Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,3,Mod(391,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.391");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.f (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: | \(40.0545988610\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.5 | ||
Root | \(-2.10711 + 3.64962i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.391 |
Dual form | 1470.3.f.d.391.3 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − 2.23607i | − 0.447214i | ||||||||
\(6\) | − 2.44949i | − 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | −10.8220 | −0.983816 | −0.491908 | − | 0.870647i | \(-0.663700\pi\) | ||||
−0.491908 | + | 0.870647i | \(0.663700\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − 19.2715i | − 1.48242i | −0.671273 | − | 0.741211i | \(-0.734252\pi\) | ||||
0.671273 | − | 0.741211i | \(-0.265748\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 10.2737i | 0.604336i | 0.953255 | + | 0.302168i | \(0.0977104\pi\) | ||||
−0.953255 | + | 0.302168i | \(0.902290\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | − 20.8719i | − 1.09852i | −0.835652 | − | 0.549260i | \(-0.814910\pi\) | ||||
0.835652 | − | 0.549260i | \(-0.185090\pi\) | |||||||
\(20\) | − 4.47214i | − 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 15.3046 | 0.695663 | ||||||||
\(23\) | 21.0746 | 0.916286 | 0.458143 | − | 0.888878i | \(-0.348515\pi\) | ||||
0.458143 | + | 0.888878i | \(0.348515\pi\) | |||||||
\(24\) | − 4.89898i | − 0.204124i | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 27.2540i | 1.04823i | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 19.0888 | 0.658235 | 0.329118 | − | 0.944289i | \(-0.393249\pi\) | ||||
0.329118 | + | 0.944289i | \(0.393249\pi\) | |||||||
\(30\) | −5.47723 | −0.182574 | ||||||||
\(31\) | 40.0169i | 1.29087i | 0.763816 | + | 0.645434i | \(0.223323\pi\) | ||||
−0.763816 | + | 0.645434i | \(0.776677\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − 18.7442i | − 0.568007i | ||||||||
\(34\) | − 14.5292i | − 0.427330i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −50.3654 | −1.36123 | −0.680614 | − | 0.732643i | \(-0.738287\pi\) | ||||
−0.680614 | + | 0.732643i | \(0.738287\pi\) | |||||||
\(38\) | 29.5173i | 0.776771i | ||||||||
\(39\) | 33.3792 | 0.855876 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 22.7706i | 0.555382i | 0.960671 | + | 0.277691i | \(0.0895691\pi\) | ||||
−0.960671 | + | 0.277691i | \(0.910431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −48.4307 | −1.12629 | −0.563147 | − | 0.826357i | \(-0.690410\pi\) | ||||
−0.563147 | + | 0.826357i | \(0.690410\pi\) | |||||||
\(44\) | −21.6440 | −0.491908 | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | −29.8040 | −0.647912 | ||||||||
\(47\) | 66.5380i | 1.41570i | 0.706362 | + | 0.707851i | \(0.250335\pi\) | ||||
−0.706362 | + | 0.707851i | \(0.749665\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | −17.7946 | −0.348914 | ||||||||
\(52\) | − 38.5430i | − 0.741211i | ||||||||
\(53\) | 4.95062 | 0.0934079 | 0.0467040 | − | 0.998909i | \(-0.485128\pi\) | ||||
0.0467040 | + | 0.998909i | \(0.485128\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 24.1987i | 0.439976i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 36.1511 | 0.634231 | ||||||||
\(58\) | −26.9957 | −0.465442 | ||||||||
\(59\) | 28.1868i | 0.477742i | 0.971051 | + | 0.238871i | \(0.0767773\pi\) | ||||
−0.971051 | + | 0.238871i | \(0.923223\pi\) | |||||||
\(60\) | 7.74597 | 0.129099 | ||||||||
\(61\) | − 70.0889i | − 1.14900i | −0.818505 | − | 0.574499i | \(-0.805197\pi\) | ||||
0.818505 | − | 0.574499i | \(-0.194803\pi\) | |||||||
\(62\) | − 56.5924i | − 0.912781i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −43.0923 | −0.662959 | ||||||||
\(66\) | 26.5083i | 0.401641i | ||||||||
\(67\) | 19.3057 | 0.288145 | 0.144073 | − | 0.989567i | \(-0.453980\pi\) | ||||
0.144073 | + | 0.989567i | \(0.453980\pi\) | |||||||
\(68\) | 20.5474i | 0.302168i | ||||||||
\(69\) | 36.5023i | 0.529018i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 49.4968 | 0.697138 | 0.348569 | − | 0.937283i | \(-0.386668\pi\) | ||||
0.348569 | + | 0.937283i | \(0.386668\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | 132.974i | 1.82157i | 0.412886 | + | 0.910783i | \(0.364521\pi\) | ||||
−0.412886 | + | 0.910783i | \(0.635479\pi\) | |||||||
\(74\) | 71.2274 | 0.962533 | ||||||||
\(75\) | − 8.66025i | − 0.115470i | ||||||||
\(76\) | − 41.7437i | − 0.549260i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −47.2053 | −0.605196 | ||||||||
\(79\) | −90.0808 | −1.14026 | −0.570132 | − | 0.821553i | \(-0.693108\pi\) | ||||
−0.570132 | + | 0.821553i | \(0.693108\pi\) | |||||||
\(80\) | − 8.94427i | − 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − 32.2026i | − 0.392714i | ||||||||
\(83\) | − 101.045i | − 1.21741i | −0.793396 | − | 0.608706i | \(-0.791689\pi\) | ||||
0.793396 | − | 0.608706i | \(-0.208311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.9727 | 0.270267 | ||||||||
\(86\) | 68.4913 | 0.796410 | ||||||||
\(87\) | 33.0628i | 0.380032i | ||||||||
\(88\) | 30.6092 | 0.347832 | ||||||||
\(89\) | 39.6151i | 0.445113i | 0.974920 | + | 0.222557i | \(0.0714402\pi\) | ||||
−0.974920 | + | 0.222557i | \(0.928560\pi\) | |||||||
\(90\) | − 9.48683i | − 0.105409i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 42.1492 | 0.458143 | ||||||||
\(93\) | −69.3113 | −0.745283 | ||||||||
\(94\) | − 94.0989i | − 1.00105i | ||||||||
\(95\) | −46.6709 | −0.491273 | ||||||||
\(96\) | − 9.79796i | − 0.102062i | ||||||||
\(97\) | 68.6944i | 0.708190i | 0.935210 | + | 0.354095i | \(0.115211\pi\) | ||||
−0.935210 | + | 0.354095i | \(0.884789\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 32.4659 | 0.327939 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 8.03902i | 0.0795942i | 0.999208 | + | 0.0397971i | \(0.0126712\pi\) | ||||
−0.999208 | + | 0.0397971i | \(0.987329\pi\) | |||||||
\(102\) | 25.1654 | 0.246719 | ||||||||
\(103\) | 204.565i | 1.98607i | 0.117839 | + | 0.993033i | \(0.462403\pi\) | ||||
−0.117839 | + | 0.993033i | \(0.537597\pi\) | |||||||
\(104\) | 54.5080i | 0.524115i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.00124 | −0.0660494 | ||||||||
\(107\) | 164.554 | 1.53789 | 0.768943 | − | 0.639317i | \(-0.220783\pi\) | ||||
0.768943 | + | 0.639317i | \(0.220783\pi\) | |||||||
\(108\) | − 10.3923i | − 0.0962250i | ||||||||
\(109\) | −79.0101 | −0.724863 | −0.362432 | − | 0.932010i | \(-0.618053\pi\) | ||||
−0.362432 | + | 0.932010i | \(0.618053\pi\) | |||||||
\(110\) | − 34.2221i | − 0.311110i | ||||||||
\(111\) | − 87.2354i | − 0.785905i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 84.5690 | 0.748398 | 0.374199 | − | 0.927348i | \(-0.377918\pi\) | ||||
0.374199 | + | 0.927348i | \(0.377918\pi\) | |||||||
\(114\) | −51.1254 | −0.448469 | ||||||||
\(115\) | − 47.1242i | − 0.409776i | ||||||||
\(116\) | 38.1776 | 0.329118 | ||||||||
\(117\) | 57.8144i | 0.494140i | ||||||||
\(118\) | − 39.8621i | − 0.337815i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.9545 | −0.0912871 | ||||||||
\(121\) | −3.88480 | −0.0321058 | ||||||||
\(122\) | 99.1207i | 0.812465i | ||||||||
\(123\) | −39.4399 | −0.320650 | ||||||||
\(124\) | 80.0338i | 0.645434i | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −101.777 | −0.801393 | −0.400697 | − | 0.916211i | \(-0.631232\pi\) | ||||
−0.400697 | + | 0.916211i | \(0.631232\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − 83.8844i | − 0.650266i | ||||||||
\(130\) | 60.9418 | 0.468783 | ||||||||
\(131\) | 70.6982i | 0.539681i | 0.962905 | + | 0.269840i | \(0.0869709\pi\) | ||||
−0.962905 | + | 0.269840i | \(0.913029\pi\) | |||||||
\(132\) | − 37.4884i | − 0.284003i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −27.3024 | −0.203750 | ||||||||
\(135\) | −11.6190 | −0.0860663 | ||||||||
\(136\) | − 29.0585i | − 0.213665i | ||||||||
\(137\) | −117.828 | −0.860055 | −0.430027 | − | 0.902816i | \(-0.641496\pi\) | ||||
−0.430027 | + | 0.902816i | \(0.641496\pi\) | |||||||
\(138\) | − 51.6220i | − 0.374072i | ||||||||
\(139\) | − 158.507i | − 1.14034i | −0.821528 | − | 0.570168i | \(-0.806878\pi\) | ||||
0.821528 | − | 0.570168i | \(-0.193122\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −115.247 | −0.817356 | ||||||||
\(142\) | −69.9990 | −0.492951 | ||||||||
\(143\) | 208.555i | 1.45843i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | − 42.6839i | − 0.294372i | ||||||||
\(146\) | − 188.054i | − 1.28804i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −100.731 | −0.680614 | ||||||||
\(149\) | −295.896 | −1.98588 | −0.992940 | − | 0.118615i | \(-0.962155\pi\) | ||||
−0.992940 | + | 0.118615i | \(0.962155\pi\) | |||||||
\(150\) | 12.2474i | 0.0816497i | ||||||||
\(151\) | −125.296 | −0.829773 | −0.414886 | − | 0.909873i | \(-0.636179\pi\) | ||||
−0.414886 | + | 0.909873i | \(0.636179\pi\) | |||||||
\(152\) | 59.0346i | 0.388385i | ||||||||
\(153\) | − 30.8212i | − 0.201445i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 89.4805 | 0.577293 | ||||||||
\(156\) | 66.7584 | 0.427938 | ||||||||
\(157\) | − 5.33367i | − 0.0339724i | −0.999856 | − | 0.0169862i | \(-0.994593\pi\) | ||||
0.999856 | − | 0.0169862i | \(-0.00540714\pi\) | |||||||
\(158\) | 127.393 | 0.806288 | ||||||||
\(159\) | 8.57473i | 0.0539291i | ||||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 239.246 | 1.46777 | 0.733883 | − | 0.679276i | \(-0.237706\pi\) | ||||
0.733883 | + | 0.679276i | \(0.237706\pi\) | |||||||
\(164\) | 45.5413i | 0.277691i | ||||||||
\(165\) | −41.9133 | −0.254020 | ||||||||
\(166\) | 142.899i | 0.860840i | ||||||||
\(167\) | 310.440i | 1.85892i | 0.368918 | + | 0.929462i | \(0.379728\pi\) | ||||
−0.368918 | + | 0.929462i | \(0.620272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −202.390 | −1.19757 | ||||||||
\(170\) | −32.4884 | −0.191108 | ||||||||
\(171\) | 62.6156i | 0.366173i | ||||||||
\(172\) | −96.8613 | −0.563147 | ||||||||
\(173\) | 90.9078i | 0.525479i | 0.964867 | + | 0.262739i | \(0.0846259\pi\) | ||||
−0.964867 | + | 0.262739i | \(0.915374\pi\) | |||||||
\(174\) | − 46.7579i | − 0.268723i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −43.2879 | −0.245954 | ||||||||
\(177\) | −48.8209 | −0.275825 | ||||||||
\(178\) | − 56.0242i | − 0.314743i | ||||||||
\(179\) | −243.154 | −1.35840 | −0.679200 | − | 0.733953i | \(-0.737673\pi\) | ||||
−0.679200 | + | 0.733953i | \(0.737673\pi\) | |||||||
\(180\) | 13.4164i | 0.0745356i | ||||||||
\(181\) | − 245.993i | − 1.35907i | −0.733641 | − | 0.679537i | \(-0.762181\pi\) | ||||
0.733641 | − | 0.679537i | \(-0.237819\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 121.398 | 0.663375 | ||||||||
\(184\) | −59.6079 | −0.323956 | ||||||||
\(185\) | 112.620i | 0.608759i | ||||||||
\(186\) | 98.0209 | 0.526994 | ||||||||
\(187\) | − 111.182i | − 0.594556i | ||||||||
\(188\) | 133.076i | 0.707851i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 66.0027 | 0.347382 | ||||||||
\(191\) | −41.2215 | −0.215820 | −0.107910 | − | 0.994161i | \(-0.534416\pi\) | ||||
−0.107910 | + | 0.994161i | \(0.534416\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −189.745 | −0.983137 | −0.491568 | − | 0.870839i | \(-0.663576\pi\) | ||||
−0.491568 | + | 0.870839i | \(0.663576\pi\) | |||||||
\(194\) | − 97.1486i | − 0.500766i | ||||||||
\(195\) | − 74.6381i | − 0.382760i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −362.318 | −1.83918 | −0.919589 | − | 0.392882i | \(-0.871478\pi\) | ||||
−0.919589 | + | 0.392882i | \(0.871478\pi\) | |||||||
\(198\) | −45.9138 | −0.231888 | ||||||||
\(199\) | 38.6170i | 0.194056i | 0.995282 | + | 0.0970278i | \(0.0309336\pi\) | ||||
−0.995282 | + | 0.0970278i | \(0.969066\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | 33.4385i | 0.166361i | ||||||||
\(202\) | − 11.3689i | − 0.0562816i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −35.5892 | −0.174457 | ||||||||
\(205\) | 50.9167 | 0.248374 | ||||||||
\(206\) | − 289.298i | − 1.40436i | ||||||||
\(207\) | −63.2238 | −0.305429 | ||||||||
\(208\) | − 77.0859i | − 0.370605i | ||||||||
\(209\) | 225.875i | 1.08074i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −136.551 | −0.647163 | −0.323581 | − | 0.946200i | \(-0.604887\pi\) | ||||
−0.323581 | + | 0.946200i | \(0.604887\pi\) | |||||||
\(212\) | 9.90124 | 0.0467040 | ||||||||
\(213\) | 85.7309i | 0.402493i | ||||||||
\(214\) | −232.714 | −1.08745 | ||||||||
\(215\) | 108.294i | 0.503694i | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 111.737 | 0.512556 | ||||||||
\(219\) | −230.318 | −1.05168 | ||||||||
\(220\) | 48.3974i | 0.219988i | ||||||||
\(221\) | 197.990 | 0.895881 | ||||||||
\(222\) | 123.370i | 0.555719i | ||||||||
\(223\) | 154.949i | 0.694839i | 0.937710 | + | 0.347419i | \(0.112942\pi\) | ||||
−0.937710 | + | 0.347419i | \(0.887058\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | −119.599 | −0.529198 | ||||||||
\(227\) | − 22.3538i | − 0.0984750i | −0.998787 | − | 0.0492375i | \(-0.984321\pi\) | ||||
0.998787 | − | 0.0492375i | \(-0.0156791\pi\) | |||||||
\(228\) | 72.3023 | 0.317115 | ||||||||
\(229\) | 29.9188i | 0.130650i | 0.997864 | + | 0.0653250i | \(0.0208084\pi\) | ||||
−0.997864 | + | 0.0653250i | \(0.979192\pi\) | |||||||
\(230\) | 66.6437i | 0.289755i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −53.9913 | −0.232721 | ||||||||
\(233\) | −253.082 | −1.08619 | −0.543095 | − | 0.839671i | \(-0.682748\pi\) | ||||
−0.543095 | + | 0.839671i | \(0.682748\pi\) | |||||||
\(234\) | − 81.7620i | − 0.349410i | ||||||||
\(235\) | 148.783 | 0.633121 | ||||||||
\(236\) | 56.3736i | 0.238871i | ||||||||
\(237\) | − 156.024i | − 0.658331i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 121.009 | 0.506315 | 0.253158 | − | 0.967425i | \(-0.418531\pi\) | ||||
0.253158 | + | 0.967425i | \(0.418531\pi\) | |||||||
\(240\) | 15.4919 | 0.0645497 | ||||||||
\(241\) | − 288.392i | − 1.19665i | −0.801255 | − | 0.598323i | \(-0.795834\pi\) | ||||
0.801255 | − | 0.598323i | \(-0.204166\pi\) | |||||||
\(242\) | 5.49394 | 0.0227022 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | − 140.178i | − 0.574499i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 55.7765 | 0.226734 | ||||||||
\(247\) | −402.232 | −1.62847 | ||||||||
\(248\) | − 113.185i | − 0.456390i | ||||||||
\(249\) | 175.015 | 0.702873 | ||||||||
\(250\) | − 15.8114i | − 0.0632456i | ||||||||
\(251\) | 422.260i | 1.68231i | 0.540795 | + | 0.841155i | \(0.318124\pi\) | ||||
−0.540795 | + | 0.841155i | \(0.681876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −228.069 | −0.901457 | ||||||||
\(254\) | 143.934 | 0.566671 | ||||||||
\(255\) | 39.7899i | 0.156039i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 74.4871i | 0.289833i | 0.989444 | + | 0.144916i | \(0.0462913\pi\) | ||||
−0.989444 | + | 0.144916i | \(0.953709\pi\) | |||||||
\(258\) | 118.630i | 0.459808i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −86.1847 | −0.331479 | ||||||||
\(261\) | −57.2665 | −0.219412 | ||||||||
\(262\) | − 99.9823i | − 0.381612i | ||||||||
\(263\) | 313.275 | 1.19116 | 0.595579 | − | 0.803296i | \(-0.296923\pi\) | ||||
0.595579 | + | 0.803296i | \(0.296923\pi\) | |||||||
\(264\) | 53.0166i | 0.200821i | ||||||||
\(265\) | − 11.0699i | − 0.0417733i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −68.6153 | −0.256986 | ||||||||
\(268\) | 38.6115 | 0.144073 | ||||||||
\(269\) | 159.362i | 0.592423i | 0.955122 | + | 0.296211i | \(0.0957233\pi\) | ||||
−0.955122 | + | 0.296211i | \(0.904277\pi\) | |||||||
\(270\) | 16.4317 | 0.0608581 | ||||||||
\(271\) | − 188.264i | − 0.694701i | −0.937735 | − | 0.347350i | \(-0.887081\pi\) | ||||
0.937735 | − | 0.347350i | \(-0.112919\pi\) | |||||||
\(272\) | 41.0949i | 0.151084i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 166.633 | 0.608151 | ||||||||
\(275\) | 54.1099 | 0.196763 | ||||||||
\(276\) | 73.0045i | 0.264509i | ||||||||
\(277\) | 7.04744 | 0.0254420 | 0.0127210 | − | 0.999919i | \(-0.495951\pi\) | ||||
0.0127210 | + | 0.999919i | \(0.495951\pi\) | |||||||
\(278\) | 224.162i | 0.806340i | ||||||||
\(279\) | − 120.051i | − 0.430289i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 198.386 | 0.705998 | 0.352999 | − | 0.935624i | \(-0.385162\pi\) | ||||
0.352999 | + | 0.935624i | \(0.385162\pi\) | |||||||
\(282\) | 162.984 | 0.577958 | ||||||||
\(283\) | 189.128i | 0.668297i | 0.942520 | + | 0.334149i | \(0.108449\pi\) | ||||
−0.942520 | + | 0.334149i | \(0.891551\pi\) | |||||||
\(284\) | 98.9936 | 0.348569 | ||||||||
\(285\) | − 80.8364i | − 0.283637i | ||||||||
\(286\) | − 294.942i | − 1.03127i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 183.451 | 0.634777 | ||||||||
\(290\) | 60.3641i | 0.208152i | ||||||||
\(291\) | −118.982 | −0.408874 | ||||||||
\(292\) | 265.949i | 0.910783i | ||||||||
\(293\) | 486.090i | 1.65901i | 0.558499 | + | 0.829505i | \(0.311378\pi\) | ||||
−0.558499 | + | 0.829505i | \(0.688622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 63.0276 | 0.213653 | ||||||||
\(296\) | 142.455 | 0.481266 | ||||||||
\(297\) | 56.2326i | 0.189336i | ||||||||
\(298\) | 418.460 | 1.40423 | ||||||||
\(299\) | − 406.138i | − 1.35832i | ||||||||
\(300\) | − 17.3205i | − 0.0577350i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 177.195 | 0.586738 | ||||||||
\(303\) | −13.9240 | −0.0459538 | ||||||||
\(304\) | − 83.4875i | − 0.274630i | ||||||||
\(305\) | −156.724 | −0.513848 | ||||||||
\(306\) | 43.5877i | 0.142443i | ||||||||
\(307\) | 427.589i | 1.39280i | 0.717655 | + | 0.696399i | \(0.245216\pi\) | ||||
−0.717655 | + | 0.696399i | \(0.754784\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −354.317 | −1.14666 | ||||||||
\(310\) | −126.545 | −0.408208 | ||||||||
\(311\) | 360.095i | 1.15786i | 0.815376 | + | 0.578931i | \(0.196530\pi\) | ||||
−0.815376 | + | 0.578931i | \(0.803470\pi\) | |||||||
\(312\) | −94.4106 | −0.302598 | ||||||||
\(313\) | 583.928i | 1.86558i | 0.360415 | + | 0.932792i | \(0.382635\pi\) | ||||
−0.360415 | + | 0.932792i | \(0.617365\pi\) | |||||||
\(314\) | 7.54295i | 0.0240221i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −180.162 | −0.570132 | ||||||||
\(317\) | 361.400 | 1.14006 | 0.570032 | − | 0.821623i | \(-0.306931\pi\) | ||||
0.570032 | + | 0.821623i | \(0.306931\pi\) | |||||||
\(318\) | − 12.1265i | − 0.0381336i | ||||||||
\(319\) | −206.579 | −0.647582 | ||||||||
\(320\) | − 17.8885i | − 0.0559017i | ||||||||
\(321\) | 285.016i | 0.887899i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 214.432 | 0.663875 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 96.3574i | 0.296484i | ||||||||
\(326\) | −338.345 | −1.03787 | ||||||||
\(327\) | − 136.849i | − 0.418500i | ||||||||
\(328\) | − 64.4051i | − 0.196357i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 59.2744 | 0.179619 | ||||||||
\(331\) | 295.986 | 0.894217 | 0.447108 | − | 0.894480i | \(-0.352454\pi\) | ||||
0.447108 | + | 0.894480i | \(0.352454\pi\) | |||||||
\(332\) | − 202.090i | − 0.608706i | ||||||||
\(333\) | 151.096 | 0.453742 | ||||||||
\(334\) | − 439.029i | − 1.31446i | ||||||||
\(335\) | − 43.1689i | − 0.128863i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0162 | −0.0653300 | −0.0326650 | − | 0.999466i | \(-0.510399\pi\) | ||||
−0.0326650 | + | 0.999466i | \(0.510399\pi\) | |||||||
\(338\) | 286.222 | 0.846812 | ||||||||
\(339\) | 146.478i | 0.432088i | ||||||||
\(340\) | 45.9455 | 0.135134 | ||||||||
\(341\) | − 433.062i | − 1.26998i | ||||||||
\(342\) | − 88.5519i | − 0.258924i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 136.983 | 0.398205 | ||||||||
\(345\) | 81.6215 | 0.236584 | ||||||||
\(346\) | − 128.563i | − 0.371570i | ||||||||
\(347\) | −283.906 | −0.818173 | −0.409086 | − | 0.912496i | \(-0.634153\pi\) | ||||
−0.409086 | + | 0.912496i | \(0.634153\pi\) | |||||||
\(348\) | 66.1256i | 0.190016i | ||||||||
\(349\) | − 317.175i | − 0.908811i | −0.890795 | − | 0.454406i | \(-0.849852\pi\) | ||||
0.890795 | − | 0.454406i | \(-0.150148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −100.138 | −0.285292 | ||||||||
\(352\) | 61.2183 | 0.173916 | ||||||||
\(353\) | 116.942i | 0.331282i | 0.986186 | + | 0.165641i | \(0.0529692\pi\) | ||||
−0.986186 | + | 0.165641i | \(0.947031\pi\) | |||||||
\(354\) | 69.0432 | 0.195037 | ||||||||
\(355\) | − 110.678i | − 0.311769i | ||||||||
\(356\) | 79.2302i | 0.222557i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 343.871 | 0.960534 | ||||||||
\(359\) | 233.586 | 0.650657 | 0.325329 | − | 0.945601i | \(-0.394525\pi\) | ||||
0.325329 | + | 0.945601i | \(0.394525\pi\) | |||||||
\(360\) | − 18.9737i | − 0.0527046i | ||||||||
\(361\) | −74.6351 | −0.206745 | ||||||||
\(362\) | 347.886i | 0.961011i | ||||||||
\(363\) | − 6.72867i | − 0.0185363i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 297.340 | 0.814629 | ||||||||
\(366\) | −171.682 | −0.469077 | ||||||||
\(367\) | − 512.073i | − 1.39530i | −0.716441 | − | 0.697648i | \(-0.754230\pi\) | ||||
0.716441 | − | 0.697648i | \(-0.245770\pi\) | |||||||
\(368\) | 84.2984 | 0.229072 | ||||||||
\(369\) | − 68.3119i | − 0.185127i | ||||||||
\(370\) | − 159.269i | − 0.430458i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −138.623 | −0.372641 | ||||||||
\(373\) | −556.407 | −1.49171 | −0.745854 | − | 0.666109i | \(-0.767958\pi\) | ||||
−0.745854 | + | 0.666109i | \(0.767958\pi\) | |||||||
\(374\) | 157.235i | 0.420415i | ||||||||
\(375\) | −19.3649 | −0.0516398 | ||||||||
\(376\) | − 188.198i | − 0.500526i | ||||||||
\(377\) | − 367.870i | − 0.975782i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −536.301 | −1.41504 | −0.707521 | − | 0.706692i | \(-0.750187\pi\) | ||||
−0.707521 | + | 0.706692i | \(0.750187\pi\) | |||||||
\(380\) | −93.3419 | −0.245636 | ||||||||
\(381\) | − 176.283i | − 0.462685i | ||||||||
\(382\) | 58.2961 | 0.152608 | ||||||||
\(383\) | 29.3507i | 0.0766336i | 0.999266 | + | 0.0383168i | \(0.0121996\pi\) | ||||
−0.999266 | + | 0.0383168i | \(0.987800\pi\) | |||||||
\(384\) | − 19.5959i | − 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 268.341 | 0.695183 | ||||||||
\(387\) | 145.292 | 0.375431 | ||||||||
\(388\) | 137.389i | 0.354095i | ||||||||
\(389\) | −698.484 | −1.79559 | −0.897795 | − | 0.440414i | \(-0.854832\pi\) | ||||
−0.897795 | + | 0.440414i | \(0.854832\pi\) | |||||||
\(390\) | 105.554i | 0.270652i | ||||||||
\(391\) | 216.514i | 0.553745i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −122.453 | −0.311585 | ||||||||
\(394\) | 512.395 | 1.30050 | ||||||||
\(395\) | 201.427i | 0.509941i | ||||||||
\(396\) | 64.9319 | 0.163969 | ||||||||
\(397\) | − 204.694i | − 0.515602i | −0.966198 | − | 0.257801i | \(-0.917002\pi\) | ||||
0.966198 | − | 0.257801i | \(-0.0829980\pi\) | |||||||
\(398\) | − 54.6127i | − 0.137218i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 429.967 | 1.07224 | 0.536119 | − | 0.844142i | \(-0.319890\pi\) | ||||
0.536119 | + | 0.844142i | \(0.319890\pi\) | |||||||
\(402\) | − 47.2892i | − 0.117635i | ||||||||
\(403\) | 771.184 | 1.91361 | ||||||||
\(404\) | 16.0780i | 0.0397971i | ||||||||
\(405\) | − 20.1246i | − 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 545.053 | 1.33920 | ||||||||
\(408\) | 50.3307 | 0.123360 | ||||||||
\(409\) | − 17.7324i | − 0.0433554i | −0.999765 | − | 0.0216777i | \(-0.993099\pi\) | ||||
0.999765 | − | 0.0216777i | \(-0.00690077\pi\) | |||||||
\(410\) | −72.0071 | −0.175627 | ||||||||
\(411\) | − 204.083i | − 0.496553i | ||||||||
\(412\) | 409.129i | 0.993033i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 89.4119 | 0.215971 | ||||||||
\(415\) | −225.944 | −0.544443 | ||||||||
\(416\) | 109.016i | 0.262058i | ||||||||
\(417\) | 274.542 | 0.658374 | ||||||||
\(418\) | − 319.435i | − 0.764200i | ||||||||
\(419\) | − 440.768i | − 1.05195i | −0.850499 | − | 0.525977i | \(-0.823700\pi\) | ||||
0.850499 | − | 0.525977i | \(-0.176300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −143.012 | −0.339696 | −0.169848 | − | 0.985470i | \(-0.554328\pi\) | ||||
−0.169848 | + | 0.985470i | \(0.554328\pi\) | |||||||
\(422\) | 193.113 | 0.457613 | ||||||||
\(423\) | − 199.614i | − 0.471901i | ||||||||
\(424\) | −14.0025 | −0.0330247 | ||||||||
\(425\) | − 51.3686i | − 0.120867i | ||||||||
\(426\) | − 121.242i | − 0.284605i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 329.108 | 0.768943 | ||||||||
\(429\) | −361.229 | −0.842025 | ||||||||
\(430\) | − 153.151i | − 0.356166i | ||||||||
\(431\) | −783.217 | −1.81721 | −0.908604 | − | 0.417659i | \(-0.862851\pi\) | ||||
−0.908604 | + | 0.417659i | \(0.862851\pi\) | |||||||
\(432\) | − 20.7846i | − 0.0481125i | ||||||||
\(433\) | − 286.669i | − 0.662053i | −0.943622 | − | 0.331026i | \(-0.892605\pi\) | ||||
0.943622 | − | 0.331026i | \(-0.107395\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 73.9307 | 0.169956 | ||||||||
\(436\) | −158.020 | −0.362432 | ||||||||
\(437\) | − 439.866i | − 1.00656i | ||||||||
\(438\) | 325.719 | 0.743651 | ||||||||
\(439\) | − 340.655i | − 0.775980i | −0.921664 | − | 0.387990i | \(-0.873170\pi\) | ||||
0.921664 | − | 0.387990i | \(-0.126830\pi\) | |||||||
\(440\) | − 68.4442i | − 0.155555i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −280.000 | −0.633484 | ||||||||
\(443\) | 395.259 | 0.892232 | 0.446116 | − | 0.894975i | \(-0.352807\pi\) | ||||
0.446116 | + | 0.894975i | \(0.352807\pi\) | |||||||
\(444\) | − 174.471i | − 0.392952i | ||||||||
\(445\) | 88.5820 | 0.199061 | ||||||||
\(446\) | − 219.131i | − 0.491325i | ||||||||
\(447\) | − 512.507i | − 1.14655i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 665.078 | 1.48124 | 0.740621 | − | 0.671923i | \(-0.234531\pi\) | ||||
0.740621 | + | 0.671923i | \(0.234531\pi\) | |||||||
\(450\) | −21.2132 | −0.0471405 | ||||||||
\(451\) | − 246.423i | − 0.546393i | ||||||||
\(452\) | 169.138 | 0.374199 | ||||||||
\(453\) | − 217.019i | − 0.479070i | ||||||||
\(454\) | 31.6131i | 0.0696323i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −102.251 | −0.224234 | ||||||||
\(457\) | 510.937 | 1.11802 | 0.559012 | − | 0.829160i | \(-0.311181\pi\) | ||||
0.559012 | + | 0.829160i | \(0.311181\pi\) | |||||||
\(458\) | − 42.3116i | − 0.0923834i | ||||||||
\(459\) | 53.3838 | 0.116305 | ||||||||
\(460\) | − 94.2484i | − 0.204888i | ||||||||
\(461\) | 174.303i | 0.378097i | 0.981968 | + | 0.189049i | \(0.0605404\pi\) | ||||
−0.981968 | + | 0.189049i | \(0.939460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 755.187 | 1.63107 | 0.815537 | − | 0.578705i | \(-0.196442\pi\) | ||||
0.815537 | + | 0.578705i | \(0.196442\pi\) | |||||||
\(464\) | 76.3553 | 0.164559 | ||||||||
\(465\) | 154.985i | 0.333300i | ||||||||
\(466\) | 357.913 | 0.768053 | ||||||||
\(467\) | − 566.573i | − 1.21322i | −0.795000 | − | 0.606609i | \(-0.792529\pi\) | ||||
0.795000 | − | 0.606609i | \(-0.207471\pi\) | |||||||
\(468\) | 115.629i | 0.247070i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −210.412 | −0.447684 | ||||||||
\(471\) | 9.23819 | 0.0196140 | ||||||||
\(472\) | − 79.7243i | − 0.168907i | ||||||||
\(473\) | 524.115 | 1.10807 | ||||||||
\(474\) | 220.652i | 0.465510i | ||||||||
\(475\) | 104.359i | 0.219704i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.8519 | −0.0311360 | ||||||||
\(478\) | −171.133 | −0.358019 | ||||||||
\(479\) | − 514.172i | − 1.07343i | −0.843764 | − | 0.536714i | \(-0.819666\pi\) | ||||
0.843764 | − | 0.536714i | \(-0.180334\pi\) | |||||||
\(480\) | −21.9089 | −0.0456435 | ||||||||
\(481\) | 970.616i | 2.01791i | ||||||||
\(482\) | 407.848i | 0.846157i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.76960 | −0.0160529 | ||||||||
\(485\) | 153.605 | 0.316712 | ||||||||
\(486\) | − 22.0454i | − 0.0453609i | ||||||||
\(487\) | 327.327 | 0.672129 | 0.336064 | − | 0.941839i | \(-0.390904\pi\) | ||||
0.336064 | + | 0.941839i | \(0.390904\pi\) | |||||||
\(488\) | 198.241i | 0.406232i | ||||||||
\(489\) | 414.386i | 0.847415i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.8889 | −0.0853134 | −0.0426567 | − | 0.999090i | \(-0.513582\pi\) | ||||
−0.0426567 | + | 0.999090i | \(0.513582\pi\) | |||||||
\(492\) | −78.8798 | −0.160325 | ||||||||
\(493\) | 196.113i | 0.397795i | ||||||||
\(494\) | 568.842 | 1.15150 | ||||||||
\(495\) | − 72.5960i | − 0.146659i | ||||||||
\(496\) | 160.068i | 0.322717i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −247.509 | −0.497006 | ||||||||
\(499\) | 415.370 | 0.832406 | 0.416203 | − | 0.909272i | \(-0.363361\pi\) | ||||
0.416203 | + | 0.909272i | \(0.363361\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −537.698 | −1.07325 | ||||||||
\(502\) | − 597.165i | − 1.18957i | ||||||||
\(503\) | 51.7604i | 0.102903i | 0.998675 | + | 0.0514517i | \(0.0163848\pi\) | ||||
−0.998675 | + | 0.0514517i | \(0.983615\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.9758 | 0.0355956 | ||||||||
\(506\) | 322.538 | 0.637427 | ||||||||
\(507\) | − 350.549i | − 0.691419i | ||||||||
\(508\) | −203.554 | −0.400697 | ||||||||
\(509\) | 158.097i | 0.310604i | 0.987867 | + | 0.155302i | \(0.0496350\pi\) | ||||
−0.987867 | + | 0.155302i | \(0.950365\pi\) | |||||||
\(510\) | − 56.2715i | − 0.110336i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −108.453 | −0.211410 | ||||||||
\(514\) | − 105.341i | − 0.204943i | ||||||||
\(515\) | 457.421 | 0.888195 | ||||||||
\(516\) | − 167.769i | − 0.325133i | ||||||||
\(517\) | − 720.073i | − 1.39279i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −157.457 | −0.303385 | ||||||||
\(520\) | 121.884 | 0.234391 | ||||||||
\(521\) | − 353.586i | − 0.678668i | −0.940666 | − | 0.339334i | \(-0.889798\pi\) | ||||
0.940666 | − | 0.339334i | \(-0.110202\pi\) | |||||||
\(522\) | 80.9870 | 0.155147 | ||||||||
\(523\) | − 119.551i | − 0.228587i | −0.993447 | − | 0.114294i | \(-0.963540\pi\) | ||||
0.993447 | − | 0.114294i | \(-0.0364605\pi\) | |||||||
\(524\) | 141.396i | 0.269840i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −443.037 | −0.842277 | ||||||||
\(527\) | −411.122 | −0.780118 | ||||||||
\(528\) | − 74.9769i | − 0.142002i | ||||||||
\(529\) | −84.8617 | −0.160419 | ||||||||
\(530\) | 15.6552i | 0.0295382i | ||||||||
\(531\) | − 84.5604i | − 0.159247i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 438.824 | 0.823309 | ||||||||
\(534\) | 97.0368 | 0.181717 | ||||||||
\(535\) | − 367.954i | − 0.687764i | ||||||||
\(536\) | −54.6049 | −0.101875 | ||||||||
\(537\) | − 421.155i | − 0.784273i | ||||||||
\(538\) | − 225.372i | − 0.418906i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −23.2379 | −0.0430331 | ||||||||
\(541\) | 545.383 | 1.00810 | 0.504051 | − | 0.863674i | \(-0.331843\pi\) | ||||
0.504051 | + | 0.863674i | \(0.331843\pi\) | |||||||
\(542\) | 266.245i | 0.491228i | ||||||||
\(543\) | 426.072 | 0.784662 | ||||||||
\(544\) | − 58.1169i | − 0.106833i | ||||||||
\(545\) | 176.672i | 0.324169i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −117.783 | −0.215325 | −0.107663 | − | 0.994188i | \(-0.534337\pi\) | ||||
−0.107663 | + | 0.994188i | \(0.534337\pi\) | |||||||
\(548\) | −235.655 | −0.430027 | ||||||||
\(549\) | 210.267i | 0.383000i | ||||||||
\(550\) | −76.5229 | −0.139133 | ||||||||
\(551\) | − 398.419i | − 0.723084i | ||||||||
\(552\) | − 103.244i | − 0.187036i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.96659 | −0.0179902 | ||||||||
\(555\) | −195.064 | −0.351467 | ||||||||
\(556\) | − 317.014i | − 0.570168i | ||||||||
\(557\) | −615.488 | −1.10501 | −0.552503 | − | 0.833511i | \(-0.686327\pi\) | ||||
−0.552503 | + | 0.833511i | \(0.686327\pi\) | |||||||
\(558\) | 169.777i | 0.304260i | ||||||||
\(559\) | 933.330i | 1.66964i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 192.573 | 0.343267 | ||||||||
\(562\) | −280.560 | −0.499216 | ||||||||
\(563\) | 479.255i | 0.851253i | 0.904899 | + | 0.425626i | \(0.139946\pi\) | ||||
−0.904899 | + | 0.425626i | \(0.860054\pi\) | |||||||
\(564\) | −230.494 | −0.408678 | ||||||||
\(565\) | − 189.102i | − 0.334694i | ||||||||
\(566\) | − 267.468i | − 0.472558i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −139.998 | −0.246475 | ||||||||
\(569\) | −457.347 | −0.803774 | −0.401887 | − | 0.915689i | \(-0.631645\pi\) | ||||
−0.401887 | + | 0.915689i | \(0.631645\pi\) | |||||||
\(570\) | 114.320i | 0.200561i | ||||||||
\(571\) | 373.202 | 0.653595 | 0.326797 | − | 0.945094i | \(-0.394031\pi\) | ||||
0.326797 | + | 0.945094i | \(0.394031\pi\) | |||||||
\(572\) | 417.111i | 0.729215i | ||||||||
\(573\) | − 71.3978i | − 0.124604i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −105.373 | −0.183257 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 891.554i | 1.54515i | 0.634921 | + | 0.772577i | \(0.281033\pi\) | ||||
−0.634921 | + | 0.772577i | \(0.718967\pi\) | |||||||
\(578\) | −259.438 | −0.448855 | ||||||||
\(579\) | − 328.649i | − 0.567614i | ||||||||
\(580\) | − 85.3678i | − 0.147186i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 168.266 | 0.289117 | ||||||||
\(583\) | −53.5755 | −0.0918962 | ||||||||
\(584\) | − 376.108i | − 0.644021i | ||||||||
\(585\) | 129.277 | 0.220986 | ||||||||
\(586\) | − 687.435i | − 1.17310i | ||||||||
\(587\) | 786.758i | 1.34030i | 0.742224 | + | 0.670151i | \(0.233771\pi\) | ||||
−0.742224 | + | 0.670151i | \(0.766229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 835.227 | 1.41804 | ||||||||
\(590\) | −89.1344 | −0.151075 | ||||||||
\(591\) | − 627.553i | − 1.06185i | ||||||||
\(592\) | −201.462 | −0.340307 | ||||||||
\(593\) | − 625.352i | − 1.05456i | −0.849693 | − | 0.527278i | \(-0.823212\pi\) | ||||
0.849693 | − | 0.527278i | \(-0.176788\pi\) | |||||||
\(594\) | − 79.5250i | − 0.133880i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −591.792 | −0.992940 | ||||||||
\(597\) | −66.8867 | −0.112038 | ||||||||
\(598\) | 574.367i | 0.960479i | ||||||||
\(599\) | 150.495 | 0.251244 | 0.125622 | − | 0.992078i | \(-0.459907\pi\) | ||||
0.125622 | + | 0.992078i | \(0.459907\pi\) | |||||||
\(600\) | 24.4949i | 0.0408248i | ||||||||
\(601\) | − 521.601i | − 0.867888i | −0.900940 | − | 0.433944i | \(-0.857122\pi\) | ||||
0.900940 | − | 0.433944i | \(-0.142878\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −57.9172 | −0.0960485 | ||||||||
\(604\) | −250.591 | −0.414886 | ||||||||
\(605\) | 8.68668i | 0.0143581i | ||||||||
\(606\) | 19.6915 | 0.0324942 | ||||||||
\(607\) | − 696.750i | − 1.14786i | −0.818905 | − | 0.573930i | \(-0.805418\pi\) | ||||
0.818905 | − | 0.573930i | \(-0.194582\pi\) | |||||||
\(608\) | 118.069i | 0.194193i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 221.641 | 0.363345 | ||||||||
\(611\) | 1282.29 | 2.09867 | ||||||||
\(612\) | − 61.6423i | − 0.100723i | ||||||||
\(613\) | 54.2489 | 0.0884974 | 0.0442487 | − | 0.999021i | \(-0.485911\pi\) | ||||
0.0442487 | + | 0.999021i | \(0.485911\pi\) | |||||||
\(614\) | − 604.702i | − 0.984857i | ||||||||
\(615\) | 88.1903i | 0.143399i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −969.852 | −1.57188 | −0.785941 | − | 0.618301i | \(-0.787821\pi\) | ||||
−0.785941 | + | 0.618301i | \(0.787821\pi\) | |||||||
\(618\) | 501.079 | 0.810808 | ||||||||
\(619\) | 128.449i | 0.207511i | 0.994603 | + | 0.103756i | \(0.0330860\pi\) | ||||
−0.994603 | + | 0.103756i | \(0.966914\pi\) | |||||||
\(620\) | 178.961 | 0.288647 | ||||||||
\(621\) | − 109.507i | − 0.176339i | ||||||||
\(622\) | − 509.252i | − 0.818733i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 133.517 | 0.213969 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − 825.799i | − 1.31917i | ||||||||
\(627\) | −391.227 | −0.623966 | ||||||||
\(628\) | − 10.6673i | − 0.0169862i | ||||||||
\(629\) | − 517.440i | − 0.822639i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 115.457 | 0.182975 | 0.0914877 | − | 0.995806i | \(-0.470838\pi\) | ||||
0.0914877 | + | 0.995806i | \(0.470838\pi\) | |||||||
\(632\) | 254.787 | 0.403144 | ||||||||
\(633\) | − 236.514i | − 0.373640i | ||||||||
\(634\) | −511.097 | −0.806147 | ||||||||
\(635\) | 227.580i | 0.358394i | ||||||||
\(636\) | 17.1495i | 0.0269646i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 292.146 | 0.457910 | ||||||||
\(639\) | −148.490 | −0.232379 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | −952.498 | −1.48596 | −0.742978 | − | 0.669316i | \(-0.766587\pi\) | ||||
−0.742978 | + | 0.669316i | \(0.766587\pi\) | |||||||
\(642\) | − 403.073i | − 0.627840i | ||||||||
\(643\) | 253.254i | 0.393863i | 0.980417 | + | 0.196931i | \(0.0630976\pi\) | ||||
−0.980417 | + | 0.196931i | \(0.936902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −187.571 | −0.290808 | ||||||||
\(646\) | −303.252 | −0.469431 | ||||||||
\(647\) | − 1004.78i | − 1.55298i | −0.630132 | − | 0.776488i | \(-0.716999\pi\) | ||||
0.630132 | − | 0.776488i | \(-0.283001\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | − 305.037i | − 0.470010i | ||||||||
\(650\) | − 136.270i | − 0.209646i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 478.492 | 0.733883 | ||||||||
\(653\) | 1065.59 | 1.63184 | 0.815922 | − | 0.578162i | \(-0.196230\pi\) | ||||
0.815922 | + | 0.578162i | \(0.196230\pi\) | |||||||
\(654\) | 193.534i | 0.295924i | ||||||||
\(655\) | 158.086 | 0.241353 | ||||||||
\(656\) | 91.0826i | 0.138845i | ||||||||
\(657\) | − 398.923i | − 0.607189i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 432.265 | 0.655941 | 0.327970 | − | 0.944688i | \(-0.393635\pi\) | ||||
0.327970 | + | 0.944688i | \(0.393635\pi\) | |||||||
\(660\) | −83.8267 | −0.127010 | ||||||||
\(661\) | − 378.310i | − 0.572329i | −0.958180 | − | 0.286165i | \(-0.907620\pi\) | ||||
0.958180 | − | 0.286165i | \(-0.0923804\pi\) | |||||||
\(662\) | −418.587 | −0.632307 | ||||||||
\(663\) | 342.928i | 0.517237i | ||||||||
\(664\) | 285.799i | 0.430420i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −213.682 | −0.320844 | ||||||||
\(667\) | 402.289 | 0.603132 | ||||||||
\(668\) | 620.880i | 0.929462i | ||||||||
\(669\) | −268.380 | −0.401165 | ||||||||
\(670\) | 61.0501i | 0.0911196i | ||||||||
\(671\) | 758.501i | 1.13040i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −689.666 | −1.02476 | −0.512382 | − | 0.858758i | \(-0.671237\pi\) | ||||
−0.512382 | + | 0.858758i | \(0.671237\pi\) | |||||||
\(674\) | 31.1356 | 0.0461953 | ||||||||
\(675\) | 25.9808i | 0.0384900i | ||||||||
\(676\) | −404.780 | −0.598786 | ||||||||
\(677\) | 379.508i | 0.560572i | 0.959916 | + | 0.280286i | \(0.0904294\pi\) | ||||
−0.959916 | + | 0.280286i | \(0.909571\pi\) | |||||||
\(678\) | − 207.151i | − 0.305532i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −64.9767 | −0.0955540 | ||||||||
\(681\) | 38.7179 | 0.0568545 | ||||||||
\(682\) | 612.442i | 0.898009i | ||||||||
\(683\) | 747.507 | 1.09445 | 0.547223 | − | 0.836987i | \(-0.315685\pi\) | ||||
0.547223 | + | 0.836987i | \(0.315685\pi\) | |||||||
\(684\) | 125.231i | 0.183087i | ||||||||
\(685\) | 263.470i | 0.384628i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −51.8209 | −0.0754308 | ||||||||
\(688\) | −193.723 | −0.281574 | ||||||||
\(689\) | − 95.4058i | − 0.138470i | ||||||||
\(690\) | −115.430 | −0.167290 | ||||||||
\(691\) | 890.304i | 1.28843i | 0.764845 | + | 0.644214i | \(0.222815\pi\) | ||||
−0.764845 | + | 0.644214i | \(0.777185\pi\) | |||||||
\(692\) | 181.816i | 0.262739i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 401.504 | 0.578536 | ||||||||
\(695\) | −354.432 | −0.509974 | ||||||||
\(696\) | − 93.5157i | − 0.134362i | ||||||||
\(697\) | −233.939 | −0.335637 | ||||||||
\(698\) | 448.553i | 0.642627i | ||||||||
\(699\) | − 438.352i | − 0.627112i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −650.703 | −0.928250 | −0.464125 | − | 0.885770i | \(-0.653631\pi\) | ||||
−0.464125 | + | 0.885770i | \(0.653631\pi\) | |||||||
\(702\) | 141.616 | 0.201732 | ||||||||
\(703\) | 1051.22i | 1.49533i | ||||||||
\(704\) | −86.5758 | −0.122977 | ||||||||
\(705\) | 257.700i | 0.365533i | ||||||||
\(706\) | − 165.382i | − 0.234251i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −97.6419 | −0.137912 | ||||||||
\(709\) | −392.855 | −0.554097 | −0.277048 | − | 0.960856i | \(-0.589356\pi\) | ||||
−0.277048 | + | 0.960856i | \(0.589356\pi\) | |||||||
\(710\) | 156.523i | 0.220454i | ||||||||
\(711\) | 270.242 | 0.380088 | ||||||||
\(712\) | − 112.048i | − 0.157371i | ||||||||
\(713\) | 843.339i | 1.18280i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 466.344 | 0.652230 | ||||||||
\(716\) | −486.307 | −0.679200 | ||||||||
\(717\) | 209.594i | 0.292321i | ||||||||
\(718\) | −330.340 | −0.460084 | ||||||||
\(719\) | 1039.14i | 1.44525i | 0.691238 | + | 0.722627i | \(0.257065\pi\) | ||||
−0.691238 | + | 0.722627i | \(0.742935\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 105.550 | 0.146191 | ||||||||
\(723\) | 499.509 | 0.690884 | ||||||||
\(724\) | − 491.985i | − 0.679537i | ||||||||
\(725\) | −95.4441 | −0.131647 | ||||||||
\(726\) | 9.51578i | 0.0131071i | ||||||||
\(727\) | − 610.568i | − 0.839846i | −0.907560 | − | 0.419923i | \(-0.862057\pi\) | ||||
0.907560 | − | 0.419923i | \(-0.137943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −420.502 | −0.576030 | ||||||||
\(731\) | − 497.563i | − 0.680661i | ||||||||
\(732\) | 242.795 | 0.331687 | ||||||||
\(733\) | 1079.15i | 1.47224i | 0.676850 | + | 0.736121i | \(0.263344\pi\) | ||||
−0.676850 | + | 0.736121i | \(0.736656\pi\) | |||||||
\(734\) | 724.181i | 0.986623i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −119.216 | −0.161978 | ||||||||
\(737\) | −208.926 | −0.283482 | ||||||||
\(738\) | 96.6077i | 0.130905i | ||||||||
\(739\) | 756.164 | 1.02323 | 0.511613 | − | 0.859216i | \(-0.329048\pi\) | ||||
0.511613 | + | 0.859216i | \(0.329048\pi\) | |||||||
\(740\) | 225.241i | 0.304380i | ||||||||
\(741\) | − 696.686i | − 0.940197i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 963.993 | 1.29743 | 0.648717 | − | 0.761030i | \(-0.275306\pi\) | ||||
0.648717 | + | 0.761030i | \(0.275306\pi\) | |||||||
\(744\) | 196.042 | 0.263497 | ||||||||
\(745\) | 661.644i | 0.888113i | ||||||||
\(746\) | 786.879 | 1.05480 | ||||||||
\(747\) | 303.135i | 0.405804i | ||||||||
\(748\) | − 222.364i | − 0.297278i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 27.3861 | 0.0365148 | ||||||||
\(751\) | 833.612 | 1.11000 | 0.555001 | − | 0.831850i | \(-0.312718\pi\) | ||||
0.555001 | + | 0.831850i | \(0.312718\pi\) | |||||||
\(752\) | 266.152i | 0.353925i | ||||||||
\(753\) | −731.375 | −0.971282 | ||||||||
\(754\) | 520.246i | 0.689982i | ||||||||
\(755\) | 280.170i | 0.371086i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −744.966 | −0.984103 | −0.492051 | − | 0.870566i | \(-0.663753\pi\) | ||||
−0.492051 | + | 0.870566i | \(0.663753\pi\) | |||||||
\(758\) | 758.444 | 1.00059 | ||||||||
\(759\) | − 395.027i | − 0.520457i | ||||||||
\(760\) | 132.005 | 0.173691 | ||||||||
\(761\) | − 74.0761i | − 0.0973405i | −0.998815 | − | 0.0486702i | \(-0.984502\pi\) | ||||
0.998815 | − | 0.0486702i | \(-0.0154983\pi\) | |||||||
\(762\) | 249.302i | 0.327167i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −82.4431 | −0.107910 | ||||||||
\(765\) | −68.9182 | −0.0900892 | ||||||||
\(766\) | − 41.5081i | − 0.0541881i | ||||||||
\(767\) | 543.201 | 0.708215 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | 961.553i | 1.25039i | 0.780467 | + | 0.625197i | \(0.214981\pi\) | ||||
−0.780467 | + | 0.625197i | \(0.785019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −129.015 | −0.167335 | ||||||||
\(772\) | −379.491 | −0.491568 | ||||||||
\(773\) | 1375.45i | 1.77936i | 0.456584 | + | 0.889680i | \(0.349073\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(774\) | −205.474 | −0.265470 | ||||||||
\(775\) | − 200.084i | − 0.258173i | ||||||||
\(776\) | − 194.297i | − 0.250383i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 987.806 | 1.26967 | ||||||||
\(779\) | 475.266 | 0.610098 | ||||||||
\(780\) | − 149.276i | − 0.191380i | ||||||||
\(781\) | −535.653 | −0.685855 | ||||||||
\(782\) | − 306.198i | − 0.391557i | ||||||||
\(783\) | − 99.1884i | − 0.126677i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.9264 | −0.0151929 | ||||||||
\(786\) | 173.174 | 0.220324 | ||||||||
\(787\) | − 380.681i | − 0.483711i | −0.970312 | − | 0.241856i | \(-0.922244\pi\) | ||||
0.970312 | − | 0.241856i | \(-0.0777560\pi\) | |||||||
\(788\) | −724.636 | −0.919589 | ||||||||
\(789\) | 542.608i | 0.687716i | ||||||||
\(790\) | − 284.860i | − 0.360583i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −91.8275 | −0.115944 | ||||||||
\(793\) | −1350.72 | −1.70330 | ||||||||
\(794\) | 289.481i | 0.364586i | ||||||||
\(795\) | 19.1737 | 0.0241178 | ||||||||
\(796\) | 77.2341i | 0.0970278i | ||||||||
\(797\) | − 511.440i | − 0.641706i | −0.947129 | − | 0.320853i | \(-0.896030\pi\) | ||||
0.947129 | − | 0.320853i | \(-0.103970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −683.593 | −0.855560 | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | − 118.845i | − 0.148371i | ||||||||
\(802\) | −608.066 | −0.758187 | ||||||||
\(803\) | − 1439.04i | − 1.79209i | ||||||||
\(804\) | 66.8770i | 0.0831804i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1090.62 | −1.35313 | ||||||||
\(807\) | −276.023 | −0.342036 | ||||||||
\(808\) | − 22.7378i | − 0.0281408i | ||||||||
\(809\) | 1158.37 | 1.43186 | 0.715930 | − | 0.698173i | \(-0.246003\pi\) | ||||
0.715930 | + | 0.698173i | \(0.246003\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | 92.0692i | 0.113526i | 0.998388 | + | 0.0567628i | \(0.0180779\pi\) | ||||
−0.998388 | + | 0.0567628i | \(0.981922\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 326.083 | 0.401086 | ||||||||
\(814\) | −770.822 | −0.946956 | ||||||||
\(815\) | − 534.970i | − 0.656405i | ||||||||
\(816\) | −71.1784 | −0.0872285 | ||||||||
\(817\) | 1010.84i | 1.23726i | ||||||||
\(818\) | 25.0774i | 0.0306569i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 101.833 | 0.124187 | ||||||||
\(821\) | −986.935 | −1.20211 | −0.601057 | − | 0.799206i | \(-0.705253\pi\) | ||||
−0.601057 | + | 0.799206i | \(0.705253\pi\) | |||||||
\(822\) | 288.617i | 0.351116i | ||||||||
\(823\) | 555.497 | 0.674966 | 0.337483 | − | 0.941332i | \(-0.390424\pi\) | ||||
0.337483 | + | 0.941332i | \(0.390424\pi\) | |||||||
\(824\) | − 578.596i | − 0.702180i | ||||||||
\(825\) | 93.7211i | 0.113601i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1323.46 | −1.60032 | −0.800160 | − | 0.599787i | \(-0.795252\pi\) | ||||
−0.800160 | + | 0.599787i | \(0.795252\pi\) | |||||||
\(828\) | −126.448 | −0.152714 | ||||||||
\(829\) | − 1052.98i | − 1.27018i | −0.772440 | − | 0.635088i | \(-0.780964\pi\) | ||||
0.772440 | − | 0.635088i | \(-0.219036\pi\) | |||||||
\(830\) | 319.533 | 0.384979 | ||||||||
\(831\) | 12.2065i | 0.0146890i | ||||||||
\(832\) | − 154.172i | − 0.185303i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −388.261 | −0.465540 | ||||||||
\(835\) | 694.165 | 0.831336 | ||||||||
\(836\) | 451.750i | 0.540371i | ||||||||
\(837\) | 207.934 | 0.248428 | ||||||||
\(838\) | 623.341i | 0.743843i | ||||||||
\(839\) | − 1254.98i | − 1.49580i | −0.663810 | − | 0.747901i | \(-0.731062\pi\) | ||||
0.663810 | − | 0.747901i | \(-0.268938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −476.617 | −0.566727 | ||||||||
\(842\) | 202.249 | 0.240201 | ||||||||
\(843\) | 343.614i | 0.407608i | ||||||||
\(844\) | −273.103 | −0.323581 | ||||||||
\(845\) | 452.557i | 0.535571i | ||||||||
\(846\) | 282.297i | 0.333684i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.8025 | 0.0233520 | ||||||||
\(849\) | −327.580 | −0.385842 | ||||||||
\(850\) | 72.6462i | 0.0854661i | ||||||||
\(851\) | −1061.43 | −1.24727 | ||||||||
\(852\) | 171.462i | 0.201246i | ||||||||
\(853\) | 454.825i | 0.533207i | 0.963806 | + | 0.266603i | \(0.0859014\pi\) | ||||
−0.963806 | + | 0.266603i | \(0.914099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 140.013 | 0.163758 | ||||||||
\(856\) | −465.429 | −0.543725 | ||||||||
\(857\) | 168.738i | 0.196894i | 0.995142 | + | 0.0984470i | \(0.0313875\pi\) | ||||
−0.995142 | + | 0.0984470i | \(0.968613\pi\) | |||||||
\(858\) | 510.855 | 0.595402 | ||||||||
\(859\) | − 817.199i | − 0.951337i | −0.879625 | − | 0.475669i | \(-0.842206\pi\) | ||||
0.879625 | − | 0.475669i | \(-0.157794\pi\) | |||||||
\(860\) | 216.588i | 0.251847i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1107.64 | 1.28496 | ||||||||
\(863\) | −1233.90 | −1.42978 | −0.714890 | − | 0.699237i | \(-0.753523\pi\) | ||||
−0.714890 | + | 0.699237i | \(0.753523\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 203.276 | 0.235001 | ||||||||
\(866\) | 405.411i | 0.468142i | ||||||||
\(867\) | 317.746i | 0.366489i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 974.852 | 1.12181 | ||||||||
\(870\) | −104.554 | −0.120177 | ||||||||
\(871\) | − 372.050i | − 0.427153i | ||||||||
\(872\) | 223.474 | 0.256278 | ||||||||
\(873\) | − 206.083i | − 0.236063i | ||||||||
\(874\) | 622.065i | 0.711744i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −460.637 | −0.525841 | ||||||||
\(877\) | 74.9557 | 0.0854683 | 0.0427342 | − | 0.999086i | \(-0.486393\pi\) | ||||
0.0427342 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(878\) | 481.759i | 0.548701i | ||||||||
\(879\) | −841.933 | −0.957830 | ||||||||
\(880\) | 96.7947i | 0.109994i | ||||||||
\(881\) | − 461.343i | − 0.523658i | −0.965114 | − | 0.261829i | \(-0.915674\pi\) | ||||
0.965114 | − | 0.261829i | \(-0.0843257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 237.840 | 0.269354 | 0.134677 | − | 0.990890i | \(-0.457000\pi\) | ||||
0.134677 | + | 0.990890i | \(0.457000\pi\) | |||||||
\(884\) | 395.980 | 0.447941 | ||||||||
\(885\) | 109.167i | 0.123352i | ||||||||
\(886\) | −558.981 | −0.630904 | ||||||||
\(887\) | 9.11359i | 0.0102746i | 0.999987 | + | 0.00513731i | \(0.00163526\pi\) | ||||
−0.999987 | + | 0.00513731i | \(0.998365\pi\) | |||||||
\(888\) | 246.739i | 0.277859i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −125.274 | −0.140757 | ||||||||
\(891\) | −97.3978 | −0.109313 | ||||||||
\(892\) | 309.898i | 0.347419i | ||||||||
\(893\) | 1388.77 | 1.55518 | ||||||||
\(894\) | 724.795i | 0.810732i | ||||||||
\(895\) | 543.708i | 0.607495i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 703.452 | 0.784228 | ||||||||
\(898\) | −940.562 | −1.04740 | ||||||||
\(899\) | 763.875i | 0.849694i | ||||||||
\(900\) | 30.0000 | 0.0333333 | ||||||||
\(901\) | 50.8613i | 0.0564498i | ||||||||
\(902\) | 348.495i | 0.386358i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −239.197 | −0.264599 | ||||||||
\(905\) | −550.056 | −0.607797 | ||||||||
\(906\) | 306.911i | 0.338753i | ||||||||
\(907\) | 840.703 | 0.926905 | 0.463453 | − | 0.886122i | \(-0.346610\pi\) | ||||
0.463453 | + | 0.886122i | \(0.346610\pi\) | |||||||
\(908\) | − 44.7076i | − 0.0492375i | ||||||||
\(909\) | − 24.1171i | − 0.0265314i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.4735 | −0.0389390 | −0.0194695 | − | 0.999810i | \(-0.506198\pi\) | ||||
−0.0194695 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(912\) | 144.605 | 0.158558 | ||||||||
\(913\) | 1093.51i | 1.19771i | ||||||||
\(914\) | −722.573 | −0.790562 | ||||||||
\(915\) | − 271.453i | − 0.296670i | ||||||||
\(916\) | 59.8377i | 0.0653250i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −75.4961 | −0.0822398 | ||||||||
\(919\) | 431.360 | 0.469380 | 0.234690 | − | 0.972070i | \(-0.424593\pi\) | ||||
0.234690 | + | 0.972070i | \(0.424593\pi\) | |||||||
\(920\) | 133.287i | 0.144878i | ||||||||
\(921\) | −740.606 | −0.804132 | ||||||||
\(922\) | − 246.502i | − 0.267355i | ||||||||
\(923\) | − 953.876i | − 1.03345i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 251.827 | 0.272245 | ||||||||
\(926\) | −1068.00 | −1.15334 | ||||||||
\(927\) | − 613.694i | − 0.662022i | ||||||||
\(928\) | −107.983 | −0.116361 | ||||||||
\(929\) | 613.207i | 0.660072i | 0.943968 | + | 0.330036i | \(0.107061\pi\) | ||||
−0.943968 | + | 0.330036i | \(0.892939\pi\) | |||||||
\(930\) | − 219.182i | − 0.235679i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −506.165 | −0.543095 | ||||||||
\(933\) | −623.703 | −0.668492 | ||||||||
\(934\) | 801.255i | 0.857875i | ||||||||
\(935\) | −248.610 | −0.265894 | ||||||||
\(936\) | − 163.524i | − 0.174705i | ||||||||
\(937\) | − 1360.68i | − 1.45216i | −0.687609 | − | 0.726081i | \(-0.741340\pi\) | ||||
0.687609 | − | 0.726081i | \(-0.258660\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1011.39 | −1.07710 | ||||||||
\(940\) | 297.567 | 0.316561 | ||||||||
\(941\) | 169.361i | 0.179980i | 0.995943 | + | 0.0899900i | \(0.0286835\pi\) | ||||
−0.995943 | + | 0.0899900i | \(0.971316\pi\) | |||||||
\(942\) | −13.0648 | −0.0138692 | ||||||||
\(943\) | 479.882i | 0.508889i | ||||||||
\(944\) | 112.747i | 0.119436i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −741.211 | −0.783521 | ||||||||
\(947\) | −1279.17 | −1.35076 | −0.675378 | − | 0.737472i | \(-0.736019\pi\) | ||||
−0.675378 | + | 0.737472i | \(0.736019\pi\) | |||||||
\(948\) | − 312.049i | − 0.329166i | ||||||||
\(949\) | 2562.61 | 2.70033 | ||||||||
\(950\) | − 147.586i | − 0.155354i | ||||||||
\(951\) | 625.964i | 0.658216i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.43779 | −0.00150870 | −0.000754349 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000754349 | 1.00000i | \(0.500240\pi\) | ||||||||
\(954\) | 21.0037 | 0.0220165 | ||||||||
\(955\) | 92.1742i | 0.0965175i | ||||||||
\(956\) | 242.019 | 0.253158 | ||||||||
\(957\) | − 357.805i | − 0.373882i | ||||||||
\(958\) | 727.149i | 0.759028i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.9839 | 0.0322749 | ||||||||
\(961\) | −640.351 | −0.666338 | ||||||||
\(962\) | − 1372.66i | − 1.42688i | ||||||||
\(963\) | −493.662 | −0.512629 | ||||||||
\(964\) | − 576.784i | − 0.598323i | ||||||||
\(965\) | 424.284i | 0.439672i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 486.815 | 0.503428 | 0.251714 | − | 0.967802i | \(-0.419006\pi\) | ||||
0.251714 | + | 0.967802i | \(0.419006\pi\) | |||||||
\(968\) | 10.9879 | 0.0113511 | ||||||||
\(969\) | 371.407i | 0.383289i | ||||||||
\(970\) | −217.231 | −0.223949 | ||||||||
\(971\) | 436.725i | 0.449768i | 0.974386 | + | 0.224884i | \(0.0722004\pi\) | ||||
−0.974386 | + | 0.224884i | \(0.927800\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −462.910 | −0.475267 | ||||||||
\(975\) | −166.896 | −0.171175 | ||||||||
\(976\) | − 280.356i | − 0.287250i | ||||||||
\(977\) | 255.034 | 0.261038 | 0.130519 | − | 0.991446i | \(-0.458336\pi\) | ||||
0.130519 | + | 0.991446i | \(0.458336\pi\) | |||||||
\(978\) | − 586.030i | − 0.599213i | ||||||||
\(979\) | − 428.714i | − 0.437910i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 237.030 | 0.241621 | ||||||||
\(982\) | 59.2398 | 0.0603257 | ||||||||
\(983\) | − 1380.89i | − 1.40477i | −0.711799 | − | 0.702383i | \(-0.752119\pi\) | ||||
0.711799 | − | 0.702383i | \(-0.247881\pi\) | |||||||
\(984\) | 111.553 | 0.113367 | ||||||||
\(985\) | 810.168i | 0.822505i | ||||||||
\(986\) | − 277.346i | − 0.281284i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −804.464 | −0.814234 | ||||||||
\(989\) | −1020.66 | −1.03201 | ||||||||
\(990\) | 102.666i | 0.103703i | ||||||||
\(991\) | −623.108 | −0.628767 | −0.314384 | − | 0.949296i | \(-0.601798\pi\) | ||||
−0.314384 | + | 0.949296i | \(0.601798\pi\) | |||||||
\(992\) | − 226.370i | − 0.228195i | ||||||||
\(993\) | 512.662i | 0.516276i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 86.3503 | 0.0867843 | ||||||||
\(996\) | 350.031 | 0.351436 | ||||||||
\(997\) | − 560.317i | − 0.562003i | −0.959707 | − | 0.281001i | \(-0.909333\pi\) | ||||
0.959707 | − | 0.281001i | \(-0.0906665\pi\) | |||||||
\(998\) | −587.423 | −0.588600 | ||||||||
\(999\) | 261.706i | 0.261968i |
(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 | 1470.3.f.d.391.5 | 16 | ||
7.2 | even | 3 | 210.3.o.b.31.5 | ✓ | 16 | ||
7.3 | odd | 6 | 210.3.o.b.61.5 | yes | 16 | ||
7.6 | odd | 2 | inner | 1470.3.f.d.391.3 | 16 | ||
21.2 | odd | 6 | 630.3.v.c.451.3 | 16 | |||
21.17 | even | 6 | 630.3.v.c.271.3 | 16 | |||
35.2 | odd | 12 | 1050.3.q.e.199.7 | 32 | |||
35.3 | even | 12 | 1050.3.q.e.649.7 | 32 | |||
35.9 | even | 6 | 1050.3.p.i.451.3 | 16 | |||
35.17 | even | 12 | 1050.3.q.e.649.16 | 32 | |||
35.23 | odd | 12 | 1050.3.q.e.199.16 | 32 | |||
35.24 | odd | 6 | 1050.3.p.i.901.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.5 | ✓ | 16 | 7.2 | even | 3 | ||
210.3.o.b.61.5 | yes | 16 | 7.3 | odd | 6 | ||
630.3.v.c.271.3 | 16 | 21.17 | even | 6 | |||
630.3.v.c.451.3 | 16 | 21.2 | odd | 6 | |||
1050.3.p.i.451.3 | 16 | 35.9 | even | 6 | |||
1050.3.p.i.901.3 | 16 | 35.24 | odd | 6 | |||
1050.3.q.e.199.7 | 32 | 35.2 | odd | 12 | |||
1050.3.q.e.199.16 | 32 | 35.23 | odd | 12 | |||
1050.3.q.e.649.7 | 32 | 35.3 | even | 12 | |||
1050.3.q.e.649.16 | 32 | 35.17 | even | 12 | |||
1470.3.f.d.391.3 | 16 | 7.6 | odd | 2 | inner | ||
1470.3.f.d.391.5 | 16 | 1.1 | even | 1 | trivial |