Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 152x^{2} - 177x + 2922 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(13.2349\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.9580 | −1.69566 | −0.847828 | − | 0.530271i | \(-0.822090\pi\) | ||||
−0.847828 | + | 0.530271i | \(0.822090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54.7308 | −1.50018 | −0.750089 | − | 0.661337i | \(-0.769989\pi\) | ||||
−0.750089 | + | 0.661337i | \(0.769989\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −62.0173 | −1.32312 | −0.661558 | − | 0.749894i | \(-0.730104\pi\) | ||||
−0.661558 | + | 0.749894i | \(0.730104\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −56.8741 | −0.978988 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −122.439 | −1.74681 | −0.873407 | − | 0.486991i | \(-0.838095\pi\) | ||||
−0.873407 | + | 0.486991i | \(0.838095\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.5058 | −0.151001 | −0.0755004 | − | 0.997146i | \(-0.524055\pi\) | ||||
−0.0755004 | + | 0.997146i | \(0.524055\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 74.4391 | 0.674853 | 0.337427 | − | 0.941352i | \(-0.390444\pi\) | ||||
0.337427 | + | 0.941352i | \(0.390444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 234.406 | 1.87525 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −232.572 | −1.48923 | −0.744613 | − | 0.667496i | \(-0.767366\pi\) | ||||
−0.744613 | + | 0.667496i | \(0.767366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3677 | 0.0600677 | 0.0300339 | − | 0.999549i | \(-0.490438\pi\) | ||||
0.0300339 | + | 0.999549i | \(0.490438\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −164.192 | −0.866128 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −245.987 | −1.09297 | −0.546486 | − | 0.837468i | \(-0.684035\pi\) | ||||
−0.546486 | + | 0.837468i | \(0.684035\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −186.052 | −0.763901 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −238.653 | −0.909056 | −0.454528 | − | 0.890733i | \(-0.650192\pi\) | ||||
−0.454528 | + | 0.890733i | \(0.650192\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 92.9718 | 0.329722 | 0.164861 | − | 0.986317i | \(-0.447282\pi\) | ||||
0.164861 | + | 0.986317i | \(0.447282\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −170.622 | −0.565219 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −485.645 | −1.50720 | −0.753601 | − | 0.657332i | \(-0.771685\pi\) | ||||
−0.753601 | + | 0.657332i | \(0.771685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −367.317 | −1.00852 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −378.557 | −0.981109 | −0.490555 | − | 0.871410i | \(-0.663206\pi\) | ||||
−0.490555 | + | 0.871410i | \(0.663206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1037.59 | 2.54379 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −37.5173 | −0.0871804 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −182.784 | −0.403329 | −0.201664 | − | 0.979455i | \(-0.564635\pi\) | ||||
−0.201664 | + | 0.979455i | \(0.564635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −396.470 | −0.832177 | −0.416088 | − | 0.909324i | \(-0.636599\pi\) | ||||
−0.416088 | + | 0.909324i | \(0.636599\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1175.73 | 2.24355 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 261.239 | 0.476350 | 0.238175 | − | 0.971222i | \(-0.423451\pi\) | ||||
0.238175 | + | 0.971222i | \(0.423451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 223.317 | 0.389627 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 874.523 | 1.46179 | 0.730893 | − | 0.682492i | \(-0.239104\pi\) | ||||
0.730893 | + | 0.682492i | \(0.239104\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −152.406 | −0.244354 | −0.122177 | − | 0.992508i | \(-0.538988\pi\) | ||||
−0.122177 | + | 0.992508i | \(0.538988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 703.219 | 1.08268 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −573.357 | −0.816554 | −0.408277 | − | 0.912858i | \(-0.633870\pi\) | ||||
−0.408277 | + | 0.912858i | \(0.633870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 317.754 | 0.420217 | 0.210108 | − | 0.977678i | \(-0.432618\pi\) | ||||
0.210108 | + | 0.977678i | \(0.432618\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2321.20 | 2.96200 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −697.717 | −0.859806 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 95.0160 | 0.113165 | 0.0565824 | − | 0.998398i | \(-0.481980\pi\) | ||||
0.0565824 | + | 0.998398i | \(0.481980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 31.1032 | 0.0346801 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 237.084 | 0.256046 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1608.78 | 1.68398 | 0.841992 | − | 0.539490i | \(-0.181383\pi\) | ||||
0.841992 | + | 0.539490i | \(0.181383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −492.577 | −0.500059 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 783.043 | 0.771442 | 0.385721 | − | 0.922615i | \(-0.373953\pi\) | ||||
0.385721 | + | 0.922615i | \(0.373953\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1489.61 | −1.42501 | −0.712503 | − | 0.701669i | \(-0.752438\pi\) | ||||
−0.712503 | + | 0.701669i | \(0.752438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −712.769 | −0.643981 | −0.321991 | − | 0.946743i | \(-0.604352\pi\) | ||||
−0.321991 | + | 0.946743i | \(0.604352\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1041.85 | 0.915513 | 0.457757 | − | 0.889078i | \(-0.348653\pi\) | ||||
0.457757 | + | 0.889078i | \(0.348653\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −737.960 | −0.631028 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 352.093 | 0.293116 | 0.146558 | − | 0.989202i | \(-0.453181\pi\) | ||||
0.146558 | + | 0.989202i | \(0.453181\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1411.22 | −1.14432 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −558.156 | −0.441039 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1664.46 | 1.25053 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −715.958 | −0.524844 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2074.13 | −1.48413 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1093.73 | 0.764194 | 0.382097 | − | 0.924122i | \(-0.375202\pi\) | ||||
0.382097 | + | 0.924122i | \(0.375202\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 278.915 | 0.190365 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2166.37 | −1.44486 | −0.722430 | − | 0.691444i | \(-0.756975\pi\) | ||||
−0.722430 | + | 0.691444i | \(0.756975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −511.866 | −0.326329 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1964.92 | −1.22536 | −0.612681 | − | 0.790330i | \(-0.709909\pi\) | ||||
−0.612681 | + | 0.790330i | \(0.709909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −136.976 | −0.0835840 | −0.0417920 | − | 0.999126i | \(-0.513307\pi\) | ||||
−0.0417920 | + | 0.999126i | \(0.513307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1456.93 | −0.870184 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3394.26 | 1.98491 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4409.11 | 2.52522 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −280.105 | −0.154007 | −0.0770037 | − | 0.997031i | \(-0.524535\pi\) | ||||
−0.0770037 | + | 0.997031i | \(0.524535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2194.13 | −1.18249 | −0.591245 | − | 0.806492i | \(-0.701363\pi\) | ||||
−0.591245 | + | 0.806492i | \(0.701363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1101.95 | −0.582271 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −196.552 | −0.101854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 220.818 | 0.112250 | 0.0561248 | − | 0.998424i | \(-0.482126\pi\) | ||||
0.0561248 | + | 0.998424i | \(0.482126\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1135.67 | −0.566444 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1476.86 | −0.709674 | −0.354837 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354837 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3112.76 | 1.46866 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2197.66 | 1.01832 | 0.509162 | − | 0.860671i | \(-0.329955\pi\) | ||||
0.509162 | + | 0.860671i | \(0.329955\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1649.15 | 0.750635 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −112.552 | −0.0503336 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2091.61 | −0.919201 | −0.459601 | − | 0.888126i | \(-0.652007\pi\) | ||||
−0.459601 | + | 0.888126i | \(0.652007\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −548.351 | −0.232862 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2334.54 | −0.974813 | −0.487406 | − | 0.873175i | \(-0.662057\pi\) | ||||
−0.487406 | + | 0.873175i | \(0.662057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1758.40 | −0.722105 | −0.361053 | − | 0.932545i | \(-0.617583\pi\) | ||||
−0.361053 | + | 0.932545i | \(0.617583\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1189.41 | −0.480457 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4663.42 | 1.85330 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6701.19 | 2.62053 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3700.68 | 1.40195 | 0.700973 | − | 0.713188i | \(-0.252749\pi\) | ||||
0.700973 | + | 0.713188i | \(0.252749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2708.45 | 1.01015 | 0.505073 | − | 0.863077i | \(-0.331466\pi\) | ||||
0.505073 | + | 0.863077i | \(0.331466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3527.18 | 1.29531 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −160.686 | −0.0581138 | −0.0290569 | − | 0.999578i | \(-0.509250\pi\) | ||||
−0.0290569 | + | 0.999578i | \(0.509250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2065.99 | −0.735951 | −0.367976 | − | 0.929835i | \(-0.619949\pi\) | ||||
−0.367976 | + | 0.929835i | \(0.619949\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 783.717 | 0.275021 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4524.38 | 1.54145 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 669.952 | 0.224951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 684.450 | 0.226528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1007.12 | 0.328592 | 0.164296 | − | 0.986411i | \(-0.447465\pi\) | ||||
0.164296 | + | 0.986411i | \(0.447465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2623.57 | 0.843962 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1762.56 | −0.559096 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −457.219 | −0.141078 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7593.34 | 2.31124 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1644.83 | 0.493929 | 0.246964 | − | 0.969025i | \(-0.420567\pi\) | ||||
0.246964 | + | 0.969025i | \(0.420567\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2109.66 | 0.625084 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 318.874 | 0.0932354 | 0.0466177 | − | 0.998913i | \(-0.485156\pi\) | ||||
0.0466177 | + | 0.998913i | \(0.485156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2536.11 | −0.731837 | −0.365918 | − | 0.930647i | \(-0.619245\pi\) | ||||
−0.365918 | + | 0.930647i | \(0.619245\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2332.81 | 0.655913 | 0.327957 | − | 0.944693i | \(-0.393640\pi\) | ||||
0.327957 | + | 0.944693i | \(0.393640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9206.86 | 2.55570 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1720.07 | −0.471438 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2713.85 | −0.734495 | −0.367248 | − | 0.930123i | \(-0.619700\pi\) | ||||
−0.367248 | + | 0.930123i | \(0.619700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4174.59 | 1.11580 | 0.557902 | − | 0.829907i | \(-0.311606\pi\) | ||||
0.557902 | + | 0.829907i | \(0.311606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 775.573 | 0.199792 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 953.261 | 0.242612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6123.58 | 1.53991 | 0.769954 | − | 0.638099i | \(-0.220279\pi\) | ||||
0.769954 | + | 0.638099i | \(0.220279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4074.11 | −1.01240 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6963.61 | 1.71011 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4633.91 | −1.12473 | −0.562365 | − | 0.826889i | \(-0.690108\pi\) | ||||
−0.562365 | + | 0.826889i | \(0.690108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2093.15 | −0.496409 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3283.23 | −0.769781 | −0.384891 | − | 0.922962i | \(-0.625761\pi\) | ||||
−0.384891 | + | 0.922962i | \(0.625761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7176.69 | 1.66362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 285.048 | 0.0653358 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 798.985 | 0.181097 | 0.0905483 | − | 0.995892i | \(-0.471138\pi\) | ||||
0.0905483 | + | 0.995892i | \(0.471138\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6706.07 | −1.50319 | −0.751596 | − | 0.659624i | \(-0.770716\pi\) | ||||
−0.751596 | + | 0.659624i | \(0.770716\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12829.3 | −2.81321 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1162.27 | 0.252108 | 0.126054 | − | 0.992023i | \(-0.459769\pi\) | ||||
0.126054 | + | 0.992023i | \(0.459769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 93.3096 | 0.0200226 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2718.17 | 0.577055 | 0.288527 | − | 0.957472i | \(-0.406834\pi\) | ||||
0.288527 | + | 0.957472i | \(0.406834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3009.48 | −0.632138 | −0.316069 | − | 0.948736i | \(-0.602363\pi\) | ||||
−0.316069 | + | 0.948736i | \(0.602363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 711.253 | 0.147828 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10078.3 | 2.05136 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4826.33 | 0.972249 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4209.15 | −0.839252 | −0.419626 | − | 0.907697i | \(-0.637839\pi\) | ||||
−0.419626 | + | 0.907697i | \(0.637839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3465.21 | 0.683907 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1477.73 | −0.288709 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4616.51 | −0.892909 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2349.13 | 0.445392 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7516.28 | 1.41109 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3114.82 | −0.579063 | −0.289531 | − | 0.957169i | \(-0.593499\pi\) | ||||
−0.289531 | + | 0.957169i | \(0.593499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4468.83 | −0.822727 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8487.24 | −1.54748 | −0.773741 | − | 0.633501i | \(-0.781617\pi\) | ||||
−0.773741 | + | 0.633501i | \(0.781617\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4954.91 | 0.894786 | 0.447393 | − | 0.894337i | \(-0.352352\pi\) | ||||
0.447393 | + | 0.894337i | \(0.352352\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5608.79 | −0.993757 | −0.496879 | − | 0.867820i | \(-0.665521\pi\) | ||||
−0.496879 | + | 0.867820i | \(0.665521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12728.9 | 2.23411 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2138.31 | −0.371803 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1531.19 | 0.263770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14537.3 | −2.48117 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3125.54 | 0.528572 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6609.49 | 1.09755 | 0.548777 | − | 0.835969i | \(-0.315094\pi\) | ||||
0.548777 | + | 0.835969i | \(0.315094\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2213.88 | −0.364324 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4952.57 | −0.807725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11455.5 | 1.85170 | 0.925850 | − | 0.377891i | \(-0.123350\pi\) | ||||
0.925850 | + | 0.377891i | \(0.123350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1056.28 | 0.169231 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −567.434 | −0.0901123 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4233.65 | −0.660673 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6044.15 | 0.935064 | 0.467532 | − | 0.883976i | \(-0.345143\pi\) | ||||
0.467532 | + | 0.883976i | \(0.345143\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5487.93 | 0.841726 | 0.420863 | − | 0.907124i | \(-0.361727\pi\) | ||||
0.420863 | + | 0.907124i | \(0.361727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1674.47 | −0.254634 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6880.15 | −1.03738 | −0.518688 | − | 0.854964i | \(-0.673579\pi\) | ||||
−0.518688 | + | 0.854964i | \(0.673579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16579.2 | −2.47869 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3938.34 | 0.578990 | 0.289495 | − | 0.957180i | \(-0.406513\pi\) | ||||
0.289495 | + | 0.957180i | \(0.406513\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6702.61 | −0.977199 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4993.38 | 0.721996 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2889.32 | 0.414340 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1439.63 | 0.204763 | 0.102381 | − | 0.994745i | \(-0.467354\pi\) | ||||
0.102381 | + | 0.994745i | \(0.467354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2147.87 | −0.303019 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2494.11 | −0.346220 | −0.173110 | − | 0.984903i | \(-0.555382\pi\) | ||||
−0.173110 | + | 0.984903i | \(0.555382\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6222.39 | −0.856861 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14423.5 | 1.97042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1309.25 | 0.177445 | 0.0887225 | − | 0.996056i | \(-0.471722\pi\) | ||||
0.0887225 | + | 0.996056i | \(0.471722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3281.18 | 0.441208 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6961.80 | 0.928803 | 0.464402 | − | 0.885625i | \(-0.346269\pi\) | ||||
0.464402 | + | 0.885625i | \(0.346269\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 836.746 | 0.109907 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6353.45 | 0.828104 | 0.414052 | − | 0.910253i | \(-0.364113\pi\) | ||||
0.414052 | + | 0.910253i | \(0.364113\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9114.25 | −1.17884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6499.11 | −0.834191 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10869.7 | 1.38459 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11505.4 | −1.45451 | −0.727254 | − | 0.686368i | \(-0.759204\pi\) | ||||
−0.727254 | + | 0.686368i | \(0.759204\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1653.33 | 0.205893 | 0.102947 | − | 0.994687i | \(-0.467173\pi\) | ||||
0.102947 | + | 0.994687i | \(0.467173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −642.979 | −0.0794766 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1535.60 | −0.188406 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13463.0 | 1.63965 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4894.83 | 0.591769 | 0.295885 | − | 0.955224i | \(-0.404386\pi\) | ||||
0.295885 | + | 0.955224i | \(0.404386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5894.77 | −0.707463 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6023.98 | −0.712544 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −410.929 | −0.0482573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −265.504 | −0.0309563 | −0.0154782 | − | 0.999880i | \(-0.504927\pi\) | ||||
−0.0154782 | + | 0.999880i | \(0.504927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11136.8 | 1.28925 | 0.644623 | − | 0.764500i | \(-0.277014\pi\) | ||||
0.644623 | + | 0.764500i | \(0.277014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4370.80 | −0.502401 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28700.5 | −3.27572 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10182.8 | 1.14599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5193.41 | −0.580413 | −0.290206 | − | 0.956964i | \(-0.593724\pi\) | ||||
−0.290206 | + | 0.956964i | \(0.593724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6314.17 | −0.700785 | −0.350392 | − | 0.936603i | \(-0.613952\pi\) | ||||
−0.350392 | + | 0.936603i | \(0.613952\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13227.3 | 1.45794 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −930.917 | −0.101903 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15423.3 | −1.67680 | −0.838399 | − | 0.545056i | \(-0.816508\pi\) | ||||
−0.838399 | + | 0.545056i | \(0.816508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8706.11 | 0.933725 | 0.466862 | − | 0.884330i | \(-0.345384\pi\) | ||||
0.466862 | + | 0.884330i | \(0.345384\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1801.31 | −0.191889 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −840.315 | −0.0889162 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5495.91 | 0.577657 | 0.288829 | − | 0.957381i | \(-0.406734\pi\) | ||||
0.288829 | + | 0.957381i | \(0.406734\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13061.7 | 1.36375 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6582.40 | −0.682711 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11357.3 | −1.16252 | −0.581258 | − | 0.813719i | \(-0.697439\pi\) | ||||
−0.581258 | + | 0.813719i | \(0.697439\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3305.86 | −0.336175 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14514.2 | −1.46637 | −0.733184 | − | 0.680030i | \(-0.761967\pi\) | ||||
−0.733184 | + | 0.680030i | \(0.761967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9971.00 | −1.00085 | −0.500423 | − | 0.865781i | \(-0.666822\pi\) | ||||
−0.500423 | + | 0.865781i | \(0.666822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −589.655 | −0.0588056 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −397.477 | −0.0393856 | −0.0196928 | − | 0.999806i | \(-0.506269\pi\) | ||||
−0.0196928 | + | 0.999806i | \(0.506269\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 662.454 | 0.0648074 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5088.42 | −0.494642 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2931.43 | −0.283165 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3407.01 | −0.327036 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14060.4 | −1.34120 | −0.670602 | − | 0.741818i | \(-0.733964\pi\) | ||||
−0.670602 | + | 0.741818i | \(0.733964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15255.4 | 1.44613 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30499.2 | −2.85546 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13534.7 | 1.25937 | 0.629687 | − | 0.776849i | \(-0.283183\pi\) | ||||
0.629687 | + | 0.776849i | \(0.283183\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4430.59 | −0.409730 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8693.29 | 0.799028 | 0.399514 | − | 0.916727i | \(-0.369179\pi\) | ||||
0.399514 | + | 0.916727i | \(0.369179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28475.9 | 2.60140 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9338.29 | 0.847929 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4017.93 | −0.360455 | −0.180228 | − | 0.983625i | \(-0.557683\pi\) | ||||
−0.180228 | + | 0.983625i | \(0.557683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6592.98 | 0.587929 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 52.2455 | 0.00463124 | 0.00231562 | − | 0.999997i | \(-0.499263\pi\) | ||||
0.00231562 | + | 0.999997i | \(0.499263\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14844.9 | −1.30810 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4947.44 | 0.433379 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9239.10 | −0.804550 | −0.402275 | − | 0.915519i | \(-0.631780\pi\) | ||||
−0.402275 | + | 0.915519i | \(0.631780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −337.655 | −0.0290601 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28240.0 | 2.41632 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26579.7 | 2.26107 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6274.82 | −0.530701 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14973.4 | −1.25911 | −0.629555 | − | 0.776956i | \(-0.716763\pi\) | ||||
−0.629555 | + | 0.776956i | \(0.716763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13603.5 | 1.13736 | 0.568681 | − | 0.822558i | \(-0.307454\pi\) | ||||
0.568681 | + | 0.822558i | \(0.307454\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1269.42 | −0.104927 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6625.82 | −0.544573 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1645.05 | −0.134443 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14800.6 | 1.20279 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13512.7 | 1.09197 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7003.61 | −0.562808 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16886.4 | −1.34196 | −0.670981 | − | 0.741474i | \(-0.734127\pi\) | ||||
−0.670981 | + | 0.741474i | \(0.734127\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5275.21 | −0.416908 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19751.4 | −1.55240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5987.25 | 0.468001 | 0.234000 | − | 0.972237i | \(-0.424818\pi\) | ||||
0.234000 | + | 0.972237i | \(0.424818\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3568.23 | −0.277392 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2908.49 | 0.224875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13990.3 | 1.07001 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2238.71 | 0.170300 | 0.0851499 | − | 0.996368i | \(-0.472863\pi\) | ||||
0.0851499 | + | 0.996368i | \(0.472863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5765.86 | −0.436261 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20103.6 | 1.51297 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8452.84 | 0.632762 | 0.316381 | − | 0.948632i | \(-0.397532\pi\) | ||||
0.316381 | + | 0.948632i | \(0.397532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6674.98 | −0.497024 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14953.6 | 1.10173 | 0.550866 | − | 0.834594i | \(-0.314298\pi\) | ||||
0.550866 | + | 0.834594i | \(0.314298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16021.8 | −1.17424 | −0.587122 | − | 0.809498i | \(-0.699739\pi\) | ||||
−0.587122 | + | 0.809498i | \(0.699739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11102.0 | 0.809414 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17449.0 | 1.26552 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16113.1 | 1.16256 | 0.581279 | − | 0.813704i | \(-0.302552\pi\) | ||||
0.581279 | + | 0.813704i | \(0.302552\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8125.34 | 0.583208 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20718.7 | 1.47184 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10581.5 | 0.747850 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9552.04 | −0.671644 | −0.335822 | − | 0.941925i | \(-0.609014\pi\) | ||||
−0.335822 | + | 0.941925i | \(0.609014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −129.656 | −0.00907028 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −482.058 | −0.0335520 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24167.8 | 1.67361 | 0.836807 | − | 0.547499i | \(-0.184420\pi\) | ||||
0.836807 | + | 0.547499i | \(0.184420\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6197.98 | −0.424902 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −821.331 | −0.0560245 | −0.0280122 | − | 0.999608i | \(-0.508918\pi\) | ||||
−0.0280122 | + | 0.999608i | \(0.508918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14674.7 | 0.995996 | 0.497998 | − | 0.867178i | \(-0.334069\pi\) | ||||
0.497998 | + | 0.867178i | \(0.334069\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2351.15 | 0.158783 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31554.9 | −2.12048 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5083.12 | 0.339897 | 0.169949 | − | 0.985453i | \(-0.445640\pi\) | ||||
0.169949 | + | 0.985453i | \(0.445640\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30118.4 | 1.99420 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22202.0 | −1.46286 | −0.731428 | − | 0.681919i | \(-0.761146\pi\) | ||||
−0.731428 | + | 0.681919i | \(0.761146\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13573.1 | 0.889954 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14990.6 | −0.978121 | −0.489060 | − | 0.872250i | \(-0.662660\pi\) | ||||
−0.489060 | + | 0.872250i | \(0.662660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3073.02 | 0.199540 | 0.0997700 | − | 0.995011i | \(-0.468189\pi\) | ||||
0.0997700 | + | 0.995011i | \(0.468189\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2009.86 | 0.129876 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10020.6 | 0.641317 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2053.35 | 0.130786 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30118.4 | 1.90922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26012.7 | −1.64113 | −0.820563 | − | 0.571556i | \(-0.806340\pi\) | ||||
−0.820563 | + | 0.571556i | \(0.806340\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3021.36 | 0.189713 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20734.9 | −1.29581 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7870.70 | 0.487262 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8032.23 | 0.494936 | 0.247468 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247468 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24887.7 | −1.52640 | −0.763200 | − | 0.646162i | \(-0.776373\pi\) | ||||
−0.763200 | + | 0.646162i | \(0.776373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5287.68 | −0.322794 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21084.3 | −1.28116 | −0.640580 | − | 0.767891i | \(-0.721306\pi\) | ||||
−0.640580 | + | 0.767891i | \(0.721306\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10003.9 | 0.605065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13166.3 | 0.789033 | 0.394516 | − | 0.918889i | \(-0.370912\pi\) | ||||
0.394516 | + | 0.918889i | \(0.370912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41070.1 | 2.44999 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1371.66 | −0.0814513 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13903.4 | 0.821851 | 0.410926 | − | 0.911669i | \(-0.365206\pi\) | ||||
0.410926 | + | 0.911669i | \(0.365206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6306.61 | −0.371102 | −0.185551 | − | 0.982635i | \(-0.559407\pi\) | ||||
−0.185551 | + | 0.982635i | \(0.559407\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22780.0 | 1.33439 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17312.5 | −1.00501 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4934.50 | 0.285170 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21699.1 | 1.24841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24407.6 | −1.39798 | −0.698992 | − | 0.715129i | \(-0.746368\pi\) | ||||
−0.698992 | + | 0.715129i | \(0.746368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6328.97 | 0.360892 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31080.3 | 1.76442 | 0.882209 | − | 0.470858i | \(-0.156055\pi\) | ||||
0.882209 | + | 0.470858i | \(0.156055\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 956.623 | 0.0538295 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28759.5 | −1.61120 | −0.805601 | − | 0.592458i | \(-0.798157\pi\) | ||||
−0.805601 | + | 0.592458i | \(0.798157\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37251.0 | 2.07779 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7608.32 | −0.422526 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23477.1 | 1.29812 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24895.4 | 1.37057 | 0.685287 | − | 0.728273i | \(-0.259677\pi\) | ||||
0.685287 | + | 0.728273i | \(0.259677\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2596.80 | 0.141730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29220.4 | 1.58795 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6998.44 | 0.378692 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1702.74 | −0.0917427 | −0.0458714 | − | 0.998947i | \(-0.514606\pi\) | ||||
−0.0458714 | + | 0.998947i | \(0.514606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3076.25 | 0.165040 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27620.6 | 1.47553 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6523.21 | 0.345535 | 0.172767 | − | 0.984963i | \(-0.444729\pi\) | ||||
0.172767 | + | 0.984963i | \(0.444729\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5160.22 | −0.272185 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 771.765 | 0.0405369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −64348.4 | −3.36572 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8141.55 | −0.424061 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25254.4 | −1.30992 | −0.654959 | − | 0.755664i | \(-0.727314\pi\) | ||||
−0.654959 | + | 0.755664i | \(0.727314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12523.8 | 0.644210 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −54516.4 | −2.79268 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27964.9 | −1.42663 | −0.713316 | − | 0.700843i | \(-0.752808\pi\) | ||||
−0.713316 | + | 0.700843i | \(0.752808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11383.4 | −0.575964 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9294.38 | 0.468344 | 0.234172 | − | 0.972195i | \(-0.424762\pi\) | ||||
0.234172 | + | 0.972195i | \(0.424762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14297.8 | −0.714609 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18291.2 | −0.910490 | −0.455245 | − | 0.890366i | \(-0.650448\pi\) | ||||
−0.455245 | + | 0.890366i | \(0.650448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2326.72 | 0.115350 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14742.4 | −0.727921 | −0.363960 | − | 0.931414i | \(-0.618576\pi\) | ||||
−0.363960 | + | 0.931414i | \(0.618576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5310.24 | 0.261144 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2859.78 | 0.140072 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28463.4 | −1.38301 | −0.691507 | − | 0.722370i | \(-0.743053\pi\) | ||||
−0.691507 | + | 0.722370i | \(0.743053\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18370.7 | 0.889067 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41596.4 | 2.00510 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20336.7 | −0.976422 | −0.488211 | − | 0.872726i | \(-0.662350\pi\) | ||||
−0.488211 | + | 0.872726i | \(0.662350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12222.3 | −0.584509 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39581.6 | −1.88546 | −0.942728 | − | 0.333564i | \(-0.891749\pi\) | ||||
−0.942728 | + | 0.333564i | \(0.891749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20890.8 | 0.987332 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11335.7 | 0.533650 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10580.3 | −0.496146 | −0.248073 | − | 0.968741i | \(-0.579797\pi\) | ||||
−0.248073 | + | 0.968741i | \(0.579797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13901.7 | −0.649363 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25922.2 | −1.20615 | −0.603077 | − | 0.797683i | \(-0.706059\pi\) | ||||
−0.603077 | + | 0.797683i | \(0.706059\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2430.26 | 0.112642 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2984.53 | 0.137268 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47863.3 | −2.19294 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6279.45 | −0.286602 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4186.27 | −0.190337 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17220.0 | 0.779958 | 0.389979 | − | 0.920824i | \(-0.372482\pi\) | ||||
0.389979 | + | 0.920824i | \(0.372482\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9849.68 | −0.444433 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24588.0 | 1.10107 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21530.1 | 0.960494 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6275.52 | 0.278909 | 0.139454 | − | 0.990228i | \(-0.455465\pi\) | ||||
0.139454 | + | 0.990228i | \(0.455465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59461.9 | 2.63280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 855.144 | 0.0377216 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8341.33 | 0.366574 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2396.96 | 0.104556 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4604.03 | −0.200085 | −0.100043 | − | 0.994983i | \(-0.531898\pi\) | ||||
−0.100043 | + | 0.994983i | \(0.531898\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5104.36 | 0.221009 | 0.110505 | − | 0.993876i | \(-0.464753\pi\) | ||||
0.110505 | + | 0.993876i | \(0.464753\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20118.2 | −0.867868 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27998.4 | 1.20336 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1162.68 | −0.0497884 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45635.4 | −1.93993 | −0.969967 | − | 0.243237i | \(-0.921791\pi\) | ||||
−0.969967 | + | 0.243237i | \(0.921791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39377.1 | 1.66780 | 0.833901 | − | 0.551915i | \(-0.186103\pi\) | ||||
0.833901 | + | 0.551915i | \(0.186103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38487.8 | −1.62421 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30916.3 | 1.29996 | 0.649978 | − | 0.759953i | \(-0.274778\pi\) | ||||
0.649978 | + | 0.759953i | \(0.274778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2543.33 | 0.106554 | 0.0532771 | − | 0.998580i | \(-0.483033\pi\) | ||||
0.0532771 | + | 0.998580i | \(0.483033\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3486.81 | 0.145555 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41663.3 | −1.72673 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 279.929 | 0.0115600 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7930.82 | −0.326343 | −0.163172 | − | 0.986598i | \(-0.552172\pi\) | ||||
−0.163172 | + | 0.986598i | \(0.552172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29700.8 | 1.21780 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8154.51 | 0.333163 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31264.5 | −1.27282 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9028.45 | −0.364965 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18311.0 | −0.737595 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41983.2 | −1.68520 | −0.842601 | − | 0.538538i | \(-0.818977\pi\) | ||||
−0.842601 | + | 0.538538i | \(0.818977\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2133.76 | 0.0853485 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11854.3 | 0.472504 | 0.236252 | − | 0.971692i | \(-0.424081\pi\) | ||||
0.236252 | + | 0.971692i | \(0.424081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8113.88 | −0.322284 | −0.161142 | − | 0.986931i | \(-0.551518\pi\) | ||||
−0.161142 | + | 0.986931i | \(0.551518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45817.0 | −1.80722 | −0.903609 | − | 0.428358i | \(-0.859092\pi\) | ||||
−0.903609 | + | 0.428358i | \(0.859092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39652.7 | 1.55865 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30235.0 | 1.18435 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31380.3 | 1.22498 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16201.3 | −0.630266 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14479.0 | 0.561328 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31813.0 | 1.22491 | 0.612456 | − | 0.790504i | \(-0.290182\pi\) | ||||
0.612456 | + | 0.790504i | \(0.290182\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12627.4 | −0.484543 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43551.6 | −1.66548 | −0.832742 | − | 0.553661i | \(-0.813230\pi\) | ||||
−0.832742 | + | 0.553661i | \(0.813230\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40645.1 | −1.54906 | −0.774528 | − | 0.632540i | \(-0.782012\pi\) | ||||
−0.774528 | + | 0.632540i | \(0.782012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10395.6 | 0.394854 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34028.2 | 1.28811 | 0.644056 | − | 0.764978i | \(-0.277250\pi\) | ||||
0.644056 | + | 0.764978i | \(0.277250\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4433.20 | −0.166686 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6073.35 | 0.227589 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44258.2 | 1.65295 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13849.5 | −0.515521 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2411.25 | −0.0894545 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46350.2 | 1.71382 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33335.8 | 1.22444 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50804.7 | −1.85992 | −0.929958 | − | 0.367666i | \(-0.880157\pi\) | ||||
−0.929958 | + | 0.367666i | \(0.880157\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7047.38 | 0.257147 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28738.3 | −1.04516 | −0.522582 | − | 0.852589i | \(-0.675031\pi\) | ||||
−0.522582 | + | 0.852589i | \(0.675031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17390.9 | −0.630400 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22548.9 | 0.814691 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54742.2 | 1.96494 | 0.982470 | − | 0.186420i | \(-0.0596886\pi\) | ||||
0.982470 | + | 0.186420i | \(0.0596886\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9344.46 | −0.334322 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54235.5 | −1.93411 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57660.9 | −2.04960 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13406.5 | −0.475002 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43775.8 | −1.54600 | −0.773002 | − | 0.634403i | \(-0.781246\pi\) | ||||
−0.773002 | + | 0.634403i | \(0.781246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25461.7 | −0.893440 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −127041. | −4.44352 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35090.9 | −1.22345 | −0.611724 | − | 0.791071i | \(-0.709524\pi\) | ||||
−0.611724 | + | 0.791071i | \(0.709524\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14864.7 | 0.516605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31784.8 | 1.10112 | 0.550560 | − | 0.834795i | \(-0.314414\pi\) | ||||
0.550560 | + | 0.834795i | \(0.314414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17765.1 | −0.613479 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56500.9 | −1.93879 | −0.969394 | − | 0.245510i | \(-0.921045\pi\) | ||||
−0.969394 | + | 0.245510i | \(0.921045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9451.84 | 0.323308 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16826.4 | −0.573746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36669.1 | 1.24641 | 0.623204 | − | 0.782059i | \(-0.285831\pi\) | ||||
0.623204 | + | 0.782059i | \(0.285831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −70157.5 | −2.37722 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38186.6 | 1.28986 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29683.5 | −0.996392 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6414.92 | −0.214660 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −51346.8 | −1.71286 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12012.4 | 0.399474 | 0.199737 | − | 0.979850i | \(-0.435991\pi\) | ||||
0.199737 | + | 0.979850i | \(0.435991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4593.58 | 0.152288 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37296.2 | −1.23264 | −0.616320 | − | 0.787496i | \(-0.711377\pi\) | ||||
−0.616320 | + | 0.787496i | \(0.711377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −43611.8 | −1.43251 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9788.45 | 0.320532 | 0.160266 | − | 0.987074i | \(-0.448765\pi\) | ||||
0.160266 | + | 0.987074i | \(0.448765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5200.30 | −0.169767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9376.63 | 0.305171 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4620.40 | −0.149917 | −0.0749583 | − | 0.997187i | \(-0.523882\pi\) | ||||
−0.0749583 | + | 0.997187i | \(0.523882\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3046.29 | 0.0985410 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6920.73 | 0.222514 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40365.3 | −1.29389 | −0.646946 | − | 0.762536i | \(-0.723954\pi\) | ||||
−0.646946 | + | 0.762536i | \(0.723954\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19828.5 | 0.633673 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39167.1 | 1.24792 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2994.35 | 0.0951175 | 0.0475587 | − | 0.998868i | \(-0.484856\pi\) | ||||
0.0475587 | + | 0.998868i | \(0.484856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6641.64 | −0.210343 |
(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 | 2352.4.a.cp.1.1 | 4 | ||
4.3 | odd | 2 | 1176.4.a.ba.1.1 | 4 | |||
7.3 | odd | 6 | 336.4.q.m.289.1 | 8 | |||
7.5 | odd | 6 | 336.4.q.m.193.1 | 8 | |||
7.6 | odd | 2 | 2352.4.a.cm.1.4 | 4 | |||
28.3 | even | 6 | 168.4.q.f.121.1 | yes | 8 | ||
28.19 | even | 6 | 168.4.q.f.25.1 | ✓ | 8 | ||
28.27 | even | 2 | 1176.4.a.bd.1.4 | 4 | |||
84.47 | odd | 6 | 504.4.s.j.361.4 | 8 | |||
84.59 | odd | 6 | 504.4.s.j.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.1 | ✓ | 8 | 28.19 | even | 6 | ||
168.4.q.f.121.1 | yes | 8 | 28.3 | even | 6 | ||
336.4.q.m.193.1 | 8 | 7.5 | odd | 6 | |||
336.4.q.m.289.1 | 8 | 7.3 | odd | 6 | |||
504.4.s.j.289.4 | 8 | 84.59 | odd | 6 | |||
504.4.s.j.361.4 | 8 | 84.47 | odd | 6 | |||
1176.4.a.ba.1.1 | 4 | 4.3 | odd | 2 | |||
1176.4.a.bd.1.4 | 4 | 28.27 | even | 2 | |||
2352.4.a.cm.1.4 | 4 | 7.6 | odd | 2 | |||
2352.4.a.cp.1.1 | 4 | 1.1 | even | 1 | trivial |