Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(829,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 690) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.829 |
Dual form | 2070.2.d.a.829.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.707107 | + | 2.12132i | −0.316228 | + | 0.948683i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.12132 | − | 0.707107i | −0.670820 | − | 0.223607i | ||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843i | 1.33916i | 0.742738 | + | 0.669582i | \(0.233527\pi\) | ||||
−0.742738 | + | 0.669582i | \(0.766473\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.17157i | 0.284148i | 0.989856 | + | 0.142074i | \(0.0453771\pi\) | ||||
−0.989856 | + | 0.142074i | \(0.954623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.24264 | 0.514497 | 0.257249 | − | 0.966345i | \(-0.417184\pi\) | ||||
0.257249 | + | 0.966345i | \(0.417184\pi\) | |||||||
\(20\) | 0.707107 | − | 2.12132i | 0.158114 | − | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.24264i | − | 0.904534i | ||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | − | 3.00000i | −0.800000 | − | 0.600000i | ||||
\(26\) | −4.82843 | −0.946932 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | −7.65685 | −1.42184 | −0.710921 | − | 0.703272i | \(-0.751722\pi\) | ||||
−0.710921 | + | 0.703272i | \(0.751722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.17157 | −0.200923 | ||||||||
\(35\) | −4.24264 | − | 1.41421i | −0.717137 | − | 0.239046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.41421i | − | 0.561293i | −0.959811 | − | 0.280647i | \(-0.909451\pi\) | ||
0.959811 | − | 0.280647i | \(-0.0905489\pi\) | |||||||
\(38\) | 2.24264i | 0.363804i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.12132 | + | 0.707107i | 0.335410 | + | 0.111803i | ||||
\(41\) | 1.17157 | 0.182969 | 0.0914845 | − | 0.995807i | \(-0.470839\pi\) | ||||
0.0914845 | + | 0.995807i | \(0.470839\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.75736i | 0.267995i | 0.990982 | + | 0.133997i | \(0.0427814\pi\) | ||||
−0.990982 | + | 0.133997i | \(0.957219\pi\) | |||||||
\(44\) | 4.24264 | 0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 4.82843i | 0.704298i | 0.935944 | + | 0.352149i | \(0.114549\pi\) | ||||
−0.935944 | + | 0.352149i | \(0.885451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 3.00000 | − | 4.00000i | 0.424264 | − | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.82843i | − | 0.669582i | ||||||
\(53\) | − | 13.4142i | − | 1.84258i | −0.388872 | − | 0.921292i | \(-0.627135\pi\) | ||
0.388872 | − | 0.921292i | \(-0.372865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | − | 9.00000i | 0.404520 | − | 1.21356i | ||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.65685i | − | 1.00539i | ||||||
\(59\) | −8.48528 | −1.10469 | −0.552345 | − | 0.833616i | \(-0.686267\pi\) | ||||
−0.552345 | + | 0.833616i | \(0.686267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.41421 | −0.437145 | −0.218573 | − | 0.975821i | \(-0.570140\pi\) | ||||
−0.218573 | + | 0.975821i | \(0.570140\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −10.2426 | − | 3.41421i | −1.27044 | − | 0.423481i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.585786i | 0.0715652i | 0.999360 | + | 0.0357826i | \(0.0113924\pi\) | ||||
−0.999360 | + | 0.0357826i | \(0.988608\pi\) | |||||||
\(68\) | − | 1.17157i | − | 0.142074i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.41421 | − | 4.24264i | 0.169031 | − | 0.507093i | ||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.65685i | − | 0.428002i | −0.976833 | − | 0.214001i | \(-0.931350\pi\) | ||
0.976833 | − | 0.214001i | \(-0.0686496\pi\) | |||||||
\(74\) | 3.41421 | 0.396894 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.24264 | −0.257249 | ||||||||
\(77\) | − | 8.48528i | − | 0.966988i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.65685 | −0.861463 | −0.430732 | − | 0.902480i | \(-0.641744\pi\) | ||||
−0.430732 | + | 0.902480i | \(0.641744\pi\) | |||||||
\(80\) | −0.707107 | + | 2.12132i | −0.0790569 | + | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.17157i | 0.129379i | ||||||||
\(83\) | 1.41421i | 0.155230i | 0.996983 | + | 0.0776151i | \(0.0247305\pi\) | ||||
−0.996983 | + | 0.0776151i | \(0.975269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.48528 | − | 0.828427i | −0.269567 | − | 0.0898555i | ||||
\(86\) | −1.75736 | −0.189501 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264i | 0.452267i | ||||||||
\(89\) | 14.8284 | 1.57181 | 0.785905 | − | 0.618347i | \(-0.212197\pi\) | ||||
0.785905 | + | 0.618347i | \(0.212197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.65685 | −1.01231 | ||||||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.82843 | −0.498014 | ||||||||
\(95\) | −1.58579 | + | 4.75736i | −0.162698 | + | 0.488095i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | 3.00000i | 0.303046i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | + | 3.00000i | 0.400000 | + | 0.300000i | ||||
\(101\) | 9.31371 | 0.926749 | 0.463374 | − | 0.886163i | \(-0.346639\pi\) | ||||
0.463374 | + | 0.886163i | \(0.346639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.1421i | − | 1.19640i | −0.801347 | − | 0.598200i | \(-0.795883\pi\) | ||
0.801347 | − | 0.598200i | \(-0.204117\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4142 | 1.30290 | ||||||||
\(107\) | 15.0711i | 1.45698i | 0.685059 | + | 0.728488i | \(0.259776\pi\) | ||||
−0.685059 | + | 0.728488i | \(0.740224\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.4142 | −1.47641 | −0.738207 | − | 0.674574i | \(-0.764327\pi\) | ||||
−0.738207 | + | 0.674574i | \(0.764327\pi\) | |||||||
\(110\) | 9.00000 | + | 3.00000i | 0.858116 | + | 0.286039i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | − | 16.9706i | − | 1.59646i | −0.602355 | − | 0.798228i | \(-0.705771\pi\) | ||
0.602355 | − | 0.798228i | \(-0.294229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12132 | − | 0.707107i | −0.197814 | − | 0.0659380i | ||||
\(116\) | 7.65685 | 0.710921 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.48528i | − | 0.781133i | ||||||
\(119\) | −2.34315 | −0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | − | 3.41421i | − | 0.309108i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | 9.19239 | − | 6.36396i | 0.822192 | − | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.41421 | − | 10.2426i | 0.299446 | − | 0.898339i | ||||
\(131\) | 10.3431 | 0.903685 | 0.451842 | − | 0.892098i | \(-0.350767\pi\) | ||||
0.451842 | + | 0.892098i | \(0.350767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.48528i | 0.388923i | ||||||||
\(134\) | −0.585786 | −0.0506042 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.17157 | 0.100462 | ||||||||
\(137\) | 8.48528i | 0.724947i | 0.931994 | + | 0.362473i | \(0.118068\pi\) | ||||
−0.931994 | + | 0.362473i | \(0.881932\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9706 | −1.43942 | −0.719712 | − | 0.694273i | \(-0.755726\pi\) | ||||
−0.719712 | + | 0.694273i | \(0.755726\pi\) | |||||||
\(140\) | 4.24264 | + | 1.41421i | 0.358569 | + | 0.119523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 5.65685i | − | 0.474713i | ||||||
\(143\) | − | 20.4853i | − | 1.71307i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.41421 | − | 16.2426i | 0.449626 | − | 1.34888i | ||||
\(146\) | 3.65685 | 0.302643 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.41421i | 0.280647i | ||||||||
\(149\) | −12.7279 | −1.04271 | −0.521356 | − | 0.853339i | \(-0.674574\pi\) | ||||
−0.521356 | + | 0.853339i | \(0.674574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.6569 | −1.27414 | −0.637068 | − | 0.770807i | \(-0.719853\pi\) | ||||
−0.637068 | + | 0.770807i | \(0.719853\pi\) | |||||||
\(152\) | − | 2.24264i | − | 0.181902i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.48528 | 0.683763 | ||||||||
\(155\) | −4.24264 | + | 12.7279i | −0.340777 | + | 1.02233i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.92893i | − | 0.552989i | −0.961016 | − | 0.276494i | \(-0.910827\pi\) | ||
0.961016 | − | 0.276494i | \(-0.0891728\pi\) | |||||||
\(158\) | − | 7.65685i | − | 0.609147i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.12132 | − | 0.707107i | −0.167705 | − | 0.0559017i | ||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.17157i | 0.0917647i | 0.998947 | + | 0.0458823i | \(0.0146099\pi\) | ||||
−0.998947 | + | 0.0458823i | \(0.985390\pi\) | |||||||
\(164\) | −1.17157 | −0.0914845 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.41421 | −0.109764 | ||||||||
\(167\) | − | 8.82843i | − | 0.683164i | −0.939852 | − | 0.341582i | \(-0.889037\pi\) | ||
0.939852 | − | 0.341582i | \(-0.110963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3137 | −0.793362 | ||||||||
\(170\) | 0.828427 | − | 2.48528i | 0.0635375 | − | 0.190612i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.75736i | − | 0.133997i | ||||||
\(173\) | − | 3.17157i | − | 0.241130i | −0.992705 | − | 0.120565i | \(-0.961529\pi\) | ||
0.992705 | − | 0.120565i | \(-0.0384707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.00000 | − | 8.00000i | 0.453557 | − | 0.604743i | ||||
\(176\) | −4.24264 | −0.319801 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.8284i | 1.11144i | ||||||||
\(179\) | −10.3431 | −0.773083 | −0.386542 | − | 0.922272i | \(-0.626330\pi\) | ||||
−0.386542 | + | 0.922272i | \(0.626330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3848 | 1.21787 | 0.608935 | − | 0.793220i | \(-0.291597\pi\) | ||||
0.608935 | + | 0.793220i | \(0.291597\pi\) | |||||||
\(182\) | − | 9.65685i | − | 0.715814i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 7.24264 | + | 2.41421i | 0.532490 | + | 0.177497i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.97056i | − | 0.363484i | ||||||
\(188\) | − | 4.82843i | − | 0.352149i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.75736 | − | 1.58579i | −0.345135 | − | 0.115045i | ||||
\(191\) | 5.17157 | 0.374202 | 0.187101 | − | 0.982341i | \(-0.440091\pi\) | ||||
0.187101 | + | 0.982341i | \(0.440091\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9706i | 0.933642i | 0.884352 | + | 0.466821i | \(0.154601\pi\) | ||||
−0.884352 | + | 0.466821i | \(0.845399\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − | 24.6274i | − | 1.75463i | −0.479914 | − | 0.877315i | \(-0.659332\pi\) | ||
0.479914 | − | 0.877315i | \(-0.340668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | −3.00000 | + | 4.00000i | −0.212132 | + | 0.282843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.31371i | 0.655310i | ||||||||
\(203\) | − | 15.3137i | − | 1.07481i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.828427 | + | 2.48528i | −0.0578599 | + | 0.173580i | ||||
\(206\) | 12.1421 | 0.845983 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.82843i | 0.334791i | ||||||||
\(209\) | −9.51472 | −0.658147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4853 | −1.41026 | −0.705132 | − | 0.709076i | \(-0.749112\pi\) | ||||
−0.705132 | + | 0.709076i | \(0.749112\pi\) | |||||||
\(212\) | 13.4142i | 0.921292i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.0711 | −1.03024 | ||||||||
\(215\) | −3.72792 | − | 1.24264i | −0.254242 | − | 0.0847474i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000i | 0.814613i | ||||||||
\(218\) | − | 15.4142i | − | 1.04398i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.00000 | + | 9.00000i | −0.202260 | + | 0.606780i | ||||
\(221\) | −5.65685 | −0.380521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.9706 | 1.12887 | ||||||||
\(227\) | 14.3848i | 0.954751i | 0.878699 | + | 0.477376i | \(0.158412\pi\) | ||||
−0.878699 | + | 0.477376i | \(0.841588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.75736 | −0.116130 | −0.0580648 | − | 0.998313i | \(-0.518493\pi\) | ||||
−0.0580648 | + | 0.998313i | \(0.518493\pi\) | |||||||
\(230\) | 0.707107 | − | 2.12132i | 0.0466252 | − | 0.139876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.65685i | 0.502697i | ||||||||
\(233\) | 26.1421i | 1.71263i | 0.516455 | + | 0.856314i | \(0.327251\pi\) | ||||
−0.516455 | + | 0.856314i | \(0.672749\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2426 | − | 3.41421i | −0.668156 | − | 0.222719i | ||||
\(236\) | 8.48528 | 0.552345 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.34315i | − | 0.151884i | ||||||
\(239\) | −11.1716 | −0.722629 | −0.361314 | − | 0.932444i | \(-0.617672\pi\) | ||||
−0.361314 | + | 0.932444i | \(0.617672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4853 | −0.675416 | −0.337708 | − | 0.941251i | \(-0.609652\pi\) | ||||
−0.337708 | + | 0.941251i | \(0.609652\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.41421 | 0.218573 | ||||||||
\(245\) | −2.12132 | + | 6.36396i | −0.135526 | + | 0.406579i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.8284i | 0.688996i | ||||||||
\(248\) | − | 6.00000i | − | 0.381000i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.36396 | + | 9.19239i | 0.402492 | + | 0.581378i | ||||
\(251\) | 24.7279 | 1.56081 | 0.780406 | − | 0.625273i | \(-0.215012\pi\) | ||||
0.780406 | + | 0.625273i | \(0.215012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.24264i | − | 0.266733i | ||||||
\(254\) | −2.00000 | −0.125491 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.82843 | 0.424298 | ||||||||
\(260\) | 10.2426 | + | 3.41421i | 0.635222 | + | 0.211741i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.3431i | 0.639002i | ||||||||
\(263\) | 17.6569i | 1.08877i | 0.838836 | + | 0.544384i | \(0.183237\pi\) | ||||
−0.838836 | + | 0.544384i | \(0.816763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.4558 | + | 9.48528i | 1.74803 | + | 0.582676i | ||||
\(266\) | −4.48528 | −0.275010 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 0.585786i | − | 0.0357826i | ||||||
\(269\) | −24.8284 | −1.51382 | −0.756908 | − | 0.653521i | \(-0.773291\pi\) | ||||
−0.756908 | + | 0.653521i | \(0.773291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.65685 | −0.100647 | −0.0503234 | − | 0.998733i | \(-0.516025\pi\) | ||||
−0.0503234 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(272\) | 1.17157i | 0.0710370i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.48528 | −0.512615 | ||||||||
\(275\) | 16.9706 | + | 12.7279i | 1.02336 | + | 0.767523i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 30.4853i | − | 1.83168i | −0.401540 | − | 0.915842i | \(-0.631525\pi\) | ||
0.401540 | − | 0.915842i | \(-0.368475\pi\) | |||||||
\(278\) | − | 16.9706i | − | 1.01783i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.41421 | + | 4.24264i | −0.0845154 | + | 0.253546i | ||||
\(281\) | 30.1421 | 1.79813 | 0.899065 | − | 0.437816i | \(-0.144248\pi\) | ||||
0.899065 | + | 0.437816i | \(0.144248\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 27.2132i | − | 1.61766i | −0.588045 | − | 0.808829i | \(-0.700102\pi\) | ||
0.588045 | − | 0.808829i | \(-0.299898\pi\) | |||||||
\(284\) | 5.65685 | 0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.4853 | 1.21132 | ||||||||
\(287\) | 2.34315i | 0.138312i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6274 | 0.919260 | ||||||||
\(290\) | 16.2426 | + | 5.41421i | 0.953801 | + | 0.317934i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.65685i | 0.214001i | ||||||||
\(293\) | 28.0416i | 1.63821i | 0.573644 | + | 0.819105i | \(0.305529\pi\) | ||||
−0.573644 | + | 0.819105i | \(0.694471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | − | 18.0000i | 0.349334 | − | 1.04800i | ||||
\(296\) | −3.41421 | −0.198447 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 12.7279i | − | 0.737309i | ||||||
\(299\) | −4.82843 | −0.279235 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.51472 | −0.202585 | ||||||||
\(302\) | − | 15.6569i | − | 0.900951i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.24264 | 0.128624 | ||||||||
\(305\) | 2.41421 | − | 7.24264i | 0.138237 | − | 0.414712i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4558i | 1.45284i | 0.687250 | + | 0.726421i | \(0.258818\pi\) | ||||
−0.687250 | + | 0.726421i | \(0.741182\pi\) | |||||||
\(308\) | 8.48528i | 0.483494i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.7279 | − | 4.24264i | −0.722897 | − | 0.240966i | ||||
\(311\) | −17.7990 | −1.00929 | −0.504644 | − | 0.863328i | \(-0.668376\pi\) | ||||
−0.504644 | + | 0.863328i | \(0.668376\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0000i | 1.01742i | 0.860938 | + | 0.508710i | \(0.169877\pi\) | ||||
−0.860938 | + | 0.508710i | \(0.830123\pi\) | |||||||
\(314\) | 6.92893 | 0.391022 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.65685 | 0.430732 | ||||||||
\(317\) | 2.48528i | 0.139587i | 0.997561 | + | 0.0697937i | \(0.0222341\pi\) | ||||
−0.997561 | + | 0.0697937i | \(0.977766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.4853 | 1.81883 | ||||||||
\(320\) | 0.707107 | − | 2.12132i | 0.0395285 | − | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 2.00000i | − | 0.111456i | ||||||
\(323\) | 2.62742i | 0.146193i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.4853 | − | 19.3137i | 0.803499 | − | 1.07133i | ||||
\(326\) | −1.17157 | −0.0648874 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 1.17157i | − | 0.0646893i | ||||||
\(329\) | −9.65685 | −0.532400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.51472 | −0.193186 | −0.0965932 | − | 0.995324i | \(-0.530795\pi\) | ||||
−0.0965932 | + | 0.995324i | \(0.530795\pi\) | |||||||
\(332\) | − | 1.41421i | − | 0.0776151i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.82843 | 0.483070 | ||||||||
\(335\) | −1.24264 | − | 0.414214i | −0.0678927 | − | 0.0226309i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.51472i | 0.518300i | 0.965837 | + | 0.259150i | \(0.0834424\pi\) | ||||
−0.965837 | + | 0.259150i | \(0.916558\pi\) | |||||||
\(338\) | − | 10.3137i | − | 0.560992i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.48528 | + | 0.828427i | 0.134783 | + | 0.0449278i | ||||
\(341\) | −25.4558 | −1.37851 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 1.75736 | 0.0947505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.17157 | 0.170505 | ||||||||
\(347\) | 7.79899i | 0.418672i | 0.977844 | + | 0.209336i | \(0.0671302\pi\) | ||||
−0.977844 | + | 0.209336i | \(0.932870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.3137 | −1.35501 | −0.677506 | − | 0.735517i | \(-0.736939\pi\) | ||||
−0.677506 | + | 0.735517i | \(0.736939\pi\) | |||||||
\(350\) | 8.00000 | + | 6.00000i | 0.427618 | + | 0.320713i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.24264i | − | 0.226134i | ||||||
\(353\) | 26.1421i | 1.39141i | 0.718330 | + | 0.695703i | \(0.244907\pi\) | ||||
−0.718330 | + | 0.695703i | \(0.755093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | − | 12.0000i | 0.212298 | − | 0.636894i | ||||
\(356\) | −14.8284 | −0.785905 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 10.3431i | − | 0.546652i | ||||||
\(359\) | −19.7990 | −1.04495 | −0.522475 | − | 0.852654i | \(-0.674991\pi\) | ||||
−0.522475 | + | 0.852654i | \(0.674991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9706 | −0.735293 | ||||||||
\(362\) | 16.3848i | 0.861165i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.65685 | 0.506157 | ||||||||
\(365\) | 7.75736 | + | 2.58579i | 0.406039 | + | 0.135346i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 34.9706i | − | 1.82545i | −0.408576 | − | 0.912724i | \(-0.633975\pi\) | ||
0.408576 | − | 0.912724i | \(-0.366025\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.41421 | + | 7.24264i | −0.125509 | + | 0.376527i | ||||
\(371\) | 26.8284 | 1.39286 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.2132i | 0.994822i | 0.867515 | + | 0.497411i | \(0.165716\pi\) | ||||
−0.867515 | + | 0.497411i | \(0.834284\pi\) | |||||||
\(374\) | 4.97056 | 0.257022 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.82843 | 0.249007 | ||||||||
\(377\) | − | 36.9706i | − | 1.90408i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2132 | 0.986916 | 0.493458 | − | 0.869770i | \(-0.335733\pi\) | ||||
0.493458 | + | 0.869770i | \(0.335733\pi\) | |||||||
\(380\) | 1.58579 | − | 4.75736i | 0.0813491 | − | 0.244047i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.17157i | 0.264601i | ||||||||
\(383\) | 18.6274i | 0.951817i | 0.879495 | + | 0.475908i | \(0.157881\pi\) | ||||
−0.879495 | + | 0.475908i | \(0.842119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | + | 6.00000i | 0.917365 | + | 0.305788i | ||||
\(386\) | −12.9706 | −0.660184 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 6.00000i | − | 0.304604i | ||||||
\(389\) | 6.38478 | 0.323721 | 0.161861 | − | 0.986814i | \(-0.448251\pi\) | ||||
0.161861 | + | 0.986814i | \(0.448251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.17157 | −0.0592490 | ||||||||
\(392\) | − | 3.00000i | − | 0.151523i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.6274 | 1.24071 | ||||||||
\(395\) | 5.41421 | − | 16.2426i | 0.272419 | − | 0.817256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.34315i | 0.418730i | 0.977838 | + | 0.209365i | \(0.0671398\pi\) | ||||
−0.977838 | + | 0.209365i | \(0.932860\pi\) | |||||||
\(398\) | 14.0000i | 0.701757i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | − | 3.00000i | −0.200000 | − | 0.150000i | ||||
\(401\) | 28.9706 | 1.44672 | 0.723360 | − | 0.690471i | \(-0.242597\pi\) | ||||
0.723360 | + | 0.690471i | \(0.242597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9706i | 1.44313i | ||||||||
\(404\) | −9.31371 | −0.463374 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.3137 | 0.760007 | ||||||||
\(407\) | 14.4853i | 0.718009i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0000 | −0.890043 | −0.445021 | − | 0.895520i | \(-0.646804\pi\) | ||||
−0.445021 | + | 0.895520i | \(0.646804\pi\) | |||||||
\(410\) | −2.48528 | − | 0.828427i | −0.122739 | − | 0.0409131i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.1421i | 0.598200i | ||||||||
\(413\) | − | 16.9706i | − | 0.835067i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | − | 1.00000i | −0.147264 | − | 0.0490881i | ||||
\(416\) | −4.82843 | −0.236733 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 9.51472i | − | 0.465380i | ||||||
\(419\) | −24.9289 | −1.21786 | −0.608929 | − | 0.793225i | \(-0.708401\pi\) | ||||
−0.608929 | + | 0.793225i | \(0.708401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2426 | 0.499196 | 0.249598 | − | 0.968350i | \(-0.419702\pi\) | ||||
0.249598 | + | 0.968350i | \(0.419702\pi\) | |||||||
\(422\) | − | 20.4853i | − | 0.997208i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.4142 | −0.651452 | ||||||||
\(425\) | 3.51472 | − | 4.68629i | 0.170489 | − | 0.227319i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.82843i | − | 0.330451i | ||||||
\(428\) | − | 15.0711i | − | 0.728488i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.24264 | − | 3.72792i | 0.0599255 | − | 0.179776i | ||||
\(431\) | −8.48528 | −0.408722 | −0.204361 | − | 0.978896i | \(-0.565512\pi\) | ||||
−0.204361 | + | 0.978896i | \(0.565512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.9706i | 1.29612i | 0.761588 | + | 0.648061i | \(0.224420\pi\) | ||||
−0.761588 | + | 0.648061i | \(0.775580\pi\) | |||||||
\(434\) | −12.0000 | −0.576018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.4142 | 0.738207 | ||||||||
\(437\) | 2.24264i | 0.107280i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −9.00000 | − | 3.00000i | −0.429058 | − | 0.143019i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 5.65685i | − | 0.269069i | ||||||
\(443\) | 23.3137i | 1.10767i | 0.832627 | + | 0.553834i | \(0.186836\pi\) | ||||
−0.832627 | + | 0.553834i | \(0.813164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4853 | + | 31.4558i | −0.497050 | + | 1.49115i | ||||
\(446\) | −16.0000 | −0.757622 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.00000i | − | 0.0944911i | ||||||
\(449\) | −22.8284 | −1.07734 | −0.538670 | − | 0.842517i | \(-0.681073\pi\) | ||||
−0.538670 | + | 0.842517i | \(0.681073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.97056 | −0.234055 | ||||||||
\(452\) | 16.9706i | 0.798228i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.3848 | −0.675111 | ||||||||
\(455\) | 6.82843 | − | 20.4853i | 0.320122 | − | 0.960365i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.02944i | − | 0.0481550i | −0.999710 | − | 0.0240775i | \(-0.992335\pi\) | ||
0.999710 | − | 0.0240775i | \(-0.00766485\pi\) | |||||||
\(458\) | − | 1.75736i | − | 0.0821160i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.12132 | + | 0.707107i | 0.0989071 | + | 0.0329690i | ||||
\(461\) | 12.8284 | 0.597479 | 0.298740 | − | 0.954335i | \(-0.403434\pi\) | ||||
0.298740 | + | 0.954335i | \(0.403434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.97056i | 0.138054i | 0.997615 | + | 0.0690269i | \(0.0219894\pi\) | ||||
−0.997615 | + | 0.0690269i | \(0.978011\pi\) | |||||||
\(464\) | −7.65685 | −0.355461 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.1421 | −1.21101 | ||||||||
\(467\) | 39.3553i | 1.82115i | 0.413346 | + | 0.910574i | \(0.364360\pi\) | ||||
−0.413346 | + | 0.910574i | \(0.635640\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.17157 | −0.0540982 | ||||||||
\(470\) | 3.41421 | − | 10.2426i | 0.157486 | − | 0.472458i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.48528i | 0.390567i | ||||||||
\(473\) | − | 7.45584i | − | 0.342820i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.97056 | − | 6.72792i | −0.411598 | − | 0.308698i | ||||
\(476\) | 2.34315 | 0.107398 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 11.1716i | − | 0.510976i | ||||||
\(479\) | 4.68629 | 0.214122 | 0.107061 | − | 0.994252i | \(-0.465856\pi\) | ||||
0.107061 | + | 0.994252i | \(0.465856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4853 | 0.751664 | ||||||||
\(482\) | − | 10.4853i | − | 0.477591i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | −12.7279 | − | 4.24264i | −0.577945 | − | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.9411i | 1.26613i | 0.774097 | + | 0.633067i | \(0.218204\pi\) | ||||
−0.774097 | + | 0.633067i | \(0.781796\pi\) | |||||||
\(488\) | 3.41421i | 0.154554i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.36396 | − | 2.12132i | −0.287494 | − | 0.0958315i | ||||
\(491\) | −26.6274 | −1.20168 | −0.600839 | − | 0.799370i | \(-0.705167\pi\) | ||||
−0.600839 | + | 0.799370i | \(0.705167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.97056i | − | 0.404014i | ||||||
\(494\) | −10.8284 | −0.487194 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | − | 11.3137i | − | 0.507489i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4558 | −0.602366 | −0.301183 | − | 0.953566i | \(-0.597382\pi\) | ||||
−0.301183 | + | 0.953566i | \(0.597382\pi\) | |||||||
\(500\) | −9.19239 | + | 6.36396i | −0.411096 | + | 0.284605i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.7279i | 1.10366i | ||||||||
\(503\) | − | 22.1421i | − | 0.987269i | −0.869669 | − | 0.493635i | \(-0.835668\pi\) | ||
0.869669 | − | 0.493635i | \(-0.164332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.58579 | + | 19.7574i | −0.293064 | + | 0.879191i | ||||
\(506\) | 4.24264 | 0.188608 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 2.00000i | − | 0.0887357i | ||||||
\(509\) | 22.9706 | 1.01815 | 0.509076 | − | 0.860721i | \(-0.329987\pi\) | ||||
0.509076 | + | 0.860721i | \(0.329987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.31371 | 0.323539 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 25.7574 | + | 8.58579i | 1.13500 | + | 0.378335i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.4853i | − | 0.900942i | ||||||
\(518\) | 6.82843i | 0.300024i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.41421 | + | 10.2426i | −0.149723 | + | 0.449170i | ||||
\(521\) | 16.2843 | 0.713427 | 0.356713 | − | 0.934214i | \(-0.383897\pi\) | ||||
0.356713 | + | 0.934214i | \(0.383897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.92893i | − | 0.128073i | −0.997948 | − | 0.0640366i | \(-0.979603\pi\) | ||
0.997948 | − | 0.0640366i | \(-0.0203974\pi\) | |||||||
\(524\) | −10.3431 | −0.451842 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6569 | −0.769875 | ||||||||
\(527\) | 7.02944i | 0.306207i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | −9.48528 | + | 28.4558i | −0.412014 | + | 1.23604i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 4.48528i | − | 0.194462i | ||||||
\(533\) | 5.65685i | 0.245026i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.9706 | − | 10.6569i | −1.38221 | − | 0.460736i | ||||
\(536\) | 0.585786 | 0.0253021 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 24.8284i | − | 1.07043i | ||||||
\(539\) | −12.7279 | −0.548230 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.9411 | 1.54523 | 0.772615 | − | 0.634875i | \(-0.218948\pi\) | ||||
0.772615 | + | 0.634875i | \(0.218948\pi\) | |||||||
\(542\) | − | 1.65685i | − | 0.0711680i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.17157 | −0.0502308 | ||||||||
\(545\) | 10.8995 | − | 32.6985i | 0.466883 | − | 1.40065i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.48528i | 0.191777i | 0.995392 | + | 0.0958884i | \(0.0305692\pi\) | ||||
−0.995392 | + | 0.0958884i | \(0.969431\pi\) | |||||||
\(548\) | − | 8.48528i | − | 0.362473i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.7279 | + | 16.9706i | −0.542720 | + | 0.723627i | ||||
\(551\) | −17.1716 | −0.731534 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.3137i | − | 0.651205i | ||||||
\(554\) | 30.4853 | 1.29520 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.9706 | 0.719712 | ||||||||
\(557\) | − | 14.8701i | − | 0.630065i | −0.949081 | − | 0.315032i | \(-0.897985\pi\) | ||
0.949081 | − | 0.315032i | \(-0.102015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.48528 | −0.358889 | ||||||||
\(560\) | −4.24264 | − | 1.41421i | −0.179284 | − | 0.0597614i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.1421i | 1.27147i | ||||||||
\(563\) | 21.8995i | 0.922954i | 0.887152 | + | 0.461477i | \(0.152680\pi\) | ||||
−0.887152 | + | 0.461477i | \(0.847320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.0000 | + | 12.0000i | 1.51453 | + | 0.504844i | ||||
\(566\) | 27.2132 | 1.14386 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.65685i | 0.237356i | ||||||||
\(569\) | 25.6569 | 1.07559 | 0.537796 | − | 0.843075i | \(-0.319257\pi\) | ||||
0.537796 | + | 0.843075i | \(0.319257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.7279 | −1.78811 | −0.894054 | − | 0.447959i | \(-0.852151\pi\) | ||||
−0.894054 | + | 0.447959i | \(0.852151\pi\) | |||||||
\(572\) | 20.4853i | 0.856533i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.34315 | −0.0978010 | ||||||||
\(575\) | 3.00000 | − | 4.00000i | 0.125109 | − | 0.166812i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.6274i | 0.858731i | 0.903131 | + | 0.429365i | \(0.141263\pi\) | ||||
−0.903131 | + | 0.429365i | \(0.858737\pi\) | |||||||
\(578\) | 15.6274i | 0.650015i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.41421 | + | 16.2426i | −0.224813 | + | 0.674439i | ||||
\(581\) | −2.82843 | −0.117343 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56.9117i | 2.35704i | ||||||||
\(584\) | −3.65685 | −0.151322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.0416 | −1.15839 | ||||||||
\(587\) | 26.8284i | 1.10733i | 0.832740 | + | 0.553664i | \(0.186771\pi\) | ||||
−0.832740 | + | 0.553664i | \(0.813229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4558 | 0.554438 | ||||||||
\(590\) | 18.0000 | + | 6.00000i | 0.741048 | + | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 3.41421i | − | 0.140323i | ||||||
\(593\) | 12.3431i | 0.506872i | 0.967352 | + | 0.253436i | \(0.0815608\pi\) | ||||
−0.967352 | + | 0.253436i | \(0.918439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.65685 | − | 4.97056i | 0.0679244 | − | 0.203773i | ||||
\(596\) | 12.7279 | 0.521356 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 4.82843i | − | 0.197449i | ||||||
\(599\) | −40.1421 | −1.64016 | −0.820082 | − | 0.572247i | \(-0.806072\pi\) | ||||
−0.820082 | + | 0.572247i | \(0.806072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9706 | −0.855407 | −0.427704 | − | 0.903919i | \(-0.640677\pi\) | ||||
−0.427704 | + | 0.903919i | \(0.640677\pi\) | |||||||
\(602\) | − | 3.51472i | − | 0.143249i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.6569 | 0.637068 | ||||||||
\(605\) | −4.94975 | + | 14.8492i | −0.201236 | + | 0.603708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.9706i | 0.688814i | 0.938820 | + | 0.344407i | \(0.111920\pi\) | ||||
−0.938820 | + | 0.344407i | \(0.888080\pi\) | |||||||
\(608\) | 2.24264i | 0.0909511i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.24264 | + | 2.41421i | 0.293246 | + | 0.0977486i | ||||
\(611\) | −23.3137 | −0.943172 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 14.2426i | − | 0.575255i | −0.957742 | − | 0.287627i | \(-0.907134\pi\) | ||
0.957742 | − | 0.287627i | \(-0.0928665\pi\) | |||||||
\(614\) | −25.4558 | −1.02731 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.48528 | −0.341882 | ||||||||
\(617\) | − | 31.3137i | − | 1.26064i | −0.776334 | − | 0.630321i | \(-0.782923\pi\) | ||
0.776334 | − | 0.630321i | \(-0.217077\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.2132 | 0.772244 | 0.386122 | − | 0.922448i | \(-0.373814\pi\) | ||||
0.386122 | + | 0.922448i | \(0.373814\pi\) | |||||||
\(620\) | 4.24264 | − | 12.7279i | 0.170389 | − | 0.511166i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 17.7990i | − | 0.713674i | ||||||
\(623\) | 29.6569i | 1.18818i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | −18.0000 | −0.719425 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.92893i | 0.276494i | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.1716 | 1.40016 | 0.700079 | − | 0.714065i | \(-0.253148\pi\) | ||||
0.700079 | + | 0.714065i | \(0.253148\pi\) | |||||||
\(632\) | 7.65685i | 0.304573i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.48528 | −0.0987031 | ||||||||
\(635\) | −4.24264 | − | 1.41421i | −0.168364 | − | 0.0561214i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.4853i | 0.573928i | ||||||||
\(638\) | 32.4853i | 1.28610i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12132 | + | 0.707107i | 0.0838525 | + | 0.0279508i | ||||
\(641\) | 8.28427 | 0.327209 | 0.163605 | − | 0.986526i | \(-0.447688\pi\) | ||||
0.163605 | + | 0.986526i | \(0.447688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 32.3848i | − | 1.27713i | −0.769568 | − | 0.638565i | \(-0.779528\pi\) | ||
0.769568 | − | 0.638565i | \(-0.220472\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.62742 | −0.103374 | ||||||||
\(647\) | − | 29.6569i | − | 1.16593i | −0.812497 | − | 0.582966i | \(-0.801892\pi\) | ||
0.812497 | − | 0.582966i | \(-0.198108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.0000 | 1.41312 | ||||||||
\(650\) | 19.3137 | + | 14.4853i | 0.757546 | + | 0.568159i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 1.17157i | − | 0.0458823i | ||||||
\(653\) | − | 43.4558i | − | 1.70056i | −0.526332 | − | 0.850279i | \(-0.676433\pi\) | ||
0.526332 | − | 0.850279i | \(-0.323567\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.31371 | + | 21.9411i | −0.285770 | + | 0.857311i | ||||
\(656\) | 1.17157 | 0.0457422 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 9.65685i | − | 0.376463i | ||||||
\(659\) | −26.1005 | −1.01673 | −0.508366 | − | 0.861141i | \(-0.669750\pi\) | ||||
−0.508366 | + | 0.861141i | \(0.669750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.27208 | 0.360642 | 0.180321 | − | 0.983608i | \(-0.442286\pi\) | ||||
0.180321 | + | 0.983608i | \(0.442286\pi\) | |||||||
\(662\) | − | 3.51472i | − | 0.136603i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.41421 | 0.0548821 | ||||||||
\(665\) | −9.51472 | − | 3.17157i | −0.368965 | − | 0.122988i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.65685i | − | 0.296475i | ||||||
\(668\) | 8.82843i | 0.341582i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.414214 | − | 1.24264i | 0.0160025 | − | 0.0480074i | ||||
\(671\) | 14.4853 | 0.559198 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 39.9411i | − | 1.53962i | −0.638275 | − | 0.769809i | \(-0.720352\pi\) | ||
0.638275 | − | 0.769809i | \(-0.279648\pi\) | |||||||
\(674\) | −9.51472 | −0.366493 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3137 | 0.396681 | ||||||||
\(677\) | 24.5269i | 0.942646i | 0.881961 | + | 0.471323i | \(0.156223\pi\) | ||||
−0.881961 | + | 0.471323i | \(0.843777\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | −0.460518 | ||||||||
\(680\) | −0.828427 | + | 2.48528i | −0.0317687 | + | 0.0953062i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 25.4558i | − | 0.974755i | ||||||
\(683\) | − | 8.48528i | − | 0.324680i | −0.986735 | − | 0.162340i | \(-0.948096\pi\) | ||
0.986735 | − | 0.162340i | \(-0.0519042\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | − | 6.00000i | −0.687745 | − | 0.229248i | ||||
\(686\) | −20.0000 | −0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.75736i | 0.0669987i | ||||||||
\(689\) | 64.7696 | 2.46752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8284 | −0.716267 | −0.358134 | − | 0.933670i | \(-0.616587\pi\) | ||||
−0.358134 | + | 0.933670i | \(0.616587\pi\) | |||||||
\(692\) | 3.17157i | 0.120565i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.79899 | −0.296046 | ||||||||
\(695\) | 12.0000 | − | 36.0000i | 0.455186 | − | 1.36556i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.37258i | 0.0519903i | ||||||||
\(698\) | − | 25.3137i | − | 0.958138i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.00000 | + | 8.00000i | −0.226779 | + | 0.302372i | ||||
\(701\) | −38.1838 | −1.44218 | −0.721090 | − | 0.692841i | \(-0.756359\pi\) | ||||
−0.721090 | + | 0.692841i | \(0.756359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.65685i | − | 0.288784i | ||||||
\(704\) | 4.24264 | 0.159901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.1421 | −0.983872 | ||||||||
\(707\) | 18.6274i | 0.700556i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.4142 | −1.33001 | −0.665004 | − | 0.746839i | \(-0.731570\pi\) | ||||
−0.665004 | + | 0.746839i | \(0.731570\pi\) | |||||||
\(710\) | 12.0000 | + | 4.00000i | 0.450352 | + | 0.150117i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 14.8284i | − | 0.555719i | ||||||
\(713\) | 6.00000i | 0.224702i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.4558 | + | 14.4853i | 1.62516 | + | 0.541719i | ||||
\(716\) | 10.3431 | 0.386542 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 19.7990i | − | 0.738892i | ||||||
\(719\) | 28.1421 | 1.04952 | 0.524762 | − | 0.851249i | \(-0.324154\pi\) | ||||
0.524762 | + | 0.851249i | \(0.324154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.2843 | 0.904394 | ||||||||
\(722\) | − | 13.9706i | − | 0.519931i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.3848 | −0.608935 | ||||||||
\(725\) | 30.6274 | + | 22.9706i | 1.13747 | + | 0.853105i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.6569i | 1.17409i | 0.809555 | + | 0.587044i | \(0.199708\pi\) | ||||
−0.809555 | + | 0.587044i | \(0.800292\pi\) | |||||||
\(728\) | 9.65685i | 0.357907i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.58579 | + | 7.75736i | −0.0957042 | + | 0.287113i | ||||
\(731\) | −2.05887 | −0.0761502 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.58579i | 0.317123i | 0.987349 | + | 0.158562i | \(0.0506857\pi\) | ||||
−0.987349 | + | 0.158562i | \(0.949314\pi\) | |||||||
\(734\) | 34.9706 | 1.29079 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | − | 2.48528i | − | 0.0915465i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.6274 | −1.56807 | −0.784037 | − | 0.620714i | \(-0.786843\pi\) | ||||
−0.784037 | + | 0.620714i | \(0.786843\pi\) | |||||||
\(740\) | −7.24264 | − | 2.41421i | −0.266245 | − | 0.0887483i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.8284i | 0.984903i | ||||||||
\(743\) | − | 2.34315i | − | 0.0859617i | −0.999076 | − | 0.0429808i | \(-0.986315\pi\) | ||
0.999076 | − | 0.0429808i | \(-0.0136854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 27.0000i | 0.329734 | − | 0.989203i | ||||
\(746\) | −19.2132 | −0.703445 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.97056i | 0.181742i | ||||||||
\(749\) | −30.1421 | −1.10137 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.8284 | −1.78177 | −0.890887 | − | 0.454224i | \(-0.849916\pi\) | ||||
−0.890887 | + | 0.454224i | \(0.849916\pi\) | |||||||
\(752\) | 4.82843i | 0.176075i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 36.9706 | 1.34639 | ||||||||
\(755\) | 11.0711 | − | 33.2132i | 0.402917 | − | 1.20875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 42.2426i | − | 1.53533i | −0.640848 | − | 0.767667i | \(-0.721417\pi\) | ||
0.640848 | − | 0.767667i | \(-0.278583\pi\) | |||||||
\(758\) | 19.2132i | 0.697855i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.75736 | + | 1.58579i | 0.172568 | + | 0.0575225i | ||||
\(761\) | 24.3431 | 0.882438 | 0.441219 | − | 0.897399i | \(-0.354546\pi\) | ||||
0.441219 | + | 0.897399i | \(0.354546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 30.8284i | − | 1.11606i | ||||||
\(764\) | −5.17157 | −0.187101 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.6274 | −0.673036 | ||||||||
\(767\) | − | 40.9706i | − | 1.47936i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.7990 | −1.65155 | −0.825777 | − | 0.563997i | \(-0.809263\pi\) | ||||
−0.825777 | + | 0.563997i | \(0.809263\pi\) | |||||||
\(770\) | −6.00000 | + | 18.0000i | −0.216225 | + | 0.648675i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 12.9706i | − | 0.466821i | ||||||
\(773\) | 16.9289i | 0.608891i | 0.952530 | + | 0.304446i | \(0.0984712\pi\) | ||||
−0.952530 | + | 0.304446i | \(0.901529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.0000 | − | 18.0000i | −0.862105 | − | 0.646579i | ||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.38478i | 0.228905i | ||||||||
\(779\) | 2.62742 | 0.0941370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | − | 1.17157i | − | 0.0418954i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 14.6985 | + | 4.89949i | 0.524611 | + | 0.174870i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.72792i | − | 0.0972399i | −0.998817 | − | 0.0486200i | \(-0.984518\pi\) | ||
0.998817 | − | 0.0486200i | \(-0.0154823\pi\) | |||||||
\(788\) | 24.6274i | 0.877315i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.2426 | + | 5.41421i | 0.577887 | + | 0.192629i | ||||
\(791\) | 33.9411 | 1.20681 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.4853i | − | 0.585410i | ||||||
\(794\) | −8.34315 | −0.296087 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | − | 21.4142i | − | 0.758530i | −0.925288 | − | 0.379265i | \(-0.876177\pi\) | ||
0.925288 | − | 0.379265i | \(-0.123823\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.65685 | −0.200125 | ||||||||
\(800\) | 3.00000 | − | 4.00000i | 0.106066 | − | 0.141421i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.9706i | 1.02299i | ||||||||
\(803\) | 15.5147i | 0.547503i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.41421 | − | 4.24264i | 0.0498445 | − | 0.149533i | ||||
\(806\) | −28.9706 | −1.02044 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 9.31371i | − | 0.327655i | ||||||
\(809\) | 13.3137 | 0.468085 | 0.234043 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234043 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.82843 | 0.239779 | 0.119889 | − | 0.992787i | \(-0.461746\pi\) | ||||
0.119889 | + | 0.992787i | \(0.461746\pi\) | |||||||
\(812\) | 15.3137i | 0.537406i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.4853 | −0.507709 | ||||||||
\(815\) | −2.48528 | − | 0.828427i | −0.0870556 | − | 0.0290185i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.94113i | 0.137883i | ||||||||
\(818\) | − | 18.0000i | − | 0.629355i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.828427 | − | 2.48528i | 0.0289299 | − | 0.0867898i | ||||
\(821\) | 6.68629 | 0.233353 | 0.116677 | − | 0.993170i | \(-0.462776\pi\) | ||||
0.116677 | + | 0.993170i | \(0.462776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.2843i | 1.12536i | 0.826675 | + | 0.562679i | \(0.190229\pi\) | ||||
−0.826675 | + | 0.562679i | \(0.809771\pi\) | |||||||
\(824\) | −12.1421 | −0.422991 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.9706 | 0.590481 | ||||||||
\(827\) | 18.1005i | 0.629416i | 0.949188 | + | 0.314708i | \(0.101907\pi\) | ||||
−0.949188 | + | 0.314708i | \(0.898093\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.2843 | −1.74644 | −0.873222 | − | 0.487322i | \(-0.837974\pi\) | ||||
−0.873222 | + | 0.487322i | \(0.837974\pi\) | |||||||
\(830\) | 1.00000 | − | 3.00000i | 0.0347105 | − | 0.104132i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.82843i | − | 0.167396i | ||||||
\(833\) | 3.51472i | 0.121778i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.7279 | + | 6.24264i | 0.648106 | + | 0.216035i | ||||
\(836\) | 9.51472 | 0.329073 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 24.9289i | − | 0.861156i | ||||||
\(839\) | −33.9411 | −1.17178 | −0.585889 | − | 0.810391i | \(-0.699255\pi\) | ||||
−0.585889 | + | 0.810391i | \(0.699255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | 10.2426i | 0.352985i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.4853 | 0.705132 | ||||||||
\(845\) | 7.29289 | − | 21.8787i | 0.250883 | − | 0.752649i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0000i | 0.481046i | ||||||||
\(848\) | − | 13.4142i | − | 0.460646i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.68629 | + | 3.51472i | 0.160738 | + | 0.120554i | ||||
\(851\) | 3.41421 | 0.117038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.31371i | 0.0449805i | 0.999747 | + | 0.0224903i | \(0.00715948\pi\) | ||||
−0.999747 | + | 0.0224903i | \(0.992841\pi\) | |||||||
\(854\) | 6.82843 | 0.233664 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.0711 | 0.515118 | ||||||||
\(857\) | − | 45.1716i | − | 1.54303i | −0.636210 | − | 0.771516i | \(-0.719499\pi\) | ||
0.636210 | − | 0.771516i | \(-0.280501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.2843 | 1.10153 | 0.550763 | − | 0.834662i | \(-0.314337\pi\) | ||||
0.550763 | + | 0.834662i | \(0.314337\pi\) | |||||||
\(860\) | 3.72792 | + | 1.24264i | 0.127121 | + | 0.0423737i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 8.48528i | − | 0.289010i | ||||||
\(863\) | − | 22.6274i | − | 0.770246i | −0.922865 | − | 0.385123i | \(-0.874159\pi\) | ||
0.922865 | − | 0.385123i | \(-0.125841\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.72792 | + | 2.24264i | 0.228756 | + | 0.0762521i | ||||
\(866\) | −26.9706 | −0.916497 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 12.0000i | − | 0.407307i | ||||||
\(869\) | 32.4853 | 1.10199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82843 | −0.0958376 | ||||||||
\(872\) | 15.4142i | 0.521991i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.24264 | −0.0758585 | ||||||||
\(875\) | 12.7279 | + | 18.3848i | 0.430282 | + | 0.621519i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1716i | 0.377237i | 0.982050 | + | 0.188619i | \(0.0604010\pi\) | ||||
−0.982050 | + | 0.188619i | \(0.939599\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.00000 | − | 9.00000i | 0.101130 | − | 0.303390i | ||||
\(881\) | 2.14214 | 0.0721704 | 0.0360852 | − | 0.999349i | \(-0.488511\pi\) | ||||
0.0360852 | + | 0.999349i | \(0.488511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.1716i | 0.443259i | 0.975131 | + | 0.221629i | \(0.0711375\pi\) | ||||
−0.975131 | + | 0.221629i | \(0.928862\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.3137 | −0.783239 | ||||||||
\(887\) | − | 48.4264i | − | 1.62600i | −0.582264 | − | 0.813000i | \(-0.697833\pi\) | ||
0.582264 | − | 0.813000i | \(-0.302167\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | −31.4558 | − | 10.4853i | −1.05440 | − | 0.351467i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 16.0000i | − | 0.535720i | ||||||
\(893\) | 10.8284i | 0.362359i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.31371 | − | 21.9411i | 0.244470 | − | 0.733411i | ||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 22.8284i | − | 0.761794i | ||||||
\(899\) | −45.9411 | −1.53222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7157 | 0.523567 | ||||||||
\(902\) | − | 4.97056i | − | 0.165502i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.9706 | −0.564433 | ||||||||
\(905\) | −11.5858 | + | 34.7574i | −0.385125 | + | 1.15537i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 27.2132i | − | 0.903600i | −0.892119 | − | 0.451800i | \(-0.850782\pi\) | ||
0.892119 | − | 0.451800i | \(-0.149218\pi\) | |||||||
\(908\) | − | 14.3848i | − | 0.477376i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20.4853 | + | 6.82843i | 0.679080 | + | 0.226360i | ||||
\(911\) | 0.201010 | 0.00665976 | 0.00332988 | − | 0.999994i | \(-0.498940\pi\) | ||||
0.00332988 | + | 0.999994i | \(0.498940\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.00000i | − | 0.198571i | ||||||
\(914\) | 1.02944 | 0.0340508 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.75736 | 0.0580648 | ||||||||
\(917\) | 20.6863i | 0.683122i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.02944 | −0.165906 | −0.0829529 | − | 0.996553i | \(-0.526435\pi\) | ||||
−0.0829529 | + | 0.996553i | \(0.526435\pi\) | |||||||
\(920\) | −0.707107 | + | 2.12132i | −0.0233126 | + | 0.0699379i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.8284i | 0.422482i | ||||||||
\(923\) | − | 27.3137i | − | 0.899042i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.2426 | + | 13.6569i | −0.336776 | + | 0.449035i | ||||
\(926\) | −2.97056 | −0.0976187 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7.65685i | − | 0.251349i | ||||||
\(929\) | 42.1421 | 1.38264 | 0.691319 | − | 0.722549i | \(-0.257030\pi\) | ||||
0.691319 | + | 0.722549i | \(0.257030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.72792 | 0.220499 | ||||||||
\(932\) | − | 26.1421i | − | 0.856314i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −39.3553 | −1.28775 | ||||||||
\(935\) | 10.5442 | + | 3.51472i | 0.344831 | + | 0.114944i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.4264i | − | 1.45135i | −0.688039 | − | 0.725674i | \(-0.741528\pi\) | ||
0.688039 | − | 0.725674i | \(-0.258472\pi\) | |||||||
\(938\) | − | 1.17157i | − | 0.0382532i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.2426 | + | 3.41421i | 0.334078 | + | 0.111359i | ||||
\(941\) | 31.5563 | 1.02871 | 0.514354 | − | 0.857578i | \(-0.328032\pi\) | ||||
0.514354 | + | 0.857578i | \(0.328032\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.17157i | 0.0381517i | ||||||||
\(944\) | −8.48528 | −0.276172 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.45584 | 0.242410 | ||||||||
\(947\) | 1.45584i | 0.0473086i | 0.999720 | + | 0.0236543i | \(0.00753010\pi\) | ||||
−0.999720 | + | 0.0236543i | \(0.992470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.6569 | 0.573166 | ||||||||
\(950\) | 6.72792 | − | 8.97056i | 0.218283 | − | 0.291043i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.34315i | 0.0759418i | ||||||||
\(953\) | − | 40.0833i | − | 1.29842i | −0.760607 | − | 0.649212i | \(-0.775099\pi\) | ||
0.760607 | − | 0.649212i | \(-0.224901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.65685 | + | 10.9706i | −0.118333 | + | 0.354999i | ||||
\(956\) | 11.1716 | 0.361314 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.68629i | 0.151407i | ||||||||
\(959\) | −16.9706 | −0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 16.4853i | 0.531507i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.4853 | 0.337708 | ||||||||
\(965\) | −27.5147 | − | 9.17157i | −0.885730 | − | 0.295243i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.97056i | − | 0.159843i | −0.996801 | − | 0.0799213i | \(-0.974533\pi\) | ||
0.996801 | − | 0.0799213i | \(-0.0254669\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.24264 | − | 12.7279i | 0.136223 | − | 0.408669i | ||||
\(971\) | 17.6152 | 0.565299 | 0.282650 | − | 0.959223i | \(-0.408787\pi\) | ||||
0.282650 | + | 0.959223i | \(0.408787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 33.9411i | − | 1.08810i | ||||||
\(974\) | −27.9411 | −0.895291 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.41421 | −0.109286 | ||||||||
\(977\) | 19.7990i | 0.633426i | 0.948521 | + | 0.316713i | \(0.102579\pi\) | ||||
−0.948521 | + | 0.316713i | \(0.897421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.9117 | −2.01067 | ||||||||
\(980\) | 2.12132 | − | 6.36396i | 0.0677631 | − | 0.203289i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 26.6274i | − | 0.849715i | ||||||
\(983\) | 20.4853i | 0.653379i | 0.945132 | + | 0.326690i | \(0.105933\pi\) | ||||
−0.945132 | + | 0.326690i | \(0.894067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.2426 | + | 17.4142i | 1.66459 | + | 0.554863i | ||||
\(986\) | 8.97056 | 0.285681 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 10.8284i | − | 0.344498i | ||||||
\(989\) | −1.75736 | −0.0558808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.9411 | 1.64996 | 0.824982 | − | 0.565159i | \(-0.191185\pi\) | ||||
0.824982 | + | 0.565159i | \(0.191185\pi\) | |||||||
\(992\) | 6.00000i | 0.190500i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.3137 | 0.358849 | ||||||||
\(995\) | −9.89949 | + | 29.6985i | −0.313835 | + | 0.941505i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.9706i | 1.48757i | 0.668417 | + | 0.743786i | \(0.266972\pi\) | ||||
−0.668417 | + | 0.743786i | \(0.733028\pi\) | |||||||
\(998\) | − | 13.4558i | − | 0.425937i | ||||||
\(999\) | 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 | 2070.2.d.a.829.3 | 4 | ||
3.2 | odd | 2 | 690.2.d.b.139.2 | ✓ | 4 | ||
5.4 | even | 2 | inner | 2070.2.d.a.829.1 | 4 | ||
15.2 | even | 4 | 3450.2.a.bk.1.2 | 2 | |||
15.8 | even | 4 | 3450.2.a.bg.1.2 | 2 | |||
15.14 | odd | 2 | 690.2.d.b.139.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.b.139.2 | ✓ | 4 | 3.2 | odd | 2 | ||
690.2.d.b.139.4 | yes | 4 | 15.14 | odd | 2 | ||
2070.2.d.a.829.1 | 4 | 5.4 | even | 2 | inner | ||
2070.2.d.a.829.3 | 4 | 1.1 | even | 1 | trivial | ||
3450.2.a.bg.1.2 | 2 | 15.8 | even | 4 | |||
3450.2.a.bk.1.2 | 2 | 15.2 | even | 4 |