Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1122,2,Mod(463,1122)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1122, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1122.463");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1122.l (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: | \(8.95921510679\) |
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 | 463.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1122.463 |
Dual form | 1122.2.l.a.727.2 |
$q$-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 \(\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times\).
\(n\) | \(409\) | \(749\) | \(1057\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.41421 | + | 2.41421i | −1.07967 | + | 1.07967i | −0.0831305 | + | 0.996539i | \(0.526492\pi\) |
−0.996539 | + | 0.0831305i | \(0.973508\pi\) | |||||||
\(6\) | 0.707107 | + | 0.707107i | 0.288675 | + | 0.288675i | ||||
\(7\) | 1.41421 | + | 1.41421i | 0.534522 | + | 0.534522i | 0.921915 | − | 0.387392i | \(-0.126624\pi\) |
−0.387392 | + | 0.921915i | \(0.626624\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −2.41421 | − | 2.41421i | −0.763441 | − | 0.763441i | ||||
\(11\) | −0.707107 | − | 0.707107i | −0.213201 | − | 0.213201i | ||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 6.82843 | 1.89386 | 0.946932 | − | 0.321433i | \(-0.104164\pi\) | ||||
0.946932 | + | 0.321433i | \(0.104164\pi\) | |||||||
\(14\) | −1.41421 | + | 1.41421i | −0.377964 | + | 0.377964i | ||||
\(15\) | 3.41421i | 0.881546i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | + | 4.00000i | 0.242536 | + | 0.970143i | ||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 2.41421 | − | 2.41421i | 0.539835 | − | 0.539835i | ||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0.707107 | − | 0.707107i | 0.150756 | − | 0.150756i | ||||
\(23\) | −1.41421 | − | 1.41421i | −0.294884 | − | 0.294884i | 0.544122 | − | 0.839006i | \(-0.316863\pi\) |
−0.839006 | + | 0.544122i | \(0.816863\pi\) | |||||||
\(24\) | −0.707107 | − | 0.707107i | −0.144338 | − | 0.144338i | ||||
\(25\) | − | 6.65685i | − | 1.33137i | ||||||
\(26\) | 6.82843i | 1.33916i | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −1.41421 | − | 1.41421i | −0.267261 | − | 0.267261i | ||||
\(29\) | −6.41421 | + | 6.41421i | −1.19109 | + | 1.19109i | −0.214328 | + | 0.976762i | \(0.568756\pi\) |
−0.976762 | + | 0.214328i | \(0.931244\pi\) | |||||||
\(30\) | −3.41421 | −0.623347 | ||||||||
\(31\) | −5.41421 | + | 5.41421i | −0.972421 | + | 0.972421i | −0.999630 | − | 0.0272083i | \(-0.991338\pi\) |
0.0272083 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −4.00000 | + | 1.00000i | −0.685994 | + | 0.171499i | ||||
\(35\) | −6.82843 | −1.15421 | ||||||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −6.41421 | + | 6.41421i | −1.05449 | + | 1.05449i | −0.0560630 | + | 0.998427i | \(0.517855\pi\) |
−0.998427 | + | 0.0560630i | \(0.982145\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82843 | − | 4.82843i | 0.773167 | − | 0.773167i | ||||
\(40\) | 2.41421 | + | 2.41421i | 0.381721 | + | 0.381721i | ||||
\(41\) | 3.00000 | + | 3.00000i | 0.468521 | + | 0.468521i | 0.901435 | − | 0.432914i | \(-0.142515\pi\) |
−0.432914 | + | 0.901435i | \(0.642515\pi\) | |||||||
\(42\) | 2.00000i | 0.308607i | ||||||||
\(43\) | 6.82843i | 1.04133i | 0.853762 | + | 0.520663i | \(0.174315\pi\) | ||||
−0.853762 | + | 0.520663i | \(0.825685\pi\) | |||||||
\(44\) | 0.707107 | + | 0.707107i | 0.106600 | + | 0.106600i | ||||
\(45\) | 2.41421 | + | 2.41421i | 0.359890 | + | 0.359890i | ||||
\(46\) | 1.41421 | − | 1.41421i | 0.208514 | − | 0.208514i | ||||
\(47\) | −9.65685 | −1.40860 | −0.704298 | − | 0.709904i | \(-0.748738\pi\) | ||||
−0.704298 | + | 0.709904i | \(0.748738\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 3.00000i | − | 0.428571i | ||||||
\(50\) | 6.65685 | 0.941421 | ||||||||
\(51\) | 3.53553 | + | 2.12132i | 0.495074 | + | 0.297044i | ||||
\(52\) | −6.82843 | −0.946932 | ||||||||
\(53\) | − | 12.4853i | − | 1.71499i | −0.514496 | − | 0.857493i | \(-0.672021\pi\) | ||
0.514496 | − | 0.857493i | \(-0.327979\pi\) | |||||||
\(54\) | 0.707107 | − | 0.707107i | 0.0962250 | − | 0.0962250i | ||||
\(55\) | 3.41421 | 0.460372 | ||||||||
\(56\) | 1.41421 | − | 1.41421i | 0.188982 | − | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.41421 | − | 6.41421i | −0.842228 | − | 0.842228i | ||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | − | 3.41421i | − | 0.440773i | ||||||
\(61\) | 0.757359 | + | 0.757359i | 0.0969699 | + | 0.0969699i | 0.753928 | − | 0.656958i | \(-0.228157\pi\) |
−0.656958 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(62\) | −5.41421 | − | 5.41421i | −0.687606 | − | 0.687606i | ||||
\(63\) | 1.41421 | − | 1.41421i | 0.178174 | − | 0.178174i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −16.4853 | + | 16.4853i | −2.04475 | + | 2.04475i | ||||
\(66\) | − | 1.00000i | − | 0.123091i | ||||||
\(67\) | 8.48528 | 1.03664 | 0.518321 | − | 0.855186i | \(-0.326557\pi\) | ||||
0.518321 | + | 0.855186i | \(0.326557\pi\) | |||||||
\(68\) | −1.00000 | − | 4.00000i | −0.121268 | − | 0.485071i | ||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | − | 6.82843i | − | 0.816153i | ||||||
\(71\) | −11.0711 | + | 11.0711i | −1.31389 | + | 1.31389i | −0.395374 | + | 0.918520i | \(0.629385\pi\) |
−0.918520 | + | 0.395374i | \(0.870615\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 4.65685 | − | 4.65685i | 0.545044 | − | 0.545044i | −0.379960 | − | 0.925003i | \(-0.624062\pi\) |
0.925003 | + | 0.379960i | \(0.124062\pi\) | |||||||
\(74\) | −6.41421 | − | 6.41421i | −0.745637 | − | 0.745637i | ||||
\(75\) | −4.70711 | − | 4.70711i | −0.543530 | − | 0.543530i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.00000i | − | 0.227921i | ||||||
\(78\) | 4.82843 | + | 4.82843i | 0.546712 | + | 0.546712i | ||||
\(79\) | 8.24264 | + | 8.24264i | 0.927370 | + | 0.927370i | 0.997535 | − | 0.0701658i | \(-0.0223528\pi\) |
−0.0701658 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(80\) | −2.41421 | + | 2.41421i | −0.269917 | + | 0.269917i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.00000 | + | 3.00000i | −0.331295 | + | 0.331295i | ||||
\(83\) | 2.82843i | 0.310460i | 0.987878 | + | 0.155230i | \(0.0496119\pi\) | ||||
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | −12.0711 | − | 7.24264i | −1.30929 | − | 0.785575i | ||||
\(86\) | −6.82843 | −0.736328 | ||||||||
\(87\) | 9.07107i | 0.972521i | ||||||||
\(88\) | −0.707107 | + | 0.707107i | −0.0753778 | + | 0.0753778i | ||||
\(89\) | 17.6569 | 1.87162 | 0.935811 | − | 0.352501i | \(-0.114669\pi\) | ||||
0.935811 | + | 0.352501i | \(0.114669\pi\) | |||||||
\(90\) | −2.41421 | + | 2.41421i | −0.254480 | + | 0.254480i | ||||
\(91\) | 9.65685 | + | 9.65685i | 1.01231 | + | 1.01231i | ||||
\(92\) | 1.41421 | + | 1.41421i | 0.147442 | + | 0.147442i | ||||
\(93\) | 7.65685i | 0.793979i | ||||||||
\(94\) | − | 9.65685i | − | 0.996028i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.707107 | + | 0.707107i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | 7.48528 | − | 7.48528i | 0.760015 | − | 0.760015i | −0.216310 | − | 0.976325i | \(-0.569402\pi\) |
0.976325 | + | 0.216310i | \(0.0694021\pi\) | |||||||
\(98\) | 3.00000 | 0.303046 | ||||||||
\(99\) | −0.707107 | + | 0.707107i | −0.0710669 | + | 0.0710669i | ||||
\(100\) | 6.65685i | 0.665685i | ||||||||
\(101\) | 12.4853 | 1.24233 | 0.621166 | − | 0.783679i | \(-0.286659\pi\) | ||||
0.621166 | + | 0.783679i | \(0.286659\pi\) | |||||||
\(102\) | −2.12132 | + | 3.53553i | −0.210042 | + | 0.350070i | ||||
\(103\) | −10.8284 | −1.06696 | −0.533478 | − | 0.845814i | \(-0.679115\pi\) | ||||
−0.533478 | + | 0.845814i | \(0.679115\pi\) | |||||||
\(104\) | − | 6.82843i | − | 0.669582i | ||||||
\(105\) | −4.82843 | + | 4.82843i | −0.471206 | + | 0.471206i | ||||
\(106\) | 12.4853 | 1.21268 | ||||||||
\(107\) | 5.17157 | − | 5.17157i | 0.499955 | − | 0.499955i | −0.411469 | − | 0.911424i | \(-0.634984\pi\) |
0.911424 | + | 0.411469i | \(0.134984\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −0.414214 | − | 0.414214i | −0.0396745 | − | 0.0396745i | 0.686991 | − | 0.726666i | \(-0.258931\pi\) |
−0.726666 | + | 0.686991i | \(0.758931\pi\) | |||||||
\(110\) | 3.41421i | 0.325532i | ||||||||
\(111\) | 9.07107i | 0.860988i | ||||||||
\(112\) | 1.41421 | + | 1.41421i | 0.133631 | + | 0.133631i | ||||
\(113\) | 5.82843 | + | 5.82843i | 0.548292 | + | 0.548292i | 0.925947 | − | 0.377654i | \(-0.123269\pi\) |
−0.377654 | + | 0.925947i | \(0.623269\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.82843 | 0.636754 | ||||||||
\(116\) | 6.41421 | − | 6.41421i | 0.595545 | − | 0.595545i | ||||
\(117\) | − | 6.82843i | − | 0.631288i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.24264 | + | 7.07107i | −0.388922 | + | 0.648204i | ||||
\(120\) | 3.41421 | 0.311674 | ||||||||
\(121\) | 1.00000i | 0.0909091i | ||||||||
\(122\) | −0.757359 | + | 0.757359i | −0.0685681 | + | 0.0685681i | ||||
\(123\) | 4.24264 | 0.382546 | ||||||||
\(124\) | 5.41421 | − | 5.41421i | 0.486211 | − | 0.486211i | ||||
\(125\) | 4.00000 | + | 4.00000i | 0.357771 | + | 0.357771i | ||||
\(126\) | 1.41421 | + | 1.41421i | 0.125988 | + | 0.125988i | ||||
\(127\) | 9.17157i | 0.813845i | 0.913463 | + | 0.406923i | \(0.133398\pi\) | ||||
−0.913463 | + | 0.406923i | \(0.866602\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 4.82843 | + | 4.82843i | 0.425119 | + | 0.425119i | ||||
\(130\) | −16.4853 | − | 16.4853i | −1.44585 | − | 1.44585i | ||||
\(131\) | −1.17157 | + | 1.17157i | −0.102361 | + | 0.102361i | −0.756433 | − | 0.654072i | \(-0.773059\pi\) |
0.654072 | + | 0.756433i | \(0.273059\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.48528i | 0.733017i | ||||||||
\(135\) | 3.41421 | 0.293849 | ||||||||
\(136\) | 4.00000 | − | 1.00000i | 0.342997 | − | 0.0857493i | ||||
\(137\) | −8.00000 | −0.683486 | −0.341743 | − | 0.939793i | \(-0.611017\pi\) | ||||
−0.341743 | + | 0.939793i | \(0.611017\pi\) | |||||||
\(138\) | − | 2.00000i | − | 0.170251i | ||||||
\(139\) | 1.65685 | − | 1.65685i | 0.140533 | − | 0.140533i | −0.633341 | − | 0.773873i | \(-0.718317\pi\) |
0.773873 | + | 0.633341i | \(0.218317\pi\) | |||||||
\(140\) | 6.82843 | 0.577107 | ||||||||
\(141\) | −6.82843 | + | 6.82843i | −0.575057 | + | 0.575057i | ||||
\(142\) | −11.0711 | − | 11.0711i | −0.929063 | − | 0.929063i | ||||
\(143\) | −4.82843 | − | 4.82843i | −0.403773 | − | 0.403773i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | − | 30.9706i | − | 2.57197i | ||||||
\(146\) | 4.65685 | + | 4.65685i | 0.385404 | + | 0.385404i | ||||
\(147\) | −2.12132 | − | 2.12132i | −0.174964 | − | 0.174964i | ||||
\(148\) | 6.41421 | − | 6.41421i | 0.527245 | − | 0.527245i | ||||
\(149\) | −9.31371 | −0.763009 | −0.381504 | − | 0.924367i | \(-0.624594\pi\) | ||||
−0.381504 | + | 0.924367i | \(0.624594\pi\) | |||||||
\(150\) | 4.70711 | − | 4.70711i | 0.384334 | − | 0.384334i | ||||
\(151\) | − | 1.17157i | − | 0.0953412i | −0.998863 | − | 0.0476706i | \(-0.984820\pi\) | ||
0.998863 | − | 0.0476706i | \(-0.0151798\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | − | 1.00000i | 0.323381 | − | 0.0808452i | ||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | − | 26.1421i | − | 2.09979i | ||||||
\(156\) | −4.82843 | + | 4.82843i | −0.386584 | + | 0.386584i | ||||
\(157\) | −13.3137 | −1.06255 | −0.531275 | − | 0.847200i | \(-0.678287\pi\) | ||||
−0.531275 | + | 0.847200i | \(0.678287\pi\) | |||||||
\(158\) | −8.24264 | + | 8.24264i | −0.655749 | + | 0.655749i | ||||
\(159\) | −8.82843 | − | 8.82843i | −0.700140 | − | 0.700140i | ||||
\(160\) | −2.41421 | − | 2.41421i | −0.190860 | − | 0.190860i | ||||
\(161\) | − | 4.00000i | − | 0.315244i | ||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −8.48528 | − | 8.48528i | −0.664619 | − | 0.664619i | 0.291847 | − | 0.956465i | \(-0.405730\pi\) |
−0.956465 | + | 0.291847i | \(0.905730\pi\) | |||||||
\(164\) | −3.00000 | − | 3.00000i | −0.234261 | − | 0.234261i | ||||
\(165\) | 2.41421 | − | 2.41421i | 0.187946 | − | 0.187946i | ||||
\(166\) | −2.82843 | −0.219529 | ||||||||
\(167\) | 0.928932 | − | 0.928932i | 0.0718829 | − | 0.0718829i | −0.670251 | − | 0.742134i | \(-0.733814\pi\) |
0.742134 | + | 0.670251i | \(0.233814\pi\) | |||||||
\(168\) | − | 2.00000i | − | 0.154303i | ||||||
\(169\) | 33.6274 | 2.58672 | ||||||||
\(170\) | 7.24264 | − | 12.0711i | 0.555485 | − | 0.925809i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 6.82843i | − | 0.520663i | ||||||
\(173\) | 11.2426 | − | 11.2426i | 0.854762 | − | 0.854762i | −0.135953 | − | 0.990715i | \(-0.543410\pi\) |
0.990715 | + | 0.135953i | \(0.0434097\pi\) | |||||||
\(174\) | −9.07107 | −0.687676 | ||||||||
\(175\) | 9.41421 | − | 9.41421i | 0.711648 | − | 0.711648i | ||||
\(176\) | −0.707107 | − | 0.707107i | −0.0533002 | − | 0.0533002i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.6569i | 1.32344i | ||||||||
\(179\) | 18.1421i | 1.35601i | 0.735059 | + | 0.678003i | \(0.237155\pi\) | ||||
−0.735059 | + | 0.678003i | \(0.762845\pi\) | |||||||
\(180\) | −2.41421 | − | 2.41421i | −0.179945 | − | 0.179945i | ||||
\(181\) | 1.58579 | + | 1.58579i | 0.117871 | + | 0.117871i | 0.763582 | − | 0.645711i | \(-0.223439\pi\) |
−0.645711 | + | 0.763582i | \(0.723439\pi\) | |||||||
\(182\) | −9.65685 | + | 9.65685i | −0.715814 | + | 0.715814i | ||||
\(183\) | 1.07107 | 0.0791756 | ||||||||
\(184\) | −1.41421 | + | 1.41421i | −0.104257 | + | 0.104257i | ||||
\(185\) | − | 30.9706i | − | 2.27700i | ||||||
\(186\) | −7.65685 | −0.561428 | ||||||||
\(187\) | 2.12132 | − | 3.53553i | 0.155126 | − | 0.258544i | ||||
\(188\) | 9.65685 | 0.704298 | ||||||||
\(189\) | − | 2.00000i | − | 0.145479i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.6569 | 1.85646 | 0.928232 | − | 0.372001i | \(-0.121328\pi\) | ||||
0.928232 | + | 0.372001i | \(0.121328\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −1.48528 | − | 1.48528i | −0.106913 | − | 0.106913i | 0.651627 | − | 0.758540i | \(-0.274087\pi\) |
−0.758540 | + | 0.651627i | \(0.774087\pi\) | |||||||
\(194\) | 7.48528 | + | 7.48528i | 0.537412 | + | 0.537412i | ||||
\(195\) | 23.3137i | 1.66953i | ||||||||
\(196\) | 3.00000i | 0.214286i | ||||||||
\(197\) | −1.24264 | − | 1.24264i | −0.0885345 | − | 0.0885345i | 0.661453 | − | 0.749987i | \(-0.269940\pi\) |
−0.749987 | + | 0.661453i | \(0.769940\pi\) | |||||||
\(198\) | −0.707107 | − | 0.707107i | −0.0502519 | − | 0.0502519i | ||||
\(199\) | 9.89949 | − | 9.89949i | 0.701757 | − | 0.701757i | −0.263031 | − | 0.964787i | \(-0.584722\pi\) |
0.964787 | + | 0.263031i | \(0.0847221\pi\) | |||||||
\(200\) | −6.65685 | −0.470711 | ||||||||
\(201\) | 6.00000 | − | 6.00000i | 0.423207 | − | 0.423207i | ||||
\(202\) | 12.4853i | 0.878461i | ||||||||
\(203\) | −18.1421 | −1.27333 | ||||||||
\(204\) | −3.53553 | − | 2.12132i | −0.247537 | − | 0.148522i | ||||
\(205\) | −14.4853 | −1.01170 | ||||||||
\(206\) | − | 10.8284i | − | 0.754452i | ||||||
\(207\) | −1.41421 | + | 1.41421i | −0.0982946 | + | 0.0982946i | ||||
\(208\) | 6.82843 | 0.473466 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.82843 | − | 4.82843i | −0.333193 | − | 0.333193i | ||||
\(211\) | −14.8284 | − | 14.8284i | −1.02083 | − | 1.02083i | −0.999778 | − | 0.0210527i | \(-0.993298\pi\) |
−0.0210527 | − | 0.999778i | \(-0.506702\pi\) | |||||||
\(212\) | 12.4853i | 0.857493i | ||||||||
\(213\) | 15.6569i | 1.07279i | ||||||||
\(214\) | 5.17157 | + | 5.17157i | 0.353521 | + | 0.353521i | ||||
\(215\) | −16.4853 | − | 16.4853i | −1.12429 | − | 1.12429i | ||||
\(216\) | −0.707107 | + | 0.707107i | −0.0481125 | + | 0.0481125i | ||||
\(217\) | −15.3137 | −1.03956 | ||||||||
\(218\) | 0.414214 | − | 0.414214i | 0.0280541 | − | 0.0280541i | ||||
\(219\) | − | 6.58579i | − | 0.445026i | ||||||
\(220\) | −3.41421 | −0.230186 | ||||||||
\(221\) | 6.82843 | + | 27.3137i | 0.459330 | + | 1.83732i | ||||
\(222\) | −9.07107 | −0.608810 | ||||||||
\(223\) | 8.48528i | 0.568216i | 0.958792 | + | 0.284108i | \(0.0916975\pi\) | ||||
−0.958792 | + | 0.284108i | \(0.908302\pi\) | |||||||
\(224\) | −1.41421 | + | 1.41421i | −0.0944911 | + | 0.0944911i | ||||
\(225\) | −6.65685 | −0.443790 | ||||||||
\(226\) | −5.82843 | + | 5.82843i | −0.387701 | + | 0.387701i | ||||
\(227\) | 18.1421 | + | 18.1421i | 1.20414 | + | 1.20414i | 0.972897 | + | 0.231239i | \(0.0742779\pi\) |
0.231239 | + | 0.972897i | \(0.425722\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.0000i | − | 1.18947i | −0.803921 | − | 0.594737i | \(-0.797256\pi\) | ||
0.803921 | − | 0.594737i | \(-0.202744\pi\) | |||||||
\(230\) | 6.82843i | 0.450253i | ||||||||
\(231\) | −1.41421 | − | 1.41421i | −0.0930484 | − | 0.0930484i | ||||
\(232\) | 6.41421 | + | 6.41421i | 0.421114 | + | 0.421114i | ||||
\(233\) | 13.4853 | − | 13.4853i | 0.883450 | − | 0.883450i | −0.110433 | − | 0.993884i | \(-0.535224\pi\) |
0.993884 | + | 0.110433i | \(0.0352239\pi\) | |||||||
\(234\) | 6.82843 | 0.446388 | ||||||||
\(235\) | 23.3137 | − | 23.3137i | 1.52082 | − | 1.52082i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.6569 | 0.757194 | ||||||||
\(238\) | −7.07107 | − | 4.24264i | −0.458349 | − | 0.275010i | ||||
\(239\) | −2.82843 | −0.182956 | −0.0914779 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914779 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(240\) | 3.41421i | 0.220387i | ||||||||
\(241\) | −5.48528 | + | 5.48528i | −0.353338 | + | 0.353338i | −0.861350 | − | 0.508012i | \(-0.830381\pi\) |
0.508012 | + | 0.861350i | \(0.330381\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −0.757359 | − | 0.757359i | −0.0484850 | − | 0.0484850i | ||||
\(245\) | 7.24264 | + | 7.24264i | 0.462715 | + | 0.462715i | ||||
\(246\) | 4.24264i | 0.270501i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.41421 | + | 5.41421i | 0.343803 | + | 0.343803i | ||||
\(249\) | 2.00000 | + | 2.00000i | 0.126745 | + | 0.126745i | ||||
\(250\) | −4.00000 | + | 4.00000i | −0.252982 | + | 0.252982i | ||||
\(251\) | −18.1421 | −1.14512 | −0.572561 | − | 0.819862i | \(-0.694050\pi\) | ||||
−0.572561 | + | 0.819862i | \(0.694050\pi\) | |||||||
\(252\) | −1.41421 | + | 1.41421i | −0.0890871 | + | 0.0890871i | ||||
\(253\) | 2.00000i | 0.125739i | ||||||||
\(254\) | −9.17157 | −0.575476 | ||||||||
\(255\) | −13.6569 | + | 3.41421i | −0.855225 | + | 0.213806i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.3137i | 1.08000i | 0.841665 | + | 0.540000i | \(0.181576\pi\) | ||||
−0.841665 | + | 0.540000i | \(0.818424\pi\) | |||||||
\(258\) | −4.82843 | + | 4.82843i | −0.300605 | + | 0.300605i | ||||
\(259\) | −18.1421 | −1.12730 | ||||||||
\(260\) | 16.4853 | − | 16.4853i | 1.02237 | − | 1.02237i | ||||
\(261\) | 6.41421 | + | 6.41421i | 0.397030 | + | 0.397030i | ||||
\(262\) | −1.17157 | − | 1.17157i | −0.0723800 | − | 0.0723800i | ||||
\(263\) | − | 16.4853i | − | 1.01653i | −0.861202 | − | 0.508263i | \(-0.830288\pi\) | ||
0.861202 | − | 0.508263i | \(-0.169712\pi\) | |||||||
\(264\) | 1.00000i | 0.0615457i | ||||||||
\(265\) | 30.1421 | + | 30.1421i | 1.85162 | + | 1.85162i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4853 | − | 12.4853i | 0.764087 | − | 0.764087i | ||||
\(268\) | −8.48528 | −0.518321 | ||||||||
\(269\) | −0.0710678 | + | 0.0710678i | −0.00433308 | + | 0.00433308i | −0.709270 | − | 0.704937i | \(-0.750975\pi\) |
0.704937 | + | 0.709270i | \(0.250975\pi\) | |||||||
\(270\) | 3.41421i | 0.207782i | ||||||||
\(271\) | −6.82843 | −0.414797 | −0.207399 | − | 0.978256i | \(-0.566500\pi\) | ||||
−0.207399 | + | 0.978256i | \(0.566500\pi\) | |||||||
\(272\) | 1.00000 | + | 4.00000i | 0.0606339 | + | 0.242536i | ||||
\(273\) | 13.6569 | 0.826550 | ||||||||
\(274\) | − | 8.00000i | − | 0.483298i | ||||||
\(275\) | −4.70711 | + | 4.70711i | −0.283849 | + | 0.283849i | ||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | −3.58579 | + | 3.58579i | −0.215449 | + | 0.215449i | −0.806577 | − | 0.591128i | \(-0.798683\pi\) |
0.591128 | + | 0.806577i | \(0.298683\pi\) | |||||||
\(278\) | 1.65685 | + | 1.65685i | 0.0993715 | + | 0.0993715i | ||||
\(279\) | 5.41421 | + | 5.41421i | 0.324140 | + | 0.324140i | ||||
\(280\) | 6.82843i | 0.408077i | ||||||||
\(281\) | 29.6569i | 1.76918i | 0.466370 | + | 0.884590i | \(0.345562\pi\) | ||||
−0.466370 | + | 0.884590i | \(0.654438\pi\) | |||||||
\(282\) | −6.82843 | − | 6.82843i | −0.406627 | − | 0.406627i | ||||
\(283\) | −9.65685 | − | 9.65685i | −0.574040 | − | 0.574040i | 0.359215 | − | 0.933255i | \(-0.383045\pi\) |
−0.933255 | + | 0.359215i | \(0.883045\pi\) | |||||||
\(284\) | 11.0711 | − | 11.0711i | 0.656947 | − | 0.656947i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.82843 | − | 4.82843i | 0.285511 | − | 0.285511i | ||||
\(287\) | 8.48528i | 0.500870i | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.0000 | + | 8.00000i | −0.882353 | + | 0.470588i | ||||
\(290\) | 30.9706 | 1.81865 | ||||||||
\(291\) | − | 10.5858i | − | 0.620550i | ||||||
\(292\) | −4.65685 | + | 4.65685i | −0.272522 | + | 0.272522i | ||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 2.12132 | − | 2.12132i | 0.123718 | − | 0.123718i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.41421 | + | 6.41421i | 0.372819 | + | 0.372819i | ||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | − | 9.31371i | − | 0.539529i | ||||||
\(299\) | −9.65685 | − | 9.65685i | −0.558470 | − | 0.558470i | ||||
\(300\) | 4.70711 | + | 4.70711i | 0.271765 | + | 0.271765i | ||||
\(301\) | −9.65685 | + | 9.65685i | −0.556612 | + | 0.556612i | ||||
\(302\) | 1.17157 | 0.0674164 | ||||||||
\(303\) | 8.82843 | − | 8.82843i | 0.507180 | − | 0.507180i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.65685 | −0.209391 | ||||||||
\(306\) | 1.00000 | + | 4.00000i | 0.0571662 | + | 0.228665i | ||||
\(307\) | 1.17157 | 0.0668652 | 0.0334326 | − | 0.999441i | \(-0.489356\pi\) | ||||
0.0334326 | + | 0.999441i | \(0.489356\pi\) | |||||||
\(308\) | 2.00000i | 0.113961i | ||||||||
\(309\) | −7.65685 | + | 7.65685i | −0.435583 | + | 0.435583i | ||||
\(310\) | 26.1421 | 1.48477 | ||||||||
\(311\) | 17.8995 | − | 17.8995i | 1.01499 | − | 1.01499i | 0.0151013 | − | 0.999886i | \(-0.495193\pi\) |
0.999886 | − | 0.0151013i | \(-0.00480707\pi\) | |||||||
\(312\) | −4.82843 | − | 4.82843i | −0.273356 | − | 0.273356i | ||||
\(313\) | 21.4853 | + | 21.4853i | 1.21442 | + | 1.21442i | 0.969558 | + | 0.244862i | \(0.0787426\pi\) |
0.244862 | + | 0.969558i | \(0.421257\pi\) | |||||||
\(314\) | − | 13.3137i | − | 0.751336i | ||||||
\(315\) | 6.82843i | 0.384738i | ||||||||
\(316\) | −8.24264 | − | 8.24264i | −0.463685 | − | 0.463685i | ||||
\(317\) | 14.8995 | + | 14.8995i | 0.836839 | + | 0.836839i | 0.988442 | − | 0.151603i | \(-0.0484434\pi\) |
−0.151603 | + | 0.988442i | \(0.548443\pi\) | |||||||
\(318\) | 8.82843 | − | 8.82843i | 0.495074 | − | 0.495074i | ||||
\(319\) | 9.07107 | 0.507882 | ||||||||
\(320\) | 2.41421 | − | 2.41421i | 0.134959 | − | 0.134959i | ||||
\(321\) | − | 7.31371i | − | 0.408211i | ||||||
\(322\) | 4.00000 | 0.222911 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | − | 45.4558i | − | 2.52144i | ||||||
\(326\) | 8.48528 | − | 8.48528i | 0.469956 | − | 0.469956i | ||||
\(327\) | −0.585786 | −0.0323941 | ||||||||
\(328\) | 3.00000 | − | 3.00000i | 0.165647 | − | 0.165647i | ||||
\(329\) | −13.6569 | − | 13.6569i | −0.752927 | − | 0.752927i | ||||
\(330\) | 2.41421 | + | 2.41421i | 0.132898 | + | 0.132898i | ||||
\(331\) | 4.97056i | 0.273207i | 0.990626 | + | 0.136603i | \(0.0436186\pi\) | ||||
−0.990626 | + | 0.136603i | \(0.956381\pi\) | |||||||
\(332\) | − | 2.82843i | − | 0.155230i | ||||||
\(333\) | 6.41421 | + | 6.41421i | 0.351497 | + | 0.351497i | ||||
\(334\) | 0.928932 | + | 0.928932i | 0.0508289 | + | 0.0508289i | ||||
\(335\) | −20.4853 | + | 20.4853i | −1.11923 | + | 1.11923i | ||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | 19.9706 | − | 19.9706i | 1.08787 | − | 1.08787i | 0.0921178 | − | 0.995748i | \(-0.470636\pi\) |
0.995748 | − | 0.0921178i | \(-0.0293636\pi\) | |||||||
\(338\) | 33.6274i | 1.82909i | ||||||||
\(339\) | 8.24264 | 0.447679 | ||||||||
\(340\) | 12.0711 | + | 7.24264i | 0.654646 | + | 0.392787i | ||||
\(341\) | 7.65685 | 0.414642 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.1421 | − | 14.1421i | 0.763604 | − | 0.763604i | ||||
\(344\) | 6.82843 | 0.368164 | ||||||||
\(345\) | 4.82843 | − | 4.82843i | 0.259954 | − | 0.259954i | ||||
\(346\) | 11.2426 | + | 11.2426i | 0.604408 | + | 0.604408i | ||||
\(347\) | −18.1421 | − | 18.1421i | −0.973921 | − | 0.973921i | 0.0257476 | − | 0.999668i | \(-0.491803\pi\) |
−0.999668 | + | 0.0257476i | \(0.991803\pi\) | |||||||
\(348\) | − | 9.07107i | − | 0.486260i | ||||||
\(349\) | 4.48528i | 0.240092i | 0.992768 | + | 0.120046i | \(0.0383041\pi\) | ||||
−0.992768 | + | 0.120046i | \(0.961696\pi\) | |||||||
\(350\) | 9.41421 | + | 9.41421i | 0.503211 | + | 0.503211i | ||||
\(351\) | −4.82843 | − | 4.82843i | −0.257722 | − | 0.257722i | ||||
\(352\) | 0.707107 | − | 0.707107i | 0.0376889 | − | 0.0376889i | ||||
\(353\) | 16.6274 | 0.884988 | 0.442494 | − | 0.896771i | \(-0.354094\pi\) | ||||
0.442494 | + | 0.896771i | \(0.354094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 53.4558i | − | 2.83714i | ||||||
\(356\) | −17.6569 | −0.935811 | ||||||||
\(357\) | 2.00000 | + | 8.00000i | 0.105851 | + | 0.423405i | ||||
\(358\) | −18.1421 | −0.958842 | ||||||||
\(359\) | − | 16.0000i | − | 0.844448i | −0.906492 | − | 0.422224i | \(-0.861250\pi\) | ||
0.906492 | − | 0.422224i | \(-0.138750\pi\) | |||||||
\(360\) | 2.41421 | − | 2.41421i | 0.127240 | − | 0.127240i | ||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | −1.58579 | + | 1.58579i | −0.0833471 | + | 0.0833471i | ||||
\(363\) | 0.707107 | + | 0.707107i | 0.0371135 | + | 0.0371135i | ||||
\(364\) | −9.65685 | − | 9.65685i | −0.506157 | − | 0.506157i | ||||
\(365\) | 22.4853i | 1.17693i | ||||||||
\(366\) | 1.07107i | 0.0559856i | ||||||||
\(367\) | −3.75736 | − | 3.75736i | −0.196133 | − | 0.196133i | 0.602207 | − | 0.798340i | \(-0.294288\pi\) |
−0.798340 | + | 0.602207i | \(0.794288\pi\) | |||||||
\(368\) | −1.41421 | − | 1.41421i | −0.0737210 | − | 0.0737210i | ||||
\(369\) | 3.00000 | − | 3.00000i | 0.156174 | − | 0.156174i | ||||
\(370\) | 30.9706 | 1.61008 | ||||||||
\(371\) | 17.6569 | − | 17.6569i | 0.916698 | − | 0.916698i | ||||
\(372\) | − | 7.65685i | − | 0.396989i | ||||||
\(373\) | 22.8284 | 1.18201 | 0.591006 | − | 0.806667i | \(-0.298731\pi\) | ||||
0.591006 | + | 0.806667i | \(0.298731\pi\) | |||||||
\(374\) | 3.53553 | + | 2.12132i | 0.182818 | + | 0.109691i | ||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 9.65685i | 0.498014i | ||||||||
\(377\) | −43.7990 | + | 43.7990i | −2.25576 | + | 2.25576i | ||||
\(378\) | 2.00000 | 0.102869 | ||||||||
\(379\) | 13.6569 | − | 13.6569i | 0.701505 | − | 0.701505i | −0.263228 | − | 0.964734i | \(-0.584787\pi\) |
0.964734 | + | 0.263228i | \(0.0847872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.48528 | + | 6.48528i | 0.332251 | + | 0.332251i | ||||
\(382\) | 25.6569i | 1.31272i | ||||||||
\(383\) | 25.6569i | 1.31100i | 0.755193 | + | 0.655502i | \(0.227543\pi\) | ||||
−0.755193 | + | 0.655502i | \(0.772457\pi\) | |||||||
\(384\) | −0.707107 | − | 0.707107i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | 4.82843 | + | 4.82843i | 0.246079 | + | 0.246079i | ||||
\(386\) | 1.48528 | − | 1.48528i | 0.0755988 | − | 0.0755988i | ||||
\(387\) | 6.82843 | 0.347108 | ||||||||
\(388\) | −7.48528 | + | 7.48528i | −0.380008 | + | 0.380008i | ||||
\(389\) | − | 12.3431i | − | 0.625822i | −0.949782 | − | 0.312911i | \(-0.898696\pi\) | ||
0.949782 | − | 0.312911i | \(-0.101304\pi\) | |||||||
\(390\) | −23.3137 | −1.18054 | ||||||||
\(391\) | 4.24264 | − | 7.07107i | 0.214560 | − | 0.357599i | ||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | 1.65685i | 0.0835772i | ||||||||
\(394\) | 1.24264 | − | 1.24264i | 0.0626033 | − | 0.0626033i | ||||
\(395\) | −39.7990 | −2.00250 | ||||||||
\(396\) | 0.707107 | − | 0.707107i | 0.0355335 | − | 0.0355335i | ||||
\(397\) | −3.10051 | − | 3.10051i | −0.155610 | − | 0.155610i | 0.625008 | − | 0.780618i | \(-0.285096\pi\) |
−0.780618 | + | 0.625008i | \(0.785096\pi\) | |||||||
\(398\) | 9.89949 | + | 9.89949i | 0.496217 | + | 0.496217i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 6.65685i | − | 0.332843i | ||||||
\(401\) | −18.3137 | − | 18.3137i | −0.914543 | − | 0.914543i | 0.0820826 | − | 0.996626i | \(-0.473843\pi\) |
−0.996626 | + | 0.0820826i | \(0.973843\pi\) | |||||||
\(402\) | 6.00000 | + | 6.00000i | 0.299253 | + | 0.299253i | ||||
\(403\) | −36.9706 | + | 36.9706i | −1.84163 | + | 1.84163i | ||||
\(404\) | −12.4853 | −0.621166 | ||||||||
\(405\) | 2.41421 | − | 2.41421i | 0.119963 | − | 0.119963i | ||||
\(406\) | − | 18.1421i | − | 0.900379i | ||||||
\(407\) | 9.07107 | 0.449636 | ||||||||
\(408\) | 2.12132 | − | 3.53553i | 0.105021 | − | 0.175035i | ||||
\(409\) | −9.31371 | −0.460533 | −0.230267 | − | 0.973128i | \(-0.573960\pi\) | ||||
−0.230267 | + | 0.973128i | \(0.573960\pi\) | |||||||
\(410\) | − | 14.4853i | − | 0.715377i | ||||||
\(411\) | −5.65685 | + | 5.65685i | −0.279032 | + | 0.279032i | ||||
\(412\) | 10.8284 | 0.533478 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.41421 | − | 1.41421i | −0.0695048 | − | 0.0695048i | ||||
\(415\) | −6.82843 | − | 6.82843i | −0.335194 | − | 0.335194i | ||||
\(416\) | 6.82843i | 0.334791i | ||||||||
\(417\) | − | 2.34315i | − | 0.114744i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.686292 | − | 0.686292i | −0.0335275 | − | 0.0335275i | 0.690144 | − | 0.723672i | \(-0.257547\pi\) |
−0.723672 | + | 0.690144i | \(0.757547\pi\) | |||||||
\(420\) | 4.82843 | − | 4.82843i | 0.235603 | − | 0.235603i | ||||
\(421\) | 26.1421 | 1.27409 | 0.637045 | − | 0.770827i | \(-0.280157\pi\) | ||||
0.637045 | + | 0.770827i | \(0.280157\pi\) | |||||||
\(422\) | 14.8284 | − | 14.8284i | 0.721837 | − | 0.721837i | ||||
\(423\) | 9.65685i | 0.469532i | ||||||||
\(424\) | −12.4853 | −0.606339 | ||||||||
\(425\) | 26.6274 | − | 6.65685i | 1.29162 | − | 0.322905i | ||||
\(426\) | −15.6569 | −0.758577 | ||||||||
\(427\) | 2.14214i | 0.103665i | ||||||||
\(428\) | −5.17157 | + | 5.17157i | −0.249977 | + | 0.249977i | ||||
\(429\) | −6.82843 | −0.329680 | ||||||||
\(430\) | 16.4853 | − | 16.4853i | 0.794991 | − | 0.794991i | ||||
\(431\) | 9.41421 | + | 9.41421i | 0.453467 | + | 0.453467i | 0.896503 | − | 0.443037i | \(-0.146099\pi\) |
−0.443037 | + | 0.896503i | \(0.646099\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 2.00000i | 0.0961139i | 0.998845 | + | 0.0480569i | \(0.0153029\pi\) | ||||
−0.998845 | + | 0.0480569i | \(0.984697\pi\) | |||||||
\(434\) | − | 15.3137i | − | 0.735082i | ||||||
\(435\) | −21.8995 | − | 21.8995i | −1.05000 | − | 1.05000i | ||||
\(436\) | 0.414214 | + | 0.414214i | 0.0198372 | + | 0.0198372i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 6.58579 | 0.314681 | ||||||||
\(439\) | −26.3848 | + | 26.3848i | −1.25928 | + | 1.25928i | −0.307838 | + | 0.951439i | \(0.599605\pi\) |
−0.951439 | + | 0.307838i | \(0.900395\pi\) | |||||||
\(440\) | − | 3.41421i | − | 0.162766i | ||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −27.3137 | + | 6.82843i | −1.29918 | + | 0.324795i | ||||
\(443\) | 7.79899 | 0.370541 | 0.185271 | − | 0.982688i | \(-0.440684\pi\) | ||||
0.185271 | + | 0.982688i | \(0.440684\pi\) | |||||||
\(444\) | − | 9.07107i | − | 0.430494i | ||||||
\(445\) | −42.6274 | + | 42.6274i | −2.02073 | + | 2.02073i | ||||
\(446\) | −8.48528 | −0.401790 | ||||||||
\(447\) | −6.58579 | + | 6.58579i | −0.311497 | + | 0.311497i | ||||
\(448\) | −1.41421 | − | 1.41421i | −0.0668153 | − | 0.0668153i | ||||
\(449\) | 16.6569 | + | 16.6569i | 0.786086 | + | 0.786086i | 0.980850 | − | 0.194764i | \(-0.0623943\pi\) |
−0.194764 | + | 0.980850i | \(0.562394\pi\) | |||||||
\(450\) | − | 6.65685i | − | 0.313807i | ||||||
\(451\) | − | 4.24264i | − | 0.199778i | ||||||
\(452\) | −5.82843 | − | 5.82843i | −0.274146 | − | 0.274146i | ||||
\(453\) | −0.828427 | − | 0.828427i | −0.0389229 | − | 0.0389229i | ||||
\(454\) | −18.1421 | + | 18.1421i | −0.851453 | + | 0.851453i | ||||
\(455\) | −46.6274 | −2.18593 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.68629i | − | 0.125659i | −0.998024 | − | 0.0628297i | \(-0.979988\pi\) | ||
0.998024 | − | 0.0628297i | \(-0.0200125\pi\) | |||||||
\(458\) | 18.0000 | 0.841085 | ||||||||
\(459\) | 2.12132 | − | 3.53553i | 0.0990148 | − | 0.165025i | ||||
\(460\) | −6.82843 | −0.318377 | ||||||||
\(461\) | − | 4.48528i | − | 0.208900i | −0.994530 | − | 0.104450i | \(-0.966692\pi\) | ||
0.994530 | − | 0.104450i | \(-0.0333083\pi\) | |||||||
\(462\) | 1.41421 | − | 1.41421i | 0.0657952 | − | 0.0657952i | ||||
\(463\) | 2.82843 | 0.131448 | 0.0657241 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657241 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(464\) | −6.41421 | + | 6.41421i | −0.297772 | + | 0.297772i | ||||
\(465\) | −18.4853 | − | 18.4853i | −0.857234 | − | 0.857234i | ||||
\(466\) | 13.4853 | + | 13.4853i | 0.624694 | + | 0.624694i | ||||
\(467\) | − | 30.8284i | − | 1.42657i | −0.700874 | − | 0.713285i | \(-0.747207\pi\) | ||
0.700874 | − | 0.713285i | \(-0.252793\pi\) | |||||||
\(468\) | 6.82843i | 0.315644i | ||||||||
\(469\) | 12.0000 | + | 12.0000i | 0.554109 | + | 0.554109i | ||||
\(470\) | 23.3137 | + | 23.3137i | 1.07538 | + | 1.07538i | ||||
\(471\) | −9.41421 | + | 9.41421i | −0.433784 | + | 0.433784i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.82843 | − | 4.82843i | 0.222011 | − | 0.222011i | ||||
\(474\) | 11.6569i | 0.535417i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.24264 | − | 7.07107i | 0.194461 | − | 0.324102i | ||||
\(477\) | −12.4853 | −0.571662 | ||||||||
\(478\) | − | 2.82843i | − | 0.129369i | ||||||
\(479\) | 16.7279 | − | 16.7279i | 0.764318 | − | 0.764318i | −0.212782 | − | 0.977100i | \(-0.568252\pi\) |
0.977100 | + | 0.212782i | \(0.0682523\pi\) | |||||||
\(480\) | −3.41421 | −0.155837 | ||||||||
\(481\) | −43.7990 | + | 43.7990i | −1.99706 | + | 1.99706i | ||||
\(482\) | −5.48528 | − | 5.48528i | −0.249848 | − | 0.249848i | ||||
\(483\) | −2.82843 | − | 2.82843i | −0.128698 | − | 0.128698i | ||||
\(484\) | − | 1.00000i | − | 0.0454545i | ||||||
\(485\) | 36.1421i | 1.64113i | ||||||||
\(486\) | −0.707107 | − | 0.707107i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | 20.2426 | + | 20.2426i | 0.917282 | + | 0.917282i | 0.996831 | − | 0.0795493i | \(-0.0253481\pi\) |
−0.0795493 | + | 0.996831i | \(0.525348\pi\) | |||||||
\(488\) | 0.757359 | − | 0.757359i | 0.0342840 | − | 0.0342840i | ||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | −7.24264 | + | 7.24264i | −0.327189 | + | 0.327189i | ||||
\(491\) | − | 25.6569i | − | 1.15788i | −0.815371 | − | 0.578939i | \(-0.803467\pi\) | ||
0.815371 | − | 0.578939i | \(-0.196533\pi\) | |||||||
\(492\) | −4.24264 | −0.191273 | ||||||||
\(493\) | −32.0711 | − | 19.2426i | −1.44441 | − | 0.866645i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 3.41421i | − | 0.153457i | ||||||
\(496\) | −5.41421 | + | 5.41421i | −0.243105 | + | 0.243105i | ||||
\(497\) | −31.3137 | −1.40461 | ||||||||
\(498\) | −2.00000 | + | 2.00000i | −0.0896221 | + | 0.0896221i | ||||
\(499\) | −7.51472 | − | 7.51472i | −0.336405 | − | 0.336405i | 0.518607 | − | 0.855012i | \(-0.326451\pi\) |
−0.855012 | + | 0.518607i | \(0.826451\pi\) | |||||||
\(500\) | −4.00000 | − | 4.00000i | −0.178885 | − | 0.178885i | ||||
\(501\) | − | 1.31371i | − | 0.0586922i | ||||||
\(502\) | − | 18.1421i | − | 0.809723i | ||||||
\(503\) | 8.92893 | + | 8.92893i | 0.398121 | + | 0.398121i | 0.877570 | − | 0.479449i | \(-0.159163\pi\) |
−0.479449 | + | 0.877570i | \(0.659163\pi\) | |||||||
\(504\) | −1.41421 | − | 1.41421i | −0.0629941 | − | 0.0629941i | ||||
\(505\) | −30.1421 | + | 30.1421i | −1.34131 | + | 1.34131i | ||||
\(506\) | −2.00000 | −0.0889108 | ||||||||
\(507\) | 23.7782 | − | 23.7782i | 1.05603 | − | 1.05603i | ||||
\(508\) | − | 9.17157i | − | 0.406923i | ||||||
\(509\) | −8.34315 | −0.369803 | −0.184902 | − | 0.982757i | \(-0.559197\pi\) | ||||
−0.184902 | + | 0.982757i | \(0.559197\pi\) | |||||||
\(510\) | −3.41421 | − | 13.6569i | −0.151184 | − | 0.604736i | ||||
\(511\) | 13.1716 | 0.582676 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.3137 | −0.763675 | ||||||||
\(515\) | 26.1421 | − | 26.1421i | 1.15196 | − | 1.15196i | ||||
\(516\) | −4.82843 | − | 4.82843i | −0.212560 | − | 0.212560i | ||||
\(517\) | 6.82843 | + | 6.82843i | 0.300314 | + | 0.300314i | ||||
\(518\) | − | 18.1421i | − | 0.797120i | ||||||
\(519\) | − | 15.8995i | − | 0.697910i | ||||||
\(520\) | 16.4853 | + | 16.4853i | 0.722927 | + | 0.722927i | ||||
\(521\) | −14.3137 | − | 14.3137i | −0.627095 | − | 0.627095i | 0.320241 | − | 0.947336i | \(-0.396236\pi\) |
−0.947336 | + | 0.320241i | \(0.896236\pi\) | |||||||
\(522\) | −6.41421 | + | 6.41421i | −0.280743 | + | 0.280743i | ||||
\(523\) | 11.3137 | 0.494714 | 0.247357 | − | 0.968924i | \(-0.420438\pi\) | ||||
0.247357 | + | 0.968924i | \(0.420438\pi\) | |||||||
\(524\) | 1.17157 | − | 1.17157i | 0.0511804 | − | 0.0511804i | ||||
\(525\) | − | 13.3137i | − | 0.581058i | ||||||
\(526\) | 16.4853 | 0.718792 | ||||||||
\(527\) | −27.0711 | − | 16.2426i | −1.17923 | − | 0.707541i | ||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | − | 19.0000i | − | 0.826087i | ||||||
\(530\) | −30.1421 | + | 30.1421i | −1.30929 | + | 1.30929i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.4853 | + | 20.4853i | 0.887316 | + | 0.887316i | ||||
\(534\) | 12.4853 | + | 12.4853i | 0.540291 | + | 0.540291i | ||||
\(535\) | 24.9706i | 1.07957i | ||||||||
\(536\) | − | 8.48528i | − | 0.366508i | ||||||
\(537\) | 12.8284 | + | 12.8284i | 0.553587 | + | 0.553587i | ||||
\(538\) | −0.0710678 | − | 0.0710678i | −0.00306395 | − | 0.00306395i | ||||
\(539\) | −2.12132 | + | 2.12132i | −0.0913717 | + | 0.0913717i | ||||
\(540\) | −3.41421 | −0.146924 | ||||||||
\(541\) | 6.41421 | − | 6.41421i | 0.275769 | − | 0.275769i | −0.555649 | − | 0.831417i | \(-0.687530\pi\) |
0.831417 | + | 0.555649i | \(0.187530\pi\) | |||||||
\(542\) | − | 6.82843i | − | 0.293306i | ||||||
\(543\) | 2.24264 | 0.0962409 | ||||||||
\(544\) | −4.00000 | + | 1.00000i | −0.171499 | + | 0.0428746i | ||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 13.6569i | 0.584459i | ||||||||
\(547\) | 6.14214 | − | 6.14214i | 0.262619 | − | 0.262619i | −0.563498 | − | 0.826117i | \(-0.690545\pi\) |
0.826117 | + | 0.563498i | \(0.190545\pi\) | |||||||
\(548\) | 8.00000 | 0.341743 | ||||||||
\(549\) | 0.757359 | − | 0.757359i | 0.0323233 | − | 0.0323233i | ||||
\(550\) | −4.70711 | − | 4.70711i | −0.200712 | − | 0.200712i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.00000i | 0.0851257i | ||||||||
\(553\) | 23.3137i | 0.991400i | ||||||||
\(554\) | −3.58579 | − | 3.58579i | −0.152345 | − | 0.152345i | ||||
\(555\) | −21.8995 | − | 21.8995i | −0.929582 | − | 0.929582i | ||||
\(556\) | −1.65685 | + | 1.65685i | −0.0702663 | + | 0.0702663i | ||||
\(557\) | −3.51472 | −0.148923 | −0.0744617 | − | 0.997224i | \(-0.523724\pi\) | ||||
−0.0744617 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(558\) | −5.41421 | + | 5.41421i | −0.229202 | + | 0.229202i | ||||
\(559\) | 46.6274i | 1.97213i | ||||||||
\(560\) | −6.82843 | −0.288554 | ||||||||
\(561\) | −1.00000 | − | 4.00000i | −0.0422200 | − | 0.168880i | ||||
\(562\) | −29.6569 | −1.25100 | ||||||||
\(563\) | − | 41.4558i | − | 1.74716i | −0.486685 | − | 0.873578i | \(-0.661794\pi\) | ||
0.486685 | − | 0.873578i | \(-0.338206\pi\) | |||||||
\(564\) | 6.82843 | − | 6.82843i | 0.287529 | − | 0.287529i | ||||
\(565\) | −28.1421 | −1.18395 | ||||||||
\(566\) | 9.65685 | − | 9.65685i | 0.405908 | − | 0.405908i | ||||
\(567\) | −1.41421 | − | 1.41421i | −0.0593914 | − | 0.0593914i | ||||
\(568\) | 11.0711 | + | 11.0711i | 0.464532 | + | 0.464532i | ||||
\(569\) | 29.9411i | 1.25520i | 0.778537 | + | 0.627599i | \(0.215962\pi\) | ||||
−0.778537 | + | 0.627599i | \(0.784038\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | − | 8.00000i | −0.334790 | − | 0.334790i | 0.519612 | − | 0.854402i | \(-0.326076\pi\) |
−0.854402 | + | 0.519612i | \(0.826076\pi\) | |||||||
\(572\) | 4.82843 | + | 4.82843i | 0.201887 | + | 0.201887i | ||||
\(573\) | 18.1421 | − | 18.1421i | 0.757899 | − | 0.757899i | ||||
\(574\) | −8.48528 | −0.354169 | ||||||||
\(575\) | −9.41421 | + | 9.41421i | −0.392600 | + | 0.392600i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | −8.00000 | −0.333044 | −0.166522 | − | 0.986038i | \(-0.553254\pi\) | ||||
−0.166522 | + | 0.986038i | \(0.553254\pi\) | |||||||
\(578\) | −8.00000 | − | 15.0000i | −0.332756 | − | 0.623918i | ||||
\(579\) | −2.10051 | −0.0872940 | ||||||||
\(580\) | 30.9706i | 1.28598i | ||||||||
\(581\) | −4.00000 | + | 4.00000i | −0.165948 | + | 0.165948i | ||||
\(582\) | 10.5858 | 0.438795 | ||||||||
\(583\) | −8.82843 | + | 8.82843i | −0.365636 | + | 0.365636i | ||||
\(584\) | −4.65685 | − | 4.65685i | −0.192702 | − | 0.192702i | ||||
\(585\) | 16.4853 | + | 16.4853i | 0.681582 | + | 0.681582i | ||||
\(586\) | 14.0000i | 0.578335i | ||||||||
\(587\) | − | 29.4558i | − | 1.21577i | −0.794024 | − | 0.607886i | \(-0.792018\pi\) | ||
0.794024 | − | 0.607886i | \(-0.207982\pi\) | |||||||
\(588\) | 2.12132 | + | 2.12132i | 0.0874818 | + | 0.0874818i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.75736 | −0.0722881 | ||||||||
\(592\) | −6.41421 | + | 6.41421i | −0.263623 | + | 0.263623i | ||||
\(593\) | − | 40.2843i | − | 1.65428i | −0.561998 | − | 0.827138i | \(-0.689967\pi\) | ||
0.561998 | − | 0.827138i | \(-0.310033\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −6.82843 | − | 27.3137i | −0.279938 | − | 1.11975i | ||||
\(596\) | 9.31371 | 0.381504 | ||||||||
\(597\) | − | 14.0000i | − | 0.572982i | ||||||
\(598\) | 9.65685 | − | 9.65685i | 0.394898 | − | 0.394898i | ||||
\(599\) | 27.5147 | 1.12422 | 0.562110 | − | 0.827062i | \(-0.309990\pi\) | ||||
0.562110 | + | 0.827062i | \(0.309990\pi\) | |||||||
\(600\) | −4.70711 | + | 4.70711i | −0.192167 | + | 0.192167i | ||||
\(601\) | 7.00000 | + | 7.00000i | 0.285536 | + | 0.285536i | 0.835312 | − | 0.549776i | \(-0.185287\pi\) |
−0.549776 | + | 0.835312i | \(0.685287\pi\) | |||||||
\(602\) | −9.65685 | − | 9.65685i | −0.393584 | − | 0.393584i | ||||
\(603\) | − | 8.48528i | − | 0.345547i | ||||||
\(604\) | 1.17157i | 0.0476706i | ||||||||
\(605\) | −2.41421 | − | 2.41421i | −0.0981517 | − | 0.0981517i | ||||
\(606\) | 8.82843 | + | 8.82843i | 0.358630 | + | 0.358630i | ||||
\(607\) | −11.7574 | + | 11.7574i | −0.477216 | + | 0.477216i | −0.904240 | − | 0.427024i | \(-0.859562\pi\) |
0.427024 | + | 0.904240i | \(0.359562\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.8284 | + | 12.8284i | −0.519834 | + | 0.519834i | ||||
\(610\) | − | 3.65685i | − | 0.148062i | ||||||
\(611\) | −65.9411 | −2.66769 | ||||||||
\(612\) | −4.00000 | + | 1.00000i | −0.161690 | + | 0.0404226i | ||||
\(613\) | −34.2843 | −1.38473 | −0.692364 | − | 0.721548i | \(-0.743431\pi\) | ||||
−0.692364 | + | 0.721548i | \(0.743431\pi\) | |||||||
\(614\) | 1.17157i | 0.0472808i | ||||||||
\(615\) | −10.2426 | + | 10.2426i | −0.413023 | + | 0.413023i | ||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | −3.82843 | + | 3.82843i | −0.154127 | + | 0.154127i | −0.779958 | − | 0.625832i | \(-0.784760\pi\) |
0.625832 | + | 0.779958i | \(0.284760\pi\) | |||||||
\(618\) | −7.65685 | − | 7.65685i | −0.308004 | − | 0.308004i | ||||
\(619\) | −22.3431 | − | 22.3431i | −0.898047 | − | 0.898047i | 0.0972164 | − | 0.995263i | \(-0.469006\pi\) |
−0.995263 | + | 0.0972164i | \(0.969006\pi\) | |||||||
\(620\) | 26.1421i | 1.04989i | ||||||||
\(621\) | 2.00000i | 0.0802572i | ||||||||
\(622\) | 17.8995 | + | 17.8995i | 0.717704 | + | 0.717704i | ||||
\(623\) | 24.9706 | + | 24.9706i | 1.00042 | + | 1.00042i | ||||
\(624\) | 4.82843 | − | 4.82843i | 0.193292 | − | 0.193292i | ||||
\(625\) | 13.9706 | 0.558823 | ||||||||
\(626\) | −21.4853 | + | 21.4853i | −0.858725 | + | 0.858725i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.3137 | 0.531275 | ||||||||
\(629\) | −32.0711 | − | 19.2426i | −1.27876 | − | 0.767254i | ||||
\(630\) | −6.82843 | −0.272051 | ||||||||
\(631\) | 39.1127i | 1.55705i | 0.627612 | + | 0.778526i | \(0.284032\pi\) | ||||
−0.627612 | + | 0.778526i | \(0.715968\pi\) | |||||||
\(632\) | 8.24264 | − | 8.24264i | 0.327875 | − | 0.327875i | ||||
\(633\) | −20.9706 | −0.833505 | ||||||||
\(634\) | −14.8995 | + | 14.8995i | −0.591735 | + | 0.591735i | ||||
\(635\) | −22.1421 | − | 22.1421i | −0.878684 | − | 0.878684i | ||||
\(636\) | 8.82843 | + | 8.82843i | 0.350070 | + | 0.350070i | ||||
\(637\) | − | 20.4853i | − | 0.811656i | ||||||
\(638\) | 9.07107i | 0.359127i | ||||||||
\(639\) | 11.0711 | + | 11.0711i | 0.437965 | + | 0.437965i | ||||
\(640\) | 2.41421 | + | 2.41421i | 0.0954302 | + | 0.0954302i | ||||
\(641\) | 13.6274 | − | 13.6274i | 0.538251 | − | 0.538251i | −0.384764 | − | 0.923015i | \(-0.625717\pi\) |
0.923015 | + | 0.384764i | \(0.125717\pi\) | |||||||
\(642\) | 7.31371 | 0.288649 | ||||||||
\(643\) | 5.65685 | − | 5.65685i | 0.223085 | − | 0.223085i | −0.586711 | − | 0.809796i | \(-0.699578\pi\) |
0.809796 | + | 0.586711i | \(0.199578\pi\) | |||||||
\(644\) | 4.00000i | 0.157622i | ||||||||
\(645\) | −23.3137 | −0.917976 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.6569 | −0.694163 | −0.347081 | − | 0.937835i | \(-0.612827\pi\) | ||||
−0.347081 | + | 0.937835i | \(0.612827\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 45.4558 | 1.78292 | ||||||||
\(651\) | −10.8284 | + | 10.8284i | −0.424400 | + | 0.424400i | ||||
\(652\) | 8.48528 | + | 8.48528i | 0.332309 | + | 0.332309i | ||||
\(653\) | 12.7574 | + | 12.7574i | 0.499234 | + | 0.499234i | 0.911199 | − | 0.411965i | \(-0.135158\pi\) |
−0.411965 | + | 0.911199i | \(0.635158\pi\) | |||||||
\(654\) | − | 0.585786i | − | 0.0229061i | ||||||
\(655\) | − | 5.65685i | − | 0.221032i | ||||||
\(656\) | 3.00000 | + | 3.00000i | 0.117130 | + | 0.117130i | ||||
\(657\) | −4.65685 | − | 4.65685i | −0.181681 | − | 0.181681i | ||||
\(658\) | 13.6569 | − | 13.6569i | 0.532400 | − | 0.532400i | ||||
\(659\) | −10.8284 | −0.421816 | −0.210908 | − | 0.977506i | \(-0.567642\pi\) | ||||
−0.210908 | + | 0.977506i | \(0.567642\pi\) | |||||||
\(660\) | −2.41421 | + | 2.41421i | −0.0939731 | + | 0.0939731i | ||||
\(661\) | 2.14214i | 0.0833194i | 0.999132 | + | 0.0416597i | \(0.0132645\pi\) | ||||
−0.999132 | + | 0.0416597i | \(0.986735\pi\) | |||||||
\(662\) | −4.97056 | −0.193186 | ||||||||
\(663\) | 24.1421 | + | 14.4853i | 0.937603 | + | 0.562562i | ||||
\(664\) | 2.82843 | 0.109764 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.41421 | + | 6.41421i | −0.248546 | + | 0.248546i | ||||
\(667\) | 18.1421 | 0.702466 | ||||||||
\(668\) | −0.928932 | + | 0.928932i | −0.0359415 | + | 0.0359415i | ||||
\(669\) | 6.00000 | + | 6.00000i | 0.231973 | + | 0.231973i | ||||
\(670\) | −20.4853 | − | 20.4853i | −0.791415 | − | 0.791415i | ||||
\(671\) | − | 1.07107i | − | 0.0413481i | ||||||
\(672\) | 2.00000i | 0.0771517i | ||||||||
\(673\) | 4.51472 | + | 4.51472i | 0.174030 | + | 0.174030i | 0.788747 | − | 0.614718i | \(-0.210730\pi\) |
−0.614718 | + | 0.788747i | \(0.710730\pi\) | |||||||
\(674\) | 19.9706 | + | 19.9706i | 0.769237 | + | 0.769237i | ||||
\(675\) | −4.70711 | + | 4.70711i | −0.181177 | + | 0.181177i | ||||
\(676\) | −33.6274 | −1.29336 | ||||||||
\(677\) | 23.7279 | − | 23.7279i | 0.911938 | − | 0.911938i | −0.0844865 | − | 0.996425i | \(-0.526925\pi\) |
0.996425 | + | 0.0844865i | \(0.0269250\pi\) | |||||||
\(678\) | 8.24264i | 0.316557i | ||||||||
\(679\) | 21.1716 | 0.812490 | ||||||||
\(680\) | −7.24264 | + | 12.0711i | −0.277743 | + | 0.462904i | ||||
\(681\) | 25.6569 | 0.983173 | ||||||||
\(682\) | 7.65685i | 0.293196i | ||||||||
\(683\) | −13.1716 | + | 13.1716i | −0.503996 | + | 0.503996i | −0.912677 | − | 0.408681i | \(-0.865989\pi\) |
0.408681 | + | 0.912677i | \(0.365989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3137 | − | 19.3137i | 0.737939 | − | 0.737939i | ||||
\(686\) | 14.1421 | + | 14.1421i | 0.539949 | + | 0.539949i | ||||
\(687\) | −12.7279 | − | 12.7279i | −0.485601 | − | 0.485601i | ||||
\(688\) | 6.82843i | 0.260331i | ||||||||
\(689\) | − | 85.2548i | − | 3.24795i | ||||||
\(690\) | 4.82843 | + | 4.82843i | 0.183815 | + | 0.183815i | ||||
\(691\) | 28.9706 | + | 28.9706i | 1.10209 | + | 1.10209i | 0.994158 | + | 0.107934i | \(0.0344235\pi\) |
0.107934 | + | 0.994158i | \(0.465576\pi\) | |||||||
\(692\) | −11.2426 | + | 11.2426i | −0.427381 | + | 0.427381i | ||||
\(693\) | −2.00000 | −0.0759737 | ||||||||
\(694\) | 18.1421 | − | 18.1421i | 0.688666 | − | 0.688666i | ||||
\(695\) | 8.00000i | 0.303457i | ||||||||
\(696\) | 9.07107 | 0.343838 | ||||||||
\(697\) | −9.00000 | + | 15.0000i | −0.340899 | + | 0.568166i | ||||
\(698\) | −4.48528 | −0.169770 | ||||||||
\(699\) | − | 19.0711i | − | 0.721334i | ||||||
\(700\) | −9.41421 | + | 9.41421i | −0.355824 | + | 0.355824i | ||||
\(701\) | −13.4558 | −0.508220 | −0.254110 | − | 0.967175i | \(-0.581783\pi\) | ||||
−0.254110 | + | 0.967175i | \(0.581783\pi\) | |||||||
\(702\) | 4.82843 | − | 4.82843i | 0.182237 | − | 0.182237i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.707107 | + | 0.707107i | 0.0266501 | + | 0.0266501i | ||||
\(705\) | − | 32.9706i | − | 1.24174i | ||||||
\(706\) | 16.6274i | 0.625781i | ||||||||
\(707\) | 17.6569 | + | 17.6569i | 0.664054 | + | 0.664054i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.7279 | + | 23.7279i | −0.891121 | + | 0.891121i | −0.994629 | − | 0.103508i | \(-0.966993\pi\) |
0.103508 | + | 0.994629i | \(0.466993\pi\) | |||||||
\(710\) | 53.4558 | 2.00616 | ||||||||
\(711\) | 8.24264 | − | 8.24264i | 0.309123 | − | 0.309123i | ||||
\(712\) | − | 17.6569i | − | 0.661719i | ||||||
\(713\) | 15.3137 | 0.573503 | ||||||||
\(714\) | −8.00000 | + | 2.00000i | −0.299392 | + | 0.0748481i | ||||
\(715\) | 23.3137 | 0.871883 | ||||||||
\(716\) | − | 18.1421i | − | 0.678003i | ||||||
\(717\) | −2.00000 | + | 2.00000i | −0.0746914 | + | 0.0746914i | ||||
\(718\) | 16.0000 | 0.597115 | ||||||||
\(719\) | −10.5858 | + | 10.5858i | −0.394783 | + | 0.394783i | −0.876388 | − | 0.481605i | \(-0.840054\pi\) |
0.481605 | + | 0.876388i | \(0.340054\pi\) | |||||||
\(720\) | 2.41421 | + | 2.41421i | 0.0899724 | + | 0.0899724i | ||||
\(721\) | −15.3137 | − | 15.3137i | −0.570312 | − | 0.570312i | ||||
\(722\) | 19.0000i | 0.707107i | ||||||||
\(723\) | 7.75736i | 0.288499i | ||||||||
\(724\) | −1.58579 | − | 1.58579i | −0.0589353 | − | 0.0589353i | ||||
\(725\) | 42.6985 | + | 42.6985i | 1.58578 | + | 1.58578i | ||||
\(726\) | −0.707107 | + | 0.707107i | −0.0262432 | + | 0.0262432i | ||||
\(727\) | −20.6863 | −0.767212 | −0.383606 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383606 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(728\) | 9.65685 | − | 9.65685i | 0.357907 | − | 0.357907i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −22.4853 | −0.832218 | ||||||||
\(731\) | −27.3137 | + | 6.82843i | −1.01023 | + | 0.252559i | ||||
\(732\) | −1.07107 | −0.0395878 | ||||||||
\(733\) | 39.7990i | 1.47001i | 0.678062 | + | 0.735005i | \(0.262820\pi\) | ||||
−0.678062 | + | 0.735005i | \(0.737180\pi\) | |||||||
\(734\) | 3.75736 | − | 3.75736i | 0.138687 | − | 0.138687i | ||||
\(735\) | 10.2426 | 0.377805 | ||||||||
\(736\) | 1.41421 | − | 1.41421i | 0.0521286 | − | 0.0521286i | ||||
\(737\) | −6.00000 | − | 6.00000i | −0.221013 | − | 0.221013i | ||||
\(738\) | 3.00000 | + | 3.00000i | 0.110432 | + | 0.110432i | ||||
\(739\) | − | 51.3137i | − | 1.88761i | −0.330510 | − | 0.943803i | \(-0.607221\pi\) | ||
0.330510 | − | 0.943803i | \(-0.392779\pi\) | |||||||
\(740\) | 30.9706i | 1.13850i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.6569 | + | 17.6569i | 0.648204 | + | 0.648204i | ||||
\(743\) | −28.0416 | + | 28.0416i | −1.02875 | + | 1.02875i | −0.0291733 | + | 0.999574i | \(0.509287\pi\) |
−0.999574 | + | 0.0291733i | \(0.990713\pi\) | |||||||
\(744\) | 7.65685 | 0.280714 | ||||||||
\(745\) | 22.4853 | − | 22.4853i | 0.823797 | − | 0.823797i | ||||
\(746\) | 22.8284i | 0.835808i | ||||||||
\(747\) | 2.82843 | 0.103487 | ||||||||
\(748\) | −2.12132 | + | 3.53553i | −0.0775632 | + | 0.129272i | ||||
\(749\) | 14.6274 | 0.534474 | ||||||||
\(750\) | 5.65685i | 0.206559i | ||||||||
\(751\) | 2.58579 | − | 2.58579i | 0.0943567 | − | 0.0943567i | −0.658353 | − | 0.752709i | \(-0.728746\pi\) |
0.752709 | + | 0.658353i | \(0.228746\pi\) | |||||||
\(752\) | −9.65685 | −0.352149 | ||||||||
\(753\) | −12.8284 | + | 12.8284i | −0.467494 | + | 0.467494i | ||||
\(754\) | −43.7990 | − | 43.7990i | −1.59507 | − | 1.59507i | ||||
\(755\) | 2.82843 | + | 2.82843i | 0.102937 | + | 0.102937i | ||||
\(756\) | 2.00000i | 0.0727393i | ||||||||
\(757\) | − | 13.3137i | − | 0.483895i | −0.970289 | − | 0.241947i | \(-0.922214\pi\) | ||
0.970289 | − | 0.241947i | \(-0.0777862\pi\) | |||||||
\(758\) | 13.6569 | + | 13.6569i | 0.496039 | + | 0.496039i | ||||
\(759\) | 1.41421 | + | 1.41421i | 0.0513327 | + | 0.0513327i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0000 | 1.01500 | 0.507500 | − | 0.861652i | \(-0.330570\pi\) | ||||
0.507500 | + | 0.861652i | \(0.330570\pi\) | |||||||
\(762\) | −6.48528 | + | 6.48528i | −0.234937 | + | 0.234937i | ||||
\(763\) | − | 1.17157i | − | 0.0424138i | ||||||
\(764\) | −25.6569 | −0.928232 | ||||||||
\(765\) | −7.24264 | + | 12.0711i | −0.261858 | + | 0.436430i | ||||
\(766\) | −25.6569 | −0.927020 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | 3.02944 | 0.109244 | 0.0546222 | − | 0.998507i | \(-0.482605\pi\) | ||||
0.0546222 | + | 0.998507i | \(0.482605\pi\) | |||||||
\(770\) | −4.82843 | + | 4.82843i | −0.174004 | + | 0.174004i | ||||
\(771\) | 12.2426 | + | 12.2426i | 0.440908 | + | 0.440908i | ||||
\(772\) | 1.48528 | + | 1.48528i | 0.0534564 | + | 0.0534564i | ||||
\(773\) | − | 18.2843i | − | 0.657640i | −0.944393 | − | 0.328820i | \(-0.893349\pi\) | ||
0.944393 | − | 0.328820i | \(-0.106651\pi\) | |||||||
\(774\) | 6.82843i | 0.245443i | ||||||||
\(775\) | 36.0416 | + | 36.0416i | 1.29465 | + | 1.29465i | ||||
\(776\) | −7.48528 | − | 7.48528i | −0.268706 | − | 0.268706i | ||||
\(777\) | −12.8284 | + | 12.8284i | −0.460217 | + | 0.460217i | ||||
\(778\) | 12.3431 | 0.442523 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | − | 23.3137i | − | 0.834765i | ||||||
\(781\) | 15.6569 | 0.560246 | ||||||||
\(782\) | 7.07107 | + | 4.24264i | 0.252861 | + | 0.151717i | ||||
\(783\) | 9.07107 | 0.324174 | ||||||||
\(784\) | − | 3.00000i | − | 0.107143i | ||||||
\(785\) | 32.1421 | − | 32.1421i | 1.14720 | − | 1.14720i | ||||
\(786\) | −1.65685 | −0.0590980 | ||||||||
\(787\) | −19.3137 | + | 19.3137i | −0.688459 | + | 0.688459i | −0.961891 | − | 0.273432i | \(-0.911841\pi\) |
0.273432 | + | 0.961891i | \(0.411841\pi\) | |||||||
\(788\) | 1.24264 | + | 1.24264i | 0.0442672 | + | 0.0442672i | ||||
\(789\) | −11.6569 | − | 11.6569i | −0.414995 | − | 0.414995i | ||||
\(790\) | − | 39.7990i | − | 1.41598i | ||||||
\(791\) | 16.4853i | 0.586149i | ||||||||
\(792\) | 0.707107 | + | 0.707107i | 0.0251259 | + | 0.0251259i | ||||
\(793\) | 5.17157 | + | 5.17157i | 0.183648 | + | 0.183648i | ||||
\(794\) | 3.10051 | − | 3.10051i | 0.110033 | − | 0.110033i | ||||
\(795\) | 42.6274 | 1.51184 | ||||||||
\(796\) | −9.89949 | + | 9.89949i | −0.350878 | + | 0.350878i | ||||
\(797\) | − | 11.5147i | − | 0.407872i | −0.978984 | − | 0.203936i | \(-0.934627\pi\) | ||
0.978984 | − | 0.203936i | \(-0.0653735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.65685 | − | 38.6274i | −0.341635 | − | 1.36654i | ||||
\(800\) | 6.65685 | 0.235355 | ||||||||
\(801\) | − | 17.6569i | − | 0.623874i | ||||||
\(802\) | 18.3137 | − | 18.3137i | 0.646680 | − | 0.646680i | ||||
\(803\) | −6.58579 | −0.232407 | ||||||||
\(804\) | −6.00000 | + | 6.00000i | −0.211604 | + | 0.211604i | ||||
\(805\) | 9.65685 | + | 9.65685i | 0.340359 | + | 0.340359i | ||||
\(806\) | −36.9706 | − | 36.9706i | −1.30223 | − | 1.30223i | ||||
\(807\) | 0.100505i | 0.00353795i | ||||||||
\(808\) | − | 12.4853i | − | 0.439231i | ||||||
\(809\) | −11.9706 | − | 11.9706i | −0.420863 | − | 0.420863i | 0.464638 | − | 0.885501i | \(-0.346184\pi\) |
−0.885501 | + | 0.464638i | \(0.846184\pi\) | |||||||
\(810\) | 2.41421 | + | 2.41421i | 0.0848268 | + | 0.0848268i | ||||
\(811\) | −12.0000 | + | 12.0000i | −0.421377 | + | 0.421377i | −0.885678 | − | 0.464301i | \(-0.846306\pi\) |
0.464301 | + | 0.885678i | \(0.346306\pi\) | |||||||
\(812\) | 18.1421 | 0.636664 | ||||||||
\(813\) | −4.82843 | + | 4.82843i | −0.169340 | + | 0.169340i | ||||
\(814\) | 9.07107i | 0.317941i | ||||||||
\(815\) | 40.9706 | 1.43514 | ||||||||
\(816\) | 3.53553 | + | 2.12132i | 0.123768 | + | 0.0742611i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 9.31371i | − | 0.325646i | ||||||
\(819\) | 9.65685 | − | 9.65685i | 0.337438 | − | 0.337438i | ||||
\(820\) | 14.4853 | 0.505848 | ||||||||
\(821\) | 32.4142 | − | 32.4142i | 1.13126 | − | 1.13126i | 0.141297 | − | 0.989967i | \(-0.454873\pi\) |
0.989967 | − | 0.141297i | \(-0.0451271\pi\) | |||||||
\(822\) | −5.65685 | − | 5.65685i | −0.197305 | − | 0.197305i | ||||
\(823\) | −12.7279 | − | 12.7279i | −0.443667 | − | 0.443667i | 0.449575 | − | 0.893243i | \(-0.351575\pi\) |
−0.893243 | + | 0.449575i | \(0.851575\pi\) | |||||||
\(824\) | 10.8284i | 0.377226i | ||||||||
\(825\) | 6.65685i | 0.231762i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.85786 | + | 9.85786i | 0.342792 | + | 0.342792i | 0.857416 | − | 0.514624i | \(-0.172069\pi\) |
−0.514624 | + | 0.857416i | \(0.672069\pi\) | |||||||
\(828\) | 1.41421 | − | 1.41421i | 0.0491473 | − | 0.0491473i | ||||
\(829\) | 1.31371 | 0.0456270 | 0.0228135 | − | 0.999740i | \(-0.492738\pi\) | ||||
0.0228135 | + | 0.999740i | \(0.492738\pi\) | |||||||
\(830\) | 6.82843 | − | 6.82843i | 0.237018 | − | 0.237018i | ||||
\(831\) | 5.07107i | 0.175913i | ||||||||
\(832\) | −6.82843 | −0.236733 | ||||||||
\(833\) | 12.0000 | − | 3.00000i | 0.415775 | − | 0.103944i | ||||
\(834\) | 2.34315 | 0.0811365 | ||||||||
\(835\) | 4.48528i | 0.155220i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.65685 | 0.264660 | ||||||||
\(838\) | 0.686292 | − | 0.686292i | 0.0237075 | − | 0.0237075i | ||||
\(839\) | −19.0711 | − | 19.0711i | −0.658406 | − | 0.658406i | 0.296597 | − | 0.955003i | \(-0.404148\pi\) |
−0.955003 | + | 0.296597i | \(0.904148\pi\) | |||||||
\(840\) | 4.82843 | + | 4.82843i | 0.166597 | + | 0.166597i | ||||
\(841\) | − | 53.2843i | − | 1.83739i | ||||||
\(842\) | 26.1421i | 0.900917i | ||||||||
\(843\) | 20.9706 | + | 20.9706i | 0.722265 | + | 0.722265i | ||||
\(844\) | 14.8284 | + | 14.8284i | 0.510416 | + | 0.510416i | ||||
\(845\) | −81.1838 | + | 81.1838i | −2.79281 | + | 2.79281i | ||||
\(846\) | −9.65685 | −0.332009 | ||||||||
\(847\) | −1.41421 | + | 1.41421i | −0.0485930 | + | 0.0485930i | ||||
\(848\) | − | 12.4853i | − | 0.428746i | ||||||
\(849\) | −13.6569 | −0.468702 | ||||||||
\(850\) | 6.65685 | + | 26.6274i | 0.228328 | + | 0.913313i | ||||
\(851\) | 18.1421 | 0.621904 | ||||||||
\(852\) | − | 15.6569i | − | 0.536395i | ||||||
\(853\) | −22.0711 | + | 22.0711i | −0.755699 | + | 0.755699i | −0.975536 | − | 0.219838i | \(-0.929447\pi\) |
0.219838 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(854\) | −2.14214 | −0.0733024 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.17157 | − | 5.17157i | −0.176761 | − | 0.176761i | ||||
\(857\) | 7.00000 | + | 7.00000i | 0.239115 | + | 0.239115i | 0.816484 | − | 0.577368i | \(-0.195920\pi\) |
−0.577368 | + | 0.816484i | \(0.695920\pi\) | |||||||
\(858\) | − | 6.82843i | − | 0.233119i | ||||||
\(859\) | 4.00000i | 0.136478i | 0.997669 | + | 0.0682391i | \(0.0217381\pi\) | ||||
−0.997669 | + | 0.0682391i | \(0.978262\pi\) | |||||||
\(860\) | 16.4853 | + | 16.4853i | 0.562143 | + | 0.562143i | ||||
\(861\) | 6.00000 | + | 6.00000i | 0.204479 | + | 0.204479i | ||||
\(862\) | −9.41421 | + | 9.41421i | −0.320649 | + | 0.320649i | ||||
\(863\) | 44.4853 | 1.51430 | 0.757148 | − | 0.653243i | \(-0.226592\pi\) | ||||
0.757148 | + | 0.653243i | \(0.226592\pi\) | |||||||
\(864\) | 0.707107 | − | 0.707107i | 0.0240563 | − | 0.0240563i | ||||
\(865\) | 54.2843i | 1.84572i | ||||||||
\(866\) | −2.00000 | −0.0679628 | ||||||||
\(867\) | −4.94975 | + | 16.2635i | −0.168102 | + | 0.552336i | ||||
\(868\) | 15.3137 | 0.519781 | ||||||||
\(869\) | − | 11.6569i | − | 0.395432i | ||||||
\(870\) | 21.8995 | − | 21.8995i | 0.742462 | − | 0.742462i | ||||
\(871\) | 57.9411 | 1.96326 | ||||||||
\(872\) | −0.414214 | + | 0.414214i | −0.0140270 | + | 0.0140270i | ||||
\(873\) | −7.48528 | − | 7.48528i | −0.253338 | − | 0.253338i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137i | 0.382473i | ||||||||
\(876\) | 6.58579i | 0.222513i | ||||||||
\(877\) | 12.5563 | + | 12.5563i | 0.423998 | + | 0.423998i | 0.886578 | − | 0.462580i | \(-0.153076\pi\) |
−0.462580 | + | 0.886578i | \(0.653076\pi\) | |||||||
\(878\) | −26.3848 | − | 26.3848i | −0.890443 | − | 0.890443i | ||||
\(879\) | 9.89949 | − | 9.89949i | 0.333902 | − | 0.333902i | ||||
\(880\) | 3.41421 | 0.115093 | ||||||||
\(881\) | −34.1127 | + | 34.1127i | −1.14929 | + | 1.14929i | −0.162593 | + | 0.986693i | \(0.551986\pi\) |
−0.986693 | + | 0.162593i | \(0.948014\pi\) | |||||||
\(882\) | − | 3.00000i | − | 0.101015i | ||||||
\(883\) | −2.82843 | −0.0951842 | −0.0475921 | − | 0.998867i | \(-0.515155\pi\) | ||||
−0.0475921 | + | 0.998867i | \(0.515155\pi\) | |||||||
\(884\) | −6.82843 | − | 27.3137i | −0.229665 | − | 0.918659i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.79899i | 0.262012i | ||||||||
\(887\) | 22.3848 | − | 22.3848i | 0.751607 | − | 0.751607i | −0.223172 | − | 0.974779i | \(-0.571641\pi\) |
0.974779 | + | 0.223172i | \(0.0716411\pi\) | |||||||
\(888\) | 9.07107 | 0.304405 | ||||||||
\(889\) | −12.9706 | + | 12.9706i | −0.435019 | + | 0.435019i | ||||
\(890\) | −42.6274 | − | 42.6274i | −1.42887 | − | 1.42887i | ||||
\(891\) | 0.707107 | + | 0.707107i | 0.0236890 | + | 0.0236890i | ||||
\(892\) | − | 8.48528i | − | 0.284108i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −6.58579 | − | 6.58579i | −0.220262 | − | 0.220262i | ||||
\(895\) | −43.7990 | − | 43.7990i | −1.46404 | − | 1.46404i | ||||
\(896\) | 1.41421 | − | 1.41421i | 0.0472456 | − | 0.0472456i | ||||
\(897\) | −13.6569 | −0.455989 | ||||||||
\(898\) | −16.6569 | + | 16.6569i | −0.555846 | + | 0.555846i | ||||
\(899\) | − | 69.4558i | − | 2.31648i | ||||||
\(900\) | 6.65685 | 0.221895 | ||||||||
\(901\) | 49.9411 | − | 12.4853i | 1.66378 | − | 0.415945i | ||||
\(902\) | 4.24264 | 0.141264 | ||||||||
\(903\) | 13.6569i | 0.454472i | ||||||||
\(904\) | 5.82843 | − | 5.82843i | 0.193851 | − | 0.193851i | ||||
\(905\) | −7.65685 | −0.254522 | ||||||||
\(906\) | 0.828427 | − | 0.828427i | 0.0275226 | − | 0.0275226i | ||||
\(907\) | 36.4853 | + | 36.4853i | 1.21147 | + | 1.21147i | 0.970542 | + | 0.240932i | \(0.0774530\pi\) |
0.240932 | + | 0.970542i | \(0.422547\pi\) | |||||||
\(908\) | −18.1421 | − | 18.1421i | −0.602068 | − | 0.602068i | ||||
\(909\) | − | 12.4853i | − | 0.414111i | ||||||
\(910\) | − | 46.6274i | − | 1.54568i | ||||||
\(911\) | −28.0416 | − | 28.0416i | −0.929061 | − | 0.929061i | 0.0685846 | − | 0.997645i | \(-0.478152\pi\) |
−0.997645 | + | 0.0685846i | \(0.978152\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00000 | − | 2.00000i | 0.0661903 | − | 0.0661903i | ||||
\(914\) | 2.68629 | 0.0888546 | ||||||||
\(915\) | −2.58579 | + | 2.58579i | −0.0854835 | + | 0.0854835i | ||||
\(916\) | 18.0000i | 0.594737i | ||||||||
\(917\) | −3.31371 | −0.109428 | ||||||||
\(918\) | 3.53553 | + | 2.12132i | 0.116690 | + | 0.0700140i | ||||
\(919\) | −36.0833 | −1.19028 | −0.595138 | − | 0.803623i | \(-0.702903\pi\) | ||||
−0.595138 | + | 0.803623i | \(0.702903\pi\) | |||||||
\(920\) | − | 6.82843i | − | 0.225127i | ||||||
\(921\) | 0.828427 | − | 0.828427i | 0.0272976 | − | 0.0272976i | ||||
\(922\) | 4.48528 | 0.147715 | ||||||||
\(923\) | −75.5980 | + | 75.5980i | −2.48834 | + | 2.48834i | ||||
\(924\) | 1.41421 | + | 1.41421i | 0.0465242 | + | 0.0465242i | ||||
\(925\) | 42.6985 | + | 42.6985i | 1.40392 | + | 1.40392i | ||||
\(926\) | 2.82843i | 0.0929479i | ||||||||
\(927\) | 10.8284i | 0.355652i | ||||||||
\(928\) | −6.41421 | − | 6.41421i | −0.210557 | − | 0.210557i | ||||
\(929\) | 37.2843 | + | 37.2843i | 1.22326 | + | 1.22326i | 0.966467 | + | 0.256790i | \(0.0826649\pi\) |
0.256790 | + | 0.966467i | \(0.417335\pi\) | |||||||
\(930\) | 18.4853 | − | 18.4853i | 0.606156 | − | 0.606156i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.4853 | + | 13.4853i | −0.441725 | + | 0.441725i | ||||
\(933\) | − | 25.3137i | − | 0.828734i | ||||||
\(934\) | 30.8284 | 1.00874 | ||||||||
\(935\) | 3.41421 | + | 13.6569i | 0.111657 | + | 0.446627i | ||||
\(936\) | −6.82843 | −0.223194 | ||||||||
\(937\) | 43.3137i | 1.41500i | 0.706715 | + | 0.707499i | \(0.250176\pi\) | ||||
−0.706715 | + | 0.707499i | \(0.749824\pi\) | |||||||
\(938\) | −12.0000 | + | 12.0000i | −0.391814 | + | 0.391814i | ||||
\(939\) | 30.3848 | 0.991570 | ||||||||
\(940\) | −23.3137 | + | 23.3137i | −0.760409 | + | 0.760409i | ||||
\(941\) | 6.07107 | + | 6.07107i | 0.197911 | + | 0.197911i | 0.799104 | − | 0.601193i | \(-0.205308\pi\) |
−0.601193 | + | 0.799104i | \(0.705308\pi\) | |||||||
\(942\) | −9.41421 | − | 9.41421i | −0.306732 | − | 0.306732i | ||||
\(943\) | − | 8.48528i | − | 0.276319i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.82843 | + | 4.82843i | 0.157069 | + | 0.157069i | ||||
\(946\) | 4.82843 | + | 4.82843i | 0.156986 | + | 0.156986i | ||||
\(947\) | −32.9706 | + | 32.9706i | −1.07140 | + | 1.07140i | −0.0741524 | + | 0.997247i | \(0.523625\pi\) |
−0.997247 | + | 0.0741524i | \(0.976375\pi\) | |||||||
\(948\) | −11.6569 | −0.378597 | ||||||||
\(949\) | 31.7990 | − | 31.7990i | 1.03224 | − | 1.03224i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.0711 | 0.683276 | ||||||||
\(952\) | 7.07107 | + | 4.24264i | 0.229175 | + | 0.137505i | ||||
\(953\) | −8.00000 | −0.259145 | −0.129573 | − | 0.991570i | \(-0.541361\pi\) | ||||
−0.129573 | + | 0.991570i | \(0.541361\pi\) | |||||||
\(954\) | − | 12.4853i | − | 0.404226i | ||||||
\(955\) | −61.9411 | + | 61.9411i | −2.00437 | + | 2.00437i | ||||
\(956\) | 2.82843 | 0.0914779 | ||||||||
\(957\) | 6.41421 | − | 6.41421i | 0.207342 | − | 0.207342i | ||||
\(958\) | 16.7279 | + | 16.7279i | 0.540455 | + | 0.540455i | ||||
\(959\) | −11.3137 | − | 11.3137i | −0.365339 | − | 0.365339i | ||||
\(960\) | − | 3.41421i | − | 0.110193i | ||||||
\(961\) | − | 27.6274i | − | 0.891207i | ||||||
\(962\) | −43.7990 | − | 43.7990i | −1.41214 | − | 1.41214i | ||||
\(963\) | −5.17157 | − | 5.17157i | −0.166652 | − | 0.166652i | ||||
\(964\) | 5.48528 | − | 5.48528i | 0.176669 | − | 0.176669i | ||||
\(965\) | 7.17157 | 0.230861 | ||||||||
\(966\) | 2.82843 | − | 2.82843i | 0.0910032 | − | 0.0910032i | ||||
\(967\) | 23.3137i | 0.749718i | 0.927082 | + | 0.374859i | \(0.122309\pi\) | ||||
−0.927082 | + | 0.374859i | \(0.877691\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −36.1421 | −1.16045 | ||||||||
\(971\) | − | 8.97056i | − | 0.287879i | −0.989586 | − | 0.143940i | \(-0.954023\pi\) | ||
0.989586 | − | 0.143940i | \(-0.0459771\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 4.68629 | 0.150236 | ||||||||
\(974\) | −20.2426 | + | 20.2426i | −0.648616 | + | 0.648616i | ||||
\(975\) | −32.1421 | − | 32.1421i | −1.02937 | − | 1.02937i | ||||
\(976\) | 0.757359 | + | 0.757359i | 0.0242425 | + | 0.0242425i | ||||
\(977\) | 22.6274i | 0.723915i | 0.932195 | + | 0.361958i | \(0.117891\pi\) | ||||
−0.932195 | + | 0.361958i | \(0.882109\pi\) | |||||||
\(978\) | − | 12.0000i | − | 0.383718i | ||||||
\(979\) | −12.4853 | − | 12.4853i | −0.399031 | − | 0.399031i | ||||
\(980\) | −7.24264 | − | 7.24264i | −0.231358 | − | 0.231358i | ||||
\(981\) | −0.414214 | + | 0.414214i | −0.0132248 | + | 0.0132248i | ||||
\(982\) | 25.6569 | 0.818743 | ||||||||
\(983\) | 8.92893 | − | 8.92893i | 0.284789 | − | 0.284789i | −0.550227 | − | 0.835015i | \(-0.685459\pi\) |
0.835015 | + | 0.550227i | \(0.185459\pi\) | |||||||
\(984\) | − | 4.24264i | − | 0.135250i | ||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | 19.2426 | − | 32.0711i | 0.612811 | − | 1.02135i | ||||
\(987\) | −19.3137 | −0.614762 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.65685 | − | 9.65685i | 0.307070 | − | 0.307070i | ||||
\(990\) | 3.41421 | 0.108511 | ||||||||
\(991\) | 37.4142 | − | 37.4142i | 1.18850 | − | 1.18850i | 0.211020 | − | 0.977482i | \(-0.432322\pi\) |
0.977482 | − | 0.211020i | \(-0.0676785\pi\) | |||||||
\(992\) | −5.41421 | − | 5.41421i | −0.171901 | − | 0.171901i | ||||
\(993\) | 3.51472 | + | 3.51472i | 0.111536 | + | 0.111536i | ||||
\(994\) | − | 31.3137i | − | 0.993211i | ||||||
\(995\) | 47.7990i | 1.51533i | ||||||||
\(996\) | −2.00000 | − | 2.00000i | −0.0633724 | − | 0.0633724i | ||||
\(997\) | 38.5563 | + | 38.5563i | 1.22109 | + | 1.22109i | 0.967244 | + | 0.253848i | \(0.0816962\pi\) |
0.253848 | + | 0.967244i | \(0.418304\pi\) | |||||||
\(998\) | 7.51472 | − | 7.51472i | 0.237874 | − | 0.237874i | ||||
\(999\) | 9.07107 | 0.286996 |
(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 | 1122.2.l.a.463.2 | ✓ | 4 | |
17.13 | even | 4 | inner | 1122.2.l.a.727.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1122.2.l.a.463.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1122.2.l.a.727.2 | yes | 4 | 17.13 | even | 4 | inner |