Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.p.1351.4 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 3.00000i | 1.13389i | 0.823754 | + | 0.566947i | \(0.191875\pi\) | ||||
−0.823754 | + | 0.566947i | \(0.808125\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | − 3.73205i | − 1.12526i | −0.826710 | − | 0.562628i | \(-0.809790\pi\) | ||||
0.826710 | − | 0.562628i | \(-0.190210\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 2.26795i | 0.520303i | 0.965568 | + | 0.260152i | \(0.0837725\pi\) | ||||
−0.965568 | + | 0.260152i | \(0.916227\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | − 3.00000i | − 0.654654i | ||||||||
\(22\) | −3.73205 | −0.795676 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − 3.00000i | − 0.566947i | ||||||||
\(29\) | −5.46410 | −1.01466 | −0.507329 | − | 0.861752i | \(-0.669367\pi\) | ||||
−0.507329 | + | 0.861752i | \(0.669367\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − 8.92820i | − 1.60355i | −0.597624 | − | 0.801776i | \(-0.703889\pi\) | ||||
0.597624 | − | 0.801776i | \(-0.296111\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 3.73205i | 0.649667i | ||||||||
\(34\) | − 4.00000i | − 0.685994i | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 7.92820i | − 1.30339i | −0.758482 | − | 0.651694i | \(-0.774059\pi\) | ||||
0.758482 | − | 0.651694i | \(-0.225941\pi\) | |||||||
\(38\) | 2.26795 | 0.367910 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 4.00000i | 0.624695i | 0.949968 | + | 0.312348i | \(0.101115\pi\) | ||||
−0.949968 | + | 0.312348i | \(0.898885\pi\) | |||||||
\(42\) | −3.00000 | −0.462910 | ||||||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 3.73205i | 0.562628i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 3.46410i | 0.510754i | ||||||||
\(47\) | 0.464102i | 0.0676962i | 0.999427 | + | 0.0338481i | \(0.0107762\pi\) | ||||
−0.999427 | + | 0.0338481i | \(0.989224\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.73205 | −0.512637 | −0.256318 | − | 0.966592i | \(-0.582510\pi\) | ||||
−0.256318 | + | 0.966592i | \(0.582510\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 3.73205 | 0.503230 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | − 2.26795i | − 0.300397i | ||||||||
\(58\) | 5.46410i | 0.717472i | ||||||||
\(59\) | − 4.53590i | − 0.590524i | −0.955416 | − | 0.295262i | \(-0.904593\pi\) | ||||
0.955416 | − | 0.295262i | \(-0.0954069\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −7.46410 | −0.955680 | −0.477840 | − | 0.878447i | \(-0.658580\pi\) | ||||
−0.477840 | + | 0.878447i | \(0.658580\pi\) | |||||||
\(62\) | −8.92820 | −1.13388 | ||||||||
\(63\) | 3.00000i | 0.377964i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.73205 | 0.459384 | ||||||||
\(67\) | 5.46410i | 0.667546i | 0.942653 | + | 0.333773i | \(0.108322\pi\) | ||||
−0.942653 | + | 0.333773i | \(0.891678\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 3.00000i | 0.358569i | ||||||||
\(71\) | 0.928203i | 0.110157i | 0.998482 | + | 0.0550787i | \(0.0175410\pi\) | ||||
−0.998482 | + | 0.0550787i | \(0.982459\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | −7.92820 | −0.921635 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | − 2.26795i | − 0.260152i | ||||||||
\(77\) | 11.1962 | 1.27592 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9282 | 1.90457 | 0.952286 | − | 0.305208i | \(-0.0987259\pi\) | ||||
0.952286 | + | 0.305208i | \(0.0987259\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.00000 | 0.441726 | ||||||||
\(83\) | 2.53590i | 0.278351i | 0.990268 | + | 0.139176i | \(0.0444452\pi\) | ||||
−0.990268 | + | 0.139176i | \(0.955555\pi\) | |||||||
\(84\) | 3.00000i | 0.327327i | ||||||||
\(85\) | 4.00000i | 0.433861i | ||||||||
\(86\) | − 6.00000i | − 0.646997i | ||||||||
\(87\) | 5.46410 | 0.585813 | ||||||||
\(88\) | 3.73205 | 0.397838 | ||||||||
\(89\) | − 10.1244i | − 1.07318i | −0.843843 | − | 0.536590i | \(-0.819712\pi\) | ||||
0.843843 | − | 0.536590i | \(-0.180288\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.46410 | 0.361158 | ||||||||
\(93\) | 8.92820i | 0.925812i | ||||||||
\(94\) | 0.464102 | 0.0478684 | ||||||||
\(95\) | −2.26795 | −0.232687 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − 12.3923i | − 1.25825i | −0.777305 | − | 0.629124i | \(-0.783414\pi\) | ||||
0.777305 | − | 0.629124i | \(-0.216586\pi\) | |||||||
\(98\) | 2.00000i | 0.202031i | ||||||||
\(99\) | − 3.73205i | − 0.375085i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.39230 | −0.835066 | −0.417533 | − | 0.908662i | \(-0.637105\pi\) | ||||
−0.417533 | + | 0.908662i | \(0.637105\pi\) | |||||||
\(102\) | 4.00000i | 0.396059i | ||||||||
\(103\) | 19.5885 | 1.93011 | 0.965054 | − | 0.262051i | \(-0.0843989\pi\) | ||||
0.965054 | + | 0.262051i | \(0.0843989\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | 3.73205i | 0.362489i | ||||||||
\(107\) | 0.928203 | 0.0897328 | 0.0448664 | − | 0.998993i | \(-0.485714\pi\) | ||||
0.0448664 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.3923i | 0.995402i | 0.867349 | + | 0.497701i | \(0.165822\pi\) | ||||
−0.867349 | + | 0.497701i | \(0.834178\pi\) | |||||||
\(110\) | − 3.73205i | − 0.355837i | ||||||||
\(111\) | 7.92820i | 0.752512i | ||||||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | −2.26795 | −0.212413 | ||||||||
\(115\) | − 3.46410i | − 0.323029i | ||||||||
\(116\) | 5.46410 | 0.507329 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.53590 | −0.417563 | ||||||||
\(119\) | 12.0000i | 1.10004i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −2.92820 | −0.266200 | ||||||||
\(122\) | 7.46410i | 0.675768i | ||||||||
\(123\) | − 4.00000i | − 0.360668i | ||||||||
\(124\) | 8.92820i | 0.801776i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 3.00000 | 0.267261 | ||||||||
\(127\) | 4.66025 | 0.413531 | 0.206765 | − | 0.978391i | \(-0.433706\pi\) | ||||
0.206765 | + | 0.978391i | \(0.433706\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.3205 | −1.77541 | −0.887706 | − | 0.460412i | \(-0.847702\pi\) | ||||
−0.887706 | + | 0.460412i | \(0.847702\pi\) | |||||||
\(132\) | − 3.73205i | − 0.324833i | ||||||||
\(133\) | −6.80385 | −0.589968 | ||||||||
\(134\) | 5.46410 | 0.472026 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | 4.00000i | 0.342997i | ||||||||
\(137\) | 6.53590i | 0.558399i | 0.960233 | + | 0.279200i | \(0.0900692\pi\) | ||||
−0.960233 | + | 0.279200i | \(0.909931\pi\) | |||||||
\(138\) | − 3.46410i | − 0.294884i | ||||||||
\(139\) | 21.7846 | 1.84775 | 0.923873 | − | 0.382699i | \(-0.125005\pi\) | ||||
0.923873 | + | 0.382699i | \(0.125005\pi\) | |||||||
\(140\) | 3.00000 | 0.253546 | ||||||||
\(141\) | − 0.464102i | − 0.0390844i | ||||||||
\(142\) | 0.928203 | 0.0778931 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 5.46410i | − 0.453769i | ||||||||
\(146\) | 6.92820 | 0.573382 | ||||||||
\(147\) | 2.00000 | 0.164957 | ||||||||
\(148\) | 7.92820i | 0.651694i | ||||||||
\(149\) | − 22.7846i | − 1.86659i | −0.359113 | − | 0.933294i | \(-0.616921\pi\) | ||||
0.359113 | − | 0.933294i | \(-0.383079\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | − 18.7846i | − 1.52867i | −0.644819 | − | 0.764335i | \(-0.723067\pi\) | ||||
0.644819 | − | 0.764335i | \(-0.276933\pi\) | |||||||
\(152\) | −2.26795 | −0.183955 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | − 11.1962i | − 0.902212i | ||||||||
\(155\) | 8.92820 | 0.717131 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8038 | 0.862241 | 0.431120 | − | 0.902294i | \(-0.358118\pi\) | ||||
0.431120 | + | 0.902294i | \(0.358118\pi\) | |||||||
\(158\) | − 16.9282i | − 1.34674i | ||||||||
\(159\) | 3.73205 | 0.295971 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | − 10.3923i | − 0.819028i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 10.9282i | 0.855963i | 0.903788 | + | 0.427981i | \(0.140775\pi\) | ||||
−0.903788 | + | 0.427981i | \(0.859225\pi\) | |||||||
\(164\) | − 4.00000i | − 0.312348i | ||||||||
\(165\) | −3.73205 | −0.290540 | ||||||||
\(166\) | 2.53590 | 0.196824 | ||||||||
\(167\) | − 6.46410i | − 0.500207i | −0.968219 | − | 0.250104i | \(-0.919535\pi\) | ||||
0.968219 | − | 0.250104i | \(-0.0804647\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 2.26795i | 0.173434i | ||||||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | 22.1244 | 1.68208 | 0.841042 | − | 0.540970i | \(-0.181943\pi\) | ||||
0.841042 | + | 0.540970i | \(0.181943\pi\) | |||||||
\(174\) | − 5.46410i | − 0.414232i | ||||||||
\(175\) | − 3.00000i | − 0.226779i | ||||||||
\(176\) | − 3.73205i | − 0.281314i | ||||||||
\(177\) | 4.53590i | 0.340939i | ||||||||
\(178\) | −10.1244 | −0.758853 | ||||||||
\(179\) | 22.9282 | 1.71373 | 0.856867 | − | 0.515537i | \(-0.172408\pi\) | ||||
0.856867 | + | 0.515537i | \(0.172408\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | 3.07180 | 0.228325 | 0.114162 | − | 0.993462i | \(-0.463582\pi\) | ||||
0.114162 | + | 0.993462i | \(0.463582\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.46410 | 0.551762 | ||||||||
\(184\) | − 3.46410i | − 0.255377i | ||||||||
\(185\) | 7.92820 | 0.582893 | ||||||||
\(186\) | 8.92820 | 0.654648 | ||||||||
\(187\) | − 14.9282i | − 1.09166i | ||||||||
\(188\) | − 0.464102i | − 0.0338481i | ||||||||
\(189\) | − 3.00000i | − 0.218218i | ||||||||
\(190\) | 2.26795i | 0.164534i | ||||||||
\(191\) | 17.3205 | 1.25327 | 0.626634 | − | 0.779314i | \(-0.284432\pi\) | ||||
0.626634 | + | 0.779314i | \(0.284432\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 17.8564i | − 1.28533i | −0.766146 | − | 0.642666i | \(-0.777828\pi\) | ||||
0.766146 | − | 0.642666i | \(-0.222172\pi\) | |||||||
\(194\) | −12.3923 | −0.889716 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | − 9.39230i | − 0.669174i | −0.942365 | − | 0.334587i | \(-0.891403\pi\) | ||||
0.942365 | − | 0.334587i | \(-0.108597\pi\) | |||||||
\(198\) | −3.73205 | −0.265225 | ||||||||
\(199\) | −11.0718 | −0.784859 | −0.392429 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392429 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | − 5.46410i | − 0.385408i | ||||||||
\(202\) | 8.39230i | 0.590481i | ||||||||
\(203\) | − 16.3923i | − 1.15051i | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | −4.00000 | −0.279372 | ||||||||
\(206\) | − 19.5885i | − 1.36479i | ||||||||
\(207\) | −3.46410 | −0.240772 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.46410 | 0.585474 | ||||||||
\(210\) | − 3.00000i | − 0.207020i | ||||||||
\(211\) | −21.9282 | −1.50960 | −0.754800 | − | 0.655955i | \(-0.772266\pi\) | ||||
−0.754800 | + | 0.655955i | \(0.772266\pi\) | |||||||
\(212\) | 3.73205 | 0.256318 | ||||||||
\(213\) | − 0.928203i | − 0.0635994i | ||||||||
\(214\) | − 0.928203i | − 0.0634507i | ||||||||
\(215\) | 6.00000i | 0.409197i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 26.7846 | 1.81826 | ||||||||
\(218\) | 10.3923 | 0.703856 | ||||||||
\(219\) | − 6.92820i | − 0.468165i | ||||||||
\(220\) | −3.73205 | −0.251615 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.92820 | 0.532106 | ||||||||
\(223\) | − 8.85641i | − 0.593069i | −0.955022 | − | 0.296534i | \(-0.904169\pi\) | ||||
0.955022 | − | 0.296534i | \(-0.0958309\pi\) | |||||||
\(224\) | 3.00000 | 0.200446 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 12.0000i | 0.798228i | ||||||||
\(227\) | 13.4641i | 0.893644i | 0.894623 | + | 0.446822i | \(0.147444\pi\) | ||||
−0.894623 | + | 0.446822i | \(0.852556\pi\) | |||||||
\(228\) | 2.26795i | 0.150199i | ||||||||
\(229\) | 11.4641i | 0.757569i | 0.925485 | + | 0.378785i | \(0.123658\pi\) | ||||
−0.925485 | + | 0.378785i | \(0.876342\pi\) | |||||||
\(230\) | −3.46410 | −0.228416 | ||||||||
\(231\) | −11.1962 | −0.736653 | ||||||||
\(232\) | − 5.46410i | − 0.358736i | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.464102 | −0.0302747 | ||||||||
\(236\) | 4.53590i | 0.295262i | ||||||||
\(237\) | −16.9282 | −1.09960 | ||||||||
\(238\) | 12.0000 | 0.777844 | ||||||||
\(239\) | 3.46410i | 0.224074i | 0.993704 | + | 0.112037i | \(0.0357375\pi\) | ||||
−0.993704 | + | 0.112037i | \(0.964262\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | − 14.8038i | − 0.953600i | −0.879012 | − | 0.476800i | \(-0.841797\pi\) | ||||
0.879012 | − | 0.476800i | \(-0.158203\pi\) | |||||||
\(242\) | 2.92820i | 0.188232i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.46410 | 0.477840 | ||||||||
\(245\) | − 2.00000i | − 0.127775i | ||||||||
\(246\) | −4.00000 | −0.255031 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.92820 | 0.566941 | ||||||||
\(249\) | − 2.53590i | − 0.160706i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 26.4641 | 1.67040 | 0.835200 | − | 0.549947i | \(-0.185352\pi\) | ||||
0.835200 | + | 0.549947i | \(0.185352\pi\) | |||||||
\(252\) | − 3.00000i | − 0.188982i | ||||||||
\(253\) | 12.9282i | 0.812789i | ||||||||
\(254\) | − 4.66025i | − 0.292410i | ||||||||
\(255\) | − 4.00000i | − 0.250490i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.4641 | 1.33889 | 0.669447 | − | 0.742860i | \(-0.266531\pi\) | ||||
0.669447 | + | 0.742860i | \(0.266531\pi\) | |||||||
\(258\) | 6.00000i | 0.373544i | ||||||||
\(259\) | 23.7846 | 1.47790 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.46410 | −0.338219 | ||||||||
\(262\) | 20.3205i | 1.25541i | ||||||||
\(263\) | 20.5167 | 1.26511 | 0.632556 | − | 0.774515i | \(-0.282006\pi\) | ||||
0.632556 | + | 0.774515i | \(0.282006\pi\) | |||||||
\(264\) | −3.73205 | −0.229692 | ||||||||
\(265\) | − 3.73205i | − 0.229258i | ||||||||
\(266\) | 6.80385i | 0.417171i | ||||||||
\(267\) | 10.1244i | 0.619601i | ||||||||
\(268\) | − 5.46410i | − 0.333773i | ||||||||
\(269\) | −30.9282 | −1.88573 | −0.942863 | − | 0.333181i | \(-0.891878\pi\) | ||||
−0.942863 | + | 0.333181i | \(0.891878\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | − 3.60770i | − 0.219152i | −0.993978 | − | 0.109576i | \(-0.965051\pi\) | ||||
0.993978 | − | 0.109576i | \(-0.0349493\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.53590 | 0.394848 | ||||||||
\(275\) | 3.73205i | 0.225051i | ||||||||
\(276\) | −3.46410 | −0.208514 | ||||||||
\(277\) | −19.5885 | −1.17696 | −0.588478 | − | 0.808513i | \(-0.700273\pi\) | ||||
−0.588478 | + | 0.808513i | \(0.700273\pi\) | |||||||
\(278\) | − 21.7846i | − 1.30655i | ||||||||
\(279\) | − 8.92820i | − 0.534518i | ||||||||
\(280\) | − 3.00000i | − 0.179284i | ||||||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | −0.464102 | −0.0276368 | ||||||||
\(283\) | 14.3923 | 0.855534 | 0.427767 | − | 0.903889i | \(-0.359300\pi\) | ||||
0.427767 | + | 0.903889i | \(0.359300\pi\) | |||||||
\(284\) | − 0.928203i | − 0.0550787i | ||||||||
\(285\) | 2.26795 | 0.134342 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −5.46410 | −0.320863 | ||||||||
\(291\) | 12.3923i | 0.726450i | ||||||||
\(292\) | − 6.92820i | − 0.405442i | ||||||||
\(293\) | − 19.2487i | − 1.12452i | −0.826960 | − | 0.562261i | \(-0.809932\pi\) | ||||
0.826960 | − | 0.562261i | \(-0.190068\pi\) | |||||||
\(294\) | − 2.00000i | − 0.116642i | ||||||||
\(295\) | 4.53590 | 0.264090 | ||||||||
\(296\) | 7.92820 | 0.460817 | ||||||||
\(297\) | 3.73205i | 0.216556i | ||||||||
\(298\) | −22.7846 | −1.31988 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 18.0000i | 1.03750i | ||||||||
\(302\) | −18.7846 | −1.08093 | ||||||||
\(303\) | 8.39230 | 0.482125 | ||||||||
\(304\) | 2.26795i | 0.130076i | ||||||||
\(305\) | − 7.46410i | − 0.427393i | ||||||||
\(306\) | − 4.00000i | − 0.228665i | ||||||||
\(307\) | − 20.2487i | − 1.15565i | −0.816159 | − | 0.577827i | \(-0.803901\pi\) | ||||
0.816159 | − | 0.577827i | \(-0.196099\pi\) | |||||||
\(308\) | −11.1962 | −0.637960 | ||||||||
\(309\) | −19.5885 | −1.11435 | ||||||||
\(310\) | − 8.92820i | − 0.507088i | ||||||||
\(311\) | 5.07180 | 0.287595 | 0.143798 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143798 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.32051 | 0.0746395 | 0.0373198 | − | 0.999303i | \(-0.488118\pi\) | ||||
0.0373198 | + | 0.999303i | \(0.488118\pi\) | |||||||
\(314\) | − 10.8038i | − 0.609696i | ||||||||
\(315\) | −3.00000 | −0.169031 | ||||||||
\(316\) | −16.9282 | −0.952286 | ||||||||
\(317\) | − 23.5359i | − 1.32191i | −0.750427 | − | 0.660954i | \(-0.770152\pi\) | ||||
0.750427 | − | 0.660954i | \(-0.229848\pi\) | |||||||
\(318\) | − 3.73205i | − 0.209283i | ||||||||
\(319\) | 20.3923i | 1.14175i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | −0.928203 | −0.0518073 | ||||||||
\(322\) | −10.3923 | −0.579141 | ||||||||
\(323\) | 9.07180i | 0.504768i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.9282 | 0.605257 | ||||||||
\(327\) | − 10.3923i | − 0.574696i | ||||||||
\(328\) | −4.00000 | −0.220863 | ||||||||
\(329\) | −1.39230 | −0.0767603 | ||||||||
\(330\) | 3.73205i | 0.205443i | ||||||||
\(331\) | − 6.39230i | − 0.351353i | −0.984448 | − | 0.175676i | \(-0.943789\pi\) | ||||
0.984448 | − | 0.175676i | \(-0.0562112\pi\) | |||||||
\(332\) | − 2.53590i | − 0.139176i | ||||||||
\(333\) | − 7.92820i | − 0.434463i | ||||||||
\(334\) | −6.46410 | −0.353700 | ||||||||
\(335\) | −5.46410 | −0.298536 | ||||||||
\(336\) | − 3.00000i | − 0.163663i | ||||||||
\(337\) | −5.60770 | −0.305471 | −0.152735 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152735 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | − 4.00000i | − 0.216930i | ||||||||
\(341\) | −33.3205 | −1.80441 | ||||||||
\(342\) | 2.26795 | 0.122637 | ||||||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | 6.00000i | 0.323498i | ||||||||
\(345\) | 3.46410i | 0.186501i | ||||||||
\(346\) | − 22.1244i | − 1.18941i | ||||||||
\(347\) | −16.3923 | −0.879985 | −0.439993 | − | 0.898001i | \(-0.645019\pi\) | ||||
−0.439993 | + | 0.898001i | \(0.645019\pi\) | |||||||
\(348\) | −5.46410 | −0.292907 | ||||||||
\(349\) | 17.4641i | 0.934832i | 0.884038 | + | 0.467416i | \(0.154815\pi\) | ||||
−0.884038 | + | 0.467416i | \(0.845185\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.73205 | −0.198919 | ||||||||
\(353\) | − 28.3923i | − 1.51117i | −0.655051 | − | 0.755585i | \(-0.727353\pi\) | ||||
0.655051 | − | 0.755585i | \(-0.272647\pi\) | |||||||
\(354\) | 4.53590 | 0.241080 | ||||||||
\(355\) | −0.928203 | −0.0492639 | ||||||||
\(356\) | 10.1244i | 0.536590i | ||||||||
\(357\) | − 12.0000i | − 0.635107i | ||||||||
\(358\) | − 22.9282i | − 1.21179i | ||||||||
\(359\) | 12.9282i | 0.682324i | 0.940004 | + | 0.341162i | \(0.110821\pi\) | ||||
−0.940004 | + | 0.341162i | \(0.889179\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 13.8564 | 0.729285 | ||||||||
\(362\) | − 3.07180i | − 0.161450i | ||||||||
\(363\) | 2.92820 | 0.153691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.92820 | −0.362639 | ||||||||
\(366\) | − 7.46410i | − 0.390155i | ||||||||
\(367\) | −13.3205 | −0.695325 | −0.347662 | − | 0.937620i | \(-0.613024\pi\) | ||||
−0.347662 | + | 0.937620i | \(0.613024\pi\) | |||||||
\(368\) | −3.46410 | −0.180579 | ||||||||
\(369\) | 4.00000i | 0.208232i | ||||||||
\(370\) | − 7.92820i | − 0.412168i | ||||||||
\(371\) | − 11.1962i | − 0.581275i | ||||||||
\(372\) | − 8.92820i | − 0.462906i | ||||||||
\(373\) | 22.9282 | 1.18718 | 0.593589 | − | 0.804769i | \(-0.297711\pi\) | ||||
0.593589 | + | 0.804769i | \(0.297711\pi\) | |||||||
\(374\) | −14.9282 | −0.771919 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −0.464102 | −0.0239342 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.00000 | −0.154303 | ||||||||
\(379\) | 6.26795i | 0.321963i | 0.986957 | + | 0.160981i | \(0.0514659\pi\) | ||||
−0.986957 | + | 0.160981i | \(0.948534\pi\) | |||||||
\(380\) | 2.26795 | 0.116343 | ||||||||
\(381\) | −4.66025 | −0.238752 | ||||||||
\(382\) | − 17.3205i | − 0.886194i | ||||||||
\(383\) | − 36.7846i | − 1.87961i | −0.341717 | − | 0.939803i | \(-0.611008\pi\) | ||||
0.341717 | − | 0.939803i | \(-0.388992\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | 11.1962i | 0.570609i | ||||||||
\(386\) | −17.8564 | −0.908867 | ||||||||
\(387\) | 6.00000 | 0.304997 | ||||||||
\(388\) | 12.3923i | 0.629124i | ||||||||
\(389\) | −9.85641 | −0.499740 | −0.249870 | − | 0.968279i | \(-0.580388\pi\) | ||||
−0.249870 | + | 0.968279i | \(0.580388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.8564 | −0.700749 | ||||||||
\(392\) | − 2.00000i | − 0.101015i | ||||||||
\(393\) | 20.3205 | 1.02503 | ||||||||
\(394\) | −9.39230 | −0.473177 | ||||||||
\(395\) | 16.9282i | 0.851750i | ||||||||
\(396\) | 3.73205i | 0.187543i | ||||||||
\(397\) | 7.92820i | 0.397905i | 0.980009 | + | 0.198953i | \(0.0637540\pi\) | ||||
−0.980009 | + | 0.198953i | \(0.936246\pi\) | |||||||
\(398\) | 11.0718i | 0.554979i | ||||||||
\(399\) | 6.80385 | 0.340618 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 2.12436i | − 0.106085i | −0.998592 | − | 0.0530426i | \(-0.983108\pi\) | ||||
0.998592 | − | 0.0530426i | \(-0.0168919\pi\) | |||||||
\(402\) | −5.46410 | −0.272525 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.39230 | 0.417533 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −16.3923 | −0.813536 | ||||||||
\(407\) | −29.5885 | −1.46665 | ||||||||
\(408\) | − 4.00000i | − 0.198030i | ||||||||
\(409\) | − 0.947441i | − 0.0468479i | −0.999726 | − | 0.0234240i | \(-0.992543\pi\) | ||||
0.999726 | − | 0.0234240i | \(-0.00745676\pi\) | |||||||
\(410\) | 4.00000i | 0.197546i | ||||||||
\(411\) | − 6.53590i | − 0.322392i | ||||||||
\(412\) | −19.5885 | −0.965054 | ||||||||
\(413\) | 13.6077 | 0.669591 | ||||||||
\(414\) | 3.46410i | 0.170251i | ||||||||
\(415\) | −2.53590 | −0.124482 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7846 | −1.06680 | ||||||||
\(418\) | − 8.46410i | − 0.413993i | ||||||||
\(419\) | −17.8564 | −0.872343 | −0.436171 | − | 0.899864i | \(-0.643666\pi\) | ||||
−0.436171 | + | 0.899864i | \(0.643666\pi\) | |||||||
\(420\) | −3.00000 | −0.146385 | ||||||||
\(421\) | 5.85641i | 0.285424i | 0.989764 | + | 0.142712i | \(0.0455822\pi\) | ||||
−0.989764 | + | 0.142712i | \(0.954418\pi\) | |||||||
\(422\) | 21.9282i | 1.06745i | ||||||||
\(423\) | 0.464102i | 0.0225654i | ||||||||
\(424\) | − 3.73205i | − 0.181244i | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | −0.928203 | −0.0449716 | ||||||||
\(427\) | − 22.3923i | − 1.08364i | ||||||||
\(428\) | −0.928203 | −0.0448664 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | 0.289346 | ||||||||
\(431\) | − 13.8564i | − 0.667440i | −0.942672 | − | 0.333720i | \(-0.891696\pi\) | ||||
0.942672 | − | 0.333720i | \(-0.108304\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 32.7846 | 1.57553 | 0.787764 | − | 0.615977i | \(-0.211239\pi\) | ||||
0.787764 | + | 0.615977i | \(0.211239\pi\) | |||||||
\(434\) | − 26.7846i | − 1.28570i | ||||||||
\(435\) | 5.46410i | 0.261984i | ||||||||
\(436\) | − 10.3923i | − 0.497701i | ||||||||
\(437\) | − 7.85641i | − 0.375823i | ||||||||
\(438\) | −6.92820 | −0.331042 | ||||||||
\(439\) | 21.3205 | 1.01757 | 0.508786 | − | 0.860893i | \(-0.330094\pi\) | ||||
0.508786 | + | 0.860893i | \(0.330094\pi\) | |||||||
\(440\) | 3.73205i | 0.177919i | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.85641 | 0.373269 | 0.186635 | − | 0.982429i | \(-0.440242\pi\) | ||||
0.186635 | + | 0.982429i | \(0.440242\pi\) | |||||||
\(444\) | − 7.92820i | − 0.376256i | ||||||||
\(445\) | 10.1244 | 0.479940 | ||||||||
\(446\) | −8.85641 | −0.419363 | ||||||||
\(447\) | 22.7846i | 1.07768i | ||||||||
\(448\) | − 3.00000i | − 0.141737i | ||||||||
\(449\) | 18.1244i | 0.855341i | 0.903935 | + | 0.427671i | \(0.140666\pi\) | ||||
−0.903935 | + | 0.427671i | \(0.859334\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 14.9282 | 0.702942 | ||||||||
\(452\) | 12.0000 | 0.564433 | ||||||||
\(453\) | 18.7846i | 0.882578i | ||||||||
\(454\) | 13.4641 | 0.631902 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.26795 | 0.106206 | ||||||||
\(457\) | 0.535898i | 0.0250683i | 0.999921 | + | 0.0125341i | \(0.00398984\pi\) | ||||
−0.999921 | + | 0.0125341i | \(0.996010\pi\) | |||||||
\(458\) | 11.4641 | 0.535682 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 3.46410i | 0.161515i | ||||||||
\(461\) | − 32.3923i | − 1.50866i | −0.656495 | − | 0.754330i | \(-0.727962\pi\) | ||||
0.656495 | − | 0.754330i | \(-0.272038\pi\) | |||||||
\(462\) | 11.1962i | 0.520892i | ||||||||
\(463\) | − 0.784610i | − 0.0364639i | −0.999834 | − | 0.0182320i | \(-0.994196\pi\) | ||||
0.999834 | − | 0.0182320i | \(-0.00580373\pi\) | |||||||
\(464\) | −5.46410 | −0.253665 | ||||||||
\(465\) | −8.92820 | −0.414036 | ||||||||
\(466\) | − 18.0000i | − 0.833834i | ||||||||
\(467\) | 3.60770 | 0.166944 | 0.0834721 | − | 0.996510i | \(-0.473399\pi\) | ||||
0.0834721 | + | 0.996510i | \(0.473399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3923 | −0.756926 | ||||||||
\(470\) | 0.464102i | 0.0214074i | ||||||||
\(471\) | −10.8038 | −0.497815 | ||||||||
\(472\) | 4.53590 | 0.208782 | ||||||||
\(473\) | − 22.3923i | − 1.02960i | ||||||||
\(474\) | 16.9282i | 0.777538i | ||||||||
\(475\) | − 2.26795i | − 0.104061i | ||||||||
\(476\) | − 12.0000i | − 0.550019i | ||||||||
\(477\) | −3.73205 | −0.170879 | ||||||||
\(478\) | 3.46410 | 0.158444 | ||||||||
\(479\) | − 26.2487i | − 1.19933i | −0.800250 | − | 0.599667i | \(-0.795300\pi\) | ||||
0.800250 | − | 0.599667i | \(-0.204700\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14.8038 | −0.674297 | ||||||||
\(483\) | 10.3923i | 0.472866i | ||||||||
\(484\) | 2.92820 | 0.133100 | ||||||||
\(485\) | 12.3923 | 0.562706 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 21.0000i | 0.951601i | 0.879553 | + | 0.475800i | \(0.157842\pi\) | ||||
−0.879553 | + | 0.475800i | \(0.842158\pi\) | |||||||
\(488\) | − 7.46410i | − 0.337884i | ||||||||
\(489\) | − 10.9282i | − 0.494190i | ||||||||
\(490\) | −2.00000 | −0.0903508 | ||||||||
\(491\) | −15.3923 | −0.694645 | −0.347322 | − | 0.937746i | \(-0.612909\pi\) | ||||
−0.347322 | + | 0.937746i | \(0.612909\pi\) | |||||||
\(492\) | 4.00000i | 0.180334i | ||||||||
\(493\) | −21.8564 | −0.984363 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.73205 | 0.167743 | ||||||||
\(496\) | − 8.92820i | − 0.400888i | ||||||||
\(497\) | −2.78461 | −0.124907 | ||||||||
\(498\) | −2.53590 | −0.113636 | ||||||||
\(499\) | 1.32051i | 0.0591141i | 0.999563 | + | 0.0295570i | \(0.00940967\pi\) | ||||
−0.999563 | + | 0.0295570i | \(0.990590\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 6.46410i | 0.288795i | ||||||||
\(502\) | − 26.4641i | − 1.18115i | ||||||||
\(503\) | 0.267949 | 0.0119473 | 0.00597363 | − | 0.999982i | \(-0.498099\pi\) | ||||
0.00597363 | + | 0.999982i | \(0.498099\pi\) | |||||||
\(504\) | −3.00000 | −0.133631 | ||||||||
\(505\) | − 8.39230i | − 0.373453i | ||||||||
\(506\) | 12.9282 | 0.574729 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.66025 | −0.206765 | ||||||||
\(509\) | 5.32051i | 0.235827i | 0.993024 | + | 0.117914i | \(0.0376206\pi\) | ||||
−0.993024 | + | 0.117914i | \(0.962379\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | −20.7846 | −0.919457 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 2.26795i | − 0.100132i | ||||||||
\(514\) | − 21.4641i | − 0.946741i | ||||||||
\(515\) | 19.5885i | 0.863171i | ||||||||
\(516\) | 6.00000 | 0.264135 | ||||||||
\(517\) | 1.73205 | 0.0761755 | ||||||||
\(518\) | − 23.7846i | − 1.04504i | ||||||||
\(519\) | −22.1244 | −0.971151 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.3923 | −1.20008 | −0.600039 | − | 0.799970i | \(-0.704848\pi\) | ||||
−0.600039 | + | 0.799970i | \(0.704848\pi\) | |||||||
\(522\) | 5.46410i | 0.239157i | ||||||||
\(523\) | 13.7128 | 0.599619 | 0.299810 | − | 0.953999i | \(-0.403077\pi\) | ||||
0.299810 | + | 0.953999i | \(0.403077\pi\) | |||||||
\(524\) | 20.3205 | 0.887706 | ||||||||
\(525\) | 3.00000i | 0.130931i | ||||||||
\(526\) | − 20.5167i | − 0.894569i | ||||||||
\(527\) | − 35.7128i | − 1.55567i | ||||||||
\(528\) | 3.73205i | 0.162417i | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | −3.73205 | −0.162110 | ||||||||
\(531\) | − 4.53590i | − 0.196841i | ||||||||
\(532\) | 6.80385 | 0.294984 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10.1244 | 0.438124 | ||||||||
\(535\) | 0.928203i | 0.0401297i | ||||||||
\(536\) | −5.46410 | −0.236013 | ||||||||
\(537\) | −22.9282 | −0.989425 | ||||||||
\(538\) | 30.9282i | 1.33341i | ||||||||
\(539\) | 7.46410i | 0.321502i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 26.7846i | 1.15156i | 0.817605 | + | 0.575780i | \(0.195302\pi\) | ||||
−0.817605 | + | 0.575780i | \(0.804698\pi\) | |||||||
\(542\) | −3.60770 | −0.154964 | ||||||||
\(543\) | −3.07180 | −0.131823 | ||||||||
\(544\) | − 4.00000i | − 0.171499i | ||||||||
\(545\) | −10.3923 | −0.445157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3205 | 1.25365 | 0.626827 | − | 0.779158i | \(-0.284353\pi\) | ||||
0.626827 | + | 0.779158i | \(0.284353\pi\) | |||||||
\(548\) | − 6.53590i | − 0.279200i | ||||||||
\(549\) | −7.46410 | −0.318560 | ||||||||
\(550\) | 3.73205 | 0.159135 | ||||||||
\(551\) | − 12.3923i | − 0.527930i | ||||||||
\(552\) | 3.46410i | 0.147442i | ||||||||
\(553\) | 50.7846i | 2.15958i | ||||||||
\(554\) | 19.5885i | 0.832234i | ||||||||
\(555\) | −7.92820 | −0.336533 | ||||||||
\(556\) | −21.7846 | −0.923873 | ||||||||
\(557\) | 43.3923i | 1.83859i | 0.393568 | + | 0.919295i | \(0.371241\pi\) | ||||
−0.393568 | + | 0.919295i | \(0.628759\pi\) | |||||||
\(558\) | −8.92820 | −0.377961 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | 14.9282i | 0.630269i | ||||||||
\(562\) | 6.92820 | 0.292249 | ||||||||
\(563\) | 19.3205 | 0.814262 | 0.407131 | − | 0.913370i | \(-0.366529\pi\) | ||||
0.407131 | + | 0.913370i | \(0.366529\pi\) | |||||||
\(564\) | 0.464102i | 0.0195422i | ||||||||
\(565\) | − 12.0000i | − 0.504844i | ||||||||
\(566\) | − 14.3923i | − 0.604954i | ||||||||
\(567\) | 3.00000i | 0.125988i | ||||||||
\(568\) | −0.928203 | −0.0389465 | ||||||||
\(569\) | 18.3205 | 0.768036 | 0.384018 | − | 0.923326i | \(-0.374540\pi\) | ||||
0.384018 | + | 0.923326i | \(0.374540\pi\) | |||||||
\(570\) | − 2.26795i | − 0.0949939i | ||||||||
\(571\) | −16.8564 | −0.705419 | −0.352709 | − | 0.935733i | \(-0.614740\pi\) | ||||
−0.352709 | + | 0.935733i | \(0.614740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.3205 | −0.723575 | ||||||||
\(574\) | 12.0000i | 0.500870i | ||||||||
\(575\) | 3.46410 | 0.144463 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 25.3205i | − 1.05411i | −0.849832 | − | 0.527053i | \(-0.823297\pi\) | ||||
0.849832 | − | 0.527053i | \(-0.176703\pi\) | |||||||
\(578\) | 1.00000i | 0.0415945i | ||||||||
\(579\) | 17.8564i | 0.742087i | ||||||||
\(580\) | 5.46410i | 0.226884i | ||||||||
\(581\) | −7.60770 | −0.315620 | ||||||||
\(582\) | 12.3923 | 0.513678 | ||||||||
\(583\) | 13.9282i | 0.576847i | ||||||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.2487 | −0.795157 | ||||||||
\(587\) | − 4.92820i | − 0.203409i | −0.994815 | − | 0.101704i | \(-0.967570\pi\) | ||||
0.994815 | − | 0.101704i | \(-0.0324296\pi\) | |||||||
\(588\) | −2.00000 | −0.0824786 | ||||||||
\(589\) | 20.2487 | 0.834334 | ||||||||
\(590\) | − 4.53590i | − 0.186740i | ||||||||
\(591\) | 9.39230i | 0.386348i | ||||||||
\(592\) | − 7.92820i | − 0.325847i | ||||||||
\(593\) | 3.21539i | 0.132040i | 0.997818 | + | 0.0660201i | \(0.0210302\pi\) | ||||
−0.997818 | + | 0.0660201i | \(0.978970\pi\) | |||||||
\(594\) | 3.73205 | 0.153128 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 22.7846i | 0.933294i | ||||||||
\(597\) | 11.0718 | 0.453138 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0718 | 0.615817 | 0.307908 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307908 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −24.7128 | −1.00806 | −0.504028 | − | 0.863687i | \(-0.668149\pi\) | ||||
−0.504028 | + | 0.863687i | \(0.668149\pi\) | |||||||
\(602\) | 18.0000 | 0.733625 | ||||||||
\(603\) | 5.46410i | 0.222515i | ||||||||
\(604\) | 18.7846i | 0.764335i | ||||||||
\(605\) | − 2.92820i | − 0.119048i | ||||||||
\(606\) | − 8.39230i | − 0.340914i | ||||||||
\(607\) | 37.4449 | 1.51984 | 0.759920 | − | 0.650017i | \(-0.225238\pi\) | ||||
0.759920 | + | 0.650017i | \(0.225238\pi\) | |||||||
\(608\) | 2.26795 | 0.0919775 | ||||||||
\(609\) | 16.3923i | 0.664250i | ||||||||
\(610\) | −7.46410 | −0.302213 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | − 45.0000i | − 1.81753i | −0.417305 | − | 0.908766i | \(-0.637025\pi\) | ||||
0.417305 | − | 0.908766i | \(-0.362975\pi\) | |||||||
\(614\) | −20.2487 | −0.817171 | ||||||||
\(615\) | 4.00000 | 0.161296 | ||||||||
\(616\) | 11.1962i | 0.451106i | ||||||||
\(617\) | − 28.5359i | − 1.14881i | −0.818571 | − | 0.574406i | \(-0.805233\pi\) | ||||
0.818571 | − | 0.574406i | \(-0.194767\pi\) | |||||||
\(618\) | 19.5885i | 0.787963i | ||||||||
\(619\) | 42.5167i | 1.70889i | 0.519543 | + | 0.854444i | \(0.326102\pi\) | ||||
−0.519543 | + | 0.854444i | \(0.673898\pi\) | |||||||
\(620\) | −8.92820 | −0.358565 | ||||||||
\(621\) | 3.46410 | 0.139010 | ||||||||
\(622\) | − 5.07180i | − 0.203361i | ||||||||
\(623\) | 30.3731 | 1.21687 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 1.32051i | − 0.0527781i | ||||||||
\(627\) | −8.46410 | −0.338024 | ||||||||
\(628\) | −10.8038 | −0.431120 | ||||||||
\(629\) | − 31.7128i | − 1.26447i | ||||||||
\(630\) | 3.00000i | 0.119523i | ||||||||
\(631\) | − 8.00000i | − 0.318475i | −0.987240 | − | 0.159237i | \(-0.949096\pi\) | ||||
0.987240 | − | 0.159237i | \(-0.0509036\pi\) | |||||||
\(632\) | 16.9282i | 0.673368i | ||||||||
\(633\) | 21.9282 | 0.871568 | ||||||||
\(634\) | −23.5359 | −0.934730 | ||||||||
\(635\) | 4.66025i | 0.184937i | ||||||||
\(636\) | −3.73205 | −0.147985 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.3923 | 0.807339 | ||||||||
\(639\) | 0.928203i | 0.0367192i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 7.53590 | 0.297650 | 0.148825 | − | 0.988864i | \(-0.452451\pi\) | ||||
0.148825 | + | 0.988864i | \(0.452451\pi\) | |||||||
\(642\) | 0.928203i | 0.0366333i | ||||||||
\(643\) | − 28.7846i | − 1.13515i | −0.823320 | − | 0.567577i | \(-0.807881\pi\) | ||||
0.823320 | − | 0.567577i | \(-0.192119\pi\) | |||||||
\(644\) | 10.3923i | 0.409514i | ||||||||
\(645\) | − 6.00000i | − 0.236250i | ||||||||
\(646\) | 9.07180 | 0.356925 | ||||||||
\(647\) | −32.2679 | −1.26858 | −0.634292 | − | 0.773094i | \(-0.718708\pi\) | ||||
−0.634292 | + | 0.773094i | \(0.718708\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −16.9282 | −0.664490 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.7846 | −1.04977 | ||||||||
\(652\) | − 10.9282i | − 0.427981i | ||||||||
\(653\) | 29.5885 | 1.15789 | 0.578943 | − | 0.815368i | \(-0.303465\pi\) | ||||
0.578943 | + | 0.815368i | \(0.303465\pi\) | |||||||
\(654\) | −10.3923 | −0.406371 | ||||||||
\(655\) | − 20.3205i | − 0.793988i | ||||||||
\(656\) | 4.00000i | 0.156174i | ||||||||
\(657\) | 6.92820i | 0.270295i | ||||||||
\(658\) | 1.39230i | 0.0542777i | ||||||||
\(659\) | 15.7128 | 0.612084 | 0.306042 | − | 0.952018i | \(-0.400995\pi\) | ||||
0.306042 | + | 0.952018i | \(0.400995\pi\) | |||||||
\(660\) | 3.73205 | 0.145270 | ||||||||
\(661\) | 42.3923i | 1.64887i | 0.565957 | + | 0.824435i | \(0.308507\pi\) | ||||
−0.565957 | + | 0.824435i | \(0.691493\pi\) | |||||||
\(662\) | −6.39230 | −0.248444 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.53590 | −0.0984119 | ||||||||
\(665\) | − 6.80385i | − 0.263842i | ||||||||
\(666\) | −7.92820 | −0.307212 | ||||||||
\(667\) | 18.9282 | 0.732903 | ||||||||
\(668\) | 6.46410i | 0.250104i | ||||||||
\(669\) | 8.85641i | 0.342408i | ||||||||
\(670\) | 5.46410i | 0.211097i | ||||||||
\(671\) | 27.8564i | 1.07538i | ||||||||
\(672\) | −3.00000 | −0.115728 | ||||||||
\(673\) | 24.7846 | 0.955376 | 0.477688 | − | 0.878529i | \(-0.341475\pi\) | ||||
0.477688 | + | 0.878529i | \(0.341475\pi\) | |||||||
\(674\) | 5.60770i | 0.216000i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.92820 | −0.112540 | −0.0562700 | − | 0.998416i | \(-0.517921\pi\) | ||||
−0.0562700 | + | 0.998416i | \(0.517921\pi\) | |||||||
\(678\) | − 12.0000i | − 0.460857i | ||||||||
\(679\) | 37.1769 | 1.42672 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | − 13.4641i | − 0.515945i | ||||||||
\(682\) | 33.3205i | 1.27591i | ||||||||
\(683\) | 6.67949i | 0.255584i | 0.991801 | + | 0.127792i | \(0.0407889\pi\) | ||||
−0.991801 | + | 0.127792i | \(0.959211\pi\) | |||||||
\(684\) | − 2.26795i | − 0.0867172i | ||||||||
\(685\) | −6.53590 | −0.249724 | ||||||||
\(686\) | 15.0000 | 0.572703 | ||||||||
\(687\) | − 11.4641i | − 0.437383i | ||||||||
\(688\) | 6.00000 | 0.228748 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.46410 | 0.131876 | ||||||||
\(691\) | 23.0526i | 0.876961i | 0.898741 | + | 0.438480i | \(0.144483\pi\) | ||||
−0.898741 | + | 0.438480i | \(0.855517\pi\) | |||||||
\(692\) | −22.1244 | −0.841042 | ||||||||
\(693\) | 11.1962 | 0.425307 | ||||||||
\(694\) | 16.3923i | 0.622243i | ||||||||
\(695\) | 21.7846i | 0.826337i | ||||||||
\(696\) | 5.46410i | 0.207116i | ||||||||
\(697\) | 16.0000i | 0.606043i | ||||||||
\(698\) | 17.4641 | 0.661026 | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 3.00000i | 0.113389i | ||||||||
\(701\) | 16.3923 | 0.619129 | 0.309564 | − | 0.950878i | \(-0.399817\pi\) | ||||
0.309564 | + | 0.950878i | \(0.399817\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.9808 | 0.678157 | ||||||||
\(704\) | 3.73205i | 0.140657i | ||||||||
\(705\) | 0.464102 | 0.0174791 | ||||||||
\(706\) | −28.3923 | −1.06856 | ||||||||
\(707\) | − 25.1769i | − 0.946875i | ||||||||
\(708\) | − 4.53590i | − 0.170470i | ||||||||
\(709\) | 7.32051i | 0.274927i | 0.990507 | + | 0.137464i | \(0.0438951\pi\) | ||||
−0.990507 | + | 0.137464i | \(0.956105\pi\) | |||||||
\(710\) | 0.928203i | 0.0348348i | ||||||||
\(711\) | 16.9282 | 0.634857 | ||||||||
\(712\) | 10.1244 | 0.379426 | ||||||||
\(713\) | 30.9282i | 1.15827i | ||||||||
\(714\) | −12.0000 | −0.449089 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.9282 | −0.856867 | ||||||||
\(717\) | − 3.46410i | − 0.129369i | ||||||||
\(718\) | 12.9282 | 0.482476 | ||||||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 58.7654i | 2.18854i | ||||||||
\(722\) | − 13.8564i | − 0.515682i | ||||||||
\(723\) | 14.8038i | 0.550561i | ||||||||
\(724\) | −3.07180 | −0.114162 | ||||||||
\(725\) | 5.46410 | 0.202932 | ||||||||
\(726\) | − 2.92820i | − 0.108676i | ||||||||
\(727\) | 12.6603 | 0.469543 | 0.234771 | − | 0.972051i | \(-0.424566\pi\) | ||||
0.234771 | + | 0.972051i | \(0.424566\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.92820i | 0.256424i | ||||||||
\(731\) | 24.0000 | 0.887672 | ||||||||
\(732\) | −7.46410 | −0.275881 | ||||||||
\(733\) | 6.85641i | 0.253247i | 0.991951 | + | 0.126624i | \(0.0404140\pi\) | ||||
−0.991951 | + | 0.126624i | \(0.959586\pi\) | |||||||
\(734\) | 13.3205i | 0.491669i | ||||||||
\(735\) | 2.00000i | 0.0737711i | ||||||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | 20.3923 | 0.751160 | ||||||||
\(738\) | 4.00000 | 0.147242 | ||||||||
\(739\) | 43.8372i | 1.61258i | 0.591523 | + | 0.806288i | \(0.298527\pi\) | ||||
−0.591523 | + | 0.806288i | \(0.701473\pi\) | |||||||
\(740\) | −7.92820 | −0.291447 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.1962 | −0.411024 | ||||||||
\(743\) | − 2.92820i | − 0.107425i | −0.998556 | − | 0.0537127i | \(-0.982894\pi\) | ||||
0.998556 | − | 0.0537127i | \(-0.0171055\pi\) | |||||||
\(744\) | −8.92820 | −0.327324 | ||||||||
\(745\) | 22.7846 | 0.834764 | ||||||||
\(746\) | − 22.9282i | − 0.839461i | ||||||||
\(747\) | 2.53590i | 0.0927837i | ||||||||
\(748\) | 14.9282i | 0.545829i | ||||||||
\(749\) | 2.78461i | 0.101747i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 41.1769 | 1.50257 | 0.751283 | − | 0.659980i | \(-0.229435\pi\) | ||||
0.751283 | + | 0.659980i | \(0.229435\pi\) | |||||||
\(752\) | 0.464102i | 0.0169240i | ||||||||
\(753\) | −26.4641 | −0.964405 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.7846 | 0.683642 | ||||||||
\(756\) | 3.00000i | 0.109109i | ||||||||
\(757\) | 18.2679 | 0.663960 | 0.331980 | − | 0.943286i | \(-0.392283\pi\) | ||||
0.331980 | + | 0.943286i | \(0.392283\pi\) | |||||||
\(758\) | 6.26795 | 0.227662 | ||||||||
\(759\) | − 12.9282i | − 0.469264i | ||||||||
\(760\) | − 2.26795i | − 0.0822672i | ||||||||
\(761\) | − 43.9808i | − 1.59430i | −0.603780 | − | 0.797151i | \(-0.706340\pi\) | ||||
0.603780 | − | 0.797151i | \(-0.293660\pi\) | |||||||
\(762\) | 4.66025i | 0.168823i | ||||||||
\(763\) | −31.1769 | −1.12868 | ||||||||
\(764\) | −17.3205 | −0.626634 | ||||||||
\(765\) | 4.00000i | 0.144620i | ||||||||
\(766\) | −36.7846 | −1.32908 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 39.7128i | 1.43208i | 0.698059 | + | 0.716040i | \(0.254047\pi\) | ||||
−0.698059 | + | 0.716040i | \(0.745953\pi\) | |||||||
\(770\) | 11.1962 | 0.403481 | ||||||||
\(771\) | −21.4641 | −0.773011 | ||||||||
\(772\) | 17.8564i | 0.642666i | ||||||||
\(773\) | − 53.3923i | − 1.92039i | −0.279334 | − | 0.960194i | \(-0.590114\pi\) | ||||
0.279334 | − | 0.960194i | \(-0.409886\pi\) | |||||||
\(774\) | − 6.00000i | − 0.215666i | ||||||||
\(775\) | 8.92820i | 0.320711i | ||||||||
\(776\) | 12.3923 | 0.444858 | ||||||||
\(777\) | −23.7846 | −0.853268 | ||||||||
\(778\) | 9.85641i | 0.353369i | ||||||||
\(779\) | −9.07180 | −0.325031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.46410 | 0.123955 | ||||||||
\(782\) | 13.8564i | 0.495504i | ||||||||
\(783\) | 5.46410 | 0.195271 | ||||||||
\(784\) | −2.00000 | −0.0714286 | ||||||||
\(785\) | 10.8038i | 0.385606i | ||||||||
\(786\) | − 20.3205i | − 0.724809i | ||||||||
\(787\) | − 5.46410i | − 0.194774i | −0.995247 | − | 0.0973871i | \(-0.968952\pi\) | ||||
0.995247 | − | 0.0973871i | \(-0.0310485\pi\) | |||||||
\(788\) | 9.39230i | 0.334587i | ||||||||
\(789\) | −20.5167 | −0.730412 | ||||||||
\(790\) | 16.9282 | 0.602278 | ||||||||
\(791\) | − 36.0000i | − 1.28001i | ||||||||
\(792\) | 3.73205 | 0.132613 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.92820 | 0.281361 | ||||||||
\(795\) | 3.73205i | 0.132362i | ||||||||
\(796\) | 11.0718 | 0.392429 | ||||||||
\(797\) | −37.8564 | −1.34094 | −0.670471 | − | 0.741935i | \(-0.733908\pi\) | ||||
−0.670471 | + | 0.741935i | \(0.733908\pi\) | |||||||
\(798\) | − 6.80385i | − 0.240854i | ||||||||
\(799\) | 1.85641i | 0.0656749i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 10.1244i | − 0.357727i | ||||||||
\(802\) | −2.12436 | −0.0750136 | ||||||||
\(803\) | 25.8564 | 0.912453 | ||||||||
\(804\) | 5.46410i | 0.192704i | ||||||||
\(805\) | 10.3923 | 0.366281 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.9282 | 1.08872 | ||||||||
\(808\) | − 8.39230i | − 0.295240i | ||||||||
\(809\) | 34.7846 | 1.22296 | 0.611481 | − | 0.791259i | \(-0.290574\pi\) | ||||
0.611481 | + | 0.791259i | \(0.290574\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 7.58846i | 0.266467i | 0.991085 | + | 0.133233i | \(0.0425360\pi\) | ||||
−0.991085 | + | 0.133233i | \(0.957464\pi\) | |||||||
\(812\) | 16.3923i | 0.575257i | ||||||||
\(813\) | 3.60770i | 0.126527i | ||||||||
\(814\) | 29.5885i | 1.03707i | ||||||||
\(815\) | −10.9282 | −0.382798 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 13.6077i | 0.476073i | ||||||||
\(818\) | −0.947441 | −0.0331265 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | 49.3205i | 1.72130i | 0.509199 | + | 0.860649i | \(0.329942\pi\) | ||||
−0.509199 | + | 0.860649i | \(0.670058\pi\) | |||||||
\(822\) | −6.53590 | −0.227966 | ||||||||
\(823\) | −39.5885 | −1.37997 | −0.689983 | − | 0.723825i | \(-0.742382\pi\) | ||||
−0.689983 | + | 0.723825i | \(0.742382\pi\) | |||||||
\(824\) | 19.5885i | 0.682396i | ||||||||
\(825\) | − 3.73205i | − 0.129933i | ||||||||
\(826\) | − 13.6077i | − 0.473472i | ||||||||
\(827\) | 50.4974i | 1.75597i | 0.478690 | + | 0.877984i | \(0.341112\pi\) | ||||
−0.478690 | + | 0.877984i | \(0.658888\pi\) | |||||||
\(828\) | 3.46410 | 0.120386 | ||||||||
\(829\) | −39.3205 | −1.36566 | −0.682829 | − | 0.730578i | \(-0.739251\pi\) | ||||
−0.682829 | + | 0.730578i | \(0.739251\pi\) | |||||||
\(830\) | 2.53590i | 0.0880223i | ||||||||
\(831\) | 19.5885 | 0.679516 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.00000 | −0.277184 | ||||||||
\(834\) | 21.7846i | 0.754339i | ||||||||
\(835\) | 6.46410 | 0.223699 | ||||||||
\(836\) | −8.46410 | −0.292737 | ||||||||
\(837\) | 8.92820i | 0.308604i | ||||||||
\(838\) | 17.8564i | 0.616839i | ||||||||
\(839\) | − 43.1769i | − 1.49063i | −0.666711 | − | 0.745316i | \(-0.732298\pi\) | ||||
0.666711 | − | 0.745316i | \(-0.267702\pi\) | |||||||
\(840\) | 3.00000i | 0.103510i | ||||||||
\(841\) | 0.856406 | 0.0295313 | ||||||||
\(842\) | 5.85641 | 0.201825 | ||||||||
\(843\) | − 6.92820i | − 0.238620i | ||||||||
\(844\) | 21.9282 | 0.754800 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.464102 | 0.0159561 | ||||||||
\(847\) | − 8.78461i | − 0.301843i | ||||||||
\(848\) | −3.73205 | −0.128159 | ||||||||
\(849\) | −14.3923 | −0.493943 | ||||||||
\(850\) | 4.00000i | 0.137199i | ||||||||
\(851\) | 27.4641i | 0.941457i | ||||||||
\(852\) | 0.928203i | 0.0317997i | ||||||||
\(853\) | − 44.6410i | − 1.52848i | −0.644932 | − | 0.764240i | \(-0.723114\pi\) | ||||
0.644932 | − | 0.764240i | \(-0.276886\pi\) | |||||||
\(854\) | −22.3923 | −0.766249 | ||||||||
\(855\) | −2.26795 | −0.0775622 | ||||||||
\(856\) | 0.928203i | 0.0317253i | ||||||||
\(857\) | −15.0718 | −0.514843 | −0.257421 | − | 0.966299i | \(-0.582873\pi\) | ||||
−0.257421 | + | 0.966299i | \(0.582873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.9282 | −0.679942 | −0.339971 | − | 0.940436i | \(-0.610417\pi\) | ||||
−0.339971 | + | 0.940436i | \(0.610417\pi\) | |||||||
\(860\) | − 6.00000i | − 0.204598i | ||||||||
\(861\) | 12.0000 | 0.408959 | ||||||||
\(862\) | −13.8564 | −0.471951 | ||||||||
\(863\) | 10.9282i | 0.372000i | 0.982550 | + | 0.186000i | \(0.0595525\pi\) | ||||
−0.982550 | + | 0.186000i | \(0.940447\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 22.1244i | 0.752251i | ||||||||
\(866\) | − 32.7846i | − 1.11407i | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −26.7846 | −0.909129 | ||||||||
\(869\) | − 63.1769i | − 2.14313i | ||||||||
\(870\) | 5.46410 | 0.185250 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −10.3923 | −0.351928 | ||||||||
\(873\) | − 12.3923i | − 0.419416i | ||||||||
\(874\) | −7.85641 | −0.265747 | ||||||||
\(875\) | 3.00000 | 0.101419 | ||||||||
\(876\) | 6.92820i | 0.234082i | ||||||||
\(877\) | − 33.7128i | − 1.13840i | −0.822199 | − | 0.569200i | \(-0.807253\pi\) | ||||
0.822199 | − | 0.569200i | \(-0.192747\pi\) | |||||||
\(878\) | − 21.3205i | − 0.719532i | ||||||||
\(879\) | 19.2487i | 0.649243i | ||||||||
\(880\) | 3.73205 | 0.125807 | ||||||||
\(881\) | −37.1051 | −1.25010 | −0.625052 | − | 0.780583i | \(-0.714922\pi\) | ||||
−0.625052 | + | 0.780583i | \(0.714922\pi\) | |||||||
\(882\) | 2.00000i | 0.0673435i | ||||||||
\(883\) | 21.3205 | 0.717492 | 0.358746 | − | 0.933435i | \(-0.383204\pi\) | ||||
0.358746 | + | 0.933435i | \(0.383204\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.53590 | −0.152473 | ||||||||
\(886\) | − 7.85641i | − 0.263941i | ||||||||
\(887\) | 52.2679 | 1.75499 | 0.877493 | − | 0.479589i | \(-0.159214\pi\) | ||||
0.877493 | + | 0.479589i | \(0.159214\pi\) | |||||||
\(888\) | −7.92820 | −0.266053 | ||||||||
\(889\) | 13.9808i | 0.468900i | ||||||||
\(890\) | − 10.1244i | − 0.339369i | ||||||||
\(891\) | − 3.73205i | − 0.125028i | ||||||||
\(892\) | 8.85641i | 0.296534i | ||||||||
\(893\) | −1.05256 | −0.0352225 | ||||||||
\(894\) | 22.7846 | 0.762031 | ||||||||
\(895\) | 22.9282i | 0.766405i | ||||||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.1244 | 0.604818 | ||||||||
\(899\) | 48.7846i | 1.62706i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −14.9282 | −0.497331 | ||||||||
\(902\) | − 14.9282i | − 0.497055i | ||||||||
\(903\) | − 18.0000i | − 0.599002i | ||||||||
\(904\) | − 12.0000i | − 0.399114i | ||||||||
\(905\) | 3.07180i | 0.102110i | ||||||||
\(906\) | 18.7846 | 0.624077 | ||||||||
\(907\) | 7.07180 | 0.234815 | 0.117408 | − | 0.993084i | \(-0.462542\pi\) | ||||
0.117408 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(908\) | − 13.4641i | − 0.446822i | ||||||||
\(909\) | −8.39230 | −0.278355 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.7846 | −0.953677 | −0.476838 | − | 0.878991i | \(-0.658217\pi\) | ||||
−0.476838 | + | 0.878991i | \(0.658217\pi\) | |||||||
\(912\) | − 2.26795i | − 0.0750993i | ||||||||
\(913\) | 9.46410 | 0.313216 | ||||||||
\(914\) | 0.535898 | 0.0177259 | ||||||||
\(915\) | 7.46410i | 0.246756i | ||||||||
\(916\) | − 11.4641i | − 0.378785i | ||||||||
\(917\) | − 60.9615i | − 2.01313i | ||||||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | 55.9615 | 1.84600 | 0.923000 | − | 0.384800i | \(-0.125729\pi\) | ||||
0.923000 | + | 0.384800i | \(0.125729\pi\) | |||||||
\(920\) | 3.46410 | 0.114208 | ||||||||
\(921\) | 20.2487i | 0.667218i | ||||||||
\(922\) | −32.3923 | −1.06678 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 11.1962 | 0.368326 | ||||||||
\(925\) | 7.92820i | 0.260678i | ||||||||
\(926\) | −0.784610 | −0.0257839 | ||||||||
\(927\) | 19.5885 | 0.643369 | ||||||||
\(928\) | 5.46410i | 0.179368i | ||||||||
\(929\) | 30.1436i | 0.988979i | 0.869184 | + | 0.494490i | \(0.164645\pi\) | ||||
−0.869184 | + | 0.494490i | \(0.835355\pi\) | |||||||
\(930\) | 8.92820i | 0.292767i | ||||||||
\(931\) | − 4.53590i | − 0.148658i | ||||||||
\(932\) | −18.0000 | −0.589610 | ||||||||
\(933\) | −5.07180 | −0.166043 | ||||||||
\(934\) | − 3.60770i | − 0.118047i | ||||||||
\(935\) | 14.9282 | 0.488204 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.7128 | 1.10135 | 0.550675 | − | 0.834720i | \(-0.314370\pi\) | ||||
0.550675 | + | 0.834720i | \(0.314370\pi\) | |||||||
\(938\) | 16.3923i | 0.535228i | ||||||||
\(939\) | −1.32051 | −0.0430932 | ||||||||
\(940\) | 0.464102 | 0.0151373 | ||||||||
\(941\) | − 36.4974i | − 1.18978i | −0.803806 | − | 0.594891i | \(-0.797195\pi\) | ||||
0.803806 | − | 0.594891i | \(-0.202805\pi\) | |||||||
\(942\) | 10.8038i | 0.352008i | ||||||||
\(943\) | − 13.8564i | − 0.451227i | ||||||||
\(944\) | − 4.53590i | − 0.147631i | ||||||||
\(945\) | 3.00000 | 0.0975900 | ||||||||
\(946\) | −22.3923 | −0.728037 | ||||||||
\(947\) | − 13.6077i | − 0.442191i | −0.975252 | − | 0.221095i | \(-0.929037\pi\) | ||||
0.975252 | − | 0.221095i | \(-0.0709632\pi\) | |||||||
\(948\) | 16.9282 | 0.549802 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.26795 | −0.0735820 | ||||||||
\(951\) | 23.5359i | 0.763204i | ||||||||
\(952\) | −12.0000 | −0.388922 | ||||||||
\(953\) | −18.6795 | −0.605088 | −0.302544 | − | 0.953135i | \(-0.597836\pi\) | ||||
−0.302544 | + | 0.953135i | \(0.597836\pi\) | |||||||
\(954\) | 3.73205i | 0.120830i | ||||||||
\(955\) | 17.3205i | 0.560478i | ||||||||
\(956\) | − 3.46410i | − 0.112037i | ||||||||
\(957\) | − 20.3923i | − 0.659190i | ||||||||
\(958\) | −26.2487 | −0.848057 | ||||||||
\(959\) | −19.6077 | −0.633165 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | −48.7128 | −1.57138 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.928203 | 0.0299109 | ||||||||
\(964\) | 14.8038i | 0.476800i | ||||||||
\(965\) | 17.8564 | 0.574818 | ||||||||
\(966\) | 10.3923 | 0.334367 | ||||||||
\(967\) | 28.8564i | 0.927959i | 0.885846 | + | 0.463980i | \(0.153579\pi\) | ||||
−0.885846 | + | 0.463980i | \(0.846421\pi\) | |||||||
\(968\) | − 2.92820i | − 0.0941160i | ||||||||
\(969\) | − 9.07180i | − 0.291428i | ||||||||
\(970\) | − 12.3923i | − 0.397893i | ||||||||
\(971\) | −20.6077 | −0.661332 | −0.330666 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330666 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 65.3538i | 2.09515i | ||||||||
\(974\) | 21.0000 | 0.672883 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.46410 | −0.238920 | ||||||||
\(977\) | − 1.46410i | − 0.0468408i | −0.999726 | − | 0.0234204i | \(-0.992544\pi\) | ||||
0.999726 | − | 0.0234204i | \(-0.00745562\pi\) | |||||||
\(978\) | −10.9282 | −0.349445 | ||||||||
\(979\) | −37.7846 | −1.20760 | ||||||||
\(980\) | 2.00000i | 0.0638877i | ||||||||
\(981\) | 10.3923i | 0.331801i | ||||||||
\(982\) | 15.3923i | 0.491188i | ||||||||
\(983\) | 16.1769i | 0.515963i | 0.966150 | + | 0.257982i | \(0.0830574\pi\) | ||||
−0.966150 | + | 0.257982i | \(0.916943\pi\) | |||||||
\(984\) | 4.00000 | 0.127515 | ||||||||
\(985\) | 9.39230 | 0.299264 | ||||||||
\(986\) | 21.8564i | 0.696050i | ||||||||
\(987\) | 1.39230 | 0.0443176 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.7846 | −0.660912 | ||||||||
\(990\) | − 3.73205i | − 0.118612i | ||||||||
\(991\) | −23.1769 | −0.736239 | −0.368119 | − | 0.929778i | \(-0.619998\pi\) | ||||
−0.368119 | + | 0.929778i | \(0.619998\pi\) | |||||||
\(992\) | −8.92820 | −0.283471 | ||||||||
\(993\) | 6.39230i | 0.202854i | ||||||||
\(994\) | 2.78461i | 0.0883225i | ||||||||
\(995\) | − 11.0718i | − 0.351000i | ||||||||
\(996\) | 2.53590i | 0.0803530i | ||||||||
\(997\) | 10.0192 | 0.317312 | 0.158656 | − | 0.987334i | \(-0.449284\pi\) | ||||
0.158656 | + | 0.987334i | \(0.449284\pi\) | |||||||
\(998\) | 1.32051 | 0.0418000 | ||||||||
\(999\) | 7.92820i | 0.250837i |
(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 | 5070.2.b.p.1351.1 | 4 | ||
13.5 | odd | 4 | 5070.2.a.ba.1.2 | 2 | |||
13.8 | odd | 4 | 5070.2.a.be.1.1 | 2 | |||
13.9 | even | 3 | 390.2.bb.a.361.1 | yes | 4 | ||
13.10 | even | 6 | 390.2.bb.a.121.1 | ✓ | 4 | ||
13.12 | even | 2 | inner | 5070.2.b.p.1351.4 | 4 | ||
39.23 | odd | 6 | 1170.2.bs.d.901.2 | 4 | |||
39.35 | odd | 6 | 1170.2.bs.d.361.2 | 4 | |||
65.9 | even | 6 | 1950.2.bc.a.751.2 | 4 | |||
65.22 | odd | 12 | 1950.2.y.d.49.2 | 4 | |||
65.23 | odd | 12 | 1950.2.y.d.199.2 | 4 | |||
65.48 | odd | 12 | 1950.2.y.e.49.1 | 4 | |||
65.49 | even | 6 | 1950.2.bc.a.901.2 | 4 | |||
65.62 | odd | 12 | 1950.2.y.e.199.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.a.121.1 | ✓ | 4 | 13.10 | even | 6 | ||
390.2.bb.a.361.1 | yes | 4 | 13.9 | even | 3 | ||
1170.2.bs.d.361.2 | 4 | 39.35 | odd | 6 | |||
1170.2.bs.d.901.2 | 4 | 39.23 | odd | 6 | |||
1950.2.y.d.49.2 | 4 | 65.22 | odd | 12 | |||
1950.2.y.d.199.2 | 4 | 65.23 | odd | 12 | |||
1950.2.y.e.49.1 | 4 | 65.48 | odd | 12 | |||
1950.2.y.e.199.1 | 4 | 65.62 | odd | 12 | |||
1950.2.bc.a.751.2 | 4 | 65.9 | even | 6 | |||
1950.2.bc.a.901.2 | 4 | 65.49 | even | 6 | |||
5070.2.a.ba.1.2 | 2 | 13.5 | odd | 4 | |||
5070.2.a.be.1.1 | 2 | 13.8 | odd | 4 | |||
5070.2.b.p.1351.1 | 4 | 1.1 | even | 1 | trivial | ||
5070.2.b.p.1351.4 | 4 | 13.12 | even | 2 | inner |