Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.358541904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 111x^{2} + 756 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.69991\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.69991 | 0.477281 | 0.238641 | − | 0.971108i | \(-0.423298\pi\) | ||||
0.238641 | + | 0.971108i | \(0.423298\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −24.7105 | −0.772202 | ||||||||
\(5\) | −87.9366 | −1.57306 | −0.786528 | − | 0.617554i | \(-0.788124\pi\) | ||||
−0.786528 | + | 0.617554i | \(0.788124\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −153.113 | −0.845839 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −237.421 | −0.750791 | ||||||||
\(11\) | 41.6592 | 0.103808 | 0.0519038 | − | 0.998652i | \(-0.483471\pi\) | ||||
0.0519038 | + | 0.998652i | \(0.483471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −989.368 | −1.62368 | −0.811838 | − | 0.583883i | \(-0.801533\pi\) | ||||
−0.811838 | + | 0.583883i | \(0.801533\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 377.343 | 0.368499 | ||||||||
\(17\) | −2121.25 | −1.78021 | −0.890103 | − | 0.455760i | \(-0.849368\pi\) | ||||
−0.890103 | + | 0.455760i | \(0.849368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −928.632 | −0.590146 | −0.295073 | − | 0.955475i | \(-0.595344\pi\) | ||||
−0.295073 | + | 0.955475i | \(0.595344\pi\) | |||||||
\(20\) | 2172.95 | 1.21472 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 112.476 | 0.0495455 | ||||||||
\(23\) | −4392.21 | −1.73126 | −0.865632 | − | 0.500680i | \(-0.833083\pi\) | ||||
−0.865632 | + | 0.500680i | \(0.833083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4607.84 | 1.47451 | ||||||||
\(26\) | −2671.21 | −0.774950 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3893.93 | −0.859793 | −0.429896 | − | 0.902878i | \(-0.641450\pi\) | ||||
−0.429896 | + | 0.902878i | \(0.641450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1134.10 | −0.211957 | −0.105979 | − | 0.994368i | \(-0.533798\pi\) | ||||
−0.105979 | + | 0.994368i | \(0.533798\pi\) | |||||||
\(32\) | 5918.42 | 1.02172 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5727.20 | −0.849659 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10056.5 | −1.20766 | −0.603828 | − | 0.797115i | \(-0.706359\pi\) | ||||
−0.603828 | + | 0.797115i | \(0.706359\pi\) | |||||||
\(38\) | −2507.23 | −0.281666 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13464.3 | 1.33055 | ||||||||
\(41\) | −131.039 | −0.0121742 | −0.00608711 | − | 0.999981i | \(-0.501938\pi\) | ||||
−0.00608711 | + | 0.999981i | \(0.501938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3534.94 | −0.291549 | −0.145774 | − | 0.989318i | \(-0.546567\pi\) | ||||
−0.145774 | + | 0.989318i | \(0.546567\pi\) | |||||||
\(44\) | −1029.42 | −0.0801605 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11858.6 | −0.826301 | ||||||||
\(47\) | 16072.6 | 1.06131 | 0.530653 | − | 0.847589i | \(-0.321947\pi\) | ||||
0.530653 | + | 0.847589i | \(0.321947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 12440.8 | 0.703755 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 24447.7 | 1.25381 | ||||||||
\(53\) | 2959.15 | 0.144703 | 0.0723515 | − | 0.997379i | \(-0.476950\pi\) | ||||
0.0723515 | + | 0.997379i | \(0.476950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3663.37 | −0.163295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10513.3 | −0.410363 | ||||||||
\(59\) | 18324.9 | 0.685347 | 0.342674 | − | 0.939455i | \(-0.388667\pi\) | ||||
0.342674 | + | 0.939455i | \(0.388667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14896.5 | −0.512578 | −0.256289 | − | 0.966600i | \(-0.582500\pi\) | ||||
−0.256289 | + | 0.966600i | \(0.582500\pi\) | |||||||
\(62\) | −3061.98 | −0.101163 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3904.23 | 0.119148 | ||||||||
\(65\) | 87001.6 | 2.55413 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55504.2 | 1.51056 | 0.755282 | − | 0.655400i | \(-0.227500\pi\) | ||||
0.755282 | + | 0.655400i | \(0.227500\pi\) | |||||||
\(68\) | 52417.2 | 1.37468 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −60717.8 | −1.42945 | −0.714727 | − | 0.699404i | \(-0.753449\pi\) | ||||
−0.714727 | + | 0.699404i | \(0.753449\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 49613.7 | 1.08967 | 0.544835 | − | 0.838543i | \(-0.316592\pi\) | ||||
0.544835 | + | 0.838543i | \(0.316592\pi\) | |||||||
\(74\) | −27151.7 | −0.576392 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 22946.9 | 0.455713 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40997.4 | 0.739076 | 0.369538 | − | 0.929216i | \(-0.379516\pi\) | ||||
0.369538 | + | 0.929216i | \(0.379516\pi\) | |||||||
\(80\) | −33182.2 | −0.579670 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −353.794 | −0.00581053 | ||||||||
\(83\) | −34040.1 | −0.542370 | −0.271185 | − | 0.962527i | \(-0.587416\pi\) | ||||
−0.271185 | + | 0.962527i | \(0.587416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 186536. | 2.80036 | ||||||||
\(86\) | −9544.03 | −0.139151 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6378.58 | −0.0878046 | ||||||||
\(89\) | −5098.59 | −0.0682299 | −0.0341150 | − | 0.999418i | \(-0.510861\pi\) | ||||
−0.0341150 | + | 0.999418i | \(0.510861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 108534. | 1.33689 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 43394.5 | 0.506542 | ||||||||
\(95\) | 81660.7 | 0.928334 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −98414.9 | −1.06202 | −0.531008 | − | 0.847367i | \(-0.678187\pi\) | ||||
−0.531008 | + | 0.847367i | \(0.678187\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −113862. | −1.13862 | ||||||||
\(101\) | −2468.76 | −0.0240811 | −0.0120405 | − | 0.999928i | \(-0.503833\pi\) | ||||
−0.0120405 | + | 0.999928i | \(0.503833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67609.4 | 0.627934 | 0.313967 | − | 0.949434i | \(-0.398342\pi\) | ||||
0.313967 | + | 0.949434i | \(0.398342\pi\) | |||||||
\(104\) | 151485. | 1.37337 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7989.45 | 0.0690641 | ||||||||
\(107\) | −169653. | −1.43253 | −0.716264 | − | 0.697829i | \(-0.754149\pi\) | ||||
−0.716264 | + | 0.697829i | \(0.754149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 88433.1 | 0.712933 | 0.356466 | − | 0.934308i | \(-0.383981\pi\) | ||||
0.356466 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(110\) | −9890.77 | −0.0779378 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −195325. | −1.43901 | −0.719503 | − | 0.694489i | \(-0.755630\pi\) | ||||
−0.719503 | + | 0.694489i | \(0.755630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 386236. | 2.72338 | ||||||||
\(116\) | 96221.0 | 0.663934 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 49475.5 | 0.327104 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −159316. | −0.989224 | ||||||||
\(122\) | −40219.3 | −0.244644 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 28024.2 | 0.163674 | ||||||||
\(125\) | −130396. | −0.746428 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −61155.8 | −0.336456 | −0.168228 | − | 0.985748i | \(-0.553804\pi\) | ||||
−0.168228 | + | 0.985748i | \(0.553804\pi\) | |||||||
\(128\) | −178848. | −0.964850 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 234897. | 1.21904 | ||||||||
\(131\) | −288044. | −1.46649 | −0.733247 | − | 0.679962i | \(-0.761996\pi\) | ||||
−0.733247 | + | 0.679962i | \(0.761996\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 149856. | 0.720964 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 324792. | 1.50577 | ||||||||
\(137\) | −273332. | −1.24420 | −0.622099 | − | 0.782938i | \(-0.713720\pi\) | ||||
−0.622099 | + | 0.782938i | \(0.713720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −288985. | −1.26864 | −0.634320 | − | 0.773071i | \(-0.718720\pi\) | ||||
−0.634320 | + | 0.773071i | \(0.718720\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −163933. | −0.682252 | ||||||||
\(143\) | −41216.3 | −0.168550 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 342419. | 1.35250 | ||||||||
\(146\) | 133953. | 0.520079 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 248501. | 0.932555 | ||||||||
\(149\) | 191595. | 0.706999 | 0.353499 | − | 0.935435i | \(-0.384992\pi\) | ||||
0.353499 | + | 0.935435i | \(0.384992\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 175529. | 0.626478 | 0.313239 | − | 0.949674i | \(-0.398586\pi\) | ||||
0.313239 | + | 0.949674i | \(0.398586\pi\) | |||||||
\(152\) | 142186. | 0.499169 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 99729.1 | 0.333421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 67098.4 | 0.217252 | 0.108626 | − | 0.994083i | \(-0.465355\pi\) | ||||
0.108626 | + | 0.994083i | \(0.465355\pi\) | |||||||
\(158\) | 110689. | 0.352747 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −520445. | −1.60722 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −549231. | −1.61915 | −0.809573 | − | 0.587019i | \(-0.800301\pi\) | ||||
−0.809573 | + | 0.587019i | \(0.800301\pi\) | |||||||
\(164\) | 3238.04 | 0.00940097 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −91905.3 | −0.258863 | ||||||||
\(167\) | −244929. | −0.679592 | −0.339796 | − | 0.940499i | \(-0.610358\pi\) | ||||
−0.339796 | + | 0.940499i | \(0.610358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 607555. | 1.63632 | ||||||||
\(170\) | 503630. | 1.33656 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 87350.1 | 0.225135 | ||||||||
\(173\) | 44848.6 | 0.113929 | 0.0569644 | − | 0.998376i | \(-0.481858\pi\) | ||||
0.0569644 | + | 0.998376i | \(0.481858\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15719.8 | 0.0382530 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13765.7 | −0.0325649 | ||||||||
\(179\) | −442204. | −1.03155 | −0.515775 | − | 0.856724i | \(-0.672496\pi\) | ||||
−0.515775 | + | 0.856724i | \(0.672496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 215860. | 0.489752 | 0.244876 | − | 0.969554i | \(-0.421253\pi\) | ||||
0.244876 | + | 0.969554i | \(0.421253\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 672506. | 1.46437 | ||||||||
\(185\) | 884335. | 1.89971 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −88369.7 | −0.184799 | ||||||||
\(188\) | −397161. | −0.819543 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 220477. | 0.443077 | ||||||||
\(191\) | −187532. | −0.371957 | −0.185978 | − | 0.982554i | \(-0.559545\pi\) | ||||
−0.185978 | + | 0.982554i | \(0.559545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 735933. | 1.42215 | 0.711075 | − | 0.703117i | \(-0.248209\pi\) | ||||
0.711075 | + | 0.703117i | \(0.248209\pi\) | |||||||
\(194\) | −265711. | −0.506881 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 195426. | 0.358770 | 0.179385 | − | 0.983779i | \(-0.442589\pi\) | ||||
0.179385 | + | 0.983779i | \(0.442589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 966468. | 1.73003 | 0.865017 | − | 0.501742i | \(-0.167307\pi\) | ||||
0.865017 | + | 0.501742i | \(0.167307\pi\) | |||||||
\(200\) | −705521. | −1.24720 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6665.44 | −0.0114934 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11523.1 | 0.0191508 | ||||||||
\(206\) | 182539. | 0.299701 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −373331. | −0.598323 | ||||||||
\(209\) | −38686.1 | −0.0612617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −819549. | −1.26727 | −0.633634 | − | 0.773633i | \(-0.718438\pi\) | ||||
−0.633634 | + | 0.773633i | \(0.718438\pi\) | |||||||
\(212\) | −73122.0 | −0.111740 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −458049. | −0.683719 | ||||||||
\(215\) | 310851. | 0.458623 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 238762. | 0.340270 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 90523.6 | 0.126097 | ||||||||
\(221\) | 2.09870e6 | 2.89048 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 953789. | 1.28437 | 0.642185 | − | 0.766550i | \(-0.278028\pi\) | ||||
0.642185 | + | 0.766550i | \(0.278028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −527361. | −0.686811 | ||||||||
\(227\) | −1.47007e6 | −1.89354 | −0.946770 | − | 0.321912i | \(-0.895674\pi\) | ||||
−0.946770 | + | 0.321912i | \(0.895674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 621804. | 0.783547 | 0.391773 | − | 0.920062i | \(-0.371862\pi\) | ||||
0.391773 | + | 0.920062i | \(0.371862\pi\) | |||||||
\(230\) | 1.04280e6 | 1.29982 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 596213. | 0.727246 | ||||||||
\(233\) | −1.13371e6 | −1.36808 | −0.684042 | − | 0.729443i | \(-0.739779\pi\) | ||||
−0.684042 | + | 0.729443i | \(0.739779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.41337e6 | −1.66950 | ||||||||
\(236\) | −452816. | −0.529227 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −66697.1 | −0.0755287 | −0.0377644 | − | 0.999287i | \(-0.512024\pi\) | ||||
−0.0377644 | + | 0.999287i | \(0.512024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −662390. | −0.734634 | −0.367317 | − | 0.930096i | \(-0.619724\pi\) | ||||
−0.367317 | + | 0.930096i | \(0.619724\pi\) | |||||||
\(242\) | −430138. | −0.472138 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 368100. | 0.395814 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 918759. | 0.958207 | ||||||||
\(248\) | 173646. | 0.179282 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −352057. | −0.356256 | ||||||||
\(251\) | 256918. | 0.257401 | 0.128700 | − | 0.991684i | \(-0.458919\pi\) | ||||
0.128700 | + | 0.991684i | \(0.458919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −182976. | −0.179719 | ||||||||
\(254\) | −165115. | −0.160584 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −607810. | −0.579653 | ||||||||
\(257\) | −167500. | −0.158191 | −0.0790957 | − | 0.996867i | \(-0.525203\pi\) | ||||
−0.0790957 | + | 0.996867i | \(0.525203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.14985e6 | −1.97231 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −777693. | −0.699931 | ||||||||
\(263\) | −1.30152e6 | −1.16028 | −0.580138 | − | 0.814518i | \(-0.697001\pi\) | ||||
−0.580138 | + | 0.814518i | \(0.697001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −260218. | −0.227626 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.37154e6 | −1.16646 | ||||||||
\(269\) | −1.67615e6 | −1.41232 | −0.706158 | − | 0.708054i | \(-0.749573\pi\) | ||||
−0.706158 | + | 0.708054i | \(0.749573\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 704119. | 0.582402 | 0.291201 | − | 0.956662i | \(-0.405945\pi\) | ||||
0.291201 | + | 0.956662i | \(0.405945\pi\) | |||||||
\(272\) | −800440. | −0.656004 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −737973. | −0.593833 | ||||||||
\(275\) | 191959. | 0.153065 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.19116e6 | 0.932760 | 0.466380 | − | 0.884585i | \(-0.345558\pi\) | ||||
0.466380 | + | 0.884585i | \(0.345558\pi\) | |||||||
\(278\) | −780234. | −0.605498 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 473761. | 0.357926 | 0.178963 | − | 0.983856i | \(-0.442726\pi\) | ||||
0.178963 | + | 0.983856i | \(0.442726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.35457e6 | −1.74761 | −0.873805 | − | 0.486276i | \(-0.838355\pi\) | ||||
−0.873805 | + | 0.486276i | \(0.838355\pi\) | |||||||
\(284\) | 1.50037e6 | 1.10383 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −111280. | −0.0804458 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.07986e6 | 2.16913 | ||||||||
\(290\) | 924502. | 0.645524 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.22598e6 | −0.841445 | ||||||||
\(293\) | 1.49266e6 | 1.01576 | 0.507880 | − | 0.861428i | \(-0.330429\pi\) | ||||
0.507880 | + | 0.861428i | \(0.330429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.61143e6 | −1.07809 | ||||||||
\(296\) | 1.53979e6 | 1.02148 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 517290. | 0.337437 | ||||||||
\(299\) | 4.34551e6 | 2.81101 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 473912. | 0.299006 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −350413. | −0.217468 | ||||||||
\(305\) | 1.30995e6 | 0.806315 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −588357. | −0.356283 | −0.178141 | − | 0.984005i | \(-0.557008\pi\) | ||||
−0.178141 | + | 0.984005i | \(0.557008\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 269260. | 0.159136 | ||||||||
\(311\) | 1.37662e6 | 0.807075 | 0.403537 | − | 0.914963i | \(-0.367781\pi\) | ||||
0.403537 | + | 0.914963i | \(0.367781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.20183e6 | −1.27035 | −0.635175 | − | 0.772368i | \(-0.719072\pi\) | ||||
−0.635175 | + | 0.772368i | \(0.719072\pi\) | |||||||
\(314\) | 181160. | 0.103690 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.01307e6 | −0.570716 | ||||||||
\(317\) | 1.30372e6 | 0.728677 | 0.364338 | − | 0.931267i | \(-0.381295\pi\) | ||||
0.364338 | + | 0.931267i | \(0.381295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −162218. | −0.0892530 | ||||||||
\(320\) | −343325. | −0.187426 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.96986e6 | 1.05058 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.55885e6 | −2.39412 | ||||||||
\(326\) | −1.48288e6 | −0.772788 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20063.8 | 0.0102974 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −498571. | −0.250125 | −0.125062 | − | 0.992149i | \(-0.539913\pi\) | ||||
−0.125062 | + | 0.992149i | \(0.539913\pi\) | |||||||
\(332\) | 841147. | 0.418819 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −661285. | −0.324357 | ||||||||
\(335\) | −4.88085e6 | −2.37620 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.97199e6 | −0.945864 | −0.472932 | − | 0.881099i | \(-0.656804\pi\) | ||||
−0.472932 | + | 0.881099i | \(0.656804\pi\) | |||||||
\(338\) | 1.64035e6 | 0.780987 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.60939e6 | −2.16245 | ||||||||
\(341\) | −47245.8 | −0.0220028 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 541246. | 0.246603 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 121087. | 0.0543761 | ||||||||
\(347\) | −736785. | −0.328486 | −0.164243 | − | 0.986420i | \(-0.552518\pi\) | ||||
−0.164243 | + | 0.986420i | \(0.552518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −821566. | −0.361060 | −0.180530 | − | 0.983570i | \(-0.557781\pi\) | ||||
−0.180530 | + | 0.983570i | \(0.557781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 246557. | 0.106062 | ||||||||
\(353\) | 1.61612e6 | 0.690299 | 0.345149 | − | 0.938548i | \(-0.387828\pi\) | ||||
0.345149 | + | 0.938548i | \(0.387828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.33931e6 | 2.24861 | ||||||||
\(356\) | 125989. | 0.0526873 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.19391e6 | −0.492340 | ||||||||
\(359\) | 385547. | 0.157885 | 0.0789425 | − | 0.996879i | \(-0.474846\pi\) | ||||
0.0789425 | + | 0.996879i | \(0.474846\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.61374e6 | −0.651727 | ||||||||
\(362\) | 582803. | 0.233749 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.36286e6 | −1.71411 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.21688e6 | −1.24672 | −0.623362 | − | 0.781934i | \(-0.714234\pi\) | ||||
−0.623362 | + | 0.781934i | \(0.714234\pi\) | |||||||
\(368\) | −1.65737e6 | −0.637969 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.38763e6 | 0.906697 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.41089e6 | 0.525074 | 0.262537 | − | 0.964922i | \(-0.415441\pi\) | ||||
0.262537 | + | 0.964922i | \(0.415441\pi\) | |||||||
\(374\) | −238590. | −0.0882011 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.46092e6 | −0.897695 | ||||||||
\(377\) | 3.85253e6 | 1.39602 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −297560. | −0.106409 | −0.0532043 | − | 0.998584i | \(-0.516943\pi\) | ||||
−0.0532043 | + | 0.998584i | \(0.516943\pi\) | |||||||
\(380\) | −2.01788e6 | −0.716862 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −506320. | −0.177528 | ||||||||
\(383\) | −2.08516e6 | −0.726345 | −0.363173 | − | 0.931722i | \(-0.618306\pi\) | ||||
−0.363173 | + | 0.931722i | \(0.618306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.98695e6 | 0.678765 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.43188e6 | 0.820092 | ||||||||
\(389\) | 3.60863e6 | 1.20912 | 0.604559 | − | 0.796560i | \(-0.293349\pi\) | ||||
0.604559 | + | 0.796560i | \(0.293349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.31699e6 | 3.08201 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 527632. | 0.171234 | ||||||||
\(395\) | −3.60517e6 | −1.16261 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.04068e6 | −0.968265 | −0.484132 | − | 0.874995i | \(-0.660865\pi\) | ||||
−0.484132 | + | 0.874995i | \(0.660865\pi\) | |||||||
\(398\) | 2.60938e6 | 0.825713 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.73873e6 | 0.543355 | ||||||||
\(401\) | −3.51735e6 | −1.09233 | −0.546167 | − | 0.837677i | \(-0.683913\pi\) | ||||
−0.546167 | + | 0.837677i | \(0.683913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.12204e6 | 0.344150 | ||||||||
\(404\) | 61004.3 | 0.0185955 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −418946. | −0.125364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.88540e6 | −0.557307 | −0.278654 | − | 0.960392i | \(-0.589888\pi\) | ||||
−0.278654 | + | 0.960392i | \(0.589888\pi\) | |||||||
\(410\) | 31111.4 | 0.00914030 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.67066e6 | −0.484892 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.99337e6 | 0.853179 | ||||||||
\(416\) | −5.85549e6 | −1.65894 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −104449. | −0.0292391 | ||||||||
\(419\) | −2.23298e6 | −0.621369 | −0.310685 | − | 0.950513i | \(-0.600558\pi\) | ||||
−0.310685 | + | 0.950513i | \(0.600558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.33567e6 | −1.19221 | −0.596103 | − | 0.802908i | \(-0.703285\pi\) | ||||
−0.596103 | + | 0.802908i | \(0.703285\pi\) | |||||||
\(422\) | −2.21271e6 | −0.604844 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −453085. | −0.122395 | ||||||||
\(425\) | −9.77439e6 | −2.62493 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.19222e6 | 1.10620 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 839269. | 0.218892 | ||||||||
\(431\) | −6.40103e6 | −1.65980 | −0.829901 | − | 0.557910i | \(-0.811603\pi\) | ||||
−0.829901 | + | 0.557910i | \(0.811603\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.41837e6 | −0.619872 | −0.309936 | − | 0.950757i | \(-0.600308\pi\) | ||||
−0.309936 | + | 0.950757i | \(0.600308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.18522e6 | −0.550528 | ||||||||
\(437\) | 4.07875e6 | 1.02170 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.01835e6 | 0.499845 | 0.249923 | − | 0.968266i | \(-0.419595\pi\) | ||||
0.249923 | + | 0.968266i | \(0.419595\pi\) | |||||||
\(440\) | 560910. | 0.138122 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.66630e6 | 1.37957 | ||||||||
\(443\) | −4.51656e6 | −1.09345 | −0.546725 | − | 0.837312i | \(-0.684126\pi\) | ||||
−0.546725 | + | 0.837312i | \(0.684126\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 448352. | 0.107330 | ||||||||
\(446\) | 2.57515e6 | 0.613006 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.63815e6 | −0.851658 | −0.425829 | − | 0.904804i | \(-0.640017\pi\) | ||||
−0.425829 | + | 0.904804i | \(0.640017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5458.99 | −0.00126378 | ||||||||
\(452\) | 4.82658e6 | 1.11120 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.96907e6 | −0.903751 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.89454e6 | 0.872299 | 0.436150 | − | 0.899874i | \(-0.356342\pi\) | ||||
0.436150 | + | 0.899874i | \(0.356342\pi\) | |||||||
\(458\) | 1.67882e6 | 0.373972 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.54407e6 | −2.10300 | ||||||||
\(461\) | −959953. | −0.210377 | −0.105188 | − | 0.994452i | \(-0.533545\pi\) | ||||
−0.105188 | + | 0.994452i | \(0.533545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 514391. | 0.111517 | 0.0557584 | − | 0.998444i | \(-0.482242\pi\) | ||||
0.0557584 | + | 0.998444i | \(0.482242\pi\) | |||||||
\(464\) | −1.46935e6 | −0.316833 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.06092e6 | −0.652961 | ||||||||
\(467\) | −1.64057e6 | −0.348098 | −0.174049 | − | 0.984737i | \(-0.555685\pi\) | ||||
−0.174049 | + | 0.984737i | \(0.555685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.81596e6 | −0.796819 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.80578e6 | −0.579694 | ||||||||
\(473\) | −147263. | −0.0302650 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.27899e6 | −0.870176 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −180076. | −0.0360485 | ||||||||
\(479\) | 3.82165e6 | 0.761048 | 0.380524 | − | 0.924771i | \(-0.375744\pi\) | ||||
0.380524 | + | 0.924771i | \(0.375744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.94959e6 | 1.96084 | ||||||||
\(482\) | −1.78839e6 | −0.350627 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.93676e6 | 0.763881 | ||||||||
\(485\) | 8.65426e6 | 1.67061 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.42923e6 | 1.22839 | 0.614196 | − | 0.789154i | \(-0.289480\pi\) | ||||
0.614196 | + | 0.789154i | \(0.289480\pi\) | |||||||
\(488\) | 2.28085e6 | 0.433559 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.38701e6 | 1.38282 | 0.691409 | − | 0.722464i | \(-0.256990\pi\) | ||||
0.691409 | + | 0.722464i | \(0.256990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.26002e6 | 1.53061 | ||||||||
\(494\) | 2.48057e6 | 0.457334 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −427946. | −0.0781060 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.90542e6 | −0.702129 | −0.351064 | − | 0.936351i | \(-0.614180\pi\) | ||||
−0.351064 | + | 0.936351i | \(0.614180\pi\) | |||||||
\(500\) | 3.22214e6 | 0.576394 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 693655. | 0.122853 | ||||||||
\(503\) | −4.00168e6 | −0.705216 | −0.352608 | − | 0.935771i | \(-0.614705\pi\) | ||||
−0.352608 | + | 0.935771i | \(0.614705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 217094. | 0.0378809 | ||||||||
\(506\) | −494019. | −0.0857763 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.51119e6 | 0.259812 | ||||||||
\(509\) | 6.62556e6 | 1.13352 | 0.566759 | − | 0.823884i | \(-0.308197\pi\) | ||||
0.566759 | + | 0.823884i | \(0.308197\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.08211e6 | 0.688192 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −452236. | −0.0755018 | ||||||||
\(515\) | −5.94534e6 | −0.987776 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 669571. | 0.110172 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.33211e7 | −2.16039 | ||||||||
\(521\) | 1.88364e6 | 0.304021 | 0.152010 | − | 0.988379i | \(-0.451425\pi\) | ||||
0.152010 | + | 0.988379i | \(0.451425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.13549e6 | 1.46042 | 0.730210 | − | 0.683223i | \(-0.239422\pi\) | ||||
0.730210 | + | 0.683223i | \(0.239422\pi\) | |||||||
\(524\) | 7.11770e6 | 1.13243 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.51399e6 | −0.553778 | ||||||||
\(527\) | 2.40572e6 | 0.377327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.28552e7 | 1.99728 | ||||||||
\(530\) | −702565. | −0.108642 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 129646. | 0.0197670 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.49187e7 | 2.25345 | ||||||||
\(536\) | −8.49843e6 | −1.27769 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.52545e6 | −0.674072 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.95445e6 | −0.727783 | −0.363891 | − | 0.931441i | \(-0.618552\pi\) | ||||
−0.363891 | + | 0.931441i | \(0.618552\pi\) | |||||||
\(542\) | 1.90106e6 | 0.277970 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.25545e7 | −1.81887 | ||||||||
\(545\) | −7.77650e6 | −1.12148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.48240e6 | 0.211835 | 0.105917 | − | 0.994375i | \(-0.466222\pi\) | ||||
0.105917 | + | 0.994375i | \(0.466222\pi\) | |||||||
\(548\) | 6.75417e6 | 0.960773 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 518272. | 0.0730552 | ||||||||
\(551\) | 3.61603e6 | 0.507404 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.21602e6 | 0.445189 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.14095e6 | 0.979646 | ||||||||
\(557\) | 5.50541e6 | 0.751885 | 0.375942 | − | 0.926643i | \(-0.377319\pi\) | ||||
0.375942 | + | 0.926643i | \(0.377319\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.49736e6 | 0.473380 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.27911e6 | 0.170831 | ||||||||
\(563\) | −1.06459e7 | −1.41551 | −0.707754 | − | 0.706459i | \(-0.750292\pi\) | ||||
−0.707754 | + | 0.706459i | \(0.750292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.71762e7 | 2.26364 | ||||||||
\(566\) | −6.35712e6 | −0.834102 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.29670e6 | 1.20909 | ||||||||
\(569\) | 1.25123e7 | 1.62016 | 0.810080 | − | 0.586319i | \(-0.199424\pi\) | ||||
0.810080 | + | 0.586319i | \(0.199424\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.03238e6 | −0.517573 | −0.258786 | − | 0.965935i | \(-0.583323\pi\) | ||||
−0.258786 | + | 0.965935i | \(0.583323\pi\) | |||||||
\(572\) | 1.01847e6 | 0.130155 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.02386e7 | −2.55276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.15333e6 | 0.394303 | 0.197151 | − | 0.980373i | \(-0.436831\pi\) | ||||
0.197151 | + | 0.980373i | \(0.436831\pi\) | |||||||
\(578\) | 8.31534e6 | 1.03529 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.46134e6 | −1.04441 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 123276. | 0.0150213 | ||||||||
\(584\) | −7.59652e6 | −0.921685 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.03005e6 | 0.484804 | ||||||||
\(587\) | 1.50298e7 | 1.80036 | 0.900179 | − | 0.435520i | \(-0.143436\pi\) | ||||
0.900179 | + | 0.435520i | \(0.143436\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.05316e6 | 0.125086 | ||||||||
\(590\) | −4.35071e6 | −0.514553 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.79475e6 | −0.445020 | ||||||||
\(593\) | −2.57952e6 | −0.301233 | −0.150616 | − | 0.988592i | \(-0.548126\pi\) | ||||
−0.150616 | + | 0.988592i | \(0.548126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.73440e6 | −0.545946 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.17325e7 | 1.34164 | ||||||||
\(599\) | −1.27808e6 | −0.145543 | −0.0727713 | − | 0.997349i | \(-0.523184\pi\) | ||||
−0.0727713 | + | 0.997349i | \(0.523184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.74349e6 | −0.761550 | −0.380775 | − | 0.924668i | \(-0.624343\pi\) | ||||
−0.380775 | + | 0.924668i | \(0.624343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.33740e6 | −0.483768 | ||||||||
\(605\) | 1.40097e7 | 1.55611 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.02861e7 | −1.13313 | −0.566566 | − | 0.824017i | \(-0.691728\pi\) | ||||
−0.566566 | + | 0.824017i | \(0.691728\pi\) | |||||||
\(608\) | −5.49603e6 | −0.602963 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.53674e6 | 0.384839 | ||||||||
\(611\) | −1.59017e7 | −1.72322 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.94586e6 | 0.424122 | 0.212061 | − | 0.977256i | \(-0.431983\pi\) | ||||
0.212061 | + | 0.977256i | \(0.431983\pi\) | |||||||
\(614\) | −1.58851e6 | −0.170047 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.19763e7 | 1.26652 | 0.633259 | − | 0.773940i | \(-0.281717\pi\) | ||||
0.633259 | + | 0.773940i | \(0.281717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.11019e7 | −1.16458 | −0.582291 | − | 0.812980i | \(-0.697844\pi\) | ||||
−0.582291 | + | 0.812980i | \(0.697844\pi\) | |||||||
\(620\) | −2.46435e6 | −0.257468 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.71676e6 | 0.385202 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.93295e6 | −0.300334 | ||||||||
\(626\) | −5.94475e6 | −0.606315 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.65803e6 | −0.167762 | ||||||||
\(629\) | 2.13324e7 | 2.14988 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.99794e6 | 0.399726 | 0.199863 | − | 0.979824i | \(-0.435950\pi\) | ||||
0.199863 | + | 0.979824i | \(0.435950\pi\) | |||||||
\(632\) | −6.27725e6 | −0.625139 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.51992e6 | 0.347784 | ||||||||
\(635\) | 5.37783e6 | 0.529264 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −437975. | −0.0425988 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.57273e7 | 1.51776 | ||||||||
\(641\) | 1.75881e7 | 1.69072 | 0.845362 | − | 0.534194i | \(-0.179385\pi\) | ||||
0.845362 | + | 0.534194i | \(0.179385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.83576e6 | −0.652018 | −0.326009 | − | 0.945367i | \(-0.605704\pi\) | ||||
−0.326009 | + | 0.945367i | \(0.605704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.31846e6 | 0.501423 | ||||||||
\(647\) | −1.78136e7 | −1.67298 | −0.836490 | − | 0.547982i | \(-0.815396\pi\) | ||||
−0.836490 | + | 0.547982i | \(0.815396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 763399. | 0.0711443 | ||||||||
\(650\) | −1.23085e7 | −1.14267 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.35718e7 | 1.25031 | ||||||||
\(653\) | −1.48677e7 | −1.36446 | −0.682231 | − | 0.731137i | \(-0.738990\pi\) | ||||
−0.682231 | + | 0.731137i | \(0.738990\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.53296e7 | 2.30688 | ||||||||
\(656\) | −49446.7 | −0.00448619 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.57120e7 | 1.40935 | 0.704673 | − | 0.709532i | \(-0.251094\pi\) | ||||
0.704673 | + | 0.709532i | \(0.251094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −188221. | −0.0167557 | −0.00837787 | − | 0.999965i | \(-0.502667\pi\) | ||||
−0.00837787 | + | 0.999965i | \(0.502667\pi\) | |||||||
\(662\) | −1.34610e6 | −0.119380 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.21199e6 | 0.458758 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.71030e7 | 1.48853 | ||||||||
\(668\) | 6.05230e6 | 0.524782 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.31779e7 | −1.13412 | ||||||||
\(671\) | −620577. | −0.0532095 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.65246e6 | 0.736380 | 0.368190 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368190 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(674\) | −5.32419e6 | −0.451444 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50130e7 | −1.26357 | ||||||||
\(677\) | 2.55362e6 | 0.214134 | 0.107067 | − | 0.994252i | \(-0.465854\pi\) | ||||
0.107067 | + | 0.994252i | \(0.465854\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.85611e7 | −2.36866 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −127560. | −0.0105015 | ||||||||
\(683\) | 3.83987e6 | 0.314966 | 0.157483 | − | 0.987522i | \(-0.449662\pi\) | ||||
0.157483 | + | 0.987522i | \(0.449662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.40359e7 | 1.95720 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.33388e6 | −0.107435 | ||||||||
\(689\) | −2.92769e6 | −0.234951 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.32370e6 | 0.424149 | 0.212074 | − | 0.977254i | \(-0.431978\pi\) | ||||
0.212074 | + | 0.977254i | \(0.431978\pi\) | |||||||
\(692\) | −1.10823e6 | −0.0879761 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.98925e6 | −0.156780 | ||||||||
\(695\) | 2.54123e7 | 1.99564 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 277967. | 0.0216726 | ||||||||
\(698\) | −2.21816e6 | −0.172327 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.44705e6 | 0.188082 | 0.0940409 | − | 0.995568i | \(-0.470022\pi\) | ||||
0.0940409 | + | 0.995568i | \(0.470022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.33880e6 | 0.712694 | ||||||||
\(704\) | 162647. | 0.0123684 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.36339e6 | 0.329467 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.35056e7 | −1.00902 | −0.504509 | − | 0.863407i | \(-0.668326\pi\) | ||||
−0.504509 | + | 0.863407i | \(0.668326\pi\) | |||||||
\(710\) | 1.44157e7 | 1.07322 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 780662. | 0.0577116 | ||||||||
\(713\) | 4.98122e6 | 0.366954 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.62442e6 | 0.265139 | ||||||||
\(716\) | 1.09271e7 | 0.796566 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.04094e6 | 0.0753556 | ||||||||
\(719\) | −602676. | −0.0434772 | −0.0217386 | − | 0.999764i | \(-0.506920\pi\) | ||||
−0.0217386 | + | 0.999764i | \(0.506920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.35696e6 | −0.311057 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.33401e6 | −0.378187 | ||||||||
\(725\) | −1.79426e7 | −1.26777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.25663e7 | −1.58352 | −0.791762 | − | 0.610830i | \(-0.790836\pi\) | ||||
−0.791762 | + | 0.610830i | \(0.790836\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.17793e7 | −0.818114 | ||||||||
\(731\) | 7.49850e6 | 0.519017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.64126e7 | 1.12828 | 0.564140 | − | 0.825679i | \(-0.309208\pi\) | ||||
0.564140 | + | 0.825679i | \(0.309208\pi\) | |||||||
\(734\) | −8.68530e6 | −0.595038 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.59949e7 | −1.76886 | ||||||||
\(737\) | 2.31226e6 | 0.156808 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.85396e7 | −1.24879 | −0.624394 | − | 0.781110i | \(-0.714654\pi\) | ||||
−0.624394 | + | 0.781110i | \(0.714654\pi\) | |||||||
\(740\) | −2.18523e7 | −1.46696 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.35170e7 | 1.56282 | 0.781412 | − | 0.624016i | \(-0.214500\pi\) | ||||
0.781412 | + | 0.624016i | \(0.214500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.68482e7 | −1.11215 | ||||||||
\(746\) | 3.80928e6 | 0.250608 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.18366e6 | 0.142702 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.53822e7 | 0.995218 | 0.497609 | − | 0.867402i | \(-0.334211\pi\) | ||||
0.497609 | + | 0.867402i | \(0.334211\pi\) | |||||||
\(752\) | 6.06487e6 | 0.391090 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.04015e7 | 0.666297 | ||||||||
\(755\) | −1.54354e7 | −0.985486 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.75980e7 | −1.11615 | −0.558075 | − | 0.829790i | \(-0.688460\pi\) | ||||
−0.558075 | + | 0.829790i | \(0.688460\pi\) | |||||||
\(758\) | −803387. | −0.0507869 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.25033e7 | −0.785221 | ||||||||
\(761\) | 1.67807e7 | 1.05039 | 0.525194 | − | 0.850983i | \(-0.323993\pi\) | ||||
0.525194 | + | 0.850983i | \(0.323993\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.63401e6 | 0.287226 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.62976e6 | −0.346671 | ||||||||
\(767\) | −1.81300e7 | −1.11278 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −261764. | −0.0159622 | −0.00798112 | − | 0.999968i | \(-0.502540\pi\) | ||||
−0.00798112 | + | 0.999968i | \(0.502540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.81853e7 | −1.09819 | ||||||||
\(773\) | −2.14255e7 | −1.28968 | −0.644840 | − | 0.764317i | \(-0.723076\pi\) | ||||
−0.644840 | + | 0.764317i | \(0.723076\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.22576e6 | −0.312533 | ||||||||
\(776\) | 1.50686e7 | 0.898295 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.74299e6 | 0.577090 | ||||||||
\(779\) | 121687. | 0.00718458 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.52946e6 | −0.148388 | ||||||||
\(782\) | 2.51550e7 | 1.47098 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.90040e6 | −0.341749 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.84568e7 | −1.06223 | −0.531117 | − | 0.847299i | \(-0.678227\pi\) | ||||
−0.531117 | + | 0.847299i | \(0.678227\pi\) | |||||||
\(788\) | −4.82906e6 | −0.277043 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.73365e6 | −0.554891 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.47381e7 | 0.832261 | ||||||||
\(794\) | −8.20956e6 | −0.462135 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.38819e7 | −1.33594 | ||||||||
\(797\) | −4.94457e6 | −0.275729 | −0.137865 | − | 0.990451i | \(-0.544024\pi\) | ||||
−0.137865 | + | 0.990451i | \(0.544024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.40940e7 | −1.88934 | ||||||||
\(800\) | 2.72711e7 | 1.50653 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.49655e6 | −0.521350 | ||||||||
\(803\) | 2.06687e6 | 0.113116 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.02942e6 | 0.164256 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 378000. | 0.0203687 | ||||||||
\(809\) | −1.77802e7 | −0.955138 | −0.477569 | − | 0.878594i | \(-0.658482\pi\) | ||||
−0.477569 | + | 0.878594i | \(0.658482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.32483e7 | 1.24119 | 0.620595 | − | 0.784131i | \(-0.286891\pi\) | ||||
0.620595 | + | 0.784131i | \(0.286891\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.13112e6 | −0.0598339 | ||||||||
\(815\) | 4.82975e7 | 2.54701 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.28266e6 | 0.172056 | ||||||||
\(818\) | −5.09041e6 | −0.265992 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −284742. | −0.0147883 | ||||||||
\(821\) | −1.58161e7 | −0.818919 | −0.409459 | − | 0.912328i | \(-0.634283\pi\) | ||||
−0.409459 | + | 0.912328i | \(0.634283\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.41435e7 | 0.727875 | 0.363938 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363938 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(824\) | −1.03519e7 | −0.531131 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.64670e6 | 0.0837240 | 0.0418620 | − | 0.999123i | \(-0.486671\pi\) | ||||
0.0418620 | + | 0.999123i | \(0.486671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.32819e6 | −0.218736 | −0.109368 | − | 0.994001i | \(-0.534883\pi\) | ||||
−0.109368 | + | 0.994001i | \(0.534883\pi\) | |||||||
\(830\) | 8.08183e6 | 0.407206 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.86272e6 | −0.193457 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.15382e7 | 1.06904 | ||||||||
\(836\) | 955952. | 0.0473064 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.02885e6 | −0.296568 | ||||||||
\(839\) | −9.30618e6 | −0.456422 | −0.228211 | − | 0.973612i | \(-0.573288\pi\) | ||||
−0.228211 | + | 0.973612i | \(0.573288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.34842e6 | −0.260757 | ||||||||
\(842\) | −1.17059e7 | −0.569018 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.02514e7 | 0.978588 | ||||||||
\(845\) | −5.34263e7 | −2.57403 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.11661e6 | 0.0533229 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.63900e7 | −1.25283 | ||||||||
\(851\) | 4.41703e7 | 2.09077 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.39111e7 | −1.12519 | −0.562596 | − | 0.826732i | \(-0.690197\pi\) | ||||
−0.562596 | + | 0.826732i | \(0.690197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.59762e7 | 1.21169 | ||||||||
\(857\) | −1.42935e7 | −0.664794 | −0.332397 | − | 0.943140i | \(-0.607857\pi\) | ||||
−0.332397 | + | 0.943140i | \(0.607857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.13017e7 | −0.522590 | −0.261295 | − | 0.965259i | \(-0.584150\pi\) | ||||
−0.261295 | + | 0.965259i | \(0.584150\pi\) | |||||||
\(860\) | −7.68126e6 | −0.354149 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.72822e7 | −0.792193 | ||||||||
\(863\) | −5.31215e6 | −0.242797 | −0.121398 | − | 0.992604i | \(-0.538738\pi\) | ||||
−0.121398 | + | 0.992604i | \(0.538738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.94383e6 | −0.179217 | ||||||||
\(866\) | −6.52937e6 | −0.295854 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.70792e6 | 0.0767217 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.49141e7 | −2.45266 | ||||||||
\(872\) | −1.35403e7 | −0.603027 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.10123e7 | 0.487638 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.04440e6 | −0.353179 | −0.176590 | − | 0.984285i | \(-0.556507\pi\) | ||||
−0.176590 | + | 0.984285i | \(0.556507\pi\) | |||||||
\(878\) | 5.44937e6 | 0.238567 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.38235e6 | −0.0601741 | ||||||||
\(881\) | 1.26000e7 | 0.546930 | 0.273465 | − | 0.961882i | \(-0.411830\pi\) | ||||
0.273465 | + | 0.961882i | \(0.411830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.15646e7 | 0.930766 | 0.465383 | − | 0.885109i | \(-0.345917\pi\) | ||||
0.465383 | + | 0.885109i | \(0.345917\pi\) | |||||||
\(884\) | −5.18599e7 | −2.23203 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.21943e7 | −0.521883 | ||||||||
\(887\) | −2.49881e7 | −1.06641 | −0.533205 | − | 0.845986i | \(-0.679013\pi\) | ||||
−0.533205 | + | 0.845986i | \(0.679013\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.21051e6 | 0.0512264 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.35686e7 | −0.991794 | ||||||||
\(893\) | −1.49255e7 | −0.626326 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.88859e7 | 1.62269 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.82269e6 | −0.406480 | ||||||||
\(899\) | 4.41612e6 | 0.182239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.27711e6 | −0.257601 | ||||||||
\(902\) | −14738.8 | −0.000603178 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.99069e7 | 1.21717 | ||||||||
\(905\) | −1.89820e7 | −0.770407 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.42314e7 | −1.38168 | −0.690839 | − | 0.723008i | \(-0.742759\pi\) | ||||
−0.690839 | + | 0.723008i | \(0.742759\pi\) | |||||||
\(908\) | 3.63262e7 | 1.46220 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.32335e7 | −0.528296 | −0.264148 | − | 0.964482i | \(-0.585091\pi\) | ||||
−0.264148 | + | 0.964482i | \(0.585091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.41808e6 | −0.0563022 | ||||||||
\(914\) | 1.05149e7 | 0.416332 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.53651e7 | −0.605057 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.85336e7 | 1.11447 | 0.557235 | − | 0.830355i | \(-0.311862\pi\) | ||||
0.557235 | + | 0.830355i | \(0.311862\pi\) | |||||||
\(920\) | −5.91378e7 | −2.30354 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.59179e6 | −0.100409 | ||||||||
\(923\) | 6.00722e7 | 2.32097 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.63388e7 | −1.78070 | ||||||||
\(926\) | 1.38881e6 | 0.0532249 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.30459e7 | −0.878465 | ||||||||
\(929\) | 3.17038e7 | 1.20523 | 0.602617 | − | 0.798030i | \(-0.294125\pi\) | ||||
0.602617 | + | 0.798030i | \(0.294125\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.80145e7 | 1.05644 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.42938e6 | −0.166141 | ||||||||
\(935\) | 7.77093e6 | 0.290699 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.54930e7 | 1.32067 | 0.660333 | − | 0.750973i | \(-0.270415\pi\) | ||||
0.660333 | + | 0.750973i | \(0.270415\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.49250e7 | 1.28919 | ||||||||
\(941\) | −2.40587e7 | −0.885724 | −0.442862 | − | 0.896590i | \(-0.646037\pi\) | ||||
−0.442862 | + | 0.896590i | \(0.646037\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 575551. | 0.0210768 | ||||||||
\(944\) | 6.91476e6 | 0.252550 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −397597. | −0.0144449 | ||||||||
\(947\) | 8.23520e6 | 0.298400 | 0.149200 | − | 0.988807i | \(-0.452330\pi\) | ||||
0.149200 | + | 0.988807i | \(0.452330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.90862e7 | −1.76927 | ||||||||
\(950\) | −1.15529e7 | −0.415319 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.49957e7 | −0.891525 | −0.445763 | − | 0.895151i | \(-0.647067\pi\) | ||||
−0.445763 | + | 0.895151i | \(0.647067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.64909e7 | 0.585109 | ||||||||
\(956\) | 1.64812e6 | 0.0583235 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.03181e7 | 0.363234 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.73430e7 | −0.955074 | ||||||||
\(962\) | 2.68630e7 | 0.935873 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.63680e7 | 0.567286 | ||||||||
\(965\) | −6.47154e7 | −2.23712 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.67903e7 | −0.577420 | −0.288710 | − | 0.957417i | \(-0.593226\pi\) | ||||
−0.288710 | + | 0.957417i | \(0.593226\pi\) | |||||||
\(968\) | 2.43933e7 | 0.836725 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.33657e7 | 0.797352 | ||||||||
\(971\) | −2.25923e7 | −0.768974 | −0.384487 | − | 0.923130i | \(-0.625622\pi\) | ||||
−0.384487 | + | 0.923130i | \(0.625622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.73584e7 | 0.586289 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.62109e6 | −0.188884 | ||||||||
\(977\) | −371534. | −0.0124527 | −0.00622634 | − | 0.999981i | \(-0.501982\pi\) | ||||
−0.00622634 | + | 0.999981i | \(0.501982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −212403. | −0.00708279 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.99443e7 | 0.659993 | ||||||||
\(983\) | 2.30996e7 | 0.762466 | 0.381233 | − | 0.924479i | \(-0.375500\pi\) | ||||
0.381233 | + | 0.924479i | \(0.375500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.71850e7 | −0.564365 | ||||||||
\(986\) | 2.23013e7 | 0.730531 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.27030e7 | −0.739929 | ||||||||
\(989\) | 1.55262e7 | 0.504748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.06806e6 | −0.228621 | −0.114311 | − | 0.993445i | \(-0.536466\pi\) | ||||
−0.114311 | + | 0.993445i | \(0.536466\pi\) | |||||||
\(992\) | −6.71209e6 | −0.216560 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.49878e7 | −2.72144 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.11936e7 | 0.356643 | 0.178321 | − | 0.983972i | \(-0.442933\pi\) | ||||
0.178321 | + | 0.983972i | \(0.442933\pi\) | |||||||
\(998\) | −1.05443e7 | −0.335113 | ||||||||
\(999\) | 0 | 0 |
(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 | 441.6.a.x.1.3 | 4 | ||
3.2 | odd | 2 | inner | 441.6.a.x.1.2 | 4 | ||
7.6 | odd | 2 | 63.6.a.h.1.3 | yes | 4 | ||
21.20 | even | 2 | 63.6.a.h.1.2 | ✓ | 4 | ||
28.27 | even | 2 | 1008.6.a.by.1.4 | 4 | |||
84.83 | odd | 2 | 1008.6.a.by.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.6.a.h.1.2 | ✓ | 4 | 21.20 | even | 2 | ||
63.6.a.h.1.3 | yes | 4 | 7.6 | odd | 2 | ||
441.6.a.x.1.2 | 4 | 3.2 | odd | 2 | inner | ||
441.6.a.x.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1008.6.a.by.1.1 | 4 | 84.83 | odd | 2 | |||
1008.6.a.by.1.4 | 4 | 28.27 | even | 2 |