0715542 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.63068 | −0.221639 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.684658 | −0.0228601 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.68466 | 0.289650 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2462 | −0.341351 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.50758 | 0.249560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.1231 | −1.69751 | −0.848757 | − | 0.528782i | \(-0.822649\pi\) | ||||
−0.848757 | + | 0.528782i | \(0.822649\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.87689 | 0.228092 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.8769 | −0.956734 | −0.478367 | − | 0.878160i | \(-0.658771\pi\) | ||||
−0.478367 | + | 0.878160i | \(0.658771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.4924 | −1.47248 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.2614 | 0.438407 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.2462 | 1.78942 | 0.894709 | − | 0.446650i | \(-0.147383\pi\) | ||||
0.894709 | + | 0.446650i | \(0.147383\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4924 | −0.938857 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.94602 | −0.195716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.24621 | 0.271134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.1922 | 0.465632 | 0.232816 | − | 0.972521i | \(-0.425206\pi\) | ||||
0.232816 | + | 0.972521i | \(0.425206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.8617 | −0.716490 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.68466 | −0.284323 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.0000 | −1.04651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.2462 | 1.05344 | 0.526719 | − | 0.850040i | \(-0.323422\pi\) | ||||
0.526719 | + | 0.850040i | \(0.323422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.8769 | −1.00656 | −0.503279 | − | 0.864124i | \(-0.667873\pi\) | ||||
−0.503279 | + | 0.864124i | \(0.667873\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.80776 | 0.319385 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.56155 | −0.0507436 | −0.0253718 | − | 0.999678i | \(-0.508077\pi\) | ||||
−0.0253718 | + | 0.999678i | \(0.508077\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.43845 | 0.209001 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.86174 | −0.190080 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.7538 | 0.899033 | 0.449517 | − | 0.893272i | \(-0.351596\pi\) | ||||
0.449517 | + | 0.893272i | \(0.351596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.7386 | −1.64186 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.3693 | 0.561470 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0540 | −0.808193 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.24621 | 0.201281 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.876894 | 0.0282282 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.05398 | −0.0660514 | −0.0330257 | − | 0.999455i | \(-0.510514\pi\) | ||||
−0.0330257 | + | 0.999455i | \(0.510514\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.9848 | −0.802629 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.63068 | −0.212789 | −0.106394 | − | 0.994324i | \(-0.533931\pi\) | ||||
−0.106394 | + | 0.994324i | \(0.533931\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.684658 | −0.0219266 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.2311 | 0.807213 | 0.403607 | − | 0.914933i | \(-0.367756\pi\) | ||||
0.403607 | + | 0.914933i | \(0.367756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.5076 | 1.13483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.36932 | 0.235284 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.1080 | −1.66199 | −0.830993 | − | 0.556283i | \(-0.812227\pi\) | ||||
−0.830993 | + | 0.556283i | \(0.812227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.8617 | −1.07892 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.9848 | −1.81018 | −0.905092 | − | 0.425217i | \(-0.860198\pi\) | ||||
−0.905092 | + | 0.425217i | \(0.860198\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.0691 | 1.55716 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.2462 | −0.705252 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −45.8617 | −1.45100 |
(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 | 1472.2.a.u.1.1 | 2 | ||
4.3 | odd | 2 | 1472.2.a.p.1.2 | 2 | |||
8.3 | odd | 2 | 368.2.a.i.1.1 | 2 | |||
8.5 | even | 2 | 184.2.a.e.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 1656.2.a.j.1.2 | 2 | |||
24.11 | even | 2 | 3312.2.a.t.1.1 | 2 | |||
40.13 | odd | 4 | 4600.2.e.o.4049.3 | 4 | |||
40.19 | odd | 2 | 9200.2.a.br.1.2 | 2 | |||
40.29 | even | 2 | 4600.2.a.s.1.1 | 2 | |||
40.37 | odd | 4 | 4600.2.e.o.4049.2 | 4 | |||
56.13 | odd | 2 | 9016.2.a.w.1.1 | 2 | |||
184.45 | odd | 2 | 4232.2.a.o.1.2 | 2 | |||
184.91 | even | 2 | 8464.2.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
184.2.a.e.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
368.2.a.i.1.1 | 2 | 8.3 | odd | 2 | |||
1472.2.a.p.1.2 | 2 | 4.3 | odd | 2 | |||
1472.2.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1656.2.a.j.1.2 | 2 | 24.5 | odd | 2 | |||
3312.2.a.t.1.1 | 2 | 24.11 | even | 2 | |||
4232.2.a.o.1.2 | 2 | 184.45 | odd | 2 | |||
4600.2.a.s.1.1 | 2 | 40.29 | even | 2 | |||
4600.2.e.o.4049.2 | 4 | 40.37 | odd | 4 | |||
4600.2.e.o.4049.3 | 4 | 40.13 | odd | 4 | |||
8464.2.a.bd.1.1 | 2 | 184.91 | even | 2 | |||
9016.2.a.w.1.1 | 2 | 56.13 | odd | 2 | |||
9200.2.a.br.1.2 | 2 | 40.19 | odd | 2 |