Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.56155 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.56155 | −1.12626 | ||||||||
\(11\) | 2.56155 | 0.772337 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.56155 | −0.919589 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 7.68466 | 1.76298 | 0.881491 | − | 0.472201i | \(-0.156540\pi\) | ||||
0.881491 | + | 0.472201i | \(0.156540\pi\) | |||||||
\(20\) | −3.56155 | −0.796387 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.56155 | 0.546125 | ||||||||
\(23\) | −9.12311 | −1.90230 | −0.951150 | − | 0.308731i | \(-0.900096\pi\) | ||||
−0.951150 | + | 0.308731i | \(0.900096\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | −3.56155 | −0.650248 | ||||||||
\(31\) | 5.12311 | 0.920137 | 0.460068 | − | 0.887883i | \(-0.347825\pi\) | ||||
0.460068 | + | 0.887883i | \(0.347825\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.56155 | 0.445909 | ||||||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | 3.56155 | 0.602012 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.80776 | −1.61239 | −0.806193 | − | 0.591652i | \(-0.798476\pi\) | ||||
−0.806193 | + | 0.591652i | \(0.798476\pi\) | |||||||
\(38\) | 7.68466 | 1.24662 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.56155 | −0.563131 | ||||||||
\(41\) | 4.12311 | 0.643921 | 0.321960 | − | 0.946753i | \(-0.395658\pi\) | ||||
0.321960 | + | 0.946753i | \(0.395658\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −2.87689 | −0.438722 | −0.219361 | − | 0.975644i | \(-0.570397\pi\) | ||||
−0.219361 | + | 0.975644i | \(0.570397\pi\) | |||||||
\(44\) | 2.56155 | 0.386169 | ||||||||
\(45\) | −3.56155 | −0.530925 | ||||||||
\(46\) | −9.12311 | −1.34513 | ||||||||
\(47\) | −7.68466 | −1.12092 | −0.560461 | − | 0.828181i | \(-0.689376\pi\) | ||||
−0.560461 | + | 0.828181i | \(0.689376\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.68466 | 1.08677 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.87689 | −0.532532 | −0.266266 | − | 0.963900i | \(-0.585790\pi\) | ||||
−0.266266 | + | 0.963900i | \(0.585790\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −9.12311 | −1.23016 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 7.68466 | 1.01786 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 13.1231 | 1.70848 | 0.854241 | − | 0.519877i | \(-0.174022\pi\) | ||||
0.854241 | + | 0.519877i | \(0.174022\pi\) | |||||||
\(60\) | −3.56155 | −0.459794 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 5.12311 | 0.650635 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.56155 | 0.315305 | ||||||||
\(67\) | 1.12311 | 0.137209 | 0.0686046 | − | 0.997644i | \(-0.478145\pi\) | ||||
0.0686046 | + | 0.997644i | \(0.478145\pi\) | |||||||
\(68\) | −5.00000 | −0.606339 | ||||||||
\(69\) | −9.12311 | −1.09829 | ||||||||
\(70\) | 3.56155 | 0.425687 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.43845 | −0.285399 | −0.142699 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142699 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(74\) | −9.80776 | −1.14013 | ||||||||
\(75\) | 7.68466 | 0.887348 | ||||||||
\(76\) | 7.68466 | 0.881491 | ||||||||
\(77\) | −2.56155 | −0.291916 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.43845 | 0.161838 | 0.0809190 | − | 0.996721i | \(-0.474214\pi\) | ||||
0.0809190 | + | 0.996721i | \(0.474214\pi\) | |||||||
\(80\) | −3.56155 | −0.398194 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.12311 | 0.455321 | ||||||||
\(83\) | −10.2462 | −1.12467 | −0.562334 | − | 0.826910i | \(-0.690096\pi\) | ||||
−0.562334 | + | 0.826910i | \(0.690096\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 17.8078 | 1.93152 | ||||||||
\(86\) | −2.87689 | −0.310223 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 2.56155 | 0.273062 | ||||||||
\(89\) | −9.68466 | −1.02657 | −0.513286 | − | 0.858218i | \(-0.671572\pi\) | ||||
−0.513286 | + | 0.858218i | \(0.671572\pi\) | |||||||
\(90\) | −3.56155 | −0.375421 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.12311 | −0.951150 | ||||||||
\(93\) | 5.12311 | 0.531241 | ||||||||
\(94\) | −7.68466 | −0.792612 | ||||||||
\(95\) | −27.3693 | −2.80803 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 12.2462 | 1.24341 | 0.621707 | − | 0.783250i | \(-0.286439\pi\) | ||||
0.621707 | + | 0.783250i | \(0.286439\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 2.56155 | 0.257446 | ||||||||
\(100\) | 7.68466 | 0.768466 | ||||||||
\(101\) | −19.5616 | −1.94645 | −0.973224 | − | 0.229860i | \(-0.926173\pi\) | ||||
−0.973224 | + | 0.229860i | \(0.926173\pi\) | |||||||
\(102\) | −5.00000 | −0.495074 | ||||||||
\(103\) | −11.3693 | −1.12025 | −0.560126 | − | 0.828407i | \(-0.689247\pi\) | ||||
−0.560126 | + | 0.828407i | \(0.689247\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.56155 | 0.347572 | ||||||||
\(106\) | −3.87689 | −0.376557 | ||||||||
\(107\) | −9.43845 | −0.912449 | −0.456225 | − | 0.889865i | \(-0.650799\pi\) | ||||
−0.456225 | + | 0.889865i | \(0.650799\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 0.876894 | 0.0839912 | 0.0419956 | − | 0.999118i | \(-0.486628\pi\) | ||||
0.0419956 | + | 0.999118i | \(0.486628\pi\) | |||||||
\(110\) | −9.12311 | −0.869854 | ||||||||
\(111\) | −9.80776 | −0.930912 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 16.9309 | 1.59272 | 0.796361 | − | 0.604821i | \(-0.206756\pi\) | ||||
0.796361 | + | 0.604821i | \(0.206756\pi\) | |||||||
\(114\) | 7.68466 | 0.719734 | ||||||||
\(115\) | 32.4924 | 3.02993 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.1231 | 1.20808 | ||||||||
\(119\) | 5.00000 | 0.458349 | ||||||||
\(120\) | −3.56155 | −0.325124 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 4.12311 | 0.371768 | ||||||||
\(124\) | 5.12311 | 0.460068 | ||||||||
\(125\) | −9.56155 | −0.855211 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 2.24621 | 0.199319 | 0.0996595 | − | 0.995022i | \(-0.468225\pi\) | ||||
0.0996595 | + | 0.995022i | \(0.468225\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.87689 | −0.253296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.4924 | −1.44095 | −0.720475 | − | 0.693481i | \(-0.756076\pi\) | ||||
−0.720475 | + | 0.693481i | \(0.756076\pi\) | |||||||
\(132\) | 2.56155 | 0.222955 | ||||||||
\(133\) | −7.68466 | −0.666344 | ||||||||
\(134\) | 1.12311 | 0.0970215 | ||||||||
\(135\) | −3.56155 | −0.306530 | ||||||||
\(136\) | −5.00000 | −0.428746 | ||||||||
\(137\) | −5.80776 | −0.496191 | −0.248095 | − | 0.968736i | \(-0.579805\pi\) | ||||
−0.248095 | + | 0.968736i | \(0.579805\pi\) | |||||||
\(138\) | −9.12311 | −0.776610 | ||||||||
\(139\) | −7.68466 | −0.651804 | −0.325902 | − | 0.945404i | \(-0.605668\pi\) | ||||
−0.325902 | + | 0.945404i | \(0.605668\pi\) | |||||||
\(140\) | 3.56155 | 0.301006 | ||||||||
\(141\) | −7.68466 | −0.647165 | ||||||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.56155 | 0.295771 | ||||||||
\(146\) | −2.43845 | −0.201807 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −9.80776 | −0.806193 | ||||||||
\(149\) | −17.8078 | −1.45887 | −0.729434 | − | 0.684051i | \(-0.760217\pi\) | ||||
−0.729434 | + | 0.684051i | \(0.760217\pi\) | |||||||
\(150\) | 7.68466 | 0.627450 | ||||||||
\(151\) | −17.4384 | −1.41912 | −0.709560 | − | 0.704645i | \(-0.751106\pi\) | ||||
−0.709560 | + | 0.704645i | \(0.751106\pi\) | |||||||
\(152\) | 7.68466 | 0.623308 | ||||||||
\(153\) | −5.00000 | −0.404226 | ||||||||
\(154\) | −2.56155 | −0.206416 | ||||||||
\(155\) | −18.2462 | −1.46557 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.80776 | −0.463510 | −0.231755 | − | 0.972774i | \(-0.574447\pi\) | ||||
−0.231755 | + | 0.972774i | \(0.574447\pi\) | |||||||
\(158\) | 1.43845 | 0.114437 | ||||||||
\(159\) | −3.87689 | −0.307458 | ||||||||
\(160\) | −3.56155 | −0.281565 | ||||||||
\(161\) | 9.12311 | 0.719001 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −1.12311 | −0.0879684 | −0.0439842 | − | 0.999032i | \(-0.514005\pi\) | ||||
−0.0439842 | + | 0.999032i | \(0.514005\pi\) | |||||||
\(164\) | 4.12311 | 0.321960 | ||||||||
\(165\) | −9.12311 | −0.710233 | ||||||||
\(166\) | −10.2462 | −0.795260 | ||||||||
\(167\) | 20.4924 | 1.58575 | 0.792876 | − | 0.609383i | \(-0.208583\pi\) | ||||
0.792876 | + | 0.609383i | \(0.208583\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 17.8078 | 1.36579 | ||||||||
\(171\) | 7.68466 | 0.587661 | ||||||||
\(172\) | −2.87689 | −0.219361 | ||||||||
\(173\) | −4.87689 | −0.370783 | −0.185392 | − | 0.982665i | \(-0.559355\pi\) | ||||
−0.185392 | + | 0.982665i | \(0.559355\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | −7.68466 | −0.580906 | ||||||||
\(176\) | 2.56155 | 0.193084 | ||||||||
\(177\) | 13.1231 | 0.986393 | ||||||||
\(178\) | −9.68466 | −0.725896 | ||||||||
\(179\) | −16.4924 | −1.23270 | −0.616351 | − | 0.787472i | \(-0.711390\pi\) | ||||
−0.616351 | + | 0.787472i | \(0.711390\pi\) | |||||||
\(180\) | −3.56155 | −0.265462 | ||||||||
\(181\) | 13.2462 | 0.984583 | 0.492292 | − | 0.870430i | \(-0.336159\pi\) | ||||
0.492292 | + | 0.870430i | \(0.336159\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −9.12311 | −0.672564 | ||||||||
\(185\) | 34.9309 | 2.56817 | ||||||||
\(186\) | 5.12311 | 0.375644 | ||||||||
\(187\) | −12.8078 | −0.936596 | ||||||||
\(188\) | −7.68466 | −0.560461 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −27.3693 | −1.98558 | ||||||||
\(191\) | 5.75379 | 0.416330 | 0.208165 | − | 0.978094i | \(-0.433251\pi\) | ||||
0.208165 | + | 0.978094i | \(0.433251\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −20.3693 | −1.46622 | −0.733108 | − | 0.680113i | \(-0.761931\pi\) | ||||
−0.733108 | + | 0.680113i | \(0.761931\pi\) | |||||||
\(194\) | 12.2462 | 0.879227 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −0.561553 | −0.0400090 | −0.0200045 | − | 0.999800i | \(-0.506368\pi\) | ||||
−0.0200045 | + | 0.999800i | \(0.506368\pi\) | |||||||
\(198\) | 2.56155 | 0.182042 | ||||||||
\(199\) | −17.6155 | −1.24873 | −0.624366 | − | 0.781132i | \(-0.714643\pi\) | ||||
−0.624366 | + | 0.781132i | \(0.714643\pi\) | |||||||
\(200\) | 7.68466 | 0.543387 | ||||||||
\(201\) | 1.12311 | 0.0792178 | ||||||||
\(202\) | −19.5616 | −1.37635 | ||||||||
\(203\) | 1.00000 | 0.0701862 | ||||||||
\(204\) | −5.00000 | −0.350070 | ||||||||
\(205\) | −14.6847 | −1.02562 | ||||||||
\(206\) | −11.3693 | −0.792138 | ||||||||
\(207\) | −9.12311 | −0.634100 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.6847 | 1.36162 | ||||||||
\(210\) | 3.56155 | 0.245770 | ||||||||
\(211\) | −2.87689 | −0.198054 | −0.0990268 | − | 0.995085i | \(-0.531573\pi\) | ||||
−0.0990268 | + | 0.995085i | \(0.531573\pi\) | |||||||
\(212\) | −3.87689 | −0.266266 | ||||||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | −9.43845 | −0.645199 | ||||||||
\(215\) | 10.2462 | 0.698786 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −5.12311 | −0.347779 | ||||||||
\(218\) | 0.876894 | 0.0593908 | ||||||||
\(219\) | −2.43845 | −0.164775 | ||||||||
\(220\) | −9.12311 | −0.615080 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.80776 | −0.658254 | ||||||||
\(223\) | −16.4924 | −1.10441 | −0.552207 | − | 0.833707i | \(-0.686214\pi\) | ||||
−0.552207 | + | 0.833707i | \(0.686214\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 7.68466 | 0.512311 | ||||||||
\(226\) | 16.9309 | 1.12622 | ||||||||
\(227\) | 13.1231 | 0.871011 | 0.435506 | − | 0.900186i | \(-0.356570\pi\) | ||||
0.435506 | + | 0.900186i | \(0.356570\pi\) | |||||||
\(228\) | 7.68466 | 0.508929 | ||||||||
\(229\) | 22.8078 | 1.50718 | 0.753590 | − | 0.657345i | \(-0.228321\pi\) | ||||
0.753590 | + | 0.657345i | \(0.228321\pi\) | |||||||
\(230\) | 32.4924 | 2.14249 | ||||||||
\(231\) | −2.56155 | −0.168538 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.3693 | 1.78538 | ||||||||
\(236\) | 13.1231 | 0.854241 | ||||||||
\(237\) | 1.43845 | 0.0934372 | ||||||||
\(238\) | 5.00000 | 0.324102 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | −3.56155 | −0.229897 | ||||||||
\(241\) | 11.3153 | 0.728885 | 0.364443 | − | 0.931226i | \(-0.381260\pi\) | ||||
0.364443 | + | 0.931226i | \(0.381260\pi\) | |||||||
\(242\) | −4.43845 | −0.285314 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −3.56155 | −0.227539 | ||||||||
\(246\) | 4.12311 | 0.262880 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.12311 | 0.325318 | ||||||||
\(249\) | −10.2462 | −0.649327 | ||||||||
\(250\) | −9.56155 | −0.604726 | ||||||||
\(251\) | 8.49242 | 0.536037 | 0.268018 | − | 0.963414i | \(-0.413631\pi\) | ||||
0.268018 | + | 0.963414i | \(0.413631\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −23.3693 | −1.46922 | ||||||||
\(254\) | 2.24621 | 0.140940 | ||||||||
\(255\) | 17.8078 | 1.11517 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.7538 | −0.920316 | −0.460158 | − | 0.887837i | \(-0.652207\pi\) | ||||
−0.460158 | + | 0.887837i | \(0.652207\pi\) | |||||||
\(258\) | −2.87689 | −0.179108 | ||||||||
\(259\) | 9.80776 | 0.609425 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −16.4924 | −1.01891 | ||||||||
\(263\) | −20.4924 | −1.26362 | −0.631808 | − | 0.775125i | \(-0.717687\pi\) | ||||
−0.631808 | + | 0.775125i | \(0.717687\pi\) | |||||||
\(264\) | 2.56155 | 0.157653 | ||||||||
\(265\) | 13.8078 | 0.848204 | ||||||||
\(266\) | −7.68466 | −0.471177 | ||||||||
\(267\) | −9.68466 | −0.592691 | ||||||||
\(268\) | 1.12311 | 0.0686046 | ||||||||
\(269\) | −4.87689 | −0.297349 | −0.148675 | − | 0.988886i | \(-0.547501\pi\) | ||||
−0.148675 | + | 0.988886i | \(0.547501\pi\) | |||||||
\(270\) | −3.56155 | −0.216749 | ||||||||
\(271\) | 13.1231 | 0.797172 | 0.398586 | − | 0.917131i | \(-0.369501\pi\) | ||||
0.398586 | + | 0.917131i | \(0.369501\pi\) | |||||||
\(272\) | −5.00000 | −0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.80776 | −0.350860 | ||||||||
\(275\) | 19.6847 | 1.18703 | ||||||||
\(276\) | −9.12311 | −0.549146 | ||||||||
\(277\) | −3.56155 | −0.213993 | −0.106996 | − | 0.994259i | \(-0.534123\pi\) | ||||
−0.106996 | + | 0.994259i | \(0.534123\pi\) | |||||||
\(278\) | −7.68466 | −0.460895 | ||||||||
\(279\) | 5.12311 | 0.306712 | ||||||||
\(280\) | 3.56155 | 0.212843 | ||||||||
\(281\) | 7.80776 | 0.465772 | 0.232886 | − | 0.972504i | \(-0.425183\pi\) | ||||
0.232886 | + | 0.972504i | \(0.425183\pi\) | |||||||
\(282\) | −7.68466 | −0.457615 | ||||||||
\(283\) | 8.49242 | 0.504822 | 0.252411 | − | 0.967620i | \(-0.418776\pi\) | ||||
0.252411 | + | 0.967620i | \(0.418776\pi\) | |||||||
\(284\) | −4.00000 | −0.237356 | ||||||||
\(285\) | −27.3693 | −1.62122 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.12311 | −0.243379 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 3.56155 | 0.209142 | ||||||||
\(291\) | 12.2462 | 0.717886 | ||||||||
\(292\) | −2.43845 | −0.142699 | ||||||||
\(293\) | −4.68466 | −0.273681 | −0.136840 | − | 0.990593i | \(-0.543695\pi\) | ||||
−0.136840 | + | 0.990593i | \(0.543695\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −46.7386 | −2.72123 | ||||||||
\(296\) | −9.80776 | −0.570065 | ||||||||
\(297\) | 2.56155 | 0.148636 | ||||||||
\(298\) | −17.8078 | −1.03158 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.68466 | 0.443674 | ||||||||
\(301\) | 2.87689 | 0.165821 | ||||||||
\(302\) | −17.4384 | −1.00347 | ||||||||
\(303\) | −19.5616 | −1.12378 | ||||||||
\(304\) | 7.68466 | 0.440745 | ||||||||
\(305\) | 3.56155 | 0.203934 | ||||||||
\(306\) | −5.00000 | −0.285831 | ||||||||
\(307\) | −33.9309 | −1.93654 | −0.968269 | − | 0.249912i | \(-0.919598\pi\) | ||||
−0.968269 | + | 0.249912i | \(0.919598\pi\) | |||||||
\(308\) | −2.56155 | −0.145958 | ||||||||
\(309\) | −11.3693 | −0.646778 | ||||||||
\(310\) | −18.2462 | −1.03632 | ||||||||
\(311\) | 22.5616 | 1.27935 | 0.639674 | − | 0.768646i | \(-0.279069\pi\) | ||||
0.639674 | + | 0.768646i | \(0.279069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.6155 | 1.56092 | 0.780461 | − | 0.625205i | \(-0.214984\pi\) | ||||
0.780461 | + | 0.625205i | \(0.214984\pi\) | |||||||
\(314\) | −5.80776 | −0.327751 | ||||||||
\(315\) | 3.56155 | 0.200671 | ||||||||
\(316\) | 1.43845 | 0.0809190 | ||||||||
\(317\) | −11.5616 | −0.649362 | −0.324681 | − | 0.945824i | \(-0.605257\pi\) | ||||
−0.324681 | + | 0.945824i | \(0.605257\pi\) | |||||||
\(318\) | −3.87689 | −0.217405 | ||||||||
\(319\) | −2.56155 | −0.143419 | ||||||||
\(320\) | −3.56155 | −0.199097 | ||||||||
\(321\) | −9.43845 | −0.526803 | ||||||||
\(322\) | 9.12311 | 0.508411 | ||||||||
\(323\) | −38.4233 | −2.13793 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.12311 | −0.0622031 | ||||||||
\(327\) | 0.876894 | 0.0484924 | ||||||||
\(328\) | 4.12311 | 0.227660 | ||||||||
\(329\) | 7.68466 | 0.423669 | ||||||||
\(330\) | −9.12311 | −0.502210 | ||||||||
\(331\) | −35.3693 | −1.94407 | −0.972037 | − | 0.234829i | \(-0.924547\pi\) | ||||
−0.972037 | + | 0.234829i | \(0.924547\pi\) | |||||||
\(332\) | −10.2462 | −0.562334 | ||||||||
\(333\) | −9.80776 | −0.537462 | ||||||||
\(334\) | 20.4924 | 1.12130 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −29.4924 | −1.60655 | −0.803277 | − | 0.595605i | \(-0.796912\pi\) | ||||
−0.803277 | + | 0.595605i | \(0.796912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.9309 | 0.919559 | ||||||||
\(340\) | 17.8078 | 0.965762 | ||||||||
\(341\) | 13.1231 | 0.710656 | ||||||||
\(342\) | 7.68466 | 0.415539 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.87689 | −0.155112 | ||||||||
\(345\) | 32.4924 | 1.74933 | ||||||||
\(346\) | −4.87689 | −0.262183 | ||||||||
\(347\) | −0.315342 | −0.0169284 | −0.00846421 | − | 0.999964i | \(-0.502694\pi\) | ||||
−0.00846421 | + | 0.999964i | \(0.502694\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | −6.49242 | −0.347531 | −0.173766 | − | 0.984787i | \(-0.555594\pi\) | ||||
−0.173766 | + | 0.984787i | \(0.555594\pi\) | |||||||
\(350\) | −7.68466 | −0.410762 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.56155 | 0.136531 | ||||||||
\(353\) | −9.80776 | −0.522015 | −0.261007 | − | 0.965337i | \(-0.584055\pi\) | ||||
−0.261007 | + | 0.965337i | \(0.584055\pi\) | |||||||
\(354\) | 13.1231 | 0.697485 | ||||||||
\(355\) | 14.2462 | 0.756110 | ||||||||
\(356\) | −9.68466 | −0.513286 | ||||||||
\(357\) | 5.00000 | 0.264628 | ||||||||
\(358\) | −16.4924 | −0.871652 | ||||||||
\(359\) | −4.63068 | −0.244398 | −0.122199 | − | 0.992506i | \(-0.538995\pi\) | ||||
−0.122199 | + | 0.992506i | \(0.538995\pi\) | |||||||
\(360\) | −3.56155 | −0.187710 | ||||||||
\(361\) | 40.0540 | 2.10810 | ||||||||
\(362\) | 13.2462 | 0.696205 | ||||||||
\(363\) | −4.43845 | −0.232958 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.68466 | 0.454576 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | 11.3693 | 0.593474 | 0.296737 | − | 0.954959i | \(-0.404102\pi\) | ||||
0.296737 | + | 0.954959i | \(0.404102\pi\) | |||||||
\(368\) | −9.12311 | −0.475575 | ||||||||
\(369\) | 4.12311 | 0.214640 | ||||||||
\(370\) | 34.9309 | 1.81597 | ||||||||
\(371\) | 3.87689 | 0.201278 | ||||||||
\(372\) | 5.12311 | 0.265621 | ||||||||
\(373\) | 21.5616 | 1.11641 | 0.558207 | − | 0.829701i | \(-0.311489\pi\) | ||||
0.558207 | + | 0.829701i | \(0.311489\pi\) | |||||||
\(374\) | −12.8078 | −0.662274 | ||||||||
\(375\) | −9.56155 | −0.493756 | ||||||||
\(376\) | −7.68466 | −0.396306 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 0.492423 | 0.0252940 | 0.0126470 | − | 0.999920i | \(-0.495974\pi\) | ||||
0.0126470 | + | 0.999920i | \(0.495974\pi\) | |||||||
\(380\) | −27.3693 | −1.40402 | ||||||||
\(381\) | 2.24621 | 0.115077 | ||||||||
\(382\) | 5.75379 | 0.294389 | ||||||||
\(383\) | 8.31534 | 0.424894 | 0.212447 | − | 0.977173i | \(-0.431857\pi\) | ||||
0.212447 | + | 0.977173i | \(0.431857\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 9.12311 | 0.464957 | ||||||||
\(386\) | −20.3693 | −1.03677 | ||||||||
\(387\) | −2.87689 | −0.146241 | ||||||||
\(388\) | 12.2462 | 0.621707 | ||||||||
\(389\) | 18.6847 | 0.947350 | 0.473675 | − | 0.880700i | \(-0.342927\pi\) | ||||
0.473675 | + | 0.880700i | \(0.342927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.6155 | 2.30688 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −16.4924 | −0.831933 | ||||||||
\(394\) | −0.561553 | −0.0282906 | ||||||||
\(395\) | −5.12311 | −0.257771 | ||||||||
\(396\) | 2.56155 | 0.128723 | ||||||||
\(397\) | 1.68466 | 0.0845506 | 0.0422753 | − | 0.999106i | \(-0.486539\pi\) | ||||
0.0422753 | + | 0.999106i | \(0.486539\pi\) | |||||||
\(398\) | −17.6155 | −0.882987 | ||||||||
\(399\) | −7.68466 | −0.384714 | ||||||||
\(400\) | 7.68466 | 0.384233 | ||||||||
\(401\) | 15.1771 | 0.757907 | 0.378954 | − | 0.925416i | \(-0.376284\pi\) | ||||
0.378954 | + | 0.925416i | \(0.376284\pi\) | |||||||
\(402\) | 1.12311 | 0.0560154 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −19.5616 | −0.973224 | ||||||||
\(405\) | −3.56155 | −0.176975 | ||||||||
\(406\) | 1.00000 | 0.0496292 | ||||||||
\(407\) | −25.1231 | −1.24531 | ||||||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | −30.4384 | −1.50508 | −0.752542 | − | 0.658544i | \(-0.771173\pi\) | ||||
−0.752542 | + | 0.658544i | \(0.771173\pi\) | |||||||
\(410\) | −14.6847 | −0.725224 | ||||||||
\(411\) | −5.80776 | −0.286476 | ||||||||
\(412\) | −11.3693 | −0.560126 | ||||||||
\(413\) | −13.1231 | −0.645746 | ||||||||
\(414\) | −9.12311 | −0.448376 | ||||||||
\(415\) | 36.4924 | 1.79134 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.68466 | −0.376319 | ||||||||
\(418\) | 19.6847 | 0.962808 | ||||||||
\(419\) | 22.7386 | 1.11085 | 0.555427 | − | 0.831565i | \(-0.312555\pi\) | ||||
0.555427 | + | 0.831565i | \(0.312555\pi\) | |||||||
\(420\) | 3.56155 | 0.173786 | ||||||||
\(421\) | 8.43845 | 0.411265 | 0.205632 | − | 0.978629i | \(-0.434075\pi\) | ||||
0.205632 | + | 0.978629i | \(0.434075\pi\) | |||||||
\(422\) | −2.87689 | −0.140045 | ||||||||
\(423\) | −7.68466 | −0.373641 | ||||||||
\(424\) | −3.87689 | −0.188279 | ||||||||
\(425\) | −38.4233 | −1.86380 | ||||||||
\(426\) | −4.00000 | −0.193801 | ||||||||
\(427\) | 1.00000 | 0.0483934 | ||||||||
\(428\) | −9.43845 | −0.456225 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.2462 | 0.494116 | ||||||||
\(431\) | −18.7386 | −0.902608 | −0.451304 | − | 0.892370i | \(-0.649041\pi\) | ||||
−0.451304 | + | 0.892370i | \(0.649041\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −5.31534 | −0.255439 | −0.127720 | − | 0.991810i | \(-0.540766\pi\) | ||||
−0.127720 | + | 0.991810i | \(0.540766\pi\) | |||||||
\(434\) | −5.12311 | −0.245917 | ||||||||
\(435\) | 3.56155 | 0.170763 | ||||||||
\(436\) | 0.876894 | 0.0419956 | ||||||||
\(437\) | −70.1080 | −3.35372 | ||||||||
\(438\) | −2.43845 | −0.116514 | ||||||||
\(439\) | −28.4924 | −1.35987 | −0.679935 | − | 0.733273i | \(-0.737992\pi\) | ||||
−0.679935 | + | 0.733273i | \(0.737992\pi\) | |||||||
\(440\) | −9.12311 | −0.434927 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.4233 | −1.63550 | −0.817750 | − | 0.575574i | \(-0.804779\pi\) | ||||
−0.817750 | + | 0.575574i | \(0.804779\pi\) | |||||||
\(444\) | −9.80776 | −0.465456 | ||||||||
\(445\) | 34.4924 | 1.63510 | ||||||||
\(446\) | −16.4924 | −0.780939 | ||||||||
\(447\) | −17.8078 | −0.842278 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 7.68466 | 0.362258 | ||||||||
\(451\) | 10.5616 | 0.497324 | ||||||||
\(452\) | 16.9309 | 0.796361 | ||||||||
\(453\) | −17.4384 | −0.819330 | ||||||||
\(454\) | 13.1231 | 0.615898 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.68466 | 0.359867 | ||||||||
\(457\) | −13.3153 | −0.622865 | −0.311433 | − | 0.950268i | \(-0.600809\pi\) | ||||
−0.311433 | + | 0.950268i | \(0.600809\pi\) | |||||||
\(458\) | 22.8078 | 1.06574 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | 32.4924 | 1.51497 | ||||||||
\(461\) | 30.0540 | 1.39975 | 0.699877 | − | 0.714264i | \(-0.253238\pi\) | ||||
0.699877 | + | 0.714264i | \(0.253238\pi\) | |||||||
\(462\) | −2.56155 | −0.119174 | ||||||||
\(463\) | −11.6847 | −0.543032 | −0.271516 | − | 0.962434i | \(-0.587525\pi\) | ||||
−0.271516 | + | 0.962434i | \(0.587525\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −18.2462 | −0.846148 | ||||||||
\(466\) | −6.00000 | −0.277945 | ||||||||
\(467\) | 28.0000 | 1.29569 | 0.647843 | − | 0.761774i | \(-0.275671\pi\) | ||||
0.647843 | + | 0.761774i | \(0.275671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.12311 | −0.0518602 | ||||||||
\(470\) | 27.3693 | 1.26245 | ||||||||
\(471\) | −5.80776 | −0.267608 | ||||||||
\(472\) | 13.1231 | 0.604040 | ||||||||
\(473\) | −7.36932 | −0.338842 | ||||||||
\(474\) | 1.43845 | 0.0660701 | ||||||||
\(475\) | 59.0540 | 2.70958 | ||||||||
\(476\) | 5.00000 | 0.229175 | ||||||||
\(477\) | −3.87689 | −0.177511 | ||||||||
\(478\) | 4.00000 | 0.182956 | ||||||||
\(479\) | −2.56155 | −0.117040 | −0.0585202 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585202 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(480\) | −3.56155 | −0.162562 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.3153 | 0.515400 | ||||||||
\(483\) | 9.12311 | 0.415116 | ||||||||
\(484\) | −4.43845 | −0.201748 | ||||||||
\(485\) | −43.6155 | −1.98048 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 23.6847 | 1.07325 | 0.536627 | − | 0.843819i | \(-0.319698\pi\) | ||||
0.536627 | + | 0.843819i | \(0.319698\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | −1.12311 | −0.0507886 | ||||||||
\(490\) | −3.56155 | −0.160895 | ||||||||
\(491\) | −1.75379 | −0.0791474 | −0.0395737 | − | 0.999217i | \(-0.512600\pi\) | ||||
−0.0395737 | + | 0.999217i | \(0.512600\pi\) | |||||||
\(492\) | 4.12311 | 0.185884 | ||||||||
\(493\) | 5.00000 | 0.225189 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.12311 | −0.410053 | ||||||||
\(496\) | 5.12311 | 0.230034 | ||||||||
\(497\) | 4.00000 | 0.179425 | ||||||||
\(498\) | −10.2462 | −0.459144 | ||||||||
\(499\) | −27.3693 | −1.22522 | −0.612609 | − | 0.790386i | \(-0.709880\pi\) | ||||
−0.612609 | + | 0.790386i | \(0.709880\pi\) | |||||||
\(500\) | −9.56155 | −0.427606 | ||||||||
\(501\) | 20.4924 | 0.915534 | ||||||||
\(502\) | 8.49242 | 0.379035 | ||||||||
\(503\) | 20.4924 | 0.913712 | 0.456856 | − | 0.889541i | \(-0.348975\pi\) | ||||
0.456856 | + | 0.889541i | \(0.348975\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 69.6695 | 3.10025 | ||||||||
\(506\) | −23.3693 | −1.03889 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.24621 | 0.0996595 | ||||||||
\(509\) | 27.3153 | 1.21073 | 0.605366 | − | 0.795948i | \(-0.293027\pi\) | ||||
0.605366 | + | 0.795948i | \(0.293027\pi\) | |||||||
\(510\) | 17.8078 | 0.788541 | ||||||||
\(511\) | 2.43845 | 0.107871 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.68466 | 0.339286 | ||||||||
\(514\) | −14.7538 | −0.650762 | ||||||||
\(515\) | 40.4924 | 1.78431 | ||||||||
\(516\) | −2.87689 | −0.126648 | ||||||||
\(517\) | −19.6847 | −0.865730 | ||||||||
\(518\) | 9.80776 | 0.430928 | ||||||||
\(519\) | −4.87689 | −0.214072 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0000 | −0.744784 | −0.372392 | − | 0.928076i | \(-0.621462\pi\) | ||||
−0.372392 | + | 0.928076i | \(0.621462\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | 15.1922 | 0.664310 | 0.332155 | − | 0.943225i | \(-0.392224\pi\) | ||||
0.332155 | + | 0.943225i | \(0.392224\pi\) | |||||||
\(524\) | −16.4924 | −0.720475 | ||||||||
\(525\) | −7.68466 | −0.335386 | ||||||||
\(526\) | −20.4924 | −0.893512 | ||||||||
\(527\) | −25.6155 | −1.11583 | ||||||||
\(528\) | 2.56155 | 0.111477 | ||||||||
\(529\) | 60.2311 | 2.61874 | ||||||||
\(530\) | 13.8078 | 0.599771 | ||||||||
\(531\) | 13.1231 | 0.569494 | ||||||||
\(532\) | −7.68466 | −0.333172 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.68466 | −0.419096 | ||||||||
\(535\) | 33.6155 | 1.45333 | ||||||||
\(536\) | 1.12311 | 0.0485108 | ||||||||
\(537\) | −16.4924 | −0.711701 | ||||||||
\(538\) | −4.87689 | −0.210258 | ||||||||
\(539\) | 2.56155 | 0.110334 | ||||||||
\(540\) | −3.56155 | −0.153265 | ||||||||
\(541\) | 1.56155 | 0.0671364 | 0.0335682 | − | 0.999436i | \(-0.489313\pi\) | ||||
0.0335682 | + | 0.999436i | \(0.489313\pi\) | |||||||
\(542\) | 13.1231 | 0.563686 | ||||||||
\(543\) | 13.2462 | 0.568449 | ||||||||
\(544\) | −5.00000 | −0.214373 | ||||||||
\(545\) | −3.12311 | −0.133779 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.7386 | −0.972234 | −0.486117 | − | 0.873894i | \(-0.661587\pi\) | ||||
−0.486117 | + | 0.873894i | \(0.661587\pi\) | |||||||
\(548\) | −5.80776 | −0.248095 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 19.6847 | 0.839357 | ||||||||
\(551\) | −7.68466 | −0.327377 | ||||||||
\(552\) | −9.12311 | −0.388305 | ||||||||
\(553\) | −1.43845 | −0.0611690 | ||||||||
\(554\) | −3.56155 | −0.151316 | ||||||||
\(555\) | 34.9309 | 1.48273 | ||||||||
\(556\) | −7.68466 | −0.325902 | ||||||||
\(557\) | 21.7386 | 0.921095 | 0.460548 | − | 0.887635i | \(-0.347653\pi\) | ||||
0.460548 | + | 0.887635i | \(0.347653\pi\) | |||||||
\(558\) | 5.12311 | 0.216878 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.56155 | 0.150503 | ||||||||
\(561\) | −12.8078 | −0.540744 | ||||||||
\(562\) | 7.80776 | 0.329351 | ||||||||
\(563\) | −0.630683 | −0.0265801 | −0.0132901 | − | 0.999912i | \(-0.504230\pi\) | ||||
−0.0132901 | + | 0.999912i | \(0.504230\pi\) | |||||||
\(564\) | −7.68466 | −0.323582 | ||||||||
\(565\) | −60.3002 | −2.53685 | ||||||||
\(566\) | 8.49242 | 0.356963 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | 11.6155 | 0.486948 | 0.243474 | − | 0.969907i | \(-0.421713\pi\) | ||||
0.243474 | + | 0.969907i | \(0.421713\pi\) | |||||||
\(570\) | −27.3693 | −1.14637 | ||||||||
\(571\) | 13.7538 | 0.575578 | 0.287789 | − | 0.957694i | \(-0.407080\pi\) | ||||
0.287789 | + | 0.957694i | \(0.407080\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.75379 | 0.240368 | ||||||||
\(574\) | −4.12311 | −0.172095 | ||||||||
\(575\) | −70.1080 | −2.92370 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 31.3153 | 1.30367 | 0.651837 | − | 0.758359i | \(-0.273998\pi\) | ||||
0.651837 | + | 0.758359i | \(0.273998\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | −20.3693 | −0.846520 | ||||||||
\(580\) | 3.56155 | 0.147885 | ||||||||
\(581\) | 10.2462 | 0.425084 | ||||||||
\(582\) | 12.2462 | 0.507622 | ||||||||
\(583\) | −9.93087 | −0.411295 | ||||||||
\(584\) | −2.43845 | −0.100904 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.68466 | −0.193521 | ||||||||
\(587\) | 31.3693 | 1.29475 | 0.647375 | − | 0.762172i | \(-0.275867\pi\) | ||||
0.647375 | + | 0.762172i | \(0.275867\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 39.3693 | 1.62218 | ||||||||
\(590\) | −46.7386 | −1.92420 | ||||||||
\(591\) | −0.561553 | −0.0230992 | ||||||||
\(592\) | −9.80776 | −0.403097 | ||||||||
\(593\) | 32.6155 | 1.33936 | 0.669680 | − | 0.742650i | \(-0.266431\pi\) | ||||
0.669680 | + | 0.742650i | \(0.266431\pi\) | |||||||
\(594\) | 2.56155 | 0.105102 | ||||||||
\(595\) | −17.8078 | −0.730047 | ||||||||
\(596\) | −17.8078 | −0.729434 | ||||||||
\(597\) | −17.6155 | −0.720956 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.8769 | −0.934725 | −0.467362 | − | 0.884066i | \(-0.654796\pi\) | ||||
−0.467362 | + | 0.884066i | \(0.654796\pi\) | |||||||
\(600\) | 7.68466 | 0.313725 | ||||||||
\(601\) | 36.9309 | 1.50644 | 0.753221 | − | 0.657768i | \(-0.228499\pi\) | ||||
0.753221 | + | 0.657768i | \(0.228499\pi\) | |||||||
\(602\) | 2.87689 | 0.117253 | ||||||||
\(603\) | 1.12311 | 0.0457364 | ||||||||
\(604\) | −17.4384 | −0.709560 | ||||||||
\(605\) | 15.8078 | 0.642677 | ||||||||
\(606\) | −19.5616 | −0.794634 | ||||||||
\(607\) | 21.1231 | 0.857360 | 0.428680 | − | 0.903456i | \(-0.358979\pi\) | ||||
0.428680 | + | 0.903456i | \(0.358979\pi\) | |||||||
\(608\) | 7.68466 | 0.311654 | ||||||||
\(609\) | 1.00000 | 0.0405220 | ||||||||
\(610\) | 3.56155 | 0.144203 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.00000 | −0.202113 | ||||||||
\(613\) | 36.3002 | 1.46615 | 0.733075 | − | 0.680147i | \(-0.238084\pi\) | ||||
0.733075 | + | 0.680147i | \(0.238084\pi\) | |||||||
\(614\) | −33.9309 | −1.36934 | ||||||||
\(615\) | −14.6847 | −0.592143 | ||||||||
\(616\) | −2.56155 | −0.103208 | ||||||||
\(617\) | −27.4233 | −1.10402 | −0.552010 | − | 0.833837i | \(-0.686139\pi\) | ||||
−0.552010 | + | 0.833837i | \(0.686139\pi\) | |||||||
\(618\) | −11.3693 | −0.457341 | ||||||||
\(619\) | 4.31534 | 0.173448 | 0.0867241 | − | 0.996232i | \(-0.472360\pi\) | ||||
0.0867241 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(620\) | −18.2462 | −0.732785 | ||||||||
\(621\) | −9.12311 | −0.366098 | ||||||||
\(622\) | 22.5616 | 0.904636 | ||||||||
\(623\) | 9.68466 | 0.388008 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 27.6155 | 1.10374 | ||||||||
\(627\) | 19.6847 | 0.786130 | ||||||||
\(628\) | −5.80776 | −0.231755 | ||||||||
\(629\) | 49.0388 | 1.95531 | ||||||||
\(630\) | 3.56155 | 0.141896 | ||||||||
\(631\) | 23.1922 | 0.923268 | 0.461634 | − | 0.887070i | \(-0.347263\pi\) | ||||
0.461634 | + | 0.887070i | \(0.347263\pi\) | |||||||
\(632\) | 1.43845 | 0.0572184 | ||||||||
\(633\) | −2.87689 | −0.114346 | ||||||||
\(634\) | −11.5616 | −0.459168 | ||||||||
\(635\) | −8.00000 | −0.317470 | ||||||||
\(636\) | −3.87689 | −0.153729 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.56155 | −0.101413 | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | −3.56155 | −0.140783 | ||||||||
\(641\) | 36.9309 | 1.45868 | 0.729341 | − | 0.684151i | \(-0.239827\pi\) | ||||
0.729341 | + | 0.684151i | \(0.239827\pi\) | |||||||
\(642\) | −9.43845 | −0.372506 | ||||||||
\(643\) | −26.5616 | −1.04749 | −0.523743 | − | 0.851877i | \(-0.675465\pi\) | ||||
−0.523743 | + | 0.851877i | \(0.675465\pi\) | |||||||
\(644\) | 9.12311 | 0.359501 | ||||||||
\(645\) | 10.2462 | 0.403444 | ||||||||
\(646\) | −38.4233 | −1.51174 | ||||||||
\(647\) | −20.8078 | −0.818038 | −0.409019 | − | 0.912526i | \(-0.634129\pi\) | ||||
−0.409019 | + | 0.912526i | \(0.634129\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 33.6155 | 1.31952 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.12311 | −0.200790 | ||||||||
\(652\) | −1.12311 | −0.0439842 | ||||||||
\(653\) | −18.8078 | −0.736005 | −0.368002 | − | 0.929825i | \(-0.619958\pi\) | ||||
−0.368002 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(654\) | 0.876894 | 0.0342893 | ||||||||
\(655\) | 58.7386 | 2.29511 | ||||||||
\(656\) | 4.12311 | 0.160980 | ||||||||
\(657\) | −2.43845 | −0.0951329 | ||||||||
\(658\) | 7.68466 | 0.299579 | ||||||||
\(659\) | −28.3153 | −1.10301 | −0.551505 | − | 0.834172i | \(-0.685946\pi\) | ||||
−0.551505 | + | 0.834172i | \(0.685946\pi\) | |||||||
\(660\) | −9.12311 | −0.355116 | ||||||||
\(661\) | −9.80776 | −0.381478 | −0.190739 | − | 0.981641i | \(-0.561088\pi\) | ||||
−0.190739 | + | 0.981641i | \(0.561088\pi\) | |||||||
\(662\) | −35.3693 | −1.37467 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.2462 | −0.397630 | ||||||||
\(665\) | 27.3693 | 1.06134 | ||||||||
\(666\) | −9.80776 | −0.380043 | ||||||||
\(667\) | 9.12311 | 0.353248 | ||||||||
\(668\) | 20.4924 | 0.792876 | ||||||||
\(669\) | −16.4924 | −0.637634 | ||||||||
\(670\) | −4.00000 | −0.154533 | ||||||||
\(671\) | −2.56155 | −0.0988876 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 8.75379 | 0.337434 | 0.168717 | − | 0.985665i | \(-0.446038\pi\) | ||||
0.168717 | + | 0.985665i | \(0.446038\pi\) | |||||||
\(674\) | −29.4924 | −1.13601 | ||||||||
\(675\) | 7.68466 | 0.295783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.38447 | −0.322241 | −0.161121 | − | 0.986935i | \(-0.551511\pi\) | ||||
−0.161121 | + | 0.986935i | \(0.551511\pi\) | |||||||
\(678\) | 16.9309 | 0.650226 | ||||||||
\(679\) | −12.2462 | −0.469966 | ||||||||
\(680\) | 17.8078 | 0.682897 | ||||||||
\(681\) | 13.1231 | 0.502879 | ||||||||
\(682\) | 13.1231 | 0.502510 | ||||||||
\(683\) | 4.00000 | 0.153056 | 0.0765279 | − | 0.997067i | \(-0.475617\pi\) | ||||
0.0765279 | + | 0.997067i | \(0.475617\pi\) | |||||||
\(684\) | 7.68466 | 0.293830 | ||||||||
\(685\) | 20.6847 | 0.790320 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 22.8078 | 0.870170 | ||||||||
\(688\) | −2.87689 | −0.109681 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 32.4924 | 1.23697 | ||||||||
\(691\) | −28.4924 | −1.08390 | −0.541951 | − | 0.840410i | \(-0.682314\pi\) | ||||
−0.541951 | + | 0.840410i | \(0.682314\pi\) | |||||||
\(692\) | −4.87689 | −0.185392 | ||||||||
\(693\) | −2.56155 | −0.0973053 | ||||||||
\(694\) | −0.315342 | −0.0119702 | ||||||||
\(695\) | 27.3693 | 1.03818 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | −20.6155 | −0.780869 | ||||||||
\(698\) | −6.49242 | −0.245742 | ||||||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | −7.68466 | −0.290453 | ||||||||
\(701\) | 9.05398 | 0.341964 | 0.170982 | − | 0.985274i | \(-0.445306\pi\) | ||||
0.170982 | + | 0.985274i | \(0.445306\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −75.3693 | −2.84261 | ||||||||
\(704\) | 2.56155 | 0.0965422 | ||||||||
\(705\) | 27.3693 | 1.03079 | ||||||||
\(706\) | −9.80776 | −0.369120 | ||||||||
\(707\) | 19.5616 | 0.735688 | ||||||||
\(708\) | 13.1231 | 0.493197 | ||||||||
\(709\) | 20.3002 | 0.762390 | 0.381195 | − | 0.924495i | \(-0.375513\pi\) | ||||
0.381195 | + | 0.924495i | \(0.375513\pi\) | |||||||
\(710\) | 14.2462 | 0.534651 | ||||||||
\(711\) | 1.43845 | 0.0539460 | ||||||||
\(712\) | −9.68466 | −0.362948 | ||||||||
\(713\) | −46.7386 | −1.75038 | ||||||||
\(714\) | 5.00000 | 0.187120 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.4924 | −0.616351 | ||||||||
\(717\) | 4.00000 | 0.149383 | ||||||||
\(718\) | −4.63068 | −0.172816 | ||||||||
\(719\) | 21.9309 | 0.817883 | 0.408942 | − | 0.912561i | \(-0.365898\pi\) | ||||
0.408942 | + | 0.912561i | \(0.365898\pi\) | |||||||
\(720\) | −3.56155 | −0.132731 | ||||||||
\(721\) | 11.3693 | 0.423415 | ||||||||
\(722\) | 40.0540 | 1.49065 | ||||||||
\(723\) | 11.3153 | 0.420822 | ||||||||
\(724\) | 13.2462 | 0.492292 | ||||||||
\(725\) | −7.68466 | −0.285401 | ||||||||
\(726\) | −4.43845 | −0.164726 | ||||||||
\(727\) | 50.2462 | 1.86353 | 0.931764 | − | 0.363063i | \(-0.118269\pi\) | ||||
0.931764 | + | 0.363063i | \(0.118269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.68466 | 0.321434 | ||||||||
\(731\) | 14.3845 | 0.532029 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 32.6155 | 1.20468 | 0.602341 | − | 0.798239i | \(-0.294235\pi\) | ||||
0.602341 | + | 0.798239i | \(0.294235\pi\) | |||||||
\(734\) | 11.3693 | 0.419649 | ||||||||
\(735\) | −3.56155 | −0.131370 | ||||||||
\(736\) | −9.12311 | −0.336282 | ||||||||
\(737\) | 2.87689 | 0.105972 | ||||||||
\(738\) | 4.12311 | 0.151774 | ||||||||
\(739\) | 47.3693 | 1.74251 | 0.871254 | − | 0.490832i | \(-0.163307\pi\) | ||||
0.871254 | + | 0.490832i | \(0.163307\pi\) | |||||||
\(740\) | 34.9309 | 1.28408 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.87689 | 0.142325 | ||||||||
\(743\) | 8.63068 | 0.316629 | 0.158315 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158315 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(744\) | 5.12311 | 0.187822 | ||||||||
\(745\) | 63.4233 | 2.32365 | ||||||||
\(746\) | 21.5616 | 0.789425 | ||||||||
\(747\) | −10.2462 | −0.374889 | ||||||||
\(748\) | −12.8078 | −0.468298 | ||||||||
\(749\) | 9.43845 | 0.344873 | ||||||||
\(750\) | −9.56155 | −0.349139 | ||||||||
\(751\) | −0.807764 | −0.0294757 | −0.0147379 | − | 0.999891i | \(-0.504691\pi\) | ||||
−0.0147379 | + | 0.999891i | \(0.504691\pi\) | |||||||
\(752\) | −7.68466 | −0.280231 | ||||||||
\(753\) | 8.49242 | 0.309481 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 62.1080 | 2.26034 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −7.12311 | −0.258894 | −0.129447 | − | 0.991586i | \(-0.541320\pi\) | ||||
−0.129447 | + | 0.991586i | \(0.541320\pi\) | |||||||
\(758\) | 0.492423 | 0.0178856 | ||||||||
\(759\) | −23.3693 | −0.848252 | ||||||||
\(760\) | −27.3693 | −0.992789 | ||||||||
\(761\) | −42.4924 | −1.54035 | −0.770175 | − | 0.637833i | \(-0.779831\pi\) | ||||
−0.770175 | + | 0.637833i | \(0.779831\pi\) | |||||||
\(762\) | 2.24621 | 0.0813716 | ||||||||
\(763\) | −0.876894 | −0.0317457 | ||||||||
\(764\) | 5.75379 | 0.208165 | ||||||||
\(765\) | 17.8078 | 0.643841 | ||||||||
\(766\) | 8.31534 | 0.300446 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −22.9848 | −0.828855 | −0.414427 | − | 0.910082i | \(-0.636018\pi\) | ||||
−0.414427 | + | 0.910082i | \(0.636018\pi\) | |||||||
\(770\) | 9.12311 | 0.328774 | ||||||||
\(771\) | −14.7538 | −0.531345 | ||||||||
\(772\) | −20.3693 | −0.733108 | ||||||||
\(773\) | 26.4924 | 0.952866 | 0.476433 | − | 0.879211i | \(-0.341929\pi\) | ||||
0.476433 | + | 0.879211i | \(0.341929\pi\) | |||||||
\(774\) | −2.87689 | −0.103408 | ||||||||
\(775\) | 39.3693 | 1.41419 | ||||||||
\(776\) | 12.2462 | 0.439613 | ||||||||
\(777\) | 9.80776 | 0.351852 | ||||||||
\(778\) | 18.6847 | 0.669877 | ||||||||
\(779\) | 31.6847 | 1.13522 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2462 | −0.366638 | ||||||||
\(782\) | 45.6155 | 1.63121 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 20.6847 | 0.738267 | ||||||||
\(786\) | −16.4924 | −0.588265 | ||||||||
\(787\) | 0.807764 | 0.0287937 | 0.0143968 | − | 0.999896i | \(-0.495417\pi\) | ||||
0.0143968 | + | 0.999896i | \(0.495417\pi\) | |||||||
\(788\) | −0.561553 | −0.0200045 | ||||||||
\(789\) | −20.4924 | −0.729550 | ||||||||
\(790\) | −5.12311 | −0.182272 | ||||||||
\(791\) | −16.9309 | −0.601992 | ||||||||
\(792\) | 2.56155 | 0.0910208 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.68466 | 0.0597863 | ||||||||
\(795\) | 13.8078 | 0.489711 | ||||||||
\(796\) | −17.6155 | −0.624366 | ||||||||
\(797\) | −24.1080 | −0.853947 | −0.426974 | − | 0.904264i | \(-0.640420\pi\) | ||||
−0.426974 | + | 0.904264i | \(0.640420\pi\) | |||||||
\(798\) | −7.68466 | −0.272034 | ||||||||
\(799\) | 38.4233 | 1.35932 | ||||||||
\(800\) | 7.68466 | 0.271694 | ||||||||
\(801\) | −9.68466 | −0.342191 | ||||||||
\(802\) | 15.1771 | 0.535921 | ||||||||
\(803\) | −6.24621 | −0.220424 | ||||||||
\(804\) | 1.12311 | 0.0396089 | ||||||||
\(805\) | −32.4924 | −1.14521 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.87689 | −0.171675 | ||||||||
\(808\) | −19.5616 | −0.688173 | ||||||||
\(809\) | −10.9309 | −0.384309 | −0.192154 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192154 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(810\) | −3.56155 | −0.125140 | ||||||||
\(811\) | 5.75379 | 0.202043 | 0.101021 | − | 0.994884i | \(-0.467789\pi\) | ||||
0.101021 | + | 0.994884i | \(0.467789\pi\) | |||||||
\(812\) | 1.00000 | 0.0350931 | ||||||||
\(813\) | 13.1231 | 0.460247 | ||||||||
\(814\) | −25.1231 | −0.880564 | ||||||||
\(815\) | 4.00000 | 0.140114 | ||||||||
\(816\) | −5.00000 | −0.175035 | ||||||||
\(817\) | −22.1080 | −0.773459 | ||||||||
\(818\) | −30.4384 | −1.06426 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.6847 | −0.512811 | ||||||||
\(821\) | −12.0691 | −0.421216 | −0.210608 | − | 0.977571i | \(-0.567544\pi\) | ||||
−0.210608 | + | 0.977571i | \(0.567544\pi\) | |||||||
\(822\) | −5.80776 | −0.202569 | ||||||||
\(823\) | 14.2462 | 0.496592 | 0.248296 | − | 0.968684i | \(-0.420129\pi\) | ||||
0.248296 | + | 0.968684i | \(0.420129\pi\) | |||||||
\(824\) | −11.3693 | −0.396069 | ||||||||
\(825\) | 19.6847 | 0.685332 | ||||||||
\(826\) | −13.1231 | −0.456611 | ||||||||
\(827\) | −11.5076 | −0.400158 | −0.200079 | − | 0.979780i | \(-0.564120\pi\) | ||||
−0.200079 | + | 0.979780i | \(0.564120\pi\) | |||||||
\(828\) | −9.12311 | −0.317050 | ||||||||
\(829\) | 29.1080 | 1.01096 | 0.505480 | − | 0.862838i | \(-0.331315\pi\) | ||||
0.505480 | + | 0.862838i | \(0.331315\pi\) | |||||||
\(830\) | 36.4924 | 1.26667 | ||||||||
\(831\) | −3.56155 | −0.123549 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.00000 | −0.173240 | ||||||||
\(834\) | −7.68466 | −0.266098 | ||||||||
\(835\) | −72.9848 | −2.52574 | ||||||||
\(836\) | 19.6847 | 0.680808 | ||||||||
\(837\) | 5.12311 | 0.177080 | ||||||||
\(838\) | 22.7386 | 0.785493 | ||||||||
\(839\) | 8.00000 | 0.276191 | 0.138095 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138095 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(840\) | 3.56155 | 0.122885 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 8.43845 | 0.290808 | ||||||||
\(843\) | 7.80776 | 0.268914 | ||||||||
\(844\) | −2.87689 | −0.0990268 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.68466 | −0.264204 | ||||||||
\(847\) | 4.43845 | 0.152507 | ||||||||
\(848\) | −3.87689 | −0.133133 | ||||||||
\(849\) | 8.49242 | 0.291459 | ||||||||
\(850\) | −38.4233 | −1.31791 | ||||||||
\(851\) | 89.4773 | 3.06724 | ||||||||
\(852\) | −4.00000 | −0.137038 | ||||||||
\(853\) | −0.369317 | −0.0126452 | −0.00632258 | − | 0.999980i | \(-0.502013\pi\) | ||||
−0.00632258 | + | 0.999980i | \(0.502013\pi\) | |||||||
\(854\) | 1.00000 | 0.0342193 | ||||||||
\(855\) | −27.3693 | −0.936011 | ||||||||
\(856\) | −9.43845 | −0.322599 | ||||||||
\(857\) | −22.3002 | −0.761760 | −0.380880 | − | 0.924625i | \(-0.624379\pi\) | ||||
−0.380880 | + | 0.924625i | \(0.624379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.8078 | −1.25586 | −0.627932 | − | 0.778268i | \(-0.716099\pi\) | ||||
−0.627932 | + | 0.778268i | \(0.716099\pi\) | |||||||
\(860\) | 10.2462 | 0.349393 | ||||||||
\(861\) | −4.12311 | −0.140515 | ||||||||
\(862\) | −18.7386 | −0.638240 | ||||||||
\(863\) | 26.1080 | 0.888725 | 0.444362 | − | 0.895847i | \(-0.353430\pi\) | ||||
0.444362 | + | 0.895847i | \(0.353430\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 17.3693 | 0.590574 | ||||||||
\(866\) | −5.31534 | −0.180623 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | −5.12311 | −0.173890 | ||||||||
\(869\) | 3.68466 | 0.124993 | ||||||||
\(870\) | 3.56155 | 0.120748 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.876894 | 0.0296954 | ||||||||
\(873\) | 12.2462 | 0.414471 | ||||||||
\(874\) | −70.1080 | −2.37144 | ||||||||
\(875\) | 9.56155 | 0.323239 | ||||||||
\(876\) | −2.43845 | −0.0823875 | ||||||||
\(877\) | 8.30019 | 0.280277 | 0.140139 | − | 0.990132i | \(-0.455245\pi\) | ||||
0.140139 | + | 0.990132i | \(0.455245\pi\) | |||||||
\(878\) | −28.4924 | −0.961573 | ||||||||
\(879\) | −4.68466 | −0.158010 | ||||||||
\(880\) | −9.12311 | −0.307540 | ||||||||
\(881\) | 47.1771 | 1.58944 | 0.794718 | − | 0.606979i | \(-0.207619\pi\) | ||||
0.794718 | + | 0.606979i | \(0.207619\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 17.1231 | 0.576238 | 0.288119 | − | 0.957595i | \(-0.406970\pi\) | ||||
0.288119 | + | 0.957595i | \(0.406970\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −46.7386 | −1.57110 | ||||||||
\(886\) | −34.4233 | −1.15647 | ||||||||
\(887\) | 5.43845 | 0.182605 | 0.0913026 | − | 0.995823i | \(-0.470897\pi\) | ||||
0.0913026 | + | 0.995823i | \(0.470897\pi\) | |||||||
\(888\) | −9.80776 | −0.329127 | ||||||||
\(889\) | −2.24621 | −0.0753355 | ||||||||
\(890\) | 34.4924 | 1.15619 | ||||||||
\(891\) | 2.56155 | 0.0858152 | ||||||||
\(892\) | −16.4924 | −0.552207 | ||||||||
\(893\) | −59.0540 | −1.97617 | ||||||||
\(894\) | −17.8078 | −0.595581 | ||||||||
\(895\) | 58.7386 | 1.96342 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | −5.12311 | −0.170865 | ||||||||
\(900\) | 7.68466 | 0.256155 | ||||||||
\(901\) | 19.3845 | 0.645790 | ||||||||
\(902\) | 10.5616 | 0.351661 | ||||||||
\(903\) | 2.87689 | 0.0957371 | ||||||||
\(904\) | 16.9309 | 0.563112 | ||||||||
\(905\) | −47.1771 | −1.56822 | ||||||||
\(906\) | −17.4384 | −0.579354 | ||||||||
\(907\) | 22.8769 | 0.759615 | 0.379807 | − | 0.925066i | \(-0.375990\pi\) | ||||
0.379807 | + | 0.925066i | \(0.375990\pi\) | |||||||
\(908\) | 13.1231 | 0.435506 | ||||||||
\(909\) | −19.5616 | −0.648816 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.26137 | −0.174317 | −0.0871584 | − | 0.996194i | \(-0.527779\pi\) | ||||
−0.0871584 | + | 0.996194i | \(0.527779\pi\) | |||||||
\(912\) | 7.68466 | 0.254464 | ||||||||
\(913\) | −26.2462 | −0.868623 | ||||||||
\(914\) | −13.3153 | −0.440432 | ||||||||
\(915\) | 3.56155 | 0.117741 | ||||||||
\(916\) | 22.8078 | 0.753590 | ||||||||
\(917\) | 16.4924 | 0.544628 | ||||||||
\(918\) | −5.00000 | −0.165025 | ||||||||
\(919\) | 6.56155 | 0.216446 | 0.108223 | − | 0.994127i | \(-0.465484\pi\) | ||||
0.108223 | + | 0.994127i | \(0.465484\pi\) | |||||||
\(920\) | 32.4924 | 1.07124 | ||||||||
\(921\) | −33.9309 | −1.11806 | ||||||||
\(922\) | 30.0540 | 0.989775 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.56155 | −0.0842689 | ||||||||
\(925\) | −75.3693 | −2.47813 | ||||||||
\(926\) | −11.6847 | −0.383982 | ||||||||
\(927\) | −11.3693 | −0.373417 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −6.61553 | −0.217048 | −0.108524 | − | 0.994094i | \(-0.534613\pi\) | ||||
−0.108524 | + | 0.994094i | \(0.534613\pi\) | |||||||
\(930\) | −18.2462 | −0.598317 | ||||||||
\(931\) | 7.68466 | 0.251855 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 22.5616 | 0.738632 | ||||||||
\(934\) | 28.0000 | 0.916188 | ||||||||
\(935\) | 45.6155 | 1.49179 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5616 | 0.443037 | 0.221518 | − | 0.975156i | \(-0.428899\pi\) | ||||
0.221518 | + | 0.975156i | \(0.428899\pi\) | |||||||
\(938\) | −1.12311 | −0.0366707 | ||||||||
\(939\) | 27.6155 | 0.901199 | ||||||||
\(940\) | 27.3693 | 0.892689 | ||||||||
\(941\) | 53.3693 | 1.73979 | 0.869895 | − | 0.493237i | \(-0.164186\pi\) | ||||
0.869895 | + | 0.493237i | \(0.164186\pi\) | |||||||
\(942\) | −5.80776 | −0.189227 | ||||||||
\(943\) | −37.6155 | −1.22493 | ||||||||
\(944\) | 13.1231 | 0.427121 | ||||||||
\(945\) | 3.56155 | 0.115857 | ||||||||
\(946\) | −7.36932 | −0.239597 | ||||||||
\(947\) | −0.315342 | −0.0102472 | −0.00512361 | − | 0.999987i | \(-0.501631\pi\) | ||||
−0.00512361 | + | 0.999987i | \(0.501631\pi\) | |||||||
\(948\) | 1.43845 | 0.0467186 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 59.0540 | 1.91596 | ||||||||
\(951\) | −11.5616 | −0.374909 | ||||||||
\(952\) | 5.00000 | 0.162051 | ||||||||
\(953\) | −52.7386 | −1.70837 | −0.854186 | − | 0.519968i | \(-0.825944\pi\) | ||||
−0.854186 | + | 0.519968i | \(0.825944\pi\) | |||||||
\(954\) | −3.87689 | −0.125519 | ||||||||
\(955\) | −20.4924 | −0.663119 | ||||||||
\(956\) | 4.00000 | 0.129369 | ||||||||
\(957\) | −2.56155 | −0.0828032 | ||||||||
\(958\) | −2.56155 | −0.0827600 | ||||||||
\(959\) | 5.80776 | 0.187542 | ||||||||
\(960\) | −3.56155 | −0.114949 | ||||||||
\(961\) | −4.75379 | −0.153348 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.43845 | −0.304150 | ||||||||
\(964\) | 11.3153 | 0.364443 | ||||||||
\(965\) | 72.5464 | 2.33535 | ||||||||
\(966\) | 9.12311 | 0.293531 | ||||||||
\(967\) | −4.49242 | −0.144467 | −0.0722333 | − | 0.997388i | \(-0.523013\pi\) | ||||
−0.0722333 | + | 0.997388i | \(0.523013\pi\) | |||||||
\(968\) | −4.43845 | −0.142657 | ||||||||
\(969\) | −38.4233 | −1.23433 | ||||||||
\(970\) | −43.6155 | −1.40041 | ||||||||
\(971\) | −10.8769 | −0.349056 | −0.174528 | − | 0.984652i | \(-0.555840\pi\) | ||||
−0.174528 | + | 0.984652i | \(0.555840\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 7.68466 | 0.246359 | ||||||||
\(974\) | 23.6847 | 0.758905 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 2.05398 | 0.0657125 | 0.0328562 | − | 0.999460i | \(-0.489540\pi\) | ||||
0.0328562 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(978\) | −1.12311 | −0.0359130 | ||||||||
\(979\) | −24.8078 | −0.792860 | ||||||||
\(980\) | −3.56155 | −0.113770 | ||||||||
\(981\) | 0.876894 | 0.0279971 | ||||||||
\(982\) | −1.75379 | −0.0559656 | ||||||||
\(983\) | 55.2311 | 1.76160 | 0.880799 | − | 0.473491i | \(-0.157006\pi\) | ||||
0.880799 | + | 0.473491i | \(0.157006\pi\) | |||||||
\(984\) | 4.12311 | 0.131440 | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | 5.00000 | 0.159232 | ||||||||
\(987\) | 7.68466 | 0.244605 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.2462 | 0.834581 | ||||||||
\(990\) | −9.12311 | −0.289951 | ||||||||
\(991\) | −1.43845 | −0.0456938 | −0.0228469 | − | 0.999739i | \(-0.507273\pi\) | ||||
−0.0228469 | + | 0.999739i | \(0.507273\pi\) | |||||||
\(992\) | 5.12311 | 0.162659 | ||||||||
\(993\) | −35.3693 | −1.12241 | ||||||||
\(994\) | 4.00000 | 0.126872 | ||||||||
\(995\) | 62.7386 | 1.98895 | ||||||||
\(996\) | −10.2462 | −0.324664 | ||||||||
\(997\) | −17.0000 | −0.538395 | −0.269198 | − | 0.963085i | \(-0.586759\pi\) | ||||
−0.269198 | + | 0.963085i | \(0.586759\pi\) | |||||||
\(998\) | −27.3693 | −0.866361 | ||||||||
\(999\) | −9.80776 | −0.310304 |
(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 | 7098.2.a.bw.1.1 | 2 | ||
13.3 | even | 3 | 546.2.l.i.295.1 | yes | 4 | ||
13.9 | even | 3 | 546.2.l.i.211.1 | ✓ | 4 | ||
13.12 | even | 2 | 7098.2.a.bq.1.2 | 2 | |||
39.29 | odd | 6 | 1638.2.r.z.1387.2 | 4 | |||
39.35 | odd | 6 | 1638.2.r.z.757.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.i.211.1 | ✓ | 4 | 13.9 | even | 3 | ||
546.2.l.i.295.1 | yes | 4 | 13.3 | even | 3 | ||
1638.2.r.z.757.2 | 4 | 39.35 | odd | 6 | |||
1638.2.r.z.1387.2 | 4 | 39.29 | odd | 6 | |||
7098.2.a.bq.1.2 | 2 | 13.12 | even | 2 | |||
7098.2.a.bw.1.1 | 2 | 1.1 | even | 1 | trivial |