Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, 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("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
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 | 1.4 | ||
Root | \(13.2349\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-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 | \(-0.177910\pi\) | ||||
0.847828 | + | 0.530271i | \(0.177910\pi\) | |||||||
\(6\) | 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 | \(-0.230011\pi\) | ||||
0.750089 | + | 0.661337i | \(0.230011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.0173 | 1.32312 | 0.661558 | − | 0.749894i | \(-0.269896\pi\) | ||||
0.661558 | + | 0.749894i | \(0.269896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 56.8741 | 0.978988 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 122.439 | 1.74681 | 0.873407 | − | 0.486991i | \(-0.161905\pi\) | ||||
0.873407 | + | 0.486991i | \(0.161905\pi\) | |||||||
\(18\) | 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 | \(-0.609556\pi\) | ||||
−0.337427 | + | 0.941352i | \(0.609556\pi\) | |||||||
\(24\) | 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 | \(-0.349808\pi\) | ||||
0.454528 | + | 0.890733i | \(0.349808\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −92.9718 | −0.329722 | −0.164861 | − | 0.986317i | \(-0.552718\pi\) | ||||
−0.164861 | + | 0.986317i | \(0.552718\pi\) | |||||||
\(44\) | 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 | \(-0.363401\pi\) | ||||
0.416088 | + | 0.909324i | \(0.363401\pi\) | |||||||
\(62\) | 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 | \(-0.576549\pi\) | ||||
−0.238175 | + | 0.971222i | \(0.576549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −223.317 | −0.389627 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −874.523 | −1.46179 | −0.730893 | − | 0.682492i | \(-0.760896\pi\) | ||||
−0.730893 | + | 0.682492i | \(0.760896\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 152.406 | 0.244354 | 0.122177 | − | 0.992508i | \(-0.461012\pi\) | ||||
0.122177 | + | 0.992508i | \(0.461012\pi\) | |||||||
\(74\) | 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 | \(-0.366130\pi\) | ||||
0.408277 | + | 0.912858i | \(0.366130\pi\) | |||||||
\(80\) | 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 | \(-0.518020\pi\) | ||||
−0.0565824 | + | 0.998398i | \(0.518020\pi\) | |||||||
\(90\) | 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 | \(-0.818617\pi\) | ||||
−0.841992 | + | 0.539490i | \(0.818617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 492.577 | 0.500059 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −783.043 | −0.771442 | −0.385721 | − | 0.922615i | \(-0.626047\pi\) | ||||
−0.385721 | + | 0.922615i | \(0.626047\pi\) | |||||||
\(102\) | 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 | \(-0.395648\pi\) | ||||
0.321991 | + | 0.946743i | \(0.395648\pi\) | |||||||
\(108\) | 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 | \(-0.624798\pi\) | ||||
−0.382097 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(128\) | 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 | \(-0.298637\pi\) | ||||
0.591245 | + | 0.806492i | \(0.298637\pi\) | |||||||
\(152\) | 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 | \(-0.517874\pi\) | ||||
−0.0561248 | + | 0.998424i | \(0.517874\pi\) | |||||||
\(158\) | 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 | \(-0.384536\pi\) | ||||
0.354837 | + | 0.934928i | \(0.384536\pi\) | |||||||
\(164\) | 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 | \(-0.347993\pi\) | ||||
0.459601 | + | 0.888126i | \(0.347993\pi\) | |||||||
\(174\) | 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 | \(-0.337943\pi\) | ||||
0.487406 | + | 0.873175i | \(0.337943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1758.40 | 0.722105 | 0.361053 | − | 0.932545i | \(-0.382417\pi\) | ||||
0.361053 | + | 0.932545i | \(0.382417\pi\) | |||||||
\(182\) | 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 | \(-0.747251\pi\) | ||||
−0.700973 | + | 0.713188i | \(0.747251\pi\) | |||||||
\(192\) | 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 | \(-0.552535\pi\) | ||||
−0.164296 | + | 0.986411i | \(0.552535\pi\) | |||||||
\(212\) | 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 | \(-0.380755\pi\) | ||||
0.365918 | + | 0.930647i | \(0.380755\pi\) | |||||||
\(230\) | 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 | \(-0.380300\pi\) | ||||
0.367248 | + | 0.930123i | \(0.380300\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4174.59 | −1.11580 | −0.557902 | − | 0.829907i | \(-0.688394\pi\) | ||||
−0.557902 | + | 0.829907i | \(0.688394\pi\) | |||||||
\(242\) | 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 | \(-0.309892\pi\) | ||||
0.562365 | + | 0.826889i | \(0.309892\pi\) | |||||||
\(258\) | 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 | \(-0.374239\pi\) | ||||
0.384891 | + | 0.922962i | \(0.374239\pi\) | |||||||
\(264\) | 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 | \(-0.528862\pi\) | ||||
−0.0905483 | + | 0.995892i | \(0.528862\pi\) | |||||||
\(270\) | 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 | \(-0.362161\pi\) | ||||
0.419626 | + | 0.907697i | \(0.362161\pi\) | |||||||
\(294\) | 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 | \(-0.647648\pi\) | ||||
−0.447393 | + | 0.894337i | \(0.647648\pi\) | |||||||
\(314\) | 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 | \(-0.684906\pi\) | ||||
−0.548777 | + | 0.835969i | \(0.684906\pi\) | |||||||
\(332\) | 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 | \(-0.654857\pi\) | ||||
−0.467532 | + | 0.883976i | \(0.654857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5487.93 | −0.841726 | −0.420863 | − | 0.907124i | \(-0.638273\pi\) | ||||
−0.420863 | + | 0.907124i | \(0.638273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1674.47 | 0.254634 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6880.15 | 1.03738 | 0.518688 | − | 0.854964i | \(-0.326421\pi\) | ||||
0.518688 | + | 0.854964i | \(0.326421\pi\) | |||||||
\(354\) | 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 | \(-0.593487\pi\) | ||||
−0.289495 | + | 0.957180i | \(0.593487\pi\) | |||||||
\(360\) | 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 | \(-0.528278\pi\) | ||||
−0.0887225 | + | 0.996056i | \(0.528278\pi\) | |||||||
\(380\) | 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 | \(-0.240796\pi\) | ||||
0.727254 | + | 0.686368i | \(0.240796\pi\) | |||||||
\(398\) | 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 | \(-0.595614\pi\) | ||||
−0.295885 | + | 0.955224i | \(0.595614\pi\) | |||||||
\(410\) | 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 | \(-0.406276\pi\) | ||||
0.290206 | + | 0.956964i | \(0.406276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6314.17 | 0.700785 | 0.350392 | − | 0.936603i | \(-0.386048\pi\) | ||||
0.350392 | + | 0.936603i | \(0.386048\pi\) | |||||||
\(434\) | 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 | \(-0.654616\pi\) | ||||
−0.466862 | + | 0.884330i | \(0.654616\pi\) | |||||||
\(444\) | 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 | \(-0.238033\pi\) | ||||
0.733184 | + | 0.680030i | \(0.238033\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9971.00 | 1.00085 | 0.500423 | − | 0.865781i | \(-0.333178\pi\) | ||||
0.500423 | + | 0.865781i | \(0.333178\pi\) | |||||||
\(464\) | 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 | \(-0.716817\pi\) | ||||
−0.629687 | + | 0.776849i | \(0.716817\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4430.59 | 0.409730 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8693.29 | −0.799028 | −0.399514 | − | 0.916727i | \(-0.630821\pi\) | ||||
−0.399514 | + | 0.916727i | \(0.630821\pi\) | |||||||
\(492\) | 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 | \(-0.442317\pi\) | ||||
0.180228 | + | 0.983625i | \(0.442317\pi\) | |||||||
\(500\) | 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 | \(-0.368220\pi\) | ||||
0.402275 | + | 0.915519i | \(0.368220\pi\) | |||||||
\(510\) | 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 | \(-0.283237\pi\) | ||||
0.629555 | + | 0.776956i | \(0.283237\pi\) | |||||||
\(522\) | 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 | \(-0.575182\pi\) | ||||
−0.234000 | + | 0.972237i | \(0.575182\pi\) | |||||||
\(548\) | 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 | \(-0.300261\pi\) | ||||
0.587122 | + | 0.809498i | \(0.300261\pi\) | |||||||
\(572\) | 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 | \(-0.697448\pi\) | ||||
−0.581279 | + | 0.813704i | \(0.697448\pi\) | |||||||
\(578\) | 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 | \(-0.815580\pi\) | ||||
−0.836807 | + | 0.547499i | \(0.815580\pi\) | |||||||
\(594\) | 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 | \(-0.491082\pi\) | ||||
0.0280122 | + | 0.999608i | \(0.491082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14674.7 | −0.995996 | −0.497998 | − | 0.867178i | \(-0.665931\pi\) | ||||
−0.497998 | + | 0.867178i | \(0.665931\pi\) | |||||||
\(602\) | 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 | \(-0.193660\pi\) | ||||
0.820563 | + | 0.571556i | \(0.193660\pi\) | |||||||
\(632\) | 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 | \(-0.634794\pi\) | ||||
−0.410926 | + | 0.911669i | \(0.634794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6306.61 | 0.371102 | 0.185551 | − | 0.982635i | \(-0.440593\pi\) | ||||
0.185551 | + | 0.982635i | \(0.440593\pi\) | |||||||
\(662\) | 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 | \(-0.843945\pi\) | ||||
−0.882209 | + | 0.470858i | \(0.843945\pi\) | |||||||
\(678\) | 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 | \(-0.201843\pi\) | ||||
0.805601 | + | 0.592458i | \(0.201843\pi\) | |||||||
\(684\) | 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 | \(-0.575238\pi\) | ||||
−0.234172 | + | 0.972195i | \(0.575238\pi\) | |||||||
\(734\) | 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 | \(-0.349552\pi\) | ||||
0.455245 | + | 0.890366i | \(0.349552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2326.72 | −0.115350 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14742.4 | 0.727921 | 0.363960 | − | 0.931414i | \(-0.381424\pi\) | ||||
0.363960 | + | 0.931414i | \(0.381424\pi\) | |||||||
\(744\) | 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 | \(-0.256947\pi\) | ||||
0.691507 | + | 0.722370i | \(0.256947\pi\) | |||||||
\(752\) | 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 | \(-0.108251\pi\) | ||||
0.942728 | + | 0.333564i | \(0.108251\pi\) | |||||||
\(762\) | 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 | \(-0.420203\pi\) | ||||
0.248073 | + | 0.968741i | \(0.420203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13901.7 | 0.649363 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25922.2 | 1.20615 | 0.603077 | − | 0.797683i | \(-0.293941\pi\) | ||||
0.603077 | + | 0.797683i | \(0.293941\pi\) | |||||||
\(774\) | 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 | \(-0.544535\pi\) | ||||
−0.139454 | + | 0.990228i | \(0.544535\pi\) | |||||||
\(798\) | 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 | \(-0.813897\pi\) | ||||
−0.833901 | + | 0.551915i | \(0.813897\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38487.8 | 1.62421 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30916.3 | −1.29996 | −0.649978 | − | 0.759953i | \(-0.725222\pi\) | ||||
−0.649978 | + | 0.759953i | \(0.725222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2543.33 | −0.106554 | −0.0532771 | − | 0.998580i | \(-0.516967\pi\) | ||||
−0.0532771 | + | 0.998580i | \(0.516967\pi\) | |||||||
\(830\) | 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 | \(-0.181023\pi\) | ||||
0.842601 | + | 0.538538i | \(0.181023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2133.76 | −0.0853485 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11854.3 | −0.472504 | −0.236252 | − | 0.971692i | \(-0.575919\pi\) | ||||
−0.236252 | + | 0.971692i | \(0.575919\pi\) | |||||||
\(858\) | 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 | \(-0.140908\pi\) | ||||
0.903609 | + | 0.428358i | \(0.140908\pi\) | |||||||
\(864\) | 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 | \(-0.186770\pi\) | ||||
0.832742 | + | 0.553661i | \(0.186770\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40645.1 | 1.54906 | 0.774528 | − | 0.632540i | \(-0.217988\pi\) | ||||
0.774528 | + | 0.632540i | \(0.217988\pi\) | |||||||
\(884\) | 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 | \(-0.119843\pi\) | ||||
0.929958 | + | 0.367666i | \(0.119843\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7047.38 | −0.257147 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28738.3 | 1.04516 | 0.522582 | − | 0.852589i | \(-0.324969\pi\) | ||||
0.522582 | + | 0.852589i | \(0.324969\pi\) | |||||||
\(912\) | 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 | \(-0.940311\pi\) | ||||
−0.982470 | + | 0.186420i | \(0.940311\pi\) | |||||||
\(920\) | 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 | \(-0.218754\pi\) | ||||
0.773002 | + | 0.634403i | \(0.218754\pi\) | |||||||
\(930\) | 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 | \(-0.290476\pi\) | ||||
0.611724 | + | 0.791071i | \(0.290476\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14864.7 | −0.516605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31784.8 | −1.10112 | −0.550560 | − | 0.834795i | \(-0.685586\pi\) | ||||
−0.550560 | + | 0.834795i | \(0.685586\pi\) | |||||||
\(942\) | 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 | \(-0.0789554\pi\) | ||||
0.969394 | + | 0.245510i | \(0.0789554\pi\) | |||||||
\(948\) | 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 | \(-0.564009\pi\) | ||||
−0.199737 | + | 0.979850i | \(0.564009\pi\) | |||||||
\(968\) | 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 | \(-0.276046\pi\) | ||||
0.646946 | + | 0.762536i | \(0.276046\pi\) | |||||||
\(992\) | 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 | \(-0.515144\pi\) | ||||
−0.0475587 | + | 0.998868i | \(0.515144\pi\) | |||||||
\(998\) | 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 | 1176.4.a.bd.1.4 | 4 | ||
4.3 | odd | 2 | 2352.4.a.cm.1.4 | 4 | |||
7.2 | even | 3 | 168.4.q.f.25.1 | ✓ | 8 | ||
7.4 | even | 3 | 168.4.q.f.121.1 | yes | 8 | ||
7.6 | odd | 2 | 1176.4.a.ba.1.1 | 4 | |||
21.2 | odd | 6 | 504.4.s.j.361.4 | 8 | |||
21.11 | odd | 6 | 504.4.s.j.289.4 | 8 | |||
28.11 | odd | 6 | 336.4.q.m.289.1 | 8 | |||
28.23 | odd | 6 | 336.4.q.m.193.1 | 8 | |||
28.27 | even | 2 | 2352.4.a.cp.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.1 | ✓ | 8 | 7.2 | even | 3 | ||
168.4.q.f.121.1 | yes | 8 | 7.4 | even | 3 | ||
336.4.q.m.193.1 | 8 | 28.23 | odd | 6 | |||
336.4.q.m.289.1 | 8 | 28.11 | odd | 6 | |||
504.4.s.j.289.4 | 8 | 21.11 | odd | 6 | |||
504.4.s.j.361.4 | 8 | 21.2 | odd | 6 | |||
1176.4.a.ba.1.1 | 4 | 7.6 | odd | 2 | |||
1176.4.a.bd.1.4 | 4 | 1.1 | even | 1 | trivial | ||
2352.4.a.cm.1.4 | 4 | 4.3 | odd | 2 | |||
2352.4.a.cp.1.1 | 4 | 28.27 | even | 2 |