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 | 246.4 | ||
Root | \(-0.332375i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.f.246.5 |
$q$-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 | \(-0.962508\pi\) | ||
0.993071 | − | 0.117512i | \(-0.0374920\pi\) | |||||||
\(3\) | 1.45984 | 0.842837 | 0.421419 | − | 0.906866i | \(-0.361532\pi\) | ||||
0.421419 | + | 0.906866i | \(0.361532\pi\) | |||||||
\(4\) | 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 | \(-0.645183\pi\) | ||
0.440456 | − | 0.897774i | \(-0.354817\pi\) | |||||||
\(12\) | 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 | \(-0.675910\pi\) | ||||
−0.524933 | + | 0.851143i | \(0.675910\pi\) | |||||||
\(18\) | 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 | \(0.229429\pi\) | ||||
−0.751297 | + | 0.659964i | \(0.770571\pi\) | |||||||
\(38\) | −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 | \(-0.357107\pi\) | ||||
0.433984 | + | 0.900920i | \(0.357107\pi\) | |||||||
\(62\) | 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 | \(0.0192048\pi\) | ||||
−0.998180 | + | 0.0602971i | \(0.980795\pi\) | |||||||
\(68\) | −8.17922 | −0.991876 | ||||||||
\(69\) | 0.788550 | 0.0949302 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.76223i | − | 0.446494i | −0.974762 | − | 0.223247i | \(-0.928334\pi\) | ||
0.974762 | − | 0.223247i | \(-0.0716657\pi\) | |||||||
\(72\) | 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 | \(-0.498878\pi\) | ||||
0.00352387 | + | 0.999994i | \(0.498878\pi\) | |||||||
\(102\) | 2.10035i | 0.207966i | ||||||||
\(103\) | −6.33821 | −0.624522 | −0.312261 | − | 0.949996i | \(-0.601086\pi\) | ||||
−0.312261 | + | 0.949996i | \(0.601086\pi\) | |||||||
\(104\) | 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 | \(0.000511633\pi\) | ||||
−0.999999 | + | 0.00160734i | \(0.999488\pi\) | |||||||
\(110\) | 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 | \(-0.635737\pi\) | ||||
−0.413624 | + | 0.910448i | \(0.635737\pi\) | |||||||
\(132\) | − | 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 | \(0.251027\pi\) | ||||
−0.704822 | + | 0.709384i | \(0.748973\pi\) | |||||||
\(138\) | − | 0.262094i | − | 0.0223110i | ||||||
\(139\) | 18.4778 | 1.56726 | 0.783632 | − | 0.621225i | \(-0.213365\pi\) | ||||
0.783632 | + | 0.621225i | \(0.213365\pi\) | |||||||
\(140\) | 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 | \(0.0402763\pi\) | ||||
−0.992006 | + | 0.126195i | \(0.959724\pi\) | |||||||
\(150\) | − | 1.41206i | − | 0.115294i | ||||||
\(151\) | 2.54885i | 0.207422i | 0.994607 | + | 0.103711i | \(0.0330717\pi\) | ||||
−0.994607 | + | 0.103711i | \(0.966928\pi\) | |||||||
\(152\) | −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 | \(-0.622516\pi\) | ||||
−0.375461 | + | 0.926838i | \(0.622516\pi\) | |||||||
\(158\) | 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 | \(0.00866688\pi\) | ||||
−0.999629 | + | 0.0272244i | \(0.991333\pi\) | |||||||
\(164\) | 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 | \(-0.433739\pi\) | ||||
0.206664 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(174\) | − | 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 | \(-0.590410\pi\) | ||||
−0.280228 | + | 0.959933i | \(0.590410\pi\) | |||||||
\(182\) | 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 | \(0.232787\pi\) | ||||
−0.744293 | + | 0.667853i | \(0.767213\pi\) | |||||||
\(194\) | −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 | \(0.0303004\pi\) | ||||
−0.995473 | + | 0.0950480i | \(0.969700\pi\) | |||||||
\(198\) | 1.71981 | 0.122221 | ||||||||
\(199\) | −20.1999 | −1.43193 | −0.715965 | − | 0.698136i | \(-0.754013\pi\) | ||||
−0.715965 | + | 0.698136i | \(0.754013\pi\) | |||||||
\(200\) | − | 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 | \(-0.776499\pi\) | ||
0.763455 | − | 0.645861i | \(-0.223501\pi\) | |||||||
\(240\) | − | 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 | \(-0.628990\pi\) | ||||
−0.394233 | + | 0.919011i | \(0.628990\pi\) | |||||||
\(252\) | 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 | \(-0.558178\pi\) | ||||
−0.181757 | + | 0.983343i | \(0.558178\pi\) | |||||||
\(258\) | 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 | \(-0.261675\pi\) | ||||
0.680703 | + | 0.732560i | \(0.261675\pi\) | |||||||
\(270\) | 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 | \(-0.822119\pi\) | ||
0.847876 | − | 0.530195i | \(-0.177881\pi\) | |||||||
\(282\) | 3.03785 | 0.180901 | ||||||||
\(283\) | 9.60662 | 0.571055 | 0.285527 | − | 0.958371i | \(-0.407831\pi\) | ||||
0.285527 | + | 0.958371i | \(0.407831\pi\) | |||||||
\(284\) | − | 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 | \(-0.836416\pi\) | ||||
−0.870827 | + | 0.491590i | \(0.836416\pi\) | |||||||
\(312\) | 5.79534 | − | 3.56601i | 0.328096 | − | 0.201886i | ||||
\(313\) | 11.0867 | 0.626657 | 0.313328 | − | 0.949645i | \(-0.398556\pi\) | ||||
0.313328 | + | 0.949645i | \(0.398556\pi\) | |||||||
\(314\) | 3.12733i | 0.176486i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.247764 | −0.0139378 | ||||||||
\(317\) | 23.8834i | 1.34142i | 0.741718 | + | 0.670712i | \(0.234011\pi\) | ||||
−0.741718 | + | 0.670712i | \(0.765989\pi\) | |||||||
\(318\) | 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 | \(0.167987\pi\) | ||||
−0.863943 | + | 0.503589i | \(0.832013\pi\) | |||||||
\(332\) | − | 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 | \(-0.828644\pi\) | ||
0.858566 | − | 0.512703i | \(-0.171356\pi\) | |||||||
\(360\) | 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 | \(-0.545051\pi\) | ||||
−0.141061 | + | 0.990001i | \(0.545051\pi\) | |||||||
\(368\) | 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 | \(-0.776222\pi\) | ||
0.762893 | − | 0.646525i | \(-0.223778\pi\) | |||||||
\(380\) | −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 | \(0.0238518\pi\) | ||||
−0.997194 | + | 0.0748625i | \(0.976148\pi\) | |||||||
\(402\) | 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 | \(-0.176929\pi\) | ||||
0.849457 | + | 0.527657i | \(0.176929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.1400i | 1.17651i | 0.808674 | + | 0.588257i | \(0.200186\pi\) | ||||
−0.808674 | + | 0.588257i | \(0.799814\pi\) | |||||||
\(422\) | − | 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 | \(0.0366084\pi\) | ||||
−0.993394 | + | 0.114755i | \(0.963392\pi\) | |||||||
\(432\) | −18.9170 | −0.910143 | ||||||||
\(433\) | −22.0231 | −1.05836 | −0.529181 | − | 0.848509i | \(-0.677501\pi\) | ||||
−0.529181 | + | 0.848509i | \(0.677501\pi\) | |||||||
\(434\) | 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 | \(-0.526102\pi\) | ||||
−0.0819097 | + | 0.996640i | \(0.526102\pi\) | |||||||
\(440\) | 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 | \(-0.863579\pi\) | ||
0.909557 | − | 0.415580i | \(-0.136421\pi\) | |||||||
\(450\) | 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 | \(-0.931937\pi\) | ||
0.977226 | − | 0.212201i | \(-0.0680631\pi\) | |||||||
\(458\) | −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 | \(-0.974281\pi\) | ||
0.996737 | − | 0.0807121i | \(-0.0257194\pi\) | |||||||
\(464\) | 23.9766 | 1.11309 | ||||||||
\(465\) | 12.8901 | 0.597766 | ||||||||
\(466\) | 7.22585i | 0.334731i | ||||||||
\(467\) | −29.7854 | −1.37830 | −0.689152 | − | 0.724617i | \(-0.742017\pi\) | ||||
−0.689152 | + | 0.724617i | \(0.742017\pi\) | |||||||
\(468\) | −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 | \(-0.987004\pi\) | ||
0.999167 | − | 0.0408178i | \(-0.0129963\pi\) | |||||||
\(488\) | − | 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 | \(-0.695442\pi\) | ||
0.576141 | − | 0.817350i | \(-0.304558\pi\) | |||||||
\(500\) | − | 21.6070i | − | 0.966293i | ||||||
\(501\) | 20.4143i | 0.912045i | ||||||||
\(502\) | 4.15192i | 0.185309i | ||||||||
\(503\) | −3.02972 | −0.135089 | −0.0675443 | − | 0.997716i | \(-0.521516\pi\) | ||||
−0.0675443 | + | 0.997716i | \(0.521516\pi\) | |||||||
\(504\) | 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 | \(-0.725330\pi\) | ||||
−0.650236 | + | 0.759732i | \(0.725330\pi\) | |||||||
\(522\) | 2.06734i | 0.0904851i | ||||||||
\(523\) | 20.5727 | 0.899583 | 0.449791 | − | 0.893134i | \(-0.351498\pi\) | ||||
0.449791 | + | 0.893134i | \(0.351498\pi\) | |||||||
\(524\) | −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 | \(0.261564\pi\) | ||||
−0.680957 | + | 0.732324i | \(0.738436\pi\) | |||||||
\(542\) | −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 | \(-0.877443\pi\) | ||
0.926789 | − | 0.375581i | \(-0.122557\pi\) | |||||||
\(558\) | −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 | \(-0.329814\pi\) | ||||
0.509545 | + | 0.860444i | \(0.329814\pi\) | |||||||
\(564\) | 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 | \(-0.483755\pi\) | ||||
0.0510118 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(602\) | 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 | \(-0.417386\pi\) | ||||
0.256635 | + | 0.966508i | \(0.417386\pi\) | |||||||
\(608\) | −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 | \(-0.867459\pi\) | ||
0.914555 | − | 0.404462i | \(-0.132541\pi\) | |||||||
\(614\) | 4.59608 | 0.185483 | ||||||||
\(615\) | 15.9409 | 0.642801 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.2926i | 1.82341i | 0.410846 | + | 0.911705i | \(0.365233\pi\) | ||||
−0.410846 | + | 0.911705i | \(0.634767\pi\) | |||||||
\(618\) | 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 | \(0.128506\pi\) | ||||
−0.919609 | + | 0.392836i | \(0.871494\pi\) | |||||||
\(632\) | 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 | \(-0.399844\pi\) | ||||
0.309482 | + | 0.950905i | \(0.399844\pi\) | |||||||
\(648\) | 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 | \(-0.695548\pi\) | ||||
−0.576413 | + | 0.817159i | \(0.695548\pi\) | |||||||
\(678\) | 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 | \(0.242546\pi\) | ||||
−0.723469 | + | 0.690356i | \(0.757454\pi\) | |||||||
\(684\) | 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 | \(-0.997945\pi\) | ||
0.999979 | − | 0.00645673i | \(-0.00205525\pi\) | |||||||
\(710\) | 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 | \(-0.552350\pi\) | ||||
−0.163721 | + | 0.986507i | \(0.552350\pi\) | |||||||
\(720\) | 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 | \(-0.395634\pi\) | ||||
0.322032 | + | 0.946729i | \(0.395634\pi\) | |||||||
\(728\) | 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 | \(0.0415594\pi\) | ||||
−0.991489 | + | 0.130192i | \(0.958441\pi\) | |||||||
\(740\) | 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 | \(-0.913228\pi\) | ||
0.963073 | − | 0.269240i | \(-0.0867724\pi\) | |||||||
\(744\) | 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 | \(-0.876854\pi\) | ||||
−0.926093 | + | 0.377296i | \(0.876854\pi\) | |||||||
\(798\) | 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 | \(-0.980115\pi\) | ||
0.998049 | − | 0.0624284i | \(-0.0198845\pi\) | |||||||
\(822\) | 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 | \(0.0518435\pi\) | ||||
−0.986766 | + | 0.162152i | \(0.948157\pi\) | |||||||
\(828\) | −0.886819 | −0.0308191 | ||||||||
\(829\) | −38.2268 | −1.32767 | −0.663836 | − | 0.747878i | \(-0.731073\pi\) | ||||
−0.663836 | + | 0.747878i | \(0.731073\pi\) | |||||||
\(830\) | 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 | \(-0.436171\pi\) | ||||
0.199183 | + | 0.979962i | \(0.436171\pi\) | |||||||
\(858\) | −5.45984 | − | 8.87310i | −0.186396 | − | 0.302923i | ||||
\(859\) | 28.2776 | 0.964820 | 0.482410 | − | 0.875945i | \(-0.339762\pi\) | ||||
0.482410 | + | 0.875945i | \(0.339762\pi\) | |||||||
\(860\) | 11.6046i | 0.395715i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.58369 | 0.0539407 | ||||||||
\(863\) | − | 11.4442i | − | 0.389567i | −0.980846 | − | 0.194783i | \(-0.937600\pi\) | ||
0.980846 | − | 0.194783i | \(-0.0624004\pi\) | |||||||
\(864\) | 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 | \(-0.599668\pi\) | ||
0.308026 | − | 0.951378i | \(-0.400332\pi\) | |||||||
\(878\) | 1.14084i | 0.0385016i | ||||||||
\(879\) | − | 16.9835i | − | 0.572838i | ||||||
\(880\) | −28.8344 | −0.972006 | ||||||||
\(881\) | 1.16418 | 0.0392221 | 0.0196111 | − | 0.999808i | \(-0.493757\pi\) | ||||
0.0196111 | + | 0.999808i | \(0.493757\pi\) | |||||||
\(882\) | 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 | \(-0.327866\pi\) | ||||
0.514799 | + | 0.857311i | \(0.327866\pi\) | |||||||
\(888\) | 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 | \(-0.890875\pi\) | ||||
−0.941808 | + | 0.336150i | \(0.890875\pi\) | |||||||
\(938\) | 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 | \(0.0874457\pi\) | ||||
−0.962502 | + | 0.271276i | \(0.912554\pi\) | |||||||
\(948\) | −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 | \(-0.842199\pi\) | ||
0.879615 | − | 0.475687i | \(-0.157801\pi\) | |||||||
\(968\) | 31.6265i | 1.01652i | ||||||||
\(969\) | 12.3701i | 0.397384i | ||||||||
\(970\) | 3.16315i | 0.101563i | ||||||||
\(971\) | 15.1301 | 0.485548 | 0.242774 | − | 0.970083i | \(-0.421943\pi\) | ||||
0.242774 | + | 0.970083i | \(0.421943\pi\) | |||||||
\(972\) | 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 | \(0.173808\pi\) | ||||
−0.854591 | + | 0.519301i | \(0.826192\pi\) | |||||||
\(978\) | 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 | \(-0.534236\pi\) | ||||
−0.107347 | + | 0.994222i | \(0.534236\pi\) | |||||||
\(998\) | −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.f.246.4 | 8 | ||
7.2 | even | 3 | 91.2.r.a.25.4 | ✓ | 16 | ||
7.3 | odd | 6 | 637.2.r.f.324.5 | 16 | |||
7.4 | even | 3 | 91.2.r.a.51.5 | yes | 16 | ||
7.5 | odd | 6 | 637.2.r.f.116.4 | 16 | |||
7.6 | odd | 2 | 637.2.c.e.246.4 | 8 | |||
13.5 | odd | 4 | 8281.2.a.ck.1.4 | 8 | |||
13.8 | odd | 4 | 8281.2.a.ck.1.5 | 8 | |||
13.12 | even | 2 | inner | 637.2.c.f.246.5 | 8 | ||
21.2 | odd | 6 | 819.2.dl.e.298.5 | 16 | |||
21.11 | odd | 6 | 819.2.dl.e.415.4 | 16 | |||
91.12 | odd | 6 | 637.2.r.f.116.5 | 16 | |||
91.18 | odd | 12 | 1183.2.e.i.170.5 | 16 | |||
91.25 | even | 6 | 91.2.r.a.51.4 | yes | 16 | ||
91.34 | even | 4 | 8281.2.a.cj.1.5 | 8 | |||
91.38 | odd | 6 | 637.2.r.f.324.4 | 16 | |||
91.44 | odd | 12 | 1183.2.e.i.508.5 | 16 | |||
91.51 | even | 6 | 91.2.r.a.25.5 | yes | 16 | ||
91.60 | odd | 12 | 1183.2.e.i.170.4 | 16 | |||
91.83 | even | 4 | 8281.2.a.cj.1.4 | 8 | |||
91.86 | odd | 12 | 1183.2.e.i.508.4 | 16 | |||
91.90 | odd | 2 | 637.2.c.e.246.5 | 8 | |||
273.116 | odd | 6 | 819.2.dl.e.415.5 | 16 | |||
273.233 | odd | 6 | 819.2.dl.e.298.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.4 | ✓ | 16 | 7.2 | even | 3 | ||
91.2.r.a.25.5 | yes | 16 | 91.51 | even | 6 | ||
91.2.r.a.51.4 | yes | 16 | 91.25 | even | 6 | ||
91.2.r.a.51.5 | yes | 16 | 7.4 | even | 3 | ||
637.2.c.e.246.4 | 8 | 7.6 | odd | 2 | |||
637.2.c.e.246.5 | 8 | 91.90 | odd | 2 | |||
637.2.c.f.246.4 | 8 | 1.1 | even | 1 | trivial | ||
637.2.c.f.246.5 | 8 | 13.12 | even | 2 | inner | ||
637.2.r.f.116.4 | 16 | 7.5 | odd | 6 | |||
637.2.r.f.116.5 | 16 | 91.12 | odd | 6 | |||
637.2.r.f.324.4 | 16 | 91.38 | odd | 6 | |||
637.2.r.f.324.5 | 16 | 7.3 | odd | 6 | |||
819.2.dl.e.298.4 | 16 | 273.233 | odd | 6 | |||
819.2.dl.e.298.5 | 16 | 21.2 | odd | 6 | |||
819.2.dl.e.415.4 | 16 | 21.11 | odd | 6 | |||
819.2.dl.e.415.5 | 16 | 273.116 | odd | 6 | |||
1183.2.e.i.170.4 | 16 | 91.60 | odd | 12 | |||
1183.2.e.i.170.5 | 16 | 91.18 | odd | 12 | |||
1183.2.e.i.508.4 | 16 | 91.86 | odd | 12 | |||
1183.2.e.i.508.5 | 16 | 91.44 | odd | 12 | |||
8281.2.a.cj.1.4 | 8 | 91.83 | even | 4 | |||
8281.2.a.cj.1.5 | 8 | 91.34 | even | 4 | |||
8281.2.a.ck.1.4 | 8 | 13.5 | odd | 4 | |||
8281.2.a.ck.1.5 | 8 | 13.8 | odd | 4 |