Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9702,2,Mod(1,9702)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9702, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9702.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9702.a (trivial) |
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: | yes |
Analytic conductor: | \(77.4708600410\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3234) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9702.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.41421 | 1.50163 | 0.750816 | − | 0.660511i | \(-0.229660\pi\) | ||||
0.750816 | + | 0.660511i | \(0.229660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.24264 | −0.514497 | −0.257249 | − | 0.966345i | \(-0.582816\pi\) | ||||
−0.257249 | + | 0.966345i | \(0.582816\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 4.82843 | 1.00680 | 0.503398 | − | 0.864054i | \(-0.332083\pi\) | ||||
0.503398 | + | 0.864054i | \(0.332083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −5.41421 | −1.06181 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.65685 | −1.79323 | −0.896616 | − | 0.442808i | \(-0.853982\pi\) | ||||
−0.896616 | + | 0.442808i | \(0.853982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24264 | 1.12121 | 0.560606 | − | 0.828083i | \(-0.310568\pi\) | ||||
0.560606 | + | 0.828083i | \(0.310568\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.828427 | 0.136193 | 0.0680963 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680963 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(38\) | 2.24264 | 0.363804 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | 0.316228 | ||||||||
\(41\) | −11.6569 | −1.82049 | −0.910247 | − | 0.414065i | \(-0.864109\pi\) | ||||
−0.910247 | + | 0.414065i | \(0.864109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.82843 | −0.736328 | −0.368164 | − | 0.929761i | \(-0.620014\pi\) | ||||
−0.368164 | + | 0.929761i | \(0.620014\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.82843 | −0.711913 | ||||||||
\(47\) | 7.89949 | 1.15226 | 0.576130 | − | 0.817358i | \(-0.304562\pi\) | ||||
0.576130 | + | 0.817358i | \(0.304562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.41421 | 0.750816 | ||||||||
\(53\) | 10.4853 | 1.44026 | 0.720132 | − | 0.693837i | \(-0.244081\pi\) | ||||
0.720132 | + | 0.693837i | \(0.244081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.65685 | 1.26801 | ||||||||
\(59\) | −6.82843 | −0.888985 | −0.444493 | − | 0.895782i | \(-0.646616\pi\) | ||||
−0.444493 | + | 0.895782i | \(0.646616\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.58579 | 0.331076 | 0.165538 | − | 0.986203i | \(-0.447064\pi\) | ||||
0.165538 | + | 0.986203i | \(0.447064\pi\) | |||||||
\(62\) | −6.24264 | −0.792816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.8284 | −1.34310 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.17157 | −0.143130 | −0.0715652 | − | 0.997436i | \(-0.522799\pi\) | ||||
−0.0715652 | + | 0.997436i | \(0.522799\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6569 | 1.36433 | 0.682166 | − | 0.731198i | \(-0.261038\pi\) | ||||
0.682166 | + | 0.731198i | \(0.261038\pi\) | |||||||
\(74\) | −0.828427 | −0.0963027 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.24264 | −0.257249 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.4853 | −1.85474 | −0.927370 | − | 0.374147i | \(-0.877936\pi\) | ||||
−0.927370 | + | 0.374147i | \(0.877936\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.6569 | 1.28728 | ||||||||
\(83\) | −5.07107 | −0.556622 | −0.278311 | − | 0.960491i | \(-0.589775\pi\) | ||||
−0.278311 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 4.82843 | 0.520663 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −3.75736 | −0.398279 | −0.199140 | − | 0.979971i | \(-0.563815\pi\) | ||||
−0.199140 | + | 0.979971i | \(0.563815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.82843 | 0.503398 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.89949 | −0.814771 | ||||||||
\(95\) | 4.48528 | 0.460180 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.89949 | −1.00514 | −0.502571 | − | 0.864536i | \(-0.667612\pi\) | ||||
−0.502571 | + | 0.864536i | \(0.667612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 15.0711 | 1.49963 | 0.749814 | − | 0.661649i | \(-0.230143\pi\) | ||||
0.749814 | + | 0.661649i | \(0.230143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.24264 | 0.615106 | 0.307553 | − | 0.951531i | \(-0.400490\pi\) | ||||
0.307553 | + | 0.951531i | \(0.400490\pi\) | |||||||
\(104\) | −5.41421 | −0.530907 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4853 | −1.01842 | ||||||||
\(107\) | −12.8284 | −1.24017 | −0.620085 | − | 0.784534i | \(-0.712902\pi\) | ||||
−0.620085 | + | 0.784534i | \(0.712902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.34315 | 0.415998 | 0.207999 | − | 0.978129i | \(-0.433305\pi\) | ||||
0.207999 | + | 0.978129i | \(0.433305\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.65685 | −0.532152 | −0.266076 | − | 0.963952i | \(-0.585727\pi\) | ||||
−0.266076 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.65685 | −0.900506 | ||||||||
\(116\) | −9.65685 | −0.896616 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.82843 | 0.628608 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.58579 | −0.234106 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.24264 | 0.560606 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1421 | 1.25491 | 0.627456 | − | 0.778652i | \(-0.284096\pi\) | ||||
0.627456 | + | 0.778652i | \(0.284096\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.8284 | 0.949716 | ||||||||
\(131\) | −17.5563 | −1.53391 | −0.766953 | − | 0.641704i | \(-0.778228\pi\) | ||||
−0.766953 | + | 0.641704i | \(0.778228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.17157 | 0.101208 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | 5.31371 | 0.453981 | 0.226990 | − | 0.973897i | \(-0.427111\pi\) | ||||
0.226990 | + | 0.973897i | \(0.427111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.100505 | 0.00852473 | 0.00426236 | − | 0.999991i | \(-0.498643\pi\) | ||||
0.00426236 | + | 0.999991i | \(0.498643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.65685 | 0.474713 | ||||||||
\(143\) | 5.41421 | 0.452759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.3137 | 1.60392 | ||||||||
\(146\) | −11.6569 | −0.964728 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.828427 | 0.0680963 | ||||||||
\(149\) | −4.00000 | −0.327693 | −0.163846 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163846 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 2.24264 | 0.181902 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.4853 | −1.00284 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8284 | 1.02382 | 0.511910 | − | 0.859039i | \(-0.328938\pi\) | ||||
0.511910 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(158\) | 16.4853 | 1.31150 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.00000 | 0.158114 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.34315 | −0.183529 | −0.0917647 | − | 0.995781i | \(-0.529251\pi\) | ||||
−0.0917647 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(164\) | −11.6569 | −0.910247 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.07107 | 0.393591 | ||||||||
\(167\) | 5.17157 | 0.400188 | 0.200094 | − | 0.979777i | \(-0.435875\pi\) | ||||
0.200094 | + | 0.979777i | \(0.435875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.3137 | 1.25490 | ||||||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.82843 | −0.368164 | ||||||||
\(173\) | 5.89949 | 0.448530 | 0.224265 | − | 0.974528i | \(-0.428002\pi\) | ||||
0.224265 | + | 0.974528i | \(0.428002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.75736 | 0.281626 | ||||||||
\(179\) | 20.4853 | 1.53114 | 0.765571 | − | 0.643352i | \(-0.222457\pi\) | ||||
0.765571 | + | 0.643352i | \(0.222457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.31371 | −0.692283 | −0.346141 | − | 0.938182i | \(-0.612508\pi\) | ||||
−0.346141 | + | 0.938182i | \(0.612508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.82843 | −0.355956 | ||||||||
\(185\) | −1.65685 | −0.121814 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | −0.146254 | ||||||||
\(188\) | 7.89949 | 0.576130 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.48528 | −0.325397 | ||||||||
\(191\) | −21.7990 | −1.57732 | −0.788660 | − | 0.614830i | \(-0.789225\pi\) | ||||
−0.788660 | + | 0.614830i | \(0.789225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.9706 | −1.07760 | −0.538802 | − | 0.842432i | \(-0.681123\pi\) | ||||
−0.538802 | + | 0.842432i | \(0.681123\pi\) | |||||||
\(194\) | 9.89949 | 0.710742 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.6569 | −1.11550 | −0.557752 | − | 0.830007i | \(-0.688336\pi\) | ||||
−0.557752 | + | 0.830007i | \(0.688336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2132 | 1.07844 | 0.539218 | − | 0.842166i | \(-0.318720\pi\) | ||||
0.539218 | + | 0.842166i | \(0.318720\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.0711 | −1.06040 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.3137 | 1.62830 | ||||||||
\(206\) | −6.24264 | −0.434945 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.41421 | 0.375408 | ||||||||
\(209\) | −2.24264 | −0.155127 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.1716 | −1.59520 | −0.797598 | − | 0.603189i | \(-0.793897\pi\) | ||||
−0.797598 | + | 0.603189i | \(0.793897\pi\) | |||||||
\(212\) | 10.4853 | 0.720132 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.8284 | 0.876933 | ||||||||
\(215\) | 9.65685 | 0.658592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.34315 | −0.294155 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | −10.8284 | −0.728399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.24264 | 0.418038 | 0.209019 | − | 0.977912i | \(-0.432973\pi\) | ||||
0.209019 | + | 0.977912i | \(0.432973\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.65685 | 0.376288 | ||||||||
\(227\) | 11.8995 | 0.789797 | 0.394899 | − | 0.918725i | \(-0.370780\pi\) | ||||
0.394899 | + | 0.918725i | \(0.370780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 9.65685 | 0.636754 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.65685 | 0.634004 | ||||||||
\(233\) | 7.65685 | 0.501617 | 0.250809 | − | 0.968037i | \(-0.419304\pi\) | ||||
0.250809 | + | 0.968037i | \(0.419304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7990 | −1.03061 | ||||||||
\(236\) | −6.82843 | −0.444493 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.686292 | −0.0443925 | −0.0221963 | − | 0.999754i | \(-0.507066\pi\) | ||||
−0.0221963 | + | 0.999754i | \(0.507066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.65685 | −0.493221 | −0.246611 | − | 0.969115i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969115i | \(0.579317\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.58579 | 0.165538 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.1421 | −0.772586 | ||||||||
\(248\) | −6.24264 | −0.396408 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0000 | −0.758947 | ||||||||
\(251\) | −8.48528 | −0.535586 | −0.267793 | − | 0.963476i | \(-0.586294\pi\) | ||||
−0.267793 | + | 0.963476i | \(0.586294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.82843 | 0.303561 | ||||||||
\(254\) | −14.1421 | −0.887357 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.2132 | 1.82227 | 0.911135 | − | 0.412108i | \(-0.135208\pi\) | ||||
0.911135 | + | 0.412108i | \(0.135208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.8284 | −0.671551 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.5563 | 1.08463 | ||||||||
\(263\) | −9.17157 | −0.565543 | −0.282772 | − | 0.959187i | \(-0.591254\pi\) | ||||
−0.282772 | + | 0.959187i | \(0.591254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.9706 | −1.28821 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.17157 | −0.0715652 | ||||||||
\(269\) | −5.31371 | −0.323983 | −0.161991 | − | 0.986792i | \(-0.551792\pi\) | ||||
−0.161991 | + | 0.986792i | \(0.551792\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.1421 | 1.34504 | 0.672519 | − | 0.740079i | \(-0.265212\pi\) | ||||
0.672519 | + | 0.740079i | \(0.265212\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.31371 | −0.321013 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | −0.100505 | −0.00602789 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.31371 | 0.0783693 | 0.0391846 | − | 0.999232i | \(-0.487524\pi\) | ||||
0.0391846 | + | 0.999232i | \(0.487524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.24264 | −0.133311 | −0.0666556 | − | 0.997776i | \(-0.521233\pi\) | ||||
−0.0666556 | + | 0.997776i | \(0.521233\pi\) | |||||||
\(284\) | −5.65685 | −0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.41421 | −0.320149 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −19.3137 | −1.13414 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.6569 | 0.682166 | ||||||||
\(293\) | 4.92893 | 0.287951 | 0.143976 | − | 0.989581i | \(-0.454011\pi\) | ||||
0.143976 | + | 0.989581i | \(0.454011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6569 | 0.795133 | ||||||||
\(296\) | −0.828427 | −0.0481513 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | 26.1421 | 1.51184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.00000 | −0.230174 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.24264 | −0.128624 | ||||||||
\(305\) | −5.17157 | −0.296123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0711 | −1.43088 | −0.715441 | − | 0.698673i | \(-0.753774\pi\) | ||||
−0.715441 | + | 0.698673i | \(0.753774\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.4853 | 0.709116 | ||||||||
\(311\) | −8.10051 | −0.459338 | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229669 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.24264 | −0.465902 | −0.232951 | − | 0.972489i | \(-0.574838\pi\) | ||||
−0.232951 | + | 0.972489i | \(0.574838\pi\) | |||||||
\(314\) | −12.8284 | −0.723950 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.4853 | −0.927370 | ||||||||
\(317\) | −12.8284 | −0.720516 | −0.360258 | − | 0.932853i | \(-0.617311\pi\) | ||||
−0.360258 | + | 0.932853i | \(0.617311\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.65685 | −0.540680 | ||||||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.48528 | 0.249568 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.41421 | −0.300327 | ||||||||
\(326\) | 2.34315 | 0.129775 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.6569 | 0.643642 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.7990 | −1.52797 | −0.763985 | − | 0.645234i | \(-0.776760\pi\) | ||||
−0.763985 | + | 0.645234i | \(0.776760\pi\) | |||||||
\(332\) | −5.07107 | −0.278311 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.17157 | −0.282976 | ||||||||
\(335\) | 2.34315 | 0.128020 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8284 | 0.698809 | 0.349404 | − | 0.936972i | \(-0.386384\pi\) | ||||
0.349404 | + | 0.936972i | \(0.386384\pi\) | |||||||
\(338\) | −16.3137 | −0.887349 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 6.24264 | 0.338058 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.82843 | 0.260331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.89949 | −0.317159 | ||||||||
\(347\) | −19.4558 | −1.04444 | −0.522222 | − | 0.852809i | \(-0.674897\pi\) | ||||
−0.522222 | + | 0.852809i | \(0.674897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.4142 | −0.932161 | −0.466081 | − | 0.884742i | \(-0.654334\pi\) | ||||
−0.466081 | + | 0.884742i | \(0.654334\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −21.2132 | −1.12906 | −0.564532 | − | 0.825411i | \(-0.690943\pi\) | ||||
−0.564532 | + | 0.825411i | \(0.690943\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137 | 0.600469 | ||||||||
\(356\) | −3.75736 | −0.199140 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.4853 | −1.08268 | ||||||||
\(359\) | −5.17157 | −0.272945 | −0.136473 | − | 0.990644i | \(-0.543577\pi\) | ||||
−0.136473 | + | 0.990644i | \(0.543577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9706 | −0.735293 | ||||||||
\(362\) | 9.31371 | 0.489518 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.3137 | −1.22030 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.5858 | −1.70096 | −0.850482 | − | 0.526004i | \(-0.823690\pi\) | ||||
−0.850482 | + | 0.526004i | \(0.823690\pi\) | |||||||
\(368\) | 4.82843 | 0.251699 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.65685 | 0.0861358 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.9411 | 1.86096 | 0.930480 | − | 0.366342i | \(-0.119390\pi\) | ||||
0.930480 | + | 0.366342i | \(0.119390\pi\) | |||||||
\(374\) | 2.00000 | 0.103418 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.89949 | −0.407385 | ||||||||
\(377\) | −52.2843 | −2.69278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.2843 | 1.65833 | 0.829166 | − | 0.559003i | \(-0.188816\pi\) | ||||
0.829166 | + | 0.559003i | \(0.188816\pi\) | |||||||
\(380\) | 4.48528 | 0.230090 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.7990 | 1.11533 | ||||||||
\(383\) | 22.7279 | 1.16134 | 0.580671 | − | 0.814138i | \(-0.302790\pi\) | ||||
0.580671 | + | 0.814138i | \(0.302790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.9706 | 0.761982 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.89949 | −0.502571 | ||||||||
\(389\) | 34.2843 | 1.73828 | 0.869141 | − | 0.494565i | \(-0.164673\pi\) | ||||
0.869141 | + | 0.494565i | \(0.164673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.65685 | −0.488368 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.6569 | 0.788781 | ||||||||
\(395\) | 32.9706 | 1.65893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1716 | −0.560685 | −0.280343 | − | 0.959900i | \(-0.590448\pi\) | ||||
−0.280343 | + | 0.959900i | \(0.590448\pi\) | |||||||
\(398\) | −15.2132 | −0.762569 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −10.6863 | −0.533648 | −0.266824 | − | 0.963745i | \(-0.585974\pi\) | ||||
−0.266824 | + | 0.963745i | \(0.585974\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.7990 | 1.68365 | ||||||||
\(404\) | 15.0711 | 0.749814 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.828427 | 0.0410636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.51472 | −0.0748980 | −0.0374490 | − | 0.999299i | \(-0.511923\pi\) | ||||
−0.0374490 | + | 0.999299i | \(0.511923\pi\) | |||||||
\(410\) | −23.3137 | −1.15138 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.24264 | 0.307553 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1421 | 0.497858 | ||||||||
\(416\) | −5.41421 | −0.265454 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.24264 | 0.109691 | ||||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.6569 | −1.34791 | −0.673956 | − | 0.738771i | \(-0.735406\pi\) | ||||
−0.673956 | + | 0.738771i | \(0.735406\pi\) | |||||||
\(422\) | 23.1716 | 1.12797 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.4853 | −0.509210 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.8284 | −0.620085 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.65685 | −0.465695 | ||||||||
\(431\) | −2.14214 | −0.103183 | −0.0515915 | − | 0.998668i | \(-0.516429\pi\) | ||||
−0.0515915 | + | 0.998668i | \(0.516429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.3848 | −1.65243 | −0.826213 | − | 0.563357i | \(-0.809509\pi\) | ||||
−0.826213 | + | 0.563357i | \(0.809509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.34315 | 0.207999 | ||||||||
\(437\) | −10.8284 | −0.517994 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.1716 | −1.39228 | −0.696142 | − | 0.717904i | \(-0.745101\pi\) | ||||
−0.696142 | + | 0.717904i | \(0.745101\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.8284 | 0.515056 | ||||||||
\(443\) | −12.4853 | −0.593194 | −0.296597 | − | 0.955003i | \(-0.595852\pi\) | ||||
−0.296597 | + | 0.955003i | \(0.595852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.51472 | 0.356232 | ||||||||
\(446\) | −6.24264 | −0.295598 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.9706 | −0.800890 | −0.400445 | − | 0.916321i | \(-0.631145\pi\) | ||||
−0.400445 | + | 0.916321i | \(0.631145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.6569 | −0.548900 | ||||||||
\(452\) | −5.65685 | −0.266076 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.8995 | −0.558471 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.3137 | −1.37124 | −0.685619 | − | 0.727961i | \(-0.740468\pi\) | ||||
−0.685619 | + | 0.727961i | \(0.740468\pi\) | |||||||
\(458\) | −14.0000 | −0.654177 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.65685 | −0.450253 | ||||||||
\(461\) | 30.5858 | 1.42452 | 0.712261 | − | 0.701915i | \(-0.247671\pi\) | ||||
0.712261 | + | 0.701915i | \(0.247671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.31371 | −0.154001 | −0.0770005 | − | 0.997031i | \(-0.524534\pi\) | ||||
−0.0770005 | + | 0.997031i | \(0.524534\pi\) | |||||||
\(464\) | −9.65685 | −0.448308 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.65685 | −0.354697 | ||||||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.7990 | 0.728753 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.82843 | 0.314304 | ||||||||
\(473\) | −4.82843 | −0.222011 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.24264 | 0.102899 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.686292 | 0.0313902 | ||||||||
\(479\) | −7.31371 | −0.334172 | −0.167086 | − | 0.985942i | \(-0.553436\pi\) | ||||
−0.167086 | + | 0.985942i | \(0.553436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.48528 | 0.204511 | ||||||||
\(482\) | 7.65685 | 0.348760 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 19.7990 | 0.899026 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.142136 | 0.00644078 | 0.00322039 | − | 0.999995i | \(-0.498975\pi\) | ||||
0.00322039 | + | 0.999995i | \(0.498975\pi\) | |||||||
\(488\) | −2.58579 | −0.117053 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.6274 | 1.92375 | 0.961874 | − | 0.273492i | \(-0.0881788\pi\) | ||||
0.961874 | + | 0.273492i | \(0.0881788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3137 | 0.869846 | ||||||||
\(494\) | 12.1421 | 0.546301 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.24264 | 0.280303 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.14214 | −0.274960 | −0.137480 | − | 0.990505i | \(-0.543900\pi\) | ||||
−0.137480 | + | 0.990505i | \(0.543900\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.48528 | 0.378717 | ||||||||
\(503\) | 8.48528 | 0.378340 | 0.189170 | − | 0.981944i | \(-0.439420\pi\) | ||||
0.189170 | + | 0.981944i | \(0.439420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.1421 | −1.34131 | ||||||||
\(506\) | −4.82843 | −0.214650 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.1421 | 0.627456 | ||||||||
\(509\) | −34.0000 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.2132 | −1.28854 | ||||||||
\(515\) | −12.4853 | −0.550167 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.89949 | 0.347419 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.8284 | 0.474858 | ||||||||
\(521\) | −21.2132 | −0.929367 | −0.464684 | − | 0.885477i | \(-0.653832\pi\) | ||||
−0.464684 | + | 0.885477i | \(0.653832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.07107 | −0.396650 | −0.198325 | − | 0.980136i | \(-0.563550\pi\) | ||||
−0.198325 | + | 0.980136i | \(0.563550\pi\) | |||||||
\(524\) | −17.5563 | −0.766953 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.17157 | 0.399900 | ||||||||
\(527\) | −12.4853 | −0.543867 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 20.9706 | 0.910903 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −63.1127 | −2.73371 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.6569 | 1.10924 | ||||||||
\(536\) | 1.17157 | 0.0506042 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.31371 | 0.229090 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −45.3137 | −1.94819 | −0.974094 | − | 0.226142i | \(-0.927389\pi\) | ||||
−0.974094 | + | 0.226142i | \(0.927389\pi\) | |||||||
\(542\) | −22.1421 | −0.951086 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | −8.68629 | −0.372080 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.6274 | −1.82262 | −0.911308 | − | 0.411724i | \(-0.864927\pi\) | ||||
−0.911308 | + | 0.411724i | \(0.864927\pi\) | |||||||
\(548\) | 5.31371 | 0.226990 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 21.6569 | 0.922613 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.100505 | 0.00426236 | ||||||||
\(557\) | −19.6569 | −0.832888 | −0.416444 | − | 0.909161i | \(-0.636724\pi\) | ||||
−0.416444 | + | 0.909161i | \(0.636724\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.1421 | −1.10569 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.31371 | −0.0554154 | ||||||||
\(563\) | 21.0711 | 0.888040 | 0.444020 | − | 0.896017i | \(-0.353552\pi\) | ||||
0.444020 | + | 0.896017i | \(0.353552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3137 | 0.475971 | ||||||||
\(566\) | 2.24264 | 0.0942652 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.65685 | 0.237356 | ||||||||
\(569\) | 10.6863 | 0.447993 | 0.223996 | − | 0.974590i | \(-0.428090\pi\) | ||||
0.223996 | + | 0.974590i | \(0.428090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 5.41421 | 0.226380 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.82843 | −0.201359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.44365 | −0.184992 | −0.0924958 | − | 0.995713i | \(-0.529484\pi\) | ||||
−0.0924958 | + | 0.995713i | \(0.529484\pi\) | |||||||
\(578\) | 13.0000 | 0.540729 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.3137 | 0.801958 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4853 | 0.434256 | ||||||||
\(584\) | −11.6569 | −0.482364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.92893 | −0.203612 | ||||||||
\(587\) | −11.7990 | −0.486996 | −0.243498 | − | 0.969901i | \(-0.578295\pi\) | ||||
−0.243498 | + | 0.969901i | \(0.578295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0000 | −0.576860 | ||||||||
\(590\) | −13.6569 | −0.562244 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.828427 | 0.0340481 | ||||||||
\(593\) | 37.3137 | 1.53229 | 0.766145 | − | 0.642668i | \(-0.222172\pi\) | ||||
0.766145 | + | 0.642668i | \(0.222172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.00000 | −0.163846 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26.1421 | −1.06903 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.1716 | 0.618861 | 0.309431 | − | 0.950922i | \(-0.399862\pi\) | ||||
0.309431 | + | 0.950922i | \(0.399862\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.3137 | −1.43334 | −0.716670 | − | 0.697413i | \(-0.754334\pi\) | ||||
−0.716670 | + | 0.697413i | \(0.754334\pi\) | |||||||
\(608\) | 2.24264 | 0.0909511 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.17157 | 0.209391 | ||||||||
\(611\) | 42.7696 | 1.73027 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.3431 | −1.22555 | −0.612774 | − | 0.790258i | \(-0.709946\pi\) | ||||
−0.612774 | + | 0.790258i | \(0.709946\pi\) | |||||||
\(614\) | 25.0711 | 1.01179 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.00000 | 0.322068 | 0.161034 | − | 0.986949i | \(-0.448517\pi\) | ||||
0.161034 | + | 0.986949i | \(0.448517\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.6569 | −0.870462 | −0.435231 | − | 0.900319i | \(-0.643333\pi\) | ||||
−0.435231 | + | 0.900319i | \(0.643333\pi\) | |||||||
\(620\) | −12.4853 | −0.501421 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.10051 | 0.324801 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 8.24264 | 0.329442 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.8284 | 0.511910 | ||||||||
\(629\) | −1.65685 | −0.0660631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.1421 | 1.43880 | 0.719398 | − | 0.694598i | \(-0.244418\pi\) | ||||
0.719398 | + | 0.694598i | \(0.244418\pi\) | |||||||
\(632\) | 16.4853 | 0.655749 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.8284 | 0.509482 | ||||||||
\(635\) | −28.2843 | −1.12243 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.65685 | 0.382319 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.00000 | 0.0790569 | ||||||||
\(641\) | 35.3137 | 1.39481 | 0.697404 | − | 0.716678i | \(-0.254338\pi\) | ||||
0.697404 | + | 0.716678i | \(0.254338\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.4558 | 1.47711 | 0.738557 | − | 0.674191i | \(-0.235507\pi\) | ||||
0.738557 | + | 0.674191i | \(0.235507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.48528 | −0.176471 | ||||||||
\(647\) | −1.07107 | −0.0421080 | −0.0210540 | − | 0.999778i | \(-0.506702\pi\) | ||||
−0.0210540 | + | 0.999778i | \(0.506702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.82843 | −0.268039 | ||||||||
\(650\) | 5.41421 | 0.212363 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.34315 | −0.0917647 | ||||||||
\(653\) | −22.2843 | −0.872051 | −0.436025 | − | 0.899934i | \(-0.643614\pi\) | ||||
−0.436025 | + | 0.899934i | \(0.643614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.1127 | 1.37197 | ||||||||
\(656\) | −11.6569 | −0.455124 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.1127 | 1.91316 | 0.956580 | − | 0.291471i | \(-0.0941448\pi\) | ||||
0.956580 | + | 0.291471i | \(0.0941448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.9411 | −1.55353 | −0.776765 | − | 0.629791i | \(-0.783141\pi\) | ||||
−0.776765 | + | 0.629791i | \(0.783141\pi\) | |||||||
\(662\) | 27.7990 | 1.08044 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.07107 | 0.196796 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.6274 | −1.80542 | ||||||||
\(668\) | 5.17157 | 0.200094 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.34315 | −0.0905236 | ||||||||
\(671\) | 2.58579 | 0.0998232 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5147 | −0.675143 | −0.337571 | − | 0.941300i | \(-0.609605\pi\) | ||||
−0.337571 | + | 0.941300i | \(0.609605\pi\) | |||||||
\(674\) | −12.8284 | −0.494133 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.3137 | 0.627450 | ||||||||
\(677\) | 36.0416 | 1.38519 | 0.692596 | − | 0.721326i | \(-0.256467\pi\) | ||||
0.692596 | + | 0.721326i | \(0.256467\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.24264 | −0.239043 | ||||||||
\(683\) | −28.7696 | −1.10084 | −0.550418 | − | 0.834889i | \(-0.685532\pi\) | ||||
−0.550418 | + | 0.834889i | \(0.685532\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.6274 | −0.406053 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.82843 | −0.184082 | ||||||||
\(689\) | 56.7696 | 2.16275 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1421 | −0.537992 | −0.268996 | − | 0.963141i | \(-0.586692\pi\) | ||||
−0.268996 | + | 0.963141i | \(0.586692\pi\) | |||||||
\(692\) | 5.89949 | 0.224265 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.4558 | 0.738534 | ||||||||
\(695\) | −0.201010 | −0.00762475 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.3137 | 0.883070 | ||||||||
\(698\) | 17.4142 | 0.659138 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.31371 | −0.351774 | −0.175887 | − | 0.984410i | \(-0.556279\pi\) | ||||
−0.175887 | + | 0.984410i | \(0.556279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.85786 | −0.0700707 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.2132 | 0.798369 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.7696 | −1.30580 | −0.652899 | − | 0.757445i | \(-0.726447\pi\) | ||||
−0.652899 | + | 0.757445i | \(0.726447\pi\) | |||||||
\(710\) | −11.3137 | −0.424596 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.75736 | 0.140813 | ||||||||
\(713\) | 30.1421 | 1.12883 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8284 | −0.404960 | ||||||||
\(716\) | 20.4853 | 0.765571 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.17157 | 0.193001 | ||||||||
\(719\) | 44.1838 | 1.64778 | 0.823888 | − | 0.566752i | \(-0.191800\pi\) | ||||
0.823888 | + | 0.566752i | \(0.191800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.9706 | 0.519931 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.31371 | −0.346141 | ||||||||
\(725\) | 9.65685 | 0.358647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.2132 | 1.15763 | 0.578817 | − | 0.815458i | \(-0.303515\pi\) | ||||
0.578817 | + | 0.815458i | \(0.303515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23.3137 | 0.862879 | ||||||||
\(731\) | 9.65685 | 0.357172 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5563 | 0.722330 | 0.361165 | − | 0.932502i | \(-0.382379\pi\) | ||||
0.361165 | + | 0.932502i | \(0.382379\pi\) | |||||||
\(734\) | 32.5858 | 1.20276 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.82843 | −0.177978 | ||||||||
\(737\) | −1.17157 | −0.0431554 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.62742 | 0.0966511 | 0.0483255 | − | 0.998832i | \(-0.484612\pi\) | ||||
0.0483255 | + | 0.998832i | \(0.484612\pi\) | |||||||
\(740\) | −1.65685 | −0.0609072 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.6274 | 0.683374 | 0.341687 | − | 0.939814i | \(-0.389002\pi\) | ||||
0.341687 | + | 0.939814i | \(0.389002\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | 0.293097 | ||||||||
\(746\) | −35.9411 | −1.31590 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.00000 | −0.0731272 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1421 | −0.443073 | −0.221536 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221536 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(752\) | 7.89949 | 0.288065 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 52.2843 | 1.90408 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.1421 | −1.74976 | −0.874878 | − | 0.484344i | \(-0.839058\pi\) | ||||
−0.874878 | + | 0.484344i | \(0.839058\pi\) | |||||||
\(758\) | −32.2843 | −1.17262 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.48528 | −0.162698 | ||||||||
\(761\) | 1.51472 | 0.0549085 | 0.0274543 | − | 0.999623i | \(-0.491260\pi\) | ||||
0.0274543 | + | 0.999623i | \(0.491260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21.7990 | −0.788660 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.7279 | −0.821193 | ||||||||
\(767\) | −36.9706 | −1.33493 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.8579 | −0.571849 | −0.285925 | − | 0.958252i | \(-0.592301\pi\) | ||||
−0.285925 | + | 0.958252i | \(0.592301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.9706 | −0.538802 | ||||||||
\(773\) | −5.51472 | −0.198351 | −0.0991753 | − | 0.995070i | \(-0.531620\pi\) | ||||
−0.0991753 | + | 0.995070i | \(0.531620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.24264 | −0.224242 | ||||||||
\(776\) | 9.89949 | 0.355371 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.2843 | −1.22915 | ||||||||
\(779\) | 26.1421 | 0.936639 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.65685 | −0.202418 | ||||||||
\(782\) | 9.65685 | 0.345328 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.6569 | −0.915732 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.41421 | −0.121704 | −0.0608518 | − | 0.998147i | \(-0.519382\pi\) | ||||
−0.0608518 | + | 0.998147i | \(0.519382\pi\) | |||||||
\(788\) | −15.6569 | −0.557752 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.9706 | −1.17304 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0000 | 0.497155 | ||||||||
\(794\) | 11.1716 | 0.396464 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.2132 | 0.539218 | ||||||||
\(797\) | −17.5147 | −0.620403 | −0.310202 | − | 0.950671i | \(-0.600397\pi\) | ||||
−0.310202 | + | 0.950671i | \(0.600397\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7990 | −0.558928 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.6863 | 0.377346 | ||||||||
\(803\) | 11.6569 | 0.411361 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.7990 | −1.19052 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.0711 | −0.530198 | ||||||||
\(809\) | −26.7696 | −0.941167 | −0.470584 | − | 0.882355i | \(-0.655957\pi\) | ||||
−0.470584 | + | 0.882355i | \(0.655957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.3848 | 1.27764 | 0.638821 | − | 0.769355i | \(-0.279422\pi\) | ||||
0.638821 | + | 0.769355i | \(0.279422\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.828427 | −0.0290364 | ||||||||
\(815\) | 4.68629 | 0.164154 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.8284 | 0.378839 | ||||||||
\(818\) | 1.51472 | 0.0529609 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.3137 | 0.814150 | ||||||||
\(821\) | −47.3137 | −1.65126 | −0.825630 | − | 0.564212i | \(-0.809180\pi\) | ||||
−0.825630 | + | 0.564212i | \(0.809180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.1421 | −0.980973 | −0.490487 | − | 0.871449i | \(-0.663181\pi\) | ||||
−0.490487 | + | 0.871449i | \(0.663181\pi\) | |||||||
\(824\) | −6.24264 | −0.217473 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.3137 | −1.36707 | −0.683536 | − | 0.729917i | \(-0.739559\pi\) | ||||
−0.683536 | + | 0.729917i | \(0.739559\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.2843 | 1.74644 | 0.873222 | − | 0.487322i | \(-0.162026\pi\) | ||||
0.873222 | + | 0.487322i | \(0.162026\pi\) | |||||||
\(830\) | −10.1421 | −0.352039 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.41421 | 0.187704 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.3431 | −0.357939 | ||||||||
\(836\) | −2.24264 | −0.0775634 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.0000 | 0.552711 | ||||||||
\(839\) | 17.0711 | 0.589359 | 0.294679 | − | 0.955596i | \(-0.404787\pi\) | ||||
0.294679 | + | 0.955596i | \(0.404787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.2548 | 2.21568 | ||||||||
\(842\) | 27.6569 | 0.953118 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.1716 | −0.797598 | ||||||||
\(845\) | −32.6274 | −1.12242 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.4853 | 0.360066 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.00000 | −0.0685994 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.5563 | 1.21743 | 0.608713 | − | 0.793390i | \(-0.291686\pi\) | ||||
0.608713 | + | 0.793390i | \(0.291686\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.8284 | 0.438467 | ||||||||
\(857\) | −0.142136 | −0.00485526 | −0.00242763 | − | 0.999997i | \(-0.500773\pi\) | ||||
−0.00242763 | + | 0.999997i | \(0.500773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.4264 | −1.03814 | −0.519068 | − | 0.854733i | \(-0.673721\pi\) | ||||
−0.519068 | + | 0.854733i | \(0.673721\pi\) | |||||||
\(860\) | 9.65685 | 0.329296 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.14214 | 0.0729614 | ||||||||
\(863\) | 38.7696 | 1.31973 | 0.659865 | − | 0.751384i | \(-0.270613\pi\) | ||||
0.659865 | + | 0.751384i | \(0.270613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.7990 | −0.401178 | ||||||||
\(866\) | 34.3848 | 1.16844 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.4853 | −0.559225 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.34315 | −0.214929 | ||||||||
\(872\) | −4.34315 | −0.147077 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.8284 | 0.366277 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.68629 | −0.225780 | −0.112890 | − | 0.993607i | \(-0.536011\pi\) | ||||
−0.112890 | + | 0.993607i | \(0.536011\pi\) | |||||||
\(878\) | 29.1716 | 0.984493 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.00000 | −0.0674200 | ||||||||
\(881\) | −37.8995 | −1.27687 | −0.638433 | − | 0.769677i | \(-0.720417\pi\) | ||||
−0.638433 | + | 0.769677i | \(0.720417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6274 | −0.357641 | −0.178821 | − | 0.983882i | \(-0.557228\pi\) | ||||
−0.178821 | + | 0.983882i | \(0.557228\pi\) | |||||||
\(884\) | −10.8284 | −0.364199 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.4853 | 0.419451 | ||||||||
\(887\) | −4.28427 | −0.143852 | −0.0719259 | − | 0.997410i | \(-0.522915\pi\) | ||||
−0.0719259 | + | 0.997410i | \(0.522915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.51472 | −0.251894 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.24264 | 0.209019 | ||||||||
\(893\) | −17.7157 | −0.592834 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.9706 | −1.36949 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.9706 | 0.566315 | ||||||||
\(899\) | −60.2843 | −2.01059 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.9706 | −0.698631 | ||||||||
\(902\) | 11.6569 | 0.388131 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.65685 | 0.188144 | ||||||||
\(905\) | 18.6274 | 0.619196 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.20101 | −0.272310 | −0.136155 | − | 0.990688i | \(-0.543475\pi\) | ||||
−0.136155 | + | 0.990688i | \(0.543475\pi\) | |||||||
\(908\) | 11.8995 | 0.394899 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4558 | 0.379549 | 0.189775 | − | 0.981828i | \(-0.439224\pi\) | ||||
0.189775 | + | 0.981828i | \(0.439224\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.07107 | −0.167828 | ||||||||
\(914\) | 29.3137 | 0.969611 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.970563 | −0.0320159 | −0.0160080 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160080 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(920\) | 9.65685 | 0.318377 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.5858 | −1.00729 | ||||||||
\(923\) | −30.6274 | −1.00811 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.828427 | −0.0272385 | ||||||||
\(926\) | 3.31371 | 0.108895 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.65685 | 0.317002 | ||||||||
\(929\) | −10.7868 | −0.353903 | −0.176952 | − | 0.984220i | \(-0.556624\pi\) | ||||
−0.176952 | + | 0.984220i | \(0.556624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.65685 | 0.250809 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.9117 | −1.85922 | −0.929612 | − | 0.368540i | \(-0.879858\pi\) | ||||
−0.929612 | + | 0.368540i | \(0.879858\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.7990 | −0.515306 | ||||||||
\(941\) | −27.5563 | −0.898311 | −0.449156 | − | 0.893454i | \(-0.648275\pi\) | ||||
−0.449156 | + | 0.893454i | \(0.648275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.2843 | −1.83287 | ||||||||
\(944\) | −6.82843 | −0.222246 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.82843 | 0.156986 | ||||||||
\(947\) | 52.5685 | 1.70825 | 0.854124 | − | 0.520069i | \(-0.174094\pi\) | ||||
0.854124 | + | 0.520069i | \(0.174094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.1127 | 2.04872 | ||||||||
\(950\) | −2.24264 | −0.0727609 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.51472 | −0.308212 | −0.154106 | − | 0.988054i | \(-0.549250\pi\) | ||||
−0.154106 | + | 0.988054i | \(0.549250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.5980 | 1.41080 | ||||||||
\(956\) | −0.686292 | −0.0221963 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.31371 | 0.236295 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.97056 | 0.257115 | ||||||||
\(962\) | −4.48528 | −0.144611 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.65685 | −0.246611 | ||||||||
\(965\) | 29.9411 | 0.963839 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.94113 | −0.319685 | −0.159843 | − | 0.987143i | \(-0.551099\pi\) | ||||
−0.159843 | + | 0.987143i | \(0.551099\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.7990 | −0.635707 | ||||||||
\(971\) | −4.68629 | −0.150390 | −0.0751951 | − | 0.997169i | \(-0.523958\pi\) | ||||
−0.0751951 | + | 0.997169i | \(0.523958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.142136 | −0.00455432 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.58579 | 0.0827690 | ||||||||
\(977\) | −26.6274 | −0.851887 | −0.425943 | − | 0.904750i | \(-0.640058\pi\) | ||||
−0.425943 | + | 0.904750i | \(0.640058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.75736 | −0.120086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.6274 | −1.36030 | ||||||||
\(983\) | −0.870058 | −0.0277505 | −0.0138753 | − | 0.999904i | \(-0.504417\pi\) | ||||
−0.0138753 | + | 0.999904i | \(0.504417\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.3137 | 0.997738 | ||||||||
\(986\) | −19.3137 | −0.615074 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.1421 | −0.386293 | ||||||||
\(989\) | −23.3137 | −0.741333 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9117 | 1.61726 | 0.808632 | − | 0.588315i | \(-0.200209\pi\) | ||||
0.808632 | + | 0.588315i | \(0.200209\pi\) | |||||||
\(992\) | −6.24264 | −0.198204 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.4264 | −0.964582 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.5858 | 0.968662 | 0.484331 | − | 0.874885i | \(-0.339063\pi\) | ||||
0.484331 | + | 0.874885i | \(0.339063\pi\) | |||||||
\(998\) | 6.14214 | 0.194426 | ||||||||
\(999\) | 0 | 0 |
(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 | 9702.2.a.ci.1.2 | 2 | ||
3.2 | odd | 2 | 3234.2.a.bc.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 9702.2.a.cy.1.1 | 2 | |||
21.20 | even | 2 | 3234.2.a.bd.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bc.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
3234.2.a.bd.1.1 | yes | 2 | 21.20 | even | 2 | ||
9702.2.a.ci.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9702.2.a.cy.1.1 | 2 | 7.6 | odd | 2 |