Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(246,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("637.246");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.c (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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 31x^{2} + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 246.5 | ||
Root | \(0.332375i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.e.246.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.332375i | 0.235025i | 0.993071 | + | 0.117512i | \(0.0374920\pi\) | ||||
−0.993071 | + | 0.117512i | \(0.962508\pi\) | |||||||
\(3\) | −1.45984 | −0.842837 | −0.421419 | − | 0.906866i | \(-0.638468\pi\) | ||||
−0.421419 | + | 0.906866i | \(0.638468\pi\) | |||||||
\(4\) | 1.88953 | 0.944763 | ||||||||
\(5\) | − | 1.44562i | − | 0.646502i | −0.946313 | − | 0.323251i | \(-0.895224\pi\) | ||
0.946313 | − | 0.323251i | \(-0.104776\pi\) | |||||||
\(6\) | − | 0.485214i | − | 0.198088i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.29278i | 0.457068i | ||||||||
\(9\) | −0.868875 | −0.289625 | ||||||||
\(10\) | 0.480489 | 0.151944 | ||||||||
\(11\) | 5.95516i | 1.79555i | 0.440456 | + | 0.897774i | \(0.354817\pi\) | ||||
−0.440456 | + | 0.897774i | \(0.645183\pi\) | |||||||
\(12\) | −2.75840 | −0.796282 | ||||||||
\(13\) | −1.88953 | + | 3.07078i | −0.524060 | + | 0.851681i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.11037i | 0.544896i | ||||||||
\(16\) | 3.34936 | 0.837341 | ||||||||
\(17\) | 4.32871 | 1.04987 | 0.524933 | − | 0.851143i | \(-0.324090\pi\) | ||||
0.524933 | + | 0.851143i | \(0.324090\pi\) | |||||||
\(18\) | − | 0.288793i | − | 0.0680691i | ||||||
\(19\) | − | 1.95753i | − | 0.449089i | −0.974464 | − | 0.224545i | \(-0.927911\pi\) | ||
0.974464 | − | 0.224545i | \(-0.0720894\pi\) | |||||||
\(20\) | − | 2.73154i | − | 0.610791i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.97935 | −0.421998 | ||||||||
\(23\) | 0.540163 | 0.112632 | 0.0563158 | − | 0.998413i | \(-0.482065\pi\) | ||||
0.0563158 | + | 0.998413i | \(0.482065\pi\) | |||||||
\(24\) | − | 1.88725i | − | 0.385234i | ||||||
\(25\) | 2.91018 | 0.582036 | ||||||||
\(26\) | −1.02065 | − | 0.628032i | −0.200166 | − | 0.123167i | ||||
\(27\) | 5.64793 | 1.08694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.15857 | 1.32931 | 0.664656 | − | 0.747149i | \(-0.268578\pi\) | ||||
0.664656 | + | 0.747149i | \(0.268578\pi\) | |||||||
\(30\) | −0.701436 | −0.128064 | ||||||||
\(31\) | 6.10800i | 1.09703i | 0.836141 | + | 0.548514i | \(0.184806\pi\) | ||||
−0.836141 | + | 0.548514i | \(0.815194\pi\) | |||||||
\(32\) | 3.69881i | 0.653864i | ||||||||
\(33\) | − | 8.69356i | − | 1.51336i | ||||||
\(34\) | 1.43876i | 0.246745i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.64176 | −0.273627 | ||||||||
\(37\) | − | 8.02881i | − | 1.31993i | −0.751297 | − | 0.659964i | \(-0.770571\pi\) | ||
0.751297 | − | 0.659964i | \(-0.229429\pi\) | |||||||
\(38\) | 0.650636 | 0.105547 | ||||||||
\(39\) | 2.75840 | − | 4.48284i | 0.441698 | − | 0.717829i | ||||
\(40\) | 1.86887 | 0.295495 | ||||||||
\(41\) | 7.55362i | 1.17968i | 0.807521 | + | 0.589839i | \(0.200809\pi\) | ||||
−0.807521 | + | 0.589839i | \(0.799191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24839 | −0.647873 | −0.323936 | − | 0.946079i | \(-0.605006\pi\) | ||||
−0.323936 | + | 0.946079i | \(0.605006\pi\) | |||||||
\(44\) | 11.2524i | 1.69637i | ||||||||
\(45\) | 1.25606i | 0.187243i | ||||||||
\(46\) | 0.179537i | 0.0264713i | ||||||||
\(47\) | 6.26084i | 0.913237i | 0.889663 | + | 0.456618i | \(0.150940\pi\) | ||||
−0.889663 | + | 0.456618i | \(0.849060\pi\) | |||||||
\(48\) | −4.88953 | −0.705742 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.967272i | 0.136793i | ||||||||
\(51\) | −6.31922 | −0.884867 | ||||||||
\(52\) | −3.57031 | + | 5.80232i | −0.495113 | + | 0.804637i | ||||
\(53\) | −2.77905 | −0.381732 | −0.190866 | − | 0.981616i | \(-0.561130\pi\) | ||||
−0.190866 | + | 0.981616i | \(0.561130\pi\) | |||||||
\(54\) | 1.87723i | 0.255459i | ||||||||
\(55\) | 8.60891 | 1.16082 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.85768i | 0.378509i | ||||||||
\(58\) | 2.37933i | 0.312421i | ||||||||
\(59\) | − | 0.851152i | − | 0.110811i | −0.998464 | − | 0.0554053i | \(-0.982355\pi\) | ||
0.998464 | − | 0.0554053i | \(-0.0176451\pi\) | |||||||
\(60\) | 3.98760i | 0.514798i | ||||||||
\(61\) | −6.77905 | −0.867969 | −0.433984 | − | 0.900920i | \(-0.642893\pi\) | ||||
−0.433984 | + | 0.900920i | \(0.642893\pi\) | |||||||
\(62\) | −2.03015 | −0.257829 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.46933 | 0.683667 | ||||||||
\(65\) | 4.43919 | + | 2.73154i | 0.550613 | + | 0.338806i | ||||
\(66\) | 2.88953 | 0.355676 | ||||||||
\(67\) | − | 0.987106i | − | 0.120594i | −0.998180 | − | 0.0602971i | \(-0.980795\pi\) | ||
0.998180 | − | 0.0602971i | \(-0.0192048\pi\) | |||||||
\(68\) | 8.17922 | 0.991876 | ||||||||
\(69\) | −0.788550 | −0.0949302 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.76223i | 0.446494i | 0.974762 | + | 0.223247i | \(0.0716657\pi\) | ||||
−0.974762 | + | 0.223247i | \(0.928334\pi\) | |||||||
\(72\) | − | 1.12327i | − | 0.132378i | ||||||
\(73\) | − | 9.13519i | − | 1.06919i | −0.845107 | − | 0.534597i | \(-0.820463\pi\) | ||
0.845107 | − | 0.534597i | \(-0.179537\pi\) | |||||||
\(74\) | 2.66858 | 0.310216 | ||||||||
\(75\) | −4.24839 | −0.490561 | ||||||||
\(76\) | − | 3.69881i | − | 0.424283i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.48999 | + | 0.916825i | 0.168708 | + | 0.103810i | ||||
\(79\) | −0.131125 | −0.0147527 | −0.00737636 | − | 0.999973i | \(-0.502348\pi\) | ||||
−0.00737636 | + | 0.999973i | \(0.502348\pi\) | |||||||
\(80\) | − | 4.84191i | − | 0.541342i | ||||||
\(81\) | −5.63843 | −0.626492 | ||||||||
\(82\) | −2.51064 | −0.277253 | ||||||||
\(83\) | − | 2.66812i | − | 0.292865i | −0.989221 | − | 0.146432i | \(-0.953221\pi\) | ||
0.989221 | − | 0.146432i | \(-0.0467791\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.25768i | − | 0.678741i | ||||||
\(86\) | − | 1.41206i | − | 0.152266i | ||||||
\(87\) | −10.4503 | −1.12039 | ||||||||
\(88\) | −7.69873 | −0.820687 | ||||||||
\(89\) | 9.71739i | 1.03004i | 0.857178 | + | 0.515021i | \(0.172216\pi\) | ||||
−0.857178 | + | 0.515021i | \(0.827784\pi\) | |||||||
\(90\) | −0.417485 | −0.0440068 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.02065 | 0.106410 | ||||||||
\(93\) | − | 8.91668i | − | 0.924617i | ||||||
\(94\) | −2.08095 | −0.214633 | ||||||||
\(95\) | −2.82985 | −0.290337 | ||||||||
\(96\) | − | 5.39966i | − | 0.551101i | ||||||
\(97\) | − | 6.58319i | − | 0.668422i | −0.942498 | − | 0.334211i | \(-0.891530\pi\) | ||
0.942498 | − | 0.334211i | \(-0.108470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.17429i | − | 0.520036i | ||||||
\(100\) | 5.49886 | 0.549886 | ||||||||
\(101\) | −0.0708289 | −0.00704774 | −0.00352387 | − | 0.999994i | \(-0.501122\pi\) | ||||
−0.00352387 | + | 0.999994i | \(0.501122\pi\) | |||||||
\(102\) | − | 2.10035i | − | 0.207966i | ||||||
\(103\) | 6.33821 | 0.624522 | 0.312261 | − | 0.949996i | \(-0.398914\pi\) | ||||
0.312261 | + | 0.949996i | \(0.398914\pi\) | |||||||
\(104\) | −3.96985 | − | 2.44275i | −0.389276 | − | 0.239531i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 0.923689i | − | 0.0897166i | ||||||
\(107\) | 7.74953 | 0.749175 | 0.374588 | − | 0.927192i | \(-0.377784\pi\) | ||||
0.374588 | + | 0.927192i | \(0.377784\pi\) | |||||||
\(108\) | 10.6719 | 1.02691 | ||||||||
\(109\) | − | 0.0335623i | − | 0.00321468i | −0.999999 | − | 0.00160734i | \(-0.999488\pi\) | ||
0.999999 | − | 0.00160734i | \(-0.000511633\pi\) | |||||||
\(110\) | 2.86139i | 0.272823i | ||||||||
\(111\) | 11.7208i | 1.11249i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.19987 | −0.865451 | −0.432725 | − | 0.901526i | \(-0.642448\pi\) | ||||
−0.432725 | + | 0.901526i | \(0.642448\pi\) | |||||||
\(114\) | −0.949823 | −0.0889591 | ||||||||
\(115\) | − | 0.780871i | − | 0.0728166i | ||||||
\(116\) | 13.5263 | 1.25589 | ||||||||
\(117\) | 1.64176 | − | 2.66812i | 0.151781 | − | 0.246668i | ||||
\(118\) | 0.282902 | 0.0260432 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.72825 | −0.249054 | ||||||||
\(121\) | −24.4639 | −2.22399 | ||||||||
\(122\) | − | 2.25319i | − | 0.203994i | ||||||
\(123\) | − | 11.0271i | − | 0.994276i | ||||||
\(124\) | 11.5412i | 1.03643i | ||||||||
\(125\) | − | 11.4351i | − | 1.02279i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3952 | −1.27737 | −0.638683 | − | 0.769470i | \(-0.720520\pi\) | ||||
−0.638683 | + | 0.769470i | \(0.720520\pi\) | |||||||
\(128\) | 9.21550i | 0.814542i | ||||||||
\(129\) | 6.20195 | 0.546052 | ||||||||
\(130\) | −0.907897 | + | 1.47548i | −0.0796278 | + | 0.129408i | ||||
\(131\) | 9.46828 | 0.827248 | 0.413624 | − | 0.910448i | \(-0.364263\pi\) | ||||
0.413624 | + | 0.910448i | \(0.364263\pi\) | |||||||
\(132\) | − | 16.4267i | − | 1.42976i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.328090 | 0.0283426 | ||||||||
\(135\) | − | 8.16477i | − | 0.702711i | ||||||
\(136\) | 5.59609i | 0.479860i | ||||||||
\(137\) | − | 16.6063i | − | 1.41877i | −0.704822 | − | 0.709384i | \(-0.748973\pi\) | ||
0.704822 | − | 0.709384i | \(-0.251027\pi\) | |||||||
\(138\) | − | 0.262094i | − | 0.0223110i | ||||||
\(139\) | −18.4778 | −1.56726 | −0.783632 | − | 0.621225i | \(-0.786635\pi\) | ||||
−0.783632 | + | 0.621225i | \(0.786635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.13980i | − | 0.769710i | ||||||
\(142\) | −1.25047 | −0.104937 | ||||||||
\(143\) | −18.2870 | − | 11.2524i | −1.52923 | − | 0.940976i | ||||
\(144\) | −2.91018 | −0.242515 | ||||||||
\(145\) | − | 10.3486i | − | 0.859402i | ||||||
\(146\) | 3.03631 | 0.251287 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 15.1707i | − | 1.24702i | ||||||
\(149\) | − | 3.08080i | − | 0.252389i | −0.992006 | − | 0.126195i | \(-0.959724\pi\) | ||
0.992006 | − | 0.126195i | \(-0.0402763\pi\) | |||||||
\(150\) | − | 1.41206i | − | 0.115294i | ||||||
\(151\) | − | 2.54885i | − | 0.207422i | −0.994607 | − | 0.103711i | \(-0.966928\pi\) | ||
0.994607 | − | 0.103711i | \(-0.0330717\pi\) | |||||||
\(152\) | 2.53067 | 0.205264 | ||||||||
\(153\) | −3.76111 | −0.304068 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.82985 | 0.709231 | ||||||||
\(156\) | 5.21207 | − | 8.47044i | 0.417300 | − | 0.678178i | ||||
\(157\) | 9.40904 | 0.750923 | 0.375461 | − | 0.926838i | \(-0.377484\pi\) | ||||
0.375461 | + | 0.926838i | \(0.377484\pi\) | |||||||
\(158\) | − | 0.0435828i | − | 0.00346726i | ||||||
\(159\) | 4.05697 | 0.321738 | ||||||||
\(160\) | 5.34708 | 0.422724 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.87408i | − | 0.147241i | ||||||
\(163\) | − | 0.695157i | − | 0.0544489i | −0.999629 | − | 0.0272244i | \(-0.991333\pi\) | ||
0.999629 | − | 0.0272244i | \(-0.00866688\pi\) | |||||||
\(164\) | 14.2728i | 1.11452i | ||||||||
\(165\) | −12.5676 | −0.978387 | ||||||||
\(166\) | 0.886819 | 0.0688305 | ||||||||
\(167\) | 13.9840i | 1.08211i | 0.840986 | + | 0.541056i | \(0.181975\pi\) | ||||
−0.840986 | + | 0.541056i | \(0.818025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.85938 | − | 11.6046i | −0.450721 | − | 0.892665i | ||||
\(170\) | 2.07990 | 0.159521 | ||||||||
\(171\) | 1.70085i | 0.130067i | ||||||||
\(172\) | −8.02744 | −0.612087 | ||||||||
\(173\) | −5.43648 | −0.413328 | −0.206664 | − | 0.978412i | \(-0.566261\pi\) | ||||
−0.206664 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(174\) | − | 3.47344i | − | 0.263321i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.9460i | 1.50349i | ||||||||
\(177\) | 1.24254i | 0.0933953i | ||||||||
\(178\) | −3.22982 | −0.242085 | ||||||||
\(179\) | −5.35824 | −0.400493 | −0.200247 | − | 0.979745i | \(-0.564174\pi\) | ||||
−0.200247 | + | 0.979745i | \(0.564174\pi\) | |||||||
\(180\) | 2.37337i | 0.176900i | ||||||||
\(181\) | 7.54016 | 0.560456 | 0.280228 | − | 0.959933i | \(-0.409590\pi\) | ||||
0.280228 | + | 0.959933i | \(0.409590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.89632 | 0.731557 | ||||||||
\(184\) | 0.698313i | 0.0514803i | ||||||||
\(185\) | −11.6066 | −0.853336 | ||||||||
\(186\) | 2.96369 | 0.217308 | ||||||||
\(187\) | 25.7782i | 1.88509i | ||||||||
\(188\) | 11.8300i | 0.862793i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 0.940574i | − | 0.0682364i | ||||||
\(191\) | 13.5463 | 0.980178 | 0.490089 | − | 0.871672i | \(-0.336964\pi\) | ||||
0.490089 | + | 0.871672i | \(0.336964\pi\) | |||||||
\(192\) | −7.98434 | −0.576220 | ||||||||
\(193\) | − | 18.5562i | − | 1.33571i | −0.744293 | − | 0.667853i | \(-0.767213\pi\) | ||
0.744293 | − | 0.667853i | \(-0.232787\pi\) | |||||||
\(194\) | 2.18809 | 0.157096 | ||||||||
\(195\) | −6.48049 | − | 3.98760i | −0.464077 | − | 0.285558i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.66812i | − | 0.190096i | −0.995473 | − | 0.0950480i | \(-0.969700\pi\) | ||
0.995473 | − | 0.0950480i | \(-0.0303004\pi\) | |||||||
\(198\) | 1.71981 | 0.122221 | ||||||||
\(199\) | 20.1999 | 1.43193 | 0.715965 | − | 0.698136i | \(-0.245987\pi\) | ||||
0.715965 | + | 0.698136i | \(0.245987\pi\) | |||||||
\(200\) | 3.76223i | 0.266030i | ||||||||
\(201\) | 1.44101i | 0.101641i | ||||||||
\(202\) | − | 0.0235418i | − | 0.00165639i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.9403 | −0.835990 | ||||||||
\(205\) | 10.9197 | 0.762663 | ||||||||
\(206\) | 2.10666i | 0.146778i | ||||||||
\(207\) | −0.469334 | −0.0326210 | ||||||||
\(208\) | −6.32871 | + | 10.2852i | −0.438817 | + | 0.713148i | ||||
\(209\) | 11.6574 | 0.806361 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1268 | 0.903683 | 0.451842 | − | 0.892098i | \(-0.350767\pi\) | ||||
0.451842 | + | 0.892098i | \(0.350767\pi\) | |||||||
\(212\) | −5.25109 | −0.360647 | ||||||||
\(213\) | − | 5.49224i | − | 0.376322i | ||||||
\(214\) | 2.57575i | 0.176075i | ||||||||
\(215\) | 6.14156i | 0.418851i | ||||||||
\(216\) | 7.30155i | 0.496807i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.0111553 | 0.000755530 | ||||||||
\(219\) | 13.3359i | 0.901157i | ||||||||
\(220\) | 16.2668 | 1.09670 | ||||||||
\(221\) | −8.17922 | + | 13.2925i | −0.550194 | + | 0.894152i | ||||
\(222\) | −3.89569 | −0.261462 | ||||||||
\(223\) | 2.22334i | 0.148886i | 0.997225 | + | 0.0744428i | \(0.0237178\pi\) | ||||
−0.997225 | + | 0.0744428i | \(0.976282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.52858 | −0.168572 | ||||||||
\(226\) | − | 3.05781i | − | 0.203402i | ||||||
\(227\) | − | 27.1045i | − | 1.79899i | −0.436931 | − | 0.899495i | \(-0.643935\pi\) | ||
0.436931 | − | 0.899495i | \(-0.356065\pi\) | |||||||
\(228\) | 5.39966i | 0.357601i | ||||||||
\(229\) | − | 18.9887i | − | 1.25481i | −0.778693 | − | 0.627406i | \(-0.784117\pi\) | ||
0.778693 | − | 0.627406i | \(-0.215883\pi\) | |||||||
\(230\) | 0.259542 | 0.0171137 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.25447i | 0.607586i | ||||||||
\(233\) | −21.7400 | −1.42424 | −0.712118 | − | 0.702059i | \(-0.752264\pi\) | ||||
−0.712118 | + | 0.702059i | \(0.752264\pi\) | |||||||
\(234\) | 0.886819 | + | 0.545681i | 0.0579731 | + | 0.0356723i | ||||
\(235\) | 9.05080 | 0.590409 | ||||||||
\(236\) | − | 1.60827i | − | 0.104690i | ||||||
\(237\) | 0.191421 | 0.0124342 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.9695i | 1.29172i | 0.763455 | + | 0.645861i | \(0.223501\pi\) | ||||
−0.763455 | + | 0.645861i | \(0.776499\pi\) | |||||||
\(240\) | 7.06841i | 0.456264i | ||||||||
\(241\) | 3.23048i | 0.208094i | 0.994572 | + | 0.104047i | \(0.0331792\pi\) | ||||
−0.994572 | + | 0.104047i | \(0.966821\pi\) | |||||||
\(242\) | − | 8.13120i | − | 0.522694i | ||||||
\(243\) | −8.71259 | −0.558913 | ||||||||
\(244\) | −12.8092 | −0.820025 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.66512 | 0.233680 | ||||||||
\(247\) | 6.01116 | + | 3.69881i | 0.382481 | + | 0.235350i | ||||
\(248\) | −7.89632 | −0.501417 | ||||||||
\(249\) | 3.89503i | 0.246837i | ||||||||
\(250\) | 3.80075 | 0.240381 | ||||||||
\(251\) | 12.4916 | 0.788466 | 0.394233 | − | 0.919011i | \(-0.371010\pi\) | ||||
0.394233 | + | 0.919011i | \(0.371010\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.21675i | 0.202236i | ||||||||
\(254\) | − | 4.78460i | − | 0.300213i | ||||||
\(255\) | 9.13519i | 0.572068i | ||||||||
\(256\) | 7.87566 | 0.492229 | ||||||||
\(257\) | 5.82757 | 0.363514 | 0.181757 | − | 0.983343i | \(-0.441822\pi\) | ||||
0.181757 | + | 0.983343i | \(0.441822\pi\) | |||||||
\(258\) | 2.06138i | 0.128336i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.38796 | + | 5.16132i | 0.520199 | + | 0.320091i | ||||
\(261\) | −6.21990 | −0.385002 | ||||||||
\(262\) | 3.14702i | 0.194424i | ||||||||
\(263\) | 17.5147 | 1.08000 | 0.540002 | − | 0.841664i | \(-0.318424\pi\) | ||||
0.540002 | + | 0.841664i | \(0.318424\pi\) | |||||||
\(264\) | 11.2389 | 0.691706 | ||||||||
\(265\) | 4.01746i | 0.246791i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.1858i | − | 0.868157i | ||||||
\(268\) | − | 1.86516i | − | 0.113933i | ||||||
\(269\) | −22.3287 | −1.36141 | −0.680703 | − | 0.732560i | \(-0.738325\pi\) | ||||
−0.680703 | + | 0.732560i | \(0.738325\pi\) | |||||||
\(270\) | 2.71377 | 0.165155 | ||||||||
\(271\) | − | 26.3695i | − | 1.60183i | −0.598777 | − | 0.800916i | \(-0.704346\pi\) | ||
0.598777 | − | 0.800916i | \(-0.295654\pi\) | |||||||
\(272\) | 14.4984 | 0.879097 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.51951 | 0.333446 | ||||||||
\(275\) | 17.3306i | 1.04507i | ||||||||
\(276\) | −1.48999 | −0.0896866 | ||||||||
\(277\) | 9.37618 | 0.563360 | 0.281680 | − | 0.959508i | \(-0.409108\pi\) | ||||
0.281680 | + | 0.959508i | \(0.409108\pi\) | |||||||
\(278\) | − | 6.14156i | − | 0.368346i | ||||||
\(279\) | − | 5.30709i | − | 0.317727i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7754i | 1.06039i | 0.847876 | + | 0.530195i | \(0.177881\pi\) | ||||
−0.847876 | + | 0.530195i | \(0.822119\pi\) | |||||||
\(282\) | 3.03785 | 0.180901 | ||||||||
\(283\) | −9.60662 | −0.571055 | −0.285527 | − | 0.958371i | \(-0.592169\pi\) | ||||
−0.285527 | + | 0.958371i | \(0.592169\pi\) | |||||||
\(284\) | 7.10883i | 0.421832i | ||||||||
\(285\) | 4.13113 | 0.244707 | ||||||||
\(286\) | 3.74003 | − | 6.07814i | 0.221153 | − | 0.359408i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 3.21380i | − | 0.189375i | ||||||
\(289\) | 1.73775 | 0.102221 | ||||||||
\(290\) | 3.43961 | 0.201981 | ||||||||
\(291\) | 9.61039i | 0.563371i | ||||||||
\(292\) | − | 17.2612i | − | 1.01013i | ||||||
\(293\) | − | 11.6338i | − | 0.679654i | −0.940488 | − | 0.339827i | \(-0.889631\pi\) | ||
0.940488 | − | 0.339827i | \(-0.110369\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.23044 | −0.0716392 | ||||||||
\(296\) | 10.3795 | 0.603297 | ||||||||
\(297\) | 33.6343i | 1.95166i | ||||||||
\(298\) | 1.02398 | 0.0593177 | ||||||||
\(299\) | −1.02065 | + | 1.65872i | −0.0590258 | + | 0.0959263i | ||||
\(300\) | −8.02744 | −0.463464 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.847174 | 0.0487494 | ||||||||
\(303\) | 0.103399 | 0.00594010 | ||||||||
\(304\) | − | 6.55649i | − | 0.376041i | ||||||
\(305\) | 9.79995i | 0.561143i | ||||||||
\(306\) | − | 1.25010i | − | 0.0714635i | ||||||
\(307\) | 13.8280i | 0.789204i | 0.918852 | + | 0.394602i | \(0.129118\pi\) | ||||
−0.918852 | + | 0.394602i | \(0.870882\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.25275 | −0.526371 | ||||||||
\(310\) | 2.93483i | 0.166687i | ||||||||
\(311\) | 30.7144 | 1.74165 | 0.870827 | − | 0.491590i | \(-0.163584\pi\) | ||||
0.870827 | + | 0.491590i | \(0.163584\pi\) | |||||||
\(312\) | 5.79534 | + | 3.56601i | 0.328096 | + | 0.201886i | ||||
\(313\) | −11.0867 | −0.626657 | −0.313328 | − | 0.949645i | \(-0.601444\pi\) | ||||
−0.313328 | + | 0.949645i | \(0.601444\pi\) | |||||||
\(314\) | 3.12733i | 0.176486i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.247764 | −0.0139378 | ||||||||
\(317\) | − | 23.8834i | − | 1.34142i | −0.741718 | − | 0.670712i | \(-0.765989\pi\) | ||
0.741718 | − | 0.670712i | \(-0.234011\pi\) | |||||||
\(318\) | 1.34844i | 0.0756165i | ||||||||
\(319\) | 42.6304i | 2.38684i | ||||||||
\(320\) | − | 7.90659i | − | 0.441992i | ||||||
\(321\) | −11.3130 | −0.631433 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.47360i | − | 0.471484i | ||||||
\(324\) | −10.6540 | −0.591887 | ||||||||
\(325\) | −5.49886 | + | 8.93652i | −0.305022 | + | 0.495709i | ||||
\(326\) | 0.231053 | 0.0127968 | ||||||||
\(327\) | 0.0489954i | 0.00270945i | ||||||||
\(328\) | −9.76519 | −0.539192 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 4.17716i | − | 0.229945i | ||||||
\(331\) | − | 18.3240i | − | 1.00718i | −0.863943 | − | 0.503589i | \(-0.832013\pi\) | ||
0.863943 | − | 0.503589i | \(-0.167987\pi\) | |||||||
\(332\) | − | 5.04149i | − | 0.276688i | ||||||
\(333\) | 6.97603i | 0.382284i | ||||||||
\(334\) | −4.64793 | −0.254323 | ||||||||
\(335\) | −1.42698 | −0.0779643 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.21762 | 0.393169 | 0.196584 | − | 0.980487i | \(-0.437015\pi\) | ||||
0.196584 | + | 0.980487i | \(0.437015\pi\) | |||||||
\(338\) | 3.85710 | − | 1.94751i | 0.209798 | − | 0.105931i | ||||
\(339\) | 13.4303 | 0.729434 | ||||||||
\(340\) | − | 11.8241i | − | 0.641249i | ||||||
\(341\) | −36.3741 | −1.96977 | ||||||||
\(342\) | −0.565321 | −0.0305691 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 5.49224i | − | 0.296122i | ||||||
\(345\) | 1.13994i | 0.0613725i | ||||||||
\(346\) | − | 1.80695i | − | 0.0971423i | ||||||
\(347\) | −21.0782 | −1.13154 | −0.565770 | − | 0.824563i | \(-0.691421\pi\) | ||||
−0.565770 | + | 0.824563i | \(0.691421\pi\) | |||||||
\(348\) | −19.7462 | −1.05851 | ||||||||
\(349\) | − | 30.7629i | − | 1.64670i | −0.567534 | − | 0.823350i | \(-0.692102\pi\) | ||
0.567534 | − | 0.823350i | \(-0.307898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.6719 | + | 17.3435i | −0.569624 | + | 0.925730i | ||||
\(352\) | −22.0270 | −1.17404 | ||||||||
\(353\) | − | 6.12173i | − | 0.325827i | −0.986640 | − | 0.162913i | \(-0.947911\pi\) | ||
0.986640 | − | 0.162913i | \(-0.0520891\pi\) | |||||||
\(354\) | −0.412991 | −0.0219502 | ||||||||
\(355\) | 5.43876 | 0.288659 | ||||||||
\(356\) | 18.3613i | 0.973145i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 1.78095i | − | 0.0941259i | ||||||
\(359\) | 19.4287i | 1.02541i | 0.858566 | + | 0.512703i | \(0.171356\pi\) | ||||
−0.858566 | + | 0.512703i | \(0.828644\pi\) | |||||||
\(360\) | −1.62382 | −0.0855827 | ||||||||
\(361\) | 15.1681 | 0.798319 | ||||||||
\(362\) | 2.50616i | 0.131721i | ||||||||
\(363\) | 35.7133 | 1.87446 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.2060 | −0.691235 | ||||||||
\(366\) | 3.28929i | 0.171934i | ||||||||
\(367\) | 5.40467 | 0.282122 | 0.141061 | − | 0.990001i | \(-0.454949\pi\) | ||||
0.141061 | + | 0.990001i | \(0.454949\pi\) | |||||||
\(368\) | 1.80920 | 0.0943111 | ||||||||
\(369\) | − | 6.56315i | − | 0.341664i | ||||||
\(370\) | − | 3.85776i | − | 0.200555i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 16.8483i | − | 0.873544i | ||||||
\(373\) | 16.2507 | 0.841428 | 0.420714 | − | 0.907193i | \(-0.361780\pi\) | ||||
0.420714 | + | 0.907193i | \(0.361780\pi\) | |||||||
\(374\) | −8.56803 | −0.443042 | ||||||||
\(375\) | 16.6934i | 0.862045i | ||||||||
\(376\) | −8.09390 | −0.417411 | ||||||||
\(377\) | −13.5263 | + | 21.9824i | −0.696640 | + | 1.13215i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1730i | 1.29305i | 0.762893 | + | 0.646525i | \(0.223778\pi\) | ||||
−0.762893 | + | 0.646525i | \(0.776222\pi\) | |||||||
\(380\) | −5.34708 | −0.274300 | ||||||||
\(381\) | 21.0146 | 1.07661 | ||||||||
\(382\) | 4.50247i | 0.230366i | ||||||||
\(383\) | − | 3.81438i | − | 0.194906i | −0.995240 | − | 0.0974529i | \(-0.968930\pi\) | ||
0.995240 | − | 0.0974529i | \(-0.0310695\pi\) | |||||||
\(384\) | − | 13.4531i | − | 0.686527i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.16764 | 0.313924 | ||||||||
\(387\) | 3.69132 | 0.187640 | ||||||||
\(388\) | − | 12.4391i | − | 0.631500i | ||||||
\(389\) | 2.87096 | 0.145563 | 0.0727817 | − | 0.997348i | \(-0.476812\pi\) | ||||
0.0727817 | + | 0.997348i | \(0.476812\pi\) | |||||||
\(390\) | 1.32538 | − | 2.15396i | 0.0671133 | − | 0.109070i | ||||
\(391\) | 2.33821 | 0.118248 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8222 | −0.697236 | ||||||||
\(394\) | 0.886819 | 0.0446773 | ||||||||
\(395\) | 0.189557i | 0.00953766i | ||||||||
\(396\) | − | 9.77696i | − | 0.491310i | ||||||
\(397\) | − | 19.1184i | − | 0.959524i | −0.877399 | − | 0.479762i | \(-0.840723\pi\) | ||
0.877399 | − | 0.479762i | \(-0.159277\pi\) | |||||||
\(398\) | 6.71394i | 0.336539i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.74725 | 0.487362 | ||||||||
\(401\) | − | 2.99824i | − | 0.149725i | −0.997194 | − | 0.0748625i | \(-0.976148\pi\) | ||
0.997194 | − | 0.0748625i | \(-0.0238518\pi\) | |||||||
\(402\) | −0.478958 | −0.0238882 | ||||||||
\(403\) | −18.7563 | − | 11.5412i | −0.934319 | − | 0.574909i | ||||
\(404\) | −0.133833 | −0.00665844 | ||||||||
\(405\) | 8.15104i | 0.405028i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.8129 | 2.37000 | ||||||||
\(408\) | − | 8.16937i | − | 0.404444i | ||||||
\(409\) | 34.0805i | 1.68517i | 0.538560 | + | 0.842587i | \(0.318969\pi\) | ||||
−0.538560 | + | 0.842587i | \(0.681031\pi\) | |||||||
\(410\) | 3.62943i | 0.179245i | ||||||||
\(411\) | 24.2424i | 1.19579i | ||||||||
\(412\) | 11.9762 | 0.590026 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 0.155995i | − | 0.00766674i | ||||||
\(415\) | −3.85710 | −0.189337 | ||||||||
\(416\) | −11.3582 | − | 6.98900i | −0.556883 | − | 0.342664i | ||||
\(417\) | 26.9746 | 1.32095 | ||||||||
\(418\) | 3.87464i | 0.189515i | ||||||||
\(419\) | −34.7759 | −1.69891 | −0.849457 | − | 0.527657i | \(-0.823071\pi\) | ||||
−0.849457 | + | 0.527657i | \(0.823071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 24.1400i | − | 1.17651i | −0.808674 | − | 0.588257i | \(-0.799814\pi\) | ||
0.808674 | − | 0.588257i | \(-0.200186\pi\) | |||||||
\(422\) | 4.36301i | 0.212388i | ||||||||
\(423\) | − | 5.43988i | − | 0.264496i | ||||||
\(424\) | − | 3.59271i | − | 0.174478i | ||||||
\(425\) | 12.5973 | 0.611060 | ||||||||
\(426\) | 1.82549 | 0.0884451 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.6429 | 0.707793 | ||||||||
\(429\) | 26.6960 | + | 16.4267i | 1.28890 | + | 0.793089i | ||||
\(430\) | −2.04130 | −0.0984404 | ||||||||
\(431\) | − | 4.76477i | − | 0.229511i | −0.993394 | − | 0.114755i | \(-0.963392\pi\) | ||
0.993394 | − | 0.114755i | \(-0.0366084\pi\) | |||||||
\(432\) | 18.9170 | 0.910143 | ||||||||
\(433\) | 22.0231 | 1.05836 | 0.529181 | − | 0.848509i | \(-0.322499\pi\) | ||||
0.529181 | + | 0.848509i | \(0.322499\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.1072i | 0.724337i | ||||||||
\(436\) | − | 0.0634168i | − | 0.00303711i | ||||||
\(437\) | − | 1.05739i | − | 0.0505817i | ||||||
\(438\) | −4.43252 | −0.211794 | ||||||||
\(439\) | 3.43240 | 0.163819 | 0.0819097 | − | 0.996640i | \(-0.473898\pi\) | ||||
0.0819097 | + | 0.996640i | \(0.473898\pi\) | |||||||
\(440\) | 11.1294i | 0.530576i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.41811 | − | 2.71857i | −0.210148 | − | 0.129309i | ||||
\(443\) | −8.70594 | −0.413632 | −0.206816 | − | 0.978380i | \(-0.566310\pi\) | ||||
−0.206816 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(444\) | 22.1467i | 1.05104i | ||||||||
\(445\) | 14.0477 | 0.665923 | ||||||||
\(446\) | −0.738982 | −0.0349918 | ||||||||
\(447\) | 4.49747i | 0.212723i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.6120i | 0.831159i | 0.909557 | + | 0.415580i | \(0.136421\pi\) | ||||
−0.909557 | + | 0.415580i | \(0.863579\pi\) | |||||||
\(450\) | − | 0.840438i | − | 0.0396186i | ||||||
\(451\) | −44.9830 | −2.11817 | ||||||||
\(452\) | −17.3834 | −0.817646 | ||||||||
\(453\) | 3.72090i | 0.174823i | ||||||||
\(454\) | 9.00887 | 0.422807 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.69436 | −0.173004 | ||||||||
\(457\) | 9.07268i | 0.424402i | 0.977226 | + | 0.212201i | \(0.0680631\pi\) | ||||
−0.977226 | + | 0.212201i | \(0.931937\pi\) | |||||||
\(458\) | 6.31139 | 0.294912 | ||||||||
\(459\) | 24.4483 | 1.14115 | ||||||||
\(460\) | − | 1.47548i | − | 0.0687944i | ||||||
\(461\) | 6.58319i | 0.306610i | 0.988179 | + | 0.153305i | \(0.0489917\pi\) | ||||
−0.988179 | + | 0.153305i | \(0.951008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.47344i | 0.161424i | 0.996737 | + | 0.0807121i | \(0.0257194\pi\) | ||||
−0.996737 | + | 0.0807121i | \(0.974281\pi\) | |||||||
\(464\) | 23.9766 | 1.11309 | ||||||||
\(465\) | −12.8901 | −0.597766 | ||||||||
\(466\) | − | 7.22585i | − | 0.334731i | ||||||
\(467\) | 29.7854 | 1.37830 | 0.689152 | − | 0.724617i | \(-0.257983\pi\) | ||||
0.689152 | + | 0.724617i | \(0.257983\pi\) | |||||||
\(468\) | 3.10215 | − | 5.04149i | 0.143397 | − | 0.233043i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.00826i | 0.138761i | ||||||||
\(471\) | −13.7357 | −0.632906 | ||||||||
\(472\) | 1.10035 | 0.0506479 | ||||||||
\(473\) | − | 25.2998i | − | 1.16329i | ||||||
\(474\) | 0.0636237i | 0.00292233i | ||||||||
\(475\) | − | 5.69677i | − | 0.261386i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.41465 | 0.110559 | ||||||||
\(478\) | −6.63738 | −0.303587 | ||||||||
\(479\) | − | 35.1855i | − | 1.60767i | −0.594855 | − | 0.803833i | \(-0.702791\pi\) | ||
0.594855 | − | 0.803833i | \(-0.297209\pi\) | |||||||
\(480\) | −7.80587 | −0.356288 | ||||||||
\(481\) | 24.6547 | + | 15.1707i | 1.12416 | + | 0.691722i | ||||
\(482\) | −1.07373 | −0.0489072 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −46.2252 | −2.10115 | ||||||||
\(485\) | −9.51680 | −0.432136 | ||||||||
\(486\) | − | 2.89585i | − | 0.131358i | ||||||
\(487\) | 1.80154i | 0.0816355i | 0.999167 | + | 0.0408178i | \(0.0129963\pi\) | ||||
−0.999167 | + | 0.0408178i | \(0.987004\pi\) | |||||||
\(488\) | − | 8.76384i | − | 0.396721i | ||||||
\(489\) | 1.01482i | 0.0458916i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.19322 | 0.369755 | 0.184877 | − | 0.982762i | \(-0.440811\pi\) | ||||
0.184877 | + | 0.982762i | \(0.440811\pi\) | |||||||
\(492\) | − | 20.8359i | − | 0.939356i | ||||||
\(493\) | 30.9874 | 1.39560 | ||||||||
\(494\) | −1.22939 | + | 1.99796i | −0.0553131 | + | 0.0898925i | ||||
\(495\) | −7.48006 | −0.336204 | ||||||||
\(496\) | 20.4579i | 0.918587i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.29461 | −0.0580129 | ||||||||
\(499\) | 36.5164i | 1.63470i | 0.576141 | + | 0.817350i | \(0.304558\pi\) | ||||
−0.576141 | + | 0.817350i | \(0.695442\pi\) | |||||||
\(500\) | − | 21.6070i | − | 0.966293i | ||||||
\(501\) | − | 20.4143i | − | 0.912045i | ||||||
\(502\) | 4.15192i | 0.185309i | ||||||||
\(503\) | 3.02972 | 0.135089 | 0.0675443 | − | 0.997716i | \(-0.478484\pi\) | ||||
0.0675443 | + | 0.997716i | \(0.478484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.102392i | 0.00455637i | ||||||||
\(506\) | −1.06917 | −0.0475304 | ||||||||
\(507\) | 8.55374 | + | 16.9409i | 0.379885 | + | 0.752371i | ||||
\(508\) | −27.2001 | −1.20681 | ||||||||
\(509\) | 29.3447i | 1.30068i | 0.759642 | + | 0.650341i | \(0.225374\pi\) | ||||
−0.759642 | + | 0.650341i | \(0.774626\pi\) | |||||||
\(510\) | −3.03631 | −0.134450 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.0487i | 0.930229i | ||||||||
\(513\) | − | 11.0560i | − | 0.488135i | ||||||
\(514\) | 1.93694i | 0.0854348i | ||||||||
\(515\) | − | 9.16265i | − | 0.403755i | ||||||
\(516\) | 11.7188 | 0.515890 | ||||||||
\(517\) | −37.2843 | −1.63976 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.93637 | 0.348368 | ||||||||
\(520\) | −3.53129 | + | 5.73890i | −0.154857 | + | 0.251668i | ||||
\(521\) | 29.6838 | 1.30047 | 0.650236 | − | 0.759732i | \(-0.274670\pi\) | ||||
0.650236 | + | 0.759732i | \(0.274670\pi\) | |||||||
\(522\) | − | 2.06734i | − | 0.0904851i | ||||||
\(523\) | −20.5727 | −0.899583 | −0.449791 | − | 0.893134i | \(-0.648502\pi\) | ||||
−0.449791 | + | 0.893134i | \(0.648502\pi\) | |||||||
\(524\) | 17.8906 | 0.781553 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.82146i | 0.253828i | ||||||||
\(527\) | 26.4398i | 1.15173i | ||||||||
\(528\) | − | 29.1179i | − | 1.26719i | ||||||
\(529\) | −22.7082 | −0.987314 | ||||||||
\(530\) | −1.33530 | −0.0580019 | ||||||||
\(531\) | 0.739544i | 0.0320935i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.1955 | − | 14.2728i | −1.00471 | − | 0.618222i | ||||
\(534\) | 4.71501 | 0.204039 | ||||||||
\(535\) | − | 11.2029i | − | 0.484343i | ||||||
\(536\) | 1.27611 | 0.0551197 | ||||||||
\(537\) | 7.82216 | 0.337551 | ||||||||
\(538\) | − | 7.42151i | − | 0.319964i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 15.4275i | − | 0.663896i | ||||||
\(541\) | − | 34.0668i | − | 1.46465i | −0.680957 | − | 0.732324i | \(-0.738436\pi\) | ||
0.680957 | − | 0.732324i | \(-0.261564\pi\) | |||||||
\(542\) | 8.76457 | 0.376470 | ||||||||
\(543\) | −11.0074 | −0.472373 | ||||||||
\(544\) | 16.0111i | 0.686470i | ||||||||
\(545\) | −0.0485183 | −0.00207830 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.850931 | −0.0363832 | −0.0181916 | − | 0.999835i | \(-0.505791\pi\) | ||||
−0.0181916 | + | 0.999835i | \(0.505791\pi\) | |||||||
\(548\) | − | 31.3780i | − | 1.34040i | ||||||
\(549\) | 5.89015 | 0.251385 | ||||||||
\(550\) | −5.76026 | −0.245618 | ||||||||
\(551\) | − | 14.0131i | − | 0.596980i | ||||||
\(552\) | − | 1.01942i | − | 0.0433895i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.11641i | 0.132404i | ||||||||
\(555\) | 16.9438 | 0.719224 | ||||||||
\(556\) | −34.9143 | −1.48069 | ||||||||
\(557\) | 17.7281i | 0.751162i | 0.926789 | + | 0.375581i | \(0.122557\pi\) | ||||
−0.926789 | + | 0.375581i | \(0.877443\pi\) | |||||||
\(558\) | 1.76394 | 0.0746737 | ||||||||
\(559\) | 8.02744 | − | 13.0459i | 0.339525 | − | 0.551781i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 37.6319i | − | 1.58882i | ||||||
\(562\) | −5.90809 | −0.249218 | ||||||||
\(563\) | −24.1806 | −1.01909 | −0.509545 | − | 0.860444i | \(-0.670186\pi\) | ||||
−0.509545 | + | 0.860444i | \(0.670186\pi\) | |||||||
\(564\) | − | 17.2699i | − | 0.727194i | ||||||
\(565\) | 13.2995i | 0.559515i | ||||||||
\(566\) | − | 3.19301i | − | 0.134212i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.86375 | −0.204078 | ||||||||
\(569\) | 42.7749 | 1.79322 | 0.896608 | − | 0.442825i | \(-0.146024\pi\) | ||||
0.896608 | + | 0.442825i | \(0.146024\pi\) | |||||||
\(570\) | 1.37308i | 0.0575122i | ||||||||
\(571\) | −7.36280 | −0.308124 | −0.154062 | − | 0.988061i | \(-0.549235\pi\) | ||||
−0.154062 | + | 0.988061i | \(0.549235\pi\) | |||||||
\(572\) | −34.5537 | − | 21.2618i | −1.44476 | − | 0.888999i | ||||
\(573\) | −19.7754 | −0.826131 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.57197 | 0.0655557 | ||||||||
\(576\) | −4.75217 | −0.198007 | ||||||||
\(577\) | 8.19393i | 0.341118i | 0.985347 | + | 0.170559i | \(0.0545573\pi\) | ||||
−0.985347 | + | 0.170559i | \(0.945443\pi\) | |||||||
\(578\) | 0.577585i | 0.0240244i | ||||||||
\(579\) | 27.0891i | 1.12578i | ||||||||
\(580\) | − | 19.5539i | − | 0.811932i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.19426 | −0.132406 | ||||||||
\(583\) | − | 16.5497i | − | 0.685419i | ||||||
\(584\) | 11.8098 | 0.488694 | ||||||||
\(585\) | −3.85710 | − | 2.37337i | −0.159471 | − | 0.0981266i | ||||
\(586\) | 3.86679 | 0.159736 | ||||||||
\(587\) | − | 39.1141i | − | 1.61441i | −0.590271 | − | 0.807205i | \(-0.700979\pi\) | ||
0.590271 | − | 0.807205i | \(-0.299021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9566 | 0.492664 | ||||||||
\(590\) | − | 0.408969i | − | 0.0168370i | ||||||
\(591\) | 3.89503i | 0.160220i | ||||||||
\(592\) | − | 26.8914i | − | 1.10523i | ||||||
\(593\) | − | 1.21338i | − | 0.0498276i | −0.999690 | − | 0.0249138i | \(-0.992069\pi\) | ||
0.999690 | − | 0.0249138i | \(-0.00793113\pi\) | |||||||
\(594\) | −11.1792 | −0.458689 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5.82125i | − | 0.238448i | ||||||
\(597\) | −29.4885 | −1.20688 | ||||||||
\(598\) | −0.551318 | − | 0.339240i | −0.0225451 | − | 0.0138725i | ||||
\(599\) | 32.6638 | 1.33461 | 0.667303 | − | 0.744786i | \(-0.267449\pi\) | ||||
0.667303 | + | 0.744786i | \(0.267449\pi\) | |||||||
\(600\) | − | 5.49224i | − | 0.224220i | ||||||
\(601\) | −2.50114 | −0.102024 | −0.0510118 | − | 0.998698i | \(-0.516245\pi\) | ||||
−0.0510118 | + | 0.998698i | \(0.516245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.857671i | 0.0349271i | ||||||||
\(604\) | − | 4.81611i | − | 0.195965i | ||||||
\(605\) | 35.3656i | 1.43781i | ||||||||
\(606\) | 0.0343672i | 0.00139607i | ||||||||
\(607\) | −12.6456 | −0.513271 | −0.256635 | − | 0.966508i | \(-0.582614\pi\) | ||||
−0.256635 | + | 0.966508i | \(0.582614\pi\) | |||||||
\(608\) | 7.24055 | 0.293643 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.25726 | −0.131883 | ||||||||
\(611\) | −19.2256 | − | 11.8300i | −0.777787 | − | 0.478591i | ||||
\(612\) | −7.10672 | −0.287272 | ||||||||
\(613\) | 20.0280i | 0.808923i | 0.914555 | + | 0.404462i | \(0.132541\pi\) | ||||
−0.914555 | + | 0.404462i | \(0.867459\pi\) | |||||||
\(614\) | −4.59608 | −0.185483 | ||||||||
\(615\) | −15.9409 | −0.642801 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 45.2926i | − | 1.82341i | −0.410846 | − | 0.911705i | \(-0.634767\pi\) | ||
0.410846 | − | 0.911705i | \(-0.365233\pi\) | |||||||
\(618\) | − | 3.07539i | − | 0.123710i | ||||||
\(619\) | − | 4.43315i | − | 0.178183i | −0.996023 | − | 0.0890917i | \(-0.971604\pi\) | ||
0.996023 | − | 0.0890917i | \(-0.0283964\pi\) | |||||||
\(620\) | 16.6842 | 0.670055 | ||||||||
\(621\) | 3.05080 | 0.122424 | ||||||||
\(622\) | 10.2087i | 0.409332i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.23889 | − | 15.0147i | 0.369852 | − | 0.601067i | ||||
\(625\) | −1.97997 | −0.0791988 | ||||||||
\(626\) | − | 3.68494i | − | 0.147280i | ||||||
\(627\) | −17.0179 | −0.679631 | ||||||||
\(628\) | 17.7786 | 0.709444 | ||||||||
\(629\) | − | 34.7544i | − | 1.38575i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.7358i | − | 0.785672i | −0.919609 | − | 0.392836i | \(-0.871494\pi\) | ||
0.919609 | − | 0.392836i | \(-0.128506\pi\) | |||||||
\(632\) | − | 0.169516i | − | 0.00674300i | ||||||
\(633\) | −19.1629 | −0.761658 | ||||||||
\(634\) | 7.93824 | 0.315268 | ||||||||
\(635\) | 20.8100i | 0.825819i | ||||||||
\(636\) | 7.66574 | 0.303967 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.1693 | −0.560968 | ||||||||
\(639\) | − | 3.26891i | − | 0.129316i | ||||||
\(640\) | 13.3221 | 0.526603 | ||||||||
\(641\) | −39.6425 | −1.56579 | −0.782893 | − | 0.622157i | \(-0.786257\pi\) | ||||
−0.782893 | + | 0.622157i | \(0.786257\pi\) | |||||||
\(642\) | − | 3.76018i | − | 0.148402i | ||||||
\(643\) | 20.8300i | 0.821453i | 0.911759 | + | 0.410727i | \(0.134725\pi\) | ||||
−0.911759 | + | 0.410727i | \(0.865275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 8.96568i | − | 0.353023i | ||||||
\(646\) | 2.81642 | 0.110810 | ||||||||
\(647\) | −15.7441 | −0.618965 | −0.309482 | − | 0.950905i | \(-0.600156\pi\) | ||||
−0.309482 | + | 0.950905i | \(0.600156\pi\) | |||||||
\(648\) | − | 7.28927i | − | 0.286350i | ||||||
\(649\) | 5.06874 | 0.198966 | ||||||||
\(650\) | −2.97028 | − | 1.82769i | −0.116504 | − | 0.0716877i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 1.31352i | − | 0.0514413i | ||||||
\(653\) | −27.0264 | −1.05762 | −0.528812 | − | 0.848739i | \(-0.677362\pi\) | ||||
−0.528812 | + | 0.848739i | \(0.677362\pi\) | |||||||
\(654\) | −0.0162849 | −0.000636789 | ||||||||
\(655\) | − | 13.6876i | − | 0.534817i | ||||||
\(656\) | 25.2998i | 0.987792i | ||||||||
\(657\) | 7.93734i | 0.309665i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.79491 | −0.264692 | −0.132346 | − | 0.991204i | \(-0.542251\pi\) | ||||
−0.132346 | + | 0.991204i | \(0.542251\pi\) | |||||||
\(660\) | −23.7468 | −0.924344 | ||||||||
\(661\) | − | 7.20526i | − | 0.280252i | −0.990134 | − | 0.140126i | \(-0.955249\pi\) | ||
0.990134 | − | 0.140126i | \(-0.0447508\pi\) | |||||||
\(662\) | 6.09044 | 0.236712 | ||||||||
\(663\) | 11.9403 | − | 19.4049i | 0.463724 | − | 0.753625i | ||||
\(664\) | 3.44930 | 0.133859 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.31866 | −0.0898463 | ||||||||
\(667\) | 3.86679 | 0.149723 | ||||||||
\(668\) | 26.4231i | 1.02234i | ||||||||
\(669\) | − | 3.24571i | − | 0.125486i | ||||||
\(670\) | − | 0.474293i | − | 0.0183236i | ||||||
\(671\) | − | 40.3703i | − | 1.55848i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.32130 | −0.320763 | −0.160381 | − | 0.987055i | \(-0.551272\pi\) | ||||
−0.160381 | + | 0.987055i | \(0.551272\pi\) | |||||||
\(674\) | 2.39896i | 0.0924044i | ||||||||
\(675\) | 16.4365 | 0.632640 | ||||||||
\(676\) | −11.0715 | − | 21.9273i | −0.425825 | − | 0.843357i | ||||
\(677\) | 29.9956 | 1.15283 | 0.576413 | − | 0.817159i | \(-0.304452\pi\) | ||||
0.576413 | + | 0.817159i | \(0.304452\pi\) | |||||||
\(678\) | 4.46391i | 0.171435i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.08982 | 0.310231 | ||||||||
\(681\) | 39.5682i | 1.51626i | ||||||||
\(682\) | − | 12.0899i | − | 0.462944i | ||||||
\(683\) | − | 36.0839i | − | 1.38071i | −0.723469 | − | 0.690356i | \(-0.757454\pi\) | ||
0.723469 | − | 0.690356i | \(-0.242546\pi\) | |||||||
\(684\) | 3.21380i | 0.122883i | ||||||||
\(685\) | −24.0064 | −0.917236 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.7205i | 1.05760i | ||||||||
\(688\) | −14.2294 | −0.542491 | ||||||||
\(689\) | 5.25109 | − | 8.53386i | 0.200051 | − | 0.325114i | ||||
\(690\) | −0.378889 | −0.0144241 | ||||||||
\(691\) | − | 25.7677i | − | 0.980248i | −0.871653 | − | 0.490124i | \(-0.836951\pi\) | ||
0.871653 | − | 0.490124i | \(-0.163049\pi\) | |||||||
\(692\) | −10.2724 | −0.390497 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 7.00589i | − | 0.265940i | ||||||
\(695\) | 26.7119i | 1.01324i | ||||||||
\(696\) | − | 13.5100i | − | 0.512096i | ||||||
\(697\) | 32.6974i | 1.23850i | ||||||||
\(698\) | 10.2248 | 0.387016 | ||||||||
\(699\) | 31.7369 | 1.20040 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.7872 | −1.57828 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(702\) | −5.76457 | − | 3.54708i | −0.217570 | − | 0.133876i | ||||
\(703\) | −15.7167 | −0.592765 | ||||||||
\(704\) | 32.5708i | 1.22756i | ||||||||
\(705\) | −13.2127 | −0.497619 | ||||||||
\(706\) | 2.03471 | 0.0765774 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.34782i | 0.0882364i | ||||||||
\(709\) | 0.343847i | 0.0129135i | 0.999979 | + | 0.00645673i | \(0.00205525\pi\) | ||||
−0.999979 | + | 0.00645673i | \(0.997945\pi\) | |||||||
\(710\) | 1.80771i | 0.0678421i | ||||||||
\(711\) | 0.113931 | 0.00427276 | ||||||||
\(712\) | −12.5625 | −0.470799 | ||||||||
\(713\) | 3.29931i | 0.123560i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.2668 | + | 26.4361i | −0.608342 | + | 0.988652i | ||||
\(716\) | −10.1245 | −0.378372 | ||||||||
\(717\) | − | 29.1523i | − | 1.08871i | ||||||
\(718\) | −6.45761 | −0.240996 | ||||||||
\(719\) | 8.78010 | 0.327443 | 0.163721 | − | 0.986507i | \(-0.447650\pi\) | ||||
0.163721 | + | 0.986507i | \(0.447650\pi\) | |||||||
\(720\) | 4.20702i | 0.156786i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.04149i | 0.187625i | ||||||||
\(723\) | − | 4.71598i | − | 0.175389i | ||||||
\(724\) | 14.2473 | 0.529498 | ||||||||
\(725\) | 20.8327 | 0.773707 | ||||||||
\(726\) | 11.8702i | 0.440546i | ||||||||
\(727\) | −17.3658 | −0.644064 | −0.322032 | − | 0.946729i | \(-0.604366\pi\) | ||||
−0.322032 | + | 0.946729i | \(0.604366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.6343 | 1.09757 | ||||||||
\(730\) | − | 4.38936i | − | 0.162458i | ||||||
\(731\) | −18.3900 | −0.680180 | ||||||||
\(732\) | 18.6994 | 0.691148 | ||||||||
\(733\) | − | 9.05895i | − | 0.334600i | −0.985906 | − | 0.167300i | \(-0.946495\pi\) | ||
0.985906 | − | 0.167300i | \(-0.0535048\pi\) | |||||||
\(734\) | 1.79638i | 0.0663056i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.99796i | 0.0736458i | ||||||||
\(737\) | 5.87837 | 0.216533 | ||||||||
\(738\) | 2.18143 | 0.0802995 | ||||||||
\(739\) | − | 7.07843i | − | 0.260384i | −0.991489 | − | 0.130192i | \(-0.958441\pi\) | ||
0.991489 | − | 0.130192i | \(-0.0415594\pi\) | |||||||
\(740\) | −21.9310 | −0.806201 | ||||||||
\(741\) | −8.77531 | − | 5.39966i | −0.322369 | − | 0.198362i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.6779i | 0.538479i | 0.963073 | + | 0.269240i | \(0.0867724\pi\) | ||||
−0.963073 | + | 0.269240i | \(0.913228\pi\) | |||||||
\(744\) | 11.5273 | 0.422613 | ||||||||
\(745\) | −4.45367 | −0.163170 | ||||||||
\(746\) | 5.40132i | 0.197756i | ||||||||
\(747\) | 2.31827i | 0.0848209i | ||||||||
\(748\) | 48.7085i | 1.78096i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.54848 | −0.202602 | ||||||||
\(751\) | 31.7113 | 1.15716 | 0.578580 | − | 0.815626i | \(-0.303607\pi\) | ||||
0.578580 | + | 0.815626i | \(0.303607\pi\) | |||||||
\(752\) | 20.9698i | 0.764691i | ||||||||
\(753\) | −18.2358 | −0.664548 | ||||||||
\(754\) | −7.30640 | − | 4.49581i | −0.266083 | − | 0.163728i | ||||
\(755\) | −3.68467 | −0.134099 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5317 | 0.564510 | 0.282255 | − | 0.959339i | \(-0.408918\pi\) | ||||
0.282255 | + | 0.959339i | \(0.408918\pi\) | |||||||
\(758\) | −8.36688 | −0.303899 | ||||||||
\(759\) | − | 4.69594i | − | 0.170452i | ||||||
\(760\) | − | 3.65839i | − | 0.132704i | ||||||
\(761\) | − | 0.250369i | − | 0.00907587i | −0.999990 | − | 0.00453794i | \(-0.998556\pi\) | ||
0.999990 | − | 0.00453794i | \(-0.00144447\pi\) | |||||||
\(762\) | 6.98474i | 0.253030i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25.5961 | 0.926036 | ||||||||
\(765\) | 5.43714i | 0.196580i | ||||||||
\(766\) | 1.26781 | 0.0458077 | ||||||||
\(767\) | 2.61370 | + | 1.60827i | 0.0943752 | + | 0.0580714i | ||||
\(768\) | −11.4972 | −0.414869 | ||||||||
\(769\) | − | 24.0146i | − | 0.865988i | −0.901397 | − | 0.432994i | \(-0.857457\pi\) | ||
0.901397 | − | 0.432994i | \(-0.142543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.50731 | −0.306383 | ||||||||
\(772\) | − | 35.0625i | − | 1.26193i | ||||||
\(773\) | 30.5062i | 1.09723i | 0.836074 | + | 0.548616i | \(0.184845\pi\) | ||||
−0.836074 | + | 0.548616i | \(0.815155\pi\) | |||||||
\(774\) | 1.22690i | 0.0441001i | ||||||||
\(775\) | 17.7754i | 0.638510i | ||||||||
\(776\) | 8.51064 | 0.305514 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.954237i | 0.0342110i | ||||||||
\(779\) | 14.7865 | 0.529780 | ||||||||
\(780\) | −12.2451 | − | 7.53469i | −0.438443 | − | 0.269785i | ||||
\(781\) | −22.4047 | −0.801702 | ||||||||
\(782\) | 0.777163i | 0.0277913i | ||||||||
\(783\) | 40.4311 | 1.44489 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 13.6019i | − | 0.485473i | ||||||
\(786\) | − | 4.59414i | − | 0.163868i | ||||||
\(787\) | − | 19.8492i | − | 0.707548i | −0.935331 | − | 0.353774i | \(-0.884898\pi\) | ||
0.935331 | − | 0.353774i | \(-0.115102\pi\) | |||||||
\(788\) | − | 5.04149i | − | 0.179596i | ||||||
\(789\) | −25.5686 | −0.910268 | ||||||||
\(790\) | −0.0630042 | −0.00224159 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.68923 | 0.237691 | ||||||||
\(793\) | 12.8092 | − | 20.8170i | 0.454868 | − | 0.739233i | ||||
\(794\) | 6.35448 | 0.225512 | ||||||||
\(795\) | − | 5.86484i | − | 0.208004i | ||||||
\(796\) | 38.1682 | 1.35284 | ||||||||
\(797\) | 52.2894 | 1.85219 | 0.926093 | − | 0.377296i | \(-0.123146\pi\) | ||||
0.926093 | + | 0.377296i | \(0.123146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1014i | 0.958777i | ||||||||
\(800\) | 10.7642i | 0.380572i | ||||||||
\(801\) | − | 8.44319i | − | 0.298326i | ||||||
\(802\) | 0.996542 | 0.0351891 | ||||||||
\(803\) | 54.4015 | 1.91979 | ||||||||
\(804\) | 2.72283i | 0.0960269i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.83602 | − | 6.23414i | 0.135118 | − | 0.219588i | ||||
\(807\) | 32.5963 | 1.14744 | ||||||||
\(808\) | − | 0.0915664i | − | 0.00322129i | ||||||
\(809\) | −2.36460 | −0.0831349 | −0.0415674 | − | 0.999136i | \(-0.513235\pi\) | ||||
−0.0415674 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(810\) | −2.70920 | −0.0951917 | ||||||||
\(811\) | 23.6646i | 0.830978i | 0.909598 | + | 0.415489i | \(0.136390\pi\) | ||||
−0.909598 | + | 0.415489i | \(0.863610\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.4952i | 1.35008i | ||||||||
\(814\) | 15.8918i | 0.557008i | ||||||||
\(815\) | −1.00493 | −0.0352013 | ||||||||
\(816\) | −21.1654 | −0.740936 | ||||||||
\(817\) | 8.31636i | 0.290953i | ||||||||
\(818\) | −11.3275 | −0.396058 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.6330 | 0.720536 | ||||||||
\(821\) | 3.57753i | 0.124857i | 0.998049 | + | 0.0624284i | \(0.0198845\pi\) | ||||
−0.998049 | + | 0.0624284i | \(0.980115\pi\) | |||||||
\(822\) | −8.05759 | −0.281041 | ||||||||
\(823\) | 29.9422 | 1.04372 | 0.521859 | − | 0.853032i | \(-0.325239\pi\) | ||||
0.521859 | + | 0.853032i | \(0.325239\pi\) | |||||||
\(824\) | 8.19393i | 0.285449i | ||||||||
\(825\) | − | 25.2998i | − | 0.880827i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.32620i | − | 0.324304i | −0.986766 | − | 0.162152i | \(-0.948157\pi\) | ||
0.986766 | − | 0.162152i | \(-0.0518435\pi\) | |||||||
\(828\) | −0.886819 | −0.0308191 | ||||||||
\(829\) | 38.2268 | 1.32767 | 0.663836 | − | 0.747878i | \(-0.268927\pi\) | ||||
0.663836 | + | 0.747878i | \(0.268927\pi\) | |||||||
\(830\) | − | 1.28200i | − | 0.0444990i | ||||||
\(831\) | −13.6877 | −0.474821 | ||||||||
\(832\) | −10.3345 | + | 16.7951i | −0.358283 | + | 0.582266i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.96568i | 0.310456i | ||||||||
\(835\) | 20.2155 | 0.699587 | ||||||||
\(836\) | 22.0270 | 0.761820 | ||||||||
\(837\) | 34.4975i | 1.19241i | ||||||||
\(838\) | − | 11.5587i | − | 0.399287i | ||||||
\(839\) | 23.4981i | 0.811244i | 0.914041 | + | 0.405622i | \(0.132945\pi\) | ||||
−0.914041 | + | 0.405622i | \(0.867055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2451 | 0.767071 | ||||||||
\(842\) | 8.02356 | 0.276510 | ||||||||
\(843\) | − | 25.9491i | − | 0.893736i | ||||||
\(844\) | 24.8034 | 0.853767 | ||||||||
\(845\) | −16.7759 | + | 8.47044i | −0.577109 | + | 0.291392i | ||||
\(846\) | 1.80808 | 0.0621632 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.30806 | −0.319640 | ||||||||
\(849\) | 14.0241 | 0.481306 | ||||||||
\(850\) | 4.18704i | 0.143614i | ||||||||
\(851\) | − | 4.33686i | − | 0.148666i | ||||||
\(852\) | − | 10.3777i | − | 0.355535i | ||||||
\(853\) | 40.9295i | 1.40140i | 0.713456 | + | 0.700700i | \(0.247129\pi\) | ||||
−0.713456 | + | 0.700700i | \(0.752871\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.45879 | 0.0840888 | ||||||||
\(856\) | 10.0185i | 0.342424i | ||||||||
\(857\) | −11.6620 | −0.398366 | −0.199183 | − | 0.979962i | \(-0.563829\pi\) | ||||
−0.199183 | + | 0.979962i | \(0.563829\pi\) | |||||||
\(858\) | −5.45984 | + | 8.87310i | −0.186396 | + | 0.302923i | ||||
\(859\) | −28.2776 | −0.964820 | −0.482410 | − | 0.875945i | \(-0.660238\pi\) | ||||
−0.482410 | + | 0.875945i | \(0.660238\pi\) | |||||||
\(860\) | 11.6046i | 0.395715i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.58369 | 0.0539407 | ||||||||
\(863\) | 11.4442i | 0.389567i | 0.980846 | + | 0.194783i | \(0.0624004\pi\) | ||||
−0.980846 | + | 0.194783i | \(0.937600\pi\) | |||||||
\(864\) | 20.8906i | 0.710713i | ||||||||
\(865\) | 7.85909i | 0.267217i | ||||||||
\(866\) | 7.31993i | 0.248741i | ||||||||
\(867\) | −2.53683 | −0.0861553 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 0.780871i | − | 0.0264892i | ||||||
\(870\) | −5.02127 | −0.170237 | ||||||||
\(871\) | 3.03118 | + | 1.86516i | 0.102708 | + | 0.0631986i | ||||
\(872\) | 0.0433887 | 0.00146933 | ||||||||
\(873\) | 5.71997i | 0.193592i | ||||||||
\(874\) | 0.351449 | 0.0118879 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 25.1985i | 0.851380i | ||||||||
\(877\) | 56.3486i | 1.90276i | 0.308026 | + | 0.951378i | \(0.400332\pi\) | ||||
−0.308026 | + | 0.951378i | \(0.599668\pi\) | |||||||
\(878\) | 1.14084i | 0.0385016i | ||||||||
\(879\) | 16.9835i | 0.572838i | ||||||||
\(880\) | 28.8344 | 0.972006 | ||||||||
\(881\) | −1.16418 | −0.0392221 | −0.0196111 | − | 0.999808i | \(-0.506243\pi\) | ||||
−0.0196111 | + | 0.999808i | \(0.506243\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.1881 | 0.410162 | 0.205081 | − | 0.978745i | \(-0.434254\pi\) | ||||
0.205081 | + | 0.978745i | \(0.434254\pi\) | |||||||
\(884\) | −15.4548 | + | 25.1166i | −0.519803 | + | 0.844762i | ||||
\(885\) | 1.79625 | 0.0603802 | ||||||||
\(886\) | − | 2.89364i | − | 0.0972138i | ||||||
\(887\) | −30.6641 | −1.02960 | −0.514799 | − | 0.857311i | \(-0.672134\pi\) | ||||
−0.514799 | + | 0.857311i | \(0.672134\pi\) | |||||||
\(888\) | −15.1524 | −0.508481 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.66910i | 0.156509i | ||||||||
\(891\) | − | 33.5778i | − | 1.12490i | ||||||
\(892\) | 4.20105i | 0.140662i | ||||||||
\(893\) | 12.2558 | 0.410125 | ||||||||
\(894\) | −1.49485 | −0.0499952 | ||||||||
\(895\) | 7.74598i | 0.258920i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.48999 | − | 2.42146i | 0.0497492 | − | 0.0808503i | ||||
\(898\) | −5.85378 | −0.195343 | ||||||||
\(899\) | 43.7245i | 1.45829i | ||||||||
\(900\) | −4.77782 | −0.159261 | ||||||||
\(901\) | −12.0297 | −0.400768 | ||||||||
\(902\) | − | 14.9512i | − | 0.497822i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 11.8934i | − | 0.395570i | ||||||
\(905\) | − | 10.9002i | − | 0.362336i | ||||||
\(906\) | −1.23674 | −0.0410878 | ||||||||
\(907\) | 11.6479 | 0.386763 | 0.193382 | − | 0.981124i | \(-0.438054\pi\) | ||||
0.193382 | + | 0.981124i | \(0.438054\pi\) | |||||||
\(908\) | − | 51.2147i | − | 1.69962i | ||||||
\(909\) | 0.0615414 | 0.00204120 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5833 | −0.880743 | −0.440371 | − | 0.897816i | \(-0.645153\pi\) | ||||
−0.440371 | + | 0.897816i | \(0.645153\pi\) | |||||||
\(912\) | 9.57141i | 0.316941i | ||||||||
\(913\) | 15.8891 | 0.525852 | ||||||||
\(914\) | −3.01553 | −0.0997450 | ||||||||
\(915\) | − | 14.3063i | − | 0.472953i | ||||||
\(916\) | − | 35.8797i | − | 1.18550i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.12600i | 0.268198i | ||||||||
\(919\) | −45.7079 | −1.50777 | −0.753883 | − | 0.657009i | \(-0.771821\pi\) | ||||
−0.753883 | + | 0.657009i | \(0.771821\pi\) | |||||||
\(920\) | 1.00950 | 0.0332821 | ||||||||
\(921\) | − | 20.1866i | − | 0.665171i | ||||||
\(922\) | −2.18809 | −0.0720609 | ||||||||
\(923\) | −11.5530 | − | 7.10883i | −0.380271 | − | 0.233990i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 23.3653i | − | 0.768246i | ||||||
\(926\) | −1.15448 | −0.0379387 | ||||||||
\(927\) | −5.50711 | −0.180877 | ||||||||
\(928\) | 26.4782i | 0.869189i | ||||||||
\(929\) | − | 11.0651i | − | 0.363035i | −0.983388 | − | 0.181518i | \(-0.941899\pi\) | ||
0.983388 | − | 0.181518i | \(-0.0581009\pi\) | |||||||
\(930\) | − | 4.28437i | − | 0.140490i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −41.0784 | −1.34557 | ||||||||
\(933\) | −44.8380 | −1.46793 | ||||||||
\(934\) | 9.89994i | 0.323936i | ||||||||
\(935\) | 37.2655 | 1.21871 | ||||||||
\(936\) | 3.44930 | + | 2.12244i | 0.112744 | + | 0.0693742i | ||||
\(937\) | 57.6584 | 1.88362 | 0.941808 | − | 0.336150i | \(-0.109125\pi\) | ||||
0.941808 | + | 0.336150i | \(0.109125\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.1848 | 0.528170 | ||||||||
\(940\) | 17.1017 | 0.557797 | ||||||||
\(941\) | − | 16.9745i | − | 0.553351i | −0.960963 | − | 0.276676i | \(-0.910767\pi\) | ||
0.960963 | − | 0.276676i | \(-0.0892328\pi\) | |||||||
\(942\) | − | 4.56540i | − | 0.148749i | ||||||
\(943\) | 4.08018i | 0.132869i | ||||||||
\(944\) | − | 2.85082i | − | 0.0927862i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.40904 | 0.273401 | ||||||||
\(947\) | − | 16.6962i | − | 0.542552i | −0.962502 | − | 0.271276i | \(-0.912554\pi\) | ||
0.962502 | − | 0.271276i | \(-0.0874457\pi\) | |||||||
\(948\) | 0.361696 | 0.0117473 | ||||||||
\(949\) | 28.0522 | + | 17.2612i | 0.910612 | + | 0.560322i | ||||
\(950\) | 1.89347 | 0.0614322 | ||||||||
\(951\) | 34.8658i | 1.13060i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.2473 | 0.591089 | 0.295545 | − | 0.955329i | \(-0.404499\pi\) | ||||
0.295545 | + | 0.955329i | \(0.404499\pi\) | |||||||
\(954\) | 0.802570i | 0.0259842i | ||||||||
\(955\) | − | 19.5829i | − | 0.633687i | ||||||
\(956\) | 37.7330i | 1.22037i | ||||||||
\(957\) | − | 62.2334i | − | 2.01172i | ||||||
\(958\) | 11.6948 | 0.377841 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 11.5423i | 0.372527i | ||||||||
\(961\) | −6.30763 | −0.203472 | ||||||||
\(962\) | −5.04235 | + | 8.19462i | −0.162572 | + | 0.264205i | ||||
\(963\) | −6.73337 | −0.216980 | ||||||||
\(964\) | 6.10408i | 0.196599i | ||||||||
\(965\) | −26.8253 | −0.863537 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.5845i | 0.951374i | 0.879615 | + | 0.475687i | \(0.157801\pi\) | ||||
−0.879615 | + | 0.475687i | \(0.842199\pi\) | |||||||
\(968\) | − | 31.6265i | − | 1.01652i | ||||||
\(969\) | 12.3701i | 0.397384i | ||||||||
\(970\) | − | 3.16315i | − | 0.101563i | ||||||
\(971\) | −15.1301 | −0.485548 | −0.242774 | − | 0.970083i | \(-0.578057\pi\) | ||||
−0.242774 | + | 0.970083i | \(0.578057\pi\) | |||||||
\(972\) | −16.4627 | −0.528040 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.598787 | −0.0191864 | ||||||||
\(975\) | 8.02744 | − | 13.0459i | 0.257084 | − | 0.417802i | ||||
\(976\) | −22.7055 | −0.726786 | ||||||||
\(977\) | − | 32.4636i | − | 1.03860i | −0.854591 | − | 0.519301i | \(-0.826192\pi\) | ||
0.854591 | − | 0.519301i | \(-0.173808\pi\) | |||||||
\(978\) | −0.337300 | −0.0107857 | ||||||||
\(979\) | −57.8686 | −1.84949 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0291614i | 0.000931052i | ||||||||
\(982\) | 2.72322i | 0.0869016i | ||||||||
\(983\) | 44.2945i | 1.41278i | 0.707825 | + | 0.706388i | \(0.249677\pi\) | ||||
−0.707825 | + | 0.706388i | \(0.750323\pi\) | |||||||
\(984\) | 14.2556 | 0.454452 | ||||||||
\(985\) | −3.85710 | −0.122897 | ||||||||
\(986\) | 10.2994i | 0.328001i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.3582 | + | 6.98900i | 0.361354 | + | 0.222350i | ||||
\(989\) | −2.29482 | −0.0729710 | ||||||||
\(990\) | − | 2.48619i | − | 0.0790163i | ||||||
\(991\) | −8.52117 | −0.270684 | −0.135342 | − | 0.990799i | \(-0.543213\pi\) | ||||
−0.135342 | + | 0.990799i | \(0.543213\pi\) | |||||||
\(992\) | −22.5923 | −0.717307 | ||||||||
\(993\) | 26.7500i | 0.848887i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 29.2014i | − | 0.925746i | ||||||
\(996\) | 7.35976i | 0.233203i | ||||||||
\(997\) | 6.77905 | 0.214695 | 0.107347 | − | 0.994222i | \(-0.465764\pi\) | ||||
0.107347 | + | 0.994222i | \(0.465764\pi\) | |||||||
\(998\) | −12.1372 | −0.384195 | ||||||||
\(999\) | − | 45.3462i | − | 1.43469i |
(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 | 637.2.c.e.246.5 | 8 | ||
7.2 | even | 3 | 637.2.r.f.116.5 | 16 | |||
7.3 | odd | 6 | 91.2.r.a.51.4 | yes | 16 | ||
7.4 | even | 3 | 637.2.r.f.324.4 | 16 | |||
7.5 | odd | 6 | 91.2.r.a.25.5 | yes | 16 | ||
7.6 | odd | 2 | 637.2.c.f.246.5 | 8 | |||
13.5 | odd | 4 | 8281.2.a.cj.1.5 | 8 | |||
13.8 | odd | 4 | 8281.2.a.cj.1.4 | 8 | |||
13.12 | even | 2 | inner | 637.2.c.e.246.4 | 8 | ||
21.5 | even | 6 | 819.2.dl.e.298.4 | 16 | |||
21.17 | even | 6 | 819.2.dl.e.415.5 | 16 | |||
91.5 | even | 12 | 1183.2.e.i.508.4 | 16 | |||
91.12 | odd | 6 | 91.2.r.a.25.4 | ✓ | 16 | ||
91.25 | even | 6 | 637.2.r.f.324.5 | 16 | |||
91.31 | even | 12 | 1183.2.e.i.170.4 | 16 | |||
91.34 | even | 4 | 8281.2.a.ck.1.4 | 8 | |||
91.38 | odd | 6 | 91.2.r.a.51.5 | yes | 16 | ||
91.47 | even | 12 | 1183.2.e.i.508.5 | 16 | |||
91.51 | even | 6 | 637.2.r.f.116.4 | 16 | |||
91.73 | even | 12 | 1183.2.e.i.170.5 | 16 | |||
91.83 | even | 4 | 8281.2.a.ck.1.5 | 8 | |||
91.90 | odd | 2 | 637.2.c.f.246.4 | 8 | |||
273.38 | even | 6 | 819.2.dl.e.415.4 | 16 | |||
273.194 | even | 6 | 819.2.dl.e.298.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.4 | ✓ | 16 | 91.12 | odd | 6 | ||
91.2.r.a.25.5 | yes | 16 | 7.5 | odd | 6 | ||
91.2.r.a.51.4 | yes | 16 | 7.3 | odd | 6 | ||
91.2.r.a.51.5 | yes | 16 | 91.38 | odd | 6 | ||
637.2.c.e.246.4 | 8 | 13.12 | even | 2 | inner | ||
637.2.c.e.246.5 | 8 | 1.1 | even | 1 | trivial | ||
637.2.c.f.246.4 | 8 | 91.90 | odd | 2 | |||
637.2.c.f.246.5 | 8 | 7.6 | odd | 2 | |||
637.2.r.f.116.4 | 16 | 91.51 | even | 6 | |||
637.2.r.f.116.5 | 16 | 7.2 | even | 3 | |||
637.2.r.f.324.4 | 16 | 7.4 | even | 3 | |||
637.2.r.f.324.5 | 16 | 91.25 | even | 6 | |||
819.2.dl.e.298.4 | 16 | 21.5 | even | 6 | |||
819.2.dl.e.298.5 | 16 | 273.194 | even | 6 | |||
819.2.dl.e.415.4 | 16 | 273.38 | even | 6 | |||
819.2.dl.e.415.5 | 16 | 21.17 | even | 6 | |||
1183.2.e.i.170.4 | 16 | 91.31 | even | 12 | |||
1183.2.e.i.170.5 | 16 | 91.73 | even | 12 | |||
1183.2.e.i.508.4 | 16 | 91.5 | even | 12 | |||
1183.2.e.i.508.5 | 16 | 91.47 | even | 12 | |||
8281.2.a.cj.1.4 | 8 | 13.8 | odd | 4 | |||
8281.2.a.cj.1.5 | 8 | 13.5 | odd | 4 | |||
8281.2.a.ck.1.4 | 8 | 91.34 | even | 4 | |||
8281.2.a.ck.1.5 | 8 | 91.83 | even | 4 |