Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(518,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.518");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.k (of order \(4\), degree \(2\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 782.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.782 |
Dual form | 825.2.k.f.518.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.292893 | − | 0.292893i | 0.207107 | − | 0.207107i | −0.595930 | − | 0.803037i | \(-0.703216\pi\) |
0.803037 | + | 0.595930i | \(0.203216\pi\) | |||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 1.82843i | 0.914214i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.707107 | + | 0.121320i | 0.288675 | + | 0.0495288i | ||||
\(7\) | 3.41421 | + | 3.41421i | 1.29045 | + | 1.29045i | 0.934507 | + | 0.355944i | \(0.115841\pi\) |
0.355944 | + | 0.934507i | \(0.384159\pi\) | |||||||
\(8\) | 1.12132 | + | 1.12132i | 0.396447 | + | 0.396447i | ||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | −2.58579 | + | 1.82843i | −0.746452 | + | 0.527821i | ||||
\(13\) | 2.00000 | − | 2.00000i | 0.554700 | − | 0.554700i | −0.373094 | − | 0.927794i | \(-0.621703\pi\) |
0.927794 | + | 0.373094i | \(0.121703\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 2.82843 | − | 2.82843i | 0.685994 | − | 0.685994i | −0.275350 | − | 0.961344i | \(-0.588794\pi\) |
0.961344 | + | 0.275350i | \(0.0887937\pi\) | |||||||
\(18\) | 0.535534 | + | 1.12132i | 0.126227 | + | 0.264298i | ||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | + | 8.24264i | −0.308607 | + | 1.79869i | ||||
\(22\) | −0.292893 | − | 0.292893i | −0.0624450 | − | 0.0624450i | ||||
\(23\) | −3.24264 | − | 3.24264i | −0.676137 | − | 0.676137i | 0.282987 | − | 0.959124i | \(-0.408675\pi\) |
−0.959124 | + | 0.282987i | \(0.908675\pi\) | |||||||
\(24\) | −0.464466 | + | 2.70711i | −0.0948087 | + | 0.552586i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1.17157i | − | 0.229764i | ||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | −6.24264 | + | 6.24264i | −1.17975 | + | 1.17975i | ||||
\(29\) | 0.828427 | 0.153835 | 0.0769175 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769175 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.17157 | −0.569631 | −0.284816 | − | 0.958582i | \(-0.591932\pi\) | ||||
−0.284816 | + | 0.958582i | \(0.591932\pi\) | |||||||
\(32\) | −3.12132 | + | 3.12132i | −0.551777 | + | 0.551777i | ||||
\(33\) | 1.41421 | − | 1.00000i | 0.246183 | − | 0.174078i | ||||
\(34\) | − | 1.65685i | − | 0.284148i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.17157 | − | 1.82843i | −0.861929 | − | 0.304738i | ||||
\(37\) | 0.171573 | + | 0.171573i | 0.0282064 | + | 0.0282064i | 0.721069 | − | 0.692863i | \(-0.243651\pi\) |
−0.692863 | + | 0.721069i | \(0.743651\pi\) | |||||||
\(38\) | −0.828427 | − | 0.828427i | −0.134389 | − | 0.134389i | ||||
\(39\) | 4.82843 | + | 0.828427i | 0.773167 | + | 0.132655i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.65685i | − | 1.19580i | −0.801571 | − | 0.597900i | \(-0.796002\pi\) | ||
0.801571 | − | 0.597900i | \(-0.203998\pi\) | |||||||
\(42\) | 2.00000 | + | 2.82843i | 0.308607 | + | 0.436436i | ||||
\(43\) | −0.242641 | + | 0.242641i | −0.0370024 | + | 0.0370024i | −0.725366 | − | 0.688364i | \(-0.758329\pi\) |
0.688364 | + | 0.725366i | \(0.258329\pi\) | |||||||
\(44\) | 1.82843 | 0.275646 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.89949 | −0.280065 | ||||||||
\(47\) | 7.24264 | − | 7.24264i | 1.05645 | − | 1.05645i | 0.0581392 | − | 0.998308i | \(-0.481483\pi\) |
0.998308 | − | 0.0581392i | \(-0.0185167\pi\) | |||||||
\(48\) | −3.00000 | − | 4.24264i | −0.433013 | − | 0.612372i | ||||
\(49\) | 16.3137i | 2.33053i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.82843 | + | 1.17157i | 0.956171 | + | 0.164053i | ||||
\(52\) | 3.65685 | + | 3.65685i | 0.507114 | + | 0.507114i | ||||
\(53\) | −1.00000 | − | 1.00000i | −0.137361 | − | 0.137361i | 0.635083 | − | 0.772444i | \(-0.280966\pi\) |
−0.772444 | + | 0.635083i | \(0.780966\pi\) | |||||||
\(54\) | −1.05025 | + | 1.87868i | −0.142921 | + | 0.255656i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.65685i | 1.02319i | ||||||||
\(57\) | 4.00000 | − | 2.82843i | 0.529813 | − | 0.374634i | ||||
\(58\) | 0.242641 | − | 0.242641i | 0.0318603 | − | 0.0318603i | ||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.48528 | −0.830355 | −0.415178 | − | 0.909740i | \(-0.636281\pi\) | ||||
−0.415178 | + | 0.909740i | \(0.636281\pi\) | |||||||
\(62\) | −0.928932 | + | 0.928932i | −0.117975 | + | 0.117975i | ||||
\(63\) | −13.0711 | + | 6.24264i | −1.64680 | + | 0.786499i | ||||
\(64\) | − | 4.17157i | − | 0.521447i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.121320 | − | 0.707107i | 0.0149335 | − | 0.0870388i | ||||
\(67\) | 6.41421 | + | 6.41421i | 0.783621 | + | 0.783621i | 0.980440 | − | 0.196819i | \(-0.0630611\pi\) |
−0.196819 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(68\) | 5.17157 | + | 5.17157i | 0.627145 | + | 0.627145i | ||||
\(69\) | 1.34315 | − | 7.82843i | 0.161696 | − | 0.942432i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.48528i | − | 0.294949i | −0.989066 | − | 0.147474i | \(-0.952886\pi\) | ||
0.989066 | − | 0.147474i | \(-0.0471144\pi\) | |||||||
\(72\) | −4.29289 | + | 2.05025i | −0.505922 | + | 0.241625i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0.100505 | 0.0116835 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | 3.41421 | − | 3.41421i | 0.389086 | − | 0.389086i | ||||
\(78\) | 1.65685 | − | 1.17157i | 0.187602 | − | 0.132655i | ||||
\(79\) | 10.8284i | 1.21829i | 0.793058 | + | 0.609147i | \(0.208488\pi\) | ||||
−0.793058 | + | 0.609147i | \(0.791512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | −2.24264 | − | 2.24264i | −0.247658 | − | 0.247658i | ||||
\(83\) | 9.07107 | + | 9.07107i | 0.995679 | + | 0.995679i | 0.999991 | − | 0.00431166i | \(-0.00137245\pi\) |
−0.00431166 | + | 0.999991i | \(0.501372\pi\) | |||||||
\(84\) | −15.0711 | − | 2.58579i | −1.64439 | − | 0.282132i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.142136i | 0.0153269i | ||||||||
\(87\) | 0.828427 | + | 1.17157i | 0.0888167 | + | 0.125606i | ||||
\(88\) | 1.12132 | − | 1.12132i | 0.119533 | − | 0.119533i | ||||
\(89\) | −9.65685 | −1.02362 | −0.511812 | − | 0.859097i | \(-0.671026\pi\) | ||||
−0.511812 | + | 0.859097i | \(0.671026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6569 | 1.43163 | ||||||||
\(92\) | 5.92893 | − | 5.92893i | 0.618134 | − | 0.618134i | ||||
\(93\) | −3.17157 | − | 4.48528i | −0.328877 | − | 0.465102i | ||||
\(94\) | − | 4.24264i | − | 0.437595i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.53553 | − | 1.29289i | −0.769092 | − | 0.131955i | ||||
\(97\) | −10.6569 | − | 10.6569i | −1.08204 | − | 1.08204i | −0.996319 | − | 0.0857204i | \(-0.972681\pi\) |
−0.0857204 | − | 0.996319i | \(-0.527319\pi\) | |||||||
\(98\) | 4.77817 | + | 4.77817i | 0.482669 | + | 0.482669i | ||||
\(99\) | 2.82843 | + | 1.00000i | 0.284268 | + | 0.100504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.17157i | − | 0.713598i | −0.934181 | − | 0.356799i | \(-0.883868\pi\) | ||
0.934181 | − | 0.356799i | \(-0.116132\pi\) | |||||||
\(102\) | 2.34315 | − | 1.65685i | 0.232006 | − | 0.164053i | ||||
\(103\) | 6.41421 | − | 6.41421i | 0.632011 | − | 0.632011i | −0.316561 | − | 0.948572i | \(-0.602528\pi\) |
0.948572 | + | 0.316561i | \(0.102528\pi\) | |||||||
\(104\) | 4.48528 | 0.439818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.585786 | −0.0568966 | ||||||||
\(107\) | −0.242641 | + | 0.242641i | −0.0234570 | + | 0.0234570i | −0.718738 | − | 0.695281i | \(-0.755280\pi\) |
0.695281 | + | 0.718738i | \(0.255280\pi\) | |||||||
\(108\) | −2.58579 | − | 9.14214i | −0.248817 | − | 0.879702i | ||||
\(109\) | 3.17157i | 0.303782i | 0.988397 | + | 0.151891i | \(0.0485362\pi\) | ||||
−0.988397 | + | 0.151891i | \(0.951464\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0710678 | + | 0.414214i | −0.00674546 | + | 0.0393154i | ||||
\(112\) | −10.2426 | − | 10.2426i | −0.967839 | − | 0.967839i | ||||
\(113\) | 5.82843 | + | 5.82843i | 0.548292 | + | 0.548292i | 0.925947 | − | 0.377654i | \(-0.123269\pi\) |
−0.377654 | + | 0.925947i | \(0.623269\pi\) | |||||||
\(114\) | 0.343146 | − | 2.00000i | 0.0321385 | − | 0.187317i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.51472i | 0.140638i | ||||||||
\(117\) | 3.65685 | + | 7.65685i | 0.338076 | + | 0.707876i | ||||
\(118\) | −1.17157 | + | 1.17157i | −0.107852 | + | 0.107852i | ||||
\(119\) | 19.3137 | 1.77048 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −1.89949 | + | 1.89949i | −0.171972 | + | 0.171972i | ||||
\(123\) | 10.8284 | − | 7.65685i | 0.976366 | − | 0.690395i | ||||
\(124\) | − | 5.79899i | − | 0.520765i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | + | 5.65685i | −0.178174 | + | 0.503953i | ||||
\(127\) | −1.41421 | − | 1.41421i | −0.125491 | − | 0.125491i | 0.641572 | − | 0.767063i | \(-0.278283\pi\) |
−0.767063 | + | 0.641572i | \(0.778283\pi\) | |||||||
\(128\) | −7.46447 | − | 7.46447i | −0.659772 | − | 0.659772i | ||||
\(129\) | −0.585786 | − | 0.100505i | −0.0515756 | − | 0.00884898i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.82843i | 0.596602i | 0.954472 | + | 0.298301i | \(0.0964200\pi\) | ||||
−0.954472 | + | 0.298301i | \(0.903580\pi\) | |||||||
\(132\) | 1.82843 | + | 2.58579i | 0.159144 | + | 0.225064i | ||||
\(133\) | 9.65685 | − | 9.65685i | 0.837355 | − | 0.837355i | ||||
\(134\) | 3.75736 | 0.324586 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.34315 | 0.543920 | ||||||||
\(137\) | −0.171573 | + | 0.171573i | −0.0146585 | + | 0.0146585i | −0.714398 | − | 0.699740i | \(-0.753299\pi\) |
0.699740 | + | 0.714398i | \(0.253299\pi\) | |||||||
\(138\) | −1.89949 | − | 2.68629i | −0.161696 | − | 0.228672i | ||||
\(139\) | − | 17.6569i | − | 1.49763i | −0.662776 | − | 0.748817i | \(-0.730622\pi\) | ||
0.662776 | − | 0.748817i | \(-0.269378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.4853 | + | 3.00000i | 1.47253 | + | 0.252646i | ||||
\(142\) | −0.727922 | − | 0.727922i | −0.0610859 | − | 0.0610859i | ||||
\(143\) | −2.00000 | − | 2.00000i | −0.167248 | − | 0.167248i | ||||
\(144\) | 3.00000 | − | 8.48528i | 0.250000 | − | 0.707107i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23.0711 | + | 16.3137i | −1.90287 | + | 1.34553i | ||||
\(148\) | −0.313708 | + | 0.313708i | −0.0257867 | + | 0.0257867i | ||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1421 | 0.825355 | 0.412678 | − | 0.910877i | \(-0.364594\pi\) | ||||
0.412678 | + | 0.910877i | \(0.364594\pi\) | |||||||
\(152\) | 3.17157 | − | 3.17157i | 0.257249 | − | 0.257249i | ||||
\(153\) | 5.17157 | + | 10.8284i | 0.418097 | + | 0.875426i | ||||
\(154\) | − | 2.00000i | − | 0.161165i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.51472 | + | 8.82843i | −0.121275 | + | 0.706840i | ||||
\(157\) | 9.48528 | + | 9.48528i | 0.757008 | + | 0.757008i | 0.975777 | − | 0.218769i | \(-0.0702041\pi\) |
−0.218769 | + | 0.975777i | \(0.570204\pi\) | |||||||
\(158\) | 3.17157 | + | 3.17157i | 0.252317 | + | 0.252317i | ||||
\(159\) | 0.414214 | − | 2.41421i | 0.0328493 | − | 0.191460i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 22.1421i | − | 1.74504i | ||||||
\(162\) | −3.70711 | + | 0.393398i | −0.291258 | + | 0.0309083i | ||||
\(163\) | −3.58579 | + | 3.58579i | −0.280860 | + | 0.280860i | −0.833452 | − | 0.552592i | \(-0.813639\pi\) |
0.552592 | + | 0.833452i | \(0.313639\pi\) | |||||||
\(164\) | 14.0000 | 1.09322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.31371 | 0.412424 | ||||||||
\(167\) | −14.7279 | + | 14.7279i | −1.13968 | + | 1.13968i | −0.151174 | + | 0.988507i | \(0.548305\pi\) |
−0.988507 | + | 0.151174i | \(0.951695\pi\) | |||||||
\(168\) | −10.8284 | + | 7.65685i | −0.835431 | + | 0.590739i | ||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | + | 2.82843i | 0.611775 | + | 0.216295i | ||||
\(172\) | −0.443651 | − | 0.443651i | −0.0338281 | − | 0.0338281i | ||||
\(173\) | −8.48528 | − | 8.48528i | −0.645124 | − | 0.645124i | 0.306687 | − | 0.951811i | \(-0.400780\pi\) |
−0.951811 | + | 0.306687i | \(0.900780\pi\) | |||||||
\(174\) | 0.585786 | + | 0.100505i | 0.0444084 | + | 0.00761927i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | −4.00000 | − | 5.65685i | −0.300658 | − | 0.425195i | ||||
\(178\) | −2.82843 | + | 2.82843i | −0.212000 | + | 0.212000i | ||||
\(179\) | 24.1421 | 1.80447 | 0.902234 | − | 0.431247i | \(-0.141926\pi\) | ||||
0.902234 | + | 0.431247i | \(0.141926\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.65685 | 0.420471 | 0.210235 | − | 0.977651i | \(-0.432577\pi\) | ||||
0.210235 | + | 0.977651i | \(0.432577\pi\) | |||||||
\(182\) | 4.00000 | − | 4.00000i | 0.296500 | − | 0.296500i | ||||
\(183\) | −6.48528 | − | 9.17157i | −0.479406 | − | 0.677982i | ||||
\(184\) | − | 7.27208i | − | 0.536105i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.24264 | − | 0.384776i | −0.164438 | − | 0.0282132i | ||||
\(187\) | −2.82843 | − | 2.82843i | −0.206835 | − | 0.206835i | ||||
\(188\) | 13.2426 | + | 13.2426i | 0.965819 | + | 0.965819i | ||||
\(189\) | −21.8995 | − | 12.2426i | −1.59295 | − | 0.890521i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3137i | 0.818631i | 0.912393 | + | 0.409316i | \(0.134232\pi\) | ||||
−0.912393 | + | 0.409316i | \(0.865768\pi\) | |||||||
\(192\) | 5.89949 | − | 4.17157i | 0.425759 | − | 0.301057i | ||||
\(193\) | −8.00000 | + | 8.00000i | −0.575853 | + | 0.575853i | −0.933758 | − | 0.357905i | \(-0.883491\pi\) |
0.357905 | + | 0.933758i | \(0.383491\pi\) | |||||||
\(194\) | −6.24264 | −0.448195 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.8284 | −2.13060 | ||||||||
\(197\) | 14.1421 | − | 14.1421i | 1.00759 | − | 1.00759i | 0.00761443 | − | 0.999971i | \(-0.497576\pi\) |
0.999971 | − | 0.00761443i | \(-0.00242377\pi\) | |||||||
\(198\) | 1.12132 | − | 0.535534i | 0.0796888 | − | 0.0380587i | ||||
\(199\) | − | 14.4853i | − | 1.02683i | −0.858139 | − | 0.513417i | \(-0.828379\pi\) | ||
0.858139 | − | 0.513417i | \(-0.171621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.65685 | + | 15.4853i | −0.187400 | + | 1.09225i | ||||
\(202\) | −2.10051 | − | 2.10051i | −0.147791 | − | 0.147791i | ||||
\(203\) | 2.82843 | + | 2.82843i | 0.198517 | + | 0.198517i | ||||
\(204\) | −2.14214 | + | 12.4853i | −0.149979 | + | 0.874145i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 3.75736i | − | 0.261788i | ||||||
\(207\) | 12.4142 | − | 5.92893i | 0.862847 | − | 0.412089i | ||||
\(208\) | −6.00000 | + | 6.00000i | −0.416025 | + | 0.416025i | ||||
\(209\) | −2.82843 | −0.195646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.48528 | −0.308780 | −0.154390 | − | 0.988010i | \(-0.549341\pi\) | ||||
−0.154390 | + | 0.988010i | \(0.549341\pi\) | |||||||
\(212\) | 1.82843 | − | 1.82843i | 0.125577 | − | 0.125577i | ||||
\(213\) | 3.51472 | − | 2.48528i | 0.240825 | − | 0.170289i | ||||
\(214\) | 0.142136i | 0.00971619i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.19239 | − | 4.02082i | −0.489380 | − | 0.273582i | ||||
\(217\) | −10.8284 | − | 10.8284i | −0.735082 | − | 0.735082i | ||||
\(218\) | 0.928932 | + | 0.928932i | 0.0629152 | + | 0.0629152i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 11.3137i | − | 0.761042i | ||||||
\(222\) | 0.100505 | + | 0.142136i | 0.00674546 | + | 0.00953952i | ||||
\(223\) | 16.5563 | − | 16.5563i | 1.10870 | − | 1.10870i | 0.115373 | − | 0.993322i | \(-0.463194\pi\) |
0.993322 | − | 0.115373i | \(-0.0368063\pi\) | |||||||
\(224\) | −21.3137 | −1.42408 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.41421 | 0.227110 | ||||||||
\(227\) | −10.2426 | + | 10.2426i | −0.679828 | + | 0.679828i | −0.959961 | − | 0.280133i | \(-0.909621\pi\) |
0.280133 | + | 0.959961i | \(0.409621\pi\) | |||||||
\(228\) | 5.17157 | + | 7.31371i | 0.342496 | + | 0.484362i | ||||
\(229\) | − | 9.65685i | − | 0.638143i | −0.947731 | − | 0.319071i | \(-0.896629\pi\) | ||
0.947731 | − | 0.319071i | \(-0.103371\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.24264 | + | 1.41421i | 0.542326 | + | 0.0930484i | ||||
\(232\) | 0.928932 | + | 0.928932i | 0.0609874 | + | 0.0609874i | ||||
\(233\) | −19.6569 | − | 19.6569i | −1.28776 | − | 1.28776i | −0.936143 | − | 0.351621i | \(-0.885631\pi\) |
−0.351621 | − | 0.936143i | \(-0.614369\pi\) | |||||||
\(234\) | 3.31371 | + | 1.17157i | 0.216624 | + | 0.0765881i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 7.31371i | − | 0.476082i | ||||||
\(237\) | −15.3137 | + | 10.8284i | −0.994732 | + | 0.703382i | ||||
\(238\) | 5.65685 | − | 5.65685i | 0.366679 | − | 0.366679i | ||||
\(239\) | −23.7990 | −1.53943 | −0.769714 | − | 0.638388i | \(-0.779601\pi\) | ||||
−0.769714 | + | 0.638388i | \(0.779601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.142136 | 0.00915576 | 0.00457788 | − | 0.999990i | \(-0.498543\pi\) | ||||
0.00457788 | + | 0.999990i | \(0.498543\pi\) | |||||||
\(242\) | −0.292893 | + | 0.292893i | −0.0188279 | + | 0.0188279i | ||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | − | 11.8579i | − | 0.759122i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.928932 | − | 5.41421i | 0.0592266 | − | 0.345198i | ||||
\(247\) | −5.65685 | − | 5.65685i | −0.359937 | − | 0.359937i | ||||
\(248\) | −3.55635 | − | 3.55635i | −0.225828 | − | 0.225828i | ||||
\(249\) | −3.75736 | + | 21.8995i | −0.238113 | + | 1.38782i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16.1421i | − | 1.01888i | −0.860505 | − | 0.509441i | \(-0.829852\pi\) | ||
0.860505 | − | 0.509441i | \(-0.170148\pi\) | |||||||
\(252\) | −11.4142 | − | 23.8995i | −0.719028 | − | 1.50553i | ||||
\(253\) | −3.24264 | + | 3.24264i | −0.203863 | + | 0.203863i | ||||
\(254\) | −0.828427 | −0.0519801 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 1.82843 | − | 1.82843i | 0.114054 | − | 0.114054i | −0.647776 | − | 0.761831i | \(-0.724301\pi\) |
0.761831 | + | 0.647776i | \(0.224301\pi\) | |||||||
\(258\) | −0.201010 | + | 0.142136i | −0.0125143 | + | 0.00884898i | ||||
\(259\) | 1.17157i | 0.0727980i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.828427 | + | 2.34315i | −0.0512784 | + | 0.145037i | ||||
\(262\) | 2.00000 | + | 2.00000i | 0.123560 | + | 0.123560i | ||||
\(263\) | 1.75736 | + | 1.75736i | 0.108363 | + | 0.108363i | 0.759210 | − | 0.650846i | \(-0.225586\pi\) |
−0.650846 | + | 0.759210i | \(0.725586\pi\) | |||||||
\(264\) | 2.70711 | + | 0.464466i | 0.166611 | + | 0.0285859i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 5.65685i | − | 0.346844i | ||||||
\(267\) | −9.65685 | − | 13.6569i | −0.590990 | − | 0.835786i | ||||
\(268\) | −11.7279 | + | 11.7279i | −0.716397 | + | 0.716397i | ||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.48528 | 0.515444 | 0.257722 | − | 0.966219i | \(-0.417028\pi\) | ||||
0.257722 | + | 0.966219i | \(0.417028\pi\) | |||||||
\(272\) | −8.48528 | + | 8.48528i | −0.514496 | + | 0.514496i | ||||
\(273\) | 13.6569 | + | 19.3137i | 0.826550 | + | 1.16892i | ||||
\(274\) | 0.100505i | 0.00607173i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.3137 | + | 2.45584i | 0.861584 | + | 0.147824i | ||||
\(277\) | 18.4853 | + | 18.4853i | 1.11067 | + | 1.11067i | 0.993059 | + | 0.117613i | \(0.0375244\pi\) |
0.117613 | + | 0.993059i | \(0.462476\pi\) | |||||||
\(278\) | −5.17157 | − | 5.17157i | −0.310170 | − | 0.310170i | ||||
\(279\) | 3.17157 | − | 8.97056i | 0.189877 | − | 0.537054i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6274i | 1.70777i | 0.520463 | + | 0.853884i | \(0.325759\pi\) | ||||
−0.520463 | + | 0.853884i | \(0.674241\pi\) | |||||||
\(282\) | 6.00000 | − | 4.24264i | 0.357295 | − | 0.252646i | ||||
\(283\) | 15.0711 | − | 15.0711i | 0.895882 | − | 0.895882i | −0.0991868 | − | 0.995069i | \(-0.531624\pi\) |
0.995069 | + | 0.0991868i | \(0.0316241\pi\) | |||||||
\(284\) | 4.54416 | 0.269646 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.17157 | −0.0692766 | ||||||||
\(287\) | 26.1421 | − | 26.1421i | 1.54312 | − | 1.54312i | ||||
\(288\) | −5.70711 | − | 11.9497i | −0.336294 | − | 0.704146i | ||||
\(289\) | 1.00000i | 0.0588235i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.41421 | − | 25.7279i | 0.258766 | − | 1.50820i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.65685 | + | 3.65685i | 0.213636 | + | 0.213636i | 0.805810 | − | 0.592174i | \(-0.201730\pi\) |
−0.592174 | + | 0.805810i | \(0.701730\pi\) | |||||||
\(294\) | −1.97918 | + | 11.5355i | −0.115428 | + | 0.672766i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.384776i | 0.0223647i | ||||||||
\(297\) | 1.41421 | + | 5.00000i | 0.0820610 | + | 0.290129i | ||||
\(298\) | −2.92893 | + | 2.92893i | −0.169668 | + | 0.169668i | ||||
\(299\) | −12.9706 | −0.750107 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.65685 | −0.0954995 | ||||||||
\(302\) | 2.97056 | − | 2.97056i | 0.170937 | − | 0.170937i | ||||
\(303\) | 10.1421 | − | 7.17157i | 0.582650 | − | 0.411996i | ||||
\(304\) | 8.48528i | 0.486664i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.68629 | + | 1.65685i | 0.267897 | + | 0.0947161i | ||||
\(307\) | 11.8995 | + | 11.8995i | 0.679140 | + | 0.679140i | 0.959806 | − | 0.280666i | \(-0.0905552\pi\) |
−0.280666 | + | 0.959806i | \(0.590555\pi\) | |||||||
\(308\) | 6.24264 | + | 6.24264i | 0.355707 | + | 0.355707i | ||||
\(309\) | 15.4853 | + | 2.65685i | 0.880927 | + | 0.151143i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.1421i | 1.59579i | 0.602794 | + | 0.797897i | \(0.294054\pi\) | ||||
−0.602794 | + | 0.797897i | \(0.705946\pi\) | |||||||
\(312\) | 4.48528 | + | 6.34315i | 0.253929 | + | 0.359110i | ||||
\(313\) | −12.6569 | + | 12.6569i | −0.715408 | + | 0.715408i | −0.967661 | − | 0.252253i | \(-0.918828\pi\) |
0.252253 | + | 0.967661i | \(0.418828\pi\) | |||||||
\(314\) | 5.55635 | 0.313563 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.7990 | −1.11378 | ||||||||
\(317\) | −2.31371 | + | 2.31371i | −0.129951 | + | 0.129951i | −0.769091 | − | 0.639140i | \(-0.779291\pi\) |
0.639140 | + | 0.769091i | \(0.279291\pi\) | |||||||
\(318\) | −0.585786 | − | 0.828427i | −0.0328493 | − | 0.0464559i | ||||
\(319\) | − | 0.828427i | − | 0.0463830i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.585786 | − | 0.100505i | −0.0326954 | − | 0.00560965i | ||||
\(322\) | −6.48528 | − | 6.48528i | −0.361411 | − | 0.361411i | ||||
\(323\) | −8.00000 | − | 8.00000i | −0.445132 | − | 0.445132i | ||||
\(324\) | 10.3431 | − | 12.7990i | 0.574619 | − | 0.711055i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.10051i | 0.116336i | ||||||||
\(327\) | −4.48528 | + | 3.17157i | −0.248037 | + | 0.175388i | ||||
\(328\) | 8.58579 | − | 8.58579i | 0.474071 | − | 0.474071i | ||||
\(329\) | 49.4558 | 2.72659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.48528 | −0.356463 | −0.178232 | − | 0.983989i | \(-0.557038\pi\) | ||||
−0.178232 | + | 0.983989i | \(0.557038\pi\) | |||||||
\(332\) | −16.5858 | + | 16.5858i | −0.910263 | + | 0.910263i | ||||
\(333\) | −0.656854 | + | 0.313708i | −0.0359954 | + | 0.0171911i | ||||
\(334\) | 8.62742i | 0.472071i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.24264 | − | 24.7279i | 0.231455 | − | 1.34902i | ||||
\(337\) | 10.8284 | + | 10.8284i | 0.589862 | + | 0.589862i | 0.937594 | − | 0.347732i | \(-0.113048\pi\) |
−0.347732 | + | 0.937594i | \(0.613048\pi\) | |||||||
\(338\) | 1.46447 | + | 1.46447i | 0.0796565 | + | 0.0796565i | ||||
\(339\) | −2.41421 | + | 14.0711i | −0.131122 | + | 0.764235i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.17157i | 0.171750i | ||||||||
\(342\) | 3.17157 | − | 1.51472i | 0.171499 | − | 0.0819066i | ||||
\(343\) | −31.7990 | + | 31.7990i | −1.71698 | + | 1.71698i | ||||
\(344\) | −0.544156 | −0.0293389 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.97056 | −0.267219 | ||||||||
\(347\) | −1.89949 | + | 1.89949i | −0.101970 | + | 0.101970i | −0.756251 | − | 0.654281i | \(-0.772971\pi\) |
0.654281 | + | 0.756251i | \(0.272971\pi\) | |||||||
\(348\) | −2.14214 | + | 1.51472i | −0.114831 | + | 0.0811974i | ||||
\(349\) | 30.0000i | 1.60586i | 0.596071 | + | 0.802932i | \(0.296728\pi\) | ||||
−0.596071 | + | 0.802932i | \(0.703272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.17157 | + | 12.8284i | −0.382790 | + | 0.684731i | ||||
\(352\) | 3.12132 | + | 3.12132i | 0.166367 | + | 0.166367i | ||||
\(353\) | −7.82843 | − | 7.82843i | −0.416665 | − | 0.416665i | 0.467387 | − | 0.884053i | \(-0.345195\pi\) |
−0.884053 | + | 0.467387i | \(0.845195\pi\) | |||||||
\(354\) | −2.82843 | − | 0.485281i | −0.150329 | − | 0.0257924i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 17.6569i | − | 0.935811i | ||||||
\(357\) | 19.3137 | + | 27.3137i | 1.02219 | + | 1.44559i | ||||
\(358\) | 7.07107 | − | 7.07107i | 0.373718 | − | 0.373718i | ||||
\(359\) | −22.1421 | −1.16862 | −0.584309 | − | 0.811532i | \(-0.698634\pi\) | ||||
−0.584309 | + | 0.811532i | \(0.698634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 1.65685 | − | 1.65685i | 0.0870823 | − | 0.0870823i | ||||
\(363\) | −1.00000 | − | 1.41421i | −0.0524864 | − | 0.0742270i | ||||
\(364\) | 24.9706i | 1.30881i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.58579 | − | 0.786797i | −0.239703 | − | 0.0411265i | ||||
\(367\) | 1.10051 | + | 1.10051i | 0.0574459 | + | 0.0574459i | 0.735246 | − | 0.677800i | \(-0.237067\pi\) |
−0.677800 | + | 0.735246i | \(0.737067\pi\) | |||||||
\(368\) | 9.72792 | + | 9.72792i | 0.507103 | + | 0.507103i | ||||
\(369\) | 21.6569 | + | 7.65685i | 1.12741 | + | 0.398600i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6.82843i | − | 0.354514i | ||||||
\(372\) | 8.20101 | − | 5.79899i | 0.425203 | − | 0.300664i | ||||
\(373\) | −3.51472 | + | 3.51472i | −0.181985 | + | 0.181985i | −0.792220 | − | 0.610235i | \(-0.791075\pi\) |
0.610235 | + | 0.792220i | \(0.291075\pi\) | |||||||
\(374\) | −1.65685 | −0.0856739 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.2426 | 0.837650 | ||||||||
\(377\) | 1.65685 | − | 1.65685i | 0.0853323 | − | 0.0853323i | ||||
\(378\) | −10.0000 | + | 2.82843i | −0.514344 | + | 0.145479i | ||||
\(379\) | − | 28.1421i | − | 1.44556i | −0.691076 | − | 0.722782i | \(-0.742863\pi\) | ||
0.691076 | − | 0.722782i | \(-0.257137\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.585786 | − | 3.41421i | 0.0300107 | − | 0.174915i | ||||
\(382\) | 3.31371 | + | 3.31371i | 0.169544 | + | 0.169544i | ||||
\(383\) | 6.07107 | + | 6.07107i | 0.310217 | + | 0.310217i | 0.844994 | − | 0.534776i | \(-0.179604\pi\) |
−0.534776 | + | 0.844994i | \(0.679604\pi\) | |||||||
\(384\) | 3.09188 | − | 18.0208i | 0.157782 | − | 0.919621i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.68629i | 0.238526i | ||||||||
\(387\) | −0.443651 | − | 0.928932i | −0.0225520 | − | 0.0472203i | ||||
\(388\) | 19.4853 | − | 19.4853i | 0.989215 | − | 0.989215i | ||||
\(389\) | −17.3137 | −0.877840 | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||||
−0.438920 | + | 0.898526i | \(0.644639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.3431 | −0.927653 | ||||||||
\(392\) | −18.2929 | + | 18.2929i | −0.923931 | + | 0.923931i | ||||
\(393\) | −9.65685 | + | 6.82843i | −0.487124 | + | 0.344449i | ||||
\(394\) | − | 8.28427i | − | 0.417356i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.82843 | + | 5.17157i | −0.0918819 | + | 0.259881i | ||||
\(397\) | −6.17157 | − | 6.17157i | −0.309742 | − | 0.309742i | 0.535067 | − | 0.844810i | \(-0.320286\pi\) |
−0.844810 | + | 0.535067i | \(0.820286\pi\) | |||||||
\(398\) | −4.24264 | − | 4.24264i | −0.212664 | − | 0.212664i | ||||
\(399\) | 23.3137 | + | 4.00000i | 1.16715 | + | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.6569i | 1.78062i | 0.455357 | + | 0.890309i | \(0.349512\pi\) | ||||
−0.455357 | + | 0.890309i | \(0.650488\pi\) | |||||||
\(402\) | 3.75736 | + | 5.31371i | 0.187400 | + | 0.265024i | ||||
\(403\) | −6.34315 | + | 6.34315i | −0.315975 | + | 0.315975i | ||||
\(404\) | 13.1127 | 0.652381 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.65685 | 0.0822283 | ||||||||
\(407\) | 0.171573 | − | 0.171573i | 0.00850455 | − | 0.00850455i | ||||
\(408\) | 6.34315 | + | 8.97056i | 0.314033 | + | 0.444109i | ||||
\(409\) | 18.4853i | 0.914038i | 0.889457 | + | 0.457019i | \(0.151083\pi\) | ||||
−0.889457 | + | 0.457019i | \(0.848917\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.414214 | − | 0.0710678i | −0.0204316 | − | 0.00350552i | ||||
\(412\) | 11.7279 | + | 11.7279i | 0.577793 | + | 0.577793i | ||||
\(413\) | −13.6569 | − | 13.6569i | −0.672010 | − | 0.672010i | ||||
\(414\) | 1.89949 | − | 5.37258i | 0.0933551 | − | 0.264048i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.4853i | 0.612141i | ||||||||
\(417\) | 24.9706 | − | 17.6569i | 1.22281 | − | 0.864660i | ||||
\(418\) | −0.828427 | + | 0.828427i | −0.0405197 | + | 0.0405197i | ||||
\(419\) | 15.4558 | 0.755067 | 0.377534 | − | 0.925996i | \(-0.376772\pi\) | ||||
0.377534 | + | 0.925996i | \(0.376772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | −1.31371 | + | 1.31371i | −0.0639503 | + | 0.0639503i | ||||
\(423\) | 13.2426 | + | 27.7279i | 0.643879 | + | 1.34818i | ||||
\(424\) | − | 2.24264i | − | 0.108912i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.301515 | − | 1.75736i | 0.0146085 | − | 0.0851443i | ||||
\(427\) | −22.1421 | − | 22.1421i | −1.07153 | − | 1.07153i | ||||
\(428\) | −0.443651 | − | 0.443651i | −0.0214447 | − | 0.0214447i | ||||
\(429\) | 0.828427 | − | 4.82843i | 0.0399968 | − | 0.233119i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.34315i | − | 0.305539i | −0.988262 | − | 0.152769i | \(-0.951181\pi\) | ||
0.988262 | − | 0.152769i | \(-0.0488191\pi\) | |||||||
\(432\) | 15.0000 | − | 4.24264i | 0.721688 | − | 0.204124i | ||||
\(433\) | 0.313708 | − | 0.313708i | 0.0150759 | − | 0.0150759i | −0.699529 | − | 0.714605i | \(-0.746607\pi\) |
0.714605 | + | 0.699529i | \(0.246607\pi\) | |||||||
\(434\) | −6.34315 | −0.304481 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.79899 | −0.277721 | ||||||||
\(437\) | −9.17157 | + | 9.17157i | −0.438736 | + | 0.438736i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.31371i | 0.349064i | 0.984651 | + | 0.174532i | \(0.0558413\pi\) | ||||
−0.984651 | + | 0.174532i | \(0.944159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.1421 | − | 16.3137i | −2.19724 | − | 0.776843i | ||||
\(442\) | −3.31371 | − | 3.31371i | −0.157617 | − | 0.157617i | ||||
\(443\) | 20.7574 | + | 20.7574i | 0.986212 | + | 0.986212i | 0.999906 | − | 0.0136943i | \(-0.00435918\pi\) |
−0.0136943 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(444\) | −0.757359 | − | 0.129942i | −0.0359427 | − | 0.00616679i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 9.69848i | − | 0.459237i | ||||||
\(447\) | −10.0000 | − | 14.1421i | −0.472984 | − | 0.668900i | ||||
\(448\) | 14.2426 | − | 14.2426i | 0.672902 | − | 0.672902i | ||||
\(449\) | −3.02944 | −0.142968 | −0.0714840 | − | 0.997442i | \(-0.522773\pi\) | ||||
−0.0714840 | + | 0.997442i | \(0.522773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.65685 | −0.360547 | ||||||||
\(452\) | −10.6569 | + | 10.6569i | −0.501256 | + | 0.501256i | ||||
\(453\) | 10.1421 | + | 14.3431i | 0.476519 | + | 0.673900i | ||||
\(454\) | 6.00000i | 0.281594i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.65685 | + | 1.31371i | 0.358565 | + | 0.0615200i | ||||
\(457\) | 6.48528 | + | 6.48528i | 0.303369 | + | 0.303369i | 0.842330 | − | 0.538962i | \(-0.181183\pi\) |
−0.538962 | + | 0.842330i | \(0.681183\pi\) | |||||||
\(458\) | −2.82843 | − | 2.82843i | −0.132164 | − | 0.132164i | ||||
\(459\) | −10.1421 | + | 18.1421i | −0.473394 | + | 0.846802i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.5147i | − | 0.629443i | −0.949184 | − | 0.314722i | \(-0.898089\pi\) | ||
0.949184 | − | 0.314722i | \(-0.101911\pi\) | |||||||
\(462\) | 2.82843 | − | 2.00000i | 0.131590 | − | 0.0930484i | ||||
\(463\) | −11.7279 | + | 11.7279i | −0.545043 | + | 0.545043i | −0.925003 | − | 0.379960i | \(-0.875938\pi\) |
0.379960 | + | 0.925003i | \(0.375938\pi\) | |||||||
\(464\) | −2.48528 | −0.115376 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.5147 | −0.533409 | ||||||||
\(467\) | 0.414214 | − | 0.414214i | 0.0191675 | − | 0.0191675i | −0.697458 | − | 0.716626i | \(-0.745686\pi\) |
0.716626 | + | 0.697458i | \(0.245686\pi\) | |||||||
\(468\) | −14.0000 | + | 6.68629i | −0.647150 | + | 0.309074i | ||||
\(469\) | 43.7990i | 2.02245i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.92893 | + | 22.8995i | −0.181036 | + | 1.05515i | ||||
\(472\) | −4.48528 | − | 4.48528i | −0.206452 | − | 0.206452i | ||||
\(473\) | 0.242641 | + | 0.242641i | 0.0111566 | + | 0.0111566i | ||||
\(474\) | −1.31371 | + | 7.65685i | −0.0603406 | + | 0.351691i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 35.3137i | 1.61860i | ||||||||
\(477\) | 3.82843 | − | 1.82843i | 0.175292 | − | 0.0837179i | ||||
\(478\) | −6.97056 | + | 6.97056i | −0.318826 | + | 0.318826i | ||||
\(479\) | −30.1421 | −1.37723 | −0.688615 | − | 0.725127i | \(-0.741781\pi\) | ||||
−0.688615 | + | 0.725127i | \(0.741781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.686292 | 0.0312922 | ||||||||
\(482\) | 0.0416306 | − | 0.0416306i | 0.00189622 | − | 0.00189622i | ||||
\(483\) | 31.3137 | − | 22.1421i | 1.42482 | − | 1.00750i | ||||
\(484\) | − | 1.82843i | − | 0.0831103i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.26346 | − | 4.84924i | −0.193394 | − | 0.219966i | ||||
\(487\) | −11.7279 | − | 11.7279i | −0.531443 | − | 0.531443i | 0.389559 | − | 0.921002i | \(-0.372628\pi\) |
−0.921002 | + | 0.389559i | \(0.872628\pi\) | |||||||
\(488\) | −7.27208 | − | 7.27208i | −0.329192 | − | 0.329192i | ||||
\(489\) | −8.65685 | − | 1.48528i | −0.391476 | − | 0.0671667i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.0000i | − | 0.902587i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) | ||
0.892375 | − | 0.451294i | \(-0.149037\pi\) | |||||||
\(492\) | 14.0000 | + | 19.7990i | 0.631169 | + | 0.892607i | ||||
\(493\) | 2.34315 | − | 2.34315i | 0.105530 | − | 0.105530i | ||||
\(494\) | −3.31371 | −0.149091 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.51472 | 0.427223 | ||||||||
\(497\) | 8.48528 | − | 8.48528i | 0.380617 | − | 0.380617i | ||||
\(498\) | 5.31371 | + | 7.51472i | 0.238113 | + | 0.336743i | ||||
\(499\) | − | 24.8284i | − | 1.11147i | −0.831358 | − | 0.555737i | \(-0.812436\pi\) | ||
0.831358 | − | 0.555737i | \(-0.187564\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.5563 | − | 6.10051i | −1.58854 | − | 0.272550i | ||||
\(502\) | −4.72792 | − | 4.72792i | −0.211017 | − | 0.211017i | ||||
\(503\) | −0.928932 | − | 0.928932i | −0.0414190 | − | 0.0414190i | 0.686094 | − | 0.727513i | \(-0.259324\pi\) |
−0.727513 | + | 0.686094i | \(0.759324\pi\) | |||||||
\(504\) | −21.6569 | − | 7.65685i | −0.964673 | − | 0.341063i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.89949i | 0.0844428i | ||||||||
\(507\) | −7.07107 | + | 5.00000i | −0.314037 | + | 0.222058i | ||||
\(508\) | 2.58579 | − | 2.58579i | 0.114726 | − | 0.114726i | ||||
\(509\) | 35.6569 | 1.58046 | 0.790231 | − | 0.612809i | \(-0.209960\pi\) | ||||
0.790231 | + | 0.612809i | \(0.209960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0919 | − | 16.0919i | 0.711167 | − | 0.711167i | ||||
\(513\) | 4.00000 | + | 14.1421i | 0.176604 | + | 0.624391i | ||||
\(514\) | − | 1.07107i | − | 0.0472428i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.183766 | − | 1.07107i | 0.00808986 | − | 0.0471511i | ||||
\(517\) | −7.24264 | − | 7.24264i | −0.318531 | − | 0.318531i | ||||
\(518\) | 0.343146 | + | 0.343146i | 0.0150770 | + | 0.0150770i | ||||
\(519\) | 3.51472 | − | 20.4853i | 0.154279 | − | 0.899204i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.6569i | − | 1.21167i | −0.795591 | − | 0.605834i | \(-0.792839\pi\) | ||
0.795591 | − | 0.605834i | \(-0.207161\pi\) | |||||||
\(522\) | 0.443651 | + | 0.928932i | 0.0194181 | + | 0.0406583i | ||||
\(523\) | 27.2132 | − | 27.2132i | 1.18995 | − | 1.18995i | 0.212870 | − | 0.977081i | \(-0.431719\pi\) |
0.977081 | − | 0.212870i | \(-0.0682810\pi\) | |||||||
\(524\) | −12.4853 | −0.545422 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.02944 | 0.0448856 | ||||||||
\(527\) | −8.97056 | + | 8.97056i | −0.390764 | + | 0.390764i | ||||
\(528\) | −4.24264 | + | 3.00000i | −0.184637 | + | 0.130558i | ||||
\(529\) | − | 1.97056i | − | 0.0856766i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | − | 11.3137i | 0.173585 | − | 0.490973i | ||||
\(532\) | 17.6569 | + | 17.6569i | 0.765522 | + | 0.765522i | ||||
\(533\) | −15.3137 | − | 15.3137i | −0.663310 | − | 0.663310i | ||||
\(534\) | −6.82843 | − | 1.17157i | −0.295495 | − | 0.0506989i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.3848i | 0.621328i | ||||||||
\(537\) | 24.1421 | + | 34.1421i | 1.04181 | + | 1.47334i | ||||
\(538\) | −4.10051 | + | 4.10051i | −0.176785 | + | 0.176785i | ||||
\(539\) | 16.3137 | 0.702681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6863 | −0.459440 | −0.229720 | − | 0.973257i | \(-0.573781\pi\) | ||||
−0.229720 | + | 0.973257i | \(0.573781\pi\) | |||||||
\(542\) | 2.48528 | − | 2.48528i | 0.106752 | − | 0.106752i | ||||
\(543\) | 5.65685 | + | 8.00000i | 0.242759 | + | 0.343313i | ||||
\(544\) | 17.6569i | 0.757031i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.65685 | + | 1.65685i | 0.413275 | + | 0.0709068i | ||||
\(547\) | −2.10051 | − | 2.10051i | −0.0898111 | − | 0.0898111i | 0.660774 | − | 0.750585i | \(-0.270228\pi\) |
−0.750585 | + | 0.660774i | \(0.770228\pi\) | |||||||
\(548\) | −0.313708 | − | 0.313708i | −0.0134010 | − | 0.0134010i | ||||
\(549\) | 6.48528 | − | 18.3431i | 0.276785 | − | 0.782866i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.34315i | − | 0.0998214i | ||||||
\(552\) | 10.2843 | − | 7.27208i | 0.437728 | − | 0.309520i | ||||
\(553\) | −36.9706 | + | 36.9706i | −1.57215 | + | 1.57215i | ||||
\(554\) | 10.8284 | 0.460056 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.2843 | 1.36916 | ||||||||
\(557\) | −8.97056 | + | 8.97056i | −0.380095 | + | 0.380095i | −0.871136 | − | 0.491041i | \(-0.836616\pi\) |
0.491041 | + | 0.871136i | \(0.336616\pi\) | |||||||
\(558\) | −1.69848 | − | 3.55635i | −0.0719026 | − | 0.150552i | ||||
\(559\) | 0.970563i | 0.0410504i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.17157 | − | 6.82843i | 0.0494638 | − | 0.288296i | ||||
\(562\) | 8.38478 | + | 8.38478i | 0.353690 | + | 0.353690i | ||||
\(563\) | 9.89949 | + | 9.89949i | 0.417214 | + | 0.417214i | 0.884242 | − | 0.467028i | \(-0.154675\pi\) |
−0.467028 | + | 0.884242i | \(0.654675\pi\) | |||||||
\(564\) | −5.48528 | + | 31.9706i | −0.230972 | + | 1.34620i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 8.82843i | − | 0.371086i | ||||||
\(567\) | −4.58579 | − | 43.2132i | −0.192585 | − | 1.81478i | ||||
\(568\) | 2.78680 | − | 2.78680i | 0.116931 | − | 0.116931i | ||||
\(569\) | −28.3431 | −1.18821 | −0.594103 | − | 0.804389i | \(-0.702493\pi\) | ||||
−0.594103 | + | 0.804389i | \(0.702493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.6569 | 1.24110 | 0.620550 | − | 0.784167i | \(-0.286909\pi\) | ||||
0.620550 | + | 0.784167i | \(0.286909\pi\) | |||||||
\(572\) | 3.65685 | − | 3.65685i | 0.152901 | − | 0.152901i | ||||
\(573\) | −16.0000 | + | 11.3137i | −0.668410 | + | 0.472637i | ||||
\(574\) | − | 15.3137i | − | 0.639182i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11.7990 | + | 4.17157i | 0.491625 | + | 0.173816i | ||||
\(577\) | −17.0000 | − | 17.0000i | −0.707719 | − | 0.707719i | 0.258336 | − | 0.966055i | \(-0.416826\pi\) |
−0.966055 | + | 0.258336i | \(0.916826\pi\) | |||||||
\(578\) | 0.292893 | + | 0.292893i | 0.0121828 | + | 0.0121828i | ||||
\(579\) | −19.3137 | − | 3.31371i | −0.802650 | − | 0.137713i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 61.9411i | 2.56975i | ||||||||
\(582\) | −6.24264 | − | 8.82843i | −0.258766 | − | 0.365950i | ||||
\(583\) | −1.00000 | + | 1.00000i | −0.0414158 | + | 0.0414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.14214 | 0.0884908 | ||||||||
\(587\) | 0.414214 | − | 0.414214i | 0.0170964 | − | 0.0170964i | −0.698507 | − | 0.715603i | \(-0.746152\pi\) |
0.715603 | + | 0.698507i | \(0.246152\pi\) | |||||||
\(588\) | −29.8284 | − | 42.1838i | −1.23010 | − | 1.73963i | ||||
\(589\) | 8.97056i | 0.369626i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.1421 | + | 5.85786i | 1.40442 | + | 0.240960i | ||||
\(592\) | −0.514719 | − | 0.514719i | −0.0211548 | − | 0.0211548i | ||||
\(593\) | −5.85786 | − | 5.85786i | −0.240554 | − | 0.240554i | 0.576525 | − | 0.817079i | \(-0.304408\pi\) |
−0.817079 | + | 0.576525i | \(0.804408\pi\) | |||||||
\(594\) | 1.87868 | + | 1.05025i | 0.0770832 | + | 0.0430924i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 18.2843i | − | 0.748953i | ||||||
\(597\) | 20.4853 | − | 14.4853i | 0.838407 | − | 0.592843i | ||||
\(598\) | −3.79899 | + | 3.79899i | −0.155352 | + | 0.155352i | ||||
\(599\) | −3.45584 | −0.141202 | −0.0706010 | − | 0.997505i | \(-0.522492\pi\) | ||||
−0.0706010 | + | 0.997505i | \(0.522492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.4558 | −1.11995 | −0.559974 | − | 0.828510i | \(-0.689189\pi\) | ||||
−0.559974 | + | 0.828510i | \(0.689189\pi\) | |||||||
\(602\) | −0.485281 | + | 0.485281i | −0.0197786 | + | 0.0197786i | ||||
\(603\) | −24.5563 | + | 11.7279i | −1.00001 | + | 0.477598i | ||||
\(604\) | 18.5442i | 0.754551i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.870058 | − | 5.07107i | 0.0353437 | − | 0.205998i | ||||
\(607\) | 21.8995 | + | 21.8995i | 0.888873 | + | 0.888873i | 0.994415 | − | 0.105542i | \(-0.0336577\pi\) |
−0.105542 | + | 0.994415i | \(0.533658\pi\) | |||||||
\(608\) | 8.82843 | + | 8.82843i | 0.358040 | + | 0.358040i | ||||
\(609\) | −1.17157 | + | 6.82843i | −0.0474745 | + | 0.276702i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 28.9706i | − | 1.17202i | ||||||
\(612\) | −19.7990 | + | 9.45584i | −0.800327 | + | 0.382230i | ||||
\(613\) | 16.0000 | − | 16.0000i | 0.646234 | − | 0.646234i | −0.305847 | − | 0.952081i | \(-0.598940\pi\) |
0.952081 | + | 0.305847i | \(0.0989395\pi\) | |||||||
\(614\) | 6.97056 | 0.281309 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.65685 | 0.308503 | ||||||||
\(617\) | −29.8284 | + | 29.8284i | −1.20085 | + | 1.20085i | −0.226938 | + | 0.973909i | \(0.572871\pi\) |
−0.973909 | + | 0.226938i | \(0.927129\pi\) | |||||||
\(618\) | 5.31371 | − | 3.75736i | 0.213749 | − | 0.151143i | ||||
\(619\) | 0.686292i | 0.0275844i | 0.999905 | + | 0.0137922i | \(0.00439033\pi\) | ||||
−0.999905 | + | 0.0137922i | \(0.995610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.7990 | + | 11.6274i | 0.834635 | + | 0.466592i | ||||
\(622\) | 8.24264 | + | 8.24264i | 0.330500 | + | 0.330500i | ||||
\(623\) | −32.9706 | − | 32.9706i | −1.32094 | − | 1.32094i | ||||
\(624\) | −14.4853 | − | 2.48528i | −0.579875 | − | 0.0994909i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.41421i | 0.296332i | ||||||||
\(627\) | −2.82843 | − | 4.00000i | −0.112956 | − | 0.159745i | ||||
\(628\) | −17.3431 | + | 17.3431i | −0.692067 | + | 0.692067i | ||||
\(629\) | 0.970563 | 0.0386989 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.9706 | −0.675587 | −0.337794 | − | 0.941220i | \(-0.609681\pi\) | ||||
−0.337794 | + | 0.941220i | \(0.609681\pi\) | |||||||
\(632\) | −12.1421 | + | 12.1421i | −0.482988 | + | 0.482988i | ||||
\(633\) | −4.48528 | − | 6.34315i | −0.178274 | − | 0.252117i | ||||
\(634\) | 1.35534i | 0.0538274i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.41421 | + | 0.757359i | 0.175035 | + | 0.0300313i | ||||
\(637\) | 32.6274 | + | 32.6274i | 1.29275 | + | 1.29275i | ||||
\(638\) | −0.242641 | − | 0.242641i | −0.00960624 | − | 0.00960624i | ||||
\(639\) | 7.02944 | + | 2.48528i | 0.278080 | + | 0.0983162i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 32.6274i | − | 1.28871i | −0.764728 | − | 0.644353i | \(-0.777127\pi\) | ||
0.764728 | − | 0.644353i | \(-0.222873\pi\) | |||||||
\(642\) | −0.201010 | + | 0.142136i | −0.00793324 | + | 0.00560965i | ||||
\(643\) | 9.24264 | − | 9.24264i | 0.364494 | − | 0.364494i | −0.500970 | − | 0.865464i | \(-0.667023\pi\) |
0.865464 | + | 0.500970i | \(0.167023\pi\) | |||||||
\(644\) | 40.4853 | 1.59534 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.68629 | −0.184380 | ||||||||
\(647\) | −11.7279 | + | 11.7279i | −0.461072 | + | 0.461072i | −0.899007 | − | 0.437935i | \(-0.855710\pi\) |
0.437935 | + | 0.899007i | \(0.355710\pi\) | |||||||
\(648\) | −1.50610 | − | 14.1924i | −0.0591651 | − | 0.557530i | ||||
\(649\) | 4.00000i | 0.157014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.48528 | − | 26.1421i | 0.175792 | − | 1.02459i | ||||
\(652\) | −6.55635 | − | 6.55635i | −0.256766 | − | 0.256766i | ||||
\(653\) | −8.65685 | − | 8.65685i | −0.338769 | − | 0.338769i | 0.517135 | − | 0.855904i | \(-0.326999\pi\) |
−0.855904 | + | 0.517135i | \(0.826999\pi\) | |||||||
\(654\) | −0.384776 | + | 2.24264i | −0.0150459 | + | 0.0876942i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 22.9706i | 0.896850i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.4853 | − | 14.4853i | 0.564695 | − | 0.564695i | ||||
\(659\) | −24.9706 | −0.972715 | −0.486358 | − | 0.873760i | \(-0.661675\pi\) | ||||
−0.486358 | + | 0.873760i | \(0.661675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | −1.89949 | + | 1.89949i | −0.0738260 | + | 0.0738260i | ||||
\(663\) | 16.0000 | − | 11.3137i | 0.621389 | − | 0.439388i | ||||
\(664\) | 20.3431i | 0.789467i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.100505 | + | 0.284271i | −0.00389449 | + | 0.0110153i | ||||
\(667\) | −2.68629 | − | 2.68629i | −0.104014 | − | 0.104014i | ||||
\(668\) | −26.9289 | − | 26.9289i | −1.04191 | − | 1.04191i | ||||
\(669\) | 39.9706 | + | 6.85786i | 1.54535 | + | 0.265140i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.48528i | 0.250362i | ||||||||
\(672\) | −21.3137 | − | 30.1421i | −0.822194 | − | 1.16276i | ||||
\(673\) | 22.3431 | − | 22.3431i | 0.861265 | − | 0.861265i | −0.130220 | − | 0.991485i | \(-0.541568\pi\) |
0.991485 | + | 0.130220i | \(0.0415684\pi\) | |||||||
\(674\) | 6.34315 | 0.244329 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.14214 | −0.351621 | ||||||||
\(677\) | −19.6569 | + | 19.6569i | −0.755474 | + | 0.755474i | −0.975495 | − | 0.220021i | \(-0.929387\pi\) |
0.220021 | + | 0.975495i | \(0.429387\pi\) | |||||||
\(678\) | 3.41421 | + | 4.82843i | 0.131122 | + | 0.185435i | ||||
\(679\) | − | 72.7696i | − | 2.79264i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.7279 | − | 4.24264i | −0.947576 | − | 0.162578i | ||||
\(682\) | 0.928932 | + | 0.928932i | 0.0355707 | + | 0.0355707i | ||||
\(683\) | −7.72792 | − | 7.72792i | −0.295701 | − | 0.295701i | 0.543627 | − | 0.839327i | \(-0.317051\pi\) |
−0.839327 | + | 0.543627i | \(0.817051\pi\) | |||||||
\(684\) | −5.17157 | + | 14.6274i | −0.197740 | + | 0.559293i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.6274i | 0.711198i | ||||||||
\(687\) | 13.6569 | − | 9.65685i | 0.521041 | − | 0.368432i | ||||
\(688\) | 0.727922 | − | 0.727922i | 0.0277518 | − | 0.0277518i | ||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 15.5147 | − | 15.5147i | 0.589781 | − | 0.589781i | ||||
\(693\) | 6.24264 | + | 13.0711i | 0.237138 | + | 0.496529i | ||||
\(694\) | 1.11270i | 0.0422375i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.384776 | + | 2.24264i | −0.0145849 | + | 0.0850071i | ||||
\(697\) | −21.6569 | − | 21.6569i | −0.820312 | − | 0.820312i | ||||
\(698\) | 8.78680 | + | 8.78680i | 0.332585 | + | 0.332585i | ||||
\(699\) | 8.14214 | − | 47.4558i | 0.307964 | − | 1.79494i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.31371i | 0.0496181i | 0.999692 | + | 0.0248090i | \(0.00789777\pi\) | ||||
−0.999692 | + | 0.0248090i | \(0.992102\pi\) | |||||||
\(702\) | 1.65685 | + | 5.85786i | 0.0625339 | + | 0.221091i | ||||
\(703\) | 0.485281 | − | 0.485281i | 0.0183027 | − | 0.0183027i | ||||
\(704\) | −4.17157 | −0.157222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.58579 | −0.172588 | ||||||||
\(707\) | 24.4853 | − | 24.4853i | 0.920864 | − | 0.920864i | ||||
\(708\) | 10.3431 | − | 7.31371i | 0.388719 | − | 0.274866i | ||||
\(709\) | − | 29.3137i | − | 1.10090i | −0.834868 | − | 0.550450i | \(-0.814456\pi\) | ||
0.834868 | − | 0.550450i | \(-0.185544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.6274 | − | 10.8284i | −1.14862 | − | 0.406098i | ||||
\(712\) | −10.8284 | − | 10.8284i | −0.405812 | − | 0.405812i | ||||
\(713\) | 10.2843 | + | 10.2843i | 0.385149 | + | 0.385149i | ||||
\(714\) | 13.6569 | + | 2.34315i | 0.511095 | + | 0.0876900i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 44.1421i | 1.64967i | ||||||||
\(717\) | −23.7990 | − | 33.6569i | −0.888790 | − | 1.25694i | ||||
\(718\) | −6.48528 | + | 6.48528i | −0.242029 | + | 0.242029i | ||||
\(719\) | −22.7696 | −0.849161 | −0.424581 | − | 0.905390i | \(-0.639578\pi\) | ||||
−0.424581 | + | 0.905390i | \(0.639578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.7990 | 1.63116 | ||||||||
\(722\) | 3.22183 | − | 3.22183i | 0.119904 | − | 0.119904i | ||||
\(723\) | 0.142136 | + | 0.201010i | 0.00528608 | + | 0.00747565i | ||||
\(724\) | 10.3431i | 0.384400i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.707107 | − | 0.121320i | −0.0262432 | − | 0.00450262i | ||||
\(727\) | −20.2132 | − | 20.2132i | −0.749666 | − | 0.749666i | 0.224750 | − | 0.974416i | \(-0.427843\pi\) |
−0.974416 | + | 0.224750i | \(0.927843\pi\) | |||||||
\(728\) | 15.3137 | + | 15.3137i | 0.567564 | + | 0.567564i | ||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.37258i | 0.0507668i | ||||||||
\(732\) | 16.7696 | − | 11.8579i | 0.619821 | − | 0.438279i | ||||
\(733\) | −3.79899 | + | 3.79899i | −0.140319 | + | 0.140319i | −0.773777 | − | 0.633458i | \(-0.781635\pi\) |
0.633458 | + | 0.773777i | \(0.281635\pi\) | |||||||
\(734\) | 0.644661 | 0.0237949 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.2426 | 0.746154 | ||||||||
\(737\) | 6.41421 | − | 6.41421i | 0.236271 | − | 0.236271i | ||||
\(738\) | 8.58579 | − | 4.10051i | 0.316047 | − | 0.150942i | ||||
\(739\) | 14.6274i | 0.538078i | 0.963129 | + | 0.269039i | \(0.0867061\pi\) | ||||
−0.963129 | + | 0.269039i | \(0.913294\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.34315 | − | 13.6569i | 0.0860776 | − | 0.501697i | ||||
\(742\) | −2.00000 | − | 2.00000i | −0.0734223 | − | 0.0734223i | ||||
\(743\) | 26.0416 | + | 26.0416i | 0.955375 | + | 0.955375i | 0.999046 | − | 0.0436712i | \(-0.0139054\pi\) |
−0.0436712 | + | 0.999046i | \(0.513905\pi\) | |||||||
\(744\) | 1.47309 | − | 8.58579i | 0.0540060 | − | 0.314770i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.05887i | 0.0753808i | ||||||||
\(747\) | −34.7279 | + | 16.5858i | −1.27063 | + | 0.606842i | ||||
\(748\) | 5.17157 | − | 5.17157i | 0.189091 | − | 0.189091i | ||||
\(749\) | −1.65685 | −0.0605401 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.6274 | −1.70146 | −0.850729 | − | 0.525604i | \(-0.823839\pi\) | ||||
−0.850729 | + | 0.525604i | \(0.823839\pi\) | |||||||
\(752\) | −21.7279 | + | 21.7279i | −0.792336 | + | 0.792336i | ||||
\(753\) | 22.8284 | − | 16.1421i | 0.831914 | − | 0.588252i | ||||
\(754\) | − | 0.970563i | − | 0.0353458i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 22.3848 | − | 40.0416i | 0.814126 | − | 1.45630i | ||||
\(757\) | −0.171573 | − | 0.171573i | −0.00623592 | − | 0.00623592i | 0.703982 | − | 0.710218i | \(-0.251404\pi\) |
−0.710218 | + | 0.703982i | \(0.751404\pi\) | |||||||
\(758\) | −8.24264 | − | 8.24264i | −0.299386 | − | 0.299386i | ||||
\(759\) | −7.82843 | − | 1.34315i | −0.284154 | − | 0.0487531i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.51472i | 0.0549085i | 0.999623 | + | 0.0274543i | \(0.00874006\pi\) | ||||
−0.999623 | + | 0.0274543i | \(0.991260\pi\) | |||||||
\(762\) | −0.828427 | − | 1.17157i | −0.0300107 | − | 0.0424416i | ||||
\(763\) | −10.8284 | + | 10.8284i | −0.392015 | + | 0.392015i | ||||
\(764\) | −20.6863 | −0.748404 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.55635 | 0.128496 | ||||||||
\(767\) | −8.00000 | + | 8.00000i | −0.288863 | + | 0.288863i | ||||
\(768\) | 3.97056 | + | 5.61522i | 0.143275 | + | 0.202622i | ||||
\(769\) | − | 52.6274i | − | 1.89779i | −0.315587 | − | 0.948897i | \(-0.602201\pi\) | ||
0.315587 | − | 0.948897i | \(-0.397799\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.41421 | + | 0.757359i | 0.158974 | + | 0.0272756i | ||||
\(772\) | −14.6274 | − | 14.6274i | −0.526452 | − | 0.526452i | ||||
\(773\) | −10.6569 | − | 10.6569i | −0.383300 | − | 0.383300i | 0.488989 | − | 0.872290i | \(-0.337366\pi\) |
−0.872290 | + | 0.488989i | \(0.837366\pi\) | |||||||
\(774\) | −0.402020 | − | 0.142136i | −0.0144503 | − | 0.00510896i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 23.8995i | − | 0.857942i | ||||||
\(777\) | −1.65685 | + | 1.17157i | −0.0594393 | + | 0.0420299i | ||||
\(778\) | −5.07107 | + | 5.07107i | −0.181807 | + | 0.181807i | ||||
\(779\) | −21.6569 | −0.775937 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.48528 | −0.0889304 | ||||||||
\(782\) | −5.37258 | + | 5.37258i | −0.192123 | + | 0.192123i | ||||
\(783\) | −4.14214 | + | 1.17157i | −0.148028 | + | 0.0418686i | ||||
\(784\) | − | 48.9411i | − | 1.74790i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.828427 | + | 4.82843i | −0.0295490 | + | 0.172224i | ||||
\(787\) | 28.5858 | + | 28.5858i | 1.01897 | + | 1.01897i | 0.999816 | + | 0.0191567i | \(0.00609815\pi\) |
0.0191567 | + | 0.999816i | \(0.493902\pi\) | |||||||
\(788\) | 25.8579 | + | 25.8579i | 0.921148 | + | 0.921148i | ||||
\(789\) | −0.727922 | + | 4.24264i | −0.0259147 | + | 0.151042i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.7990i | 1.41509i | ||||||||
\(792\) | 2.05025 | + | 4.29289i | 0.0728526 | + | 0.152541i | ||||
\(793\) | −12.9706 | + | 12.9706i | −0.460598 | + | 0.460598i | ||||
\(794\) | −3.61522 | −0.128299 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.4853 | 0.938746 | ||||||||
\(797\) | −25.9706 | + | 25.9706i | −0.919925 | + | 0.919925i | −0.997023 | − | 0.0770989i | \(-0.975434\pi\) |
0.0770989 | + | 0.997023i | \(0.475434\pi\) | |||||||
\(798\) | 8.00000 | − | 5.65685i | 0.283197 | − | 0.200250i | ||||
\(799\) | − | 40.9706i | − | 1.44943i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.65685 | − | 27.3137i | 0.341208 | − | 0.965082i | ||||
\(802\) | 10.4437 | + | 10.4437i | 0.368778 | + | 0.368778i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −28.3137 | − | 4.85786i | −0.998548 | − | 0.171324i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.71573i | 0.130881i | ||||||||
\(807\) | −14.0000 | − | 19.7990i | −0.492823 | − | 0.696957i | ||||
\(808\) | 8.04163 | − | 8.04163i | 0.282904 | − | 0.282904i | ||||
\(809\) | −15.8579 | −0.557533 | −0.278766 | − | 0.960359i | \(-0.589926\pi\) | ||||
−0.278766 | + | 0.960359i | \(0.589926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.6569 | −1.46277 | −0.731385 | − | 0.681965i | \(-0.761126\pi\) | ||||
−0.731385 | + | 0.681965i | \(0.761126\pi\) | |||||||
\(812\) | −5.17157 | + | 5.17157i | −0.181487 | + | 0.181487i | ||||
\(813\) | 8.48528 | + | 12.0000i | 0.297592 | + | 0.420858i | ||||
\(814\) | − | 0.100505i | − | 0.00352270i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.4853 | − | 3.51472i | −0.717128 | − | 0.123040i | ||||
\(817\) | 0.686292 | + | 0.686292i | 0.0240103 | + | 0.0240103i | ||||
\(818\) | 5.41421 | + | 5.41421i | 0.189304 | + | 0.189304i | ||||
\(819\) | −13.6569 | + | 38.6274i | −0.477209 | + | 1.34975i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 0.343146i | − | 0.0119759i | −0.999982 | − | 0.00598793i | \(-0.998094\pi\) | ||
0.999982 | − | 0.00598793i | \(-0.00190603\pi\) | |||||||
\(822\) | −0.142136 | + | 0.100505i | −0.00495755 | + | 0.00350552i | ||||
\(823\) | 18.4142 | − | 18.4142i | 0.641879 | − | 0.641879i | −0.309138 | − | 0.951017i | \(-0.600041\pi\) |
0.951017 | + | 0.309138i | \(0.100041\pi\) | |||||||
\(824\) | 14.3848 | 0.501117 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 28.0416 | − | 28.0416i | 0.975103 | − | 0.975103i | −0.0245945 | − | 0.999698i | \(-0.507829\pi\) |
0.999698 | + | 0.0245945i | \(0.00782945\pi\) | |||||||
\(828\) | 10.8406 | + | 22.6985i | 0.376738 | + | 0.788827i | ||||
\(829\) | 10.9706i | 0.381023i | 0.981685 | + | 0.190512i | \(0.0610147\pi\) | ||||
−0.981685 | + | 0.190512i | \(0.938985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.65685 | + | 44.6274i | −0.265613 | + | 1.54811i | ||||
\(832\) | −8.34315 | − | 8.34315i | −0.289247 | − | 0.289247i | ||||
\(833\) | 46.1421 | + | 46.1421i | 1.59873 | + | 1.59873i | ||||
\(834\) | 2.14214 | − | 12.4853i | 0.0741761 | − | 0.432330i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 5.17157i | − | 0.178863i | ||||||
\(837\) | 15.8579 | − | 4.48528i | 0.548128 | − | 0.155034i | ||||
\(838\) | 4.52691 | − | 4.52691i | 0.156380 | − | 0.156380i | ||||
\(839\) | −21.6569 | −0.747678 | −0.373839 | − | 0.927494i | \(-0.621959\pi\) | ||||
−0.373839 | + | 0.927494i | \(0.621959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | −1.17157 | + | 1.17157i | −0.0403751 | + | 0.0403751i | ||||
\(843\) | −40.4853 | + | 28.6274i | −1.39439 | + | 0.985981i | ||||
\(844\) | − | 8.20101i | − | 0.282290i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0000 | + | 4.24264i | 0.412568 | + | 0.145865i | ||||
\(847\) | −3.41421 | − | 3.41421i | −0.117314 | − | 0.117314i | ||||
\(848\) | 3.00000 | + | 3.00000i | 0.103020 | + | 0.103020i | ||||
\(849\) | 36.3848 | + | 6.24264i | 1.24872 | + | 0.214247i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.11270i | − | 0.0381428i | ||||||
\(852\) | 4.54416 | + | 6.42641i | 0.155680 | + | 0.220165i | ||||
\(853\) | −18.1421 | + | 18.1421i | −0.621175 | + | 0.621175i | −0.945832 | − | 0.324657i | \(-0.894751\pi\) |
0.324657 | + | 0.945832i | \(0.394751\pi\) | |||||||
\(854\) | −12.9706 | −0.443844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.544156 | −0.0185989 | ||||||||
\(857\) | 16.4853 | − | 16.4853i | 0.563126 | − | 0.563126i | −0.367068 | − | 0.930194i | \(-0.619638\pi\) |
0.930194 | + | 0.367068i | \(0.119638\pi\) | |||||||
\(858\) | −1.17157 | − | 1.65685i | −0.0399968 | − | 0.0565641i | ||||
\(859\) | 36.0000i | 1.22830i | 0.789188 | + | 0.614152i | \(0.210502\pi\) | ||||
−0.789188 | + | 0.614152i | \(0.789498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 63.1127 | + | 10.8284i | 2.15088 | + | 0.369032i | ||||
\(862\) | −1.85786 | − | 1.85786i | −0.0632791 | − | 0.0632791i | ||||
\(863\) | −12.5563 | − | 12.5563i | −0.427423 | − | 0.427423i | 0.460327 | − | 0.887750i | \(-0.347732\pi\) |
−0.887750 | + | 0.460327i | \(0.847732\pi\) | |||||||
\(864\) | 11.1924 | − | 20.0208i | 0.380773 | − | 0.681122i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 0.183766i | − | 0.00624463i | ||||||
\(867\) | −1.41421 | + | 1.00000i | −0.0480292 | + | 0.0339618i | ||||
\(868\) | 19.7990 | − | 19.7990i | 0.672022 | − | 0.672022i | ||||
\(869\) | 10.8284 | 0.367329 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.6569 | 0.869349 | ||||||||
\(872\) | −3.55635 | + | 3.55635i | −0.120433 | + | 0.120433i | ||||
\(873\) | 40.7990 | − | 19.4853i | 1.38084 | − | 0.659477i | ||||
\(874\) | 5.37258i | 0.181730i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.62742 | − | 6.62742i | −0.223792 | − | 0.223792i | 0.586301 | − | 0.810093i | \(-0.300584\pi\) |
−0.810093 | + | 0.586301i | \(0.800584\pi\) | |||||||
\(878\) | 2.14214 | + | 2.14214i | 0.0722936 | + | 0.0722936i | ||||
\(879\) | −1.51472 | + | 8.82843i | −0.0510902 | + | 0.297775i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.9706i | 0.436989i | 0.975838 | + | 0.218495i | \(0.0701146\pi\) | ||||
−0.975838 | + | 0.218495i | \(0.929885\pi\) | |||||||
\(882\) | −18.2929 | + | 8.73654i | −0.615954 | + | 0.294175i | ||||
\(883\) | 3.58579 | − | 3.58579i | 0.120671 | − | 0.120671i | −0.644192 | − | 0.764864i | \(-0.722806\pi\) |
0.764864 | + | 0.644192i | \(0.222806\pi\) | |||||||
\(884\) | 20.6863 | 0.695755 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.1594 | 0.408502 | ||||||||
\(887\) | 9.75736 | − | 9.75736i | 0.327620 | − | 0.327620i | −0.524061 | − | 0.851681i | \(-0.675584\pi\) |
0.851681 | + | 0.524061i | \(0.175584\pi\) | |||||||
\(888\) | −0.544156 | + | 0.384776i | −0.0182607 | + | 0.0129122i | ||||
\(889\) | − | 9.65685i | − | 0.323880i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.65685 | + | 7.00000i | −0.189512 | + | 0.234509i | ||||
\(892\) | 30.2721 | + | 30.2721i | 1.01358 | + | 1.01358i | ||||
\(893\) | −20.4853 | − | 20.4853i | −0.685514 | − | 0.685514i | ||||
\(894\) | −7.07107 | − | 1.21320i | −0.236492 | − | 0.0405756i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 50.9706i | − | 1.70281i | ||||||
\(897\) | −12.9706 | − | 18.3431i | −0.433074 | − | 0.612460i | ||||
\(898\) | −0.887302 | + | 0.887302i | −0.0296096 | + | 0.0296096i | ||||
\(899\) | −2.62742 | −0.0876293 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.65685 | −0.188457 | ||||||||
\(902\) | −2.24264 | + | 2.24264i | −0.0746718 | + | 0.0746718i | ||||
\(903\) | −1.65685 | − | 2.34315i | −0.0551367 | − | 0.0779750i | ||||
\(904\) | 13.0711i | 0.434737i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.17157 | + | 1.23045i | 0.238260 | + | 0.0408789i | ||||
\(907\) | −29.0416 | − | 29.0416i | −0.964312 | − | 0.964312i | 0.0350732 | − | 0.999385i | \(-0.488834\pi\) |
−0.999385 | + | 0.0350732i | \(0.988834\pi\) | |||||||
\(908\) | −18.7279 | − | 18.7279i | −0.621508 | − | 0.621508i | ||||
\(909\) | 20.2843 | + | 7.17157i | 0.672787 | + | 0.237866i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 56.0000i | − | 1.85536i | −0.373373 | − | 0.927681i | \(-0.621799\pi\) | ||
0.373373 | − | 0.927681i | \(-0.378201\pi\) | |||||||
\(912\) | −12.0000 | + | 8.48528i | −0.397360 | + | 0.280976i | ||||
\(913\) | 9.07107 | − | 9.07107i | 0.300209 | − | 0.300209i | ||||
\(914\) | 3.79899 | 0.125659 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.6569 | 0.583399 | ||||||||
\(917\) | −23.3137 | + | 23.3137i | −0.769886 | + | 0.769886i | ||||
\(918\) | 2.34315 | + | 8.28427i | 0.0773353 | + | 0.273422i | ||||
\(919\) | − | 14.6274i | − | 0.482514i | −0.970461 | − | 0.241257i | \(-0.922440\pi\) | ||
0.970461 | − | 0.241257i | \(-0.0775597\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.92893 | + | 28.7279i | −0.162414 | + | 0.946617i | ||||
\(922\) | −3.95837 | − | 3.95837i | −0.130362 | − | 0.130362i | ||||
\(923\) | −4.97056 | − | 4.97056i | −0.163608 | − | 0.163608i | ||||
\(924\) | −2.58579 | + | 15.0711i | −0.0850661 | + | 0.495802i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.87006i | 0.225764i | ||||||||
\(927\) | 11.7279 | + | 24.5563i | 0.385195 | + | 0.806536i | ||||
\(928\) | −2.58579 | + | 2.58579i | −0.0848826 | + | 0.0848826i | ||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46.1421 | 1.51225 | ||||||||
\(932\) | 35.9411 | − | 35.9411i | 1.17729 | − | 1.17729i | ||||
\(933\) | −39.7990 | + | 28.1421i | −1.30296 | + | 0.921332i | ||||
\(934\) | − | 0.242641i | − | 0.00793945i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.48528 | + | 12.6863i | −0.146606 | + | 0.414664i | ||||
\(937\) | 10.9706 | + | 10.9706i | 0.358393 | + | 0.358393i | 0.863220 | − | 0.504828i | \(-0.168444\pi\) |
−0.504828 | + | 0.863220i | \(0.668444\pi\) | |||||||
\(938\) | 12.8284 | + | 12.8284i | 0.418863 | + | 0.418863i | ||||
\(939\) | −30.5563 | − | 5.24264i | −0.997169 | − | 0.171087i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.1127i | 1.20984i | 0.796286 | + | 0.604920i | \(0.206795\pi\) | ||||
−0.796286 | + | 0.604920i | \(0.793205\pi\) | |||||||
\(942\) | 5.55635 | + | 7.85786i | 0.181036 | + | 0.256023i | ||||
\(943\) | −24.8284 | + | 24.8284i | −0.808525 | + | 0.808525i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.142136 | 0.00462123 | ||||||||
\(947\) | 17.2426 | − | 17.2426i | 0.560311 | − | 0.560311i | −0.369085 | − | 0.929396i | \(-0.620329\pi\) |
0.929396 | + | 0.369085i | \(0.120329\pi\) | |||||||
\(948\) | −19.7990 | − | 28.0000i | −0.643041 | − | 0.909398i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.58579 | − | 0.958369i | −0.181132 | − | 0.0310773i | ||||
\(952\) | 21.6569 | + | 21.6569i | 0.701903 | + | 0.701903i | ||||
\(953\) | −5.79899 | − | 5.79899i | −0.187848 | − | 0.187848i | 0.606917 | − | 0.794765i | \(-0.292406\pi\) |
−0.794765 | + | 0.606917i | \(0.792406\pi\) | |||||||
\(954\) | 0.585786 | − | 1.65685i | 0.0189655 | − | 0.0536426i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 43.5147i | − | 1.40737i | ||||||
\(957\) | 1.17157 | − | 0.828427i | 0.0378716 | − | 0.0267792i | ||||
\(958\) | −8.82843 | + | 8.82843i | −0.285234 | + | 0.285234i | ||||
\(959\) | −1.17157 | −0.0378321 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9411 | −0.675520 | ||||||||
\(962\) | 0.201010 | − | 0.201010i | 0.00648083 | − | 0.00648083i | ||||
\(963\) | −0.443651 | − | 0.928932i | −0.0142964 | − | 0.0299344i | ||||
\(964\) | 0.259885i | 0.00837032i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.68629 | − | 15.6569i | 0.0864300 | − | 0.503751i | ||||
\(967\) | −38.3848 | − | 38.3848i | −1.23437 | − | 1.23437i | −0.962268 | − | 0.272103i | \(-0.912281\pi\) |
−0.272103 | − | 0.962268i | \(-0.587719\pi\) | |||||||
\(968\) | −1.12132 | − | 1.12132i | −0.0360406 | − | 0.0360406i | ||||
\(969\) | 3.31371 | − | 19.3137i | 0.106452 | − | 0.620446i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.0000i | − | 0.641831i | −0.947108 | − | 0.320915i | \(-0.896010\pi\) | ||
0.947108 | − | 0.320915i | \(-0.103990\pi\) | |||||||
\(972\) | 28.4437 | + | 1.82843i | 0.912331 | + | 0.0586468i | ||||
\(973\) | 60.2843 | − | 60.2843i | 1.93263 | − | 1.93263i | ||||
\(974\) | −6.87006 | −0.220131 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.4558 | 0.622766 | ||||||||
\(977\) | 38.1127 | − | 38.1127i | 1.21933 | − | 1.21933i | 0.251468 | − | 0.967866i | \(-0.419087\pi\) |
0.967866 | − | 0.251468i | \(-0.0809132\pi\) | |||||||
\(978\) | −2.97056 | + | 2.10051i | −0.0949881 | + | 0.0671667i | ||||
\(979\) | 9.65685i | 0.308634i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.97056 | − | 3.17157i | −0.286408 | − | 0.101261i | ||||
\(982\) | −5.85786 | − | 5.85786i | −0.186932 | − | 0.186932i | ||||
\(983\) | −23.7279 | − | 23.7279i | −0.756803 | − | 0.756803i | 0.218936 | − | 0.975739i | \(-0.429741\pi\) |
−0.975739 | + | 0.218936i | \(0.929741\pi\) | |||||||
\(984\) | 20.7279 | + | 3.55635i | 0.660782 | + | 0.113372i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1.37258i | − | 0.0437119i | ||||||
\(987\) | 49.4558 | + | 69.9411i | 1.57420 | + | 2.22625i | ||||
\(988\) | 10.3431 | − | 10.3431i | 0.329059 | − | 0.329059i | ||||
\(989\) | 1.57359 | 0.0500374 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.8284 | 0.788701 | 0.394350 | − | 0.918960i | \(-0.370970\pi\) | ||||
0.394350 | + | 0.918960i | \(0.370970\pi\) | |||||||
\(992\) | 9.89949 | − | 9.89949i | 0.314309 | − | 0.314309i | ||||
\(993\) | −6.48528 | − | 9.17157i | −0.205804 | − | 0.291051i | ||||
\(994\) | − | 4.97056i | − | 0.157657i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −40.0416 | − | 6.87006i | −1.26877 | − | 0.217686i | ||||
\(997\) | −36.7696 | − | 36.7696i | −1.16450 | − | 1.16450i | −0.983479 | − | 0.181025i | \(-0.942059\pi\) |
−0.181025 | − | 0.983479i | \(-0.557941\pi\) | |||||||
\(998\) | −7.27208 | − | 7.27208i | −0.230194 | − | 0.230194i | ||||
\(999\) | −1.10051 | − | 0.615224i | −0.0348184 | − | 0.0194648i |
(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 | 825.2.k.f.782.1 | 4 | ||
3.2 | odd | 2 | 825.2.k.c.782.2 | 4 | |||
5.2 | odd | 4 | 165.2.k.b.23.1 | yes | 4 | ||
5.3 | odd | 4 | 825.2.k.c.518.2 | 4 | |||
5.4 | even | 2 | 165.2.k.a.122.2 | yes | 4 | ||
15.2 | even | 4 | 165.2.k.a.23.2 | ✓ | 4 | ||
15.8 | even | 4 | inner | 825.2.k.f.518.1 | 4 | ||
15.14 | odd | 2 | 165.2.k.b.122.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.k.a.23.2 | ✓ | 4 | 15.2 | even | 4 | ||
165.2.k.a.122.2 | yes | 4 | 5.4 | even | 2 | ||
165.2.k.b.23.1 | yes | 4 | 5.2 | odd | 4 | ||
165.2.k.b.122.1 | yes | 4 | 15.14 | odd | 2 | ||
825.2.k.c.518.2 | 4 | 5.3 | odd | 4 | |||
825.2.k.c.782.2 | 4 | 3.2 | odd | 2 | |||
825.2.k.f.518.1 | 4 | 15.8 | even | 4 | inner | ||
825.2.k.f.782.1 | 4 | 1.1 | even | 1 | trivial |