Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,4,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1815.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(107.088466660\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.8328 | −1.44884 | −0.724418 | − | 0.689361i | \(-0.757891\pi\) | ||||
−0.724418 | + | 0.689361i | \(0.757891\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −24.0000 | −0.577350 | ||||||||
\(13\) | −26.8328 | −0.572468 | −0.286234 | − | 0.958160i | \(-0.592403\pi\) | ||||
−0.286234 | + | 0.958160i | \(0.592403\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | 53.6656 | 0.765637 | 0.382818 | − | 0.923824i | \(-0.374953\pi\) | ||||
0.382818 | + | 0.923824i | \(0.374953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 80.4984 | 0.971979 | 0.485990 | − | 0.873965i | \(-0.338459\pi\) | ||||
0.485990 | + | 0.873965i | \(0.338459\pi\) | |||||||
\(20\) | 40.0000 | 0.447214 | ||||||||
\(21\) | −80.4984 | −0.836486 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 214.663 | 1.44884 | ||||||||
\(29\) | 295.161 | 1.89000 | 0.945000 | − | 0.327069i | \(-0.106061\pi\) | ||||
0.945000 | + | 0.327069i | \(0.106061\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.0000 | −0.115874 | −0.0579372 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579372 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 134.164 | 0.647939 | ||||||||
\(36\) | −72.0000 | −0.333333 | ||||||||
\(37\) | 214.000 | 0.950848 | 0.475424 | − | 0.879757i | \(-0.342295\pi\) | ||||
0.475424 | + | 0.879757i | \(0.342295\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −80.4984 | −0.330515 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 26.8328 | 0.102209 | 0.0511047 | − | 0.998693i | \(-0.483726\pi\) | ||||
0.0511047 | + | 0.998693i | \(0.483726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −241.495 | −0.856458 | −0.428229 | − | 0.903670i | \(-0.640862\pi\) | ||||
−0.428229 | + | 0.903670i | \(0.640862\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −264.000 | −0.819327 | −0.409663 | − | 0.912237i | \(-0.634354\pi\) | ||||
−0.409663 | + | 0.912237i | \(0.634354\pi\) | |||||||
\(48\) | 192.000 | 0.577350 | ||||||||
\(49\) | 377.000 | 1.09913 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 160.997 | 0.442041 | ||||||||
\(52\) | 214.663 | 0.572468 | ||||||||
\(53\) | 78.0000 | 0.202153 | 0.101077 | − | 0.994879i | \(-0.467771\pi\) | ||||
0.101077 | + | 0.994879i | \(0.467771\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 241.495 | 0.561173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 480.000 | 1.05916 | 0.529582 | − | 0.848259i | \(-0.322349\pi\) | ||||
0.529582 | + | 0.848259i | \(0.322349\pi\) | |||||||
\(60\) | 120.000 | 0.258199 | ||||||||
\(61\) | −107.331 | −0.225285 | −0.112642 | − | 0.993636i | \(-0.535931\pi\) | ||||
−0.112642 | + | 0.993636i | \(0.535931\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −241.495 | −0.482945 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 134.164 | 0.256015 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −524.000 | −0.955474 | −0.477737 | − | 0.878503i | \(-0.658543\pi\) | ||||
−0.477737 | + | 0.878503i | \(0.658543\pi\) | |||||||
\(68\) | −429.325 | −0.765637 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 492.000 | 0.822390 | 0.411195 | − | 0.911548i | \(-0.365112\pi\) | ||||
0.411195 | + | 0.911548i | \(0.365112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −939.149 | −1.50574 | −0.752870 | − | 0.658169i | \(-0.771331\pi\) | ||||
−0.752870 | + | 0.658169i | \(0.771331\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | −643.988 | −0.971979 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 295.161 | 0.420357 | 0.210179 | − | 0.977663i | \(-0.432595\pi\) | ||||
0.210179 | + | 0.977663i | \(0.432595\pi\) | |||||||
\(80\) | −320.000 | −0.447214 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 590.322 | 0.780678 | 0.390339 | − | 0.920671i | \(-0.372358\pi\) | ||||
0.390339 | + | 0.920671i | \(0.372358\pi\) | |||||||
\(84\) | 643.988 | 0.836486 | ||||||||
\(85\) | −268.328 | −0.342403 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 885.483 | 1.09119 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1206.00 | −1.43636 | −0.718178 | − | 0.695859i | \(-0.755024\pi\) | ||||
−0.718178 | + | 0.695859i | \(0.755024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 720.000 | 0.829412 | ||||||||
\(92\) | 576.000 | 0.652741 | ||||||||
\(93\) | −60.0000 | −0.0669001 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −402.492 | −0.434682 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1186.00 | −1.24144 | −0.620722 | − | 0.784031i | \(-0.713160\pi\) | ||||
−0.620722 | + | 0.784031i | \(0.713160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −200.000 | −0.200000 | ||||||||
\(101\) | 456.158 | 0.449400 | 0.224700 | − | 0.974428i | \(-0.427860\pi\) | ||||
0.224700 | + | 0.974428i | \(0.427860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 128.000 | 0.122449 | 0.0612243 | − | 0.998124i | \(-0.480499\pi\) | ||||
0.0612243 | + | 0.998124i | \(0.480499\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 402.492 | 0.374088 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −53.6656 | −0.0484865 | −0.0242432 | − | 0.999706i | \(-0.507718\pi\) | ||||
−0.0242432 | + | 0.999706i | \(0.507718\pi\) | |||||||
\(108\) | −216.000 | −0.192450 | ||||||||
\(109\) | 321.994 | 0.282949 | 0.141474 | − | 0.989942i | \(-0.454816\pi\) | ||||
0.141474 | + | 0.989942i | \(0.454816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 642.000 | 0.548972 | ||||||||
\(112\) | −1717.30 | −1.44884 | ||||||||
\(113\) | −762.000 | −0.634362 | −0.317181 | − | 0.948365i | \(-0.602736\pi\) | ||||
−0.317181 | + | 0.948365i | \(0.602736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 360.000 | 0.291915 | ||||||||
\(116\) | −2361.29 | −1.89000 | ||||||||
\(117\) | −241.495 | −0.190823 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1440.00 | −1.10928 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 80.4984 | 0.0590106 | ||||||||
\(124\) | 160.000 | 0.115874 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2602.78 | −1.81858 | −0.909290 | − | 0.416163i | \(-0.863375\pi\) | ||||
−0.909290 | + | 0.416163i | \(0.863375\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −724.486 | −0.494476 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2039.29 | 1.36011 | 0.680053 | − | 0.733163i | \(-0.261957\pi\) | ||||
0.680053 | + | 0.733163i | \(0.261957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2160.00 | −1.40824 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −786.000 | −0.490164 | −0.245082 | − | 0.969502i | \(-0.578815\pi\) | ||||
−0.245082 | + | 0.969502i | \(0.578815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2173.46 | −1.32626 | −0.663131 | − | 0.748504i | \(-0.730773\pi\) | ||||
−0.663131 | + | 0.748504i | \(0.730773\pi\) | |||||||
\(140\) | −1073.31 | −0.647939 | ||||||||
\(141\) | −792.000 | −0.473039 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 576.000 | 0.333333 | ||||||||
\(145\) | −1475.80 | −0.845234 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1131.00 | 0.634580 | ||||||||
\(148\) | −1712.00 | −0.950848 | ||||||||
\(149\) | 2119.79 | 1.16550 | 0.582752 | − | 0.812650i | \(-0.301976\pi\) | ||||
0.582752 | + | 0.812650i | \(0.301976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3515.10 | 1.89440 | 0.947201 | − | 0.320641i | \(-0.103898\pi\) | ||||
0.947201 | + | 0.320641i | \(0.103898\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 482.991 | 0.255212 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 100.000 | 0.0518206 | ||||||||
\(156\) | 643.988 | 0.330515 | ||||||||
\(157\) | −686.000 | −0.348718 | −0.174359 | − | 0.984682i | \(-0.555785\pi\) | ||||
−0.174359 | + | 0.984682i | \(0.555785\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 234.000 | 0.116713 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1931.96 | 0.945714 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −988.000 | −0.474762 | −0.237381 | − | 0.971417i | \(-0.576289\pi\) | ||||
−0.237381 | + | 0.971417i | \(0.576289\pi\) | |||||||
\(164\) | −214.663 | −0.102209 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3327.27 | 1.54175 | 0.770874 | − | 0.636988i | \(-0.219820\pi\) | ||||
0.770874 | + | 0.636988i | \(0.219820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1477.00 | −0.672280 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 724.486 | 0.323993 | ||||||||
\(172\) | 1931.96 | 0.856458 | ||||||||
\(173\) | −3219.94 | −1.41507 | −0.707536 | − | 0.706678i | \(-0.750193\pi\) | ||||
−0.707536 | + | 0.706678i | \(0.750193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −670.820 | −0.289767 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1440.00 | 0.611509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3336.00 | −1.39299 | −0.696493 | − | 0.717564i | \(-0.745257\pi\) | ||||
−0.696493 | + | 0.717564i | \(0.745257\pi\) | |||||||
\(180\) | 360.000 | 0.149071 | ||||||||
\(181\) | −3490.00 | −1.43320 | −0.716601 | − | 0.697483i | \(-0.754303\pi\) | ||||
−0.716601 | + | 0.697483i | \(0.754303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −321.994 | −0.130068 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1070.00 | −0.425232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2112.00 | 0.819327 | ||||||||
\(189\) | −724.486 | −0.278829 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2820.00 | 1.06831 | 0.534157 | − | 0.845385i | \(-0.320629\pi\) | ||||
0.534157 | + | 0.845385i | \(0.320629\pi\) | |||||||
\(192\) | −1536.00 | −0.577350 | ||||||||
\(193\) | 4373.75 | 1.63124 | 0.815620 | − | 0.578588i | \(-0.196396\pi\) | ||||
0.815620 | + | 0.578588i | \(0.196396\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 402.492 | 0.147811 | ||||||||
\(196\) | −3016.00 | −1.09913 | ||||||||
\(197\) | −3112.61 | −1.12571 | −0.562853 | − | 0.826557i | \(-0.690296\pi\) | ||||
−0.562853 | + | 0.826557i | \(0.690296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5060.00 | −1.80248 | −0.901241 | − | 0.433318i | \(-0.857343\pi\) | ||||
−0.901241 | + | 0.433318i | \(0.857343\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1572.00 | −0.551643 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7920.00 | −2.73830 | ||||||||
\(204\) | −1287.98 | −0.442041 | ||||||||
\(205\) | −134.164 | −0.0457094 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −648.000 | −0.217580 | ||||||||
\(208\) | −1717.30 | −0.572468 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3085.77 | 1.00679 | 0.503397 | − | 0.864055i | \(-0.332083\pi\) | ||||
0.503397 | + | 0.864055i | \(0.332083\pi\) | |||||||
\(212\) | −624.000 | −0.202153 | ||||||||
\(213\) | 1476.00 | 0.474807 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1207.48 | 0.383020 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 536.656 | 0.167883 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2817.45 | −0.869339 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1440.00 | −0.438303 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5312.00 | 1.59515 | 0.797574 | − | 0.603222i | \(-0.206117\pi\) | ||||
0.797574 | + | 0.603222i | \(0.206117\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −912.316 | −0.266751 | −0.133376 | − | 0.991066i | \(-0.542582\pi\) | ||||
−0.133376 | + | 0.991066i | \(0.542582\pi\) | |||||||
\(228\) | −1931.96 | −0.561173 | ||||||||
\(229\) | −5330.00 | −1.53806 | −0.769031 | − | 0.639211i | \(-0.779261\pi\) | ||||
−0.769031 | + | 0.639211i | \(0.779261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6815.54 | −1.91631 | −0.958156 | − | 0.286248i | \(-0.907592\pi\) | ||||
−0.958156 | + | 0.286248i | \(0.907592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1320.00 | 0.366414 | ||||||||
\(236\) | −3840.00 | −1.05916 | ||||||||
\(237\) | 885.483 | 0.242693 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5956.89 | 1.61221 | 0.806106 | − | 0.591771i | \(-0.201571\pi\) | ||||
0.806106 | + | 0.591771i | \(0.201571\pi\) | |||||||
\(240\) | −960.000 | −0.258199 | ||||||||
\(241\) | 1180.64 | 0.315568 | 0.157784 | − | 0.987474i | \(-0.449565\pi\) | ||||
0.157784 | + | 0.987474i | \(0.449565\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 858.650 | 0.225285 | ||||||||
\(245\) | −1885.00 | −0.491544 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2160.00 | −0.556427 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1770.97 | 0.450724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3312.00 | −0.832875 | −0.416437 | − | 0.909164i | \(-0.636722\pi\) | ||||
−0.416437 | + | 0.909164i | \(0.636722\pi\) | |||||||
\(252\) | 1931.96 | 0.482945 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −804.984 | −0.197687 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 4266.00 | 1.03543 | 0.517716 | − | 0.855553i | \(-0.326783\pi\) | ||||
0.517716 | + | 0.855553i | \(0.326783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5742.22 | −1.37762 | ||||||||
\(260\) | −1073.31 | −0.256015 | ||||||||
\(261\) | 2656.45 | 0.630000 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2253.96 | −0.528460 | −0.264230 | − | 0.964460i | \(-0.585118\pi\) | ||||
−0.264230 | + | 0.964460i | \(0.585118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −390.000 | −0.0904057 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3618.00 | −0.829281 | ||||||||
\(268\) | 4192.00 | 0.955474 | ||||||||
\(269\) | −1770.00 | −0.401185 | −0.200593 | − | 0.979675i | \(-0.564287\pi\) | ||||
−0.200593 | + | 0.979675i | \(0.564287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1422.14 | 0.318778 | 0.159389 | − | 0.987216i | \(-0.449048\pi\) | ||||
0.159389 | + | 0.987216i | \(0.449048\pi\) | |||||||
\(272\) | 3434.60 | 0.765637 | ||||||||
\(273\) | 2160.00 | 0.478861 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1728.00 | 0.376860 | ||||||||
\(277\) | 5017.74 | 1.08840 | 0.544200 | − | 0.838956i | \(-0.316833\pi\) | ||||
0.544200 | + | 0.838956i | \(0.316833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −180.000 | −0.0386248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1207.48 | 0.256342 | 0.128171 | − | 0.991752i | \(-0.459089\pi\) | ||||
0.128171 | + | 0.991752i | \(0.459089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6144.71 | −1.29069 | −0.645345 | − | 0.763891i | \(-0.723286\pi\) | ||||
−0.645345 | + | 0.763891i | \(0.723286\pi\) | |||||||
\(284\) | −3936.00 | −0.822390 | ||||||||
\(285\) | −1207.48 | −0.250964 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −720.000 | −0.148085 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2033.00 | −0.413800 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3558.00 | −0.716748 | ||||||||
\(292\) | 7513.19 | 1.50574 | ||||||||
\(293\) | 2253.96 | 0.449411 | 0.224706 | − | 0.974427i | \(-0.427858\pi\) | ||||
0.224706 | + | 0.974427i | \(0.427858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2400.00 | −0.473673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1931.96 | 0.373673 | ||||||||
\(300\) | −600.000 | −0.115470 | ||||||||
\(301\) | 6480.00 | 1.24087 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1368.47 | 0.259461 | ||||||||
\(304\) | 5151.90 | 0.971979 | ||||||||
\(305\) | 536.656 | 0.100750 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3676.10 | 0.683407 | 0.341703 | − | 0.939808i | \(-0.388996\pi\) | ||||
0.341703 | + | 0.939808i | \(0.388996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 384.000 | 0.0706958 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1428.00 | 0.260368 | 0.130184 | − | 0.991490i | \(-0.458443\pi\) | ||||
0.130184 | + | 0.991490i | \(0.458443\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 682.000 | 0.123159 | 0.0615797 | − | 0.998102i | \(-0.480386\pi\) | ||||
0.0615797 | + | 0.998102i | \(0.480386\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1207.48 | 0.215980 | ||||||||
\(316\) | −2361.29 | −0.420357 | ||||||||
\(317\) | 7866.00 | 1.39369 | 0.696843 | − | 0.717224i | \(-0.254587\pi\) | ||||
0.696843 | + | 0.717224i | \(0.254587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2560.00 | 0.447214 | ||||||||
\(321\) | −160.997 | −0.0279937 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4320.00 | 0.744183 | ||||||||
\(324\) | −648.000 | −0.111111 | ||||||||
\(325\) | −670.820 | −0.114494 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 965.981 | 0.163361 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7083.86 | 1.18707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3040.00 | −0.504814 | −0.252407 | − | 0.967621i | \(-0.581222\pi\) | ||||
−0.252407 | + | 0.967621i | \(0.581222\pi\) | |||||||
\(332\) | −4722.58 | −0.780678 | ||||||||
\(333\) | 1926.00 | 0.316949 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2620.00 | 0.427301 | ||||||||
\(336\) | −5151.90 | −0.836486 | ||||||||
\(337\) | −939.149 | −0.151806 | −0.0759031 | − | 0.997115i | \(-0.524184\pi\) | ||||
−0.0759031 | + | 0.997115i | \(0.524184\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2286.00 | −0.366249 | ||||||||
\(340\) | 2146.63 | 0.342403 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −912.316 | −0.143616 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1080.00 | 0.168537 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7352.19 | −1.13742 | −0.568712 | − | 0.822537i | \(-0.692558\pi\) | ||||
−0.568712 | + | 0.822537i | \(0.692558\pi\) | |||||||
\(348\) | −7083.86 | −1.09119 | ||||||||
\(349\) | −8371.84 | −1.28405 | −0.642026 | − | 0.766683i | \(-0.721906\pi\) | ||||
−0.642026 | + | 0.766683i | \(0.721906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −724.486 | −0.110172 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1062.00 | −0.160126 | −0.0800631 | − | 0.996790i | \(-0.525512\pi\) | ||||
−0.0800631 | + | 0.996790i | \(0.525512\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2460.00 | −0.367784 | ||||||||
\(356\) | 9648.00 | 1.43636 | ||||||||
\(357\) | −4320.00 | −0.640444 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11055.1 | −1.62526 | −0.812628 | − | 0.582783i | \(-0.801964\pi\) | ||||
−0.812628 | + | 0.582783i | \(0.801964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −379.000 | −0.0552559 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5760.00 | −0.829412 | ||||||||
\(365\) | 4695.74 | 0.673387 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12656.0 | 1.80010 | 0.900052 | − | 0.435783i | \(-0.143529\pi\) | ||||
0.900052 | + | 0.435783i | \(0.143529\pi\) | |||||||
\(368\) | −4608.00 | −0.652741 | ||||||||
\(369\) | 241.495 | 0.0340698 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2092.96 | −0.292887 | ||||||||
\(372\) | 480.000 | 0.0669001 | ||||||||
\(373\) | 4588.41 | 0.636941 | 0.318470 | − | 0.947933i | \(-0.396831\pi\) | ||||
0.318470 | + | 0.947933i | \(0.396831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7920.00 | −1.08196 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8840.00 | 1.19810 | 0.599051 | − | 0.800711i | \(-0.295545\pi\) | ||||
0.599051 | + | 0.800711i | \(0.295545\pi\) | |||||||
\(380\) | 3219.94 | 0.434682 | ||||||||
\(381\) | −7808.35 | −1.04996 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10968.0 | −1.46329 | −0.731643 | − | 0.681688i | \(-0.761246\pi\) | ||||
−0.731643 | + | 0.681688i | \(0.761246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2173.46 | −0.285486 | ||||||||
\(388\) | 9488.00 | 1.24144 | ||||||||
\(389\) | −4830.00 | −0.629539 | −0.314770 | − | 0.949168i | \(-0.601927\pi\) | ||||
−0.314770 | + | 0.949168i | \(0.601927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3863.93 | −0.499762 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6117.88 | 0.785258 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1475.80 | −0.187989 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13966.0 | −1.76558 | −0.882788 | − | 0.469772i | \(-0.844336\pi\) | ||||
−0.882788 | + | 0.469772i | \(0.844336\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6480.00 | −0.813047 | ||||||||
\(400\) | 1600.00 | 0.200000 | ||||||||
\(401\) | 750.000 | 0.0933995 | 0.0466998 | − | 0.998909i | \(-0.485130\pi\) | ||||
0.0466998 | + | 0.998909i | \(0.485130\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 536.656 | 0.0663344 | ||||||||
\(404\) | −3649.26 | −0.449400 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13792.1 | −1.66742 | −0.833709 | − | 0.552204i | \(-0.813787\pi\) | ||||
−0.833709 | + | 0.552204i | \(0.813787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2358.00 | −0.282997 | ||||||||
\(412\) | −1024.00 | −0.122449 | ||||||||
\(413\) | −12879.8 | −1.53455 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2951.61 | −0.349130 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6520.37 | −0.765717 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12144.0 | −1.41593 | −0.707963 | − | 0.706249i | \(-0.750386\pi\) | ||||
−0.707963 | + | 0.706249i | \(0.750386\pi\) | |||||||
\(420\) | −3219.94 | −0.374088 | ||||||||
\(421\) | 3490.00 | 0.404019 | 0.202010 | − | 0.979384i | \(-0.435253\pi\) | ||||
0.202010 | + | 0.979384i | \(0.435253\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2376.00 | −0.273109 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1341.64 | 0.153127 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2880.00 | 0.326400 | ||||||||
\(428\) | 429.325 | 0.0484865 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1985.63 | −0.221913 | −0.110956 | − | 0.993825i | \(-0.535391\pi\) | ||||
−0.110956 | + | 0.993825i | \(0.535391\pi\) | |||||||
\(432\) | 1728.00 | 0.192450 | ||||||||
\(433\) | 7742.00 | 0.859254 | 0.429627 | − | 0.903007i | \(-0.358645\pi\) | ||||
0.429627 | + | 0.903007i | \(0.358645\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4427.41 | −0.487996 | ||||||||
\(436\) | −2575.95 | −0.282949 | ||||||||
\(437\) | −5795.89 | −0.634451 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2602.78 | 0.282971 | 0.141485 | − | 0.989940i | \(-0.454812\pi\) | ||||
0.141485 | + | 0.989940i | \(0.454812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3393.00 | 0.366375 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6348.00 | 0.680818 | 0.340409 | − | 0.940277i | \(-0.389434\pi\) | ||||
0.340409 | + | 0.940277i | \(0.389434\pi\) | |||||||
\(444\) | −5136.00 | −0.548972 | ||||||||
\(445\) | 6030.00 | 0.642358 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6359.38 | 0.672904 | ||||||||
\(448\) | 13738.4 | 1.44884 | ||||||||
\(449\) | −17214.0 | −1.80931 | −0.904654 | − | 0.426148i | \(-0.859870\pi\) | ||||
−0.904654 | + | 0.426148i | \(0.859870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6096.00 | 0.634362 | ||||||||
\(453\) | 10545.3 | 1.09373 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3600.00 | −0.370924 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1583.14 | 0.162048 | 0.0810241 | − | 0.996712i | \(-0.474181\pi\) | ||||
0.0810241 | + | 0.996712i | \(0.474181\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1448.97 | 0.147347 | ||||||||
\(460\) | −2880.00 | −0.291915 | ||||||||
\(461\) | −12047.9 | −1.21720 | −0.608599 | − | 0.793478i | \(-0.708268\pi\) | ||||
−0.608599 | + | 0.793478i | \(0.708268\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14488.0 | −1.45424 | −0.727121 | − | 0.686509i | \(-0.759142\pi\) | ||||
−0.727121 | + | 0.686509i | \(0.759142\pi\) | |||||||
\(464\) | 18890.3 | 1.89000 | ||||||||
\(465\) | 300.000 | 0.0299186 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1596.00 | −0.158146 | −0.0790729 | − | 0.996869i | \(-0.525196\pi\) | ||||
−0.0790729 | + | 0.996869i | \(0.525196\pi\) | |||||||
\(468\) | 1931.96 | 0.190823 | ||||||||
\(469\) | 14060.4 | 1.38433 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2058.00 | −0.201333 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2012.46 | 0.194396 | ||||||||
\(476\) | 11520.0 | 1.10928 | ||||||||
\(477\) | 702.000 | 0.0673844 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19695.3 | 1.87871 | 0.939353 | − | 0.342951i | \(-0.111426\pi\) | ||||
0.939353 | + | 0.342951i | \(0.111426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5742.22 | −0.544330 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5795.89 | 0.546008 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5930.00 | 0.555191 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15464.0 | −1.43889 | −0.719446 | − | 0.694548i | \(-0.755604\pi\) | ||||
−0.719446 | + | 0.694548i | \(0.755604\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2964.00 | −0.274104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14114.1 | 1.29727 | 0.648634 | − | 0.761100i | \(-0.275341\pi\) | ||||
0.648634 | + | 0.761100i | \(0.275341\pi\) | |||||||
\(492\) | −643.988 | −0.0590106 | ||||||||
\(493\) | 15840.0 | 1.44705 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1280.00 | −0.115874 | ||||||||
\(497\) | −13201.7 | −1.19151 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4880.00 | −0.437793 | −0.218897 | − | 0.975748i | \(-0.570246\pi\) | ||||
−0.218897 | + | 0.975748i | \(0.570246\pi\) | |||||||
\(500\) | 1000.00 | 0.0894427 | ||||||||
\(501\) | 9981.81 | 0.890128 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14275.1 | 1.26539 | 0.632697 | − | 0.774399i | \(-0.281948\pi\) | ||||
0.632697 | + | 0.774399i | \(0.281948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2280.79 | −0.200978 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4431.00 | −0.388141 | ||||||||
\(508\) | 20822.3 | 1.81858 | ||||||||
\(509\) | −11610.0 | −1.01101 | −0.505505 | − | 0.862824i | \(-0.668694\pi\) | ||||
−0.505505 | + | 0.862824i | \(0.668694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25200.0 | 2.18157 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2173.46 | 0.187058 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −640.000 | −0.0547607 | ||||||||
\(516\) | 5795.89 | 0.494476 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9659.81 | −0.816992 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16170.0 | −1.35973 | −0.679866 | − | 0.733336i | \(-0.737962\pi\) | ||||
−0.679866 | + | 0.733336i | \(0.737962\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3568.76 | −0.298377 | −0.149189 | − | 0.988809i | \(-0.547666\pi\) | ||||
−0.149189 | + | 0.988809i | \(0.547666\pi\) | |||||||
\(524\) | −16314.4 | −1.36011 | ||||||||
\(525\) | −2012.46 | −0.167297 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1073.31 | −0.0887177 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4320.00 | 0.353055 | ||||||||
\(532\) | 17280.0 | 1.40824 | ||||||||
\(533\) | −720.000 | −0.0585116 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 268.328 | 0.0216838 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10008.0 | −0.804240 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1080.00 | 0.0860663 | ||||||||
\(541\) | −10518.5 | −0.835904 | −0.417952 | − | 0.908469i | \(-0.637252\pi\) | ||||
−0.417952 | + | 0.908469i | \(0.637252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10470.0 | −0.827460 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1609.97 | −0.126539 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4856.74 | −0.379633 | −0.189816 | − | 0.981820i | \(-0.560789\pi\) | ||||
−0.189816 | + | 0.981820i | \(0.560789\pi\) | |||||||
\(548\) | 6288.00 | 0.490164 | ||||||||
\(549\) | −965.981 | −0.0750949 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23760.0 | 1.83704 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7920.00 | −0.609028 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3210.00 | −0.245508 | ||||||||
\(556\) | 17387.7 | 1.32626 | ||||||||
\(557\) | −2307.62 | −0.175542 | −0.0877712 | − | 0.996141i | \(-0.527974\pi\) | ||||
−0.0877712 | + | 0.996141i | \(0.527974\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6480.00 | 0.490295 | ||||||||
\(560\) | 8586.50 | 0.647939 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3434.60 | −0.257107 | −0.128553 | − | 0.991703i | \(-0.541033\pi\) | ||||
−0.128553 | + | 0.991703i | \(0.541033\pi\) | |||||||
\(564\) | 6336.00 | 0.473039 | ||||||||
\(565\) | 3810.00 | 0.283695 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2173.46 | −0.160982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 885.483 | 0.0652397 | 0.0326198 | − | 0.999468i | \(-0.489615\pi\) | ||||
0.0326198 | + | 0.999468i | \(0.489615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 670.820 | 0.0491646 | 0.0245823 | − | 0.999698i | \(-0.492174\pi\) | ||||
0.0245823 | + | 0.999698i | \(0.492174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8460.00 | 0.616792 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1800.00 | −0.130548 | ||||||||
\(576\) | −4608.00 | −0.333333 | ||||||||
\(577\) | 8926.00 | 0.644011 | 0.322005 | − | 0.946738i | \(-0.395643\pi\) | ||||
0.322005 | + | 0.946738i | \(0.395643\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13121.2 | 0.941797 | ||||||||
\(580\) | 11806.4 | 0.845234 | ||||||||
\(581\) | −15840.0 | −1.13107 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1207.48 | 0.0853385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28236.0 | −1.98539 | −0.992695 | − | 0.120647i | \(-0.961503\pi\) | ||||
−0.992695 | + | 0.120647i | \(0.961503\pi\) | |||||||
\(588\) | −9048.00 | −0.634580 | ||||||||
\(589\) | −1609.97 | −0.112628 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9337.82 | −0.649927 | ||||||||
\(592\) | 13696.0 | 0.950848 | ||||||||
\(593\) | −12235.8 | −0.847323 | −0.423662 | − | 0.905821i | \(-0.639255\pi\) | ||||
−0.423662 | + | 0.905821i | \(0.639255\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7200.00 | 0.496086 | ||||||||
\(596\) | −16958.3 | −1.16550 | ||||||||
\(597\) | −15180.0 | −1.04066 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16884.0 | −1.15169 | −0.575844 | − | 0.817559i | \(-0.695327\pi\) | ||||
−0.575844 | + | 0.817559i | \(0.695327\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19480.6 | −1.32218 | −0.661091 | − | 0.750306i | \(-0.729906\pi\) | ||||
−0.661091 | + | 0.750306i | \(0.729906\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4716.00 | −0.318491 | ||||||||
\(604\) | −28120.8 | −1.89440 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11672.3 | 0.780499 | 0.390250 | − | 0.920709i | \(-0.372389\pi\) | ||||
0.390250 | + | 0.920709i | \(0.372389\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23760.0 | −1.58096 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7083.86 | 0.469038 | ||||||||
\(612\) | −3863.93 | −0.255212 | ||||||||
\(613\) | 7701.02 | 0.507408 | 0.253704 | − | 0.967282i | \(-0.418351\pi\) | ||||
0.253704 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −402.492 | −0.0263903 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10686.0 | 0.697248 | 0.348624 | − | 0.937263i | \(-0.386649\pi\) | ||||
0.348624 | + | 0.937263i | \(0.386649\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1744.00 | −0.113243 | −0.0566214 | − | 0.998396i | \(-0.518033\pi\) | ||||
−0.0566214 | + | 0.998396i | \(0.518033\pi\) | |||||||
\(620\) | −800.000 | −0.0518206 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32360.4 | 2.08105 | ||||||||
\(624\) | −5151.90 | −0.330515 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5488.00 | 0.348718 | ||||||||
\(629\) | 11484.4 | 0.728004 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5092.00 | 0.321251 | 0.160625 | − | 0.987015i | \(-0.448649\pi\) | ||||
0.160625 | + | 0.987015i | \(0.448649\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9257.32 | 0.581273 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13013.9 | 0.813294 | ||||||||
\(636\) | −1872.00 | −0.116713 | ||||||||
\(637\) | −10116.0 | −0.629214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4428.00 | 0.274130 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11970.0 | 0.737577 | 0.368788 | − | 0.929513i | \(-0.379773\pi\) | ||||
0.368788 | + | 0.929513i | \(0.379773\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17228.0 | 1.05662 | 0.528309 | − | 0.849052i | \(-0.322826\pi\) | ||||
0.528309 | + | 0.849052i | \(0.322826\pi\) | |||||||
\(644\) | −15455.7 | −0.945714 | ||||||||
\(645\) | 3622.43 | 0.221137 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20376.0 | 1.23812 | 0.619060 | − | 0.785344i | \(-0.287514\pi\) | ||||
0.619060 | + | 0.785344i | \(0.287514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1609.97 | 0.0969273 | ||||||||
\(652\) | 7904.00 | 0.474762 | ||||||||
\(653\) | −21882.0 | −1.31135 | −0.655673 | − | 0.755045i | \(-0.727615\pi\) | ||||
−0.655673 | + | 0.755045i | \(0.727615\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10196.5 | −0.608258 | ||||||||
\(656\) | 1717.30 | 0.102209 | ||||||||
\(657\) | −8452.34 | −0.501913 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5795.89 | 0.342604 | 0.171302 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171302 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20338.0 | 1.19676 | 0.598379 | − | 0.801213i | \(-0.295812\pi\) | ||||
0.598379 | + | 0.801213i | \(0.295812\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4320.00 | −0.253054 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10800.0 | 0.629784 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21251.6 | −1.23368 | ||||||||
\(668\) | −26618.2 | −1.54175 | ||||||||
\(669\) | 15936.0 | 0.920959 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8506.00 | −0.487195 | −0.243598 | − | 0.969876i | \(-0.578328\pi\) | ||||
−0.243598 | + | 0.969876i | \(0.578328\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 11816.0 | 0.672280 | ||||||||
\(677\) | 21090.6 | 1.19731 | 0.598654 | − | 0.801008i | \(-0.295703\pi\) | ||||
0.598654 | + | 0.801008i | \(0.295703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31823.7 | 1.79865 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2736.95 | −0.154009 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12108.0 | −0.678331 | −0.339165 | − | 0.940727i | \(-0.610145\pi\) | ||||
−0.339165 | + | 0.940727i | \(0.610145\pi\) | |||||||
\(684\) | −5795.89 | −0.323993 | ||||||||
\(685\) | 3930.00 | 0.219208 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15990.0 | −0.888001 | ||||||||
\(688\) | −15455.7 | −0.856458 | ||||||||
\(689\) | −2092.96 | −0.115726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13768.0 | −0.757973 | −0.378987 | − | 0.925402i | \(-0.623727\pi\) | ||||
−0.378987 | + | 0.925402i | \(0.623727\pi\) | |||||||
\(692\) | 25759.5 | 1.41507 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10867.3 | 0.593122 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1440.00 | 0.0782552 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20446.6 | −1.10638 | ||||||||
\(700\) | 5366.56 | 0.289767 | ||||||||
\(701\) | −21224.8 | −1.14358 | −0.571789 | − | 0.820401i | \(-0.693750\pi\) | ||||
−0.571789 | + | 0.820401i | \(0.693750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17226.7 | 0.924205 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3960.00 | 0.211549 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12240.0 | −0.651107 | ||||||||
\(708\) | −11520.0 | −0.611509 | ||||||||
\(709\) | 31246.0 | 1.65510 | 0.827552 | − | 0.561390i | \(-0.189733\pi\) | ||||
0.827552 | + | 0.561390i | \(0.189733\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2656.45 | 0.140119 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1440.00 | 0.0756359 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26688.0 | 1.39299 | ||||||||
\(717\) | 17870.7 | 0.930812 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11316.0 | −0.586948 | −0.293474 | − | 0.955967i | \(-0.594811\pi\) | ||||
−0.293474 | + | 0.955967i | \(0.594811\pi\) | |||||||
\(720\) | −2880.00 | −0.149071 | ||||||||
\(721\) | −3434.60 | −0.177408 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3541.93 | 0.182193 | ||||||||
\(724\) | 27920.0 | 1.43320 | ||||||||
\(725\) | 7379.02 | 0.378000 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9056.00 | −0.461992 | −0.230996 | − | 0.972955i | \(-0.574198\pi\) | ||||
−0.230996 | + | 0.972955i | \(0.574198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12960.0 | −0.655736 | ||||||||
\(732\) | 2575.95 | 0.130068 | ||||||||
\(733\) | −21546.8 | −1.08574 | −0.542870 | − | 0.839817i | \(-0.682662\pi\) | ||||
−0.542870 | + | 0.839817i | \(0.682662\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5655.00 | −0.283793 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7271.69 | −0.361967 | −0.180983 | − | 0.983486i | \(-0.557928\pi\) | ||||
−0.180983 | + | 0.983486i | \(0.557928\pi\) | |||||||
\(740\) | 8560.00 | 0.425232 | ||||||||
\(741\) | −6480.00 | −0.321253 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33970.3 | −1.67732 | −0.838662 | − | 0.544653i | \(-0.816661\pi\) | ||||
−0.838662 | + | 0.544653i | \(0.816661\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10599.0 | −0.521229 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5312.90 | 0.260226 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1440.00 | 0.0702489 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20932.0 | 1.01707 | 0.508535 | − | 0.861041i | \(-0.330187\pi\) | ||||
0.508535 | + | 0.861041i | \(0.330187\pi\) | |||||||
\(752\) | −16896.0 | −0.819327 | ||||||||
\(753\) | −9936.00 | −0.480861 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17575.5 | −0.847202 | ||||||||
\(756\) | 5795.89 | 0.278829 | ||||||||
\(757\) | 28474.0 | 1.36711 | 0.683557 | − | 0.729897i | \(-0.260432\pi\) | ||||
0.683557 | + | 0.729897i | \(0.260432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3032.11 | 0.144433 | 0.0722167 | − | 0.997389i | \(-0.476993\pi\) | ||||
0.0722167 | + | 0.997389i | \(0.476993\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8640.00 | −0.409946 | ||||||||
\(764\) | −22560.0 | −1.06831 | ||||||||
\(765\) | −2414.95 | −0.114134 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12879.8 | −0.606338 | ||||||||
\(768\) | 12288.0 | 0.577350 | ||||||||
\(769\) | 14221.4 | 0.666888 | 0.333444 | − | 0.942770i | \(-0.391789\pi\) | ||||
0.333444 | + | 0.942770i | \(0.391789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12798.0 | 0.597806 | ||||||||
\(772\) | −34990.0 | −1.63124 | ||||||||
\(773\) | −30258.0 | −1.40790 | −0.703949 | − | 0.710251i | \(-0.748581\pi\) | ||||
−0.703949 | + | 0.710251i | \(0.748581\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −500.000 | −0.0231749 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17226.7 | −0.795371 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2160.00 | 0.0993454 | ||||||||
\(780\) | −3219.94 | −0.147811 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7969.35 | 0.363731 | ||||||||
\(784\) | 24128.0 | 1.09913 | ||||||||
\(785\) | 3430.00 | 0.155952 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25142.3 | −1.13879 | −0.569395 | − | 0.822064i | \(-0.692823\pi\) | ||||
−0.569395 | + | 0.822064i | \(0.692823\pi\) | |||||||
\(788\) | 24900.9 | 1.12571 | ||||||||
\(789\) | −6761.87 | −0.305106 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20446.6 | 0.919087 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2880.00 | 0.128968 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1170.00 | −0.0521958 | ||||||||
\(796\) | 40480.0 | 1.80248 | ||||||||
\(797\) | 6954.00 | 0.309063 | 0.154532 | − | 0.987988i | \(-0.450613\pi\) | ||||
0.154532 | + | 0.987988i | \(0.450613\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14167.7 | −0.627307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10854.0 | −0.478786 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 12576.0 | 0.551643 | ||||||||
\(805\) | −9659.81 | −0.422936 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5310.00 | −0.231624 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25947.3 | 1.12764 | 0.563819 | − | 0.825898i | \(-0.309331\pi\) | ||||
0.563819 | + | 0.825898i | \(0.309331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5017.74 | 0.217258 | 0.108629 | − | 0.994082i | \(-0.465354\pi\) | ||||
0.108629 | + | 0.994082i | \(0.465354\pi\) | |||||||
\(812\) | 63360.0 | 2.73830 | ||||||||
\(813\) | 4266.42 | 0.184046 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4940.00 | 0.212320 | ||||||||
\(816\) | 10303.8 | 0.442041 | ||||||||
\(817\) | −19440.0 | −0.832460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6480.00 | 0.276471 | ||||||||
\(820\) | 1073.31 | 0.0457094 | ||||||||
\(821\) | −35660.8 | −1.51592 | −0.757960 | − | 0.652301i | \(-0.773804\pi\) | ||||
−0.757960 | + | 0.652301i | \(0.773804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20288.0 | 0.859289 | 0.429645 | − | 0.902998i | \(-0.358639\pi\) | ||||
0.429645 | + | 0.902998i | \(0.358639\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17548.7 | 0.737880 | 0.368940 | − | 0.929453i | \(-0.379721\pi\) | ||||
0.368940 | + | 0.929453i | \(0.379721\pi\) | |||||||
\(828\) | 5184.00 | 0.217580 | ||||||||
\(829\) | 9146.00 | 0.383177 | 0.191588 | − | 0.981475i | \(-0.438636\pi\) | ||||
0.191588 | + | 0.981475i | \(0.438636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15053.2 | 0.628388 | ||||||||
\(832\) | 13738.4 | 0.572468 | ||||||||
\(833\) | 20231.9 | 0.841531 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16636.3 | −0.689490 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −540.000 | −0.0223000 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9900.00 | 0.407373 | 0.203687 | − | 0.979036i | \(-0.434708\pi\) | ||||
0.203687 | + | 0.979036i | \(0.434708\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62731.0 | 2.57210 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3622.43 | 0.147999 | ||||||||
\(844\) | −24686.2 | −1.00679 | ||||||||
\(845\) | 7385.00 | 0.300653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4992.00 | 0.202153 | ||||||||
\(849\) | −18434.1 | −0.745180 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15408.0 | −0.620657 | ||||||||
\(852\) | −11808.0 | −0.474807 | ||||||||
\(853\) | 23264.1 | 0.933817 | 0.466909 | − | 0.884306i | \(-0.345368\pi\) | ||||
0.466909 | + | 0.884306i | \(0.345368\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3622.43 | −0.144894 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23988.5 | −0.956164 | −0.478082 | − | 0.878315i | \(-0.658668\pi\) | ||||
−0.478082 | + | 0.878315i | \(0.658668\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11104.0 | −0.441052 | −0.220526 | − | 0.975381i | \(-0.570777\pi\) | ||||
−0.220526 | + | 0.975381i | \(0.570777\pi\) | |||||||
\(860\) | −9659.81 | −0.383020 | ||||||||
\(861\) | −2160.00 | −0.0854966 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42192.0 | 1.66423 | 0.832116 | − | 0.554601i | \(-0.187129\pi\) | ||||
0.832116 | + | 0.554601i | \(0.187129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16099.7 | 0.632839 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6099.00 | −0.238908 | ||||||||
\(868\) | −4293.25 | −0.167883 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14060.4 | 0.546979 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10674.0 | −0.413815 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3354.10 | 0.129588 | ||||||||
\(876\) | 22539.6 | 0.869339 | ||||||||
\(877\) | −1744.13 | −0.0671553 | −0.0335776 | − | 0.999436i | \(-0.510690\pi\) | ||||
−0.0335776 | + | 0.999436i | \(0.510690\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6761.87 | 0.259468 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32142.0 | 1.22916 | 0.614581 | − | 0.788854i | \(-0.289325\pi\) | ||||
0.614581 | + | 0.788854i | \(0.289325\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20572.0 | 0.784035 | 0.392018 | − | 0.919958i | \(-0.371777\pi\) | ||||
0.392018 | + | 0.919958i | \(0.371777\pi\) | |||||||
\(884\) | 11520.0 | 0.438303 | ||||||||
\(885\) | −7200.00 | −0.273475 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30535.7 | 1.15591 | 0.577954 | − | 0.816070i | \(-0.303851\pi\) | ||||
0.577954 | + | 0.816070i | \(0.303851\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 69840.0 | 2.63482 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −42496.0 | −1.59515 | ||||||||
\(893\) | −21251.6 | −0.796369 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16680.0 | 0.622962 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5795.89 | 0.215740 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5903.22 | −0.219003 | ||||||||
\(900\) | −1800.00 | −0.0666667 | ||||||||
\(901\) | 4185.92 | 0.154776 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19440.0 | 0.716415 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17450.0 | 0.640948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32636.0 | 1.19477 | 0.597387 | − | 0.801953i | \(-0.296206\pi\) | ||||
0.597387 | + | 0.801953i | \(0.296206\pi\) | |||||||
\(908\) | 7298.53 | 0.266751 | ||||||||
\(909\) | 4105.42 | 0.149800 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37860.0 | −1.37690 | −0.688451 | − | 0.725283i | \(-0.741709\pi\) | ||||
−0.688451 | + | 0.725283i | \(0.741709\pi\) | |||||||
\(912\) | 15455.7 | 0.561173 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1609.97 | 0.0581682 | ||||||||
\(916\) | 42640.0 | 1.53806 | ||||||||
\(917\) | −54720.0 | −1.97057 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26859.6 | 0.964111 | 0.482056 | − | 0.876141i | \(-0.339890\pi\) | ||||
0.482056 | + | 0.876141i | \(0.339890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11028.3 | 0.394565 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13201.7 | −0.470792 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5350.00 | 0.190170 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1152.00 | 0.0408162 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38130.0 | −1.34661 | −0.673307 | − | 0.739363i | \(-0.735127\pi\) | ||||
−0.673307 | + | 0.739363i | \(0.735127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30347.9 | 1.06833 | ||||||||
\(932\) | 54524.3 | 1.91631 | ||||||||
\(933\) | 4284.00 | 0.150324 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2227.12 | −0.0776488 | −0.0388244 | − | 0.999246i | \(-0.512361\pi\) | ||||
−0.0388244 | + | 0.999246i | \(0.512361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2046.00 | 0.0711062 | ||||||||
\(940\) | −10560.0 | −0.366414 | ||||||||
\(941\) | −50204.2 | −1.73922 | −0.869612 | − | 0.493735i | \(-0.835631\pi\) | ||||
−0.869612 | + | 0.493735i | \(0.835631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1931.96 | −0.0667162 | ||||||||
\(944\) | 30720.0 | 1.05916 | ||||||||
\(945\) | 3622.43 | 0.124696 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −276.000 | −0.00947074 | −0.00473537 | − | 0.999989i | \(-0.501507\pi\) | ||||
−0.00473537 | + | 0.999989i | \(0.501507\pi\) | |||||||
\(948\) | −7083.86 | −0.242693 | ||||||||
\(949\) | 25200.0 | 0.861988 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23598.0 | 0.804645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42073.9 | −1.43012 | −0.715061 | − | 0.699062i | \(-0.753601\pi\) | ||||
−0.715061 | + | 0.699062i | \(0.753601\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14100.0 | −0.477765 | ||||||||
\(956\) | −47655.1 | −1.61221 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21090.6 | 0.710168 | ||||||||
\(960\) | 7680.00 | 0.258199 | ||||||||
\(961\) | −29391.0 | −0.986573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −482.991 | −0.0161622 | ||||||||
\(964\) | −9445.15 | −0.315568 | ||||||||
\(965\) | −21868.7 | −0.729513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18809.8 | −0.625525 | −0.312762 | − | 0.949831i | \(-0.601254\pi\) | ||||
−0.312762 | + | 0.949831i | \(0.601254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12960.0 | 0.429654 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5400.00 | 0.178470 | 0.0892349 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892349 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(972\) | −1944.00 | −0.0641500 | ||||||||
\(973\) | 58320.0 | 1.92153 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2012.46 | −0.0661029 | ||||||||
\(976\) | −6869.20 | −0.225285 | ||||||||
\(977\) | 54486.0 | 1.78420 | 0.892099 | − | 0.451840i | \(-0.149232\pi\) | ||||
0.892099 | + | 0.451840i | \(0.149232\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 15080.0 | 0.491544 | ||||||||
\(981\) | 2897.94 | 0.0943162 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4872.00 | −0.158080 | −0.0790400 | − | 0.996871i | \(-0.525185\pi\) | ||||
−0.0790400 | + | 0.996871i | \(0.525185\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15563.0 | 0.503431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21251.6 | 0.685355 | ||||||||
\(988\) | 17280.0 | 0.556427 | ||||||||
\(989\) | 17387.7 | 0.559045 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5020.00 | 0.160914 | 0.0804569 | − | 0.996758i | \(-0.474362\pi\) | ||||
0.0804569 | + | 0.996758i | \(0.474362\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9120.00 | −0.291455 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25300.0 | 0.806094 | ||||||||
\(996\) | −14167.7 | −0.450724 | ||||||||
\(997\) | 26484.0 | 0.841280 | 0.420640 | − | 0.907228i | \(-0.361806\pi\) | ||||
0.420640 | + | 0.907228i | \(0.361806\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5778.00 | 0.182991 |
(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 | 1815.4.a.j.1.1 | ✓ | 2 | |
11.10 | odd | 2 | inner | 1815.4.a.j.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.4.a.j.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1815.4.a.j.1.2 | yes | 2 | 11.10 | odd | 2 | inner |