Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,5,Mod(323,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.323");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(39.0738460457\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.5443747577856.29 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 24x^{6} + 180x^{4} + 488x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.7 | ||
Root | \(-2.14697i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.323 |
Dual form | 378.5.b.a.323.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 9.19100i | 0.367640i | 0.982960 | + | 0.183820i | \(0.0588463\pi\) | ||||
−0.982960 | + | 0.183820i | \(0.941154\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.5203 | 0.377964 | ||||||||
\(8\) | − 22.6274i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −25.9961 | −0.259961 | ||||||||
\(11\) | 68.1448i | 0.563180i | 0.959535 | + | 0.281590i | \(0.0908618\pi\) | ||||
−0.959535 | + | 0.281590i | \(0.909138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 212.413 | 1.25688 | 0.628441 | − | 0.777857i | \(-0.283693\pi\) | ||||
0.628441 | + | 0.777857i | \(0.283693\pi\) | |||||||
\(14\) | 52.3832i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − 340.636i | − 1.17867i | −0.807889 | − | 0.589335i | \(-0.799390\pi\) | ||||
0.807889 | − | 0.589335i | \(-0.200610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −176.519 | −0.488972 | −0.244486 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244486 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(20\) | − 73.5280i | − 0.183820i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −192.743 | −0.398228 | ||||||||
\(23\) | − 241.733i | − 0.456963i | −0.973548 | − | 0.228481i | \(-0.926624\pi\) | ||||
0.973548 | − | 0.228481i | \(-0.0733760\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 540.526 | 0.864841 | ||||||||
\(26\) | 600.795i | 0.888750i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −148.162 | −0.188982 | ||||||||
\(29\) | 549.225i | 0.653062i | 0.945186 | + | 0.326531i | \(0.105880\pi\) | ||||
−0.945186 | + | 0.326531i | \(0.894120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 980.834 | 1.02064 | 0.510319 | − | 0.859985i | \(-0.329527\pi\) | ||||
0.510319 | + | 0.859985i | \(0.329527\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 963.463 | 0.833445 | ||||||||
\(35\) | 170.220i | 0.138955i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 743.228 | 0.542899 | 0.271449 | − | 0.962453i | \(-0.412497\pi\) | ||||
0.271449 | + | 0.962453i | \(0.412497\pi\) | |||||||
\(38\) | − 499.271i | − 0.345755i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 207.968 | 0.129980 | ||||||||
\(41\) | 1964.59i | 1.16871i | 0.811500 | + | 0.584353i | \(0.198652\pi\) | ||||
−0.811500 | + | 0.584353i | \(0.801348\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1353.97 | −0.732274 | −0.366137 | − | 0.930561i | \(-0.619320\pi\) | ||||
−0.366137 | + | 0.930561i | \(0.619320\pi\) | |||||||
\(44\) | − 545.158i | − 0.281590i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 683.725 | 0.323121 | ||||||||
\(47\) | − 1321.73i | − 0.598339i | −0.954200 | − | 0.299169i | \(-0.903290\pi\) | ||||
0.954200 | − | 0.299169i | \(-0.0967095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 343.000 | 0.142857 | ||||||||
\(50\) | 1528.84i | 0.611535i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1699.30 | −0.628441 | ||||||||
\(53\) | 4062.59i | 1.44628i | 0.690703 | + | 0.723139i | \(0.257301\pi\) | ||||
−0.690703 | + | 0.723139i | \(0.742699\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −626.318 | −0.207047 | ||||||||
\(56\) | − 419.066i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1553.44 | −0.461785 | ||||||||
\(59\) | 3523.36i | 1.01217i | 0.862484 | + | 0.506085i | \(0.168908\pi\) | ||||
−0.862484 | + | 0.506085i | \(0.831092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5207.28 | 1.39943 | 0.699715 | − | 0.714423i | \(-0.253311\pi\) | ||||
0.699715 | + | 0.714423i | \(0.253311\pi\) | |||||||
\(62\) | 2774.22i | 0.721700i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 1952.29i | 0.462080i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2249.24 | 0.501056 | 0.250528 | − | 0.968109i | \(-0.419396\pi\) | ||||
0.250528 | + | 0.968109i | \(0.419396\pi\) | |||||||
\(68\) | 2725.08i | 0.589335i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −481.454 | −0.0982559 | ||||||||
\(71\) | 7437.67i | 1.47544i | 0.675109 | + | 0.737718i | \(0.264097\pi\) | ||||
−0.675109 | + | 0.737718i | \(0.735903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1051.46 | −0.197308 | −0.0986542 | − | 0.995122i | \(-0.531454\pi\) | ||||
−0.0986542 | + | 0.995122i | \(0.531454\pi\) | |||||||
\(74\) | 2102.17i | 0.383887i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1412.15 | 0.244486 | ||||||||
\(77\) | 1262.06i | 0.212862i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3149.66 | 0.504673 | 0.252336 | − | 0.967640i | \(-0.418801\pi\) | ||||
0.252336 | + | 0.967640i | \(0.418801\pi\) | |||||||
\(80\) | 588.224i | 0.0919100i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5556.71 | −0.826400 | ||||||||
\(83\) | − 467.561i | − 0.0678707i | −0.999424 | − | 0.0339354i | \(-0.989196\pi\) | ||||
0.999424 | − | 0.0339354i | \(-0.0108040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3130.78 | 0.433326 | ||||||||
\(86\) | − 3829.62i | − 0.517796i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1541.94 | 0.199114 | ||||||||
\(89\) | − 2865.60i | − 0.361773i | −0.983504 | − | 0.180886i | \(-0.942103\pi\) | ||||
0.983504 | − | 0.180886i | \(-0.0578966\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3933.94 | 0.475057 | ||||||||
\(92\) | 1933.87i | 0.228481i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3738.42 | 0.423089 | ||||||||
\(95\) | − 1622.38i | − 0.179766i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15884.4 | −1.68821 | −0.844107 | − | 0.536175i | \(-0.819869\pi\) | ||||
−0.844107 | + | 0.536175i | \(0.819869\pi\) | |||||||
\(98\) | 970.151i | 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4324.20 | −0.432420 | ||||||||
\(101\) | 8321.92i | 0.815795i | 0.913028 | + | 0.407897i | \(0.133738\pi\) | ||||
−0.913028 | + | 0.407897i | \(0.866262\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2251.19 | −0.212196 | −0.106098 | − | 0.994356i | \(-0.533836\pi\) | ||||
−0.106098 | + | 0.994356i | \(0.533836\pi\) | |||||||
\(104\) | − 4806.36i | − 0.444375i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11490.8 | −1.02267 | ||||||||
\(107\) | 21923.5i | 1.91488i | 0.288629 | + | 0.957441i | \(0.406800\pi\) | ||||
−0.288629 | + | 0.957441i | \(0.593200\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3095.26 | −0.260522 | −0.130261 | − | 0.991480i | \(-0.541582\pi\) | ||||
−0.130261 | + | 0.991480i | \(0.541582\pi\) | |||||||
\(110\) | − 1771.50i | − 0.146405i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1185.30 | 0.0944911 | ||||||||
\(113\) | − 4295.01i | − 0.336362i | −0.985756 | − | 0.168181i | \(-0.946211\pi\) | ||||
0.985756 | − | 0.168181i | \(-0.0537893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2221.77 | 0.167998 | ||||||||
\(116\) | − 4393.80i | − 0.326531i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9965.57 | −0.715712 | ||||||||
\(119\) | − 6308.66i | − 0.445495i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9997.29 | 0.682828 | ||||||||
\(122\) | 14728.4i | 0.989546i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7846.67 | −0.510319 | ||||||||
\(125\) | 10712.3i | 0.685590i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3845.70 | 0.238434 | 0.119217 | − | 0.992868i | \(-0.461962\pi\) | ||||
0.119217 | + | 0.992868i | \(0.461962\pi\) | |||||||
\(128\) | − 1448.15i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5521.90 | −0.326740 | ||||||||
\(131\) | 12992.3i | 0.757083i | 0.925584 | + | 0.378542i | \(0.123574\pi\) | ||||
−0.925584 | + | 0.378542i | \(0.876426\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3269.17 | −0.184814 | ||||||||
\(134\) | 6361.81i | 0.354300i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7707.70 | −0.416723 | ||||||||
\(137\) | − 7048.28i | − 0.375528i | −0.982214 | − | 0.187764i | \(-0.939876\pi\) | ||||
0.982214 | − | 0.187764i | \(-0.0601240\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13159.3 | 0.681089 | 0.340544 | − | 0.940228i | \(-0.389389\pi\) | ||||
0.340544 | + | 0.940228i | \(0.389389\pi\) | |||||||
\(140\) | − 1361.76i | − 0.0694774i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −21036.9 | −1.04329 | ||||||||
\(143\) | 14474.8i | 0.707851i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5047.93 | −0.240092 | ||||||||
\(146\) | − 2973.97i | − 0.139518i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5945.83 | −0.271449 | ||||||||
\(149\) | − 26816.8i | − 1.20791i | −0.797018 | − | 0.603955i | \(-0.793591\pi\) | ||||
0.797018 | − | 0.603955i | \(-0.206409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24578.6 | 1.07796 | 0.538980 | − | 0.842319i | \(-0.318810\pi\) | ||||
0.538980 | + | 0.842319i | \(0.318810\pi\) | |||||||
\(152\) | 3994.17i | 0.172878i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3569.64 | −0.150516 | ||||||||
\(155\) | 9014.84i | 0.375227i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31474.8 | 1.27692 | 0.638460 | − | 0.769655i | \(-0.279572\pi\) | ||||
0.638460 | + | 0.769655i | \(0.279572\pi\) | |||||||
\(158\) | 8908.59i | 0.356858i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1663.75 | −0.0649902 | ||||||||
\(161\) | − 4476.96i | − 0.172716i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −32656.3 | −1.22911 | −0.614556 | − | 0.788873i | \(-0.710665\pi\) | ||||
−0.614556 | + | 0.788873i | \(0.710665\pi\) | |||||||
\(164\) | − 15716.8i | − 0.584353i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1322.46 | 0.0479918 | ||||||||
\(167\) | − 30734.2i | − 1.10202i | −0.834499 | − | 0.551010i | \(-0.814243\pi\) | ||||
0.834499 | − | 0.551010i | \(-0.185757\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16558.3 | 0.579752 | ||||||||
\(170\) | 8855.18i | 0.306408i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10831.8 | 0.366137 | ||||||||
\(173\) | − 32068.3i | − 1.07148i | −0.844383 | − | 0.535740i | \(-0.820033\pi\) | ||||
0.844383 | − | 0.535740i | \(-0.179967\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10010.7 | 0.326879 | ||||||||
\(176\) | 4361.27i | 0.140795i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8105.14 | 0.255812 | ||||||||
\(179\) | − 18927.5i | − 0.590729i | −0.955385 | − | 0.295364i | \(-0.904559\pi\) | ||||
0.955385 | − | 0.295364i | \(-0.0954410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16502.4 | 0.503720 | 0.251860 | − | 0.967764i | \(-0.418958\pi\) | ||||
0.251860 | + | 0.967764i | \(0.418958\pi\) | |||||||
\(182\) | 11126.9i | 0.335916i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5469.80 | −0.161561 | ||||||||
\(185\) | 6831.01i | 0.199591i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23212.5 | 0.663803 | ||||||||
\(188\) | 10573.8i | 0.299169i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4588.79 | 0.127113 | ||||||||
\(191\) | − 33728.4i | − 0.924548i | −0.886737 | − | 0.462274i | \(-0.847034\pi\) | ||||
0.886737 | − | 0.462274i | \(-0.152966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 29108.7 | 0.781462 | 0.390731 | − | 0.920505i | \(-0.372222\pi\) | ||||
0.390731 | + | 0.920505i | \(0.372222\pi\) | |||||||
\(194\) | − 44927.9i | − 1.19375i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2744.00 | −0.0714286 | ||||||||
\(197\) | 61088.1i | 1.57407i | 0.616908 | + | 0.787035i | \(0.288385\pi\) | ||||
−0.616908 | + | 0.787035i | \(0.711615\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22664.7 | 0.572328 | 0.286164 | − | 0.958181i | \(-0.407620\pi\) | ||||
0.286164 | + | 0.958181i | \(0.407620\pi\) | |||||||
\(200\) | − 12230.7i | − 0.305767i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23538.0 | −0.576854 | ||||||||
\(203\) | 10171.8i | 0.246834i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18056.6 | −0.429663 | ||||||||
\(206\) | − 6367.33i | − 0.150045i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13594.4 | 0.314220 | ||||||||
\(209\) | − 12028.8i | − 0.275379i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −47754.5 | −1.07263 | −0.536314 | − | 0.844018i | \(-0.680184\pi\) | ||||
−0.536314 | + | 0.844018i | \(0.680184\pi\) | |||||||
\(212\) | − 32500.8i | − 0.723139i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −62009.0 | −1.35403 | ||||||||
\(215\) | − 12444.4i | − 0.269213i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18165.3 | 0.385765 | ||||||||
\(218\) | − 8754.73i | − 0.184217i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5010.55 | 0.103524 | ||||||||
\(221\) | − 72355.4i | − 1.48145i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 40317.3 | 0.810741 | 0.405370 | − | 0.914153i | \(-0.367143\pi\) | ||||
0.405370 | + | 0.914153i | \(0.367143\pi\) | |||||||
\(224\) | 3352.53i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12148.1 | 0.237844 | ||||||||
\(227\) | − 69798.9i | − 1.35455i | −0.735728 | − | 0.677277i | \(-0.763160\pi\) | ||||
0.735728 | − | 0.677277i | \(-0.236840\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 58230.3 | 1.11040 | 0.555199 | − | 0.831718i | \(-0.312642\pi\) | ||||
0.555199 | + | 0.831718i | \(0.312642\pi\) | |||||||
\(230\) | 6284.11i | 0.118792i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12427.5 | 0.230892 | ||||||||
\(233\) | − 36975.2i | − 0.681081i | −0.940230 | − | 0.340540i | \(-0.889390\pi\) | ||||
0.940230 | − | 0.340540i | \(-0.110610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12148.0 | 0.219973 | ||||||||
\(236\) | − 28186.9i | − 0.506085i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17843.6 | 0.315013 | ||||||||
\(239\) | − 44554.3i | − 0.779999i | −0.920815 | − | 0.390000i | \(-0.872475\pi\) | ||||
0.920815 | − | 0.390000i | \(-0.127525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 79999.2 | 1.37737 | 0.688686 | − | 0.725060i | \(-0.258188\pi\) | ||||
0.688686 | + | 0.725060i | \(0.258188\pi\) | |||||||
\(242\) | 28276.6i | 0.482833i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −41658.2 | −0.699715 | ||||||||
\(245\) | 3152.51i | 0.0525200i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −37494.9 | −0.614580 | ||||||||
\(248\) | − 22193.7i | − 0.360850i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −30299.1 | −0.484785 | ||||||||
\(251\) | 47272.6i | 0.750346i | 0.926955 | + | 0.375173i | \(0.122417\pi\) | ||||
−0.926955 | + | 0.375173i | \(0.877583\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16472.9 | 0.257352 | ||||||||
\(254\) | 10877.3i | 0.168598i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 53489.4i | − 0.809845i | −0.914351 | − | 0.404922i | \(-0.867299\pi\) | ||||
0.914351 | − | 0.404922i | \(-0.132701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13764.8 | 0.205196 | ||||||||
\(260\) | − 15618.3i | − 0.231040i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −36747.8 | −0.535339 | ||||||||
\(263\) | − 59690.1i | − 0.862961i | −0.902122 | − | 0.431480i | \(-0.857991\pi\) | ||||
0.902122 | − | 0.431480i | \(-0.142009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37339.3 | −0.531709 | ||||||||
\(266\) | − 9246.62i | − 0.130683i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17993.9 | −0.250528 | ||||||||
\(269\) | 76612.4i | 1.05875i | 0.848387 | + | 0.529376i | \(0.177574\pi\) | ||||
−0.848387 | + | 0.529376i | \(0.822426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13224.9 | 0.180076 | 0.0900379 | − | 0.995938i | \(-0.471301\pi\) | ||||
0.0900379 | + | 0.995938i | \(0.471301\pi\) | |||||||
\(272\) | − 21800.7i | − 0.294667i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19935.6 | 0.265538 | ||||||||
\(275\) | 36834.0i | 0.487061i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2728.19 | −0.0355562 | −0.0177781 | − | 0.999842i | \(-0.505659\pi\) | ||||
−0.0177781 | + | 0.999842i | \(0.505659\pi\) | |||||||
\(278\) | 37220.2i | 0.481602i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3851.63 | 0.0491279 | ||||||||
\(281\) | − 92335.3i | − 1.16938i | −0.811258 | − | 0.584689i | \(-0.801217\pi\) | ||||
0.811258 | − | 0.584689i | \(-0.198783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −117175. | −1.46306 | −0.731528 | − | 0.681812i | \(-0.761192\pi\) | ||||
−0.731528 | + | 0.681812i | \(0.761192\pi\) | |||||||
\(284\) | − 59501.4i | − 0.737718i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −40941.0 | −0.500526 | ||||||||
\(287\) | 36384.8i | 0.441729i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −32511.6 | −0.389262 | ||||||||
\(290\) | − 14277.7i | − 0.169770i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8411.65 | 0.0986542 | ||||||||
\(293\) | 67218.3i | 0.782982i | 0.920182 | + | 0.391491i | \(0.128041\pi\) | ||||
−0.920182 | + | 0.391491i | \(0.871959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32383.2 | −0.372114 | ||||||||
\(296\) | − 16817.3i | − 0.191944i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 75849.4 | 0.854122 | ||||||||
\(299\) | − 51347.3i | − 0.574348i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25075.9 | −0.276773 | ||||||||
\(302\) | 69518.6i | 0.762232i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11297.2 | −0.122243 | ||||||||
\(305\) | 47860.0i | 0.514486i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −108355. | −1.14966 | −0.574832 | − | 0.818271i | \(-0.694933\pi\) | ||||
−0.574832 | + | 0.818271i | \(0.694933\pi\) | |||||||
\(308\) | − 10096.5i | − 0.106431i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −25497.8 | −0.265326 | ||||||||
\(311\) | 95709.1i | 0.989538i | 0.869024 | + | 0.494769i | \(0.164747\pi\) | ||||
−0.869024 | + | 0.494769i | \(0.835253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 158112. | 1.61390 | 0.806951 | − | 0.590619i | \(-0.201116\pi\) | ||||
0.806951 | + | 0.590619i | \(0.201116\pi\) | |||||||
\(314\) | 89024.2i | 0.902919i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25197.3 | −0.252336 | ||||||||
\(317\) | − 91133.8i | − 0.906903i | −0.891281 | − | 0.453451i | \(-0.850193\pi\) | ||||
0.891281 | − | 0.453451i | \(-0.149807\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37426.8 | −0.367791 | ||||||||
\(320\) | − 4705.79i | − 0.0459550i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12662.8 | 0.122128 | ||||||||
\(323\) | 60128.6i | 0.576336i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 114815. | 1.08700 | ||||||||
\(326\) | − 92365.9i | − 0.869113i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 44453.7 | 0.413200 | ||||||||
\(329\) | − 24478.8i | − 0.226151i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −129014. | −1.17755 | −0.588777 | − | 0.808296i | \(-0.700390\pi\) | ||||
−0.588777 | + | 0.808296i | \(0.700390\pi\) | |||||||
\(332\) | 3740.49i | 0.0339354i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 86929.6 | 0.779246 | ||||||||
\(335\) | 20672.8i | 0.184208i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −166293. | −1.46425 | −0.732124 | − | 0.681172i | \(-0.761471\pi\) | ||||
−0.732124 | + | 0.681172i | \(0.761471\pi\) | |||||||
\(338\) | 46833.9i | 0.409947i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −25046.2 | −0.216663 | ||||||||
\(341\) | 66838.7i | 0.574803i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6352.45 | 0.0539949 | ||||||||
\(344\) | 30636.9i | 0.258898i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 90702.9 | 0.757650 | ||||||||
\(347\) | − 229085.i | − 1.90256i | −0.308335 | − | 0.951278i | \(-0.599772\pi\) | ||||
0.308335 | − | 0.951278i | \(-0.400228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 97978.4 | 0.804413 | 0.402207 | − | 0.915549i | \(-0.368243\pi\) | ||||
0.402207 | + | 0.915549i | \(0.368243\pi\) | |||||||
\(350\) | 28314.5i | 0.231138i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12335.5 | −0.0995571 | ||||||||
\(353\) | 212359.i | 1.70420i | 0.523380 | + | 0.852100i | \(0.324671\pi\) | ||||
−0.523380 | + | 0.852100i | \(0.675329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −68359.6 | −0.542429 | ||||||||
\(356\) | 22924.8i | 0.180886i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 53535.2 | 0.417708 | ||||||||
\(359\) | 72001.6i | 0.558668i | 0.960194 | + | 0.279334i | \(0.0901136\pi\) | ||||
−0.960194 | + | 0.279334i | \(0.909886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −99162.1 | −0.760907 | ||||||||
\(362\) | 46675.8i | 0.356184i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −31471.6 | −0.237528 | ||||||||
\(365\) | − 9663.93i | − 0.0725384i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −75888.0 | −0.563432 | −0.281716 | − | 0.959498i | \(-0.590904\pi\) | ||||
−0.281716 | + | 0.959498i | \(0.590904\pi\) | |||||||
\(368\) | − 15470.9i | − 0.114241i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19321.0 | −0.141132 | ||||||||
\(371\) | 75240.3i | 0.546642i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −141578. | −1.01760 | −0.508800 | − | 0.860885i | \(-0.669911\pi\) | ||||
−0.508800 | + | 0.860885i | \(0.669911\pi\) | |||||||
\(374\) | 65654.9i | 0.469380i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −29907.3 | −0.211545 | ||||||||
\(377\) | 116663.i | 0.820822i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 81013.3 | 0.563999 | 0.281999 | − | 0.959415i | \(-0.409002\pi\) | ||||
0.281999 | + | 0.959415i | \(0.409002\pi\) | |||||||
\(380\) | 12979.1i | 0.0898828i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 95398.4 | 0.653754 | ||||||||
\(383\) | 81113.4i | 0.552961i | 0.961019 | + | 0.276481i | \(0.0891682\pi\) | ||||
−0.961019 | + | 0.276481i | \(0.910832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11599.6 | −0.0782565 | ||||||||
\(386\) | 82331.8i | 0.552577i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 127075. | 0.844107 | ||||||||
\(389\) | − 77440.9i | − 0.511766i | −0.966708 | − | 0.255883i | \(-0.917634\pi\) | ||||
0.966708 | − | 0.255883i | \(-0.0823662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −82342.9 | −0.538608 | ||||||||
\(392\) | − 7761.20i | − 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −172783. | −1.11304 | ||||||||
\(395\) | 28948.5i | 0.185538i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18460.7 | 0.117130 | 0.0585650 | − | 0.998284i | \(-0.481348\pi\) | ||||
0.0585650 | + | 0.998284i | \(0.481348\pi\) | |||||||
\(398\) | 64105.6i | 0.404697i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 34593.6 | 0.216210 | ||||||||
\(401\) | 201249.i | 1.25154i | 0.780008 | + | 0.625769i | \(0.215215\pi\) | ||||
−0.780008 | + | 0.625769i | \(0.784785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 208342. | 1.28282 | ||||||||
\(404\) | − 66575.4i | − 0.407897i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28770.2 | −0.174538 | ||||||||
\(407\) | 50647.1i | 0.305750i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5492.43 | 0.0328335 | 0.0164168 | − | 0.999865i | \(-0.494774\pi\) | ||||
0.0164168 | + | 0.999865i | \(0.494774\pi\) | |||||||
\(410\) | − 51071.7i | − 0.303818i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18009.5 | 0.106098 | ||||||||
\(413\) | 65253.6i | 0.382564i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4297.36 | 0.0249520 | ||||||||
\(416\) | 38450.9i | 0.222187i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34022.7 | 0.194722 | ||||||||
\(419\) | 84105.3i | 0.479066i | 0.970888 | + | 0.239533i | \(0.0769943\pi\) | ||||
−0.970888 | + | 0.239533i | \(0.923006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −49470.9 | −0.279117 | −0.139558 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139558 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(422\) | − 135070.i | − 0.758463i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 91926.0 | 0.511336 | ||||||||
\(425\) | − 184122.i | − 1.01936i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 96440.1 | 0.528934 | ||||||||
\(428\) | − 175388.i | − 0.957441i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 35198.0 | 0.190362 | ||||||||
\(431\) | − 193441.i | − 1.04135i | −0.853756 | − | 0.520673i | \(-0.825681\pi\) | ||||
0.853756 | − | 0.520673i | \(-0.174319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −153071. | −0.816425 | −0.408213 | − | 0.912887i | \(-0.633848\pi\) | ||||
−0.408213 | + | 0.912887i | \(0.633848\pi\) | |||||||
\(434\) | 51379.2i | 0.272777i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24762.1 | 0.130261 | ||||||||
\(437\) | 42670.5i | 0.223442i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −138512. | −0.718717 | −0.359359 | − | 0.933200i | \(-0.617005\pi\) | ||||
−0.359359 | + | 0.933200i | \(0.617005\pi\) | |||||||
\(440\) | 14172.0i | 0.0732023i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 204652. | 1.04754 | ||||||||
\(443\) | − 32183.4i | − 0.163993i | −0.996633 | − | 0.0819963i | \(-0.973870\pi\) | ||||
0.996633 | − | 0.0819963i | \(-0.0261296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26337.7 | 0.133002 | ||||||||
\(446\) | 114035.i | 0.573280i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9482.37 | −0.0472456 | ||||||||
\(449\) | 100743.i | 0.499713i | 0.968283 | + | 0.249857i | \(0.0803835\pi\) | ||||
−0.968283 | + | 0.249857i | \(0.919617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −133877. | −0.658192 | ||||||||
\(452\) | 34360.1i | 0.168181i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 197421. | 0.957815 | ||||||||
\(455\) | 36156.9i | 0.174650i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 249340. | 1.19387 | 0.596937 | − | 0.802288i | \(-0.296384\pi\) | ||||
0.596937 | + | 0.802288i | \(0.296384\pi\) | |||||||
\(458\) | 164700.i | 0.785169i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17774.2 | −0.0839989 | ||||||||
\(461\) | 340783.i | 1.60353i | 0.597640 | + | 0.801764i | \(0.296105\pi\) | ||||
−0.597640 | + | 0.801764i | \(0.703895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −86247.9 | −0.402334 | −0.201167 | − | 0.979557i | \(-0.564473\pi\) | ||||
−0.201167 | + | 0.979557i | \(0.564473\pi\) | |||||||
\(464\) | 35150.4i | 0.163266i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 104582. | 0.481597 | ||||||||
\(467\) | 21803.1i | 0.0999734i | 0.998750 | + | 0.0499867i | \(0.0159179\pi\) | ||||
−0.998750 | + | 0.0499867i | \(0.984082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41656.5 | 0.189381 | ||||||||
\(470\) | 34359.8i | 0.155544i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 79724.5 | 0.357856 | ||||||||
\(473\) | − 92266.2i | − 0.412402i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −95412.9 | −0.422883 | ||||||||
\(476\) | 50469.3i | 0.222748i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 126019. | 0.551543 | ||||||||
\(479\) | 71881.6i | 0.313290i | 0.987655 | + | 0.156645i | \(0.0500679\pi\) | ||||
−0.987655 | + | 0.156645i | \(0.949932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 157871. | 0.682359 | ||||||||
\(482\) | 226272.i | 0.973949i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −79978.3 | −0.341414 | ||||||||
\(485\) | − 145994.i | − 0.620655i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −319320. | −1.34638 | −0.673191 | − | 0.739469i | \(-0.735077\pi\) | ||||
−0.673191 | + | 0.739469i | \(0.735077\pi\) | |||||||
\(488\) | − 117827.i | − 0.494773i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8916.65 | −0.0371372 | ||||||||
\(491\) | 250141.i | 1.03758i | 0.854902 | + | 0.518790i | \(0.173617\pi\) | ||||
−0.854902 | + | 0.518790i | \(0.826383\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 187086. | 0.769744 | ||||||||
\(494\) | − 106052.i | − 0.434574i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 62773.4 | 0.255160 | ||||||||
\(497\) | 137748.i | 0.557662i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −154356. | −0.619899 | −0.309950 | − | 0.950753i | \(-0.600312\pi\) | ||||
−0.309950 | + | 0.950753i | \(0.600312\pi\) | |||||||
\(500\) | − 85698.7i | − 0.342795i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −133707. | −0.530575 | ||||||||
\(503\) | 344575.i | 1.36191i | 0.732325 | + | 0.680955i | \(0.238435\pi\) | ||||
−0.732325 | + | 0.680955i | \(0.761565\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −76486.8 | −0.299919 | ||||||||
\(506\) | 46592.3i | 0.181976i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −30765.6 | −0.119217 | ||||||||
\(509\) | − 127372.i | − 0.491632i | −0.969317 | − | 0.245816i | \(-0.920944\pi\) | ||||
0.969317 | − | 0.245816i | \(-0.0790559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19473.3 | −0.0745756 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 151291. | 0.572647 | ||||||||
\(515\) | − 20690.7i | − 0.0780118i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 90069.0 | 0.336972 | ||||||||
\(518\) | 38932.7i | 0.145096i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 44175.2 | 0.163370 | ||||||||
\(521\) | − 310653.i | − 1.14446i | −0.820094 | − | 0.572229i | \(-0.806079\pi\) | ||||
0.820094 | − | 0.572229i | \(-0.193921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 200802. | 0.734116 | 0.367058 | − | 0.930198i | \(-0.380365\pi\) | ||||
0.367058 | + | 0.930198i | \(0.380365\pi\) | |||||||
\(524\) | − 103938.i | − 0.378542i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 168829. | 0.610205 | ||||||||
\(527\) | − 334107.i | − 1.20300i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 221406. | 0.791185 | ||||||||
\(530\) | − 105611.i | − 0.375975i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26153.4 | 0.0924070 | ||||||||
\(533\) | 417306.i | 1.46893i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −201499. | −0.703987 | ||||||||
\(536\) | − 50894.5i | − 0.177150i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −216693. | −0.748651 | ||||||||
\(539\) | 23373.7i | 0.0804543i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 286252. | 0.978033 | 0.489016 | − | 0.872275i | \(-0.337356\pi\) | ||||
0.489016 | + | 0.872275i | \(0.337356\pi\) | |||||||
\(542\) | 37405.8i | 0.127333i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 61661.6 | 0.208361 | ||||||||
\(545\) | − 28448.6i | − 0.0957783i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 78649.5 | 0.262858 | 0.131429 | − | 0.991326i | \(-0.458043\pi\) | ||||
0.131429 | + | 0.991326i | \(0.458043\pi\) | |||||||
\(548\) | 56386.3i | 0.187764i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −104182. | −0.344404 | ||||||||
\(551\) | − 96948.6i | − 0.319329i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 58332.6 | 0.190748 | ||||||||
\(554\) | − 7716.48i | − 0.0251420i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −105275. | −0.340544 | ||||||||
\(557\) | − 580730.i | − 1.87182i | −0.352241 | − | 0.935909i | \(-0.614580\pi\) | ||||
0.352241 | − | 0.935909i | \(-0.385420\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −287602. | −0.920381 | ||||||||
\(560\) | 10894.1i | 0.0347387i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 261164. | 0.826875 | ||||||||
\(563\) | 293483.i | 0.925906i | 0.886383 | + | 0.462953i | \(0.153210\pi\) | ||||
−0.886383 | + | 0.462953i | \(0.846790\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39475.4 | 0.123660 | ||||||||
\(566\) | − 331420.i | − 1.03454i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 168295. | 0.521645 | ||||||||
\(569\) | 149286.i | 0.461100i | 0.973060 | + | 0.230550i | \(0.0740526\pi\) | ||||
−0.973060 | + | 0.230550i | \(0.925947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −522954. | −1.60395 | −0.801976 | − | 0.597356i | \(-0.796218\pi\) | ||||
−0.801976 | + | 0.597356i | \(0.796218\pi\) | |||||||
\(572\) | − 115799.i | − 0.353925i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −102912. | −0.312350 | ||||||||
\(575\) | − 130663.i | − 0.395200i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −351985. | −1.05724 | −0.528619 | − | 0.848859i | \(-0.677290\pi\) | ||||
−0.528619 | + | 0.848859i | \(0.677290\pi\) | |||||||
\(578\) | − 91956.6i | − 0.275250i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 40383.4 | 0.120046 | ||||||||
\(581\) | − 8659.36i | − 0.0256527i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −276845. | −0.814515 | ||||||||
\(584\) | 23791.7i | 0.0697591i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −190122. | −0.553652 | ||||||||
\(587\) | 256546.i | 0.744541i | 0.928124 | + | 0.372270i | \(0.121421\pi\) | ||||
−0.928124 | + | 0.372270i | \(0.878579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −173136. | −0.499064 | ||||||||
\(590\) | − 91593.5i | − 0.263124i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 47566.6 | 0.135725 | ||||||||
\(593\) | − 469980.i | − 1.33650i | −0.743935 | − | 0.668252i | \(-0.767043\pi\) | ||||
0.743935 | − | 0.668252i | \(-0.232957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 57982.9 | 0.163782 | ||||||||
\(596\) | 214535.i | 0.603955i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 145232. | 0.406126 | ||||||||
\(599\) | − 667523.i | − 1.86043i | −0.367021 | − | 0.930213i | \(-0.619622\pi\) | ||||
0.367021 | − | 0.930213i | \(-0.380378\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 578943. | 1.60283 | 0.801414 | − | 0.598109i | \(-0.204081\pi\) | ||||
0.801414 | + | 0.598109i | \(0.204081\pi\) | |||||||
\(602\) | − 70925.5i | − 0.195708i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −196628. | −0.538980 | ||||||||
\(605\) | 91885.1i | 0.251035i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −393712. | −1.06857 | −0.534283 | − | 0.845306i | \(-0.679418\pi\) | ||||
−0.534283 | + | 0.845306i | \(0.679418\pi\) | |||||||
\(608\) | − 31953.3i | − 0.0864388i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −135369. | −0.363796 | ||||||||
\(611\) | − 280753.i | − 0.752041i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −112288. | −0.298823 | −0.149412 | − | 0.988775i | \(-0.547738\pi\) | ||||
−0.149412 | + | 0.988775i | \(0.547738\pi\) | |||||||
\(614\) | − 306473.i | − 0.812935i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28557.1 | 0.0752581 | ||||||||
\(617\) | 106565.i | 0.279927i | 0.990157 | + | 0.139964i | \(0.0446986\pi\) | ||||
−0.990157 | + | 0.139964i | \(0.955301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −115118. | −0.300444 | −0.150222 | − | 0.988652i | \(-0.547999\pi\) | ||||
−0.150222 | + | 0.988652i | \(0.547999\pi\) | |||||||
\(620\) | − 72118.7i | − 0.187614i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −270706. | −0.699709 | ||||||||
\(623\) | − 53071.7i | − 0.136737i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 239371. | 0.612791 | ||||||||
\(626\) | 447209.i | 1.14120i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −251798. | −0.638460 | ||||||||
\(629\) | − 253170.i | − 0.639898i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −776896. | −1.95121 | −0.975606 | − | 0.219530i | \(-0.929547\pi\) | ||||
−0.975606 | + | 0.219530i | \(0.929547\pi\) | |||||||
\(632\) | − 71268.7i | − 0.178429i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 257765. | 0.641277 | ||||||||
\(635\) | 35345.8i | 0.0876577i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 72857.7 | 0.179555 | ||||||||
\(638\) | − 105859.i | − 0.260068i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13310.0 | 0.0324951 | ||||||||
\(641\) | − 574512.i | − 1.39824i | −0.715002 | − | 0.699122i | \(-0.753574\pi\) | ||||
0.715002 | − | 0.699122i | \(-0.246426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 702571. | 1.69929 | 0.849647 | − | 0.527352i | \(-0.176815\pi\) | ||||
0.849647 | + | 0.527352i | \(0.176815\pi\) | |||||||
\(644\) | 35815.7i | 0.0863578i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −170069. | −0.407531 | ||||||||
\(647\) | − 51929.4i | − 0.124052i | −0.998075 | − | 0.0620262i | \(-0.980244\pi\) | ||||
0.998075 | − | 0.0620262i | \(-0.0197562\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −240099. | −0.570033 | ||||||||
\(650\) | 324745.i | 0.768627i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 261250. | 0.614556 | ||||||||
\(653\) | − 608223.i | − 1.42638i | −0.700969 | − | 0.713192i | \(-0.747249\pi\) | ||||
0.700969 | − | 0.713192i | \(-0.252751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −119412. | −0.278334 | ||||||||
\(656\) | 125734.i | 0.292176i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 69236.4 | 0.159913 | ||||||||
\(659\) | − 556649.i | − 1.28177i | −0.767636 | − | 0.640886i | \(-0.778567\pi\) | ||||
0.767636 | − | 0.640886i | \(-0.221433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 211725. | 0.484584 | 0.242292 | − | 0.970203i | \(-0.422101\pi\) | ||||
0.242292 | + | 0.970203i | \(0.422101\pi\) | |||||||
\(662\) | − 364907.i | − 0.832656i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10579.7 | −0.0239959 | ||||||||
\(665\) | − 30047.0i | − 0.0679450i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 132766. | 0.298425 | ||||||||
\(668\) | 245874.i | 0.551010i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −58471.4 | −0.130255 | ||||||||
\(671\) | 354849.i | 0.788130i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −476473. | −1.05198 | −0.525991 | − | 0.850490i | \(-0.676306\pi\) | ||||
−0.525991 | + | 0.850490i | \(0.676306\pi\) | |||||||
\(674\) | − 470348.i | − 1.03538i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −132466. | −0.289876 | ||||||||
\(677\) | − 582092.i | − 1.27003i | −0.772499 | − | 0.635016i | \(-0.780994\pi\) | ||||
0.772499 | − | 0.635016i | \(-0.219006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −294183. | −0.638085 | ||||||||
\(680\) | − 70841.5i | − 0.153204i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −189048. | −0.406447 | ||||||||
\(683\) | − 685947.i | − 1.47045i | −0.677825 | − | 0.735223i | \(-0.737077\pi\) | ||||
0.677825 | − | 0.735223i | \(-0.262923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 64780.8 | 0.138059 | ||||||||
\(686\) | 17967.4i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −86654.3 | −0.183068 | ||||||||
\(689\) | 862948.i | 1.81780i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −244679. | −0.512437 | −0.256219 | − | 0.966619i | \(-0.582477\pi\) | ||||
−0.256219 | + | 0.966619i | \(0.582477\pi\) | |||||||
\(692\) | 256546.i | 0.535740i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 647950. | 1.34531 | ||||||||
\(695\) | 120947.i | 0.250395i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 669211. | 1.37752 | ||||||||
\(698\) | 277125.i | 0.568806i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −80085.4 | −0.163440 | ||||||||
\(701\) | 275489.i | 0.560619i | 0.959910 | + | 0.280310i | \(0.0904371\pi\) | ||||
−0.959910 | + | 0.280310i | \(0.909563\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −131194. | −0.265462 | ||||||||
\(704\) | − 34890.1i | − 0.0703975i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −600641. | −1.20505 | ||||||||
\(707\) | 154124.i | 0.308341i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 732370. | 1.45693 | 0.728464 | − | 0.685084i | \(-0.240234\pi\) | ||||
0.728464 | + | 0.685084i | \(0.240234\pi\) | |||||||
\(710\) | − 193350.i | − 0.383555i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −64841.2 | −0.127906 | ||||||||
\(713\) | − 237100.i | − 0.466394i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −133038. | −0.260234 | ||||||||
\(716\) | 151420.i | 0.295364i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −203651. | −0.395038 | ||||||||
\(719\) | − 900565.i | − 1.74204i | −0.491251 | − | 0.871018i | \(-0.663460\pi\) | ||||
0.491251 | − | 0.871018i | \(-0.336540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41692.6 | −0.0802026 | ||||||||
\(722\) | − 280473.i | − 0.538042i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −132019. | −0.251860 | ||||||||
\(725\) | 296870.i | 0.564795i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 681602. | 1.28962 | 0.644811 | − | 0.764342i | \(-0.276936\pi\) | ||||
0.644811 | + | 0.764342i | \(0.276936\pi\) | |||||||
\(728\) | − 89015.0i | − 0.167958i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 27333.7 | 0.0512924 | ||||||||
\(731\) | 461212.i | 0.863109i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 369951. | 0.688552 | 0.344276 | − | 0.938869i | \(-0.388124\pi\) | ||||
0.344276 | + | 0.938869i | \(0.388124\pi\) | |||||||
\(734\) | − 214644.i | − 0.398406i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 43758.4 | 0.0807804 | ||||||||
\(737\) | 153274.i | 0.282185i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 318069. | 0.582416 | 0.291208 | − | 0.956660i | \(-0.405943\pi\) | ||||
0.291208 | + | 0.956660i | \(0.405943\pi\) | |||||||
\(740\) | − 54648.1i | − 0.0997956i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −212812. | −0.386534 | ||||||||
\(743\) | 531939.i | 0.963571i | 0.876289 | + | 0.481786i | \(0.160012\pi\) | ||||
−0.876289 | + | 0.481786i | \(0.839988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 246473. | 0.444076 | ||||||||
\(746\) | − 400442.i | − 0.719552i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −185700. | −0.331902 | ||||||||
\(749\) | 406029.i | 0.723757i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 411990. | 0.730477 | 0.365239 | − | 0.930914i | \(-0.380987\pi\) | ||||
0.365239 | + | 0.930914i | \(0.380987\pi\) | |||||||
\(752\) | − 84590.7i | − 0.149585i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −329972. | −0.580409 | ||||||||
\(755\) | 225901.i | 0.396301i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.11562e6 | 1.94681 | 0.973407 | − | 0.229081i | \(-0.0735722\pi\) | ||||
0.973407 | + | 0.229081i | \(0.0735722\pi\) | |||||||
\(758\) | 229140.i | 0.398807i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36710.4 | −0.0635567 | ||||||||
\(761\) | 251236.i | 0.433822i | 0.976191 | + | 0.216911i | \(0.0695982\pi\) | ||||
−0.976191 | + | 0.216911i | \(0.930402\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57325.1 | −0.0984681 | ||||||||
\(764\) | 269827.i | 0.462274i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −229423. | −0.391003 | ||||||||
\(767\) | 748408.i | 1.27218i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 215136. | 0.363799 | 0.181899 | − | 0.983317i | \(-0.441776\pi\) | ||||
0.181899 | + | 0.983317i | \(0.441776\pi\) | |||||||
\(770\) | − 32808.6i | − 0.0553357i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −232870. | −0.390731 | ||||||||
\(773\) | − 377669.i | − 0.632051i | −0.948751 | − | 0.316026i | \(-0.897651\pi\) | ||||
0.948751 | − | 0.316026i | \(-0.102349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 530166. | 0.882690 | ||||||||
\(776\) | 359423.i | 0.596874i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 219036. | 0.361873 | ||||||||
\(779\) | − 346788.i | − 0.571464i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −506838. | −0.830936 | ||||||||
\(782\) | − 232901.i | − 0.380853i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21952.0 | 0.0357143 | ||||||||
\(785\) | 289285.i | 0.469447i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −610887. | −0.986306 | −0.493153 | − | 0.869943i | \(-0.664156\pi\) | ||||
−0.493153 | + | 0.869943i | \(0.664156\pi\) | |||||||
\(788\) | − 488705.i | − 0.787035i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −81878.8 | −0.131195 | ||||||||
\(791\) | − 79544.7i | − 0.127133i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.10609e6 | 1.75892 | ||||||||
\(794\) | 52214.9i | 0.0828234i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −181318. | −0.286164 | ||||||||
\(797\) | − 144095.i | − 0.226847i | −0.993547 | − | 0.113423i | \(-0.963818\pi\) | ||||
0.993547 | − | 0.113423i | \(-0.0361817\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −450228. | −0.705243 | ||||||||
\(800\) | 97845.6i | 0.152884i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −569217. | −0.884971 | ||||||||
\(803\) | − 71651.3i | − 0.111120i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41147.8 | 0.0634972 | ||||||||
\(806\) | 589280.i | 0.907092i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 188304. | 0.288427 | ||||||||
\(809\) | − 469089.i | − 0.716735i | −0.933581 | − | 0.358367i | \(-0.883334\pi\) | ||||
0.933581 | − | 0.358367i | \(-0.116666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −651439. | −0.990449 | −0.495224 | − | 0.868765i | \(-0.664914\pi\) | ||||
−0.495224 | + | 0.868765i | \(0.664914\pi\) | |||||||
\(812\) | − 81374.3i | − 0.123417i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −143252. | −0.216198 | ||||||||
\(815\) | − 300144.i | − 0.451870i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 239002. | 0.358061 | ||||||||
\(818\) | 15534.9i | 0.0232168i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 144453. | 0.214831 | ||||||||
\(821\) | 344638.i | 0.511301i | 0.966769 | + | 0.255650i | \(0.0822896\pi\) | ||||
−0.966769 | + | 0.255650i | \(0.917710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −77588.8 | −0.114551 | −0.0572755 | − | 0.998358i | \(-0.518241\pi\) | ||||
−0.0572755 | + | 0.998358i | \(0.518241\pi\) | |||||||
\(824\) | 50938.6i | 0.0750227i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −184565. | −0.270514 | ||||||||
\(827\) | 449172.i | 0.656752i | 0.944547 | + | 0.328376i | \(0.106501\pi\) | ||||
−0.944547 | + | 0.328376i | \(0.893499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.21343e6 | −1.76565 | −0.882824 | − | 0.469704i | \(-0.844361\pi\) | ||||
−0.882824 | + | 0.469704i | \(0.844361\pi\) | |||||||
\(830\) | 12154.8i | 0.0176437i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −108755. | −0.157110 | ||||||||
\(833\) | − 116838.i | − 0.168381i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 282478. | 0.405147 | ||||||||
\(836\) | 96230.7i | 0.137690i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −237886. | −0.338751 | ||||||||
\(839\) | − 290391.i | − 0.412534i | −0.978496 | − | 0.206267i | \(-0.933868\pi\) | ||||
0.978496 | − | 0.206267i | \(-0.0661316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 405633. | 0.573510 | ||||||||
\(842\) | − 139925.i | − 0.197365i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 382036. | 0.536314 | ||||||||
\(845\) | 152187.i | 0.213140i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 185152. | 0.258085 | ||||||||
\(848\) | 260006.i | 0.361569i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 520776. | 0.720798 | ||||||||
\(851\) | − 179663.i | − 0.248084i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.13718e6 | 1.56291 | 0.781453 | − | 0.623964i | \(-0.214479\pi\) | ||||
0.781453 | + | 0.623964i | \(0.214479\pi\) | |||||||
\(854\) | 272774.i | 0.374013i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 496072. | 0.677013 | ||||||||
\(857\) | 1.10331e6i | 1.50223i | 0.660174 | + | 0.751113i | \(0.270483\pi\) | ||||
−0.660174 | + | 0.751113i | \(0.729517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57100.5 | −0.0773844 | −0.0386922 | − | 0.999251i | \(-0.512319\pi\) | ||||
−0.0386922 | + | 0.999251i | \(0.512319\pi\) | |||||||
\(860\) | 99554.9i | 0.134606i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 547135. | 0.736342 | ||||||||
\(863\) | − 787528.i | − 1.05741i | −0.848805 | − | 0.528706i | \(-0.822677\pi\) | ||||
0.848805 | − | 0.528706i | \(-0.177323\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 294740. | 0.393919 | ||||||||
\(866\) | − 432949.i | − 0.577300i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −145322. | −0.192883 | ||||||||
\(869\) | 214633.i | 0.284222i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 477768. | 0.629768 | ||||||||
\(872\) | 70037.8i | 0.0921085i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −120690. | −0.157997 | ||||||||
\(875\) | 198395.i | 0.259129i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −804114. | −1.04549 | −0.522743 | − | 0.852490i | \(-0.675091\pi\) | ||||
−0.522743 | + | 0.852490i | \(0.675091\pi\) | |||||||
\(878\) | − 391771.i | − 0.508210i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −40084.4 | −0.0517618 | ||||||||
\(881\) | 824622.i | 1.06244i | 0.847235 | + | 0.531218i | \(0.178266\pi\) | ||||
−0.847235 | + | 0.531218i | \(0.821734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −78126.7 | −0.100202 | −0.0501012 | − | 0.998744i | \(-0.515954\pi\) | ||||
−0.0501012 | + | 0.998744i | \(0.515954\pi\) | |||||||
\(884\) | 578843.i | 0.740724i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 91028.4 | 0.115960 | ||||||||
\(887\) | 372894.i | 0.473956i | 0.971515 | + | 0.236978i | \(0.0761570\pi\) | ||||
−0.971515 | + | 0.236978i | \(0.923843\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 71223.3 | 0.0901195 | ||||||||
\(890\) | 74494.3i | 0.0940466i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −322539. | −0.405370 | ||||||||
\(893\) | 233310.i | 0.292571i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 173963. | 0.217175 | ||||||||
\(896\) | − 26820.2i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −284943. | −0.353351 | ||||||||
\(899\) | 538699.i | 0.666540i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.38386e6 | 1.70468 | ||||||||
\(902\) | − 378661.i | − 0.465412i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −97184.9 | −0.118922 | ||||||||
\(905\) | 151673.i | 0.185188i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −915350. | −1.11269 | −0.556343 | − | 0.830953i | \(-0.687796\pi\) | ||||
−0.556343 | + | 0.830953i | \(0.687796\pi\) | |||||||
\(908\) | 558391.i | 0.677277i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −102267. | −0.123496 | ||||||||
\(911\) | 1.09746e6i | 1.32237i | 0.750224 | + | 0.661184i | \(0.229946\pi\) | ||||
−0.750224 | + | 0.661184i | \(0.770054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31861.9 | 0.0382234 | ||||||||
\(914\) | 705239.i | 0.844197i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −465843. | −0.555199 | ||||||||
\(917\) | 240621.i | 0.286151i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 916021. | 1.08461 | 0.542306 | − | 0.840181i | \(-0.317551\pi\) | ||||
0.542306 | + | 0.840181i | \(0.317551\pi\) | |||||||
\(920\) | − 50272.9i | − 0.0593962i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −963881. | −1.13387 | ||||||||
\(923\) | 1.57986e6i | 1.85445i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 401734. | 0.469521 | ||||||||
\(926\) | − 243946.i | − 0.284493i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −99420.4 | −0.115446 | ||||||||
\(929\) | − 977241.i | − 1.13232i | −0.824294 | − | 0.566161i | \(-0.808428\pi\) | ||||
0.824294 | − | 0.566161i | \(-0.191572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −60546.0 | −0.0698531 | ||||||||
\(932\) | 295802.i | 0.340540i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −61668.5 | −0.0706919 | ||||||||
\(935\) | 213346.i | 0.244040i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −211902. | −0.241355 | −0.120678 | − | 0.992692i | \(-0.538507\pi\) | ||||
−0.120678 | + | 0.992692i | \(0.538507\pi\) | |||||||
\(938\) | 117822.i | 0.133913i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −97184.1 | −0.109987 | ||||||||
\(941\) | − 886510.i | − 1.00116i | −0.865690 | − | 0.500581i | \(-0.833120\pi\) | ||||
0.865690 | − | 0.500581i | \(-0.166880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 474908. | 0.534055 | ||||||||
\(944\) | 225495.i | 0.253042i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 260968. | 0.291612 | ||||||||
\(947\) | 391263.i | 0.436283i | 0.975917 | + | 0.218142i | \(0.0699995\pi\) | ||||
−0.975917 | + | 0.218142i | \(0.930001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −223343. | −0.247993 | ||||||||
\(950\) | − 269869.i | − 0.299023i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −142749. | −0.157506 | ||||||||
\(953\) | − 445329.i | − 0.490337i | −0.969480 | − | 0.245169i | \(-0.921157\pi\) | ||||
0.969480 | − | 0.245169i | \(-0.0788433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 309998. | 0.339901 | ||||||||
\(956\) | 356435.i | 0.390000i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −203312. | −0.221530 | ||||||||
\(959\) | − 130536.i | − 0.141936i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38513.8 | 0.0417032 | ||||||||
\(962\) | 446528.i | 0.482501i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −639993. | −0.688686 | ||||||||
\(965\) | 267538.i | 0.287297i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.31391e6 | −1.40511 | −0.702557 | − | 0.711627i | \(-0.747959\pi\) | ||||
−0.702557 | + | 0.711627i | \(0.747959\pi\) | |||||||
\(968\) | − 226213.i | − 0.241416i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 412932. | 0.438869 | ||||||||
\(971\) | 1.12629e6i | 1.19457i | 0.802029 | + | 0.597285i | \(0.203754\pi\) | ||||
−0.802029 | + | 0.597285i | \(0.796246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 243714. | 0.257427 | ||||||||
\(974\) | − 903174.i | − 0.952036i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 333266. | 0.349857 | ||||||||
\(977\) | − 1.70721e6i | − 1.78854i | −0.447528 | − | 0.894270i | \(-0.647696\pi\) | ||||
0.447528 | − | 0.894270i | \(-0.352304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 195276. | 0.203743 | ||||||||
\(980\) | − 25220.1i | − 0.0262600i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −707505. | −0.733680 | ||||||||
\(983\) | − 438109.i | − 0.453394i | −0.973965 | − | 0.226697i | \(-0.927207\pi\) | ||||
0.973965 | − | 0.226697i | \(-0.0727926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −561460. | −0.578691 | ||||||||
\(986\) | 529158.i | 0.544292i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 299959. | 0.307290 | ||||||||
\(989\) | 327301.i | 0.334622i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.40134e6 | −1.42690 | −0.713452 | − | 0.700704i | \(-0.752870\pi\) | ||||
−0.713452 | + | 0.700704i | \(0.752870\pi\) | |||||||
\(992\) | 177550.i | 0.180425i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −389609. | −0.394327 | ||||||||
\(995\) | 208312.i | 0.210410i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −971355. | −0.977209 | −0.488605 | − | 0.872505i | \(-0.662494\pi\) | ||||
−0.488605 | + | 0.872505i | \(0.662494\pi\) | |||||||
\(998\) | − 436583.i | − 0.438335i | ||||||||
\(999\) | 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 | 378.5.b.a.323.7 | yes | 8 | |
3.2 | odd | 2 | inner | 378.5.b.a.323.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.5.b.a.323.2 | ✓ | 8 | 3.2 | odd | 2 | inner | |
378.5.b.a.323.7 | yes | 8 | 1.1 | even | 1 | trivial |