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: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 92x^{6} + 2949x^{4} + 37548x^{2} + 142884 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.8 | ||
Root | \(-4.82885i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.323 |
Dual form | 378.5.b.b.323.1 |
$q$-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 | ||||||||
\(5\) | 30.1368i | 1.20547i | 0.797940 | + | 0.602737i | \(0.205923\pi\) | ||||
−0.797940 | + | 0.602737i | \(0.794077\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.5203 | 0.377964 | ||||||||
\(8\) | − 22.6274i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −85.2398 | −0.852398 | ||||||||
\(11\) | 11.8001i | 0.0975216i | 0.998810 | + | 0.0487608i | \(0.0155272\pi\) | ||||
−0.998810 | + | 0.0487608i | \(0.984473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −159.095 | −0.941393 | −0.470696 | − | 0.882295i | \(-0.655997\pi\) | ||||
−0.470696 | + | 0.882295i | \(0.655997\pi\) | |||||||
\(14\) | 52.3832i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − 120.538i | − 0.417087i | −0.978013 | − | 0.208543i | \(-0.933128\pi\) | ||||
0.978013 | − | 0.208543i | \(-0.0668723\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −391.298 | −1.08393 | −0.541964 | − | 0.840402i | \(-0.682319\pi\) | ||||
−0.541964 | + | 0.840402i | \(0.682319\pi\) | |||||||
\(20\) | − 241.095i | − 0.602737i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −33.3758 | −0.0689582 | ||||||||
\(23\) | 371.311i | 0.701911i | 0.936392 | + | 0.350955i | \(0.114143\pi\) | ||||
−0.936392 | + | 0.350955i | \(0.885857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −283.229 | −0.453166 | ||||||||
\(26\) | − 449.990i | − 0.665665i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −148.162 | −0.188982 | ||||||||
\(29\) | 216.816i | 0.257808i | 0.991657 | + | 0.128904i | \(0.0411459\pi\) | ||||
−0.991657 | + | 0.128904i | \(0.958854\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −930.283 | −0.968037 | −0.484018 | − | 0.875058i | \(-0.660823\pi\) | ||||
−0.484018 | + | 0.875058i | \(0.660823\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 340.933 | 0.294925 | ||||||||
\(35\) | 558.142i | 0.455626i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −672.478 | −0.491219 | −0.245609 | − | 0.969369i | \(-0.578988\pi\) | ||||
−0.245609 | + | 0.969369i | \(0.578988\pi\) | |||||||
\(38\) | − 1106.76i | − 0.766453i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 681.919 | 0.426199 | ||||||||
\(41\) | − 368.730i | − 0.219351i | −0.993967 | − | 0.109676i | \(-0.965019\pi\) | ||||
0.993967 | − | 0.109676i | \(-0.0349812\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1278.43 | 0.691419 | 0.345710 | − | 0.938342i | \(-0.387638\pi\) | ||||
0.345710 | + | 0.938342i | \(0.387638\pi\) | |||||||
\(44\) | − 94.4009i | − 0.0487608i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1050.23 | −0.496326 | ||||||||
\(47\) | − 1899.14i | − 0.859730i | −0.902893 | − | 0.429865i | \(-0.858561\pi\) | ||||
0.902893 | − | 0.429865i | \(-0.141439\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 343.000 | 0.142857 | ||||||||
\(50\) | − 801.092i | − 0.320437i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1272.76 | 0.470696 | ||||||||
\(53\) | − 1723.71i | − 0.613638i | −0.951768 | − | 0.306819i | \(-0.900735\pi\) | ||||
0.951768 | − | 0.306819i | \(-0.0992647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −355.618 | −0.117560 | ||||||||
\(56\) | − 419.066i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −613.249 | −0.182298 | ||||||||
\(59\) | − 6318.71i | − 1.81520i | −0.419837 | − | 0.907600i | \(-0.637913\pi\) | ||||
0.419837 | − | 0.907600i | \(-0.362087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2529.76 | 0.679860 | 0.339930 | − | 0.940451i | \(-0.389597\pi\) | ||||
0.339930 | + | 0.940451i | \(0.389597\pi\) | |||||||
\(62\) | − 2631.24i | − 0.684505i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − 4794.63i | − 1.13482i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6171.39 | −1.37478 | −0.687391 | − | 0.726288i | \(-0.741244\pi\) | ||||
−0.687391 | + | 0.726288i | \(0.741244\pi\) | |||||||
\(68\) | 964.305i | 0.208543i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1578.66 | −0.322176 | ||||||||
\(71\) | − 907.855i | − 0.180094i | −0.995938 | − | 0.0900471i | \(-0.971298\pi\) | ||||
0.995938 | − | 0.0900471i | \(-0.0287017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3649.04 | −0.684751 | −0.342376 | − | 0.939563i | \(-0.611232\pi\) | ||||
−0.342376 | + | 0.939563i | \(0.611232\pi\) | |||||||
\(74\) | − 1902.06i | − 0.347344i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3130.38 | 0.541964 | ||||||||
\(77\) | 218.541i | 0.0368597i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6817.08 | −1.09231 | −0.546153 | − | 0.837686i | \(-0.683908\pi\) | ||||
−0.546153 | + | 0.837686i | \(0.683908\pi\) | |||||||
\(80\) | 1928.76i | 0.301368i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1042.93 | 0.155105 | ||||||||
\(83\) | − 9100.53i | − 1.32102i | −0.750816 | − | 0.660512i | \(-0.770339\pi\) | ||||
0.750816 | − | 0.660512i | \(-0.229661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3632.64 | 0.502787 | ||||||||
\(86\) | 3615.96i | 0.488907i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 267.006 | 0.0344791 | ||||||||
\(89\) | 8432.60i | 1.06459i | 0.846560 | + | 0.532294i | \(0.178670\pi\) | ||||
−0.846560 | + | 0.532294i | \(0.821330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2946.49 | −0.355813 | ||||||||
\(92\) | − 2970.49i | − 0.350955i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5371.59 | 0.607921 | ||||||||
\(95\) | − 11792.5i | − 1.30665i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −545.318 | −0.0579571 | −0.0289785 | − | 0.999580i | \(-0.509225\pi\) | ||||
−0.0289785 | + | 0.999580i | \(0.509225\pi\) | |||||||
\(98\) | 970.151i | 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2265.83 | 0.226583 | ||||||||
\(101\) | − 7298.60i | − 0.715479i | −0.933822 | − | 0.357739i | \(-0.883548\pi\) | ||||
0.933822 | − | 0.357739i | \(-0.116452\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12988.8 | 1.22432 | 0.612159 | − | 0.790735i | \(-0.290301\pi\) | ||||
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(104\) | 3599.92i | 0.332833i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4875.39 | 0.433908 | ||||||||
\(107\) | − 1506.48i | − 0.131582i | −0.997833 | − | 0.0657910i | \(-0.979043\pi\) | ||||
0.997833 | − | 0.0657910i | \(-0.0209571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11205.6 | −0.943149 | −0.471575 | − | 0.881826i | \(-0.656314\pi\) | ||||
−0.471575 | + | 0.881826i | \(0.656314\pi\) | |||||||
\(110\) | − 1005.84i | − 0.0831273i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1185.30 | 0.0944911 | ||||||||
\(113\) | − 15734.3i | − 1.23223i | −0.787658 | − | 0.616113i | \(-0.788706\pi\) | ||||
0.787658 | − | 0.616113i | \(-0.211294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11190.1 | −0.846135 | ||||||||
\(116\) | − 1734.53i | − 0.128904i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17872.0 | 1.28354 | ||||||||
\(119\) | − 2232.40i | − 0.157644i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14501.8 | 0.990490 | ||||||||
\(122\) | 7155.24i | 0.480733i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7442.27 | 0.484018 | ||||||||
\(125\) | 10299.9i | 0.659194i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14352.6 | 0.889864 | 0.444932 | − | 0.895564i | \(-0.353228\pi\) | ||||
0.444932 | + | 0.895564i | \(0.353228\pi\) | |||||||
\(128\) | − 1448.15i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13561.3 | 0.802442 | ||||||||
\(131\) | − 15941.9i | − 0.928963i | −0.885583 | − | 0.464481i | \(-0.846241\pi\) | ||||
0.885583 | − | 0.464481i | \(-0.153759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7246.94 | −0.409686 | ||||||||
\(134\) | − 17455.3i | − 0.972117i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2727.47 | −0.147462 | ||||||||
\(137\) | 27139.8i | 1.44599i | 0.690852 | + | 0.722996i | \(0.257236\pi\) | ||||
−0.690852 | + | 0.722996i | \(0.742764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20223.3 | 1.04670 | 0.523351 | − | 0.852117i | \(-0.324681\pi\) | ||||
0.523351 | + | 0.852117i | \(0.324681\pi\) | |||||||
\(140\) | − 4465.14i | − 0.227813i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2567.80 | 0.127346 | ||||||||
\(143\) | − 1877.34i | − 0.0918061i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6534.16 | −0.310780 | ||||||||
\(146\) | − 10321.0i | − 0.484192i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5379.83 | 0.245609 | ||||||||
\(149\) | 6130.36i | 0.276130i | 0.990423 | + | 0.138065i | \(0.0440882\pi\) | ||||
−0.990423 | + | 0.138065i | \(0.955912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24047.1 | −1.05465 | −0.527325 | − | 0.849664i | \(-0.676805\pi\) | ||||
−0.527325 | + | 0.849664i | \(0.676805\pi\) | |||||||
\(152\) | 8854.06i | 0.383226i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −618.128 | −0.0260637 | ||||||||
\(155\) | − 28035.8i | − 1.16694i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21025.6 | −0.852999 | −0.426499 | − | 0.904488i | \(-0.640253\pi\) | ||||
−0.426499 | + | 0.904488i | \(0.640253\pi\) | |||||||
\(158\) | − 19281.6i | − 0.772377i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5455.35 | −0.213100 | ||||||||
\(161\) | 6876.77i | 0.265297i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16709.0 | −0.628890 | −0.314445 | − | 0.949276i | \(-0.601818\pi\) | ||||
−0.314445 | + | 0.949276i | \(0.601818\pi\) | |||||||
\(164\) | 2949.84i | 0.109676i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25740.2 | 0.934105 | ||||||||
\(167\) | 28204.0i | 1.01129i | 0.862741 | + | 0.505647i | \(0.168746\pi\) | ||||
−0.862741 | + | 0.505647i | \(0.831254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3249.67 | −0.113780 | ||||||||
\(170\) | 10274.6i | 0.355524i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10227.5 | −0.345710 | ||||||||
\(173\) | 14376.2i | 0.480343i | 0.970731 | + | 0.240171i | \(0.0772036\pi\) | ||||
−0.970731 | + | 0.240171i | \(0.922796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5245.47 | −0.171281 | ||||||||
\(176\) | 755.207i | 0.0243804i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −23851.0 | −0.752777 | ||||||||
\(179\) | 55016.8i | 1.71708i | 0.512750 | + | 0.858538i | \(0.328627\pi\) | ||||
−0.512750 | + | 0.858538i | \(0.671373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −59154.3 | −1.80563 | −0.902816 | − | 0.430027i | \(-0.858504\pi\) | ||||
−0.902816 | + | 0.430027i | \(0.858504\pi\) | |||||||
\(182\) | − 8333.92i | − 0.251598i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8401.80 | 0.248163 | ||||||||
\(185\) | − 20266.4i | − 0.592151i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1422.36 | 0.0406750 | ||||||||
\(188\) | 15193.2i | 0.429865i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 33354.2 | 0.923938 | ||||||||
\(191\) | − 1660.41i | − 0.0455143i | −0.999741 | − | 0.0227572i | \(-0.992756\pi\) | ||||
0.999741 | − | 0.0227572i | \(-0.00724446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −28950.8 | −0.777224 | −0.388612 | − | 0.921402i | \(-0.627045\pi\) | ||||
−0.388612 | + | 0.921402i | \(0.627045\pi\) | |||||||
\(194\) | − 1542.39i | − 0.0409818i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2744.00 | −0.0714286 | ||||||||
\(197\) | 66964.1i | 1.72548i | 0.505650 | + | 0.862739i | \(0.331253\pi\) | ||||
−0.505650 | + | 0.862739i | \(0.668747\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25164.4 | −0.635449 | −0.317725 | − | 0.948183i | \(-0.602919\pi\) | ||||
−0.317725 | + | 0.948183i | \(0.602919\pi\) | |||||||
\(200\) | 6408.74i | 0.160218i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20643.5 | 0.505920 | ||||||||
\(203\) | 4015.49i | 0.0974421i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11112.3 | 0.264422 | ||||||||
\(206\) | 36737.8i | 0.865724i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10182.1 | −0.235348 | ||||||||
\(209\) | − 4617.36i | − 0.105706i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −68772.5 | −1.54472 | −0.772361 | − | 0.635184i | \(-0.780924\pi\) | ||||
−0.772361 | + | 0.635184i | \(0.780924\pi\) | |||||||
\(212\) | 13789.7i | 0.306819i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4260.97 | 0.0930425 | ||||||||
\(215\) | 38528.0i | 0.833488i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17229.1 | −0.365884 | ||||||||
\(218\) | − 31694.1i | − 0.666907i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2844.94 | 0.0587798 | ||||||||
\(221\) | 19177.0i | 0.392642i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 41818.0 | 0.840918 | 0.420459 | − | 0.907312i | \(-0.361869\pi\) | ||||
0.420459 | + | 0.907312i | \(0.361869\pi\) | |||||||
\(224\) | 3352.53i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 44503.3 | 0.871315 | ||||||||
\(227\) | − 88775.6i | − 1.72283i | −0.507903 | − | 0.861414i | \(-0.669579\pi\) | ||||
0.507903 | − | 0.861414i | \(-0.330421\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −88748.9 | −1.69236 | −0.846179 | − | 0.532899i | \(-0.821102\pi\) | ||||
−0.846179 | + | 0.532899i | \(0.821102\pi\) | |||||||
\(230\) | − 31650.5i | − 0.598308i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4905.99 | 0.0911488 | ||||||||
\(233\) | 27765.9i | 0.511447i | 0.966750 | + | 0.255723i | \(0.0823136\pi\) | ||||
−0.966750 | + | 0.255723i | \(0.917686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 57234.2 | 1.03638 | ||||||||
\(236\) | 50549.7i | 0.907600i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6314.17 | 0.111471 | ||||||||
\(239\) | 30454.6i | 0.533159i | 0.963813 | + | 0.266579i | \(0.0858934\pi\) | ||||
−0.963813 | + | 0.266579i | \(0.914107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 41178.6 | 0.708985 | 0.354493 | − | 0.935059i | \(-0.384654\pi\) | ||||
0.354493 | + | 0.935059i | \(0.384654\pi\) | |||||||
\(242\) | 41017.2i | 0.700382i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20238.1 | −0.339930 | ||||||||
\(245\) | 10336.9i | 0.172210i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62253.7 | 1.02040 | ||||||||
\(248\) | 21049.9i | 0.342253i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29132.5 | −0.466120 | ||||||||
\(251\) | 66882.6i | 1.06161i | 0.847493 | + | 0.530806i | \(0.178111\pi\) | ||||
−0.847493 | + | 0.530806i | \(0.821889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4381.51 | −0.0684514 | ||||||||
\(254\) | 40595.4i | 0.629229i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 64609.6i | 0.978207i | 0.872226 | + | 0.489104i | \(0.162676\pi\) | ||||
−0.872226 | + | 0.489104i | \(0.837324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12454.5 | −0.185663 | ||||||||
\(260\) | 38357.0i | 0.567412i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 45090.6 | 0.656876 | ||||||||
\(263\) | 57042.8i | 0.824688i | 0.911028 | + | 0.412344i | \(0.135290\pi\) | ||||
−0.911028 | + | 0.412344i | \(0.864710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 51947.2 | 0.739725 | ||||||||
\(266\) | − 20497.4i | − 0.289692i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 49371.1 | 0.687391 | ||||||||
\(269\) | − 41750.8i | − 0.576979i | −0.957483 | − | 0.288490i | \(-0.906847\pi\) | ||||
0.957483 | − | 0.288490i | \(-0.0931531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −76655.5 | −1.04377 | −0.521885 | − | 0.853016i | \(-0.674771\pi\) | ||||
−0.521885 | + | 0.853016i | \(0.674771\pi\) | |||||||
\(272\) | − 7714.44i | − 0.104272i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −76763.0 | −1.02247 | ||||||||
\(275\) | − 3342.13i | − 0.0441935i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19904.0 | 0.259406 | 0.129703 | − | 0.991553i | \(-0.458598\pi\) | ||||
0.129703 | + | 0.991553i | \(0.458598\pi\) | |||||||
\(278\) | 57200.3i | 0.740131i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12629.3 | 0.161088 | ||||||||
\(281\) | − 23149.0i | − 0.293170i | −0.989198 | − | 0.146585i | \(-0.953172\pi\) | ||||
0.989198 | − | 0.146585i | \(-0.0468282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −125867. | −1.57158 | −0.785792 | − | 0.618491i | \(-0.787745\pi\) | ||||
−0.785792 | + | 0.618491i | \(0.787745\pi\) | |||||||
\(284\) | 7262.84i | 0.0900471i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5309.93 | 0.0649167 | ||||||||
\(287\) | − 6828.97i | − 0.0829070i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 68991.6 | 0.826039 | ||||||||
\(290\) | − 18481.4i | − 0.219755i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 29192.3 | 0.342376 | ||||||||
\(293\) | − 150189.i | − 1.74945i | −0.484616 | − | 0.874727i | \(-0.661041\pi\) | ||||
0.484616 | − | 0.874727i | \(-0.338959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 190426. | 2.18817 | ||||||||
\(296\) | 15216.4i | 0.173672i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17339.3 | −0.195253 | ||||||||
\(299\) | − 59073.8i | − 0.660773i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23676.9 | 0.261332 | ||||||||
\(302\) | − 68015.4i | − 0.745750i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −25043.1 | −0.270982 | ||||||||
\(305\) | 76238.9i | 0.819553i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8930.45 | 0.0947538 | 0.0473769 | − | 0.998877i | \(-0.484914\pi\) | ||||
0.0473769 | + | 0.998877i | \(0.484914\pi\) | |||||||
\(308\) | − 1748.33i | − 0.0184298i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 79297.2 | 0.825153 | ||||||||
\(311\) | 60394.3i | 0.624418i | 0.950013 | + | 0.312209i | \(0.101069\pi\) | ||||
−0.950013 | + | 0.312209i | \(0.898931\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −149441. | −1.52540 | −0.762698 | − | 0.646755i | \(-0.776126\pi\) | ||||
−0.762698 | + | 0.646755i | \(0.776126\pi\) | |||||||
\(314\) | − 59469.3i | − 0.603161i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 54536.6 | 0.546153 | ||||||||
\(317\) | − 55635.4i | − 0.553647i | −0.960921 | − | 0.276823i | \(-0.910718\pi\) | ||||
0.960921 | − | 0.276823i | \(-0.0892817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2558.46 | −0.0251418 | ||||||||
\(320\) | − 15430.1i | − 0.150684i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −19450.4 | −0.187594 | ||||||||
\(323\) | 47166.3i | 0.452092i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 45060.4 | 0.426607 | ||||||||
\(326\) | − 47260.2i | − 0.444693i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8343.40 | −0.0775524 | ||||||||
\(329\) | − 35172.6i | − 0.324948i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 76613.6 | 0.699278 | 0.349639 | − | 0.936884i | \(-0.386304\pi\) | ||||
0.349639 | + | 0.936884i | \(0.386304\pi\) | |||||||
\(332\) | 72804.2i | 0.660512i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −79772.8 | −0.715092 | ||||||||
\(335\) | − 185986.i | − 1.65726i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −177974. | −1.56710 | −0.783549 | − | 0.621330i | \(-0.786593\pi\) | ||||
−0.783549 | + | 0.621330i | \(0.786593\pi\) | |||||||
\(338\) | − 9191.46i | − 0.0804547i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29061.1 | −0.251394 | ||||||||
\(341\) | − 10977.4i | − 0.0944045i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6352.45 | 0.0539949 | ||||||||
\(344\) | − 28927.7i | − 0.244454i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −40662.0 | −0.339653 | ||||||||
\(347\) | 122160.i | 1.01454i | 0.861787 | + | 0.507271i | \(0.169346\pi\) | ||||
−0.861787 | + | 0.507271i | \(0.830654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 60823.0 | 0.499363 | 0.249682 | − | 0.968328i | \(-0.419674\pi\) | ||||
0.249682 | + | 0.968328i | \(0.419674\pi\) | |||||||
\(350\) | − 14836.4i | − 0.121114i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2136.05 | −0.0172395 | ||||||||
\(353\) | − 96167.4i | − 0.771753i | −0.922550 | − | 0.385877i | \(-0.873899\pi\) | ||||
0.922550 | − | 0.385877i | \(-0.126101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27359.9 | 0.217099 | ||||||||
\(356\) | − 67460.8i | − 0.532294i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −155611. | −1.21416 | ||||||||
\(359\) | 200553.i | 1.55611i | 0.628196 | + | 0.778055i | \(0.283794\pi\) | ||||
−0.628196 | + | 0.778055i | \(0.716206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22793.1 | 0.174899 | ||||||||
\(362\) | − 167314.i | − 1.27677i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23571.9 | 0.177906 | ||||||||
\(365\) | − 109971.i | − 0.825450i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 114564. | 0.850581 | 0.425291 | − | 0.905057i | \(-0.360172\pi\) | ||||
0.425291 | + | 0.905057i | \(0.360172\pi\) | |||||||
\(368\) | 23763.9i | 0.175478i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 57322.0 | 0.418714 | ||||||||
\(371\) | − 31923.6i | − 0.231933i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 87845.8 | 0.631398 | 0.315699 | − | 0.948859i | \(-0.397761\pi\) | ||||
0.315699 | + | 0.948859i | \(0.397761\pi\) | |||||||
\(374\) | 4023.05i | 0.0287615i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −42972.7 | −0.303961 | ||||||||
\(377\) | − 34494.5i | − 0.242698i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 277656. | 1.93298 | 0.966492 | − | 0.256696i | \(-0.0826339\pi\) | ||||
0.966492 | + | 0.256696i | \(0.0826339\pi\) | |||||||
\(380\) | 94339.8i | 0.653323i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4696.34 | 0.0321835 | ||||||||
\(383\) | 92652.4i | 0.631625i | 0.948822 | + | 0.315812i | \(0.102277\pi\) | ||||
−0.948822 | + | 0.315812i | \(0.897723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6586.14 | −0.0444334 | ||||||||
\(386\) | − 81885.2i | − 0.549580i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4362.55 | 0.0289785 | ||||||||
\(389\) | 77310.8i | 0.510906i | 0.966821 | + | 0.255453i | \(0.0822246\pi\) | ||||
−0.966821 | + | 0.255453i | \(0.917775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44757.1 | 0.292758 | ||||||||
\(392\) | − 7761.20i | − 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −189403. | −1.22010 | ||||||||
\(395\) | − 205445.i | − 1.31675i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −107227. | −0.680333 | −0.340167 | − | 0.940365i | \(-0.610483\pi\) | ||||
−0.340167 | + | 0.940365i | \(0.610483\pi\) | |||||||
\(398\) | − 71175.8i | − 0.449331i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18126.6 | −0.113292 | ||||||||
\(401\) | − 140836.i | − 0.875839i | −0.899014 | − | 0.437920i | \(-0.855715\pi\) | ||||
0.899014 | − | 0.437920i | \(-0.144285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 148004. | 0.911303 | ||||||||
\(404\) | 58388.8i | 0.357739i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11357.5 | −0.0689020 | ||||||||
\(407\) | − 7935.32i | − 0.0479044i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2186.60 | 0.0130714 | 0.00653572 | − | 0.999979i | \(-0.497920\pi\) | ||||
0.00653572 | + | 0.999979i | \(0.497920\pi\) | |||||||
\(410\) | 31430.5i | 0.186975i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −103910. | −0.612159 | ||||||||
\(413\) | − 117024.i | − 0.686081i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 274261. | 1.59246 | ||||||||
\(416\) | − 28799.3i | − 0.166416i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13059.9 | 0.0747457 | ||||||||
\(419\) | − 147204.i | − 0.838480i | −0.907875 | − | 0.419240i | \(-0.862297\pi\) | ||||
0.907875 | − | 0.419240i | \(-0.137703\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3618.79 | −0.0204173 | −0.0102087 | − | 0.999948i | \(-0.503250\pi\) | ||||
−0.0102087 | + | 0.999948i | \(0.503250\pi\) | |||||||
\(422\) | − 194518.i | − 1.09228i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −39003.1 | −0.216954 | ||||||||
\(425\) | 34139.9i | 0.189010i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46851.8 | 0.256963 | ||||||||
\(428\) | 12051.9i | 0.0657910i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −108974. | −0.589365 | ||||||||
\(431\) | 269119.i | 1.44874i | 0.689411 | + | 0.724370i | \(0.257869\pi\) | ||||
−0.689411 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −278335. | −1.48454 | −0.742271 | − | 0.670100i | \(-0.766251\pi\) | ||||
−0.742271 | + | 0.670100i | \(0.766251\pi\) | |||||||
\(434\) | − 48731.2i | − 0.258719i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 89644.5 | 0.471575 | ||||||||
\(437\) | − 145293.i | − 0.760820i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12385.3 | 0.0642656 | 0.0321328 | − | 0.999484i | \(-0.489770\pi\) | ||||
0.0321328 | + | 0.999484i | \(0.489770\pi\) | |||||||
\(440\) | 8046.72i | 0.0415636i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −54240.9 | −0.277640 | ||||||||
\(443\) | − 190001.i | − 0.968164i | −0.875023 | − | 0.484082i | \(-0.839154\pi\) | ||||
0.875023 | − | 0.484082i | \(-0.160846\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −254132. | −1.28333 | ||||||||
\(446\) | 118279.i | 0.594619i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9482.37 | −0.0472456 | ||||||||
\(449\) | − 75081.0i | − 0.372424i | −0.982510 | − | 0.186212i | \(-0.940379\pi\) | ||||
0.982510 | − | 0.186212i | \(-0.0596211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4351.05 | 0.0213915 | ||||||||
\(452\) | 125874.i | 0.616113i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 251095. | 1.21822 | ||||||||
\(455\) | − 88797.8i | − 0.428923i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 58972.2 | 0.282367 | 0.141184 | − | 0.989983i | \(-0.454909\pi\) | ||||
0.141184 | + | 0.989983i | \(0.454909\pi\) | |||||||
\(458\) | − 251020.i | − 1.19668i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 89521.0 | 0.423067 | ||||||||
\(461\) | 69046.3i | 0.324892i | 0.986717 | + | 0.162446i | \(0.0519383\pi\) | ||||
−0.986717 | + | 0.162446i | \(0.948062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −112506. | −0.524824 | −0.262412 | − | 0.964956i | \(-0.584518\pi\) | ||||
−0.262412 | + | 0.964956i | \(0.584518\pi\) | |||||||
\(464\) | 13876.2i | 0.0644519i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −78533.9 | −0.361648 | ||||||||
\(467\) | − 154153.i | − 0.706836i | −0.935465 | − | 0.353418i | \(-0.885019\pi\) | ||||
0.935465 | − | 0.353418i | \(-0.114981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −114296. | −0.519618 | ||||||||
\(470\) | 161883.i | 0.732833i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −142976. | −0.641770 | ||||||||
\(473\) | 15085.7i | 0.0674283i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 110827. | 0.491199 | ||||||||
\(476\) | 17859.2i | 0.0788220i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −86138.5 | −0.377000 | ||||||||
\(479\) | 165690.i | 0.722144i | 0.932538 | + | 0.361072i | \(0.117589\pi\) | ||||
−0.932538 | + | 0.361072i | \(0.882411\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 106988. | 0.462430 | ||||||||
\(482\) | 116471.i | 0.501328i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −116014. | −0.495245 | ||||||||
\(485\) | − 16434.2i | − 0.0698657i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −154280. | −0.650508 | −0.325254 | − | 0.945627i | \(-0.605450\pi\) | ||||
−0.325254 | + | 0.945627i | \(0.605450\pi\) | |||||||
\(488\) | − 57241.9i | − 0.240367i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −29237.3 | −0.121771 | ||||||||
\(491\) | − 433288.i | − 1.79727i | −0.438695 | − | 0.898636i | \(-0.644559\pi\) | ||||
0.438695 | − | 0.898636i | \(-0.355441\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26134.6 | 0.107528 | ||||||||
\(494\) | 176080.i | 0.721533i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −59538.1 | −0.242009 | ||||||||
\(497\) | − 16813.7i | − 0.0680692i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −298370. | −1.19827 | −0.599134 | − | 0.800649i | \(-0.704488\pi\) | ||||
−0.599134 | + | 0.800649i | \(0.704488\pi\) | |||||||
\(500\) | − 82399.2i | − 0.329597i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −189173. | −0.750673 | ||||||||
\(503\) | − 284631.i | − 1.12498i | −0.826803 | − | 0.562491i | \(-0.809843\pi\) | ||||
0.826803 | − | 0.562491i | \(-0.190157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 219957. | 0.862490 | ||||||||
\(506\) | − 12392.8i | − 0.0484025i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −114821. | −0.444932 | ||||||||
\(509\) | 287223.i | 1.10862i | 0.832309 | + | 0.554312i | \(0.187019\pi\) | ||||
−0.832309 | + | 0.554312i | \(0.812981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −67581.2 | −0.258812 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −182744. | −0.691697 | ||||||||
\(515\) | 391441.i | 1.47588i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22410.1 | 0.0838423 | ||||||||
\(518\) | − 35226.6i | − 0.131284i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −108490. | −0.401221 | ||||||||
\(521\) | − 458107.i | − 1.68769i | −0.536591 | − | 0.843843i | \(-0.680288\pi\) | ||||
0.536591 | − | 0.843843i | \(-0.319712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 99411.5 | 0.363441 | 0.181720 | − | 0.983350i | \(-0.441833\pi\) | ||||
0.181720 | + | 0.983350i | \(0.441833\pi\) | |||||||
\(524\) | 127535.i | 0.464481i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −161341. | −0.583142 | ||||||||
\(527\) | 112135.i | 0.403755i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 141969. | 0.507321 | ||||||||
\(530\) | 146929.i | 0.523064i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 57975.5 | 0.204843 | ||||||||
\(533\) | 58663.2i | 0.206496i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45400.6 | 0.158619 | ||||||||
\(536\) | 139643.i | 0.486059i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 118089. | 0.407986 | ||||||||
\(539\) | 4047.44i | 0.0139317i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −355697. | −1.21531 | −0.607653 | − | 0.794202i | \(-0.707889\pi\) | ||||
−0.607653 | + | 0.794202i | \(0.707889\pi\) | |||||||
\(542\) | − 216815.i | − 0.738057i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21819.7 | 0.0737312 | ||||||||
\(545\) | − 337700.i | − 1.13694i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 356592. | 1.19178 | 0.595892 | − | 0.803065i | \(-0.296799\pi\) | ||||
0.595892 | + | 0.803065i | \(0.296799\pi\) | |||||||
\(548\) | − 217119.i | − 0.722996i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9452.98 | 0.0312495 | ||||||||
\(551\) | − 84839.7i | − 0.279445i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −126254. | −0.412853 | ||||||||
\(554\) | 56296.9i | 0.183428i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −161787. | −0.523351 | ||||||||
\(557\) | 89649.4i | 0.288960i | 0.989508 | + | 0.144480i | \(0.0461509\pi\) | ||||
−0.989508 | + | 0.144480i | \(0.953849\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −203393. | −0.650897 | ||||||||
\(560\) | 35721.1i | 0.113907i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 65475.3 | 0.207303 | ||||||||
\(563\) | 146102.i | 0.460934i | 0.973080 | + | 0.230467i | \(0.0740254\pi\) | ||||
−0.973080 | + | 0.230467i | \(0.925975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 474182. | 1.48542 | ||||||||
\(566\) | − 356005.i | − 1.11128i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20542.4 | −0.0636729 | ||||||||
\(569\) | 437298.i | 1.35068i | 0.737506 | + | 0.675341i | \(0.236003\pi\) | ||||
−0.737506 | + | 0.675341i | \(0.763997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 429334. | 1.31681 | 0.658405 | − | 0.752664i | \(-0.271232\pi\) | ||||
0.658405 | + | 0.752664i | \(0.271232\pi\) | |||||||
\(572\) | 15018.7i | 0.0459031i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19315.2 | 0.0586241 | ||||||||
\(575\) | − 105166.i | − 0.318082i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −140587. | −0.422272 | −0.211136 | − | 0.977457i | \(-0.567716\pi\) | ||||
−0.211136 | + | 0.977457i | \(0.567716\pi\) | |||||||
\(578\) | 195138.i | 0.584097i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 52273.2 | 0.155390 | ||||||||
\(581\) | − 168544.i | − 0.499300i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20340.0 | 0.0598430 | ||||||||
\(584\) | 82568.4i | 0.242096i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 424798. | 1.23705 | ||||||||
\(587\) | − 264968.i | − 0.768985i | −0.923128 | − | 0.384492i | \(-0.874377\pi\) | ||||
0.923128 | − | 0.384492i | \(-0.125623\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 364018. | 1.04928 | ||||||||
\(590\) | 538606.i | 1.54727i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −43038.6 | −0.122805 | ||||||||
\(593\) | 510014.i | 1.45035i | 0.688565 | + | 0.725175i | \(0.258241\pi\) | ||||
−0.688565 | + | 0.725175i | \(0.741759\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 67277.4 | 0.190036 | ||||||||
\(596\) | − 49042.8i | − 0.138065i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 167086. | 0.467237 | ||||||||
\(599\) | 590648.i | 1.64617i | 0.567917 | + | 0.823086i | \(0.307749\pi\) | ||||
−0.567917 | + | 0.823086i | \(0.692251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 260749. | 0.721896 | 0.360948 | − | 0.932586i | \(-0.382453\pi\) | ||||
0.360948 | + | 0.932586i | \(0.382453\pi\) | |||||||
\(602\) | 66968.5i | 0.184790i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 192377. | 0.527325 | ||||||||
\(605\) | 437037.i | 1.19401i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 432739. | 1.17449 | 0.587245 | − | 0.809409i | \(-0.300213\pi\) | ||||
0.587245 | + | 0.809409i | \(0.300213\pi\) | |||||||
\(608\) | − 70832.5i | − 0.191613i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −215636. | −0.579511 | ||||||||
\(611\) | 302145.i | 0.809344i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −509866. | −1.35686 | −0.678430 | − | 0.734665i | \(-0.737339\pi\) | ||||
−0.678430 | + | 0.734665i | \(0.737339\pi\) | |||||||
\(614\) | 25259.1i | 0.0670010i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4945.02 | 0.0130319 | ||||||||
\(617\) | 400846.i | 1.05295i | 0.850191 | + | 0.526474i | \(0.176486\pi\) | ||||
−0.850191 | + | 0.526474i | \(0.823514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 435350. | 1.13621 | 0.568103 | − | 0.822957i | \(-0.307678\pi\) | ||||
0.568103 | + | 0.822957i | \(0.307678\pi\) | |||||||
\(620\) | 224286.i | 0.583471i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −170821. | −0.441530 | ||||||||
\(623\) | 156174.i | 0.402376i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −487424. | −1.24781 | ||||||||
\(626\) | − 422684.i | − 1.07862i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 168205. | 0.426499 | ||||||||
\(629\) | 81059.3i | 0.204881i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 396490. | 0.995803 | 0.497901 | − | 0.867234i | \(-0.334104\pi\) | ||||
0.497901 | + | 0.867234i | \(0.334104\pi\) | |||||||
\(632\) | 154253.i | 0.386188i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 157361. | 0.391487 | ||||||||
\(635\) | 432543.i | 1.07271i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −54569.7 | −0.134485 | ||||||||
\(638\) | − 7236.41i | − 0.0177779i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43642.8 | 0.106550 | ||||||||
\(641\) | 568080.i | 1.38259i | 0.722572 | + | 0.691295i | \(0.242960\pi\) | ||||
−0.722572 | + | 0.691295i | \(0.757040\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 296340. | 0.716751 | 0.358376 | − | 0.933577i | \(-0.383331\pi\) | ||||
0.358376 | + | 0.933577i | \(0.383331\pi\) | |||||||
\(644\) | − 55014.2i | − 0.132649i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −133406. | −0.319677 | ||||||||
\(647\) | − 36510.4i | − 0.0872184i | −0.999049 | − | 0.0436092i | \(-0.986114\pi\) | ||||
0.999049 | − | 0.0436092i | \(-0.0138856\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 74561.5 | 0.177021 | ||||||||
\(650\) | 127450.i | 0.301657i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 133672. | 0.314445 | ||||||||
\(653\) | 596493.i | 1.39888i | 0.714693 | + | 0.699438i | \(0.246566\pi\) | ||||
−0.714693 | + | 0.699438i | \(0.753434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 480439. | 1.11984 | ||||||||
\(656\) | − 23598.7i | − 0.0548378i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 99483.3 | 0.229773 | ||||||||
\(659\) | − 746970.i | − 1.72002i | −0.510280 | − | 0.860008i | \(-0.670458\pi\) | ||||
0.510280 | − | 0.860008i | \(-0.329542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −147076. | −0.336619 | −0.168309 | − | 0.985734i | \(-0.553831\pi\) | ||||
−0.168309 | + | 0.985734i | \(0.553831\pi\) | |||||||
\(662\) | 216696.i | 0.494464i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −205921. | −0.467052 | ||||||||
\(665\) | − 218400.i | − 0.493866i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −80506.2 | −0.180958 | ||||||||
\(668\) | − 225632.i | − 0.505647i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 526049. | 1.17186 | ||||||||
\(671\) | 29851.4i | 0.0663010i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −452502. | −0.999058 | −0.499529 | − | 0.866297i | \(-0.666494\pi\) | ||||
−0.499529 | + | 0.866297i | \(0.666494\pi\) | |||||||
\(674\) | − 503386.i | − 1.10811i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25997.4 | 0.0568900 | ||||||||
\(677\) | 772073.i | 1.68454i | 0.539056 | + | 0.842270i | \(0.318781\pi\) | ||||
−0.539056 | + | 0.842270i | \(0.681219\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10099.4 | −0.0219057 | ||||||||
\(680\) | − 82197.2i | − 0.177762i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31048.9 | 0.0667541 | ||||||||
\(683\) | − 404022.i | − 0.866092i | −0.901372 | − | 0.433046i | \(-0.857439\pi\) | ||||
0.901372 | − | 0.433046i | \(-0.142561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −817909. | −1.74311 | ||||||||
\(686\) | 17967.4i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 81819.8 | 0.172855 | ||||||||
\(689\) | 274234.i | 0.577674i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −615946. | −1.28999 | −0.644995 | − | 0.764187i | \(-0.723141\pi\) | ||||
−0.644995 | + | 0.764187i | \(0.723141\pi\) | |||||||
\(692\) | − 115009.i | − 0.240171i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −345520. | −0.717389 | ||||||||
\(695\) | 609468.i | 1.26177i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44446.0 | −0.0914886 | ||||||||
\(698\) | 172033.i | 0.353103i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 41963.8 | 0.0856403 | ||||||||
\(701\) | − 510387.i | − 1.03864i | −0.854581 | − | 0.519319i | \(-0.826186\pi\) | ||||
0.854581 | − | 0.519319i | \(-0.173814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 263139. | 0.532446 | ||||||||
\(704\) | − 6041.66i | − 0.0121902i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 272003. | 0.545712 | ||||||||
\(707\) | − 135172.i | − 0.270425i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −682535. | −1.35779 | −0.678895 | − | 0.734235i | \(-0.737541\pi\) | ||||
−0.678895 | + | 0.734235i | \(0.737541\pi\) | |||||||
\(710\) | 77385.4i | 0.153512i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 190808. | 0.376389 | ||||||||
\(713\) | − 345424.i | − 0.679475i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56577.2 | 0.110670 | ||||||||
\(716\) | − 440135.i | − 0.858538i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −567250. | −1.10034 | ||||||||
\(719\) | − 108955.i | − 0.210760i | −0.994432 | − | 0.105380i | \(-0.966394\pi\) | ||||
0.994432 | − | 0.105380i | \(-0.0336059\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 240556. | 0.462749 | ||||||||
\(722\) | 64468.5i | 0.123673i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 473235. | 0.902816 | ||||||||
\(725\) | − 61408.6i | − 0.116830i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −146049. | −0.276331 | −0.138165 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138165 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(728\) | 66671.4i | 0.125799i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 311044. | 0.583681 | ||||||||
\(731\) | − 154100.i | − 0.288382i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −925797. | −1.72309 | −0.861544 | − | 0.507682i | \(-0.830502\pi\) | ||||
−0.861544 | + | 0.507682i | \(0.830502\pi\) | |||||||
\(734\) | 324036.i | 0.601452i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −67214.4 | −0.124081 | ||||||||
\(737\) | − 72823.1i | − 0.134071i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40824.3 | 0.0747532 | 0.0373766 | − | 0.999301i | \(-0.488100\pi\) | ||||
0.0373766 | + | 0.999301i | \(0.488100\pi\) | |||||||
\(740\) | 162131.i | 0.296076i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 90293.4 | 0.164002 | ||||||||
\(743\) | 106961.i | 0.193753i | 0.995296 | + | 0.0968766i | \(0.0308852\pi\) | ||||
−0.995296 | + | 0.0968766i | \(0.969115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −184750. | −0.332867 | ||||||||
\(746\) | 248465.i | 0.446466i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11378.9 | −0.0203375 | ||||||||
\(749\) | − 27900.4i | − 0.0497333i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −111510. | −0.197713 | −0.0988564 | − | 0.995102i | \(-0.531518\pi\) | ||||
−0.0988564 | + | 0.995102i | \(0.531518\pi\) | |||||||
\(752\) | − 121545.i | − 0.214933i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 97565.1 | 0.171614 | ||||||||
\(755\) | − 724703.i | − 1.27135i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −78268.3 | −0.136582 | −0.0682911 | − | 0.997665i | \(-0.521755\pi\) | ||||
−0.0682911 | + | 0.997665i | \(0.521755\pi\) | |||||||
\(758\) | 785329.i | 1.36683i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −266833. | −0.461969 | ||||||||
\(761\) | 799900.i | 1.38123i | 0.723222 | + | 0.690616i | \(0.242660\pi\) | ||||
−0.723222 | + | 0.690616i | \(0.757340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −207530. | −0.356477 | ||||||||
\(764\) | 13283.3i | 0.0227572i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −262061. | −0.446626 | ||||||||
\(767\) | 1.00528e6i | 1.70882i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −696974. | −1.17859 | −0.589296 | − | 0.807917i | \(-0.700595\pi\) | ||||
−0.589296 | + | 0.807917i | \(0.700595\pi\) | |||||||
\(770\) | − 18628.4i | − 0.0314191i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 231606. | 0.388612 | ||||||||
\(773\) | − 946901.i | − 1.58469i | −0.610071 | − | 0.792347i | \(-0.708859\pi\) | ||||
0.610071 | − | 0.792347i | \(-0.291141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 263483. | 0.438681 | ||||||||
\(776\) | 12339.1i | 0.0204909i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −218668. | −0.361265 | ||||||||
\(779\) | 144283.i | 0.237761i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10712.8 | 0.0175631 | ||||||||
\(782\) | 126592.i | 0.207011i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21952.0 | 0.0357143 | ||||||||
\(785\) | − 633644.i | − 1.02827i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 693165. | 1.11915 | 0.559574 | − | 0.828780i | \(-0.310965\pi\) | ||||
0.559574 | + | 0.828780i | \(0.310965\pi\) | |||||||
\(788\) | − 535712.i | − 0.862739i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 581087. | 0.931079 | ||||||||
\(791\) | − 291403.i | − 0.465738i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −402473. | −0.640015 | ||||||||
\(794\) | − 303283.i | − 0.481068i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 201315. | 0.317725 | ||||||||
\(797\) | 366791.i | 0.577434i | 0.957414 | + | 0.288717i | \(0.0932287\pi\) | ||||
−0.957414 | + | 0.288717i | \(0.906771\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −228919. | −0.358582 | ||||||||
\(800\) | − 51269.9i | − 0.0801092i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 398344. | 0.619312 | ||||||||
\(803\) | − 43059.1i | − 0.0667781i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −207244. | −0.319809 | ||||||||
\(806\) | 418618.i | 0.644388i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −165148. | −0.252960 | ||||||||
\(809\) | 17053.8i | 0.0260569i | 0.999915 | + | 0.0130285i | \(0.00414721\pi\) | ||||
−0.999915 | + | 0.0130285i | \(0.995853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 127087. | 0.193223 | 0.0966116 | − | 0.995322i | \(-0.469200\pi\) | ||||
0.0966116 | + | 0.995322i | \(0.469200\pi\) | |||||||
\(812\) | − 32123.9i | − 0.0487211i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22444.5 | 0.0338735 | ||||||||
\(815\) | − 503556.i | − 0.758111i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −500249. | −0.749449 | ||||||||
\(818\) | 6184.64i | 0.00924290i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −88898.8 | −0.132211 | ||||||||
\(821\) | − 870988.i | − 1.29219i | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
0.763258 | − | 0.646094i | \(-0.223599\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 590520. | 0.871836 | 0.435918 | − | 0.899986i | \(-0.356424\pi\) | ||||
0.435918 | + | 0.899986i | \(0.356424\pi\) | |||||||
\(824\) | − 293903.i | − 0.432862i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 330994. | 0.485132 | ||||||||
\(827\) | − 254863.i | − 0.372645i | −0.982489 | − | 0.186323i | \(-0.940343\pi\) | ||||
0.982489 | − | 0.186323i | \(-0.0596570\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 102666. | 0.149388 | 0.0746942 | − | 0.997206i | \(-0.476202\pi\) | ||||
0.0746942 | + | 0.997206i | \(0.476202\pi\) | |||||||
\(830\) | 775728.i | 1.12604i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 81456.8 | 0.117674 | ||||||||
\(833\) | − 41344.6i | − 0.0595838i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −849978. | −1.21909 | ||||||||
\(836\) | 36938.9i | 0.0528532i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 416357. | 0.592895 | ||||||||
\(839\) | − 428504.i | − 0.608739i | −0.952554 | − | 0.304369i | \(-0.901554\pi\) | ||||
0.952554 | − | 0.304369i | \(-0.0984458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 660272. | 0.933535 | ||||||||
\(842\) | − 10235.5i | − 0.0144372i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 550180. | 0.772361 | ||||||||
\(845\) | − 97934.8i | − 0.137159i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 268576. | 0.374370 | ||||||||
\(848\) | − 110317.i | − 0.153410i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −96562.1 | −0.133650 | ||||||||
\(851\) | − 249698.i | − 0.344792i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 248624. | 0.341700 | 0.170850 | − | 0.985297i | \(-0.445349\pi\) | ||||
0.170850 | + | 0.985297i | \(0.445349\pi\) | |||||||
\(854\) | 132517.i | 0.181700i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −34087.8 | −0.0465212 | ||||||||
\(857\) | − 222103.i | − 0.302407i | −0.988503 | − | 0.151204i | \(-0.951685\pi\) | ||||
0.988503 | − | 0.151204i | \(-0.0483149\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −893111. | −1.21037 | −0.605187 | − | 0.796084i | \(-0.706902\pi\) | ||||
−0.605187 | + | 0.796084i | \(0.706902\pi\) | |||||||
\(860\) | − 308224.i | − 0.416744i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −761185. | −1.02441 | ||||||||
\(863\) | − 153799.i | − 0.206505i | −0.994655 | − | 0.103253i | \(-0.967075\pi\) | ||||
0.994655 | − | 0.103253i | \(-0.0329250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −433252. | −0.579040 | ||||||||
\(866\) | − 787251.i | − 1.04973i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 137833. | 0.182942 | ||||||||
\(869\) | − 80442.3i | − 0.106523i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 981840. | 1.29421 | ||||||||
\(872\) | 253553.i | 0.333454i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 410951. | 0.537981 | ||||||||
\(875\) | 190757.i | 0.249152i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −845361. | −1.09912 | −0.549558 | − | 0.835456i | \(-0.685204\pi\) | ||||
−0.549558 | + | 0.835456i | \(0.685204\pi\) | |||||||
\(878\) | 35031.0i | 0.0454426i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −22759.6 | −0.0293899 | ||||||||
\(881\) | 603302.i | 0.777290i | 0.921388 | + | 0.388645i | \(0.127057\pi\) | ||||
−0.921388 | + | 0.388645i | \(0.872943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −642582. | −0.824152 | −0.412076 | − | 0.911149i | \(-0.635196\pi\) | ||||
−0.412076 | + | 0.911149i | \(0.635196\pi\) | |||||||
\(884\) | − 153416.i | − 0.196321i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 537404. | 0.684595 | ||||||||
\(887\) | − 516432.i | − 0.656396i | −0.944609 | − | 0.328198i | \(-0.893559\pi\) | ||||
0.944609 | − | 0.328198i | \(-0.106441\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 265814. | 0.336337 | ||||||||
\(890\) | − 718793.i | − 0.907453i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −334544. | −0.420459 | ||||||||
\(893\) | 743131.i | 0.931886i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.65803e6 | −2.06989 | ||||||||
\(896\) | − 26820.2i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 212361. | 0.263343 | ||||||||
\(899\) | − 201701.i | − 0.249567i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −207773. | −0.255940 | ||||||||
\(902\) | 12306.6i | 0.0151261i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −356026. | −0.435658 | ||||||||
\(905\) | − 1.78272e6i | − 2.17664i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 332852. | 0.404610 | 0.202305 | − | 0.979323i | \(-0.435157\pi\) | ||||
0.202305 | + | 0.979323i | \(0.435157\pi\) | |||||||
\(908\) | 710205.i | 0.861414i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 251158. | 0.303294 | ||||||||
\(911\) | − 128205.i | − 0.154478i | −0.997013 | − | 0.0772390i | \(-0.975390\pi\) | ||||
0.997013 | − | 0.0772390i | \(-0.0246104\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 107387. | 0.128828 | ||||||||
\(914\) | 166798.i | 0.199664i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 709991. | 0.846179 | ||||||||
\(917\) | − 295249.i | − 0.351115i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.30265e6 | 1.54240 | 0.771201 | − | 0.636592i | \(-0.219656\pi\) | ||||
0.771201 | + | 0.636592i | \(0.219656\pi\) | |||||||
\(920\) | 253204.i | 0.299154i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −195292. | −0.229733 | ||||||||
\(923\) | 144435.i | 0.169539i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 190465. | 0.222604 | ||||||||
\(926\) | − 318215.i | − 0.371106i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −39247.9 | −0.0455744 | ||||||||
\(929\) | − 1.34170e6i | − 1.55462i | −0.629117 | − | 0.777311i | \(-0.716583\pi\) | ||||
0.629117 | − | 0.777311i | \(-0.283417\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −134215. | −0.154847 | ||||||||
\(932\) | − 222127.i | − 0.255723i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 436011. | 0.499809 | ||||||||
\(935\) | 42865.5i | 0.0490326i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.49619e6 | −1.70415 | −0.852074 | − | 0.523421i | \(-0.824656\pi\) | ||||
−0.852074 | + | 0.523421i | \(0.824656\pi\) | |||||||
\(938\) | − 323277.i | − 0.367426i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −457874. | −0.518191 | ||||||||
\(941\) | − 778807.i | − 0.879530i | −0.898113 | − | 0.439765i | \(-0.855062\pi\) | ||||
0.898113 | − | 0.439765i | \(-0.144938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 136913. | 0.153965 | ||||||||
\(944\) | − 404397.i | − 0.453800i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42668.7 | −0.0476790 | ||||||||
\(947\) | 1.36722e6i | 1.52454i | 0.647258 | + | 0.762271i | \(0.275916\pi\) | ||||
−0.647258 | + | 0.762271i | \(0.724084\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 580545. | 0.644620 | ||||||||
\(950\) | 313466.i | 0.347330i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −50513.4 | −0.0557356 | ||||||||
\(953\) | 656858.i | 0.723245i | 0.932325 | + | 0.361623i | \(0.117777\pi\) | ||||
−0.932325 | + | 0.361623i | \(0.882223\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50039.5 | 0.0548663 | ||||||||
\(956\) | − 243636.i | − 0.266579i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −468641. | −0.510633 | ||||||||
\(959\) | 502637.i | 0.546534i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −58093.7 | −0.0629046 | ||||||||
\(962\) | 302608.i | 0.326987i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −329429. | −0.354493 | ||||||||
\(965\) | − 872486.i | − 0.936923i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 817206. | 0.873934 | 0.436967 | − | 0.899478i | \(-0.356053\pi\) | ||||
0.436967 | + | 0.899478i | \(0.356053\pi\) | |||||||
\(968\) | − 328137.i | − 0.350191i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 46482.8 | 0.0494025 | ||||||||
\(971\) | − 1.02544e6i | − 1.08761i | −0.839211 | − | 0.543805i | \(-0.816983\pi\) | ||||
0.839211 | − | 0.543805i | \(-0.183017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 374542. | 0.395617 | ||||||||
\(974\) | − 436370.i | − 0.459978i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 161905. | 0.169965 | ||||||||
\(977\) | − 233580.i | − 0.244707i | −0.992487 | − | 0.122354i | \(-0.960956\pi\) | ||||
0.992487 | − | 0.122354i | \(-0.0390442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −99505.6 | −0.103820 | ||||||||
\(980\) | − 82695.5i | − 0.0861052i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.22552e6 | 1.27086 | ||||||||
\(983\) | 512053.i | 0.529917i | 0.964260 | + | 0.264958i | \(0.0853582\pi\) | ||||
−0.964260 | + | 0.264958i | \(0.914642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.01808e6 | −2.08002 | ||||||||
\(986\) | 73919.9i | 0.0760339i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −498029. | −0.510201 | ||||||||
\(989\) | 474696.i | 0.485315i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 153330. | 0.156128 | 0.0780639 | − | 0.996948i | \(-0.475126\pi\) | ||||
0.0780639 | + | 0.996948i | \(0.475126\pi\) | |||||||
\(992\) | − 168399.i | − 0.171126i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 47556.3 | 0.0481322 | ||||||||
\(995\) | − 758376.i | − 0.766017i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 731704. | 0.736114 | 0.368057 | − | 0.929803i | \(-0.380023\pi\) | ||||
0.368057 | + | 0.929803i | \(0.380023\pi\) | |||||||
\(998\) | − 843917.i | − 0.847303i | ||||||||
\(999\) | 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.b.323.8 | yes | 8 | |
3.2 | odd | 2 | inner | 378.5.b.b.323.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.5.b.b.323.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
378.5.b.b.323.8 | yes | 8 | 1.1 | even | 1 | trivial |