Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not 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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-3.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.i.199.4 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.37228i | − 1.19228i | −0.802880 | − | 0.596141i | \(-0.796700\pi\) | ||||
0.802880 | − | 0.596141i | \(-0.203300\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −3.37228 | −0.421535 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 10.1168 | 0.688364 | ||||||||
\(7\) | 4.74456i | 0.256182i | 0.991762 | + | 0.128091i | \(0.0408850\pi\) | ||||
−0.991762 | + | 0.128091i | \(0.959115\pi\) | |||||||
\(8\) | − 15.6060i | − 0.689693i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | − 10.1168i | − 0.243373i | ||||||||
\(13\) | − 15.0217i | − 0.320483i | −0.987078 | − | 0.160242i | \(-0.948773\pi\) | ||||
0.987078 | − | 0.160242i | \(-0.0512274\pi\) | |||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.6060 | −1.24384 | ||||||||
\(17\) | − 73.1684i | − 1.04388i | −0.852982 | − | 0.521940i | \(-0.825209\pi\) | ||||
0.852982 | − | 0.521940i | \(-0.174791\pi\) | |||||||
\(18\) | 30.3505i | 0.397427i | ||||||||
\(19\) | 78.7011 | 0.950277 | 0.475138 | − | 0.879911i | \(-0.342398\pi\) | ||||
0.475138 | + | 0.879911i | \(0.342398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.2337 | −0.147907 | ||||||||
\(22\) | − 37.0951i | − 0.359486i | ||||||||
\(23\) | 112.000i | 1.01537i | 0.861541 | + | 0.507687i | \(0.169499\pi\) | ||||
−0.861541 | + | 0.507687i | \(0.830501\pi\) | |||||||
\(24\) | 46.8179 | 0.398194 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −50.6576 | −0.382106 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | − 16.0000i | − 0.107990i | ||||||||
\(29\) | −243.125 | −1.55680 | −0.778399 | − | 0.627769i | \(-0.783968\pi\) | ||||
−0.778399 | + | 0.627769i | \(0.783968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 278.717 | 1.61481 | 0.807405 | − | 0.589998i | \(-0.200871\pi\) | ||||
0.807405 | + | 0.589998i | \(0.200871\pi\) | |||||||
\(32\) | 143.606i | 0.793318i | ||||||||
\(33\) | 33.0000i | 0.174078i | ||||||||
\(34\) | −246.745 | −1.24460 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 30.3505 | 0.140512 | ||||||||
\(37\) | − 102.380i | − 0.454898i | −0.973790 | − | 0.227449i | \(-0.926961\pi\) | ||||
0.973790 | − | 0.227449i | \(-0.0730385\pi\) | |||||||
\(38\) | − 265.402i | − 1.13300i | ||||||||
\(39\) | 45.0652 | 0.185031 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −241.255 | −0.918970 | −0.459485 | − | 0.888186i | \(-0.651966\pi\) | ||||
−0.459485 | + | 0.888186i | \(0.651966\pi\) | |||||||
\(42\) | 48.0000i | 0.176347i | ||||||||
\(43\) | − 280.016i | − 0.993071i | −0.868016 | − | 0.496536i | \(-0.834605\pi\) | ||||
0.868016 | − | 0.496536i | \(-0.165395\pi\) | |||||||
\(44\) | −37.0951 | −0.127098 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 377.696 | 1.21061 | ||||||||
\(47\) | 169.870i | 0.527192i | 0.964633 | + | 0.263596i | \(0.0849085\pi\) | ||||
−0.964633 | + | 0.263596i | \(0.915091\pi\) | |||||||
\(48\) | − 238.818i | − 0.718133i | ||||||||
\(49\) | 320.489 | 0.934371 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 219.505 | 0.602684 | ||||||||
\(52\) | 50.6576i | 0.135095i | ||||||||
\(53\) | − 409.652i | − 1.06170i | −0.847466 | − | 0.530849i | \(-0.821873\pi\) | ||||
0.847466 | − | 0.530849i | \(-0.178127\pi\) | |||||||
\(54\) | −91.0516 | −0.229455 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 74.0435 | 0.176687 | ||||||||
\(57\) | 236.103i | 0.548643i | ||||||||
\(58\) | 819.886i | 1.85614i | ||||||||
\(59\) | −196.000 | −0.432492 | −0.216246 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216246 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −701.359 | −1.47213 | −0.736064 | − | 0.676912i | \(-0.763318\pi\) | ||||
−0.736064 | + | 0.676912i | \(0.763318\pi\) | |||||||
\(62\) | − 939.913i | − 1.92531i | ||||||||
\(63\) | − 42.7011i | − 0.0853941i | ||||||||
\(64\) | −152.568 | −0.297984 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 111.285 | 0.207550 | ||||||||
\(67\) | − 900.587i | − 1.64215i | −0.570819 | − | 0.821076i | \(-0.693374\pi\) | ||||
0.570819 | − | 0.821076i | \(-0.306626\pi\) | |||||||
\(68\) | 246.745i | 0.440032i | ||||||||
\(69\) | −336.000 | −0.586227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 756.500 | 1.26451 | 0.632254 | − | 0.774762i | \(-0.282130\pi\) | ||||
0.632254 | + | 0.774762i | \(0.282130\pi\) | |||||||
\(72\) | 140.454i | 0.229898i | ||||||||
\(73\) | − 1019.81i | − 1.63507i | −0.575877 | − | 0.817536i | \(-0.695339\pi\) | ||||
0.575877 | − | 0.817536i | \(-0.304661\pi\) | |||||||
\(74\) | −345.255 | −0.542367 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −265.402 | −0.400575 | ||||||||
\(77\) | 52.1902i | 0.0772419i | ||||||||
\(78\) | − 151.973i | − 0.220609i | ||||||||
\(79\) | 327.549 | 0.466483 | 0.233241 | − | 0.972419i | \(-0.425067\pi\) | ||||
0.233241 | + | 0.972419i | \(0.425067\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 813.581i | 1.09567i | ||||||||
\(83\) | − 756.619i | − 1.00060i | −0.865852 | − | 0.500300i | \(-0.833223\pi\) | ||||
0.865852 | − | 0.500300i | \(-0.166777\pi\) | |||||||
\(84\) | 48.0000 | 0.0623480 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −944.293 | −1.18402 | ||||||||
\(87\) | − 729.375i | − 0.898818i | ||||||||
\(88\) | − 171.666i | − 0.207950i | ||||||||
\(89\) | −508.978 | −0.606198 | −0.303099 | − | 0.952959i | \(-0.598021\pi\) | ||||
−0.303099 | + | 0.952959i | \(0.598021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 71.2716 | 0.0821022 | ||||||||
\(92\) | − 377.696i | − 0.428016i | ||||||||
\(93\) | 836.152i | 0.932311i | ||||||||
\(94\) | 572.848 | 0.628561 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −430.818 | −0.458023 | ||||||||
\(97\) | − 614.358i | − 0.643079i | −0.946896 | − | 0.321539i | \(-0.895800\pi\) | ||||
0.946896 | − | 0.321539i | \(-0.104200\pi\) | |||||||
\(98\) | − 1080.78i | − 1.11403i | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1015.92 | −1.00087 | −0.500434 | − | 0.865775i | \(-0.666826\pi\) | ||||
−0.500434 | + | 0.865775i | \(0.666826\pi\) | |||||||
\(102\) | − 740.234i | − 0.718569i | ||||||||
\(103\) | 1102.16i | 1.05436i | 0.849753 | + | 0.527181i | \(0.176751\pi\) | ||||
−0.849753 | + | 0.527181i | \(0.823249\pi\) | |||||||
\(104\) | −234.429 | −0.221035 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1381.46 | −1.26584 | ||||||||
\(107\) | − 1377.58i | − 1.24463i | −0.782767 | − | 0.622315i | \(-0.786192\pi\) | ||||
0.782767 | − | 0.622315i | \(-0.213808\pi\) | |||||||
\(108\) | 91.0516i | 0.0811245i | ||||||||
\(109\) | −320.217 | −0.281388 | −0.140694 | − | 0.990053i | \(-0.544933\pi\) | ||||
−0.140694 | + | 0.990053i | \(0.544933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 307.141 | 0.262636 | ||||||||
\(112\) | − 377.696i | − 0.318651i | ||||||||
\(113\) | − 1629.45i | − 1.35651i | −0.734828 | − | 0.678254i | \(-0.762737\pi\) | ||||
0.734828 | − | 0.678254i | \(-0.237263\pi\) | |||||||
\(114\) | 796.206 | 0.654136 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 819.886 | 0.656245 | ||||||||
\(117\) | 135.196i | 0.106828i | ||||||||
\(118\) | 660.967i | 0.515652i | ||||||||
\(119\) | 347.152 | 0.267423 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 2365.18i | 1.75519i | ||||||||
\(123\) | − 723.766i | − 0.530568i | ||||||||
\(124\) | −939.913 | −0.680699 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −144.000 | −0.101814 | ||||||||
\(127\) | − 2291.26i | − 1.60091i | −0.599390 | − | 0.800457i | \(-0.704590\pi\) | ||||
0.599390 | − | 0.800457i | \(-0.295410\pi\) | |||||||
\(128\) | 1663.35i | 1.14860i | ||||||||
\(129\) | 840.049 | 0.573350 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1147.41 | −0.765267 | −0.382633 | − | 0.923900i | \(-0.624983\pi\) | ||||
−0.382633 | + | 0.923900i | \(0.624983\pi\) | |||||||
\(132\) | − 111.285i | − 0.0733799i | ||||||||
\(133\) | 373.402i | 0.243444i | ||||||||
\(134\) | −3037.03 | −1.95791 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1141.86 | −0.719956 | ||||||||
\(137\) | − 1268.60i | − 0.791121i | −0.918440 | − | 0.395561i | \(-0.870550\pi\) | ||||
0.918440 | − | 0.395561i | \(-0.129450\pi\) | |||||||
\(138\) | 1133.09i | 0.698947i | ||||||||
\(139\) | 486.288 | 0.296737 | 0.148368 | − | 0.988932i | \(-0.452598\pi\) | ||||
0.148368 | + | 0.988932i | \(0.452598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −509.609 | −0.304374 | ||||||||
\(142\) | − 2551.13i | − 1.50765i | ||||||||
\(143\) | − 165.239i | − 0.0966294i | ||||||||
\(144\) | 716.454 | 0.414614 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3439.10 | −1.94947 | ||||||||
\(147\) | 961.467i | 0.539459i | ||||||||
\(148\) | 345.255i | 0.191756i | ||||||||
\(149\) | −2354.11 | −1.29434 | −0.647169 | − | 0.762346i | \(-0.724047\pi\) | ||||
−0.647169 | + | 0.762346i | \(0.724047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −570.070 | −0.307229 | −0.153615 | − | 0.988131i | \(-0.549091\pi\) | ||||
−0.153615 | + | 0.988131i | \(0.549091\pi\) | |||||||
\(152\) | − 1228.21i | − 0.655399i | ||||||||
\(153\) | 658.516i | 0.347960i | ||||||||
\(154\) | 176.000 | 0.0920941 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −151.973 | −0.0779971 | ||||||||
\(157\) | 2072.67i | 1.05361i | 0.849985 | + | 0.526807i | \(0.176611\pi\) | ||||
−0.849985 | + | 0.526807i | \(0.823389\pi\) | |||||||
\(158\) | − 1104.59i | − 0.556179i | ||||||||
\(159\) | 1228.96 | 0.612972 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −531.391 | −0.260121 | ||||||||
\(162\) | − 273.155i | − 0.132476i | ||||||||
\(163\) | 2676.51i | 1.28614i | 0.765808 | + | 0.643069i | \(0.222339\pi\) | ||||
−0.765808 | + | 0.643069i | \(0.777661\pi\) | |||||||
\(164\) | 813.581 | 0.387378 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2551.53 | −1.19300 | ||||||||
\(167\) | 1188.12i | 0.550536i | 0.961368 | + | 0.275268i | \(0.0887665\pi\) | ||||
−0.961368 | + | 0.275268i | \(0.911233\pi\) | |||||||
\(168\) | 222.130i | 0.102010i | ||||||||
\(169\) | 1971.35 | 0.897290 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −708.310 | −0.316759 | ||||||||
\(172\) | 944.293i | 0.418615i | ||||||||
\(173\) | 807.147i | 0.354718i | 0.984146 | + | 0.177359i | \(0.0567554\pi\) | ||||
−0.984146 | + | 0.177359i | \(0.943245\pi\) | |||||||
\(174\) | −2459.66 | −1.07164 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −875.666 | −0.375033 | ||||||||
\(177\) | − 588.000i | − 0.249699i | ||||||||
\(178\) | 1716.42i | 0.722758i | ||||||||
\(179\) | 1950.39 | 0.814408 | 0.407204 | − | 0.913337i | \(-0.366504\pi\) | ||||
0.407204 | + | 0.913337i | \(0.366504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1061.61 | 0.435959 | 0.217980 | − | 0.975953i | \(-0.430053\pi\) | ||||
0.217980 | + | 0.975953i | \(0.430053\pi\) | |||||||
\(182\) | − 240.348i | − 0.0978889i | ||||||||
\(183\) | − 2104.08i | − 0.849933i | ||||||||
\(184\) | 1747.87 | 0.700297 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2819.74 | 1.11158 | ||||||||
\(187\) | − 804.853i | − 0.314742i | ||||||||
\(188\) | − 572.848i | − 0.222230i | ||||||||
\(189\) | 128.103 | 0.0493023 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2136.41 | 0.809348 | 0.404674 | − | 0.914461i | \(-0.367385\pi\) | ||||
0.404674 | + | 0.914461i | \(0.367385\pi\) | |||||||
\(192\) | − 457.704i | − 0.172041i | ||||||||
\(193\) | 3947.76i | 1.47236i | 0.676784 | + | 0.736181i | \(0.263373\pi\) | ||||
−0.676784 | + | 0.736181i | \(0.736627\pi\) | |||||||
\(194\) | −2071.79 | −0.766731 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1080.78 | −0.393870 | ||||||||
\(197\) | − 923.886i | − 0.334133i | −0.985946 | − | 0.167066i | \(-0.946571\pi\) | ||||
0.985946 | − | 0.167066i | \(-0.0534294\pi\) | |||||||
\(198\) | 333.856i | 0.119829i | ||||||||
\(199\) | 476.152 | 0.169616 | 0.0848078 | − | 0.996397i | \(-0.472972\pi\) | ||||
0.0848078 | + | 0.996397i | \(0.472972\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2701.76 | 0.948097 | ||||||||
\(202\) | 3425.96i | 1.19332i | ||||||||
\(203\) | − 1153.52i | − 0.398824i | ||||||||
\(204\) | −740.234 | −0.254053 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3716.80 | 1.25710 | ||||||||
\(207\) | − 1008.00i | − 0.338458i | ||||||||
\(208\) | 1195.82i | 0.398631i | ||||||||
\(209\) | 865.712 | 0.286519 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4918.24 | −1.60467 | −0.802336 | − | 0.596872i | \(-0.796410\pi\) | ||||
−0.802336 | + | 0.596872i | \(0.796410\pi\) | |||||||
\(212\) | 1381.46i | 0.447543i | ||||||||
\(213\) | 2269.50i | 0.730064i | ||||||||
\(214\) | −4645.57 | −1.48395 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −421.361 | −0.132731 | ||||||||
\(217\) | 1322.39i | 0.413686i | ||||||||
\(218\) | 1079.86i | 0.335494i | ||||||||
\(219\) | 3059.44 | 0.944010 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1099.12 | −0.334546 | ||||||||
\(222\) | − 1035.77i | − 0.313136i | ||||||||
\(223\) | 2100.29i | 0.630700i | 0.948975 | + | 0.315350i | \(0.102122\pi\) | ||||
−0.948975 | + | 0.315350i | \(0.897878\pi\) | |||||||
\(224\) | −681.348 | −0.203234 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5494.95 | −1.61734 | ||||||||
\(227\) | 2257.16i | 0.659970i | 0.943986 | + | 0.329985i | \(0.107044\pi\) | ||||
−0.943986 | + | 0.329985i | \(0.892956\pi\) | |||||||
\(228\) | − 796.206i | − 0.231272i | ||||||||
\(229\) | 5311.07 | 1.53260 | 0.766301 | − | 0.642482i | \(-0.222095\pi\) | ||||
0.766301 | + | 0.642482i | \(0.222095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −156.571 | −0.0445956 | ||||||||
\(232\) | 3794.20i | 1.07371i | ||||||||
\(233\) | 2466.27i | 0.693435i | 0.937970 | + | 0.346718i | \(0.112704\pi\) | ||||
−0.937970 | + | 0.346718i | \(0.887296\pi\) | |||||||
\(234\) | 455.918 | 0.127369 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 660.967 | 0.182311 | ||||||||
\(237\) | 982.646i | 0.269324i | ||||||||
\(238\) | − 1170.70i | − 0.318844i | ||||||||
\(239\) | −1429.40 | −0.386863 | −0.193432 | − | 0.981114i | \(-0.561962\pi\) | ||||
−0.193432 | + | 0.981114i | \(0.561962\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −978.989 | −0.261669 | −0.130835 | − | 0.991404i | \(-0.541766\pi\) | ||||
−0.130835 | + | 0.991404i | \(0.541766\pi\) | |||||||
\(242\) | − 408.046i | − 0.108389i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 2365.18 | 0.620553 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2440.74 | −0.632586 | ||||||||
\(247\) | − 1182.23i | − 0.304548i | ||||||||
\(248\) | − 4349.65i | − 1.11372i | ||||||||
\(249\) | 2269.86 | 0.577696 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6530.63 | −1.64227 | −0.821135 | − | 0.570734i | \(-0.806659\pi\) | ||||
−0.821135 | + | 0.570734i | \(0.806659\pi\) | |||||||
\(252\) | 144.000i | 0.0359966i | ||||||||
\(253\) | 1232.00i | 0.306147i | ||||||||
\(254\) | −7726.76 | −1.90874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4388.74 | 1.07147 | ||||||||
\(257\) | − 8130.26i | − 1.97335i | −0.162696 | − | 0.986676i | \(-0.552019\pi\) | ||||
0.162696 | − | 0.986676i | \(-0.447981\pi\) | |||||||
\(258\) | − 2832.88i | − 0.683595i | ||||||||
\(259\) | 485.750 | 0.116537 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2188.12 | 0.518933 | ||||||||
\(262\) | 3869.40i | 0.912414i | ||||||||
\(263\) | − 4549.42i | − 1.06665i | −0.845910 | − | 0.533326i | \(-0.820942\pi\) | ||||
0.845910 | − | 0.533326i | \(-0.179058\pi\) | |||||||
\(264\) | 514.997 | 0.120060 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1259.22 | 0.290254 | ||||||||
\(267\) | − 1526.93i | − 0.349988i | ||||||||
\(268\) | 3037.03i | 0.692225i | ||||||||
\(269\) | 29.1522 | 0.00660760 | 0.00330380 | − | 0.999995i | \(-0.498948\pi\) | ||||
0.00330380 | + | 0.999995i | \(0.498948\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7711.22 | 1.72850 | 0.864250 | − | 0.503063i | \(-0.167794\pi\) | ||||
0.864250 | + | 0.503063i | \(0.167794\pi\) | |||||||
\(272\) | 5824.64i | 1.29842i | ||||||||
\(273\) | 213.815i | 0.0474017i | ||||||||
\(274\) | −4278.07 | −0.943239 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1133.09 | 0.247115 | ||||||||
\(277\) | − 1127.52i | − 0.244571i | −0.992495 | − | 0.122286i | \(-0.960978\pi\) | ||||
0.992495 | − | 0.122286i | \(-0.0390224\pi\) | |||||||
\(278\) | − 1639.90i | − 0.353794i | ||||||||
\(279\) | −2508.46 | −0.538270 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1872.47 | −0.397517 | −0.198758 | − | 0.980049i | \(-0.563691\pi\) | ||||
−0.198758 | + | 0.980049i | \(0.563691\pi\) | |||||||
\(282\) | 1718.54i | 0.362900i | ||||||||
\(283\) | 2124.48i | 0.446245i | 0.974790 | + | 0.223123i | \(0.0716251\pi\) | ||||
−0.974790 | + | 0.223123i | \(0.928375\pi\) | |||||||
\(284\) | −2551.13 | −0.533034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −557.233 | −0.115209 | ||||||||
\(287\) | − 1144.65i | − 0.235424i | ||||||||
\(288\) | − 1292.45i | − 0.264439i | ||||||||
\(289\) | −440.621 | −0.0896846 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1843.07 | 0.371282 | ||||||||
\(292\) | 3439.10i | 0.689241i | ||||||||
\(293\) | − 3324.19i | − 0.662802i | −0.943490 | − | 0.331401i | \(-0.892479\pi\) | ||||
0.943490 | − | 0.331401i | \(-0.107521\pi\) | |||||||
\(294\) | 3242.34 | 0.643187 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1597.75 | −0.313740 | ||||||||
\(297\) | − 297.000i | − 0.0580259i | ||||||||
\(298\) | 7938.73i | 1.54322i | ||||||||
\(299\) | 1682.44 | 0.325411 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1328.55 | 0.254407 | ||||||||
\(302\) | 1922.44i | 0.366304i | ||||||||
\(303\) | − 3047.75i | − 0.577851i | ||||||||
\(304\) | −6265.07 | −1.18200 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2220.70 | 0.414866 | ||||||||
\(307\) | 1698.94i | 0.315843i | 0.987452 | + | 0.157921i | \(0.0504793\pi\) | ||||
−0.987452 | + | 0.157921i | \(0.949521\pi\) | |||||||
\(308\) | − 176.000i | − 0.0325602i | ||||||||
\(309\) | −3306.49 | −0.608736 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6928.83 | 1.26334 | 0.631668 | − | 0.775239i | \(-0.282370\pi\) | ||||
0.631668 | + | 0.775239i | \(0.282370\pi\) | |||||||
\(312\) | − 703.287i | − 0.127615i | ||||||||
\(313\) | − 3560.75i | − 0.643020i | −0.946906 | − | 0.321510i | \(-0.895810\pi\) | ||||
0.946906 | − | 0.321510i | \(-0.104190\pi\) | |||||||
\(314\) | 6989.64 | 1.25620 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1104.59 | −0.196639 | ||||||||
\(317\) | − 332.750i | − 0.0589561i | −0.999565 | − | 0.0294780i | \(-0.990615\pi\) | ||||
0.999565 | − | 0.0294780i | \(-0.00938451\pi\) | |||||||
\(318\) | − 4144.39i | − 0.730835i | ||||||||
\(319\) | −2674.37 | −0.469393 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4132.73 | 0.718587 | ||||||||
\(322\) | 1792.00i | 0.310137i | ||||||||
\(323\) | − 5758.43i | − 0.991975i | ||||||||
\(324\) | −273.155 | −0.0468372 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9025.94 | 1.53344 | ||||||||
\(327\) | − 960.652i | − 0.162459i | ||||||||
\(328\) | 3765.02i | 0.633807i | ||||||||
\(329\) | −805.957 | −0.135057 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −541.445 | −0.0899108 | −0.0449554 | − | 0.998989i | \(-0.514315\pi\) | ||||
−0.0449554 | + | 0.998989i | \(0.514315\pi\) | |||||||
\(332\) | 2551.53i | 0.421788i | ||||||||
\(333\) | 921.423i | 0.151633i | ||||||||
\(334\) | 4006.67 | 0.656393 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1133.09 | 0.183973 | ||||||||
\(337\) | − 816.531i | − 0.131986i | −0.997820 | − | 0.0659930i | \(-0.978978\pi\) | ||||
0.997820 | − | 0.0659930i | \(-0.0210215\pi\) | |||||||
\(338\) | − 6647.94i | − 1.06982i | ||||||||
\(339\) | 4888.34 | 0.783180 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3065.89 | 0.486883 | ||||||||
\(342\) | 2388.62i | 0.377666i | ||||||||
\(343\) | 3147.97i | 0.495552i | ||||||||
\(344\) | −4369.92 | −0.684914 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2721.93 | 0.422924 | ||||||||
\(347\) | − 6260.53i | − 0.968539i | −0.874919 | − | 0.484269i | \(-0.839086\pi\) | ||||
0.874919 | − | 0.484269i | \(-0.160914\pi\) | |||||||
\(348\) | 2459.66i | 0.378884i | ||||||||
\(349\) | 12768.5 | 1.95840 | 0.979198 | − | 0.202906i | \(-0.0650386\pi\) | ||||
0.979198 | + | 0.202906i | \(0.0650386\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −405.587 | −0.0616771 | ||||||||
\(352\) | 1579.67i | 0.239194i | ||||||||
\(353\) | − 2649.28i | − 0.399453i | −0.979852 | − | 0.199727i | \(-0.935995\pi\) | ||||
0.979852 | − | 0.199727i | \(-0.0640054\pi\) | |||||||
\(354\) | −1982.90 | −0.297712 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1716.42 | 0.255534 | ||||||||
\(357\) | 1041.46i | 0.154397i | ||||||||
\(358\) | − 6577.27i | − 0.971004i | ||||||||
\(359\) | 3203.91 | 0.471020 | 0.235510 | − | 0.971872i | \(-0.424324\pi\) | ||||
0.235510 | + | 0.971872i | \(0.424324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −665.143 | −0.0969737 | ||||||||
\(362\) | − 3580.04i | − 0.519786i | ||||||||
\(363\) | 363.000i | 0.0524864i | ||||||||
\(364\) | −240.348 | −0.0346089 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7095.54 | −1.01336 | ||||||||
\(367\) | 8429.40i | 1.19894i | 0.800397 | + | 0.599470i | \(0.204622\pi\) | ||||
−0.800397 | + | 0.599470i | \(0.795378\pi\) | |||||||
\(368\) | − 8915.87i | − 1.26297i | ||||||||
\(369\) | 2171.30 | 0.306323 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1943.62 | 0.271988 | ||||||||
\(372\) | − 2819.74i | − 0.393002i | ||||||||
\(373\) | − 9388.53i | − 1.30327i | −0.758533 | − | 0.651635i | \(-0.774083\pi\) | ||||
0.758533 | − | 0.651635i | \(-0.225917\pi\) | |||||||
\(374\) | −2714.19 | −0.375261 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2650.98 | 0.363600 | ||||||||
\(377\) | 3652.16i | 0.498928i | ||||||||
\(378\) | − 432.000i | − 0.0587822i | ||||||||
\(379\) | 14264.5 | 1.93329 | 0.966647 | − | 0.256112i | \(-0.0824415\pi\) | ||||
0.966647 | + | 0.256112i | \(0.0824415\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6873.77 | 0.924288 | ||||||||
\(382\) | − 7204.58i | − 0.964970i | ||||||||
\(383\) | 13462.2i | 1.79605i | 0.439942 | + | 0.898026i | \(0.354999\pi\) | ||||
−0.439942 | + | 0.898026i | \(0.645001\pi\) | |||||||
\(384\) | −4990.05 | −0.663144 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13313.0 | 1.75547 | ||||||||
\(387\) | 2520.15i | 0.331024i | ||||||||
\(388\) | 2071.79i | 0.271080i | ||||||||
\(389\) | 941.881 | 0.122764 | 0.0613821 | − | 0.998114i | \(-0.480449\pi\) | ||||
0.0613821 | + | 0.998114i | \(0.480449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8194.87 | 1.05993 | ||||||||
\(392\) | − 5001.54i | − 0.644429i | ||||||||
\(393\) | − 3442.24i | − 0.441827i | ||||||||
\(394\) | −3115.60 | −0.398380 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 333.856 | 0.0423659 | ||||||||
\(397\) | 847.839i | 0.107183i | 0.998563 | + | 0.0535917i | \(0.0170669\pi\) | ||||
−0.998563 | + | 0.0535917i | \(0.982933\pi\) | |||||||
\(398\) | − 1605.72i | − 0.202230i | ||||||||
\(399\) | −1120.21 | −0.140553 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12203.6 | 1.51975 | 0.759875 | − | 0.650069i | \(-0.225260\pi\) | ||||
0.759875 | + | 0.650069i | \(0.225260\pi\) | |||||||
\(402\) | − 9111.10i | − 1.13040i | ||||||||
\(403\) | − 4186.82i | − 0.517520i | ||||||||
\(404\) | 3425.96 | 0.421901 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3890.00 | −0.475511 | ||||||||
\(407\) | − 1126.18i | − 0.137157i | ||||||||
\(408\) | − 3425.59i | − 0.415667i | ||||||||
\(409\) | −8759.53 | −1.05900 | −0.529500 | − | 0.848310i | \(-0.677620\pi\) | ||||
−0.529500 | + | 0.848310i | \(0.677620\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3805.79 | 0.456754 | ||||||||
\(412\) | − 3716.80i | − 0.444451i | ||||||||
\(413\) | − 929.934i | − 0.110797i | ||||||||
\(414\) | −3399.26 | −0.403537 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2157.21 | 0.254245 | ||||||||
\(417\) | 1458.86i | 0.171321i | ||||||||
\(418\) | − 2919.42i | − 0.341612i | ||||||||
\(419\) | 11188.4 | 1.30451 | 0.652256 | − | 0.757999i | \(-0.273823\pi\) | ||||
0.652256 | + | 0.757999i | \(0.273823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14082.3 | −1.63023 | −0.815116 | − | 0.579298i | \(-0.803327\pi\) | ||||
−0.815116 | + | 0.579298i | \(0.803327\pi\) | |||||||
\(422\) | 16585.7i | 1.91322i | ||||||||
\(423\) | − 1528.83i | − 0.175731i | ||||||||
\(424\) | −6393.02 | −0.732246 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7653.39 | 0.870441 | ||||||||
\(427\) | − 3327.64i | − 0.377133i | ||||||||
\(428\) | 4645.57i | 0.524655i | ||||||||
\(429\) | 495.718 | 0.0557890 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5616.05 | −0.627647 | −0.313823 | − | 0.949481i | \(-0.601610\pi\) | ||||
−0.313823 | + | 0.949481i | \(0.601610\pi\) | |||||||
\(432\) | 2149.36i | 0.239378i | ||||||||
\(433\) | 7195.75i | 0.798627i | 0.916814 | + | 0.399314i | \(0.130752\pi\) | ||||
−0.916814 | + | 0.399314i | \(0.869248\pi\) | |||||||
\(434\) | 4459.48 | 0.493230 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1079.86 | 0.118615 | ||||||||
\(437\) | 8814.52i | 0.964887i | ||||||||
\(438\) | − 10317.3i | − 1.12553i | ||||||||
\(439\) | −101.959 | −0.0110848 | −0.00554240 | − | 0.999985i | \(-0.501764\pi\) | ||||
−0.00554240 | + | 0.999985i | \(0.501764\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2884.40 | −0.311457 | ||||||||
\(442\) | 3706.53i | 0.398873i | ||||||||
\(443\) | 4953.74i | 0.531285i | 0.964072 | + | 0.265642i | \(0.0855841\pi\) | ||||
−0.964072 | + | 0.265642i | \(0.914416\pi\) | |||||||
\(444\) | −1035.77 | −0.110710 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7082.78 | 0.751972 | ||||||||
\(447\) | − 7062.34i | − 0.747287i | ||||||||
\(448\) | − 723.869i | − 0.0763383i | ||||||||
\(449\) | 11602.0 | 1.21945 | 0.609723 | − | 0.792615i | \(-0.291281\pi\) | ||||
0.609723 | + | 0.792615i | \(0.291281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2653.81 | −0.277080 | ||||||||
\(452\) | 5494.95i | 0.571816i | ||||||||
\(453\) | − 1710.21i | − 0.177379i | ||||||||
\(454\) | 7611.79 | 0.786870 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3684.62 | 0.378395 | ||||||||
\(457\) | 3530.68i | 0.361397i | 0.983539 | + | 0.180698i | \(0.0578358\pi\) | ||||
−0.983539 | + | 0.180698i | \(0.942164\pi\) | |||||||
\(458\) | − 17910.4i | − 1.82729i | ||||||||
\(459\) | −1975.55 | −0.200895 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11566.3 | 1.16854 | 0.584271 | − | 0.811559i | \(-0.301381\pi\) | ||||
0.584271 | + | 0.811559i | \(0.301381\pi\) | |||||||
\(462\) | 528.000i | 0.0531705i | ||||||||
\(463\) | 10888.5i | 1.09294i | 0.837479 | + | 0.546470i | \(0.184029\pi\) | ||||
−0.837479 | + | 0.546470i | \(0.815971\pi\) | |||||||
\(464\) | 19354.2 | 1.93641 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8316.94 | 0.826770 | ||||||||
\(467\) | − 10688.0i | − 1.05906i | −0.848292 | − | 0.529529i | \(-0.822369\pi\) | ||||
0.848292 | − | 0.529529i | \(-0.177631\pi\) | |||||||
\(468\) | − 455.918i | − 0.0450317i | ||||||||
\(469\) | 4272.89 | 0.420690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6218.02 | −0.608304 | ||||||||
\(472\) | 3058.77i | 0.298287i | ||||||||
\(473\) | − 3080.18i | − 0.299422i | ||||||||
\(474\) | 3313.76 | 0.321110 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1170.70 | −0.112728 | ||||||||
\(477\) | 3686.87i | 0.353900i | ||||||||
\(478\) | 4820.35i | 0.461250i | ||||||||
\(479\) | −2341.90 | −0.223391 | −0.111696 | − | 0.993742i | \(-0.535628\pi\) | ||||
−0.111696 | + | 0.993742i | \(0.535628\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1537.93 | −0.145787 | ||||||||
\(482\) | 3301.43i | 0.311983i | ||||||||
\(483\) | − 1594.17i | − 0.150181i | ||||||||
\(484\) | −408.046 | −0.0383214 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 819.464 | 0.0764849 | ||||||||
\(487\) | − 6748.91i | − 0.627972i | −0.949428 | − | 0.313986i | \(-0.898335\pi\) | ||||
0.949428 | − | 0.313986i | \(-0.101665\pi\) | |||||||
\(488\) | 10945.4i | 1.01532i | ||||||||
\(489\) | −8029.53 | −0.742552 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7361.40 | 0.676609 | 0.338305 | − | 0.941037i | \(-0.390147\pi\) | ||||
0.338305 | + | 0.941037i | \(0.390147\pi\) | |||||||
\(492\) | 2440.74i | 0.223653i | ||||||||
\(493\) | 17789.1i | 1.62511i | ||||||||
\(494\) | −3986.80 | −0.363107 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22187.6 | −2.00857 | ||||||||
\(497\) | 3589.26i | 0.323944i | ||||||||
\(498\) | − 7654.60i | − 0.688777i | ||||||||
\(499\) | −10381.7 | −0.931359 | −0.465680 | − | 0.884953i | \(-0.654190\pi\) | ||||
−0.465680 | + | 0.884953i | \(0.654190\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3564.36 | −0.317852 | ||||||||
\(502\) | 22023.1i | 1.95805i | ||||||||
\(503\) | 19149.0i | 1.69744i | 0.528840 | + | 0.848721i | \(0.322627\pi\) | ||||
−0.528840 | + | 0.848721i | \(0.677373\pi\) | |||||||
\(504\) | −666.391 | −0.0588957 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4154.65 | 0.365013 | ||||||||
\(507\) | 5914.04i | 0.518051i | ||||||||
\(508\) | 7726.76i | 0.674841i | ||||||||
\(509\) | −16073.2 | −1.39967 | −0.699836 | − | 0.714303i | \(-0.746744\pi\) | ||||
−0.699836 | + | 0.714303i | \(0.746744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4838.58 | 0.418877 | ||||||||
\(512\) | − 1493.27i | − 0.128894i | ||||||||
\(513\) | − 2124.93i | − 0.182881i | ||||||||
\(514\) | −27417.5 | −2.35279 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2832.88 | −0.241687 | ||||||||
\(517\) | 1868.56i | 0.158954i | ||||||||
\(518\) | − 1638.09i | − 0.138945i | ||||||||
\(519\) | −2421.44 | −0.204797 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18955.3 | −1.59395 | −0.796975 | − | 0.604012i | \(-0.793568\pi\) | ||||
−0.796975 | + | 0.604012i | \(0.793568\pi\) | |||||||
\(522\) | − 7378.97i | − 0.618714i | ||||||||
\(523\) | − 4442.19i | − 0.371402i | −0.982606 | − | 0.185701i | \(-0.940544\pi\) | ||||
0.982606 | − | 0.185701i | \(-0.0594556\pi\) | |||||||
\(524\) | 3869.40 | 0.322587 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15341.9 | −1.27175 | ||||||||
\(527\) | − 20393.3i | − 1.68567i | ||||||||
\(528\) | − 2627.00i | − 0.216525i | ||||||||
\(529\) | −377.000 | −0.0309855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1764.00 | 0.144164 | ||||||||
\(532\) | − 1259.22i | − 0.102620i | ||||||||
\(533\) | 3624.08i | 0.294515i | ||||||||
\(534\) | −5149.25 | −0.417285 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14054.5 | −1.13258 | ||||||||
\(537\) | 5851.17i | 0.470199i | ||||||||
\(538\) | − 98.3096i | − 0.00787812i | ||||||||
\(539\) | 3525.38 | 0.281723 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2180.90 | 0.173316 | 0.0866580 | − | 0.996238i | \(-0.472381\pi\) | ||||
0.0866580 | + | 0.996238i | \(0.472381\pi\) | |||||||
\(542\) | − 26004.4i | − 2.06086i | ||||||||
\(543\) | 3184.82i | 0.251701i | ||||||||
\(544\) | 10507.4 | 0.828129 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 721.044 | 0.0565162 | ||||||||
\(547\) | − 8225.04i | − 0.642920i | −0.946923 | − | 0.321460i | \(-0.895826\pi\) | ||||
0.946923 | − | 0.321460i | \(-0.104174\pi\) | |||||||
\(548\) | 4278.07i | 0.333485i | ||||||||
\(549\) | 6312.23 | 0.490709 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19134.2 | −1.47939 | ||||||||
\(552\) | 5243.61i | 0.404316i | ||||||||
\(553\) | 1554.08i | 0.119505i | ||||||||
\(554\) | −3802.32 | −0.291598 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1639.90 | −0.125085 | ||||||||
\(557\) | 25181.9i | 1.91561i | 0.287423 | + | 0.957804i | \(0.407201\pi\) | ||||
−0.287423 | + | 0.957804i | \(0.592799\pi\) | |||||||
\(558\) | 8459.22i | 0.641769i | ||||||||
\(559\) | −4206.33 | −0.318263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2414.56 | 0.181716 | ||||||||
\(562\) | 6314.50i | 0.473952i | ||||||||
\(563\) | − 4504.50i | − 0.337197i | −0.985685 | − | 0.168599i | \(-0.946076\pi\) | ||||
0.985685 | − | 0.168599i | \(-0.0539242\pi\) | |||||||
\(564\) | 1718.54 | 0.128304 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7164.36 | 0.532050 | ||||||||
\(567\) | 384.310i | 0.0284647i | ||||||||
\(568\) | − 11805.9i | − 0.872122i | ||||||||
\(569\) | 13447.0 | 0.990732 | 0.495366 | − | 0.868684i | \(-0.335034\pi\) | ||||
0.495366 | + | 0.868684i | \(0.335034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2605.52 | −0.190959 | −0.0954795 | − | 0.995431i | \(-0.530438\pi\) | ||||
−0.0954795 | + | 0.995431i | \(0.530438\pi\) | |||||||
\(572\) | 557.233i | 0.0407327i | ||||||||
\(573\) | 6409.24i | 0.467277i | ||||||||
\(574\) | −3860.09 | −0.280691 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1373.11 | 0.0993281 | ||||||||
\(577\) | − 6339.65i | − 0.457406i | −0.973496 | − | 0.228703i | \(-0.926552\pi\) | ||||
0.973496 | − | 0.228703i | \(-0.0734484\pi\) | |||||||
\(578\) | 1485.90i | 0.106929i | ||||||||
\(579\) | −11843.3 | −0.850069 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3589.83 | 0.256336 | ||||||||
\(582\) | − 6215.37i | − 0.442672i | ||||||||
\(583\) | − 4506.17i | − 0.320114i | ||||||||
\(584\) | −15915.2 | −1.12770 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11210.1 | −0.790247 | ||||||||
\(587\) | 13370.6i | 0.940140i | 0.882629 | + | 0.470070i | \(0.155771\pi\) | ||||
−0.882629 | + | 0.470070i | \(0.844229\pi\) | |||||||
\(588\) | − 3242.34i | − 0.227401i | ||||||||
\(589\) | 21935.3 | 1.53452 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2771.66 | 0.192912 | ||||||||
\(592\) | 8150.09i | 0.565822i | ||||||||
\(593\) | 14319.3i | 0.991608i | 0.868434 | + | 0.495804i | \(0.165127\pi\) | ||||
−0.868434 | + | 0.495804i | \(0.834873\pi\) | |||||||
\(594\) | −1001.57 | −0.0691832 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7938.73 | 0.545609 | ||||||||
\(597\) | 1428.46i | 0.0979276i | ||||||||
\(598\) | − 5673.65i | − 0.387981i | ||||||||
\(599\) | 5788.63 | 0.394853 | 0.197427 | − | 0.980318i | \(-0.436742\pi\) | ||||
0.197427 | + | 0.980318i | \(0.436742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23968.1 | 1.62675 | 0.813375 | − | 0.581739i | \(-0.197628\pi\) | ||||
0.813375 | + | 0.581739i | \(0.197628\pi\) | |||||||
\(602\) | − 4480.26i | − 0.303325i | ||||||||
\(603\) | 8105.28i | 0.547384i | ||||||||
\(604\) | 1922.44 | 0.129508 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10277.9 | −0.688961 | ||||||||
\(607\) | 23526.6i | 1.57317i | 0.617482 | + | 0.786585i | \(0.288153\pi\) | ||||
−0.617482 | + | 0.786585i | \(0.711847\pi\) | |||||||
\(608\) | 11301.9i | 0.753872i | ||||||||
\(609\) | 3460.56 | 0.230261 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2551.74 | 0.168956 | ||||||||
\(612\) | − 2220.70i | − 0.146677i | ||||||||
\(613\) | 1228.07i | 0.0809159i | 0.999181 | + | 0.0404579i | \(0.0128817\pi\) | ||||
−0.999181 | + | 0.0404579i | \(0.987118\pi\) | |||||||
\(614\) | 5729.31 | 0.376573 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 814.478 | 0.0532732 | ||||||||
\(617\) | 9844.90i | 0.642368i | 0.947017 | + | 0.321184i | \(0.104081\pi\) | ||||
−0.947017 | + | 0.321184i | \(0.895919\pi\) | |||||||
\(618\) | 11150.4i | 0.725785i | ||||||||
\(619\) | 6551.68 | 0.425419 | 0.212709 | − | 0.977115i | \(-0.431771\pi\) | ||||
0.212709 | + | 0.977115i | \(0.431771\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3024.00 | 0.195409 | ||||||||
\(622\) | − 23365.9i | − 1.50625i | ||||||||
\(623\) | − 2414.88i | − 0.155297i | ||||||||
\(624\) | −3587.46 | −0.230150 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12007.8 | −0.766661 | ||||||||
\(627\) | 2597.14i | 0.165422i | ||||||||
\(628\) | − 6989.64i | − 0.444135i | ||||||||
\(629\) | −7491.01 | −0.474859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26440.5 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(632\) | − 5111.72i | − 0.321730i | ||||||||
\(633\) | − 14754.7i | − 0.926458i | ||||||||
\(634\) | −1122.13 | −0.0702923 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4144.39 | −0.258389 | ||||||||
\(637\) | − 4814.31i | − 0.299450i | ||||||||
\(638\) | 9018.74i | 0.559648i | ||||||||
\(639\) | −6808.50 | −0.421502 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27927.2 | −1.72084 | −0.860421 | − | 0.509584i | \(-0.829799\pi\) | ||||
−0.860421 | + | 0.509584i | \(0.829799\pi\) | |||||||
\(642\) | − 13936.7i | − 0.856758i | ||||||||
\(643\) | − 16737.7i | − 1.02655i | −0.858225 | − | 0.513274i | \(-0.828432\pi\) | ||||
0.858225 | − | 0.513274i | \(-0.171568\pi\) | |||||||
\(644\) | 1792.00 | 0.109650 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19419.1 | −1.18271 | ||||||||
\(647\) | − 7818.70i | − 0.475092i | −0.971376 | − | 0.237546i | \(-0.923657\pi\) | ||||
0.971376 | − | 0.237546i | \(-0.0763431\pi\) | |||||||
\(648\) | − 1264.08i | − 0.0766325i | ||||||||
\(649\) | −2156.00 | −0.130401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3967.17 | −0.238842 | ||||||||
\(652\) | − 9025.94i | − 0.542152i | ||||||||
\(653\) | 19747.6i | 1.18344i | 0.806144 | + | 0.591719i | \(0.201550\pi\) | ||||
−0.806144 | + | 0.591719i | \(0.798450\pi\) | |||||||
\(654\) | −3239.59 | −0.193697 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19205.4 | 1.14305 | ||||||||
\(657\) | 9178.33i | 0.545024i | ||||||||
\(658\) | 2717.91i | 0.161026i | ||||||||
\(659\) | −7867.72 | −0.465072 | −0.232536 | − | 0.972588i | \(-0.574702\pi\) | ||||
−0.232536 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4227.41 | 0.248755 | 0.124378 | − | 0.992235i | \(-0.460307\pi\) | ||||
0.124378 | + | 0.992235i | \(0.460307\pi\) | |||||||
\(662\) | 1825.90i | 0.107199i | ||||||||
\(663\) | − 3297.35i | − 0.193150i | ||||||||
\(664\) | −11807.8 | −0.690106 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3107.30 | 0.180789 | ||||||||
\(667\) | − 27230.0i | − 1.58073i | ||||||||
\(668\) | − 4006.67i | − 0.232070i | ||||||||
\(669\) | −6300.88 | −0.364135 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7714.94 | −0.443863 | ||||||||
\(672\) | − 2044.04i | − 0.117337i | ||||||||
\(673\) | 29397.6i | 1.68379i | 0.539638 | + | 0.841897i | \(0.318561\pi\) | ||||
−0.539638 | + | 0.841897i | \(0.681439\pi\) | |||||||
\(674\) | −2753.57 | −0.157364 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6647.94 | −0.378239 | ||||||||
\(677\) | − 5737.14i | − 0.325696i | −0.986651 | − | 0.162848i | \(-0.947932\pi\) | ||||
0.986651 | − | 0.162848i | \(-0.0520680\pi\) | |||||||
\(678\) | − 16484.8i | − 0.933771i | ||||||||
\(679\) | 2914.86 | 0.164745 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6771.49 | −0.381034 | ||||||||
\(682\) | − 10339.0i | − 0.580502i | ||||||||
\(683\) | 32097.6i | 1.79821i | 0.437729 | + | 0.899107i | \(0.355783\pi\) | ||||
−0.437729 | + | 0.899107i | \(0.644217\pi\) | |||||||
\(684\) | 2388.62 | 0.133525 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10615.8 | 0.590837 | ||||||||
\(687\) | 15933.2i | 0.884848i | ||||||||
\(688\) | 22291.0i | 1.23523i | ||||||||
\(689\) | −6153.69 | −0.340257 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16456.2 | −0.905965 | −0.452983 | − | 0.891519i | \(-0.649640\pi\) | ||||
−0.452983 | + | 0.891519i | \(0.649640\pi\) | |||||||
\(692\) | − 2721.93i | − 0.149526i | ||||||||
\(693\) | − 469.712i | − 0.0257473i | ||||||||
\(694\) | −21112.3 | −1.15477 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11382.6 | −0.619909 | ||||||||
\(697\) | 17652.3i | 0.959294i | ||||||||
\(698\) | − 43058.9i | − 2.33496i | ||||||||
\(699\) | −7398.80 | −0.400355 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27238.1 | 1.46758 | 0.733788 | − | 0.679379i | \(-0.237751\pi\) | ||||
0.733788 | + | 0.679379i | \(0.237751\pi\) | |||||||
\(702\) | 1367.75i | 0.0735364i | ||||||||
\(703\) | − 8057.44i | − 0.432279i | ||||||||
\(704\) | −1678.25 | −0.0898457 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8934.12 | −0.476261 | ||||||||
\(707\) | − 4820.09i | − 0.256405i | ||||||||
\(708\) | 1982.90i | 0.105257i | ||||||||
\(709\) | −28761.4 | −1.52349 | −0.761747 | − | 0.647875i | \(-0.775658\pi\) | ||||
−0.761747 | + | 0.647875i | \(0.775658\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2947.94 | −0.155494 | ||||||||
\(712\) | 7943.10i | 0.418090i | ||||||||
\(713\) | 31216.3i | 1.63964i | ||||||||
\(714\) | 3512.09 | 0.184085 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6577.27 | −0.343302 | ||||||||
\(717\) | − 4288.21i | − 0.223356i | ||||||||
\(718\) | − 10804.5i | − 0.561588i | ||||||||
\(719\) | 27272.0 | 1.41456 | 0.707282 | − | 0.706931i | \(-0.249921\pi\) | ||||
0.707282 | + | 0.706931i | \(0.249921\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5229.28 | −0.270109 | ||||||||
\(722\) | 2243.05i | 0.115620i | ||||||||
\(723\) | − 2936.97i | − 0.151075i | ||||||||
\(724\) | −3580.04 | −0.183772 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1224.14 | 0.0625785 | ||||||||
\(727\) | − 3979.75i | − 0.203027i | −0.994834 | − | 0.101514i | \(-0.967631\pi\) | ||||
0.994834 | − | 0.101514i | \(-0.0323685\pi\) | |||||||
\(728\) | − 1112.26i | − 0.0566253i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20488.3 | −1.03665 | ||||||||
\(732\) | 7095.54i | 0.358277i | ||||||||
\(733\) | 9342.48i | 0.470767i | 0.971903 | + | 0.235384i | \(0.0756346\pi\) | ||||
−0.971903 | + | 0.235384i | \(0.924365\pi\) | |||||||
\(734\) | 28426.3 | 1.42947 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16083.9 | −0.805515 | ||||||||
\(737\) | − 9906.45i | − 0.495127i | ||||||||
\(738\) | − 7322.23i | − 0.365224i | ||||||||
\(739\) | 28928.0 | 1.43997 | 0.719983 | − | 0.693992i | \(-0.244150\pi\) | ||||
0.719983 | + | 0.693992i | \(0.244150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3546.68 | 0.175831 | ||||||||
\(742\) | − 6554.43i | − 0.324287i | ||||||||
\(743\) | 4857.04i | 0.239822i | 0.992785 | + | 0.119911i | \(0.0382609\pi\) | ||||
−0.992785 | + | 0.119911i | \(0.961739\pi\) | |||||||
\(744\) | 13049.0 | 0.643008 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31660.8 | −1.55386 | ||||||||
\(747\) | 6809.57i | 0.333533i | ||||||||
\(748\) | 2714.19i | 0.132675i | ||||||||
\(749\) | 6536.00 | 0.318852 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14355.4 | 0.697517 | 0.348759 | − | 0.937213i | \(-0.386603\pi\) | ||||
0.348759 | + | 0.937213i | \(0.386603\pi\) | |||||||
\(752\) | − 13522.6i | − 0.655744i | ||||||||
\(753\) | − 19591.9i | − 0.948165i | ||||||||
\(754\) | 12316.1 | 0.594863 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −432.000 | −0.0207827 | ||||||||
\(757\) | 17714.9i | 0.850538i | 0.905067 | + | 0.425269i | \(0.139821\pi\) | ||||
−0.905067 | + | 0.425269i | \(0.860179\pi\) | |||||||
\(758\) | − 48103.9i | − 2.30503i | ||||||||
\(759\) | −3696.00 | −0.176754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7945.82 | −0.378497 | −0.189248 | − | 0.981929i | \(-0.560605\pi\) | ||||
−0.189248 | + | 0.981929i | \(0.560605\pi\) | |||||||
\(762\) | − 23180.3i | − 1.10201i | ||||||||
\(763\) | − 1519.29i | − 0.0720866i | ||||||||
\(764\) | −7204.58 | −0.341168 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45398.4 | 2.14140 | ||||||||
\(767\) | 2944.26i | 0.138606i | ||||||||
\(768\) | 13166.2i | 0.618613i | ||||||||
\(769\) | −27308.1 | −1.28057 | −0.640284 | − | 0.768139i | \(-0.721183\pi\) | ||||
−0.640284 | + | 0.768139i | \(0.721183\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24390.8 | 1.13932 | ||||||||
\(772\) | − 13313.0i | − 0.620653i | ||||||||
\(773\) | − 18872.6i | − 0.878136i | −0.898454 | − | 0.439068i | \(-0.855309\pi\) | ||||
0.898454 | − | 0.439068i | \(-0.144691\pi\) | |||||||
\(774\) | 8498.64 | 0.394674 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9587.65 | −0.443527 | ||||||||
\(777\) | 1457.25i | 0.0672826i | ||||||||
\(778\) | − 3176.29i | − 0.146369i | ||||||||
\(779\) | −18987.1 | −0.873276 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8321.50 | 0.381263 | ||||||||
\(782\) | − 27635.4i | − 1.26373i | ||||||||
\(783\) | 6564.37i | 0.299606i | ||||||||
\(784\) | −25512.8 | −1.16221 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11608.2 | −0.526782 | ||||||||
\(787\) | 14512.1i | 0.657307i | 0.944450 | + | 0.328654i | \(0.106595\pi\) | ||||
−0.944450 | + | 0.328654i | \(0.893405\pi\) | |||||||
\(788\) | 3115.60i | 0.140849i | ||||||||
\(789\) | 13648.3 | 0.615832 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7731.01 | 0.347513 | ||||||||
\(792\) | 1544.99i | 0.0693167i | ||||||||
\(793\) | 10535.6i | 0.471792i | ||||||||
\(794\) | 2859.15 | 0.127793 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1605.72 | −0.0714989 | ||||||||
\(797\) | − 29108.9i | − 1.29371i | −0.762612 | − | 0.646856i | \(-0.776083\pi\) | ||||
0.762612 | − | 0.646856i | \(-0.223917\pi\) | |||||||
\(798\) | 3777.65i | 0.167578i | ||||||||
\(799\) | 12429.1 | 0.550325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4580.80 | 0.202066 | ||||||||
\(802\) | − 41154.0i | − 1.81197i | ||||||||
\(803\) | − 11218.0i | − 0.492993i | ||||||||
\(804\) | −9111.10 | −0.399656 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14119.1 | −0.617029 | ||||||||
\(807\) | 87.4567i | 0.00381490i | ||||||||
\(808\) | 15854.4i | 0.690291i | ||||||||
\(809\) | 3000.83 | 0.130413 | 0.0652063 | − | 0.997872i | \(-0.479229\pi\) | ||||
0.0652063 | + | 0.997872i | \(0.479229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6239.39 | 0.270154 | 0.135077 | − | 0.990835i | \(-0.456872\pi\) | ||||
0.135077 | + | 0.990835i | \(0.456872\pi\) | |||||||
\(812\) | 3890.00i | 0.168118i | ||||||||
\(813\) | 23133.7i | 0.997950i | ||||||||
\(814\) | −3797.81 | −0.163530 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −17473.9 | −0.749645 | ||||||||
\(817\) | − 22037.6i | − 0.943693i | ||||||||
\(818\) | 29539.6i | 1.26263i | ||||||||
\(819\) | −641.445 | −0.0273674 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14922.4 | 0.634342 | 0.317171 | − | 0.948368i | \(-0.397267\pi\) | ||||
0.317171 | + | 0.948368i | \(0.397267\pi\) | |||||||
\(822\) | − 12834.2i | − 0.544580i | ||||||||
\(823\) | − 25737.8i | − 1.09011i | −0.838399 | − | 0.545057i | \(-0.816508\pi\) | ||||
0.838399 | − | 0.545057i | \(-0.183492\pi\) | |||||||
\(824\) | 17200.3 | 0.727186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3136.00 | −0.132101 | ||||||||
\(827\) | − 27043.4i | − 1.13711i | −0.822645 | − | 0.568555i | \(-0.807503\pi\) | ||||
0.822645 | − | 0.568555i | \(-0.192497\pi\) | |||||||
\(828\) | 3399.26i | 0.142672i | ||||||||
\(829\) | 9795.41 | 0.410384 | 0.205192 | − | 0.978722i | \(-0.434218\pi\) | ||||
0.205192 | + | 0.978722i | \(0.434218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3382.56 | 0.141203 | ||||||||
\(832\) | 2291.84i | 0.0954990i | ||||||||
\(833\) | − 23449.7i | − 0.975370i | ||||||||
\(834\) | 4919.70 | 0.204263 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2919.42 | −0.120778 | ||||||||
\(837\) | − 7525.37i | − 0.310770i | ||||||||
\(838\) | − 37730.5i | − 1.55535i | ||||||||
\(839\) | −28875.5 | −1.18819 | −0.594095 | − | 0.804395i | \(-0.702490\pi\) | ||||
−0.594095 | + | 0.804395i | \(0.702490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34720.7 | 1.42362 | ||||||||
\(842\) | 47489.3i | 1.94369i | ||||||||
\(843\) | − 5617.41i | − 0.229506i | ||||||||
\(844\) | 16585.7 | 0.676426 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5155.63 | −0.209520 | ||||||||
\(847\) | 574.092i | 0.0232893i | ||||||||
\(848\) | 32610.7i | 1.32059i | ||||||||
\(849\) | −6373.45 | −0.257640 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11466.6 | 0.461892 | ||||||||
\(852\) | − 7653.39i | − 0.307747i | ||||||||
\(853\) | − 47157.1i | − 1.89288i | −0.322878 | − | 0.946441i | \(-0.604650\pi\) | ||||
0.322878 | − | 0.946441i | \(-0.395350\pi\) | |||||||
\(854\) | −11221.7 | −0.449649 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21498.4 | −0.858412 | ||||||||
\(857\) | − 5021.31i | − 0.200145i | −0.994980 | − | 0.100073i | \(-0.968092\pi\) | ||||
0.994980 | − | 0.100073i | \(-0.0319075\pi\) | |||||||
\(858\) | − 1671.70i | − 0.0665162i | ||||||||
\(859\) | 22921.1 | 0.910428 | 0.455214 | − | 0.890382i | \(-0.349563\pi\) | ||||
0.455214 | + | 0.890382i | \(0.349563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3433.95 | 0.135922 | ||||||||
\(862\) | 18938.9i | 0.748332i | ||||||||
\(863\) | − 19488.1i | − 0.768693i | −0.923189 | − | 0.384347i | \(-0.874427\pi\) | ||||
0.923189 | − | 0.384347i | \(-0.125573\pi\) | |||||||
\(864\) | 3877.36 | 0.152674 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24266.1 | 0.952188 | ||||||||
\(867\) | − 1321.86i | − 0.0517794i | ||||||||
\(868\) | − 4459.48i | − 0.174383i | ||||||||
\(869\) | 3603.04 | 0.140650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13528.4 | −0.526282 | ||||||||
\(872\) | 4997.30i | 0.194071i | ||||||||
\(873\) | 5529.22i | 0.214360i | ||||||||
\(874\) | 29725.0 | 1.15042 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10317.3 | −0.397933 | ||||||||
\(877\) | 8455.67i | 0.325573i | 0.986661 | + | 0.162787i | \(0.0520482\pi\) | ||||
−0.986661 | + | 0.162787i | \(0.947952\pi\) | |||||||
\(878\) | 343.834i | 0.0132162i | ||||||||
\(879\) | 9972.56 | 0.382669 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11291.2 | −0.431794 | −0.215897 | − | 0.976416i | \(-0.569268\pi\) | ||||
−0.215897 | + | 0.976416i | \(0.569268\pi\) | |||||||
\(882\) | 9727.02i | 0.371344i | ||||||||
\(883\) | 31818.1i | 1.21264i | 0.795219 | + | 0.606322i | \(0.207356\pi\) | ||||
−0.795219 | + | 0.606322i | \(0.792644\pi\) | |||||||
\(884\) | 3706.53 | 0.141023 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16705.4 | 0.633441 | ||||||||
\(887\) | − 17481.1i | − 0.661732i | −0.943678 | − | 0.330866i | \(-0.892659\pi\) | ||||
0.943678 | − | 0.330866i | \(-0.107341\pi\) | |||||||
\(888\) | − 4793.24i | − 0.181138i | ||||||||
\(889\) | 10871.0 | 0.410126 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | − 7082.78i | − 0.265862i | ||||||||
\(893\) | 13368.9i | 0.500978i | ||||||||
\(894\) | −23816.2 | −0.890976 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7891.87 | −0.294251 | ||||||||
\(897\) | 5047.31i | 0.187876i | ||||||||
\(898\) | − 39125.1i | − 1.45392i | ||||||||
\(899\) | −67763.1 | −2.51393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29973.6 | −1.10829 | ||||||||
\(902\) | 8949.39i | 0.330357i | ||||||||
\(903\) | 3985.66i | 0.146882i | ||||||||
\(904\) | −25429.1 | −0.935574 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5767.31 | −0.211486 | ||||||||
\(907\) | − 10607.4i | − 0.388326i | −0.980969 | − | 0.194163i | \(-0.937801\pi\) | ||||
0.980969 | − | 0.194163i | \(-0.0621990\pi\) | |||||||
\(908\) | − 7611.79i | − 0.278201i | ||||||||
\(909\) | 9143.26 | 0.333623 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41249.2 | −1.50016 | −0.750080 | − | 0.661347i | \(-0.769985\pi\) | ||||
−0.750080 | + | 0.661347i | \(0.769985\pi\) | |||||||
\(912\) | − 18795.2i | − 0.682425i | ||||||||
\(913\) | − 8322.81i | − 0.301692i | ||||||||
\(914\) | 11906.5 | 0.430887 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17910.4 | −0.646045 | ||||||||
\(917\) | − 5443.97i | − 0.196048i | ||||||||
\(918\) | 6662.10i | 0.239523i | ||||||||
\(919\) | 13858.1 | 0.497429 | 0.248714 | − | 0.968577i | \(-0.419992\pi\) | ||||
0.248714 | + | 0.968577i | \(0.419992\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5096.83 | −0.182352 | ||||||||
\(922\) | − 39004.9i | − 1.39323i | ||||||||
\(923\) | − 11363.9i | − 0.405253i | ||||||||
\(924\) | 528.000 | 0.0187986 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 36719.0 | 1.30309 | ||||||||
\(927\) | − 9919.47i | − 0.351454i | ||||||||
\(928\) | − 34914.2i | − 1.23504i | ||||||||
\(929\) | −20893.7 | −0.737890 | −0.368945 | − | 0.929451i | \(-0.620281\pi\) | ||||
−0.368945 | + | 0.929451i | \(0.620281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25222.8 | 0.887911 | ||||||||
\(932\) | − 8316.94i | − 0.292307i | ||||||||
\(933\) | 20786.5i | 0.729388i | ||||||||
\(934\) | −36042.9 | −1.26270 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2109.86 | 0.0736784 | ||||||||
\(937\) | − 3203.52i | − 0.111691i | −0.998439 | − | 0.0558454i | \(-0.982215\pi\) | ||||
0.998439 | − | 0.0558454i | \(-0.0177854\pi\) | |||||||
\(938\) | − 14409.4i | − 0.501581i | ||||||||
\(939\) | 10682.2 | 0.371248 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19951.6 | 0.691182 | 0.345591 | − | 0.938385i | \(-0.387678\pi\) | ||||
0.345591 | + | 0.938385i | \(0.387678\pi\) | |||||||
\(942\) | 20968.9i | 0.725270i | ||||||||
\(943\) | − 27020.6i | − 0.933099i | ||||||||
\(944\) | 15602.8 | 0.537952 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10387.2 | −0.356996 | ||||||||
\(947\) | 38216.7i | 1.31138i | 0.755031 | + | 0.655689i | \(0.227622\pi\) | ||||
−0.755031 | + | 0.655689i | \(0.772378\pi\) | |||||||
\(948\) | − 3313.76i | − 0.113529i | ||||||||
\(949\) | −15319.4 | −0.524014 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 998.249 | 0.0340383 | ||||||||
\(952\) | − 5417.65i | − 0.184440i | ||||||||
\(953\) | − 47661.4i | − 1.62004i | −0.586399 | − | 0.810022i | \(-0.699455\pi\) | ||||
0.586399 | − | 0.810022i | \(-0.300545\pi\) | |||||||
\(954\) | 12433.2 | 0.421948 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4820.35 | 0.163077 | ||||||||
\(957\) | − 8023.12i | − 0.271004i | ||||||||
\(958\) | 7897.56i | 0.266345i | ||||||||
\(959\) | 6018.94 | 0.202671 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47892.3 | 1.60761 | ||||||||
\(962\) | 5186.34i | 0.173819i | ||||||||
\(963\) | 12398.2i | 0.414876i | ||||||||
\(964\) | 3301.43 | 0.110303 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5376.00 | −0.179058 | ||||||||
\(967\) | − 18933.2i | − 0.629628i | −0.949153 | − | 0.314814i | \(-0.898058\pi\) | ||||
0.949153 | − | 0.314814i | \(-0.101942\pi\) | |||||||
\(968\) | − 1888.32i | − 0.0626994i | ||||||||
\(969\) | 17275.3 | 0.572717 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40660.3 | −1.34382 | −0.671911 | − | 0.740632i | \(-0.734526\pi\) | ||||
−0.671911 | + | 0.740632i | \(0.734526\pi\) | |||||||
\(972\) | − 819.464i | − 0.0270415i | ||||||||
\(973\) | 2307.23i | 0.0760188i | ||||||||
\(974\) | −22759.2 | −0.748720 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 55832.3 | 1.83110 | ||||||||
\(977\) | 22502.8i | 0.736876i | 0.929652 | + | 0.368438i | \(0.120107\pi\) | ||||
−0.929652 | + | 0.368438i | \(0.879893\pi\) | |||||||
\(978\) | 27077.8i | 0.885331i | ||||||||
\(979\) | −5598.76 | −0.182775 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2881.96 | 0.0937959 | ||||||||
\(982\) | − 24824.7i | − 0.806709i | ||||||||
\(983\) | − 4435.20i | − 0.143907i | −0.997408 | − | 0.0719536i | \(-0.977077\pi\) | ||||
0.997408 | − | 0.0719536i | \(-0.0229234\pi\) | |||||||
\(984\) | −11295.1 | −0.365929 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 59989.8 | 1.93759 | ||||||||
\(987\) | − 2417.87i | − 0.0779753i | ||||||||
\(988\) | 3986.80i | 0.128378i | ||||||||
\(989\) | 31361.8 | 1.00834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7362.76 | 0.236010 | 0.118005 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118005 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(992\) | 40025.5i | 1.28106i | ||||||||
\(993\) | − 1624.33i | − 0.0519101i | ||||||||
\(994\) | 12104.0 | 0.386233 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7654.60 | −0.243519 | ||||||||
\(997\) | 53480.1i | 1.69883i | 0.527728 | + | 0.849413i | \(0.323044\pi\) | ||||
−0.527728 | + | 0.849413i | \(0.676956\pi\) | |||||||
\(998\) | 35010.0i | 1.11044i | ||||||||
\(999\) | −2764.27 | −0.0875452 |
(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 | 825.4.c.i.199.1 | 4 | ||
5.2 | odd | 4 | 33.4.a.d.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 825.4.a.k.1.1 | 2 | |||
5.4 | even | 2 | inner | 825.4.c.i.199.4 | 4 | ||
15.2 | even | 4 | 99.4.a.e.1.1 | 2 | |||
15.8 | even | 4 | 2475.4.a.o.1.2 | 2 | |||
20.7 | even | 4 | 528.4.a.o.1.1 | 2 | |||
35.27 | even | 4 | 1617.4.a.j.1.2 | 2 | |||
40.27 | even | 4 | 2112.4.a.bh.1.2 | 2 | |||
40.37 | odd | 4 | 2112.4.a.ba.1.2 | 2 | |||
55.32 | even | 4 | 363.4.a.j.1.1 | 2 | |||
60.47 | odd | 4 | 1584.4.a.x.1.2 | 2 | |||
165.32 | odd | 4 | 1089.4.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.d.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
99.4.a.e.1.1 | 2 | 15.2 | even | 4 | |||
363.4.a.j.1.1 | 2 | 55.32 | even | 4 | |||
528.4.a.o.1.1 | 2 | 20.7 | even | 4 | |||
825.4.a.k.1.1 | 2 | 5.3 | odd | 4 | |||
825.4.c.i.199.1 | 4 | 1.1 | even | 1 | trivial | ||
825.4.c.i.199.4 | 4 | 5.4 | even | 2 | inner | ||
1089.4.a.t.1.2 | 2 | 165.32 | odd | 4 | |||
1584.4.a.x.1.2 | 2 | 60.47 | odd | 4 | |||
1617.4.a.j.1.2 | 2 | 35.27 | even | 4 | |||
2112.4.a.ba.1.2 | 2 | 40.37 | odd | 4 | |||
2112.4.a.bh.1.2 | 2 | 40.27 | even | 4 | |||
2475.4.a.o.1.2 | 2 | 15.8 | even | 4 |