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: | \(8\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.1 | ||
Root | \(1.01575 - 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.391 |
Dual form | 1470.3.f.a.391.4 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(11\) | 12.3241 | 1.12037 | 0.560187 | − | 0.828366i | \(-0.310729\pi\) | ||||
0.560187 | + | 0.828366i | \(0.310729\pi\) | |||||||
\(12\) | − 3.46410i | − 0.288675i | ||||||||
\(13\) | 7.26007i | 0.558467i | 0.960223 | + | 0.279233i | \(0.0900803\pi\) | ||||
−0.960223 | + | 0.279233i | \(0.909920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 9.29122i | − 0.546542i | −0.961937 | − | 0.273271i | \(-0.911894\pi\) | ||||
0.961937 | − | 0.273271i | \(-0.0881056\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 6.07644i | 0.319813i | 0.987132 | + | 0.159906i | \(0.0511192\pi\) | ||||
−0.987132 | + | 0.159906i | \(0.948881\pi\) | |||||||
\(20\) | − 4.47214i | − 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.4289 | −0.792224 | ||||||||
\(23\) | −2.25029 | −0.0978385 | −0.0489192 | − | 0.998803i | \(-0.515578\pi\) | ||||
−0.0489192 | + | 0.998803i | \(0.515578\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − 10.2673i | − 0.394896i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42.2122 | 1.45559 | 0.727797 | − | 0.685793i | \(-0.240544\pi\) | ||||
0.727797 | + | 0.685793i | \(0.240544\pi\) | |||||||
\(30\) | 5.47723 | 0.182574 | ||||||||
\(31\) | 1.21852i | 0.0393072i | 0.999807 | + | 0.0196536i | \(0.00625634\pi\) | ||||
−0.999807 | + | 0.0196536i | \(0.993744\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − 21.3460i | − 0.646848i | ||||||||
\(34\) | 13.1398i | 0.386464i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 35.0593 | 0.947548 | 0.473774 | − | 0.880647i | \(-0.342891\pi\) | ||||
0.473774 | + | 0.880647i | \(0.342891\pi\) | |||||||
\(38\) | − 8.59339i | − 0.226142i | ||||||||
\(39\) | 12.5748 | 0.322431 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 57.8811i | 1.41173i | 0.708345 | + | 0.705867i | \(0.249442\pi\) | ||||
−0.708345 | + | 0.705867i | \(0.750558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.0190 | −0.791140 | −0.395570 | − | 0.918436i | \(-0.629453\pi\) | ||||
−0.395570 | + | 0.918436i | \(0.629453\pi\) | |||||||
\(44\) | 24.6482 | 0.560187 | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | 3.18238 | 0.0691823 | ||||||||
\(47\) | 57.0897i | 1.21467i | 0.794444 | + | 0.607337i | \(0.207762\pi\) | ||||
−0.794444 | + | 0.607337i | \(0.792238\pi\) | |||||||
\(48\) | − 6.92820i | − 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | −16.0929 | −0.315546 | ||||||||
\(52\) | 14.5201i | 0.279233i | ||||||||
\(53\) | 14.5402 | 0.274343 | 0.137172 | − | 0.990547i | \(-0.456199\pi\) | ||||
0.137172 | + | 0.990547i | \(0.456199\pi\) | |||||||
\(54\) | − 7.34847i | − 0.136083i | ||||||||
\(55\) | − 27.5575i | − 0.501046i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.5247 | 0.184644 | ||||||||
\(58\) | −59.6971 | −1.02926 | ||||||||
\(59\) | − 57.8582i | − 0.980647i | −0.871540 | − | 0.490324i | \(-0.836879\pi\) | ||||
0.871540 | − | 0.490324i | \(-0.163121\pi\) | |||||||
\(60\) | −7.74597 | −0.129099 | ||||||||
\(61\) | − 5.86193i | − 0.0960972i | −0.998845 | − | 0.0480486i | \(-0.984700\pi\) | ||||
0.998845 | − | 0.0480486i | \(-0.0153002\pi\) | |||||||
\(62\) | − 1.72325i | − 0.0277944i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 16.2340 | 0.249754 | ||||||||
\(66\) | 30.1878i | 0.457391i | ||||||||
\(67\) | 49.4709 | 0.738372 | 0.369186 | − | 0.929356i | \(-0.379637\pi\) | ||||
0.369186 | + | 0.929356i | \(0.379637\pi\) | |||||||
\(68\) | − 18.5824i | − 0.273271i | ||||||||
\(69\) | 3.89761i | 0.0564871i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 101.986 | 1.43643 | 0.718214 | − | 0.695822i | \(-0.244960\pi\) | ||||
0.718214 | + | 0.695822i | \(0.244960\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | − 82.3051i | − 1.12747i | −0.825957 | − | 0.563733i | \(-0.809365\pi\) | ||||
0.825957 | − | 0.563733i | \(-0.190635\pi\) | |||||||
\(74\) | −49.5813 | −0.670017 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 12.1529i | 0.159906i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −17.7835 | −0.227993 | ||||||||
\(79\) | 111.706 | 1.41400 | 0.707001 | − | 0.707213i | \(-0.250048\pi\) | ||||
0.707001 | + | 0.707213i | \(0.250048\pi\) | |||||||
\(80\) | − 8.94427i | − 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − 81.8562i | − 0.998246i | ||||||||
\(83\) | 91.6237i | 1.10390i | 0.833877 | + | 0.551950i | \(0.186116\pi\) | ||||
−0.833877 | + | 0.551950i | \(0.813884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.7758 | −0.244421 | ||||||||
\(86\) | 48.1102 | 0.559420 | ||||||||
\(87\) | − 73.1137i | − 0.840387i | ||||||||
\(88\) | −34.8578 | −0.396112 | ||||||||
\(89\) | 127.795i | 1.43589i | 0.696097 | + | 0.717947i | \(0.254918\pi\) | ||||
−0.696097 | + | 0.717947i | \(0.745082\pi\) | |||||||
\(90\) | − 9.48683i | − 0.105409i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.50057 | −0.0489192 | ||||||||
\(93\) | 2.11055 | 0.0226940 | ||||||||
\(94\) | − 80.7370i | − 0.858904i | ||||||||
\(95\) | 13.5873 | 0.143025 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 61.4455i | 0.633459i | 0.948516 | + | 0.316729i | \(0.102585\pi\) | ||||
−0.948516 | + | 0.316729i | \(0.897415\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −36.9723 | −0.373458 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | − 62.1392i | − 0.615239i | −0.951509 | − | 0.307620i | \(-0.900468\pi\) | ||||
0.951509 | − | 0.307620i | \(-0.0995325\pi\) | |||||||
\(102\) | 22.7587 | 0.223125 | ||||||||
\(103\) | − 177.942i | − 1.72759i | −0.503843 | − | 0.863795i | \(-0.668081\pi\) | ||||
0.503843 | − | 0.863795i | \(-0.331919\pi\) | |||||||
\(104\) | − 20.5346i | − 0.197448i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.5629 | −0.193990 | ||||||||
\(107\) | 84.9711 | 0.794122 | 0.397061 | − | 0.917792i | \(-0.370030\pi\) | ||||
0.397061 | + | 0.917792i | \(0.370030\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | −172.858 | −1.58586 | −0.792928 | − | 0.609316i | \(-0.791444\pi\) | ||||
−0.792928 | + | 0.609316i | \(0.791444\pi\) | |||||||
\(110\) | 38.9723i | 0.354293i | ||||||||
\(111\) | − 60.7244i | − 0.547067i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −82.0616 | −0.726209 | −0.363105 | − | 0.931748i | \(-0.618283\pi\) | ||||
−0.363105 | + | 0.931748i | \(0.618283\pi\) | |||||||
\(114\) | −14.8842 | −0.130563 | ||||||||
\(115\) | 5.03179i | 0.0437547i | ||||||||
\(116\) | 84.4244 | 0.727797 | ||||||||
\(117\) | − 21.7802i | − 0.186156i | ||||||||
\(118\) | 81.8238i | 0.693422i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.9545 | 0.0912871 | ||||||||
\(121\) | 30.8837 | 0.255237 | ||||||||
\(122\) | 8.29002i | 0.0679510i | ||||||||
\(123\) | 100.253 | 0.815065 | ||||||||
\(124\) | 2.43705i | 0.0196536i | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −193.480 | −1.52346 | −0.761732 | − | 0.647892i | \(-0.775651\pi\) | ||||
−0.761732 | + | 0.647892i | \(0.775651\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 58.9227i | 0.456765i | ||||||||
\(130\) | −22.9583 | −0.176603 | ||||||||
\(131\) | − 181.114i | − 1.38255i | −0.722590 | − | 0.691276i | \(-0.757049\pi\) | ||||
0.722590 | − | 0.691276i | \(-0.242951\pi\) | |||||||
\(132\) | − 42.6920i | − 0.323424i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −69.9625 | −0.522108 | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | 26.2795i | 0.193232i | ||||||||
\(137\) | 1.26333 | 0.00922140 | 0.00461070 | − | 0.999989i | \(-0.498532\pi\) | ||||
0.00461070 | + | 0.999989i | \(0.498532\pi\) | |||||||
\(138\) | − 5.51205i | − 0.0399424i | ||||||||
\(139\) | 12.1327i | 0.0872857i | 0.999047 | + | 0.0436428i | \(0.0138964\pi\) | ||||
−0.999047 | + | 0.0436428i | \(0.986104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 98.8822 | 0.701292 | ||||||||
\(142\) | −144.231 | −1.01571 | ||||||||
\(143\) | 89.4739i | 0.625691i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | − 94.3894i | − 0.650961i | ||||||||
\(146\) | 116.397i | 0.797239i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 70.1185 | 0.473774 | ||||||||
\(149\) | 289.725 | 1.94447 | 0.972233 | − | 0.234015i | \(-0.0751866\pi\) | ||||
0.972233 | + | 0.234015i | \(0.0751866\pi\) | |||||||
\(150\) | − 12.2474i | − 0.0816497i | ||||||||
\(151\) | 117.303 | 0.776842 | 0.388421 | − | 0.921482i | \(-0.373021\pi\) | ||||
0.388421 | + | 0.921482i | \(0.373021\pi\) | |||||||
\(152\) | − 17.1868i | − 0.113071i | ||||||||
\(153\) | 27.8737i | 0.182181i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.72470 | 0.0175787 | ||||||||
\(156\) | 25.1496 | 0.161215 | ||||||||
\(157\) | − 183.737i | − 1.17030i | −0.810924 | − | 0.585151i | \(-0.801035\pi\) | ||||
0.810924 | − | 0.585151i | \(-0.198965\pi\) | |||||||
\(158\) | −157.976 | −0.999850 | ||||||||
\(159\) | − 25.1843i | − 0.158392i | ||||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 121.571 | 0.745833 | 0.372917 | − | 0.927865i | \(-0.378358\pi\) | ||||
0.372917 | + | 0.927865i | \(0.378358\pi\) | |||||||
\(164\) | 115.762i | 0.705867i | ||||||||
\(165\) | −47.7311 | −0.289279 | ||||||||
\(166\) | − 129.576i | − 0.780575i | ||||||||
\(167\) | 94.6539i | 0.566790i | 0.959003 | + | 0.283395i | \(0.0914608\pi\) | ||||
−0.959003 | + | 0.283395i | \(0.908539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 116.291 | 0.688115 | ||||||||
\(170\) | 29.3814 | 0.172832 | ||||||||
\(171\) | − 18.2293i | − 0.106604i | ||||||||
\(172\) | −68.0380 | −0.395570 | ||||||||
\(173\) | − 260.692i | − 1.50689i | −0.657511 | − | 0.753445i | \(-0.728391\pi\) | ||||
0.657511 | − | 0.753445i | \(-0.271609\pi\) | |||||||
\(174\) | 103.398i | 0.594244i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 49.2964 | 0.280093 | ||||||||
\(177\) | −100.213 | −0.566177 | ||||||||
\(178\) | − 180.729i | − 1.01533i | ||||||||
\(179\) | 306.529 | 1.71245 | 0.856225 | − | 0.516603i | \(-0.172803\pi\) | ||||
0.856225 | + | 0.516603i | \(0.172803\pi\) | |||||||
\(180\) | 13.4164i | 0.0745356i | ||||||||
\(181\) | − 314.885i | − 1.73970i | −0.493318 | − | 0.869849i | \(-0.664216\pi\) | ||||
0.493318 | − | 0.869849i | \(-0.335784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.1532 | −0.0554817 | ||||||||
\(184\) | 6.36477 | 0.0345911 | ||||||||
\(185\) | − 78.3949i | − 0.423756i | ||||||||
\(186\) | −2.98476 | −0.0160471 | ||||||||
\(187\) | − 114.506i | − 0.612331i | ||||||||
\(188\) | 114.179i | 0.607337i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −19.2154 | −0.101134 | ||||||||
\(191\) | −90.7891 | −0.475336 | −0.237668 | − | 0.971346i | \(-0.576383\pi\) | ||||
−0.237668 | + | 0.971346i | \(0.576383\pi\) | |||||||
\(192\) | − 13.8564i | − 0.0721688i | ||||||||
\(193\) | −229.655 | −1.18992 | −0.594961 | − | 0.803754i | \(-0.702833\pi\) | ||||
−0.594961 | + | 0.803754i | \(0.702833\pi\) | |||||||
\(194\) | − 86.8971i | − 0.447923i | ||||||||
\(195\) | − 28.1181i | − 0.144195i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 227.989 | 1.15730 | 0.578652 | − | 0.815574i | \(-0.303579\pi\) | ||||
0.578652 | + | 0.815574i | \(0.303579\pi\) | |||||||
\(198\) | 52.2868 | 0.264075 | ||||||||
\(199\) | − 11.0461i | − 0.0555082i | −0.999615 | − | 0.0277541i | \(-0.991164\pi\) | ||||
0.999615 | − | 0.0277541i | \(-0.00883554\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | − 85.6862i | − 0.426299i | ||||||||
\(202\) | 87.8781i | 0.435040i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −32.1857 | −0.157773 | ||||||||
\(205\) | 129.426 | 0.631346 | ||||||||
\(206\) | 251.648i | 1.22159i | ||||||||
\(207\) | 6.75086 | 0.0326128 | ||||||||
\(208\) | 29.0403i | 0.139617i | ||||||||
\(209\) | 74.8867i | 0.358310i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 151.187 | 0.716526 | 0.358263 | − | 0.933621i | \(-0.383369\pi\) | ||||
0.358263 | + | 0.933621i | \(0.383369\pi\) | |||||||
\(212\) | 29.0804 | 0.137172 | ||||||||
\(213\) | − 176.646i | − 0.829322i | ||||||||
\(214\) | −120.167 | −0.561529 | ||||||||
\(215\) | 76.0688i | 0.353809i | ||||||||
\(216\) | − 14.6969i | − 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 244.458 | 1.12137 | ||||||||
\(219\) | −142.557 | −0.650943 | ||||||||
\(220\) | − 55.1151i | − 0.250523i | ||||||||
\(221\) | 67.4549 | 0.305226 | ||||||||
\(222\) | 85.8773i | 0.386835i | ||||||||
\(223\) | − 308.586i | − 1.38379i | −0.721997 | − | 0.691896i | \(-0.756776\pi\) | ||||
0.721997 | − | 0.691896i | \(-0.243224\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 116.053 | 0.513507 | ||||||||
\(227\) | − 100.422i | − 0.442389i | −0.975230 | − | 0.221195i | \(-0.929004\pi\) | ||||
0.975230 | − | 0.221195i | \(-0.0709956\pi\) | |||||||
\(228\) | 21.0494 | 0.0923220 | ||||||||
\(229\) | 319.997i | 1.39736i | 0.715432 | + | 0.698682i | \(0.246230\pi\) | ||||
−0.715432 | + | 0.698682i | \(0.753770\pi\) | |||||||
\(230\) | − 7.11603i | − 0.0309392i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −119.394 | −0.514630 | ||||||||
\(233\) | 310.789 | 1.33386 | 0.666929 | − | 0.745121i | \(-0.267608\pi\) | ||||
0.666929 | + | 0.745121i | \(0.267608\pi\) | |||||||
\(234\) | 30.8019i | 0.131632i | ||||||||
\(235\) | 127.656 | 0.543219 | ||||||||
\(236\) | − 115.716i | − 0.490324i | ||||||||
\(237\) | − 193.481i | − 0.816374i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 136.263 | 0.570139 | 0.285069 | − | 0.958507i | \(-0.407983\pi\) | ||||
0.285069 | + | 0.958507i | \(0.407983\pi\) | |||||||
\(240\) | −15.4919 | −0.0645497 | ||||||||
\(241\) | − 386.179i | − 1.60240i | −0.598394 | − | 0.801202i | \(-0.704194\pi\) | ||||
0.598394 | − | 0.801202i | \(-0.295806\pi\) | |||||||
\(242\) | −43.6761 | −0.180480 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | − 11.7239i | − 0.0480486i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −141.779 | −0.576338 | ||||||||
\(247\) | −44.1154 | −0.178605 | ||||||||
\(248\) | − 3.44651i | − 0.0138972i | ||||||||
\(249\) | 158.697 | 0.637337 | ||||||||
\(250\) | − 15.8114i | − 0.0632456i | ||||||||
\(251\) | − 99.3717i | − 0.395903i | −0.980212 | − | 0.197952i | \(-0.936571\pi\) | ||||
0.980212 | − | 0.197952i | \(-0.0634289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.7328 | −0.109616 | ||||||||
\(254\) | 273.622 | 1.07725 | ||||||||
\(255\) | 35.9847i | 0.141117i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 21.1178i | 0.0821705i | 0.999156 | + | 0.0410852i | \(0.0130815\pi\) | ||||
−0.999156 | + | 0.0410852i | \(0.986918\pi\) | |||||||
\(258\) | − 83.3292i | − 0.322982i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 32.4680 | 0.124877 | ||||||||
\(261\) | −126.637 | −0.485198 | ||||||||
\(262\) | 256.134i | 0.977612i | ||||||||
\(263\) | −380.517 | −1.44683 | −0.723417 | − | 0.690411i | \(-0.757430\pi\) | ||||
−0.723417 | + | 0.690411i | \(0.757430\pi\) | |||||||
\(264\) | 60.3756i | 0.228695i | ||||||||
\(265\) | − 32.5128i | − 0.122690i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 221.347 | 0.829014 | ||||||||
\(268\) | 98.9419 | 0.369186 | ||||||||
\(269\) | − 16.7910i | − 0.0624202i | −0.999513 | − | 0.0312101i | \(-0.990064\pi\) | ||||
0.999513 | − | 0.0312101i | \(-0.00993609\pi\) | |||||||
\(270\) | −16.4317 | −0.0608581 | ||||||||
\(271\) | 369.672i | 1.36410i | 0.731303 | + | 0.682052i | \(0.238912\pi\) | ||||
−0.731303 | + | 0.682052i | \(0.761088\pi\) | |||||||
\(272\) | − 37.1649i | − 0.136636i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.78662 | −0.00652051 | ||||||||
\(275\) | −61.6205 | −0.224075 | ||||||||
\(276\) | 7.79522i | 0.0282435i | ||||||||
\(277\) | 485.825 | 1.75388 | 0.876940 | − | 0.480600i | \(-0.159581\pi\) | ||||
0.876940 | + | 0.480600i | \(0.159581\pi\) | |||||||
\(278\) | − 17.1582i | − 0.0617203i | ||||||||
\(279\) | − 3.65557i | − 0.0131024i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 360.234 | 1.28197 | 0.640986 | − | 0.767553i | \(-0.278526\pi\) | ||||
0.640986 | + | 0.767553i | \(0.278526\pi\) | |||||||
\(282\) | −139.841 | −0.495889 | ||||||||
\(283\) | − 270.502i | − 0.955836i | −0.878404 | − | 0.477918i | \(-0.841392\pi\) | ||||
0.878404 | − | 0.477918i | \(-0.158608\pi\) | |||||||
\(284\) | 203.973 | 0.718214 | ||||||||
\(285\) | − 23.5340i | − 0.0825753i | ||||||||
\(286\) | − 126.535i | − 0.442431i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 202.673 | 0.701292 | ||||||||
\(290\) | 133.487i | 0.460299i | ||||||||
\(291\) | 106.427 | 0.365728 | ||||||||
\(292\) | − 164.610i | − 0.563733i | ||||||||
\(293\) | − 9.63230i | − 0.0328747i | −0.999865 | − | 0.0164374i | \(-0.994768\pi\) | ||||
0.999865 | − | 0.0164374i | \(-0.00523241\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −129.375 | −0.438559 | ||||||||
\(296\) | −99.1626 | −0.335009 | ||||||||
\(297\) | 64.0379i | 0.215616i | ||||||||
\(298\) | −409.734 | −1.37494 | ||||||||
\(299\) | − 16.3372i | − 0.0546395i | ||||||||
\(300\) | 17.3205i | 0.0577350i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −165.892 | −0.549310 | ||||||||
\(303\) | −107.628 | −0.355209 | ||||||||
\(304\) | 24.3058i | 0.0799532i | ||||||||
\(305\) | −13.1077 | −0.0429760 | ||||||||
\(306\) | − 39.4193i | − 0.128821i | ||||||||
\(307\) | − 46.0412i | − 0.149971i | −0.997185 | − | 0.0749857i | \(-0.976109\pi\) | ||||
0.997185 | − | 0.0749857i | \(-0.0238911\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −308.204 | −0.997425 | ||||||||
\(310\) | −3.85331 | −0.0124300 | ||||||||
\(311\) | 436.662i | 1.40406i | 0.712148 | + | 0.702029i | \(0.247722\pi\) | ||||
−0.712148 | + | 0.702029i | \(0.752278\pi\) | |||||||
\(312\) | −35.5669 | −0.113997 | ||||||||
\(313\) | 286.522i | 0.915405i | 0.889105 | + | 0.457703i | \(0.151328\pi\) | ||||
−0.889105 | + | 0.457703i | \(0.848672\pi\) | |||||||
\(314\) | 259.844i | 0.827529i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 223.412 | 0.707001 | ||||||||
\(317\) | −1.36884 | −0.00431809 | −0.00215905 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215905 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(318\) | 35.6160i | 0.112000i | ||||||||
\(319\) | 520.228 | 1.63081 | ||||||||
\(320\) | − 17.8885i | − 0.0559017i | ||||||||
\(321\) | − 147.174i | − 0.458487i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 56.4575 | 0.174791 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | − 36.3003i | − 0.111693i | ||||||||
\(326\) | −171.927 | −0.527384 | ||||||||
\(327\) | 299.399i | 0.915594i | ||||||||
\(328\) | − 163.712i | − 0.499123i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 67.5019 | 0.204551 | ||||||||
\(331\) | −384.034 | −1.16022 | −0.580111 | − | 0.814537i | \(-0.696991\pi\) | ||||
−0.580111 | + | 0.814537i | \(0.696991\pi\) | |||||||
\(332\) | 183.247i | 0.551950i | ||||||||
\(333\) | −105.178 | −0.315849 | ||||||||
\(334\) | − 133.861i | − 0.400781i | ||||||||
\(335\) | − 110.620i | − 0.330210i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −141.948 | −0.421211 | −0.210606 | − | 0.977571i | \(-0.567544\pi\) | ||||
−0.210606 | + | 0.977571i | \(0.567544\pi\) | |||||||
\(338\) | −164.461 | −0.486571 | ||||||||
\(339\) | 142.135i | 0.419277i | ||||||||
\(340\) | −41.5516 | −0.122211 | ||||||||
\(341\) | 15.0172i | 0.0440388i | ||||||||
\(342\) | 25.7802i | 0.0753806i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 96.2203 | 0.279710 | ||||||||
\(345\) | 8.71532 | 0.0252618 | ||||||||
\(346\) | 368.674i | 1.06553i | ||||||||
\(347\) | −250.352 | −0.721475 | −0.360737 | − | 0.932667i | \(-0.617475\pi\) | ||||
−0.360737 | + | 0.932667i | \(0.617475\pi\) | |||||||
\(348\) | − 146.227i | − 0.420194i | ||||||||
\(349\) | 195.188i | 0.559277i | 0.960105 | + | 0.279639i | \(0.0902147\pi\) | ||||
−0.960105 | + | 0.279639i | \(0.909785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −37.7244 | −0.107477 | ||||||||
\(352\) | −69.7157 | −0.198056 | ||||||||
\(353\) | − 142.199i | − 0.402831i | −0.979506 | − | 0.201416i | \(-0.935446\pi\) | ||||
0.979506 | − | 0.201416i | \(-0.0645541\pi\) | |||||||
\(354\) | 141.723 | 0.400348 | ||||||||
\(355\) | − 228.049i | − 0.642390i | ||||||||
\(356\) | 255.589i | 0.717947i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −433.497 | −1.21089 | ||||||||
\(359\) | −656.886 | −1.82977 | −0.914884 | − | 0.403718i | \(-0.867718\pi\) | ||||
−0.914884 | + | 0.403718i | \(0.867718\pi\) | |||||||
\(360\) | − 18.9737i | − 0.0527046i | ||||||||
\(361\) | 324.077 | 0.897720 | ||||||||
\(362\) | 445.315i | 1.23015i | ||||||||
\(363\) | − 53.4921i | − 0.147361i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −184.040 | −0.504218 | ||||||||
\(366\) | 14.3587 | 0.0392315 | ||||||||
\(367\) | 513.152i | 1.39823i | 0.715007 | + | 0.699117i | \(0.246424\pi\) | ||||
−0.715007 | + | 0.699117i | \(0.753576\pi\) | |||||||
\(368\) | −9.00114 | −0.0244596 | ||||||||
\(369\) | − 173.643i | − 0.470578i | ||||||||
\(370\) | 110.867i | 0.299641i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.22109 | 0.0113470 | ||||||||
\(373\) | −632.524 | −1.69577 | −0.847887 | − | 0.530177i | \(-0.822126\pi\) | ||||
−0.847887 | + | 0.530177i | \(0.822126\pi\) | |||||||
\(374\) | 161.936i | 0.432984i | ||||||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | − 161.474i | − 0.429452i | ||||||||
\(377\) | 306.463i | 0.812900i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −617.180 | −1.62844 | −0.814222 | − | 0.580553i | \(-0.802836\pi\) | ||||
−0.814222 | + | 0.580553i | \(0.802836\pi\) | |||||||
\(380\) | 27.1747 | 0.0715123 | ||||||||
\(381\) | 335.117i | 0.879573i | ||||||||
\(382\) | 128.395 | 0.336113 | ||||||||
\(383\) | 173.947i | 0.454170i | 0.973875 | + | 0.227085i | \(0.0729195\pi\) | ||||
−0.973875 | + | 0.227085i | \(0.927081\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 324.781 | 0.841402 | ||||||||
\(387\) | 102.057 | 0.263713 | ||||||||
\(388\) | 122.891i | 0.316729i | ||||||||
\(389\) | 196.192 | 0.504350 | 0.252175 | − | 0.967682i | \(-0.418854\pi\) | ||||
0.252175 | + | 0.967682i | \(0.418854\pi\) | |||||||
\(390\) | 39.7650i | 0.101962i | ||||||||
\(391\) | 20.9079i | 0.0534729i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −313.699 | −0.798217 | ||||||||
\(394\) | −322.425 | −0.818338 | ||||||||
\(395\) | − 249.782i | − 0.632361i | ||||||||
\(396\) | −73.9447 | −0.186729 | ||||||||
\(397\) | − 398.701i | − 1.00428i | −0.864785 | − | 0.502142i | \(-0.832545\pi\) | ||||
0.864785 | − | 0.502142i | \(-0.167455\pi\) | |||||||
\(398\) | 15.6216i | 0.0392502i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 347.199 | 0.865832 | 0.432916 | − | 0.901434i | \(-0.357485\pi\) | ||||
0.432916 | + | 0.901434i | \(0.357485\pi\) | |||||||
\(402\) | 121.179i | 0.301439i | ||||||||
\(403\) | −8.84657 | −0.0219518 | ||||||||
\(404\) | − 124.278i | − 0.307620i | ||||||||
\(405\) | − 20.1246i | − 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 432.074 | 1.06161 | ||||||||
\(408\) | 45.5175 | 0.111562 | ||||||||
\(409\) | − 338.786i | − 0.828327i | −0.910203 | − | 0.414163i | \(-0.864074\pi\) | ||||
0.910203 | − | 0.414163i | \(-0.135926\pi\) | |||||||
\(410\) | −183.036 | −0.446429 | ||||||||
\(411\) | − 2.18815i | − 0.00532398i | ||||||||
\(412\) | − 355.884i | − 0.863795i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.54715 | −0.0230608 | ||||||||
\(415\) | 204.877 | 0.493679 | ||||||||
\(416\) | − 41.0691i | − 0.0987239i | ||||||||
\(417\) | 21.0145 | 0.0503944 | ||||||||
\(418\) | − 105.906i | − 0.253363i | ||||||||
\(419\) | 369.514i | 0.881894i | 0.897533 | + | 0.440947i | \(0.145357\pi\) | ||||
−0.897533 | + | 0.440947i | \(0.854643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −217.571 | −0.516797 | −0.258398 | − | 0.966038i | \(-0.583195\pi\) | ||||
−0.258398 | + | 0.966038i | \(0.583195\pi\) | |||||||
\(422\) | −213.811 | −0.506661 | ||||||||
\(423\) | − 171.269i | − 0.404891i | ||||||||
\(424\) | −41.1259 | −0.0969949 | ||||||||
\(425\) | 46.4561i | 0.109308i | ||||||||
\(426\) | 249.815i | 0.586420i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 169.942 | 0.397061 | ||||||||
\(429\) | 154.973 | 0.361243 | ||||||||
\(430\) | − 107.578i | − 0.250180i | ||||||||
\(431\) | −285.831 | −0.663181 | −0.331591 | − | 0.943423i | \(-0.607585\pi\) | ||||
−0.331591 | + | 0.943423i | \(0.607585\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | − 643.490i | − 1.48612i | −0.669224 | − | 0.743060i | \(-0.733374\pi\) | ||||
0.669224 | − | 0.743060i | \(-0.266626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −163.487 | −0.375833 | ||||||||
\(436\) | −345.716 | −0.792928 | ||||||||
\(437\) | − 13.6737i | − 0.0312900i | ||||||||
\(438\) | 201.605 | 0.460286 | ||||||||
\(439\) | 570.437i | 1.29940i | 0.760190 | + | 0.649700i | \(0.225106\pi\) | ||||
−0.760190 | + | 0.649700i | \(0.774894\pi\) | |||||||
\(440\) | 77.9445i | 0.177147i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −95.3956 | −0.215827 | ||||||||
\(443\) | −66.0149 | −0.149018 | −0.0745089 | − | 0.997220i | \(-0.523739\pi\) | ||||
−0.0745089 | + | 0.997220i | \(0.523739\pi\) | |||||||
\(444\) | − 121.449i | − 0.273533i | ||||||||
\(445\) | 285.758 | 0.642152 | ||||||||
\(446\) | 436.406i | 0.978489i | ||||||||
\(447\) | − 501.819i | − 1.12264i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 515.072 | 1.14715 | 0.573577 | − | 0.819152i | \(-0.305555\pi\) | ||||
0.573577 | + | 0.819152i | \(0.305555\pi\) | |||||||
\(450\) | −21.2132 | −0.0471405 | ||||||||
\(451\) | 713.333i | 1.58167i | ||||||||
\(452\) | −164.123 | −0.363105 | ||||||||
\(453\) | − 203.175i | − 0.448510i | ||||||||
\(454\) | 142.019i | 0.312816i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −29.7684 | −0.0652815 | ||||||||
\(457\) | 79.0271 | 0.172926 | 0.0864629 | − | 0.996255i | \(-0.472444\pi\) | ||||
0.0864629 | + | 0.996255i | \(0.472444\pi\) | |||||||
\(458\) | − 452.543i | − 0.988086i | ||||||||
\(459\) | 48.2786 | 0.105182 | ||||||||
\(460\) | 10.0636i | 0.0218774i | ||||||||
\(461\) | − 9.58316i | − 0.0207878i | −0.999946 | − | 0.0103939i | \(-0.996691\pi\) | ||||
0.999946 | − | 0.0103939i | \(-0.00330854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −232.103 | −0.501303 | −0.250652 | − | 0.968077i | \(-0.580645\pi\) | ||||
−0.250652 | + | 0.968077i | \(0.580645\pi\) | |||||||
\(464\) | 168.849 | 0.363898 | ||||||||
\(465\) | − 4.71932i | − 0.0101491i | ||||||||
\(466\) | −439.522 | −0.943181 | ||||||||
\(467\) | 685.536i | 1.46796i | 0.679172 | + | 0.733979i | \(0.262339\pi\) | ||||
−0.679172 | + | 0.733979i | \(0.737661\pi\) | |||||||
\(468\) | − 43.5604i | − 0.0930778i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −180.533 | −0.384114 | ||||||||
\(471\) | −318.243 | −0.675674 | ||||||||
\(472\) | 163.648i | 0.346711i | ||||||||
\(473\) | −419.254 | −0.886372 | ||||||||
\(474\) | 273.623i | 0.577264i | ||||||||
\(475\) | − 30.3822i | − 0.0639626i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −43.6206 | −0.0914477 | ||||||||
\(478\) | −192.705 | −0.403149 | ||||||||
\(479\) | 629.101i | 1.31336i | 0.754168 | + | 0.656682i | \(0.228041\pi\) | ||||
−0.754168 | + | 0.656682i | \(0.771959\pi\) | |||||||
\(480\) | 21.9089 | 0.0456435 | ||||||||
\(481\) | 254.533i | 0.529174i | ||||||||
\(482\) | 546.140i | 1.13307i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 61.7673 | 0.127618 | ||||||||
\(485\) | 137.396 | 0.283291 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −498.768 | −1.02417 | −0.512083 | − | 0.858936i | \(-0.671126\pi\) | ||||
−0.512083 | + | 0.858936i | \(0.671126\pi\) | |||||||
\(488\) | 16.5800i | 0.0339755i | ||||||||
\(489\) | − 210.567i | − 0.430607i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 166.583 | 0.339274 | 0.169637 | − | 0.985507i | \(-0.445741\pi\) | ||||
0.169637 | + | 0.985507i | \(0.445741\pi\) | |||||||
\(492\) | 200.506 | 0.407532 | ||||||||
\(493\) | − 392.203i | − 0.795543i | ||||||||
\(494\) | 62.3886 | 0.126293 | ||||||||
\(495\) | 82.6726i | 0.167015i | ||||||||
\(496\) | 4.87410i | 0.00982681i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −224.431 | −0.450665 | ||||||||
\(499\) | 36.3062 | 0.0727579 | 0.0363790 | − | 0.999338i | \(-0.488418\pi\) | ||||
0.0363790 | + | 0.999338i | \(0.488418\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 163.945 | 0.327236 | ||||||||
\(502\) | 140.533i | 0.279946i | ||||||||
\(503\) | − 634.940i | − 1.26231i | −0.775658 | − | 0.631153i | \(-0.782582\pi\) | ||||
0.775658 | − | 0.631153i | \(-0.217418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −138.947 | −0.275143 | ||||||||
\(506\) | 39.2200 | 0.0775100 | ||||||||
\(507\) | − 201.423i | − 0.397283i | ||||||||
\(508\) | −386.960 | −0.761732 | ||||||||
\(509\) | 578.347i | 1.13624i | 0.822945 | + | 0.568121i | \(0.192330\pi\) | ||||
−0.822945 | + | 0.568121i | \(0.807670\pi\) | |||||||
\(510\) | − 50.8901i | − 0.0997845i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −31.5741 | −0.0615480 | ||||||||
\(514\) | − 29.8651i | − 0.0581033i | ||||||||
\(515\) | −397.890 | −0.772602 | ||||||||
\(516\) | 117.845i | 0.228382i | ||||||||
\(517\) | 703.579i | 1.36089i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −451.532 | −0.870003 | ||||||||
\(520\) | −45.9167 | −0.0883013 | ||||||||
\(521\) | 636.210i | 1.22113i | 0.791965 | + | 0.610566i | \(0.209058\pi\) | ||||
−0.791965 | + | 0.610566i | \(0.790942\pi\) | |||||||
\(522\) | 179.091 | 0.343087 | ||||||||
\(523\) | 453.645i | 0.867390i | 0.901060 | + | 0.433695i | \(0.142791\pi\) | ||||
−0.901060 | + | 0.433695i | \(0.857209\pi\) | |||||||
\(524\) | − 362.229i | − 0.691276i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 538.133 | 1.02307 | ||||||||
\(527\) | 11.3216 | 0.0214831 | ||||||||
\(528\) | − 85.3839i | − 0.161712i | ||||||||
\(529\) | −523.936 | −0.990428 | ||||||||
\(530\) | 45.9801i | 0.0867549i | ||||||||
\(531\) | 173.575i | 0.326882i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −420.220 | −0.788406 | ||||||||
\(534\) | −313.032 | −0.586202 | ||||||||
\(535\) | − 190.001i | − 0.355142i | ||||||||
\(536\) | −139.925 | −0.261054 | ||||||||
\(537\) | − 530.923i | − 0.988684i | ||||||||
\(538\) | 23.7461i | 0.0441377i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 23.2379 | 0.0430331 | ||||||||
\(541\) | −576.318 | −1.06528 | −0.532641 | − | 0.846341i | \(-0.678800\pi\) | ||||
−0.532641 | + | 0.846341i | \(0.678800\pi\) | |||||||
\(542\) | − 522.796i | − 0.964568i | ||||||||
\(543\) | −545.397 | −1.00442 | ||||||||
\(544\) | 52.5591i | 0.0966159i | ||||||||
\(545\) | 386.523i | 0.709216i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 481.306 | 0.879901 | 0.439950 | − | 0.898022i | \(-0.354996\pi\) | ||||
0.439950 | + | 0.898022i | \(0.354996\pi\) | |||||||
\(548\) | 2.52666 | 0.00461070 | ||||||||
\(549\) | 17.5858i | 0.0320324i | ||||||||
\(550\) | 87.1446 | 0.158445 | ||||||||
\(551\) | 256.500i | 0.465517i | ||||||||
\(552\) | − 11.0241i | − 0.0199712i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −687.060 | −1.24018 | ||||||||
\(555\) | −135.784 | −0.244656 | ||||||||
\(556\) | 24.2654i | 0.0436428i | ||||||||
\(557\) | 108.811 | 0.195352 | 0.0976762 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976762 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(558\) | 5.16976i | 0.00926480i | ||||||||
\(559\) | − 246.980i | − 0.441825i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −198.330 | −0.353530 | ||||||||
\(562\) | −509.448 | −0.906491 | ||||||||
\(563\) | − 602.195i | − 1.06962i | −0.844973 | − | 0.534809i | \(-0.820384\pi\) | ||||
0.844973 | − | 0.534809i | \(-0.179616\pi\) | |||||||
\(564\) | 197.764 | 0.350646 | ||||||||
\(565\) | 183.495i | 0.324771i | ||||||||
\(566\) | 382.547i | 0.675878i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −288.461 | −0.507854 | ||||||||
\(569\) | −9.53369 | −0.0167552 | −0.00837759 | − | 0.999965i | \(-0.502667\pi\) | ||||
−0.00837759 | + | 0.999965i | \(0.502667\pi\) | |||||||
\(570\) | 33.2820i | 0.0583896i | ||||||||
\(571\) | 982.205 | 1.72015 | 0.860075 | − | 0.510168i | \(-0.170417\pi\) | ||||
0.860075 | + | 0.510168i | \(0.170417\pi\) | |||||||
\(572\) | 178.948i | 0.312846i | ||||||||
\(573\) | 157.251i | 0.274435i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.2514 | 0.0195677 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 524.235i | 0.908553i | 0.890861 | + | 0.454276i | \(0.150102\pi\) | ||||
−0.890861 | + | 0.454276i | \(0.849898\pi\) | |||||||
\(578\) | −286.623 | −0.495888 | ||||||||
\(579\) | 397.774i | 0.687002i | ||||||||
\(580\) | − 188.779i | − 0.325481i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −150.510 | −0.258608 | ||||||||
\(583\) | 179.195 | 0.307367 | ||||||||
\(584\) | 232.794i | 0.398620i | ||||||||
\(585\) | −48.7020 | −0.0832513 | ||||||||
\(586\) | 13.6221i | 0.0232460i | ||||||||
\(587\) | 651.322i | 1.10958i | 0.831991 | + | 0.554789i | \(0.187201\pi\) | ||||
−0.831991 | + | 0.554789i | \(0.812799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.40429 | −0.0125710 | ||||||||
\(590\) | 182.964 | 0.310108 | ||||||||
\(591\) | − 394.889i | − 0.668170i | ||||||||
\(592\) | 140.237 | 0.236887 | ||||||||
\(593\) | − 705.411i | − 1.18956i | −0.803887 | − | 0.594782i | \(-0.797239\pi\) | ||||
0.803887 | − | 0.594782i | \(-0.202761\pi\) | |||||||
\(594\) | − 90.5633i | − 0.152464i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 579.451 | 0.972233 | ||||||||
\(597\) | −19.1325 | −0.0320477 | ||||||||
\(598\) | 23.1043i | 0.0386360i | ||||||||
\(599\) | −593.819 | −0.991351 | −0.495676 | − | 0.868508i | \(-0.665080\pi\) | ||||
−0.495676 | + | 0.868508i | \(0.665080\pi\) | |||||||
\(600\) | − 24.4949i | − 0.0408248i | ||||||||
\(601\) | 12.1644i | 0.0202403i | 0.999949 | + | 0.0101202i | \(0.00322140\pi\) | ||||
−0.999949 | + | 0.0101202i | \(0.996779\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −148.413 | −0.246124 | ||||||||
\(604\) | 234.606 | 0.388421 | ||||||||
\(605\) | − 69.0579i | − 0.114145i | ||||||||
\(606\) | 152.209 | 0.251170 | ||||||||
\(607\) | 806.583i | 1.32880i | 0.747376 | + | 0.664401i | \(0.231313\pi\) | ||||
−0.747376 | + | 0.664401i | \(0.768687\pi\) | |||||||
\(608\) | − 34.3736i | − 0.0565354i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.5370 | 0.0303886 | ||||||||
\(611\) | −414.475 | −0.678355 | ||||||||
\(612\) | 55.7473i | 0.0910904i | ||||||||
\(613\) | −794.474 | −1.29604 | −0.648021 | − | 0.761622i | \(-0.724403\pi\) | ||||
−0.648021 | + | 0.761622i | \(0.724403\pi\) | |||||||
\(614\) | 65.1121i | 0.106046i | ||||||||
\(615\) | − 224.172i | − 0.364508i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 108.982 | 0.176633 | 0.0883164 | − | 0.996092i | \(-0.471851\pi\) | ||||
0.0883164 | + | 0.996092i | \(0.471851\pi\) | |||||||
\(618\) | 435.867 | 0.705286 | ||||||||
\(619\) | 358.795i | 0.579636i | 0.957082 | + | 0.289818i | \(0.0935948\pi\) | ||||
−0.957082 | + | 0.289818i | \(0.906405\pi\) | |||||||
\(620\) | 5.44941 | 0.00878937 | ||||||||
\(621\) | − 11.6928i | − 0.0188290i | ||||||||
\(622\) | − 617.533i | − 0.992819i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 50.2992 | 0.0806077 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − 405.203i | − 0.647289i | ||||||||
\(627\) | 129.708 | 0.206870 | ||||||||
\(628\) | − 367.475i | − 0.585151i | ||||||||
\(629\) | − 325.743i | − 0.517875i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −612.351 | −0.970446 | −0.485223 | − | 0.874391i | \(-0.661262\pi\) | ||||
−0.485223 | + | 0.874391i | \(0.661262\pi\) | |||||||
\(632\) | −315.953 | −0.499925 | ||||||||
\(633\) | − 261.864i | − 0.413687i | ||||||||
\(634\) | 1.93583 | 0.00305335 | ||||||||
\(635\) | 432.634i | 0.681314i | ||||||||
\(636\) | − 50.3687i | − 0.0791960i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −735.713 | −1.15316 | ||||||||
\(639\) | −305.959 | −0.478810 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | 919.411 | 1.43434 | 0.717169 | − | 0.696899i | \(-0.245437\pi\) | ||||
0.717169 | + | 0.696899i | \(0.245437\pi\) | |||||||
\(642\) | 208.136i | 0.324199i | ||||||||
\(643\) | 835.879i | 1.29997i | 0.759948 | + | 0.649984i | \(0.225224\pi\) | ||||
−0.759948 | + | 0.649984i | \(0.774776\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 131.755 | 0.204271 | ||||||||
\(646\) | −79.8430 | −0.123596 | ||||||||
\(647\) | 569.191i | 0.879738i | 0.898062 | + | 0.439869i | \(0.144975\pi\) | ||||
−0.898062 | + | 0.439869i | \(0.855025\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | − 713.051i | − 1.09869i | ||||||||
\(650\) | 51.3364i | 0.0789791i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 243.142 | 0.372917 | ||||||||
\(653\) | 392.324 | 0.600803 | 0.300402 | − | 0.953813i | \(-0.402879\pi\) | ||||
0.300402 | + | 0.953813i | \(0.402879\pi\) | |||||||
\(654\) | − 423.414i | − 0.647423i | ||||||||
\(655\) | −404.984 | −0.618296 | ||||||||
\(656\) | 231.524i | 0.352933i | ||||||||
\(657\) | 246.915i | 0.375822i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 505.063 | 0.766408 | 0.383204 | − | 0.923664i | \(-0.374821\pi\) | ||||
0.383204 | + | 0.923664i | \(0.374821\pi\) | |||||||
\(660\) | −95.4621 | −0.144640 | ||||||||
\(661\) | 295.390i | 0.446884i | 0.974717 | + | 0.223442i | \(0.0717293\pi\) | ||||
−0.974717 | + | 0.223442i | \(0.928271\pi\) | |||||||
\(662\) | 543.105 | 0.820401 | ||||||||
\(663\) | − 116.835i | − 0.176222i | ||||||||
\(664\) | − 259.151i | − 0.390288i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 148.744 | 0.223339 | ||||||||
\(667\) | −94.9895 | −0.142413 | ||||||||
\(668\) | 189.308i | 0.283395i | ||||||||
\(669\) | −534.486 | −0.798933 | ||||||||
\(670\) | 156.441i | 0.233494i | ||||||||
\(671\) | − 72.2430i | − 0.107665i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −624.569 | −0.928038 | −0.464019 | − | 0.885825i | \(-0.653593\pi\) | ||||
−0.464019 | + | 0.885825i | \(0.653593\pi\) | |||||||
\(674\) | 200.745 | 0.297841 | ||||||||
\(675\) | − 25.9808i | − 0.0384900i | ||||||||
\(676\) | 232.583 | 0.344057 | ||||||||
\(677\) | − 781.556i | − 1.15444i | −0.816589 | − | 0.577220i | \(-0.804138\pi\) | ||||
0.816589 | − | 0.577220i | \(-0.195862\pi\) | |||||||
\(678\) | − 201.009i | − 0.296474i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 58.7628 | 0.0864159 | ||||||||
\(681\) | −173.937 | −0.255414 | ||||||||
\(682\) | − 21.2376i | − 0.0311401i | ||||||||
\(683\) | 101.705 | 0.148909 | 0.0744546 | − | 0.997224i | \(-0.476278\pi\) | ||||
0.0744546 | + | 0.997224i | \(0.476278\pi\) | |||||||
\(684\) | − 36.4587i | − 0.0533021i | ||||||||
\(685\) | − 2.82490i | − 0.00412393i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 554.250 | 0.806769 | ||||||||
\(688\) | −136.076 | −0.197785 | ||||||||
\(689\) | 105.563i | 0.153211i | ||||||||
\(690\) | −12.3253 | −0.0178628 | ||||||||
\(691\) | 732.870i | 1.06059i | 0.847812 | + | 0.530297i | \(0.177920\pi\) | ||||
−0.847812 | + | 0.530297i | \(0.822080\pi\) | |||||||
\(692\) | − 521.384i | − 0.753445i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 354.051 | 0.510160 | ||||||||
\(695\) | 27.1296 | 0.0390353 | ||||||||
\(696\) | 206.797i | 0.297122i | ||||||||
\(697\) | 537.786 | 0.771572 | ||||||||
\(698\) | − 276.037i | − 0.395469i | ||||||||
\(699\) | − 538.303i | − 0.770104i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −795.928 | −1.13542 | −0.567709 | − | 0.823229i | \(-0.692170\pi\) | ||||
−0.567709 | + | 0.823229i | \(0.692170\pi\) | |||||||
\(702\) | 53.3504 | 0.0759977 | ||||||||
\(703\) | 213.036i | 0.303038i | ||||||||
\(704\) | 98.5929 | 0.140047 | ||||||||
\(705\) | − 221.107i | − 0.313627i | ||||||||
\(706\) | 201.100i | 0.284845i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −200.427 | −0.283089 | ||||||||
\(709\) | 1029.06 | 1.45143 | 0.725715 | − | 0.687995i | \(-0.241509\pi\) | ||||
0.725715 | + | 0.687995i | \(0.241509\pi\) | |||||||
\(710\) | 322.509i | 0.454239i | ||||||||
\(711\) | −335.118 | −0.471334 | ||||||||
\(712\) | − 361.458i | − 0.507666i | ||||||||
\(713\) | − 2.74203i | − 0.00384576i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 200.070 | 0.279818 | ||||||||
\(716\) | 613.057 | 0.856225 | ||||||||
\(717\) | − 236.015i | − 0.329170i | ||||||||
\(718\) | 928.978 | 1.29384 | ||||||||
\(719\) | − 157.673i | − 0.219295i | −0.993971 | − | 0.109648i | \(-0.965028\pi\) | ||||
0.993971 | − | 0.109648i | \(-0.0349723\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −458.314 | −0.634784 | ||||||||
\(723\) | −668.883 | −0.925149 | ||||||||
\(724\) | − 629.771i | − 0.869849i | ||||||||
\(725\) | −211.061 | −0.291119 | ||||||||
\(726\) | 75.6492i | 0.104200i | ||||||||
\(727\) | − 13.5224i | − 0.0186003i | −0.999957 | − | 0.00930013i | \(-0.997040\pi\) | ||||
0.999957 | − | 0.00930013i | \(-0.00296037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 260.271 | 0.356536 | ||||||||
\(731\) | 316.078i | 0.432391i | ||||||||
\(732\) | −20.3063 | −0.0277409 | ||||||||
\(733\) | 394.471i | 0.538159i | 0.963118 | + | 0.269080i | \(0.0867195\pi\) | ||||
−0.963118 | + | 0.269080i | \(0.913280\pi\) | |||||||
\(734\) | − 725.707i | − 0.988701i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.7295 | 0.0172956 | ||||||||
\(737\) | 609.685 | 0.827253 | ||||||||
\(738\) | 245.569i | 0.332749i | ||||||||
\(739\) | 950.161 | 1.28574 | 0.642869 | − | 0.765976i | \(-0.277744\pi\) | ||||
0.642869 | + | 0.765976i | \(0.277744\pi\) | |||||||
\(740\) | − 156.790i | − 0.211878i | ||||||||
\(741\) | 76.4101i | 0.103118i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 425.883 | 0.573194 | 0.286597 | − | 0.958051i | \(-0.407476\pi\) | ||||
0.286597 | + | 0.958051i | \(0.407476\pi\) | |||||||
\(744\) | −5.96953 | −0.00802356 | ||||||||
\(745\) | − 647.846i | − 0.869592i | ||||||||
\(746\) | 894.524 | 1.19909 | ||||||||
\(747\) | − 274.871i | − 0.367967i | ||||||||
\(748\) | − 229.012i | − 0.306166i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −27.3861 | −0.0365148 | ||||||||
\(751\) | −631.747 | −0.841208 | −0.420604 | − | 0.907244i | \(-0.638182\pi\) | ||||
−0.420604 | + | 0.907244i | \(0.638182\pi\) | |||||||
\(752\) | 228.359i | 0.303669i | ||||||||
\(753\) | −172.117 | −0.228575 | ||||||||
\(754\) | − 433.405i | − 0.574807i | ||||||||
\(755\) | − 262.298i | − 0.347414i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 882.903 | 1.16632 | 0.583159 | − | 0.812358i | \(-0.301816\pi\) | ||||
0.583159 | + | 0.812358i | \(0.301816\pi\) | |||||||
\(758\) | 872.825 | 1.15148 | ||||||||
\(759\) | 48.0346i | 0.0632866i | ||||||||
\(760\) | −38.4308 | −0.0505668 | ||||||||
\(761\) | − 1132.82i | − 1.48859i | −0.667851 | − | 0.744295i | \(-0.732786\pi\) | ||||
0.667851 | − | 0.744295i | \(-0.267214\pi\) | |||||||
\(762\) | − 473.927i | − 0.621952i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −181.578 | −0.237668 | ||||||||
\(765\) | 62.3274 | 0.0814737 | ||||||||
\(766\) | − 245.998i | − 0.321146i | ||||||||
\(767\) | 420.054 | 0.547659 | ||||||||
\(768\) | − 27.7128i | − 0.0360844i | ||||||||
\(769\) | − 41.6421i | − 0.0541510i | −0.999633 | − | 0.0270755i | \(-0.991381\pi\) | ||||
0.999633 | − | 0.0270755i | \(-0.00861944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.5771 | 0.0474411 | ||||||||
\(772\) | −459.310 | −0.594961 | ||||||||
\(773\) | − 1286.33i | − 1.66408i | −0.554715 | − | 0.832041i | \(-0.687173\pi\) | ||||
0.554715 | − | 0.832041i | \(-0.312827\pi\) | |||||||
\(774\) | −144.330 | −0.186473 | ||||||||
\(775\) | − 6.09262i | − 0.00786145i | ||||||||
\(776\) | − 173.794i | − 0.223962i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −277.458 | −0.356629 | ||||||||
\(779\) | −351.711 | −0.451490 | ||||||||
\(780\) | − 56.2362i | − 0.0720977i | ||||||||
\(781\) | 1256.89 | 1.60934 | ||||||||
\(782\) | − 29.5682i | − 0.0378110i | ||||||||
\(783\) | 219.341i | 0.280129i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −410.850 | −0.523375 | ||||||||
\(786\) | 443.638 | 0.564425 | ||||||||
\(787\) | 997.472i | 1.26744i | 0.773564 | + | 0.633718i | \(0.218472\pi\) | ||||
−0.773564 | + | 0.633718i | \(0.781528\pi\) | |||||||
\(788\) | 455.978 | 0.578652 | ||||||||
\(789\) | 659.075i | 0.835330i | ||||||||
\(790\) | 353.246i | 0.447146i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 104.574 | 0.132037 | ||||||||
\(793\) | 42.5580 | 0.0536671 | ||||||||
\(794\) | 563.848i | 0.710136i | ||||||||
\(795\) | −56.3139 | −0.0708351 | ||||||||
\(796\) | − 22.0923i | − 0.0277541i | ||||||||
\(797\) | 971.547i | 1.21901i | 0.792784 | + | 0.609503i | \(0.208631\pi\) | ||||
−0.792784 | + | 0.609503i | \(0.791369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 530.433 | 0.663871 | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | − 383.384i | − 0.478632i | ||||||||
\(802\) | −491.013 | −0.612236 | ||||||||
\(803\) | − 1014.34i | − 1.26318i | ||||||||
\(804\) | − 171.372i | − 0.213150i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.5109 | 0.0155223 | ||||||||
\(807\) | −29.0829 | −0.0360383 | ||||||||
\(808\) | 175.756i | 0.217520i | ||||||||
\(809\) | −1304.22 | −1.61214 | −0.806072 | − | 0.591817i | \(-0.798411\pi\) | ||||
−0.806072 | + | 0.591817i | \(0.798411\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | − 210.763i | − 0.259880i | −0.991522 | − | 0.129940i | \(-0.958521\pi\) | ||||
0.991522 | − | 0.129940i | \(-0.0414785\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 640.291 | 0.787566 | ||||||||
\(814\) | −611.045 | −0.750670 | ||||||||
\(815\) | − 271.841i | − 0.333547i | ||||||||
\(816\) | −64.3714 | −0.0788866 | ||||||||
\(817\) | − 206.715i | − 0.253017i | ||||||||
\(818\) | 479.115i | 0.585716i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 258.852 | 0.315673 | ||||||||
\(821\) | −724.506 | −0.882467 | −0.441234 | − | 0.897392i | \(-0.645459\pi\) | ||||
−0.441234 | + | 0.897392i | \(0.645459\pi\) | |||||||
\(822\) | 3.09452i | 0.00376462i | ||||||||
\(823\) | −446.037 | −0.541964 | −0.270982 | − | 0.962584i | \(-0.587348\pi\) | ||||
−0.270982 | + | 0.962584i | \(0.587348\pi\) | |||||||
\(824\) | 503.296i | 0.610796i | ||||||||
\(825\) | 106.730i | 0.129370i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −702.737 | −0.849743 | −0.424871 | − | 0.905254i | \(-0.639681\pi\) | ||||
−0.424871 | + | 0.905254i | \(0.639681\pi\) | |||||||
\(828\) | 13.5017 | 0.0163064 | ||||||||
\(829\) | 416.873i | 0.502863i | 0.967875 | + | 0.251431i | \(0.0809013\pi\) | ||||
−0.967875 | + | 0.251431i | \(0.919099\pi\) | |||||||
\(830\) | −289.740 | −0.349084 | ||||||||
\(831\) | − 841.473i | − 1.01260i | ||||||||
\(832\) | 58.0805i | 0.0698083i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −29.7189 | −0.0356342 | ||||||||
\(835\) | 211.653 | 0.253476 | ||||||||
\(836\) | 149.773i | 0.179155i | ||||||||
\(837\) | −6.33164 | −0.00756468 | ||||||||
\(838\) | − 522.571i | − 0.623593i | ||||||||
\(839\) | − 359.231i | − 0.428166i | −0.976815 | − | 0.214083i | \(-0.931324\pi\) | ||||
0.976815 | − | 0.214083i | \(-0.0686763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 940.871 | 1.11875 | ||||||||
\(842\) | 307.692 | 0.365430 | ||||||||
\(843\) | − 623.943i | − 0.740146i | ||||||||
\(844\) | 302.374 | 0.358263 | ||||||||
\(845\) | − 260.036i | − 0.307734i | ||||||||
\(846\) | 242.211i | 0.286301i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 58.1607 | 0.0685858 | ||||||||
\(849\) | −468.523 | −0.551852 | ||||||||
\(850\) | − 65.6988i | − 0.0772927i | ||||||||
\(851\) | −78.8933 | −0.0927066 | ||||||||
\(852\) | − 353.291i | − 0.414661i | ||||||||
\(853\) | 988.948i | 1.15938i | 0.814838 | + | 0.579688i | \(0.196826\pi\) | ||||
−0.814838 | + | 0.579688i | \(0.803174\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −40.7620 | −0.0476749 | ||||||||
\(856\) | −240.334 | −0.280765 | ||||||||
\(857\) | − 361.298i | − 0.421584i | −0.977531 | − | 0.210792i | \(-0.932396\pi\) | ||||
0.977531 | − | 0.210792i | \(-0.0676043\pi\) | |||||||
\(858\) | −219.165 | −0.255437 | ||||||||
\(859\) | − 702.593i | − 0.817920i | −0.912552 | − | 0.408960i | \(-0.865892\pi\) | ||||
0.912552 | − | 0.408960i | \(-0.134108\pi\) | |||||||
\(860\) | 152.138i | 0.176904i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 404.226 | 0.468940 | ||||||||
\(863\) | 1102.42 | 1.27742 | 0.638711 | − | 0.769447i | \(-0.279468\pi\) | ||||
0.638711 | + | 0.769447i | \(0.279468\pi\) | |||||||
\(864\) | − 29.3939i | − 0.0340207i | ||||||||
\(865\) | −582.925 | −0.673902 | ||||||||
\(866\) | 910.033i | 1.05085i | ||||||||
\(867\) | − 351.040i | − 0.404891i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1376.68 | 1.58421 | ||||||||
\(870\) | 231.206 | 0.265754 | ||||||||
\(871\) | 359.162i | 0.412356i | ||||||||
\(872\) | 488.917 | 0.560684 | ||||||||
\(873\) | − 184.337i | − 0.211153i | ||||||||
\(874\) | 19.3376i | 0.0221254i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −285.113 | −0.325472 | ||||||||
\(877\) | 668.121 | 0.761826 | 0.380913 | − | 0.924611i | \(-0.375610\pi\) | ||||
0.380913 | + | 0.924611i | \(0.375610\pi\) | |||||||
\(878\) | − 806.720i | − 0.918815i | ||||||||
\(879\) | −16.6836 | −0.0189802 | ||||||||
\(880\) | − 110.230i | − 0.125262i | ||||||||
\(881\) | 15.3854i | 0.0174636i | 0.999962 | + | 0.00873178i | \(0.00277945\pi\) | ||||
−0.999962 | + | 0.00873178i | \(0.997221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.0884 | 0.0578577 | 0.0289289 | − | 0.999581i | \(-0.490790\pi\) | ||||
0.0289289 | + | 0.999581i | \(0.490790\pi\) | |||||||
\(884\) | 134.910 | 0.152613 | ||||||||
\(885\) | 224.084i | 0.253202i | ||||||||
\(886\) | 93.3591 | 0.105371 | ||||||||
\(887\) | 30.4440i | 0.0343225i | 0.999853 | + | 0.0171612i | \(0.00546286\pi\) | ||||
−0.999853 | + | 0.0171612i | \(0.994537\pi\) | |||||||
\(888\) | 171.755i | 0.193417i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −404.122 | −0.454070 | ||||||||
\(891\) | 110.917 | 0.124486 | ||||||||
\(892\) | − 617.171i | − 0.691896i | ||||||||
\(893\) | −346.902 | −0.388468 | ||||||||
\(894\) | 709.679i | 0.793825i | ||||||||
\(895\) | − 685.419i | − 0.765831i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.2969 | −0.0315462 | ||||||||
\(898\) | −728.422 | −0.811160 | ||||||||
\(899\) | 51.4366i | 0.0572154i | ||||||||
\(900\) | 30.0000 | 0.0333333 | ||||||||
\(901\) | − 135.096i | − 0.149940i | ||||||||
\(902\) | − 1008.80i | − 1.11841i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 232.105 | 0.256754 | ||||||||
\(905\) | −704.105 | −0.778017 | ||||||||
\(906\) | 287.333i | 0.317144i | ||||||||
\(907\) | −690.016 | −0.760767 | −0.380384 | − | 0.924829i | \(-0.624208\pi\) | ||||
−0.380384 | + | 0.924829i | \(0.624208\pi\) | |||||||
\(908\) | − 200.845i | − 0.221195i | ||||||||
\(909\) | 186.418i | 0.205080i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −264.542 | −0.290386 | −0.145193 | − | 0.989403i | \(-0.546380\pi\) | ||||
−0.145193 | + | 0.989403i | \(0.546380\pi\) | |||||||
\(912\) | 42.0988 | 0.0461610 | ||||||||
\(913\) | 1129.18i | 1.23678i | ||||||||
\(914\) | −111.761 | −0.122277 | ||||||||
\(915\) | 22.7031i | 0.0248122i | ||||||||
\(916\) | 639.993i | 0.698682i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −68.2762 | −0.0743750 | ||||||||
\(919\) | 538.135 | 0.585566 | 0.292783 | − | 0.956179i | \(-0.405419\pi\) | ||||
0.292783 | + | 0.956179i | \(0.405419\pi\) | |||||||
\(920\) | − 14.2321i | − 0.0154696i | ||||||||
\(921\) | −79.7457 | −0.0865860 | ||||||||
\(922\) | 13.5526i | 0.0146992i | ||||||||
\(923\) | 740.428i | 0.802198i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −175.296 | −0.189510 | ||||||||
\(926\) | 328.244 | 0.354475 | ||||||||
\(927\) | 533.825i | 0.575864i | ||||||||
\(928\) | −238.788 | −0.257315 | ||||||||
\(929\) | − 889.199i | − 0.957157i | −0.878045 | − | 0.478579i | \(-0.841152\pi\) | ||||
0.878045 | − | 0.478579i | \(-0.158848\pi\) | |||||||
\(930\) | 6.67413i | 0.00717649i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 621.578 | 0.666929 | ||||||||
\(933\) | 756.321 | 0.810633 | ||||||||
\(934\) | − 969.495i | − 1.03800i | ||||||||
\(935\) | −256.043 | −0.273843 | ||||||||
\(936\) | 61.6037i | 0.0658159i | ||||||||
\(937\) | − 997.355i | − 1.06441i | −0.846615 | − | 0.532206i | \(-0.821363\pi\) | ||||
0.846615 | − | 0.532206i | \(-0.178637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 496.270 | 0.528509 | ||||||||
\(940\) | 255.313 | 0.271609 | ||||||||
\(941\) | 1107.47i | 1.17691i | 0.808531 | + | 0.588454i | \(0.200263\pi\) | ||||
−0.808531 | + | 0.588454i | \(0.799737\pi\) | |||||||
\(942\) | 450.063 | 0.477774 | ||||||||
\(943\) | − 130.249i | − 0.138122i | ||||||||
\(944\) | − 231.433i | − 0.245162i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 592.915 | 0.626760 | ||||||||
\(947\) | 587.602 | 0.620488 | 0.310244 | − | 0.950657i | \(-0.399589\pi\) | ||||
0.310244 | + | 0.950657i | \(0.399589\pi\) | |||||||
\(948\) | − 386.961i | − 0.408187i | ||||||||
\(949\) | 597.540 | 0.629653 | ||||||||
\(950\) | 42.9669i | 0.0452284i | ||||||||
\(951\) | 2.37089i | 0.00249305i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 441.771 | 0.463558 | 0.231779 | − | 0.972768i | \(-0.425545\pi\) | ||||
0.231779 | + | 0.972768i | \(0.425545\pi\) | |||||||
\(954\) | 61.6888 | 0.0646633 | ||||||||
\(955\) | 203.011i | 0.212577i | ||||||||
\(956\) | 272.526 | 0.285069 | ||||||||
\(957\) | − 901.061i | − 0.941548i | ||||||||
\(958\) | − 889.684i | − 0.928688i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −30.9839 | −0.0322749 | ||||||||
\(961\) | 959.515 | 0.998455 | ||||||||
\(962\) | − 359.963i | − 0.374182i | ||||||||
\(963\) | −254.913 | −0.264707 | ||||||||
\(964\) | − 772.359i | − 0.801202i | ||||||||
\(965\) | 513.524i | 0.532150i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1581.63 | 1.63561 | 0.817804 | − | 0.575497i | \(-0.195191\pi\) | ||||
0.817804 | + | 0.575497i | \(0.195191\pi\) | |||||||
\(968\) | −87.3522 | −0.0902398 | ||||||||
\(969\) | − 97.7873i | − 0.100916i | ||||||||
\(970\) | −194.308 | −0.200317 | ||||||||
\(971\) | 597.019i | 0.614849i | 0.951572 | + | 0.307425i | \(0.0994672\pi\) | ||||
−0.951572 | + | 0.307425i | \(0.900533\pi\) | |||||||
\(972\) | − 31.1769i | − 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 705.365 | 0.724194 | ||||||||
\(975\) | −62.8740 | −0.0644862 | ||||||||
\(976\) | − 23.4477i | − 0.0240243i | ||||||||
\(977\) | −211.442 | −0.216420 | −0.108210 | − | 0.994128i | \(-0.534512\pi\) | ||||
−0.108210 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(978\) | 297.787i | 0.304485i | ||||||||
\(979\) | 1574.96i | 1.60874i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 518.575 | 0.528618 | ||||||||
\(982\) | −235.584 | −0.239903 | ||||||||
\(983\) | 592.844i | 0.603096i | 0.953451 | + | 0.301548i | \(0.0975034\pi\) | ||||
−0.953451 | + | 0.301548i | \(0.902497\pi\) | |||||||
\(984\) | −283.558 | −0.288169 | ||||||||
\(985\) | − 509.799i | − 0.517562i | ||||||||
\(986\) | 554.659i | 0.562534i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −88.2308 | −0.0893024 | ||||||||
\(989\) | 76.5525 | 0.0774039 | ||||||||
\(990\) | − 116.917i | − 0.118098i | ||||||||
\(991\) | −379.941 | −0.383391 | −0.191696 | − | 0.981454i | \(-0.561399\pi\) | ||||
−0.191696 | + | 0.981454i | \(0.561399\pi\) | |||||||
\(992\) | − 6.89301i | − 0.00694860i | ||||||||
\(993\) | 665.166i | 0.669855i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.6999 | −0.0248240 | ||||||||
\(996\) | 317.394 | 0.318669 | ||||||||
\(997\) | − 206.634i | − 0.207256i | −0.994616 | − | 0.103628i | \(-0.966955\pi\) | ||||
0.994616 | − | 0.103628i | \(-0.0330451\pi\) | |||||||
\(998\) | −51.3447 | −0.0514476 | ||||||||
\(999\) | 182.173i | 0.182356i |
(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.a.391.1 | 8 | ||
7.2 | even | 3 | 210.3.o.a.31.3 | ✓ | 8 | ||
7.3 | odd | 6 | 210.3.o.a.61.3 | yes | 8 | ||
7.6 | odd | 2 | inner | 1470.3.f.a.391.4 | 8 | ||
21.2 | odd | 6 | 630.3.v.b.451.2 | 8 | |||
21.17 | even | 6 | 630.3.v.b.271.2 | 8 | |||
35.2 | odd | 12 | 1050.3.q.c.199.4 | 16 | |||
35.3 | even | 12 | 1050.3.q.c.649.4 | 16 | |||
35.9 | even | 6 | 1050.3.p.b.451.2 | 8 | |||
35.17 | even | 12 | 1050.3.q.c.649.5 | 16 | |||
35.23 | odd | 12 | 1050.3.q.c.199.5 | 16 | |||
35.24 | odd | 6 | 1050.3.p.b.901.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.a.31.3 | ✓ | 8 | 7.2 | even | 3 | ||
210.3.o.a.61.3 | yes | 8 | 7.3 | odd | 6 | ||
630.3.v.b.271.2 | 8 | 21.17 | even | 6 | |||
630.3.v.b.451.2 | 8 | 21.2 | odd | 6 | |||
1050.3.p.b.451.2 | 8 | 35.9 | even | 6 | |||
1050.3.p.b.901.2 | 8 | 35.24 | odd | 6 | |||
1050.3.q.c.199.4 | 16 | 35.2 | odd | 12 | |||
1050.3.q.c.199.5 | 16 | 35.23 | odd | 12 | |||
1050.3.q.c.649.4 | 16 | 35.3 | even | 12 | |||
1050.3.q.c.649.5 | 16 | 35.17 | even | 12 | |||
1470.3.f.a.391.1 | 8 | 1.1 | even | 1 | trivial | ||
1470.3.f.a.391.4 | 8 | 7.6 | odd | 2 | inner |