Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,2,Mod(23,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, 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("165.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(1.31753163335\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 122.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.122 |
Dual form | 165.2.k.b.23.1 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | \(0.203216\pi\) | |||||||
\(3\) | 1.41421 | + | 1.00000i | 0.816497 | + | 0.577350i | ||||
\(4\) | 1.82843i | 0.914214i | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 0.707107 | − | 0.121320i | 0.288675 | − | 0.0495288i | ||||
\(7\) | −3.41421 | − | 3.41421i | −1.29045 | − | 1.29045i | −0.934507 | − | 0.355944i | \(-0.884159\pi\) |
−0.355944 | − | 0.934507i | \(-0.615841\pi\) | |||||||
\(8\) | 1.12132 | + | 1.12132i | 0.396447 | + | 0.396447i | ||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0.292893 | − | 0.878680i | 0.0926210 | − | 0.277863i | ||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | −1.82843 | + | 2.58579i | −0.527821 | + | 0.746452i | ||||
\(13\) | −2.00000 | + | 2.00000i | −0.554700 | + | 0.554700i | −0.927794 | − | 0.373094i | \(-0.878297\pi\) |
0.373094 | + | 0.927794i | \(0.378297\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 3.82843 | + | 0.585786i | 0.988496 | + | 0.151249i | ||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 2.82843 | − | 2.82843i | 0.685994 | − | 0.685994i | −0.275350 | − | 0.961344i | \(-0.588794\pi\) |
0.961344 | + | 0.275350i | \(0.0887937\pi\) | |||||||
\(18\) | 1.12132 | + | 0.535534i | 0.264298 | + | 0.126227i | ||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 1.82843 | + | 3.65685i | 0.408849 | + | 0.817697i | ||||
\(21\) | −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 | ||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 1.17157i | 0.229764i | ||||||||
\(27\) | −1.41421 | + | 5.00000i | −0.272166 | + | 0.962250i | ||||
\(28\) | 6.24264 | − | 6.24264i | 1.17975 | − | 1.17975i | ||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 1.29289 | − | 0.949747i | 0.236049 | − | 0.173399i | ||||
\(31\) | −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 | ||||
\(33\) | −1.00000 | + | 1.41421i | −0.174078 | + | 0.246183i | ||||
\(34\) | − | 1.65685i | − | 0.284148i | ||||||
\(35\) | −10.2426 | − | 3.41421i | −1.73132 | − | 0.577107i | ||||
\(36\) | −5.17157 | + | 1.82843i | −0.861929 | + | 0.304738i | ||||
\(37\) | −0.171573 | − | 0.171573i | −0.0282064 | − | 0.0282064i | 0.692863 | − | 0.721069i | \(-0.256349\pi\) |
−0.721069 | + | 0.692863i | \(0.756349\pi\) | |||||||
\(38\) | −0.828427 | − | 0.828427i | −0.134389 | − | 0.134389i | ||||
\(39\) | −4.82843 | + | 0.828427i | −0.773167 | + | 0.132655i | ||||
\(40\) | 3.36396 | + | 1.12132i | 0.531889 | + | 0.177296i | ||||
\(41\) | 7.65685i | 1.19580i | 0.801571 | + | 0.597900i | \(0.203998\pi\) | ||||
−0.801571 | + | 0.597900i | \(0.796002\pi\) | |||||||
\(42\) | −2.82843 | − | 2.00000i | −0.436436 | − | 0.308607i | ||||
\(43\) | 0.242641 | − | 0.242641i | 0.0370024 | − | 0.0370024i | −0.688364 | − | 0.725366i | \(-0.741671\pi\) |
0.725366 | + | 0.688364i | \(0.241671\pi\) | |||||||
\(44\) | −1.82843 | −0.275646 | ||||||||
\(45\) | 4.82843 | + | 4.65685i | 0.719779 | + | 0.694203i | ||||
\(46\) | −1.89949 | −0.280065 | ||||||||
\(47\) | 7.24264 | − | 7.24264i | 1.05645 | − | 1.05645i | 0.0581392 | − | 0.998308i | \(-0.481483\pi\) |
0.998308 | − | 0.0581392i | \(-0.0185167\pi\) | |||||||
\(48\) | −4.24264 | − | 3.00000i | −0.612372 | − | 0.433013i | ||||
\(49\) | 16.3137i | 2.33053i | ||||||||
\(50\) | −0.292893 | − | 2.05025i | −0.0414214 | − | 0.289949i | ||||
\(51\) | 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 | ||||
\(55\) | 1.00000 | + | 2.00000i | 0.134840 | + | 0.269680i | ||||
\(56\) | − | 7.65685i | − | 1.02319i | ||||||
\(57\) | 2.82843 | − | 4.00000i | 0.374634 | − | 0.529813i | ||||
\(58\) | −0.242641 | + | 0.242641i | −0.0318603 | + | 0.0318603i | ||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | −1.07107 | + | 7.00000i | −0.138274 | + | 0.903696i | ||||
\(61\) | −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 | ||||
\(63\) | 6.24264 | − | 13.0711i | 0.786499 | − | 1.64680i | ||||
\(64\) | − | 4.17157i | − | 0.521447i | ||||||
\(65\) | −2.00000 | + | 6.00000i | −0.248069 | + | 0.744208i | ||||
\(66\) | 0.121320 | + | 0.707107i | 0.0149335 | + | 0.0870388i | ||||
\(67\) | −6.41421 | − | 6.41421i | −0.783621 | − | 0.783621i | 0.196819 | − | 0.980440i | \(-0.436939\pi\) |
−0.980440 | + | 0.196819i | \(0.936939\pi\) | |||||||
\(68\) | 5.17157 | + | 5.17157i | 0.627145 | + | 0.627145i | ||||
\(69\) | −1.34315 | − | 7.82843i | −0.161696 | − | 0.942432i | ||||
\(70\) | −4.00000 | + | 2.00000i | −0.478091 | + | 0.239046i | ||||
\(71\) | 2.48528i | 0.294949i | 0.989066 | + | 0.147474i | \(0.0471144\pi\) | ||||
−0.989066 | + | 0.147474i | \(0.952886\pi\) | |||||||
\(72\) | −2.05025 | + | 4.29289i | −0.241625 | + | 0.505922i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | −0.100505 | −0.0116835 | ||||||||
\(75\) | 8.24264 | − | 2.65685i | 0.951778 | − | 0.306787i | ||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | 3.41421 | − | 3.41421i | 0.389086 | − | 0.389086i | ||||
\(78\) | −1.17157 | + | 1.65685i | −0.132655 | + | 0.187602i | ||||
\(79\) | 10.8284i | 1.21829i | 0.793058 | + | 0.609147i | \(0.208488\pi\) | ||||
−0.793058 | + | 0.609147i | \(0.791512\pi\) | |||||||
\(80\) | −6.00000 | + | 3.00000i | −0.670820 | + | 0.335410i | ||||
\(81\) | −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 | ||||
\(85\) | 2.82843 | − | 8.48528i | 0.306786 | − | 0.920358i | ||||
\(86\) | − | 0.142136i | − | 0.0153269i | ||||||
\(87\) | −1.17157 | − | 0.828427i | −0.125606 | − | 0.0888167i | ||||
\(88\) | −1.12132 | + | 1.12132i | −0.119533 | + | 0.119533i | ||||
\(89\) | 9.65685 | 1.02362 | 0.511812 | − | 0.859097i | \(-0.328974\pi\) | ||||
0.511812 | + | 0.859097i | \(0.328974\pi\) | |||||||
\(90\) | 2.77817 | − | 0.0502525i | 0.292845 | − | 0.00529708i | ||||
\(91\) | 13.6569 | 1.43163 | ||||||||
\(92\) | 5.92893 | − | 5.92893i | 0.618134 | − | 0.618134i | ||||
\(93\) | −4.48528 | − | 3.17157i | −0.465102 | − | 0.328877i | ||||
\(94\) | − | 4.24264i | − | 0.437595i | ||||||
\(95\) | −2.82843 | − | 5.65685i | −0.290191 | − | 0.580381i | ||||
\(96\) | −7.53553 | + | 1.29289i | −0.769092 | + | 0.131955i | ||||
\(97\) | 10.6569 | + | 10.6569i | 1.08204 | + | 1.08204i | 0.996319 | + | 0.0857204i | \(0.0273192\pi\) |
0.0857204 | + | 0.996319i | \(0.472681\pi\) | |||||||
\(98\) | 4.77817 | + | 4.77817i | 0.482669 | + | 0.482669i | ||||
\(99\) | −2.82843 | + | 1.00000i | −0.284268 | + | 0.100504i | ||||
\(100\) | 7.31371 | + | 5.48528i | 0.731371 | + | 0.548528i | ||||
\(101\) | 7.17157i | 0.713598i | 0.934181 | + | 0.356799i | \(0.116132\pi\) | ||||
−0.934181 | + | 0.356799i | \(0.883868\pi\) | |||||||
\(102\) | 1.65685 | − | 2.34315i | 0.164053 | − | 0.232006i | ||||
\(103\) | −6.41421 | + | 6.41421i | −0.632011 | + | 0.632011i | −0.948572 | − | 0.316561i | \(-0.897472\pi\) |
0.316561 | + | 0.948572i | \(0.397472\pi\) | |||||||
\(104\) | −4.48528 | −0.439818 | ||||||||
\(105\) | −11.0711 | − | 15.0711i | −1.08043 | − | 1.47079i | ||||
\(106\) | −0.585786 | −0.0568966 | ||||||||
\(107\) | −0.242641 | + | 0.242641i | −0.0234570 | + | 0.0234570i | −0.718738 | − | 0.695281i | \(-0.755280\pi\) |
0.695281 | + | 0.718738i | \(0.255280\pi\) | |||||||
\(108\) | −9.14214 | − | 2.58579i | −0.879702 | − | 0.248817i | ||||
\(109\) | 3.17157i | 0.303782i | 0.988397 | + | 0.151891i | \(0.0485362\pi\) | ||||
−0.988397 | + | 0.151891i | \(0.951464\pi\) | |||||||
\(110\) | 0.878680 | + | 0.292893i | 0.0837788 | + | 0.0279263i | ||||
\(111\) | −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 | ||||
\(115\) | −9.72792 | − | 3.24264i | −0.907133 | − | 0.302378i | ||||
\(116\) | − | 1.51472i | − | 0.140638i | ||||||
\(117\) | −7.65685 | − | 3.65685i | −0.707876 | − | 0.338076i | ||||
\(118\) | 1.17157 | − | 1.17157i | 0.107852 | − | 0.107852i | ||||
\(119\) | −19.3137 | −1.77048 | ||||||||
\(120\) | 3.63604 | + | 4.94975i | 0.331923 | + | 0.451848i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −1.89949 | + | 1.89949i | −0.171972 | + | 0.171972i | ||||
\(123\) | −7.65685 | + | 10.8284i | −0.690395 | + | 0.976366i | ||||
\(124\) | − | 5.79899i | − | 0.520765i | ||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | −2.00000 | − | 5.65685i | −0.178174 | − | 0.503953i | ||||
\(127\) | 1.41421 | + | 1.41421i | 0.125491 | + | 0.125491i | 0.767063 | − | 0.641572i | \(-0.221717\pi\) |
−0.641572 | + | 0.767063i | \(0.721717\pi\) | |||||||
\(128\) | −7.46447 | − | 7.46447i | −0.659772 | − | 0.659772i | ||||
\(129\) | 0.585786 | − | 0.100505i | 0.0515756 | − | 0.00884898i | ||||
\(130\) | 1.17157 | + | 2.34315i | 0.102754 | + | 0.205507i | ||||
\(131\) | − | 6.82843i | − | 0.596602i | −0.954472 | − | 0.298301i | \(-0.903580\pi\) | ||
0.954472 | − | 0.298301i | \(-0.0964200\pi\) | |||||||
\(132\) | −2.58579 | − | 1.82843i | −0.225064 | − | 0.159144i | ||||
\(133\) | −9.65685 | + | 9.65685i | −0.837355 | + | 0.837355i | ||||
\(134\) | −3.75736 | −0.324586 | ||||||||
\(135\) | 2.17157 | + | 11.4142i | 0.186899 | + | 0.982379i | ||||
\(136\) | 6.34315 | 0.543920 | ||||||||
\(137\) | −0.171573 | + | 0.171573i | −0.0146585 | + | 0.0146585i | −0.714398 | − | 0.699740i | \(-0.753299\pi\) |
0.699740 | + | 0.714398i | \(0.253299\pi\) | |||||||
\(138\) | −2.68629 | − | 1.89949i | −0.228672 | − | 0.161696i | ||||
\(139\) | − | 17.6569i | − | 1.49763i | −0.662776 | − | 0.748817i | \(-0.730622\pi\) | ||
0.662776 | − | 0.748817i | \(-0.269378\pi\) | |||||||
\(140\) | 6.24264 | − | 18.7279i | 0.527599 | − | 1.58280i | ||||
\(141\) | 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 | ||||
\(145\) | −1.65685 | + | 0.828427i | −0.137594 | + | 0.0687971i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.3137 | + | 23.0711i | −1.34553 | + | 1.90287i | ||||
\(148\) | 0.313708 | − | 0.313708i | 0.0257867 | − | 0.0257867i | ||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 1.63604 | − | 3.19239i | 0.133582 | − | 0.260657i | ||||
\(151\) | 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 | ||||
\(153\) | 10.8284 | + | 5.17157i | 0.875426 | + | 0.418097i | ||||
\(154\) | − | 2.00000i | − | 0.161165i | ||||||
\(155\) | −6.34315 | + | 3.17157i | −0.509494 | + | 0.254747i | ||||
\(156\) | −1.51472 | − | 8.82843i | −0.121275 | − | 0.706840i | ||||
\(157\) | −9.48528 | − | 9.48528i | −0.757008 | − | 0.757008i | 0.218769 | − | 0.975777i | \(-0.429796\pi\) |
−0.975777 | + | 0.218769i | \(0.929796\pi\) | |||||||
\(158\) | 3.17157 | + | 3.17157i | 0.252317 | + | 0.252317i | ||||
\(159\) | −0.414214 | − | 2.41421i | −0.0328493 | − | 0.191460i | ||||
\(160\) | −3.12132 | + | 9.36396i | −0.246762 | + | 0.740286i | ||||
\(161\) | 22.1421i | 1.74504i | ||||||||
\(162\) | −0.393398 | + | 3.70711i | −0.0309083 | + | 0.291258i | ||||
\(163\) | 3.58579 | − | 3.58579i | 0.280860 | − | 0.280860i | −0.552592 | − | 0.833452i | \(-0.686361\pi\) |
0.833452 | + | 0.552592i | \(0.186361\pi\) | |||||||
\(164\) | −14.0000 | −1.09322 | ||||||||
\(165\) | −0.585786 | + | 3.82843i | −0.0456034 | + | 0.298043i | ||||
\(166\) | 5.31371 | 0.412424 | ||||||||
\(167\) | −14.7279 | + | 14.7279i | −1.13968 | + | 1.13968i | −0.151174 | + | 0.988507i | \(0.548305\pi\) |
−0.988507 | + | 0.151174i | \(0.951695\pi\) | |||||||
\(168\) | 7.65685 | − | 10.8284i | 0.590739 | − | 0.835431i | ||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | −1.65685 | − | 3.31371i | −0.127075 | − | 0.254150i | ||||
\(171\) | 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 | ||||
\(175\) | −23.8995 | + | 3.41421i | −1.80663 | + | 0.258090i | ||||
\(176\) | − | 3.00000i | − | 0.226134i | ||||||
\(177\) | 5.65685 | + | 4.00000i | 0.425195 | + | 0.300658i | ||||
\(178\) | 2.82843 | − | 2.82843i | 0.212000 | − | 0.212000i | ||||
\(179\) | −24.1421 | −1.80447 | −0.902234 | − | 0.431247i | \(-0.858074\pi\) | ||||
−0.902234 | + | 0.431247i | \(0.858074\pi\) | |||||||
\(180\) | −8.51472 | + | 8.82843i | −0.634650 | + | 0.658032i | ||||
\(181\) | 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 | ||||
\(183\) | −9.17157 | − | 6.48528i | −0.677982 | − | 0.479406i | ||||
\(184\) | − | 7.27208i | − | 0.536105i | ||||||
\(185\) | −0.514719 | − | 0.171573i | −0.0378429 | − | 0.0126143i | ||||
\(186\) | −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 | ||||
\(190\) | −2.48528 | − | 0.828427i | −0.180301 | − | 0.0601004i | ||||
\(191\) | − | 11.3137i | − | 0.818631i | −0.912393 | − | 0.409316i | \(-0.865768\pi\) | ||
0.912393 | − | 0.409316i | \(-0.134232\pi\) | |||||||
\(192\) | 4.17157 | − | 5.89949i | 0.301057 | − | 0.425759i | ||||
\(193\) | 8.00000 | − | 8.00000i | 0.575853 | − | 0.575853i | −0.357905 | − | 0.933758i | \(-0.616509\pi\) |
0.933758 | + | 0.357905i | \(0.116509\pi\) | |||||||
\(194\) | 6.24264 | 0.448195 | ||||||||
\(195\) | −8.82843 | + | 6.48528i | −0.632217 | + | 0.464421i | ||||
\(196\) | −29.8284 | −2.13060 | ||||||||
\(197\) | 14.1421 | − | 14.1421i | 1.00759 | − | 1.00759i | 0.00761443 | − | 0.999971i | \(-0.497576\pi\) |
0.999971 | − | 0.00761443i | \(-0.00242377\pi\) | |||||||
\(198\) | −0.535534 | + | 1.12132i | −0.0380587 | + | 0.0796888i | ||||
\(199\) | − | 14.4853i | − | 1.02683i | −0.858139 | − | 0.513417i | \(-0.828379\pi\) | ||
0.858139 | − | 0.513417i | \(-0.171621\pi\) | |||||||
\(200\) | 7.84924 | − | 1.12132i | 0.555025 | − | 0.0792893i | ||||
\(201\) | −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 | ||||
\(205\) | 7.65685 | + | 15.3137i | 0.534778 | + | 1.06956i | ||||
\(206\) | 3.75736i | 0.261788i | ||||||||
\(207\) | 5.92893 | − | 12.4142i | 0.412089 | − | 0.862847i | ||||
\(208\) | 6.00000 | − | 6.00000i | 0.416025 | − | 0.416025i | ||||
\(209\) | 2.82843 | 0.195646 | ||||||||
\(210\) | −7.65685 | − | 1.17157i | −0.528373 | − | 0.0808462i | ||||
\(211\) | −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 | ||||
\(213\) | −2.48528 | + | 3.51472i | −0.170289 | + | 0.240825i | ||||
\(214\) | 0.142136i | 0.00971619i | ||||||||
\(215\) | 0.242641 | − | 0.727922i | 0.0165480 | − | 0.0496439i | ||||
\(216\) | −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 | ||||||||
\(220\) | −3.65685 | + | 1.82843i | −0.246545 | + | 0.123273i | ||||
\(221\) | 11.3137i | 0.761042i | ||||||||
\(222\) | −0.142136 | − | 0.100505i | −0.00953952 | − | 0.00674546i | ||||
\(223\) | −16.5563 | + | 16.5563i | −1.10870 | + | 1.10870i | −0.115373 | + | 0.993322i | \(0.536806\pi\) |
−0.993322 | + | 0.115373i | \(0.963194\pi\) | |||||||
\(224\) | 21.3137 | 1.42408 | ||||||||
\(225\) | 14.3137 | + | 4.48528i | 0.954247 | + | 0.299019i | ||||
\(226\) | 3.41421 | 0.227110 | ||||||||
\(227\) | −10.2426 | + | 10.2426i | −0.679828 | + | 0.679828i | −0.959961 | − | 0.280133i | \(-0.909621\pi\) |
0.280133 | + | 0.959961i | \(0.409621\pi\) | |||||||
\(228\) | 7.31371 | + | 5.17157i | 0.484362 | + | 0.342496i | ||||
\(229\) | − | 9.65685i | − | 0.638143i | −0.947731 | − | 0.319071i | \(-0.896629\pi\) | ||
0.947731 | − | 0.319071i | \(-0.103371\pi\) | |||||||
\(230\) | −3.79899 | + | 1.89949i | −0.250498 | + | 0.125249i | ||||
\(231\) | 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 | ||||
\(235\) | 7.24264 | − | 21.7279i | 0.472458 | − | 1.41737i | ||||
\(236\) | 7.31371i | 0.476082i | ||||||||
\(237\) | −10.8284 | + | 15.3137i | −0.703382 | + | 0.994732i | ||||
\(238\) | −5.65685 | + | 5.65685i | −0.366679 | + | 0.366679i | ||||
\(239\) | 23.7990 | 1.53943 | 0.769714 | − | 0.638388i | \(-0.220399\pi\) | ||||
0.769714 | + | 0.638388i | \(0.220399\pi\) | |||||||
\(240\) | −11.4853 | − | 1.75736i | −0.741372 | − | 0.113437i | ||||
\(241\) | 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 | ||||
\(243\) | −15.5563 | + | 1.00000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | − | 11.8579i | − | 0.759122i | ||||||
\(245\) | 16.3137 | + | 32.6274i | 1.04224 | + | 2.08449i | ||||
\(246\) | 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 | ||||
\(250\) | −2.63604 | − | 3.80761i | −0.166718 | − | 0.240815i | ||||
\(251\) | 16.1421i | 1.01888i | 0.860505 | + | 0.509441i | \(0.170148\pi\) | ||||
−0.860505 | + | 0.509441i | \(0.829852\pi\) | |||||||
\(252\) | 23.8995 | + | 11.4142i | 1.50553 | + | 0.719028i | ||||
\(253\) | 3.24264 | − | 3.24264i | 0.203863 | − | 0.203863i | ||||
\(254\) | 0.828427 | 0.0519801 | ||||||||
\(255\) | 12.4853 | − | 9.17157i | 0.781859 | − | 0.574346i | ||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 1.82843 | − | 1.82843i | 0.114054 | − | 0.114054i | −0.647776 | − | 0.761831i | \(-0.724301\pi\) |
0.761831 | + | 0.647776i | \(0.224301\pi\) | |||||||
\(258\) | 0.142136 | − | 0.201010i | 0.00884898 | − | 0.0125143i | ||||
\(259\) | 1.17157i | 0.0727980i | ||||||||
\(260\) | −10.9706 | − | 3.65685i | −0.680365 | − | 0.226788i | ||||
\(261\) | −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 | ||||
\(265\) | −3.00000 | − | 1.00000i | −0.184289 | − | 0.0614295i | ||||
\(266\) | 5.65685i | 0.346844i | ||||||||
\(267\) | 13.6569 | + | 9.65685i | 0.835786 | + | 0.590990i | ||||
\(268\) | 11.7279 | − | 11.7279i | 0.716397 | − | 0.716397i | ||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 3.97918 | + | 2.70711i | 0.242165 | + | 0.164749i | ||||
\(271\) | 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 | ||||
\(273\) | 19.3137 | + | 13.6569i | 1.16892 | + | 0.826550i | ||||
\(274\) | 0.100505i | 0.00607173i | ||||||||
\(275\) | 4.00000 | + | 3.00000i | 0.241209 | + | 0.180907i | ||||
\(276\) | 14.3137 | − | 2.45584i | 0.861584 | − | 0.147824i | ||||
\(277\) | −18.4853 | − | 18.4853i | −1.11067 | − | 1.11067i | −0.993059 | − | 0.117613i | \(-0.962476\pi\) |
−0.117613 | − | 0.993059i | \(-0.537524\pi\) | |||||||
\(278\) | −5.17157 | − | 5.17157i | −0.310170 | − | 0.310170i | ||||
\(279\) | −3.17157 | − | 8.97056i | −0.189877 | − | 0.537054i | ||||
\(280\) | −7.65685 | − | 15.3137i | −0.457585 | − | 0.915169i | ||||
\(281\) | − | 28.6274i | − | 1.70777i | −0.520463 | − | 0.853884i | \(-0.674241\pi\) | ||
0.520463 | − | 0.853884i | \(-0.325759\pi\) | |||||||
\(282\) | 4.24264 | − | 6.00000i | 0.252646 | − | 0.357295i | ||||
\(283\) | −15.0711 | + | 15.0711i | −0.895882 | + | 0.895882i | −0.995069 | − | 0.0991868i | \(-0.968376\pi\) |
0.0991868 | + | 0.995069i | \(0.468376\pi\) | |||||||
\(284\) | −4.54416 | −0.269646 | ||||||||
\(285\) | 1.65685 | − | 10.8284i | 0.0981436 | − | 0.641421i | ||||
\(286\) | −1.17157 | −0.0692766 | ||||||||
\(287\) | 26.1421 | − | 26.1421i | 1.54312 | − | 1.54312i | ||||
\(288\) | −11.9497 | − | 5.70711i | −0.704146 | − | 0.336294i | ||||
\(289\) | 1.00000i | 0.0588235i | ||||||||
\(290\) | −0.242641 | + | 0.727922i | −0.0142484 | + | 0.0427451i | ||||
\(291\) | 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 | ||||
\(295\) | 8.00000 | − | 4.00000i | 0.465778 | − | 0.232889i | ||||
\(296\) | − | 0.384776i | − | 0.0223647i | ||||||
\(297\) | −5.00000 | − | 1.41421i | −0.290129 | − | 0.0820610i | ||||
\(298\) | 2.92893 | − | 2.92893i | 0.169668 | − | 0.169668i | ||||
\(299\) | 12.9706 | 0.750107 | ||||||||
\(300\) | 4.85786 | + | 15.0711i | 0.280469 | + | 0.870129i | ||||
\(301\) | −1.65685 | −0.0954995 | ||||||||
\(302\) | 2.97056 | − | 2.97056i | 0.170937 | − | 0.170937i | ||||
\(303\) | −7.17157 | + | 10.1421i | −0.411996 | + | 0.582650i | ||||
\(304\) | 8.48528i | 0.486664i | ||||||||
\(305\) | −12.9706 | + | 6.48528i | −0.742692 | + | 0.371346i | ||||
\(306\) | 4.68629 | − | 1.65685i | 0.267897 | − | 0.0947161i | ||||
\(307\) | −11.8995 | − | 11.8995i | −0.679140 | − | 0.679140i | 0.280666 | − | 0.959806i | \(-0.409445\pi\) |
−0.959806 | + | 0.280666i | \(0.909445\pi\) | |||||||
\(308\) | 6.24264 | + | 6.24264i | 0.355707 | + | 0.355707i | ||||
\(309\) | −15.4853 | + | 2.65685i | −0.880927 | + | 0.151143i | ||||
\(310\) | −0.928932 | + | 2.78680i | −0.0527598 | + | 0.158279i | ||||
\(311\) | − | 28.1421i | − | 1.59579i | −0.602794 | − | 0.797897i | \(-0.705946\pi\) | ||
0.602794 | − | 0.797897i | \(-0.294054\pi\) | |||||||
\(312\) | −6.34315 | − | 4.48528i | −0.359110 | − | 0.253929i | ||||
\(313\) | 12.6569 | − | 12.6569i | 0.715408 | − | 0.715408i | −0.252253 | − | 0.967661i | \(-0.581172\pi\) |
0.967661 | + | 0.252253i | \(0.0811717\pi\) | |||||||
\(314\) | −5.55635 | −0.313563 | ||||||||
\(315\) | −0.585786 | − | 32.3848i | −0.0330053 | − | 1.82468i | ||||
\(316\) | −19.7990 | −1.11378 | ||||||||
\(317\) | −2.31371 | + | 2.31371i | −0.129951 | + | 0.129951i | −0.769091 | − | 0.639140i | \(-0.779291\pi\) |
0.639140 | + | 0.769091i | \(0.279291\pi\) | |||||||
\(318\) | −0.828427 | − | 0.585786i | −0.0464559 | − | 0.0328493i | ||||
\(319\) | − | 0.828427i | − | 0.0463830i | ||||||
\(320\) | −4.17157 | − | 8.34315i | −0.233198 | − | 0.466396i | ||||
\(321\) | −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 | ||||
\(325\) | 2.00000 | + | 14.0000i | 0.110940 | + | 0.776580i | ||||
\(326\) | − | 2.10051i | − | 0.116336i | ||||||
\(327\) | −3.17157 | + | 4.48528i | −0.175388 | + | 0.248037i | ||||
\(328\) | −8.58579 | + | 8.58579i | −0.474071 | + | 0.474071i | ||||
\(329\) | −49.4558 | −2.72659 | ||||||||
\(330\) | 0.949747 | + | 1.29289i | 0.0522819 | + | 0.0711714i | ||||
\(331\) | −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 | ||||
\(333\) | 0.313708 | − | 0.656854i | 0.0171911 | − | 0.0359954i | ||||
\(334\) | 8.62742i | 0.472071i | ||||||||
\(335\) | −19.2426 | − | 6.41421i | −1.05134 | − | 0.350446i | ||||
\(336\) | 4.24264 | + | 24.7279i | 0.231455 | + | 1.34902i | ||||
\(337\) | −10.8284 | − | 10.8284i | −0.589862 | − | 0.589862i | 0.347732 | − | 0.937594i | \(-0.386952\pi\) |
−0.937594 | + | 0.347732i | \(0.886952\pi\) | |||||||
\(338\) | 1.46447 | + | 1.46447i | 0.0796565 | + | 0.0796565i | ||||
\(339\) | 2.41421 | + | 14.0711i | 0.131122 | + | 0.764235i | ||||
\(340\) | 15.5147 | + | 5.17157i | 0.841404 | + | 0.280468i | ||||
\(341\) | − | 3.17157i | − | 0.171750i | ||||||
\(342\) | 1.51472 | − | 3.17157i | 0.0819066 | − | 0.171499i | ||||
\(343\) | 31.7990 | − | 31.7990i | 1.71698 | − | 1.71698i | ||||
\(344\) | 0.544156 | 0.0293389 | ||||||||
\(345\) | −10.5147 | − | 14.3137i | −0.566093 | − | 0.770624i | ||||
\(346\) | −4.97056 | −0.267219 | ||||||||
\(347\) | −1.89949 | + | 1.89949i | −0.101970 | + | 0.101970i | −0.756251 | − | 0.654281i | \(-0.772971\pi\) |
0.654281 | + | 0.756251i | \(0.272971\pi\) | |||||||
\(348\) | 1.51472 | − | 2.14214i | 0.0811974 | − | 0.114831i | ||||
\(349\) | 30.0000i | 1.60586i | 0.596071 | + | 0.802932i | \(0.296728\pi\) | ||||
−0.596071 | + | 0.802932i | \(0.703272\pi\) | |||||||
\(350\) | −6.00000 | + | 8.00000i | −0.320713 | + | 0.427618i | ||||
\(351\) | −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 | ||||
\(355\) | 2.48528 | + | 4.97056i | 0.131905 | + | 0.263810i | ||||
\(356\) | 17.6569i | 0.935811i | ||||||||
\(357\) | −27.3137 | − | 19.3137i | −1.44559 | − | 1.02219i | ||||
\(358\) | −7.07107 | + | 7.07107i | −0.373718 | + | 0.373718i | ||||
\(359\) | 22.1421 | 1.16862 | 0.584309 | − | 0.811532i | \(-0.301366\pi\) | ||||
0.584309 | + | 0.811532i | \(0.301366\pi\) | |||||||
\(360\) | 0.192388 | + | 10.6360i | 0.0101397 | + | 0.560568i | ||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 1.65685 | − | 1.65685i | 0.0870823 | − | 0.0870823i | ||||
\(363\) | −1.41421 | − | 1.00000i | −0.0742270 | − | 0.0524864i | ||||
\(364\) | 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 | 0.677800 | − | 0.735246i | \(-0.262933\pi\) |
−0.735246 | + | 0.677800i | \(0.762933\pi\) | |||||||
\(368\) | 9.72792 | + | 9.72792i | 0.507103 | + | 0.507103i | ||||
\(369\) | −21.6569 | + | 7.65685i | −1.12741 | + | 0.398600i | ||||
\(370\) | −0.201010 | + | 0.100505i | −0.0104500 | + | 0.00522501i | ||||
\(371\) | 6.82843i | 0.354514i | ||||||||
\(372\) | 5.79899 | − | 8.20101i | 0.300664 | − | 0.425203i | ||||
\(373\) | 3.51472 | − | 3.51472i | 0.181985 | − | 0.181985i | −0.610235 | − | 0.792220i | \(-0.708925\pi\) |
0.792220 | + | 0.610235i | \(0.208925\pi\) | |||||||
\(374\) | 1.65685 | 0.0856739 | ||||||||
\(375\) | 13.8284 | − | 13.5563i | 0.714097 | − | 0.700047i | ||||
\(376\) | 16.2426 | 0.837650 | ||||||||
\(377\) | 1.65685 | − | 1.65685i | 0.0853323 | − | 0.0853323i | ||||
\(378\) | 2.82843 | − | 10.0000i | 0.145479 | − | 0.514344i | ||||
\(379\) | − | 28.1421i | − | 1.44556i | −0.691076 | − | 0.722782i | \(-0.742863\pi\) | ||
0.691076 | − | 0.722782i | \(-0.257137\pi\) | |||||||
\(380\) | 10.3431 | − | 5.17157i | 0.530592 | − | 0.265296i | ||||
\(381\) | 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 | ||||
\(385\) | 3.41421 | − | 10.2426i | 0.174004 | − | 0.522013i | ||||
\(386\) | − | 4.68629i | − | 0.238526i | ||||||
\(387\) | 0.928932 | + | 0.443651i | 0.0472203 | + | 0.0225520i | ||||
\(388\) | −19.4853 | + | 19.4853i | −0.989215 | + | 0.989215i | ||||
\(389\) | 17.3137 | 0.877840 | 0.438920 | − | 0.898526i | \(-0.355361\pi\) | ||||
0.438920 | + | 0.898526i | \(0.355361\pi\) | |||||||
\(390\) | −0.686292 | + | 4.48528i | −0.0347517 | + | 0.227121i | ||||
\(391\) | −18.3431 | −0.927653 | ||||||||
\(392\) | −18.2929 | + | 18.2929i | −0.923931 | + | 0.923931i | ||||
\(393\) | 6.82843 | − | 9.65685i | 0.344449 | − | 0.487124i | ||||
\(394\) | − | 8.28427i | − | 0.417356i | ||||||
\(395\) | 10.8284 | + | 21.6569i | 0.544837 | + | 1.08967i | ||||
\(396\) | −1.82843 | − | 5.17157i | −0.0918819 | − | 0.259881i | ||||
\(397\) | 6.17157 | + | 6.17157i | 0.309742 | + | 0.309742i | 0.844810 | − | 0.535067i | \(-0.179714\pi\) |
−0.535067 | + | 0.844810i | \(0.679714\pi\) | |||||||
\(398\) | −4.24264 | − | 4.24264i | −0.212664 | − | 0.212664i | ||||
\(399\) | −23.3137 | + | 4.00000i | −1.16715 | + | 0.200250i | ||||
\(400\) | −9.00000 | + | 12.0000i | −0.450000 | + | 0.600000i | ||||
\(401\) | − | 35.6569i | − | 1.78062i | −0.455357 | − | 0.890309i | \(-0.650488\pi\) | ||
0.455357 | − | 0.890309i | \(-0.349512\pi\) | |||||||
\(402\) | −5.31371 | − | 3.75736i | −0.265024 | − | 0.187400i | ||||
\(403\) | 6.34315 | − | 6.34315i | 0.315975 | − | 0.315975i | ||||
\(404\) | −13.1127 | −0.652381 | ||||||||
\(405\) | −8.34315 | + | 18.3137i | −0.414574 | + | 0.910015i | ||||
\(406\) | 1.65685 | 0.0822283 | ||||||||
\(407\) | 0.171573 | − | 0.171573i | 0.00850455 | − | 0.00850455i | ||||
\(408\) | 8.97056 | + | 6.34315i | 0.444109 | + | 0.314033i | ||||
\(409\) | 18.4853i | 0.914038i | 0.889457 | + | 0.457019i | \(0.151083\pi\) | ||||
−0.889457 | + | 0.457019i | \(0.848917\pi\) | |||||||
\(410\) | 6.72792 | + | 2.24264i | 0.332268 | + | 0.110756i | ||||
\(411\) | −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 | ||||
\(415\) | 27.2132 | + | 9.07107i | 1.33584 | + | 0.445281i | ||||
\(416\) | − | 12.4853i | − | 0.612141i | ||||||
\(417\) | 17.6569 | − | 24.9706i | 0.864660 | − | 1.22281i | ||||
\(418\) | 0.828427 | − | 0.828427i | 0.0405197 | − | 0.0405197i | ||||
\(419\) | −15.4558 | −0.755067 | −0.377534 | − | 0.925996i | \(-0.623228\pi\) | ||||
−0.377534 | + | 0.925996i | \(0.623228\pi\) | |||||||
\(420\) | 27.5563 | − | 20.2426i | 1.34461 | − | 0.987740i | ||||
\(421\) | −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 | ||||
\(423\) | 27.7279 | + | 13.2426i | 1.34818 | + | 0.643879i | ||||
\(424\) | − | 2.24264i | − | 0.108912i | ||||||
\(425\) | −2.82843 | − | 19.7990i | −0.137199 | − | 0.960392i | ||||
\(426\) | 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 | ||||
\(430\) | −0.142136 | − | 0.284271i | −0.00685439 | − | 0.0137088i | ||||
\(431\) | 6.34315i | 0.305539i | 0.988262 | + | 0.152769i | \(0.0488191\pi\) | ||||
−0.988262 | + | 0.152769i | \(0.951181\pi\) | |||||||
\(432\) | 4.24264 | − | 15.0000i | 0.204124 | − | 0.721688i | ||||
\(433\) | −0.313708 | + | 0.313708i | −0.0150759 | + | 0.0150759i | −0.714605 | − | 0.699529i | \(-0.753393\pi\) |
0.699529 | + | 0.714605i | \(0.253393\pi\) | |||||||
\(434\) | 6.34315 | 0.304481 | ||||||||
\(435\) | −3.17157 | − | 0.485281i | −0.152065 | − | 0.0232675i | ||||
\(436\) | −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 | \(0.944159\pi\) | |||||||
\(440\) | −1.12132 | + | 3.36396i | −0.0534568 | + | 0.160371i | ||||
\(441\) | −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 | ||||
\(445\) | 19.3137 | − | 9.65685i | 0.915558 | − | 0.457779i | ||||
\(446\) | 9.69848i | 0.459237i | ||||||||
\(447\) | 14.1421 | + | 10.0000i | 0.668900 | + | 0.472984i | ||||
\(448\) | −14.2426 | + | 14.2426i | −0.672902 | + | 0.672902i | ||||
\(449\) | 3.02944 | 0.142968 | 0.0714840 | − | 0.997442i | \(-0.477227\pi\) | ||||
0.0714840 | + | 0.997442i | \(0.477227\pi\) | |||||||
\(450\) | 5.50610 | − | 2.87868i | 0.259560 | − | 0.135702i | ||||
\(451\) | −7.65685 | −0.360547 | ||||||||
\(452\) | −10.6569 | + | 10.6569i | −0.501256 | + | 0.501256i | ||||
\(453\) | 14.3431 | + | 10.1421i | 0.673900 | + | 0.476519i | ||||
\(454\) | 6.00000i | 0.281594i | ||||||||
\(455\) | 27.3137 | − | 13.6569i | 1.28049 | − | 0.640243i | ||||
\(456\) | 7.65685 | − | 1.31371i | 0.358565 | − | 0.0615200i | ||||
\(457\) | −6.48528 | − | 6.48528i | −0.303369 | − | 0.303369i | 0.538962 | − | 0.842330i | \(-0.318817\pi\) |
−0.842330 | + | 0.538962i | \(0.818817\pi\) | |||||||
\(458\) | −2.82843 | − | 2.82843i | −0.132164 | − | 0.132164i | ||||
\(459\) | 10.1421 | + | 18.1421i | 0.473394 | + | 0.846802i | ||||
\(460\) | 5.92893 | − | 17.7868i | 0.276438 | − | 0.829314i | ||||
\(461\) | 13.5147i | 0.629443i | 0.949184 | + | 0.314722i | \(0.101911\pi\) | ||||
−0.949184 | + | 0.314722i | \(0.898089\pi\) | |||||||
\(462\) | 2.00000 | − | 2.82843i | 0.0930484 | − | 0.131590i | ||||
\(463\) | 11.7279 | − | 11.7279i | 0.545043 | − | 0.545043i | −0.379960 | − | 0.925003i | \(-0.624062\pi\) |
0.925003 | + | 0.379960i | \(0.124062\pi\) | |||||||
\(464\) | 2.48528 | 0.115376 | ||||||||
\(465\) | −12.1421 | − | 1.85786i | −0.563078 | − | 0.0861564i | ||||
\(466\) | −11.5147 | −0.533409 | ||||||||
\(467\) | 0.414214 | − | 0.414214i | 0.0191675 | − | 0.0191675i | −0.697458 | − | 0.716626i | \(-0.745686\pi\) |
0.716626 | + | 0.697458i | \(0.245686\pi\) | |||||||
\(468\) | 6.68629 | − | 14.0000i | 0.309074 | − | 0.647150i | ||||
\(469\) | 43.7990i | 2.02245i | ||||||||
\(470\) | −4.24264 | − | 8.48528i | −0.195698 | − | 0.391397i | ||||
\(471\) | −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 | ||||
\(475\) | −11.3137 | − | 8.48528i | −0.519109 | − | 0.389331i | ||||
\(476\) | − | 35.3137i | − | 1.61860i | ||||||
\(477\) | 1.82843 | − | 3.82843i | 0.0837179 | − | 0.175292i | ||||
\(478\) | 6.97056 | − | 6.97056i | 0.318826 | − | 0.318826i | ||||
\(479\) | 30.1421 | 1.37723 | 0.688615 | − | 0.725127i | \(-0.258219\pi\) | ||||
0.688615 | + | 0.725127i | \(0.258219\pi\) | |||||||
\(480\) | −13.7782 | + | 10.1213i | −0.628885 | + | 0.461973i | ||||
\(481\) | 0.686292 | 0.0312922 | ||||||||
\(482\) | 0.0416306 | − | 0.0416306i | 0.00189622 | − | 0.00189622i | ||||
\(483\) | −22.1421 | + | 31.3137i | −1.00750 | + | 1.42482i | ||||
\(484\) | − | 1.82843i | − | 0.0831103i | ||||||
\(485\) | 31.9706 | + | 10.6569i | 1.45171 | + | 0.483903i | ||||
\(486\) | −4.26346 | + | 4.84924i | −0.193394 | + | 0.219966i | ||||
\(487\) | 11.7279 | + | 11.7279i | 0.531443 | + | 0.531443i | 0.921002 | − | 0.389559i | \(-0.127372\pi\) |
−0.389559 | + | 0.921002i | \(0.627372\pi\) | |||||||
\(488\) | −7.27208 | − | 7.27208i | −0.329192 | − | 0.329192i | ||||
\(489\) | 8.65685 | − | 1.48528i | 0.391476 | − | 0.0671667i | ||||
\(490\) | 14.3345 | + | 4.77817i | 0.647568 | + | 0.215856i | ||||
\(491\) | 20.0000i | 0.902587i | 0.892375 | + | 0.451294i | \(0.149037\pi\) | ||||
−0.892375 | + | 0.451294i | \(0.850963\pi\) | |||||||
\(492\) | −19.7990 | − | 14.0000i | −0.892607 | − | 0.631169i | ||||
\(493\) | −2.34315 | + | 2.34315i | −0.105530 | + | 0.105530i | ||||
\(494\) | 3.31371 | 0.149091 | ||||||||
\(495\) | −4.65685 | + | 4.82843i | −0.209310 | + | 0.217022i | ||||
\(496\) | 9.51472 | 0.427223 | ||||||||
\(497\) | 8.48528 | − | 8.48528i | 0.380617 | − | 0.380617i | ||||
\(498\) | 7.51472 | + | 5.31371i | 0.336743 | + | 0.238113i | ||||
\(499\) | − | 24.8284i | − | 1.11147i | −0.831358 | − | 0.555737i | \(-0.812436\pi\) | ||
0.831358 | − | 0.555737i | \(-0.187564\pi\) | |||||||
\(500\) | 20.1127 | + | 3.65685i | 0.899467 | + | 0.163539i | ||||
\(501\) | −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 | ||||
\(505\) | 7.17157 | + | 14.3431i | 0.319131 | + | 0.638262i | ||||
\(506\) | − | 1.89949i | − | 0.0844428i | ||||||
\(507\) | −5.00000 | + | 7.07107i | −0.222058 | + | 0.314037i | ||||
\(508\) | −2.58579 | + | 2.58579i | −0.114726 | + | 0.114726i | ||||
\(509\) | −35.6569 | −1.58046 | −0.790231 | − | 0.612809i | \(-0.790040\pi\) | ||||
−0.790231 | + | 0.612809i | \(0.790040\pi\) | |||||||
\(510\) | 0.970563 | − | 6.34315i | 0.0429772 | − | 0.280879i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0919 | − | 16.0919i | 0.711167 | − | 0.711167i | ||||
\(513\) | 14.1421 | + | 4.00000i | 0.624391 | + | 0.176604i | ||||
\(514\) | − | 1.07107i | − | 0.0472428i | ||||||
\(515\) | −6.41421 | + | 19.2426i | −0.282644 | + | 0.847932i | ||||
\(516\) | 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 | ||||
\(520\) | −8.97056 | + | 4.48528i | −0.393385 | + | 0.196693i | ||||
\(521\) | 27.6569i | 1.21167i | 0.795591 | + | 0.605834i | \(0.207161\pi\) | ||||
−0.795591 | + | 0.605834i | \(0.792839\pi\) | |||||||
\(522\) | −0.928932 | − | 0.443651i | −0.0406583 | − | 0.0194181i | ||||
\(523\) | −27.2132 | + | 27.2132i | −1.18995 | + | 1.18995i | −0.212870 | + | 0.977081i | \(0.568281\pi\) |
−0.977081 | + | 0.212870i | \(0.931719\pi\) | |||||||
\(524\) | 12.4853 | 0.545422 | ||||||||
\(525\) | −37.2132 | − | 19.0711i | −1.62412 | − | 0.832330i | ||||
\(526\) | 1.02944 | 0.0448856 | ||||||||
\(527\) | −8.97056 | + | 8.97056i | −0.390764 | + | 0.390764i | ||||
\(528\) | 3.00000 | − | 4.24264i | 0.130558 | − | 0.184637i | ||||
\(529\) | − | 1.97056i | − | 0.0856766i | ||||||
\(530\) | −1.17157 | + | 0.585786i | −0.0508899 | + | 0.0254449i | ||||
\(531\) | 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 | ||||
\(535\) | −0.242641 | + | 0.727922i | −0.0104903 | + | 0.0314708i | ||||
\(536\) | − | 14.3848i | − | 0.621328i | ||||||
\(537\) | −34.1421 | − | 24.1421i | −1.47334 | − | 1.04181i | ||||
\(538\) | 4.10051 | − | 4.10051i | 0.176785 | − | 0.176785i | ||||
\(539\) | −16.3137 | −0.702681 | ||||||||
\(540\) | −20.8701 | + | 3.97056i | −0.898104 | + | 0.170866i | ||||
\(541\) | −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 | ||||
\(543\) | 8.00000 | + | 5.65685i | 0.343313 | + | 0.242759i | ||||
\(544\) | 17.6569i | 0.757031i | ||||||||
\(545\) | 3.17157 | + | 6.34315i | 0.135855 | + | 0.271711i | ||||
\(546\) | 9.65685 | − | 1.65685i | 0.413275 | − | 0.0709068i | ||||
\(547\) | 2.10051 | + | 2.10051i | 0.0898111 | + | 0.0898111i | 0.750585 | − | 0.660774i | \(-0.229772\pi\) |
−0.660774 | + | 0.750585i | \(0.729772\pi\) | |||||||
\(548\) | −0.313708 | − | 0.313708i | −0.0134010 | − | 0.0134010i | ||||
\(549\) | −6.48528 | − | 18.3431i | −0.276785 | − | 0.782866i | ||||
\(550\) | 2.05025 | − | 0.292893i | 0.0874231 | − | 0.0124890i | ||||
\(551\) | 2.34315i | 0.0998214i | ||||||||
\(552\) | 7.27208 | − | 10.2843i | 0.309520 | − | 0.437728i | ||||
\(553\) | 36.9706 | − | 36.9706i | 1.57215 | − | 1.57215i | ||||
\(554\) | −10.8284 | −0.460056 | ||||||||
\(555\) | −0.556349 | − | 0.757359i | −0.0236157 | − | 0.0321481i | ||||
\(556\) | 32.2843 | 1.36916 | ||||||||
\(557\) | −8.97056 | + | 8.97056i | −0.380095 | + | 0.380095i | −0.871136 | − | 0.491041i | \(-0.836616\pi\) |
0.491041 | + | 0.871136i | \(0.336616\pi\) | |||||||
\(558\) | −3.55635 | − | 1.69848i | −0.150552 | − | 0.0719026i | ||||
\(559\) | 0.970563i | 0.0410504i | ||||||||
\(560\) | 30.7279 | + | 10.2426i | 1.29849 | + | 0.432831i | ||||
\(561\) | 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 | ||||
\(565\) | 17.4853 | + | 5.82843i | 0.735611 | + | 0.245204i | ||||
\(566\) | 8.82843i | 0.371086i | ||||||||
\(567\) | 43.2132 | + | 4.58579i | 1.81478 | + | 0.192585i | ||||
\(568\) | −2.78680 | + | 2.78680i | −0.116931 | + | 0.116931i | ||||
\(569\) | 28.3431 | 1.18821 | 0.594103 | − | 0.804389i | \(-0.297507\pi\) | ||||
0.594103 | + | 0.804389i | \(0.297507\pi\) | |||||||
\(570\) | −2.68629 | − | 3.65685i | −0.112516 | − | 0.153169i | ||||
\(571\) | 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 | ||||
\(573\) | 11.3137 | − | 16.0000i | 0.472637 | − | 0.668410i | ||||
\(574\) | − | 15.3137i | − | 0.639182i | ||||||
\(575\) | −22.6985 | + | 3.24264i | −0.946592 | + | 0.135227i | ||||
\(576\) | 11.7990 | − | 4.17157i | 0.491625 | − | 0.173816i | ||||
\(577\) | 17.0000 | + | 17.0000i | 0.707719 | + | 0.707719i | 0.966055 | − | 0.258336i | \(-0.0831741\pi\) |
−0.258336 | + | 0.966055i | \(0.583174\pi\) | |||||||
\(578\) | 0.292893 | + | 0.292893i | 0.0121828 | + | 0.0121828i | ||||
\(579\) | 19.3137 | − | 3.31371i | 0.802650 | − | 0.137713i | ||||
\(580\) | −1.51472 | − | 3.02944i | −0.0628953 | − | 0.125791i | ||||
\(581\) | − | 61.9411i | − | 2.56975i | ||||||
\(582\) | 8.82843 | + | 6.24264i | 0.365950 | + | 0.258766i | ||||
\(583\) | 1.00000 | − | 1.00000i | 0.0414158 | − | 0.0414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.9706 | + | 0.343146i | −0.784336 | + | 0.0141873i | ||||
\(586\) | 2.14214 | 0.0884908 | ||||||||
\(587\) | 0.414214 | − | 0.414214i | 0.0170964 | − | 0.0170964i | −0.698507 | − | 0.715603i | \(-0.746152\pi\) |
0.715603 | + | 0.698507i | \(0.246152\pi\) | |||||||
\(588\) | −42.1838 | − | 29.8284i | −1.73963 | − | 1.23010i | ||||
\(589\) | 8.97056i | 0.369626i | ||||||||
\(590\) | 1.17157 | − | 3.51472i | 0.0482329 | − | 0.144699i | ||||
\(591\) | 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 | ||||
\(595\) | −38.6274 | + | 19.3137i | −1.58357 | + | 0.791785i | ||||
\(596\) | 18.2843i | 0.748953i | ||||||||
\(597\) | 14.4853 | − | 20.4853i | 0.592843 | − | 0.838407i | ||||
\(598\) | 3.79899 | − | 3.79899i | 0.155352 | − | 0.155352i | ||||
\(599\) | 3.45584 | 0.141202 | 0.0706010 | − | 0.997505i | \(-0.477508\pi\) | ||||
0.0706010 | + | 0.997505i | \(0.477508\pi\) | |||||||
\(600\) | 12.2218 | + | 6.26346i | 0.498954 | + | 0.255705i | ||||
\(601\) | −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 | ||||
\(603\) | 11.7279 | − | 24.5563i | 0.477598 | − | 1.00001i | ||||
\(604\) | 18.5442i | 0.754551i | ||||||||
\(605\) | −2.00000 | + | 1.00000i | −0.0813116 | + | 0.0406558i | ||||
\(606\) | 0.870058 | + | 5.07107i | 0.0353437 | + | 0.205998i | ||||
\(607\) | −21.8995 | − | 21.8995i | −0.888873 | − | 0.888873i | 0.105542 | − | 0.994415i | \(-0.466342\pi\) |
−0.994415 | + | 0.105542i | \(0.966342\pi\) | |||||||
\(608\) | 8.82843 | + | 8.82843i | 0.358040 | + | 0.358040i | ||||
\(609\) | 1.17157 | + | 6.82843i | 0.0474745 | + | 0.276702i | ||||
\(610\) | −1.89949 | + | 5.69848i | −0.0769083 | + | 0.230725i | ||||
\(611\) | 28.9706i | 1.17202i | ||||||||
\(612\) | −9.45584 | + | 19.7990i | −0.382230 | + | 0.800327i | ||||
\(613\) | −16.0000 | + | 16.0000i | −0.646234 | + | 0.646234i | −0.952081 | − | 0.305847i | \(-0.901060\pi\) |
0.305847 | + | 0.952081i | \(0.401060\pi\) | |||||||
\(614\) | −6.97056 | −0.281309 | ||||||||
\(615\) | −4.48528 | + | 29.3137i | −0.180864 | + | 1.18204i | ||||
\(616\) | 7.65685 | 0.308503 | ||||||||
\(617\) | −29.8284 | + | 29.8284i | −1.20085 | + | 1.20085i | −0.226938 | + | 0.973909i | \(0.572871\pi\) |
−0.973909 | + | 0.226938i | \(0.927129\pi\) | |||||||
\(618\) | −3.75736 | + | 5.31371i | −0.151143 | + | 0.213749i | ||||
\(619\) | 0.686292i | 0.0275844i | 0.999905 | + | 0.0137922i | \(0.00439033\pi\) | ||||
−0.999905 | + | 0.0137922i | \(0.995610\pi\) | |||||||
\(620\) | −5.79899 | − | 11.5980i | −0.232893 | − | 0.465786i | ||||
\(621\) | 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 | ||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | − | 7.41421i | − | 0.296332i | ||||||
\(627\) | 4.00000 | + | 2.82843i | 0.159745 | + | 0.112956i | ||||
\(628\) | 17.3431 | − | 17.3431i | 0.692067 | − | 0.692067i | ||||
\(629\) | −0.970563 | −0.0386989 | ||||||||
\(630\) | −9.65685 | − | 9.31371i | −0.384738 | − | 0.371067i | ||||
\(631\) | −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 | ||||
\(633\) | −6.34315 | − | 4.48528i | −0.252117 | − | 0.178274i | ||||
\(634\) | 1.35534i | 0.0538274i | ||||||||
\(635\) | 4.24264 | + | 1.41421i | 0.168364 | + | 0.0561214i | ||||
\(636\) | 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 | ||||
\(640\) | −22.3934 | − | 7.46447i | −0.885177 | − | 0.295059i | ||||
\(641\) | 32.6274i | 1.28871i | 0.764728 | + | 0.644353i | \(0.222873\pi\) | ||||
−0.764728 | + | 0.644353i | \(0.777127\pi\) | |||||||
\(642\) | −0.142136 | + | 0.201010i | −0.00560965 | + | 0.00793324i | ||||
\(643\) | −9.24264 | + | 9.24264i | −0.364494 | + | 0.364494i | −0.865464 | − | 0.500970i | \(-0.832977\pi\) |
0.500970 | + | 0.865464i | \(0.332977\pi\) | |||||||
\(644\) | −40.4853 | −1.59534 | ||||||||
\(645\) | 1.07107 | − | 0.786797i | 0.0421733 | − | 0.0309801i | ||||
\(646\) | −4.68629 | −0.184380 | ||||||||
\(647\) | −11.7279 | + | 11.7279i | −0.461072 | + | 0.461072i | −0.899007 | − | 0.437935i | \(-0.855710\pi\) |
0.437935 | + | 0.899007i | \(0.355710\pi\) | |||||||
\(648\) | −14.1924 | − | 1.50610i | −0.557530 | − | 0.0591651i | ||||
\(649\) | 4.00000i | 0.157014i | ||||||||
\(650\) | 4.68629 | + | 3.51472i | 0.183811 | + | 0.137859i | ||||
\(651\) | 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 | ||||
\(655\) | −6.82843 | − | 13.6569i | −0.266809 | − | 0.533617i | ||||
\(656\) | − | 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 | \(-0.338325\pi\) | ||||
0.486358 | + | 0.873760i | \(0.338325\pi\) | |||||||
\(660\) | −7.00000 | − | 1.07107i | −0.272475 | − | 0.0416913i | ||||
\(661\) | 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 | ||||
\(663\) | −11.3137 | + | 16.0000i | −0.439388 | + | 0.621389i | ||||
\(664\) | 20.3431i | 0.789467i | ||||||||
\(665\) | −9.65685 | + | 28.9706i | −0.374477 | + | 1.12343i | ||||
\(666\) | −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 | ||||
\(670\) | −7.51472 | + | 3.75736i | −0.290319 | + | 0.145159i | ||||
\(671\) | − | 6.48528i | − | 0.250362i | ||||||
\(672\) | 30.1421 | + | 21.3137i | 1.16276 | + | 0.822194i | ||||
\(673\) | −22.3431 | + | 22.3431i | −0.861265 | + | 0.861265i | −0.991485 | − | 0.130220i | \(-0.958432\pi\) |
0.130220 | + | 0.991485i | \(0.458432\pi\) | |||||||
\(674\) | −6.34315 | −0.244329 | ||||||||
\(675\) | 15.7574 | + | 20.6569i | 0.606501 | + | 0.795083i | ||||
\(676\) | −9.14214 | −0.351621 | ||||||||
\(677\) | −19.6569 | + | 19.6569i | −0.755474 | + | 0.755474i | −0.975495 | − | 0.220021i | \(-0.929387\pi\) |
0.220021 | + | 0.975495i | \(0.429387\pi\) | |||||||
\(678\) | 4.82843 | + | 3.41421i | 0.185435 | + | 0.131122i | ||||
\(679\) | − | 72.7696i | − | 2.79264i | ||||||
\(680\) | 12.6863 | − | 6.34315i | 0.486497 | − | 0.243249i | ||||
\(681\) | −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 | ||||
\(685\) | −0.171573 | + | 0.514719i | −0.00655546 | + | 0.0196664i | ||||
\(686\) | − | 18.6274i | − | 0.711198i | ||||||
\(687\) | 9.65685 | − | 13.6569i | 0.368432 | − | 0.521041i | ||||
\(688\) | −0.727922 | + | 0.727922i | −0.0277518 | + | 0.0277518i | ||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | −7.27208 | − | 1.11270i | −0.276843 | − | 0.0423597i | ||||
\(691\) | 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 | ||||
\(693\) | 13.0711 | + | 6.24264i | 0.496529 | + | 0.237138i | ||||
\(694\) | 1.11270i | 0.0422375i | ||||||||
\(695\) | −17.6569 | − | 35.3137i | −0.669763 | − | 1.33953i | ||||
\(696\) | −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 | ||||
\(700\) | −6.24264 | − | 43.6985i | −0.235950 | − | 1.65165i | ||||
\(701\) | − | 1.31371i | − | 0.0496181i | −0.999692 | − | 0.0248090i | \(-0.992102\pi\) | ||
0.999692 | − | 0.0248090i | \(-0.00789777\pi\) | |||||||
\(702\) | −5.85786 | − | 1.65685i | −0.221091 | − | 0.0625339i | ||||
\(703\) | −0.485281 | + | 0.485281i | −0.0183027 | + | 0.0183027i | ||||
\(704\) | 4.17157 | 0.157222 | ||||||||
\(705\) | 31.9706 | − | 23.4853i | 1.20408 | − | 0.884507i | ||||
\(706\) | −4.58579 | −0.172588 | ||||||||
\(707\) | 24.4853 | − | 24.4853i | 0.920864 | − | 0.920864i | ||||
\(708\) | −7.31371 | + | 10.3431i | −0.274866 | + | 0.388719i | ||||
\(709\) | − | 29.3137i | − | 1.10090i | −0.834868 | − | 0.550450i | \(-0.814456\pi\) | ||
0.834868 | − | 0.550450i | \(-0.185544\pi\) | |||||||
\(710\) | 2.18377 | + | 0.727922i | 0.0819553 | + | 0.0273184i | ||||
\(711\) | −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 | ||||
\(715\) | −6.00000 | − | 2.00000i | −0.224387 | − | 0.0747958i | ||||
\(716\) | − | 44.1421i | − | 1.64967i | ||||||
\(717\) | 33.6569 | + | 23.7990i | 1.25694 | + | 0.888790i | ||||
\(718\) | 6.48528 | − | 6.48528i | 0.242029 | − | 0.242029i | ||||
\(719\) | 22.7696 | 0.849161 | 0.424581 | − | 0.905390i | \(-0.360422\pi\) | ||||
0.424581 | + | 0.905390i | \(0.360422\pi\) | |||||||
\(720\) | −14.4853 | − | 13.9706i | −0.539835 | − | 0.520652i | ||||
\(721\) | 43.7990 | 1.63116 | ||||||||
\(722\) | 3.22183 | − | 3.22183i | 0.119904 | − | 0.119904i | ||||
\(723\) | 0.201010 | + | 0.142136i | 0.00747565 | + | 0.00528608i | ||||
\(724\) | 10.3431i | 0.384400i | ||||||||
\(725\) | −2.48528 | + | 3.31371i | −0.0923010 | + | 0.123068i | ||||
\(726\) | −0.707107 | + | 0.121320i | −0.0262432 | + | 0.00450262i | ||||
\(727\) | 20.2132 | + | 20.2132i | 0.749666 | + | 0.749666i | 0.974416 | − | 0.224750i | \(-0.0721566\pi\) |
−0.224750 | + | 0.974416i | \(0.572157\pi\) | |||||||
\(728\) | 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 | ||||||
\(732\) | 11.8579 | − | 16.7696i | 0.438279 | − | 0.619821i | ||||
\(733\) | 3.79899 | − | 3.79899i | 0.140319 | − | 0.140319i | −0.633458 | − | 0.773777i | \(-0.718365\pi\) |
0.773777 | + | 0.633458i | \(0.218365\pi\) | |||||||
\(734\) | −0.644661 | −0.0237949 | ||||||||
\(735\) | −9.55635 | + | 62.4558i | −0.352491 | + | 2.30372i | ||||
\(736\) | 20.2426 | 0.746154 | ||||||||
\(737\) | 6.41421 | − | 6.41421i | 0.236271 | − | 0.236271i | ||||
\(738\) | −4.10051 | + | 8.58579i | −0.150942 | + | 0.316047i | ||||
\(739\) | 14.6274i | 0.538078i | 0.963129 | + | 0.269039i | \(0.0867061\pi\) | ||||
−0.963129 | + | 0.269039i | \(0.913294\pi\) | |||||||
\(740\) | 0.313708 | − | 0.941125i | 0.0115322 | − | 0.0345965i | ||||
\(741\) | 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 | ||||
\(745\) | 20.0000 | − | 10.0000i | 0.732743 | − | 0.366372i | ||||
\(746\) | − | 2.05887i | − | 0.0753808i | ||||||
\(747\) | −16.5858 | + | 34.7279i | −0.606842 | + | 1.27063i | ||||
\(748\) | −5.17157 | + | 5.17157i | −0.189091 | + | 0.189091i | ||||
\(749\) | 1.65685 | 0.0605401 | ||||||||
\(750\) | 0.0796898 | − | 8.02082i | 0.00290986 | − | 0.292879i | ||||
\(751\) | −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 | ||||
\(753\) | −16.1421 | + | 22.8284i | −0.588252 | + | 0.831914i | ||||
\(754\) | − | 0.970563i | − | 0.0353458i | ||||||
\(755\) | 20.2843 | − | 10.1421i | 0.738220 | − | 0.369110i | ||||
\(756\) | 22.3848 | + | 40.0416i | 0.814126 | + | 1.45630i | ||||
\(757\) | 0.171573 | + | 0.171573i | 0.00623592 | + | 0.00623592i | 0.710218 | − | 0.703982i | \(-0.248596\pi\) |
−0.703982 | + | 0.710218i | \(0.748596\pi\) | |||||||
\(758\) | −8.24264 | − | 8.24264i | −0.299386 | − | 0.299386i | ||||
\(759\) | 7.82843 | − | 1.34315i | 0.284154 | − | 0.0487531i | ||||
\(760\) | 3.17157 | − | 9.51472i | 0.115045 | − | 0.345135i | ||||
\(761\) | − | 1.51472i | − | 0.0549085i | −0.999623 | − | 0.0274543i | \(-0.991260\pi\) | ||
0.999623 | − | 0.0274543i | \(-0.00874006\pi\) | |||||||
\(762\) | 1.17157 | + | 0.828427i | 0.0424416 | + | 0.0300107i | ||||
\(763\) | 10.8284 | − | 10.8284i | 0.392015 | − | 0.392015i | ||||
\(764\) | 20.6863 | 0.748404 | ||||||||
\(765\) | 26.8284 | − | 0.485281i | 0.969984 | − | 0.0175454i | ||||
\(766\) | 3.55635 | 0.128496 | ||||||||
\(767\) | −8.00000 | + | 8.00000i | −0.288863 | + | 0.288863i | ||||
\(768\) | 5.61522 | + | 3.97056i | 0.202622 | + | 0.143275i | ||||
\(769\) | − | 52.6274i | − | 1.89779i | −0.315587 | − | 0.948897i | \(-0.602201\pi\) | ||
0.315587 | − | 0.948897i | \(-0.397799\pi\) | |||||||
\(770\) | −2.00000 | − | 4.00000i | −0.0720750 | − | 0.144150i | ||||
\(771\) | 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 | ||||
\(775\) | −9.51472 | + | 12.6863i | −0.341779 | + | 0.455705i | ||||
\(776\) | 23.8995i | 0.857942i | ||||||||
\(777\) | −1.17157 | + | 1.65685i | −0.0420299 | + | 0.0594393i | ||||
\(778\) | 5.07107 | − | 5.07107i | 0.181807 | − | 0.181807i | ||||
\(779\) | 21.6569 | 0.775937 | ||||||||
\(780\) | −11.8579 | − | 16.1421i | −0.424580 | − | 0.577981i | ||||
\(781\) | −2.48528 | −0.0889304 | ||||||||
\(782\) | −5.37258 | + | 5.37258i | −0.192123 | + | 0.192123i | ||||
\(783\) | 1.17157 | − | 4.14214i | 0.0418686 | − | 0.148028i | ||||
\(784\) | − | 48.9411i | − | 1.74790i | ||||||
\(785\) | −28.4558 | − | 9.48528i | −1.01563 | − | 0.338544i | ||||
\(786\) | −0.828427 | − | 4.82843i | −0.0295490 | − | 0.172224i | ||||
\(787\) | −28.5858 | − | 28.5858i | −1.01897 | − | 1.01897i | −0.999816 | − | 0.0191567i | \(-0.993902\pi\) |
−0.0191567 | − | 0.999816i | \(-0.506098\pi\) | |||||||
\(788\) | 25.8579 | + | 25.8579i | 0.921148 | + | 0.921148i | ||||
\(789\) | 0.727922 | + | 4.24264i | 0.0259147 | + | 0.151042i | ||||
\(790\) | 9.51472 | + | 3.17157i | 0.338518 | + | 0.112839i | ||||
\(791\) | − | 39.7990i | − | 1.41509i | ||||||
\(792\) | −4.29289 | − | 2.05025i | −0.152541 | − | 0.0728526i | ||||
\(793\) | 12.9706 | − | 12.9706i | 0.460598 | − | 0.460598i | ||||
\(794\) | 3.61522 | 0.128299 | ||||||||
\(795\) | −3.24264 | − | 4.41421i | −0.115005 | − | 0.156556i | ||||
\(796\) | 26.4853 | 0.938746 | ||||||||
\(797\) | −25.9706 | + | 25.9706i | −0.919925 | + | 0.919925i | −0.997023 | − | 0.0770989i | \(-0.975434\pi\) |
0.0770989 | + | 0.997023i | \(0.475434\pi\) | |||||||
\(798\) | −5.65685 | + | 8.00000i | −0.200250 | + | 0.283197i | ||||
\(799\) | − | 40.9706i | − | 1.44943i | ||||||
\(800\) | 3.12132 | + | 21.8492i | 0.110355 | + | 0.772487i | ||||
\(801\) | 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 | ||||
\(805\) | 22.1421 | + | 44.2843i | 0.780408 | + | 1.56082i | ||||
\(806\) | − | 3.71573i | − | 0.130881i | ||||||
\(807\) | 19.7990 | + | 14.0000i | 0.696957 | + | 0.492823i | ||||
\(808\) | −8.04163 | + | 8.04163i | −0.282904 | + | 0.282904i | ||||
\(809\) | 15.8579 | 0.557533 | 0.278766 | − | 0.960359i | \(-0.410074\pi\) | ||||
0.278766 | + | 0.960359i | \(0.410074\pi\) | |||||||
\(810\) | 2.92031 | + | 7.80761i | 0.102609 | + | 0.274332i | ||||
\(811\) | −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 | ||||
\(813\) | 12.0000 | + | 8.48528i | 0.420858 | + | 0.297592i | ||||
\(814\) | − | 0.100505i | − | 0.00352270i | ||||||
\(815\) | 3.58579 | − | 10.7574i | 0.125605 | − | 0.376814i | ||||
\(816\) | −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 | ||||
\(820\) | −28.0000 | + | 14.0000i | −0.977802 | + | 0.488901i | ||||
\(821\) | 0.343146i | 0.0119759i | 0.999982 | + | 0.00598793i | \(0.00190603\pi\) | ||||
−0.999982 | + | 0.00598793i | \(0.998094\pi\) | |||||||
\(822\) | −0.100505 | + | 0.142136i | −0.00350552 | + | 0.00495755i | ||||
\(823\) | −18.4142 | + | 18.4142i | −0.641879 | + | 0.641879i | −0.951017 | − | 0.309138i | \(-0.899959\pi\) |
0.309138 | + | 0.951017i | \(0.399959\pi\) | |||||||
\(824\) | −14.3848 | −0.501117 | ||||||||
\(825\) | 2.65685 | + | 8.24264i | 0.0924998 | + | 0.286972i | ||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 28.0416 | − | 28.0416i | 0.975103 | − | 0.975103i | −0.0245945 | − | 0.999698i | \(-0.507829\pi\) |
0.999698 | + | 0.0245945i | \(0.00782945\pi\) | |||||||
\(828\) | 22.6985 | + | 10.8406i | 0.788827 | + | 0.376738i | ||||
\(829\) | 10.9706i | 0.381023i | 0.981685 | + | 0.190512i | \(0.0610147\pi\) | ||||
−0.981685 | + | 0.190512i | \(0.938985\pi\) | |||||||
\(830\) | 10.6274 | − | 5.31371i | 0.368883 | − | 0.184442i | ||||
\(831\) | −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 | ||||
\(835\) | −14.7279 | + | 44.1838i | −0.509681 | + | 1.52904i | ||||
\(836\) | 5.17157i | 0.178863i | ||||||||
\(837\) | 4.48528 | − | 15.8579i | 0.155034 | − | 0.548128i | ||||
\(838\) | −4.52691 | + | 4.52691i | −0.156380 | + | 0.156380i | ||||
\(839\) | 21.6569 | 0.747678 | 0.373839 | − | 0.927494i | \(-0.378041\pi\) | ||||
0.373839 | + | 0.927494i | \(0.378041\pi\) | |||||||
\(840\) | 4.48528 | − | 29.3137i | 0.154757 | − | 1.01142i | ||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | −1.17157 | + | 1.17157i | −0.0403751 | + | 0.0403751i | ||||
\(843\) | 28.6274 | − | 40.4853i | 0.985981 | − | 1.39439i | ||||
\(844\) | − | 8.20101i | − | 0.282290i | ||||||
\(845\) | 5.00000 | + | 10.0000i | 0.172005 | + | 0.344010i | ||||
\(846\) | 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 | ||||
\(850\) | −6.62742 | − | 4.97056i | −0.227319 | − | 0.170489i | ||||
\(851\) | 1.11270i | 0.0381428i | ||||||||
\(852\) | −6.42641 | − | 4.54416i | −0.220165 | − | 0.155680i | ||||
\(853\) | 18.1421 | − | 18.1421i | 0.621175 | − | 0.621175i | −0.324657 | − | 0.945832i | \(-0.605249\pi\) |
0.945832 | + | 0.324657i | \(0.105249\pi\) | |||||||
\(854\) | 12.9706 | 0.443844 | ||||||||
\(855\) | 13.1716 | − | 13.6569i | 0.450458 | − | 0.467055i | ||||
\(856\) | −0.544156 | −0.0185989 | ||||||||
\(857\) | 16.4853 | − | 16.4853i | 0.563126 | − | 0.563126i | −0.367068 | − | 0.930194i | \(-0.619638\pi\) |
0.930194 | + | 0.367068i | \(0.119638\pi\) | |||||||
\(858\) | −1.65685 | − | 1.17157i | −0.0565641 | − | 0.0399968i | ||||
\(859\) | 36.0000i | 1.22830i | 0.789188 | + | 0.614152i | \(0.210502\pi\) | ||||
−0.789188 | + | 0.614152i | \(0.789498\pi\) | |||||||
\(860\) | 1.33095 | + | 0.443651i | 0.0453851 | + | 0.0151284i | ||||
\(861\) | 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 | ||||
\(865\) | −25.4558 | − | 8.48528i | −0.865525 | − | 0.288508i | ||||
\(866\) | 0.183766i | 0.00624463i | ||||||||
\(867\) | −1.00000 | + | 1.41421i | −0.0339618 | + | 0.0480292i | ||||
\(868\) | −19.7990 | + | 19.7990i | −0.672022 | + | 0.672022i | ||||
\(869\) | −10.8284 | −0.367329 | ||||||||
\(870\) | −1.07107 | + | 0.786797i | −0.0363126 | + | 0.0266749i | ||||
\(871\) | 25.6569 | 0.869349 | ||||||||
\(872\) | −3.55635 | + | 3.55635i | −0.120433 | + | 0.120433i | ||||
\(873\) | −19.4853 | + | 40.7990i | −0.659477 | + | 1.38084i | ||||
\(874\) | 5.37258i | 0.181730i | ||||||||
\(875\) | −44.3848 | + | 30.7279i | −1.50048 | + | 1.03879i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.62742 | + | 6.62742i | 0.223792 | + | 0.223792i | 0.810093 | − | 0.586301i | \(-0.199416\pi\) |
−0.586301 | + | 0.810093i | \(0.699416\pi\) | |||||||
\(878\) | 2.14214 | + | 2.14214i | 0.0722936 | + | 0.0722936i | ||||
\(879\) | 1.51472 | + | 8.82843i | 0.0510902 | + | 0.297775i | ||||
\(880\) | −3.00000 | − | 6.00000i | −0.101130 | − | 0.202260i | ||||
\(881\) | − | 12.9706i | − | 0.436989i | −0.975838 | − | 0.218495i | \(-0.929885\pi\) | ||
0.975838 | − | 0.218495i | \(-0.0701146\pi\) | |||||||
\(882\) | −8.73654 | + | 18.2929i | −0.294175 | + | 0.615954i | ||||
\(883\) | −3.58579 | + | 3.58579i | −0.120671 | + | 0.120671i | −0.764864 | − | 0.644192i | \(-0.777194\pi\) |
0.644192 | + | 0.764864i | \(0.277194\pi\) | |||||||
\(884\) | −20.6863 | −0.695755 | ||||||||
\(885\) | 15.3137 | + | 2.34315i | 0.514765 | + | 0.0787640i | ||||
\(886\) | 12.1594 | 0.408502 | ||||||||
\(887\) | 9.75736 | − | 9.75736i | 0.327620 | − | 0.327620i | −0.524061 | − | 0.851681i | \(-0.675584\pi\) |
0.851681 | + | 0.524061i | \(0.175584\pi\) | |||||||
\(888\) | 0.384776 | − | 0.544156i | 0.0129122 | − | 0.0182607i | ||||
\(889\) | − | 9.65685i | − | 0.323880i | ||||||
\(890\) | 2.82843 | − | 8.48528i | 0.0948091 | − | 0.284427i | ||||
\(891\) | −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 | ||||
\(895\) | −48.2843 | + | 24.1421i | −1.61397 | + | 0.806983i | ||||
\(896\) | 50.9706i | 1.70281i | ||||||||
\(897\) | 18.3431 | + | 12.9706i | 0.612460 | + | 0.433074i | ||||
\(898\) | 0.887302 | − | 0.887302i | 0.0296096 | − | 0.0296096i | ||||
\(899\) | 2.62742 | 0.0876293 | ||||||||
\(900\) | −8.20101 | + | 26.1716i | −0.273367 | + | 0.872386i | ||||
\(901\) | −5.65685 | −0.188457 | ||||||||
\(902\) | −2.24264 | + | 2.24264i | −0.0746718 | + | 0.0746718i | ||||
\(903\) | −2.34315 | − | 1.65685i | −0.0779750 | − | 0.0551367i | ||||
\(904\) | 13.0711i | 0.434737i | ||||||||
\(905\) | 11.3137 | − | 5.65685i | 0.376080 | − | 0.188040i | ||||
\(906\) | 7.17157 | − | 1.23045i | 0.238260 | − | 0.0408789i | ||||
\(907\) | 29.0416 | + | 29.0416i | 0.964312 | + | 0.964312i | 0.999385 | − | 0.0350732i | \(-0.0111664\pi\) |
−0.0350732 | + | 0.999385i | \(0.511166\pi\) | |||||||
\(908\) | −18.7279 | − | 18.7279i | −0.621508 | − | 0.621508i | ||||
\(909\) | −20.2843 | + | 7.17157i | −0.672787 | + | 0.237866i | ||||
\(910\) | 4.00000 | − | 12.0000i | 0.132599 | − | 0.397796i | ||||
\(911\) | 56.0000i | 1.85536i | 0.373373 | + | 0.927681i | \(0.378201\pi\) | ||||
−0.373373 | + | 0.927681i | \(0.621799\pi\) | |||||||
\(912\) | −8.48528 | + | 12.0000i | −0.280976 | + | 0.397360i | ||||
\(913\) | −9.07107 | + | 9.07107i | −0.300209 | + | 0.300209i | ||||
\(914\) | −3.79899 | −0.125659 | ||||||||
\(915\) | −24.8284 | − | 3.79899i | −0.820802 | − | 0.125591i | ||||
\(916\) | 17.6569 | 0.583399 | ||||||||
\(917\) | −23.3137 | + | 23.3137i | −0.769886 | + | 0.769886i | ||||
\(918\) | 8.28427 | + | 2.34315i | 0.273422 | + | 0.0773353i | ||||
\(919\) | − | 14.6274i | − | 0.482514i | −0.970461 | − | 0.241257i | \(-0.922440\pi\) | ||
0.970461 | − | 0.241257i | \(-0.0775597\pi\) | |||||||
\(920\) | −7.27208 | − | 14.5442i | −0.239753 | − | 0.479507i | ||||
\(921\) | −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 | ||||
\(925\) | −1.20101 | + | 0.171573i | −0.0394890 | + | 0.00564128i | ||||
\(926\) | − | 6.87006i | − | 0.225764i | ||||||
\(927\) | −24.5563 | − | 11.7279i | −0.806536 | − | 0.385195i | ||||
\(928\) | 2.58579 | − | 2.58579i | 0.0848826 | − | 0.0848826i | ||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | −4.10051 | + | 3.01219i | −0.134461 | + | 0.0987737i | ||||
\(931\) | 46.1421 | 1.51225 | ||||||||
\(932\) | 35.9411 | − | 35.9411i | 1.17729 | − | 1.17729i | ||||
\(933\) | 28.1421 | − | 39.7990i | 0.921332 | − | 1.30296i | ||||
\(934\) | − | 0.242641i | − | 0.00793945i | ||||||
\(935\) | 8.48528 | + | 2.82843i | 0.277498 | + | 0.0924995i | ||||
\(936\) | −4.48528 | − | 12.6863i | −0.146606 | − | 0.414664i | ||||
\(937\) | −10.9706 | − | 10.9706i | −0.358393 | − | 0.358393i | 0.504828 | − | 0.863220i | \(-0.331556\pi\) |
−0.863220 | + | 0.504828i | \(0.831556\pi\) | |||||||
\(938\) | 12.8284 | + | 12.8284i | 0.418863 | + | 0.418863i | ||||
\(939\) | 30.5563 | − | 5.24264i | 0.997169 | − | 0.171087i | ||||
\(940\) | 39.7279 | + | 13.2426i | 1.29578 | + | 0.431927i | ||||
\(941\) | − | 37.1127i | − | 1.20984i | −0.796286 | − | 0.604920i | \(-0.793205\pi\) | ||
0.796286 | − | 0.604920i | \(-0.206795\pi\) | |||||||
\(942\) | −7.85786 | − | 5.55635i | −0.256023 | − | 0.181036i | ||||
\(943\) | 24.8284 | − | 24.8284i | 0.808525 | − | 0.808525i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 31.5563 | − | 46.3848i | 1.02653 | − | 1.50890i | ||||
\(946\) | 0.142136 | 0.00462123 | ||||||||
\(947\) | 17.2426 | − | 17.2426i | 0.560311 | − | 0.560311i | −0.369085 | − | 0.929396i | \(-0.620329\pi\) |
0.929396 | + | 0.369085i | \(0.120329\pi\) | |||||||
\(948\) | −28.0000 | − | 19.7990i | −0.909398 | − | 0.643041i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −5.79899 | + | 0.828427i | −0.188144 | + | 0.0268777i | ||||
\(951\) | −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 | ||||
\(955\) | −11.3137 | − | 22.6274i | −0.366103 | − | 0.732206i | ||||
\(956\) | 43.5147i | 1.40737i | ||||||||
\(957\) | 0.828427 | − | 1.17157i | 0.0267792 | − | 0.0378716i | ||||
\(958\) | 8.82843 | − | 8.82843i | 0.285234 | − | 0.285234i | ||||
\(959\) | 1.17157 | 0.0378321 | ||||||||
\(960\) | 2.44365 | − | 15.9706i | 0.0788685 | − | 0.515448i | ||||
\(961\) | −20.9411 | −0.675520 | ||||||||
\(962\) | 0.201010 | − | 0.201010i | 0.00648083 | − | 0.00648083i | ||||
\(963\) | −0.928932 | − | 0.443651i | −0.0299344 | − | 0.0142964i | ||||
\(964\) | 0.259885i | 0.00837032i | ||||||||
\(965\) | 8.00000 | − | 24.0000i | 0.257529 | − | 0.772587i | ||||
\(966\) | 2.68629 | + | 15.6569i | 0.0864300 | + | 0.503751i | ||||
\(967\) | 38.3848 | + | 38.3848i | 1.23437 | + | 1.23437i | 0.962268 | + | 0.272103i | \(0.0877192\pi\) |
0.272103 | + | 0.962268i | \(0.412281\pi\) | |||||||
\(968\) | −1.12132 | − | 1.12132i | −0.0360406 | − | 0.0360406i | ||||
\(969\) | −3.31371 | − | 19.3137i | −0.106452 | − | 0.620446i | ||||
\(970\) | 12.4853 | − | 6.24264i | 0.400878 | − | 0.200439i | ||||
\(971\) | 20.0000i | 0.641831i | 0.947108 | + | 0.320915i | \(0.103990\pi\) | ||||
−0.947108 | + | 0.320915i | \(0.896010\pi\) | |||||||
\(972\) | −1.82843 | − | 28.4437i | −0.0586468 | − | 0.912331i | ||||
\(973\) | −60.2843 | + | 60.2843i | −1.93263 | + | 1.93263i | ||||
\(974\) | 6.87006 | 0.220131 | ||||||||
\(975\) | −11.1716 | + | 21.7990i | −0.357777 | + | 0.698126i | ||||
\(976\) | 19.4558 | 0.622766 | ||||||||
\(977\) | 38.1127 | − | 38.1127i | 1.21933 | − | 1.21933i | 0.251468 | − | 0.967866i | \(-0.419087\pi\) |
0.967866 | − | 0.251468i | \(-0.0809132\pi\) | |||||||
\(978\) | 2.10051 | − | 2.97056i | 0.0671667 | − | 0.0949881i | ||||
\(979\) | 9.65685i | 0.308634i | ||||||||
\(980\) | −59.6569 | + | 29.8284i | −1.90567 | + | 0.952834i | ||||
\(981\) | −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 | ||||
\(985\) | 14.1421 | − | 42.4264i | 0.450606 | − | 1.35182i | ||||
\(986\) | 1.37258i | 0.0437119i | ||||||||
\(987\) | −69.9411 | − | 49.4558i | −2.22625 | − | 1.57420i | ||||
\(988\) | −10.3431 | + | 10.3431i | −0.329059 | + | 0.329059i | ||||
\(989\) | −1.57359 | −0.0500374 | ||||||||
\(990\) | 0.0502525 | + | 2.77817i | 0.00159713 | + | 0.0882962i | ||||
\(991\) | 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 | ||||
\(993\) | −9.17157 | − | 6.48528i | −0.291051 | − | 0.205804i | ||||
\(994\) | − | 4.97056i | − | 0.157657i | ||||||
\(995\) | −14.4853 | − | 28.9706i | −0.459214 | − | 0.918429i | ||||
\(996\) | −40.0416 | + | 6.87006i | −1.26877 | + | 0.217686i | ||||
\(997\) | 36.7696 | + | 36.7696i | 1.16450 | + | 1.16450i | 0.983479 | + | 0.181025i | \(0.0579415\pi\) |
0.181025 | + | 0.983479i | \(0.442059\pi\) | |||||||
\(998\) | −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 | 165.2.k.b.122.1 | yes | 4 | |
3.2 | odd | 2 | 165.2.k.a.122.2 | yes | 4 | ||
5.2 | odd | 4 | 825.2.k.f.518.1 | 4 | |||
5.3 | odd | 4 | 165.2.k.a.23.2 | ✓ | 4 | ||
5.4 | even | 2 | 825.2.k.c.782.2 | 4 | |||
15.2 | even | 4 | 825.2.k.c.518.2 | 4 | |||
15.8 | even | 4 | inner | 165.2.k.b.23.1 | yes | 4 | |
15.14 | odd | 2 | 825.2.k.f.782.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.k.a.23.2 | ✓ | 4 | 5.3 | odd | 4 | ||
165.2.k.a.122.2 | yes | 4 | 3.2 | odd | 2 | ||
165.2.k.b.23.1 | yes | 4 | 15.8 | even | 4 | inner | |
165.2.k.b.122.1 | yes | 4 | 1.1 | even | 1 | trivial | |
825.2.k.c.518.2 | 4 | 15.2 | even | 4 | |||
825.2.k.c.782.2 | 4 | 5.4 | even | 2 | |||
825.2.k.f.518.1 | 4 | 5.2 | odd | 4 | |||
825.2.k.f.782.1 | 4 | 15.14 | odd | 2 |