Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
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: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.41421 | −1.50163 | −0.750816 | − | 0.660511i | \(-0.770340\pi\) | ||||
−0.750816 | + | 0.660511i | \(0.770340\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.24264 | 0.514497 | 0.257249 | − | 0.966345i | \(-0.417184\pi\) | ||||
0.257249 | + | 0.966345i | \(0.417184\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −5.41421 | −1.06181 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.65685 | 1.79323 | 0.896616 | − | 0.442808i | \(-0.146018\pi\) | ||||
0.896616 | + | 0.442808i | \(0.146018\pi\) | |||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | −6.24264 | −1.12121 | −0.560606 | − | 0.828083i | \(-0.689432\pi\) | ||||
−0.560606 | + | 0.828083i | \(0.689432\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.828427 | 0.136193 | 0.0680963 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680963 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(38\) | 2.24264 | 0.363804 | ||||||||
\(39\) | −5.41421 | −0.866968 | ||||||||
\(40\) | −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 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | −4.82843 | −0.711913 | ||||||||
\(47\) | 7.89949 | 1.15226 | 0.576130 | − | 0.817358i | \(-0.304562\pi\) | ||||
0.576130 | + | 0.817358i | \(0.304562\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −5.41421 | −0.750816 | ||||||||
\(53\) | −10.4853 | −1.44026 | −0.720132 | − | 0.693837i | \(-0.755919\pi\) | ||||
−0.720132 | + | 0.693837i | \(0.755919\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.24264 | 0.297045 | ||||||||
\(58\) | 9.65685 | 1.26801 | ||||||||
\(59\) | −6.82843 | −0.888985 | −0.444493 | − | 0.895782i | \(-0.646616\pi\) | ||||
−0.444493 | + | 0.895782i | \(0.646616\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | −2.58579 | −0.331076 | −0.165538 | − | 0.986203i | \(-0.552936\pi\) | ||||
−0.165538 | + | 0.986203i | \(0.552936\pi\) | |||||||
\(62\) | −6.24264 | −0.792816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.8284 | 1.34310 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −1.17157 | −0.143130 | −0.0715652 | − | 0.997436i | \(-0.522799\pi\) | ||||
−0.0715652 | + | 0.997436i | \(0.522799\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | −4.82843 | −0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −11.6569 | −1.36433 | −0.682166 | − | 0.731198i | \(-0.738962\pi\) | ||||
−0.682166 | + | 0.731198i | \(0.738962\pi\) | |||||||
\(74\) | 0.828427 | 0.0963027 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.24264 | 0.257249 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.41421 | −0.613039 | ||||||||
\(79\) | −16.4853 | −1.85474 | −0.927370 | − | 0.374147i | \(-0.877936\pi\) | ||||
−0.927370 | + | 0.374147i | \(0.877936\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −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 | ||||||||
\(87\) | 9.65685 | 1.03532 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −3.75736 | −0.398279 | −0.199140 | − | 0.979971i | \(-0.563815\pi\) | ||||
−0.199140 | + | 0.979971i | \(0.563815\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.82843 | −0.503398 | ||||||||
\(93\) | −6.24264 | −0.647332 | ||||||||
\(94\) | 7.89949 | 0.814771 | ||||||||
\(95\) | −4.48528 | −0.460180 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.89949 | 1.00514 | 0.502571 | − | 0.864536i | \(-0.332388\pi\) | ||||
0.502571 | + | 0.864536i | \(0.332388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 15.0711 | 1.49963 | 0.749814 | − | 0.661649i | \(-0.230143\pi\) | ||||
0.749814 | + | 0.661649i | \(0.230143\pi\) | |||||||
\(102\) | −2.00000 | −0.198030 | ||||||||
\(103\) | −6.24264 | −0.615106 | −0.307553 | − | 0.951531i | \(-0.599510\pi\) | ||||
−0.307553 | + | 0.951531i | \(0.599510\pi\) | |||||||
\(104\) | −5.41421 | −0.530907 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4853 | −1.01842 | ||||||||
\(107\) | 12.8284 | 1.24017 | 0.620085 | − | 0.784534i | \(-0.287098\pi\) | ||||
0.620085 | + | 0.784534i | \(0.287098\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 4.34315 | 0.415998 | 0.207999 | − | 0.978129i | \(-0.433305\pi\) | ||||
0.207999 | + | 0.978129i | \(0.433305\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 0.828427 | 0.0786308 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.65685 | 0.532152 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(114\) | 2.24264 | 0.210043 | ||||||||
\(115\) | 9.65685 | 0.900506 | ||||||||
\(116\) | 9.65685 | 0.896616 | ||||||||
\(117\) | −5.41421 | −0.500544 | ||||||||
\(118\) | −6.82843 | −0.628608 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.00000 | −0.182574 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.58579 | −0.234106 | ||||||||
\(123\) | −11.6569 | −1.05106 | ||||||||
\(124\) | −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 | ||||||||
\(129\) | −4.82843 | −0.425119 | ||||||||
\(130\) | 10.8284 | 0.949716 | ||||||||
\(131\) | −17.5563 | −1.53391 | −0.766953 | − | 0.641704i | \(-0.778228\pi\) | ||||
−0.766953 | + | 0.641704i | \(0.778228\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.17157 | −0.101208 | ||||||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | −5.31371 | −0.453981 | −0.226990 | − | 0.973897i | \(-0.572889\pi\) | ||||
−0.226990 | + | 0.973897i | \(0.572889\pi\) | |||||||
\(138\) | −4.82843 | −0.411023 | ||||||||
\(139\) | −0.100505 | −0.00852473 | −0.00426236 | − | 0.999991i | \(-0.501357\pi\) | ||||
−0.00426236 | + | 0.999991i | \(0.501357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.89949 | 0.665257 | ||||||||
\(142\) | 5.65685 | 0.474713 | ||||||||
\(143\) | 5.41421 | 0.452759 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −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 | \(-0.447610\pi\) | ||||
0.163846 | + | 0.986486i | \(0.447610\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 2.24264 | 0.181902 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.4853 | 1.00284 | ||||||||
\(156\) | −5.41421 | −0.433484 | ||||||||
\(157\) | −12.8284 | −1.02382 | −0.511910 | − | 0.859039i | \(-0.671062\pi\) | ||||
−0.511910 | + | 0.859039i | \(0.671062\pi\) | |||||||
\(158\) | −16.4853 | −1.31150 | ||||||||
\(159\) | −10.4853 | −0.831537 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −2.34315 | −0.183529 | −0.0917647 | − | 0.995781i | \(-0.529251\pi\) | ||||
−0.0917647 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(164\) | −11.6569 | −0.910247 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | −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 | ||||||||
\(171\) | 2.24264 | 0.171499 | ||||||||
\(172\) | −4.82843 | −0.368164 | ||||||||
\(173\) | 5.89949 | 0.448530 | 0.224265 | − | 0.974528i | \(-0.428002\pi\) | ||||
0.224265 | + | 0.974528i | \(0.428002\pi\) | |||||||
\(174\) | 9.65685 | 0.732084 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −6.82843 | −0.513256 | ||||||||
\(178\) | −3.75736 | −0.281626 | ||||||||
\(179\) | −20.4853 | −1.53114 | −0.765571 | − | 0.643352i | \(-0.777543\pi\) | ||||
−0.765571 | + | 0.643352i | \(0.777543\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 9.31371 | 0.692283 | 0.346141 | − | 0.938182i | \(-0.387492\pi\) | ||||
0.346141 | + | 0.938182i | \(0.387492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.58579 | −0.191147 | ||||||||
\(184\) | −4.82843 | −0.355956 | ||||||||
\(185\) | −1.65685 | −0.121814 | ||||||||
\(186\) | −6.24264 | −0.457733 | ||||||||
\(187\) | 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 | \(-0.210775\pi\) | ||||
0.788660 | + | 0.614830i | \(0.210775\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −14.9706 | −1.07760 | −0.538802 | − | 0.842432i | \(-0.681123\pi\) | ||||
−0.538802 | + | 0.842432i | \(0.681123\pi\) | |||||||
\(194\) | 9.89949 | 0.710742 | ||||||||
\(195\) | 10.8284 | 0.775440 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.6569 | 1.11550 | 0.557752 | − | 0.830007i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830007i | \(0.311664\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −15.2132 | −1.07844 | −0.539218 | − | 0.842166i | \(-0.681280\pi\) | ||||
−0.539218 | + | 0.842166i | \(0.681280\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −1.17157 | −0.0826364 | ||||||||
\(202\) | 15.0711 | 1.06040 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | 23.3137 | 1.62830 | ||||||||
\(206\) | −6.24264 | −0.434945 | ||||||||
\(207\) | −4.82843 | −0.335599 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | 5.65685 | 0.387601 | ||||||||
\(214\) | 12.8284 | 0.876933 | ||||||||
\(215\) | 9.65685 | 0.658592 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.34315 | 0.294155 | ||||||||
\(219\) | −11.6569 | −0.787697 | ||||||||
\(220\) | 2.00000 | 0.134840 | ||||||||
\(221\) | 10.8284 | 0.728399 | ||||||||
\(222\) | 0.828427 | 0.0556004 | ||||||||
\(223\) | −6.24264 | −0.418038 | −0.209019 | − | 0.977912i | \(-0.567027\pi\) | ||||
−0.209019 | + | 0.977912i | \(0.567027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 5.65685 | 0.376288 | ||||||||
\(227\) | 11.8995 | 0.789797 | 0.394899 | − | 0.918725i | \(-0.370780\pi\) | ||||
0.394899 | + | 0.918725i | \(0.370780\pi\) | |||||||
\(228\) | 2.24264 | 0.148523 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 9.65685 | 0.636754 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.65685 | 0.634004 | ||||||||
\(233\) | −7.65685 | −0.501617 | −0.250809 | − | 0.968037i | \(-0.580696\pi\) | ||||
−0.250809 | + | 0.968037i | \(0.580696\pi\) | |||||||
\(234\) | −5.41421 | −0.353938 | ||||||||
\(235\) | −15.7990 | −1.03061 | ||||||||
\(236\) | −6.82843 | −0.444493 | ||||||||
\(237\) | −16.4853 | −1.07083 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.686292 | 0.0443925 | 0.0221963 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221963 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(240\) | −2.00000 | −0.129099 | ||||||||
\(241\) | 7.65685 | 0.493221 | 0.246611 | − | 0.969115i | \(-0.420683\pi\) | ||||
0.246611 | + | 0.969115i | \(0.420683\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.58579 | −0.165538 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.6569 | −0.743214 | ||||||||
\(247\) | −12.1421 | −0.772586 | ||||||||
\(248\) | −6.24264 | −0.396408 | ||||||||
\(249\) | −5.07107 | −0.321366 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.2132 | 1.82227 | 0.911135 | − | 0.412108i | \(-0.135208\pi\) | ||||
0.911135 | + | 0.412108i | \(0.135208\pi\) | |||||||
\(258\) | −4.82843 | −0.300605 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.8284 | 0.671551 | ||||||||
\(261\) | 9.65685 | 0.597744 | ||||||||
\(262\) | −17.5563 | −1.08463 | ||||||||
\(263\) | 9.17157 | 0.565543 | 0.282772 | − | 0.959187i | \(-0.408746\pi\) | ||||
0.282772 | + | 0.959187i | \(0.408746\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 20.9706 | 1.28821 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.75736 | −0.229947 | ||||||||
\(268\) | −1.17157 | −0.0715652 | ||||||||
\(269\) | −5.31371 | −0.323983 | −0.161991 | − | 0.986792i | \(-0.551792\pi\) | ||||
−0.161991 | + | 0.986792i | \(0.551792\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | −22.1421 | −1.34504 | −0.672519 | − | 0.740079i | \(-0.734788\pi\) | ||||
−0.672519 | + | 0.740079i | \(0.734788\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.31371 | −0.321013 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −4.82843 | −0.290637 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | −0.100505 | −0.00602789 | ||||||||
\(279\) | −6.24264 | −0.373737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.31371 | −0.0783693 | −0.0391846 | − | 0.999232i | \(-0.512476\pi\) | ||||
−0.0391846 | + | 0.999232i | \(0.512476\pi\) | |||||||
\(282\) | 7.89949 | 0.470408 | ||||||||
\(283\) | 2.24264 | 0.133311 | 0.0666556 | − | 0.997776i | \(-0.478767\pi\) | ||||
0.0666556 | + | 0.997776i | \(0.478767\pi\) | |||||||
\(284\) | 5.65685 | 0.335673 | ||||||||
\(285\) | −4.48528 | −0.265685 | ||||||||
\(286\) | 5.41421 | 0.320149 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −19.3137 | −1.13414 | ||||||||
\(291\) | 9.89949 | 0.580319 | ||||||||
\(292\) | −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 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | 26.1421 | 1.51184 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.00000 | 0.230174 | ||||||||
\(303\) | 15.0711 | 0.865810 | ||||||||
\(304\) | 2.24264 | 0.128624 | ||||||||
\(305\) | 5.17157 | 0.296123 | ||||||||
\(306\) | −2.00000 | −0.114332 | ||||||||
\(307\) | 25.0711 | 1.43088 | 0.715441 | − | 0.698673i | \(-0.246226\pi\) | ||||
0.715441 | + | 0.698673i | \(0.246226\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.24264 | −0.355131 | ||||||||
\(310\) | 12.4853 | 0.709116 | ||||||||
\(311\) | −8.10051 | −0.459338 | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229669 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(312\) | −5.41421 | −0.306519 | ||||||||
\(313\) | 8.24264 | 0.465902 | 0.232951 | − | 0.972489i | \(-0.425162\pi\) | ||||
0.232951 | + | 0.972489i | \(0.425162\pi\) | |||||||
\(314\) | −12.8284 | −0.723950 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.4853 | −0.927370 | ||||||||
\(317\) | 12.8284 | 0.720516 | 0.360258 | − | 0.932853i | \(-0.382689\pi\) | ||||
0.360258 | + | 0.932853i | \(0.382689\pi\) | |||||||
\(318\) | −10.4853 | −0.587985 | ||||||||
\(319\) | −9.65685 | −0.540680 | ||||||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 12.8284 | 0.716013 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.48528 | −0.249568 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.41421 | 0.300327 | ||||||||
\(326\) | −2.34315 | −0.129775 | ||||||||
\(327\) | 4.34315 | 0.240177 | ||||||||
\(328\) | −11.6569 | −0.643642 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.00000 | 0.110096 | ||||||||
\(331\) | −27.7990 | −1.52797 | −0.763985 | − | 0.645234i | \(-0.776760\pi\) | ||||
−0.763985 | + | 0.645234i | \(0.776760\pi\) | |||||||
\(332\) | −5.07107 | −0.278311 | ||||||||
\(333\) | 0.828427 | 0.0453975 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 5.65685 | 0.307238 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 6.24264 | 0.338058 | ||||||||
\(342\) | 2.24264 | 0.121268 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.82843 | −0.260331 | ||||||||
\(345\) | 9.65685 | 0.519908 | ||||||||
\(346\) | 5.89949 | 0.317159 | ||||||||
\(347\) | 19.4558 | 1.04444 | 0.522222 | − | 0.852809i | \(-0.325103\pi\) | ||||
0.522222 | + | 0.852809i | \(0.325103\pi\) | |||||||
\(348\) | 9.65685 | 0.517662 | ||||||||
\(349\) | 17.4142 | 0.932161 | 0.466081 | − | 0.884742i | \(-0.345666\pi\) | ||||
0.466081 | + | 0.884742i | \(0.345666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.41421 | −0.288989 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −21.2132 | −1.12906 | −0.564532 | − | 0.825411i | \(-0.690943\pi\) | ||||
−0.564532 | + | 0.825411i | \(0.690943\pi\) | |||||||
\(354\) | −6.82843 | −0.362927 | ||||||||
\(355\) | −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 | \(-0.456423\pi\) | ||||
0.136473 | + | 0.990644i | \(0.456423\pi\) | |||||||
\(360\) | −2.00000 | −0.105409 | ||||||||
\(361\) | −13.9706 | −0.735293 | ||||||||
\(362\) | 9.31371 | 0.489518 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.3137 | 1.22030 | ||||||||
\(366\) | −2.58579 | −0.135161 | ||||||||
\(367\) | 32.5858 | 1.70096 | 0.850482 | − | 0.526004i | \(-0.176310\pi\) | ||||
0.850482 | + | 0.526004i | \(0.176310\pi\) | |||||||
\(368\) | −4.82843 | −0.251699 | ||||||||
\(369\) | −11.6569 | −0.606832 | ||||||||
\(370\) | −1.65685 | −0.0861358 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.24264 | −0.323666 | ||||||||
\(373\) | 35.9411 | 1.86096 | 0.930480 | − | 0.366342i | \(-0.119390\pi\) | ||||
0.930480 | + | 0.366342i | \(0.119390\pi\) | |||||||
\(374\) | 2.00000 | 0.103418 | ||||||||
\(375\) | 12.0000 | 0.619677 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 14.1421 | 0.724524 | ||||||||
\(382\) | 21.7990 | 1.11533 | ||||||||
\(383\) | 22.7279 | 1.16134 | 0.580671 | − | 0.814138i | \(-0.302790\pi\) | ||||
0.580671 | + | 0.814138i | \(0.302790\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.9706 | −0.761982 | ||||||||
\(387\) | −4.82843 | −0.245443 | ||||||||
\(388\) | 9.89949 | 0.502571 | ||||||||
\(389\) | −34.2843 | −1.73828 | −0.869141 | − | 0.494565i | \(-0.835327\pi\) | ||||
−0.869141 | + | 0.494565i | \(0.835327\pi\) | |||||||
\(390\) | 10.8284 | 0.548319 | ||||||||
\(391\) | 9.65685 | 0.488368 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.5563 | −0.885601 | ||||||||
\(394\) | 15.6569 | 0.788781 | ||||||||
\(395\) | 32.9706 | 1.65893 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 11.1716 | 0.560685 | 0.280343 | − | 0.959900i | \(-0.409552\pi\) | ||||
0.280343 | + | 0.959900i | \(0.409552\pi\) | |||||||
\(398\) | −15.2132 | −0.762569 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 10.6863 | 0.533648 | 0.266824 | − | 0.963745i | \(-0.414026\pi\) | ||||
0.266824 | + | 0.963745i | \(0.414026\pi\) | |||||||
\(402\) | −1.17157 | −0.0584327 | ||||||||
\(403\) | 33.7990 | 1.68365 | ||||||||
\(404\) | 15.0711 | 0.749814 | ||||||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.828427 | −0.0410636 | ||||||||
\(408\) | −2.00000 | −0.0990148 | ||||||||
\(409\) | 1.51472 | 0.0748980 | 0.0374490 | − | 0.999299i | \(-0.488077\pi\) | ||||
0.0374490 | + | 0.999299i | \(0.488077\pi\) | |||||||
\(410\) | 23.3137 | 1.15138 | ||||||||
\(411\) | −5.31371 | −0.262106 | ||||||||
\(412\) | −6.24264 | −0.307553 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.82843 | −0.237304 | ||||||||
\(415\) | 10.1421 | 0.497858 | ||||||||
\(416\) | −5.41421 | −0.265454 | ||||||||
\(417\) | −0.100505 | −0.00492175 | ||||||||
\(418\) | −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 | ||||||||
\(423\) | 7.89949 | 0.384087 | ||||||||
\(424\) | −10.4853 | −0.509210 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 5.65685 | 0.274075 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.8284 | 0.620085 | ||||||||
\(429\) | 5.41421 | 0.261401 | ||||||||
\(430\) | 9.65685 | 0.465695 | ||||||||
\(431\) | 2.14214 | 0.103183 | 0.0515915 | − | 0.998668i | \(-0.483571\pi\) | ||||
0.0515915 | + | 0.998668i | \(0.483571\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 34.3848 | 1.65243 | 0.826213 | − | 0.563357i | \(-0.190491\pi\) | ||||
0.826213 | + | 0.563357i | \(0.190491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.3137 | −0.926021 | ||||||||
\(436\) | 4.34315 | 0.207999 | ||||||||
\(437\) | −10.8284 | −0.517994 | ||||||||
\(438\) | −11.6569 | −0.556986 | ||||||||
\(439\) | 29.1716 | 1.39228 | 0.696142 | − | 0.717904i | \(-0.254899\pi\) | ||||
0.696142 | + | 0.717904i | \(0.254899\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.8284 | 0.515056 | ||||||||
\(443\) | 12.4853 | 0.593194 | 0.296597 | − | 0.955003i | \(-0.404148\pi\) | ||||
0.296597 | + | 0.955003i | \(0.404148\pi\) | |||||||
\(444\) | 0.828427 | 0.0393154 | ||||||||
\(445\) | 7.51472 | 0.356232 | ||||||||
\(446\) | −6.24264 | −0.295598 | ||||||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9706 | 0.800890 | 0.400445 | − | 0.916321i | \(-0.368855\pi\) | ||||
0.400445 | + | 0.916321i | \(0.368855\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 11.6569 | 0.548900 | ||||||||
\(452\) | 5.65685 | 0.266076 | ||||||||
\(453\) | 4.00000 | 0.187936 | ||||||||
\(454\) | 11.8995 | 0.558471 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.24264 | 0.105021 | ||||||||
\(457\) | −29.3137 | −1.37124 | −0.685619 | − | 0.727961i | \(-0.740468\pi\) | ||||
−0.685619 | + | 0.727961i | \(0.740468\pi\) | |||||||
\(458\) | −14.0000 | −0.654177 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 12.4853 | 0.578991 | ||||||||
\(466\) | −7.65685 | −0.354697 | ||||||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | −5.41421 | −0.250272 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −15.7990 | −0.728753 | ||||||||
\(471\) | −12.8284 | −0.591103 | ||||||||
\(472\) | −6.82843 | −0.314304 | ||||||||
\(473\) | 4.82843 | 0.222011 | ||||||||
\(474\) | −16.4853 | −0.757194 | ||||||||
\(475\) | −2.24264 | −0.102899 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.4853 | −0.480088 | ||||||||
\(478\) | 0.686292 | 0.0313902 | ||||||||
\(479\) | −7.31371 | −0.334172 | −0.167086 | − | 0.985942i | \(-0.553436\pi\) | ||||
−0.167086 | + | 0.985942i | \(0.553436\pi\) | |||||||
\(480\) | −2.00000 | −0.0912871 | ||||||||
\(481\) | −4.48528 | −0.204511 | ||||||||
\(482\) | 7.65685 | 0.348760 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −19.7990 | −0.899026 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 0.142136 | 0.00644078 | 0.00322039 | − | 0.999995i | \(-0.498975\pi\) | ||||
0.00322039 | + | 0.999995i | \(0.498975\pi\) | |||||||
\(488\) | −2.58579 | −0.117053 | ||||||||
\(489\) | −2.34315 | −0.105961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.6274 | −1.92375 | −0.961874 | − | 0.273492i | \(-0.911821\pi\) | ||||
−0.961874 | + | 0.273492i | \(0.911821\pi\) | |||||||
\(492\) | −11.6569 | −0.525532 | ||||||||
\(493\) | −19.3137 | −0.869846 | ||||||||
\(494\) | −12.1421 | −0.546301 | ||||||||
\(495\) | 2.00000 | 0.0898933 | ||||||||
\(496\) | −6.24264 | −0.280303 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.07107 | −0.227240 | ||||||||
\(499\) | −6.14214 | −0.274960 | −0.137480 | − | 0.990505i | \(-0.543900\pi\) | ||||
−0.137480 | + | 0.990505i | \(0.543900\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 5.17157 | 0.231049 | ||||||||
\(502\) | −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 | ||||||||
\(507\) | 16.3137 | 0.724517 | ||||||||
\(508\) | 14.1421 | 0.627456 | ||||||||
\(509\) | −34.0000 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(510\) | 4.00000 | 0.177123 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.24264 | 0.0990150 | ||||||||
\(514\) | 29.2132 | 1.28854 | ||||||||
\(515\) | 12.4853 | 0.550167 | ||||||||
\(516\) | −4.82843 | −0.212560 | ||||||||
\(517\) | −7.89949 | −0.347419 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.89949 | 0.258959 | ||||||||
\(520\) | 10.8284 | 0.474858 | ||||||||
\(521\) | −21.2132 | −0.929367 | −0.464684 | − | 0.885477i | \(-0.653832\pi\) | ||||
−0.464684 | + | 0.885477i | \(0.653832\pi\) | |||||||
\(522\) | 9.65685 | 0.422669 | ||||||||
\(523\) | 9.07107 | 0.396650 | 0.198325 | − | 0.980136i | \(-0.436450\pi\) | ||||
0.198325 | + | 0.980136i | \(0.436450\pi\) | |||||||
\(524\) | −17.5563 | −0.766953 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.17157 | 0.399900 | ||||||||
\(527\) | 12.4853 | 0.543867 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 20.9706 | 0.910903 | ||||||||
\(531\) | −6.82843 | −0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 63.1127 | 2.73371 | ||||||||
\(534\) | −3.75736 | −0.162597 | ||||||||
\(535\) | −25.6569 | −1.10924 | ||||||||
\(536\) | −1.17157 | −0.0506042 | ||||||||
\(537\) | −20.4853 | −0.884005 | ||||||||
\(538\) | −5.31371 | −0.229090 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.00000 | −0.0860663 | ||||||||
\(541\) | −45.3137 | −1.94819 | −0.974094 | − | 0.226142i | \(-0.927389\pi\) | ||||
−0.974094 | + | 0.226142i | \(0.927389\pi\) | |||||||
\(542\) | −22.1421 | −0.951086 | ||||||||
\(543\) | 9.31371 | 0.399689 | ||||||||
\(544\) | −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 | ||||||||
\(549\) | −2.58579 | −0.110359 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 21.6569 | 0.922613 | ||||||||
\(552\) | −4.82843 | −0.205512 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | −1.65685 | −0.0703295 | ||||||||
\(556\) | −0.100505 | −0.00426236 | ||||||||
\(557\) | 19.6569 | 0.832888 | 0.416444 | − | 0.909161i | \(-0.363276\pi\) | ||||
0.416444 | + | 0.909161i | \(0.363276\pi\) | |||||||
\(558\) | −6.24264 | −0.264272 | ||||||||
\(559\) | 26.1421 | 1.10569 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.00000 | 0.0844401 | ||||||||
\(562\) | −1.31371 | −0.0554154 | ||||||||
\(563\) | 21.0711 | 0.888040 | 0.444020 | − | 0.896017i | \(-0.353552\pi\) | ||||
0.444020 | + | 0.896017i | \(0.353552\pi\) | |||||||
\(564\) | 7.89949 | 0.332629 | ||||||||
\(565\) | −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 | \(-0.571910\pi\) | ||||
−0.223996 | + | 0.974590i | \(0.571910\pi\) | |||||||
\(570\) | −4.48528 | −0.187868 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 5.41421 | 0.226380 | ||||||||
\(573\) | 21.7990 | 0.910666 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.82843 | 0.201359 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.44365 | 0.184992 | 0.0924958 | − | 0.995713i | \(-0.470516\pi\) | ||||
0.0924958 | + | 0.995713i | \(0.470516\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | −14.9706 | −0.622155 | ||||||||
\(580\) | −19.3137 | −0.801958 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.89949 | 0.410347 | ||||||||
\(583\) | 10.4853 | 0.434256 | ||||||||
\(584\) | −11.6569 | −0.482364 | ||||||||
\(585\) | 10.8284 | 0.447700 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 15.6569 | 0.644037 | ||||||||
\(592\) | 0.828427 | 0.0340481 | ||||||||
\(593\) | 37.3137 | 1.53229 | 0.766145 | − | 0.642668i | \(-0.222172\pi\) | ||||
0.766145 | + | 0.642668i | \(0.222172\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | −15.2132 | −0.622635 | ||||||||
\(598\) | 26.1421 | 1.06903 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −15.1716 | −0.618861 | −0.309431 | − | 0.950922i | \(-0.600138\pi\) | ||||
−0.309431 | + | 0.950922i | \(0.600138\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.17157 | −0.0477101 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | 15.0711 | 0.612220 | ||||||||
\(607\) | 35.3137 | 1.43334 | 0.716670 | − | 0.697413i | \(-0.245666\pi\) | ||||
0.716670 | + | 0.697413i | \(0.245666\pi\) | |||||||
\(608\) | 2.24264 | 0.0909511 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.17157 | 0.209391 | ||||||||
\(611\) | −42.7696 | −1.73027 | ||||||||
\(612\) | −2.00000 | −0.0808452 | ||||||||
\(613\) | −30.3431 | −1.22555 | −0.612774 | − | 0.790258i | \(-0.709946\pi\) | ||||
−0.612774 | + | 0.790258i | \(0.709946\pi\) | |||||||
\(614\) | 25.0711 | 1.01179 | ||||||||
\(615\) | 23.3137 | 0.940099 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.00000 | −0.322068 | −0.161034 | − | 0.986949i | \(-0.551483\pi\) | ||||
−0.161034 | + | 0.986949i | \(0.551483\pi\) | |||||||
\(618\) | −6.24264 | −0.251116 | ||||||||
\(619\) | 21.6569 | 0.870462 | 0.435231 | − | 0.900319i | \(-0.356667\pi\) | ||||
0.435231 | + | 0.900319i | \(0.356667\pi\) | |||||||
\(620\) | 12.4853 | 0.501421 | ||||||||
\(621\) | −4.82843 | −0.193758 | ||||||||
\(622\) | −8.10051 | −0.324801 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.41421 | −0.216742 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 8.24264 | 0.329442 | ||||||||
\(627\) | −2.24264 | −0.0895624 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | −23.1716 | −0.920987 | ||||||||
\(634\) | 12.8284 | 0.509482 | ||||||||
\(635\) | −28.2843 | −1.12243 | ||||||||
\(636\) | −10.4853 | −0.415768 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.65685 | −0.382319 | ||||||||
\(639\) | 5.65685 | 0.223782 | ||||||||
\(640\) | −2.00000 | −0.0790569 | ||||||||
\(641\) | −35.3137 | −1.39481 | −0.697404 | − | 0.716678i | \(-0.745662\pi\) | ||||
−0.697404 | + | 0.716678i | \(0.745662\pi\) | |||||||
\(642\) | 12.8284 | 0.506298 | ||||||||
\(643\) | −37.4558 | −1.47711 | −0.738557 | − | 0.674191i | \(-0.764493\pi\) | ||||
−0.738557 | + | 0.674191i | \(0.764493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.65685 | 0.380238 | ||||||||
\(646\) | −4.48528 | −0.176471 | ||||||||
\(647\) | −1.07107 | −0.0421080 | −0.0210540 | − | 0.999778i | \(-0.506702\pi\) | ||||
−0.0210540 | + | 0.999778i | \(0.506702\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 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 | \(-0.356386\pi\) | ||||
0.436025 | + | 0.899934i | \(0.356386\pi\) | |||||||
\(654\) | 4.34315 | 0.169830 | ||||||||
\(655\) | 35.1127 | 1.37197 | ||||||||
\(656\) | −11.6569 | −0.455124 | ||||||||
\(657\) | −11.6569 | −0.454777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.1127 | −1.91316 | −0.956580 | − | 0.291471i | \(-0.905855\pi\) | ||||
−0.956580 | + | 0.291471i | \(0.905855\pi\) | |||||||
\(660\) | 2.00000 | 0.0778499 | ||||||||
\(661\) | 39.9411 | 1.55353 | 0.776765 | − | 0.629791i | \(-0.216859\pi\) | ||||
0.776765 | + | 0.629791i | \(0.216859\pi\) | |||||||
\(662\) | −27.7990 | −1.08044 | ||||||||
\(663\) | 10.8284 | 0.420541 | ||||||||
\(664\) | −5.07107 | −0.196796 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.828427 | 0.0321009 | ||||||||
\(667\) | −46.6274 | −1.80542 | ||||||||
\(668\) | 5.17157 | 0.200094 | ||||||||
\(669\) | −6.24264 | −0.241354 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 16.3137 | 0.627450 | ||||||||
\(677\) | 36.0416 | 1.38519 | 0.692596 | − | 0.721326i | \(-0.256467\pi\) | ||||
0.692596 | + | 0.721326i | \(0.256467\pi\) | |||||||
\(678\) | 5.65685 | 0.217250 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | 11.8995 | 0.455990 | ||||||||
\(682\) | 6.24264 | 0.239043 | ||||||||
\(683\) | 28.7696 | 1.10084 | 0.550418 | − | 0.834889i | \(-0.314468\pi\) | ||||
0.550418 | + | 0.834889i | \(0.314468\pi\) | |||||||
\(684\) | 2.24264 | 0.0857495 | ||||||||
\(685\) | 10.6274 | 0.406053 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | −4.82843 | −0.184082 | ||||||||
\(689\) | 56.7696 | 2.16275 | ||||||||
\(690\) | 9.65685 | 0.367630 | ||||||||
\(691\) | 14.1421 | 0.537992 | 0.268996 | − | 0.963141i | \(-0.413308\pi\) | ||||
0.268996 | + | 0.963141i | \(0.413308\pi\) | |||||||
\(692\) | 5.89949 | 0.224265 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.4558 | 0.738534 | ||||||||
\(695\) | 0.201010 | 0.00762475 | ||||||||
\(696\) | 9.65685 | 0.366042 | ||||||||
\(697\) | 23.3137 | 0.883070 | ||||||||
\(698\) | 17.4142 | 0.659138 | ||||||||
\(699\) | −7.65685 | −0.289609 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.31371 | 0.351774 | 0.175887 | − | 0.984410i | \(-0.443721\pi\) | ||||
0.175887 | + | 0.984410i | \(0.443721\pi\) | |||||||
\(702\) | −5.41421 | −0.204346 | ||||||||
\(703\) | 1.85786 | 0.0700707 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −15.7990 | −0.595024 | ||||||||
\(706\) | −21.2132 | −0.798369 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.82843 | −0.256628 | ||||||||
\(709\) | −34.7696 | −1.30580 | −0.652899 | − | 0.757445i | \(-0.726447\pi\) | ||||
−0.652899 | + | 0.757445i | \(0.726447\pi\) | |||||||
\(710\) | −11.3137 | −0.424596 | ||||||||
\(711\) | −16.4853 | −0.618246 | ||||||||
\(712\) | −3.75736 | −0.140813 | ||||||||
\(713\) | 30.1421 | 1.12883 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8284 | −0.404960 | ||||||||
\(716\) | −20.4853 | −0.765571 | ||||||||
\(717\) | 0.686292 | 0.0256300 | ||||||||
\(718\) | 5.17157 | 0.193001 | ||||||||
\(719\) | 44.1838 | 1.64778 | 0.823888 | − | 0.566752i | \(-0.191800\pi\) | ||||
0.823888 | + | 0.566752i | \(0.191800\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.9706 | −0.519931 | ||||||||
\(723\) | 7.65685 | 0.284761 | ||||||||
\(724\) | 9.31371 | 0.346141 | ||||||||
\(725\) | −9.65685 | −0.358647 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −31.2132 | −1.15763 | −0.578817 | − | 0.815458i | \(-0.696485\pi\) | ||||
−0.578817 | + | 0.815458i | \(0.696485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 23.3137 | 0.862879 | ||||||||
\(731\) | 9.65685 | 0.357172 | ||||||||
\(732\) | −2.58579 | −0.0955734 | ||||||||
\(733\) | −19.5563 | −0.722330 | −0.361165 | − | 0.932502i | \(-0.617621\pi\) | ||||
−0.361165 | + | 0.932502i | \(0.617621\pi\) | |||||||
\(734\) | 32.5858 | 1.20276 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.82843 | −0.177978 | ||||||||
\(737\) | 1.17157 | 0.0431554 | ||||||||
\(738\) | −11.6569 | −0.429095 | ||||||||
\(739\) | 2.62742 | 0.0966511 | 0.0483255 | − | 0.998832i | \(-0.484612\pi\) | ||||
0.0483255 | + | 0.998832i | \(0.484612\pi\) | |||||||
\(740\) | −1.65685 | −0.0609072 | ||||||||
\(741\) | −12.1421 | −0.446052 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.6274 | −0.683374 | −0.341687 | − | 0.939814i | \(-0.610998\pi\) | ||||
−0.341687 | + | 0.939814i | \(0.610998\pi\) | |||||||
\(744\) | −6.24264 | −0.228866 | ||||||||
\(745\) | −8.00000 | −0.293097 | ||||||||
\(746\) | 35.9411 | 1.31590 | ||||||||
\(747\) | −5.07107 | −0.185541 | ||||||||
\(748\) | 2.00000 | 0.0731272 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.0000 | 0.438178 | ||||||||
\(751\) | −12.1421 | −0.443073 | −0.221536 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221536 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(752\) | 7.89949 | 0.288065 | ||||||||
\(753\) | −8.48528 | −0.309221 | ||||||||
\(754\) | −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 | ||||||||
\(759\) | 4.82843 | 0.175261 | ||||||||
\(760\) | −4.48528 | −0.162698 | ||||||||
\(761\) | 1.51472 | 0.0549085 | 0.0274543 | − | 0.999623i | \(-0.491260\pi\) | ||||
0.0274543 | + | 0.999623i | \(0.491260\pi\) | |||||||
\(762\) | 14.1421 | 0.512316 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.7990 | 0.788660 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | 22.7279 | 0.821193 | ||||||||
\(767\) | 36.9706 | 1.33493 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 15.8579 | 0.571849 | 0.285925 | − | 0.958252i | \(-0.407699\pi\) | ||||
0.285925 | + | 0.958252i | \(0.407699\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.2132 | 1.05209 | ||||||||
\(772\) | −14.9706 | −0.538802 | ||||||||
\(773\) | −5.51472 | −0.198351 | −0.0991753 | − | 0.995070i | \(-0.531620\pi\) | ||||
−0.0991753 | + | 0.995070i | \(0.531620\pi\) | |||||||
\(774\) | −4.82843 | −0.173554 | ||||||||
\(775\) | 6.24264 | 0.224242 | ||||||||
\(776\) | 9.89949 | 0.355371 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.2843 | −1.22915 | ||||||||
\(779\) | −26.1421 | −0.936639 | ||||||||
\(780\) | 10.8284 | 0.387720 | ||||||||
\(781\) | −5.65685 | −0.202418 | ||||||||
\(782\) | 9.65685 | 0.345328 | ||||||||
\(783\) | 9.65685 | 0.345108 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.6569 | 0.915732 | ||||||||
\(786\) | −17.5563 | −0.626214 | ||||||||
\(787\) | 3.41421 | 0.121704 | 0.0608518 | − | 0.998147i | \(-0.480618\pi\) | ||||
0.0608518 | + | 0.998147i | \(0.480618\pi\) | |||||||
\(788\) | 15.6569 | 0.557752 | ||||||||
\(789\) | 9.17157 | 0.326517 | ||||||||
\(790\) | 32.9706 | 1.17304 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 14.0000 | 0.497155 | ||||||||
\(794\) | 11.1716 | 0.396464 | ||||||||
\(795\) | 20.9706 | 0.743749 | ||||||||
\(796\) | −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 | ||||||||
\(801\) | −3.75736 | −0.132760 | ||||||||
\(802\) | 10.6863 | 0.377346 | ||||||||
\(803\) | 11.6569 | 0.411361 | ||||||||
\(804\) | −1.17157 | −0.0413182 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33.7990 | 1.19052 | ||||||||
\(807\) | −5.31371 | −0.187051 | ||||||||
\(808\) | 15.0711 | 0.530198 | ||||||||
\(809\) | 26.7696 | 0.941167 | 0.470584 | − | 0.882355i | \(-0.344043\pi\) | ||||
0.470584 | + | 0.882355i | \(0.344043\pi\) | |||||||
\(810\) | −2.00000 | −0.0702728 | ||||||||
\(811\) | −36.3848 | −1.27764 | −0.638821 | − | 0.769355i | \(-0.720578\pi\) | ||||
−0.638821 | + | 0.769355i | \(0.720578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.1421 | −0.776559 | ||||||||
\(814\) | −0.828427 | −0.0290364 | ||||||||
\(815\) | 4.68629 | 0.164154 | ||||||||
\(816\) | −2.00000 | −0.0700140 | ||||||||
\(817\) | −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 | \(-0.190820\pi\) | ||||
0.825630 | + | 0.564212i | \(0.190820\pi\) | |||||||
\(822\) | −5.31371 | −0.185337 | ||||||||
\(823\) | −28.1421 | −0.980973 | −0.490487 | − | 0.871449i | \(-0.663181\pi\) | ||||
−0.490487 | + | 0.871449i | \(0.663181\pi\) | |||||||
\(824\) | −6.24264 | −0.217473 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.3137 | 1.36707 | 0.683536 | − | 0.729917i | \(-0.260441\pi\) | ||||
0.683536 | + | 0.729917i | \(0.260441\pi\) | |||||||
\(828\) | −4.82843 | −0.167799 | ||||||||
\(829\) | −50.2843 | −1.74644 | −0.873222 | − | 0.487322i | \(-0.837974\pi\) | ||||
−0.873222 | + | 0.487322i | \(0.837974\pi\) | |||||||
\(830\) | 10.1421 | 0.352039 | ||||||||
\(831\) | −16.0000 | −0.555034 | ||||||||
\(832\) | −5.41421 | −0.187704 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.100505 | −0.00348021 | ||||||||
\(835\) | −10.3431 | −0.357939 | ||||||||
\(836\) | −2.24264 | −0.0775634 | ||||||||
\(837\) | −6.24264 | −0.215777 | ||||||||
\(838\) | −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 | ||||||||
\(843\) | −1.31371 | −0.0452465 | ||||||||
\(844\) | −23.1716 | −0.797598 | ||||||||
\(845\) | −32.6274 | −1.12242 | ||||||||
\(846\) | 7.89949 | 0.271590 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.4853 | −0.360066 | ||||||||
\(849\) | 2.24264 | 0.0769672 | ||||||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | 5.65685 | 0.193801 | ||||||||
\(853\) | −35.5563 | −1.21743 | −0.608713 | − | 0.793390i | \(-0.708314\pi\) | ||||
−0.608713 | + | 0.793390i | \(0.708314\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.48528 | −0.153393 | ||||||||
\(856\) | 12.8284 | 0.438467 | ||||||||
\(857\) | −0.142136 | −0.00485526 | −0.00242763 | − | 0.999997i | \(-0.500773\pi\) | ||||
−0.00242763 | + | 0.999997i | \(0.500773\pi\) | |||||||
\(858\) | 5.41421 | 0.184838 | ||||||||
\(859\) | 30.4264 | 1.03814 | 0.519068 | − | 0.854733i | \(-0.326279\pi\) | ||||
0.519068 | + | 0.854733i | \(0.326279\pi\) | |||||||
\(860\) | 9.65685 | 0.329296 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.14214 | 0.0729614 | ||||||||
\(863\) | −38.7696 | −1.31973 | −0.659865 | − | 0.751384i | \(-0.729387\pi\) | ||||
−0.659865 | + | 0.751384i | \(0.729387\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −11.7990 | −0.401178 | ||||||||
\(866\) | 34.3848 | 1.16844 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.4853 | 0.559225 | ||||||||
\(870\) | −19.3137 | −0.654796 | ||||||||
\(871\) | 6.34315 | 0.214929 | ||||||||
\(872\) | 4.34315 | 0.147077 | ||||||||
\(873\) | 9.89949 | 0.335047 | ||||||||
\(874\) | −10.8284 | −0.366277 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.6569 | −0.393849 | ||||||||
\(877\) | −6.68629 | −0.225780 | −0.112890 | − | 0.993607i | \(-0.536011\pi\) | ||||
−0.112890 | + | 0.993607i | \(0.536011\pi\) | |||||||
\(878\) | 29.1716 | 0.984493 | ||||||||
\(879\) | 4.92893 | 0.166249 | ||||||||
\(880\) | 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 | ||||||||
\(885\) | 13.6569 | 0.459070 | ||||||||
\(886\) | 12.4853 | 0.419451 | ||||||||
\(887\) | −4.28427 | −0.143852 | −0.0719259 | − | 0.997410i | \(-0.522915\pi\) | ||||
−0.0719259 | + | 0.997410i | \(0.522915\pi\) | |||||||
\(888\) | 0.828427 | 0.0278002 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.51472 | 0.251894 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −6.24264 | −0.209019 | ||||||||
\(893\) | 17.7157 | 0.592834 | ||||||||
\(894\) | 4.00000 | 0.133780 | ||||||||
\(895\) | 40.9706 | 1.36949 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.1421 | 0.872861 | ||||||||
\(898\) | 16.9706 | 0.566315 | ||||||||
\(899\) | −60.2843 | −2.01059 | ||||||||
\(900\) | −1.00000 | −0.0333333 | ||||||||
\(901\) | 20.9706 | 0.698631 | ||||||||
\(902\) | 11.6569 | 0.388131 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.65685 | 0.188144 | ||||||||
\(905\) | −18.6274 | −0.619196 | ||||||||
\(906\) | 4.00000 | 0.132891 | ||||||||
\(907\) | −8.20101 | −0.272310 | −0.136155 | − | 0.990688i | \(-0.543475\pi\) | ||||
−0.136155 | + | 0.990688i | \(0.543475\pi\) | |||||||
\(908\) | 11.8995 | 0.394899 | ||||||||
\(909\) | 15.0711 | 0.499876 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.4558 | −0.379549 | −0.189775 | − | 0.981828i | \(-0.560776\pi\) | ||||
−0.189775 | + | 0.981828i | \(0.560776\pi\) | |||||||
\(912\) | 2.24264 | 0.0742613 | ||||||||
\(913\) | 5.07107 | 0.167828 | ||||||||
\(914\) | −29.3137 | −0.969611 | ||||||||
\(915\) | 5.17157 | 0.170967 | ||||||||
\(916\) | −14.0000 | −0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.00000 | −0.0660098 | ||||||||
\(919\) | −0.970563 | −0.0320159 | −0.0160080 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160080 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(920\) | 9.65685 | 0.318377 | ||||||||
\(921\) | 25.0711 | 0.826120 | ||||||||
\(922\) | 30.5858 | 1.00729 | ||||||||
\(923\) | −30.6274 | −1.00811 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.828427 | −0.0272385 | ||||||||
\(926\) | −3.31371 | −0.108895 | ||||||||
\(927\) | −6.24264 | −0.205035 | ||||||||
\(928\) | 9.65685 | 0.317002 | ||||||||
\(929\) | −10.7868 | −0.353903 | −0.176952 | − | 0.984220i | \(-0.556624\pi\) | ||||
−0.176952 | + | 0.984220i | \(0.556624\pi\) | |||||||
\(930\) | 12.4853 | 0.409409 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.65685 | −0.250809 | ||||||||
\(933\) | −8.10051 | −0.265199 | ||||||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | −5.41421 | −0.176969 | ||||||||
\(937\) | 56.9117 | 1.85922 | 0.929612 | − | 0.368540i | \(-0.120142\pi\) | ||||
0.929612 | + | 0.368540i | \(0.120142\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.24264 | 0.268988 | ||||||||
\(940\) | −15.7990 | −0.515306 | ||||||||
\(941\) | −27.5563 | −0.898311 | −0.449156 | − | 0.893454i | \(-0.648275\pi\) | ||||
−0.449156 | + | 0.893454i | \(0.648275\pi\) | |||||||
\(942\) | −12.8284 | −0.417973 | ||||||||
\(943\) | 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 | \(-0.825906\pi\) | ||||
−0.854124 | + | 0.520069i | \(0.825906\pi\) | |||||||
\(948\) | −16.4853 | −0.535417 | ||||||||
\(949\) | 63.1127 | 2.04872 | ||||||||
\(950\) | −2.24264 | −0.0727609 | ||||||||
\(951\) | 12.8284 | 0.415990 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.51472 | 0.308212 | 0.154106 | − | 0.988054i | \(-0.450750\pi\) | ||||
0.154106 | + | 0.988054i | \(0.450750\pi\) | |||||||
\(954\) | −10.4853 | −0.339474 | ||||||||
\(955\) | −43.5980 | −1.41080 | ||||||||
\(956\) | 0.686292 | 0.0221963 | ||||||||
\(957\) | −9.65685 | −0.312162 | ||||||||
\(958\) | −7.31371 | −0.236295 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.00000 | −0.0645497 | ||||||||
\(961\) | 7.97056 | 0.257115 | ||||||||
\(962\) | −4.48528 | −0.144611 | ||||||||
\(963\) | 12.8284 | 0.413390 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | −4.48528 | −0.144088 | ||||||||
\(970\) | −19.7990 | −0.635707 | ||||||||
\(971\) | −4.68629 | −0.150390 | −0.0751951 | − | 0.997169i | \(-0.523958\pi\) | ||||
−0.0751951 | + | 0.997169i | \(0.523958\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.142136 | 0.00455432 | ||||||||
\(975\) | 5.41421 | 0.173394 | ||||||||
\(976\) | −2.58579 | −0.0827690 | ||||||||
\(977\) | 26.6274 | 0.851887 | 0.425943 | − | 0.904750i | \(-0.359942\pi\) | ||||
0.425943 | + | 0.904750i | \(0.359942\pi\) | |||||||
\(978\) | −2.34315 | −0.0749255 | ||||||||
\(979\) | 3.75736 | 0.120086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.34315 | 0.138666 | ||||||||
\(982\) | −42.6274 | −1.36030 | ||||||||
\(983\) | −0.870058 | −0.0277505 | −0.0138753 | − | 0.999904i | \(-0.504417\pi\) | ||||
−0.0138753 | + | 0.999904i | \(0.504417\pi\) | |||||||
\(984\) | −11.6569 | −0.371607 | ||||||||
\(985\) | −31.3137 | −0.997738 | ||||||||
\(986\) | −19.3137 | −0.615074 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.1421 | −0.386293 | ||||||||
\(989\) | 23.3137 | 0.741333 | ||||||||
\(990\) | 2.00000 | 0.0635642 | ||||||||
\(991\) | 50.9117 | 1.61726 | 0.808632 | − | 0.588315i | \(-0.200209\pi\) | ||||
0.808632 | + | 0.588315i | \(0.200209\pi\) | |||||||
\(992\) | −6.24264 | −0.198204 | ||||||||
\(993\) | −27.7990 | −0.882174 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.4264 | 0.964582 | ||||||||
\(996\) | −5.07107 | −0.160683 | ||||||||
\(997\) | −30.5858 | −0.968662 | −0.484331 | − | 0.874885i | \(-0.660937\pi\) | ||||
−0.484331 | + | 0.874885i | \(0.660937\pi\) | |||||||
\(998\) | −6.14214 | −0.194426 | ||||||||
\(999\) | 0.828427 | 0.0262103 |
(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 | 3234.2.a.bd.1.1 | yes | 2 | |
3.2 | odd | 2 | 9702.2.a.cy.1.1 | 2 | |||
7.6 | odd | 2 | 3234.2.a.bc.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 9702.2.a.ci.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bc.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
3234.2.a.bd.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
9702.2.a.ci.1.2 | 2 | 21.20 | even | 2 | |||
9702.2.a.cy.1.1 | 2 | 3.2 | odd | 2 |