Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(161,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("390.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.p (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: | \(3.11416567883\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.161 |
Dual form | 390.2.p.e.281.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0.292893 | + | 1.70711i | 0.169102 | + | 0.985599i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | −1.00000 | + | 1.41421i | −0.408248 | + | 0.577350i | ||||
\(7\) | 2.00000 | + | 2.00000i | 0.755929 | + | 0.755929i | 0.975579 | − | 0.219650i | \(-0.0704915\pi\) |
−0.219650 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | −2.00000 | + | 2.00000i | −0.603023 | + | 0.603023i | −0.941113 | − | 0.338091i | \(-0.890219\pi\) |
0.338091 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(12\) | −1.70711 | + | 0.292893i | −0.492799 | + | 0.0845510i | ||||
\(13\) | 3.53553 | − | 0.707107i | 0.980581 | − | 0.196116i | ||||
\(14\) | 2.82843i | 0.755929i | ||||||||
\(15\) | 1.00000 | − | 1.41421i | 0.258199 | − | 0.365148i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.82843 | −1.17107 | −0.585533 | − | 0.810649i | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810649i | \(0.699115\pi\) | |||||||
\(18\) | −2.70711 | − | 1.29289i | −0.638071 | − | 0.304738i | ||||
\(19\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | −2.82843 | + | 4.00000i | −0.617213 | + | 0.872872i | ||||
\(22\) | −2.82843 | −0.603023 | ||||||||
\(23\) | 6.82843 | 1.42383 | 0.711913 | − | 0.702268i | \(-0.247829\pi\) | ||||
0.711913 | + | 0.702268i | \(0.247829\pi\) | |||||||
\(24\) | −1.41421 | − | 1.00000i | −0.288675 | − | 0.204124i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 3.00000 | + | 2.00000i | 0.588348 | + | 0.392232i | ||||
\(27\) | −2.53553 | − | 4.53553i | −0.487964 | − | 0.872864i | ||||
\(28\) | −2.00000 | + | 2.00000i | −0.377964 | + | 0.377964i | ||||
\(29\) | 3.65685i | 0.679061i | 0.940595 | + | 0.339530i | \(0.110268\pi\) | ||||
−0.940595 | + | 0.339530i | \(0.889732\pi\) | |||||||
\(30\) | 1.70711 | − | 0.292893i | 0.311674 | − | 0.0534747i | ||||
\(31\) | 4.41421 | − | 4.41421i | 0.792816 | − | 0.792816i | −0.189135 | − | 0.981951i | \(-0.560568\pi\) |
0.981951 | + | 0.189135i | \(0.0605684\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −4.00000 | − | 2.82843i | −0.696311 | − | 0.492366i | ||||
\(34\) | −3.41421 | − | 3.41421i | −0.585533 | − | 0.585533i | ||||
\(35\) | − | 2.82843i | − | 0.478091i | ||||||
\(36\) | −1.00000 | − | 2.82843i | −0.166667 | − | 0.471405i | ||||
\(37\) | −4.00000 | − | 4.00000i | −0.657596 | − | 0.657596i | 0.297215 | − | 0.954811i | \(-0.403942\pi\) |
−0.954811 | + | 0.297215i | \(0.903942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.24264 | + | 5.82843i | 0.359110 | + | 0.933295i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.17157 | + | 2.17157i | 0.339143 | + | 0.339143i | 0.856045 | − | 0.516902i | \(-0.172915\pi\) |
−0.516902 | + | 0.856045i | \(0.672915\pi\) | |||||||
\(42\) | −4.82843 | + | 0.828427i | −0.745042 | + | 0.127829i | ||||
\(43\) | 5.07107i | 0.773331i | 0.922220 | + | 0.386665i | \(0.126373\pi\) | ||||
−0.922220 | + | 0.386665i | \(0.873627\pi\) | |||||||
\(44\) | −2.00000 | − | 2.00000i | −0.301511 | − | 0.301511i | ||||
\(45\) | 2.70711 | + | 1.29289i | 0.403552 | + | 0.192733i | ||||
\(46\) | 4.82843 | + | 4.82843i | 0.711913 | + | 0.711913i | ||||
\(47\) | 2.00000 | − | 2.00000i | 0.291730 | − | 0.291730i | −0.546033 | − | 0.837763i | \(-0.683863\pi\) |
0.837763 | + | 0.546033i | \(0.183863\pi\) | |||||||
\(48\) | −0.292893 | − | 1.70711i | −0.0422755 | − | 0.246400i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −0.707107 | + | 0.707107i | −0.100000 | + | 0.100000i | ||||
\(51\) | −1.41421 | − | 8.24264i | −0.198030 | − | 1.15420i | ||||
\(52\) | 0.707107 | + | 3.53553i | 0.0980581 | + | 0.490290i | ||||
\(53\) | − | 9.41421i | − | 1.29314i | −0.762854 | − | 0.646571i | \(-0.776202\pi\) | ||
0.762854 | − | 0.646571i | \(-0.223798\pi\) | |||||||
\(54\) | 1.41421 | − | 5.00000i | 0.192450 | − | 0.680414i | ||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | −2.82843 | −0.377964 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.58579 | + | 2.58579i | −0.339530 | + | 0.339530i | ||||
\(59\) | 4.00000 | − | 4.00000i | 0.520756 | − | 0.520756i | −0.397044 | − | 0.917800i | \(-0.629964\pi\) |
0.917800 | + | 0.397044i | \(0.129964\pi\) | |||||||
\(60\) | 1.41421 | + | 1.00000i | 0.182574 | + | 0.129099i | ||||
\(61\) | 12.8284 | 1.64251 | 0.821256 | − | 0.570560i | \(-0.193274\pi\) | ||||
0.821256 | + | 0.570560i | \(0.193274\pi\) | |||||||
\(62\) | 6.24264 | 0.792816 | ||||||||
\(63\) | −7.65685 | − | 3.65685i | −0.964673 | − | 0.460720i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −3.00000 | − | 2.00000i | −0.372104 | − | 0.248069i | ||||
\(66\) | −0.828427 | − | 4.82843i | −0.101972 | − | 0.594338i | ||||
\(67\) | 2.24264 | − | 2.24264i | 0.273982 | − | 0.273982i | −0.556719 | − | 0.830701i | \(-0.687940\pi\) |
0.830701 | + | 0.556719i | \(0.187940\pi\) | |||||||
\(68\) | − | 4.82843i | − | 0.585533i | ||||||
\(69\) | 2.00000 | + | 11.6569i | 0.240772 | + | 1.40332i | ||||
\(70\) | 2.00000 | − | 2.00000i | 0.239046 | − | 0.239046i | ||||
\(71\) | 10.4142 | + | 10.4142i | 1.23594 | + | 1.23594i | 0.961646 | + | 0.274294i | \(0.0884441\pi\) |
0.274294 | + | 0.961646i | \(0.411556\pi\) | |||||||
\(72\) | 1.29289 | − | 2.70711i | 0.152369 | − | 0.319036i | ||||
\(73\) | 9.89949 | + | 9.89949i | 1.15865 | + | 1.15865i | 0.984767 | + | 0.173882i | \(0.0556310\pi\) |
0.173882 | + | 0.984767i | \(0.444369\pi\) | |||||||
\(74\) | − | 5.65685i | − | 0.657596i | ||||||
\(75\) | −1.70711 | + | 0.292893i | −0.197120 | + | 0.0338204i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00000 | −0.911685 | ||||||||
\(78\) | −2.53553 | + | 5.70711i | −0.287093 | + | 0.646203i | ||||
\(79\) | −8.82843 | −0.993276 | −0.496638 | − | 0.867958i | \(-0.665432\pi\) | ||||
−0.496638 | + | 0.867958i | \(0.665432\pi\) | |||||||
\(80\) | 0.707107 | + | 0.707107i | 0.0790569 | + | 0.0790569i | ||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 3.07107i | 0.339143i | ||||||||
\(83\) | −1.17157 | − | 1.17157i | −0.128597 | − | 0.128597i | 0.639879 | − | 0.768476i | \(-0.278984\pi\) |
−0.768476 | + | 0.639879i | \(0.778984\pi\) | |||||||
\(84\) | −4.00000 | − | 2.82843i | −0.436436 | − | 0.308607i | ||||
\(85\) | 3.41421 | + | 3.41421i | 0.370323 | + | 0.370323i | ||||
\(86\) | −3.58579 | + | 3.58579i | −0.386665 | + | 0.386665i | ||||
\(87\) | −6.24264 | + | 1.07107i | −0.669281 | + | 0.114831i | ||||
\(88\) | − | 2.82843i | − | 0.301511i | ||||||
\(89\) | 2.65685 | − | 2.65685i | 0.281626 | − | 0.281626i | −0.552131 | − | 0.833757i | \(-0.686185\pi\) |
0.833757 | + | 0.552131i | \(0.186185\pi\) | |||||||
\(90\) | 1.00000 | + | 2.82843i | 0.105409 | + | 0.298142i | ||||
\(91\) | 8.48528 | + | 5.65685i | 0.889499 | + | 0.592999i | ||||
\(92\) | 6.82843i | 0.711913i | ||||||||
\(93\) | 8.82843 | + | 6.24264i | 0.915465 | + | 0.647332i | ||||
\(94\) | 2.82843 | 0.291730 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | − | 1.41421i | 0.102062 | − | 0.144338i | ||||
\(97\) | −8.58579 | + | 8.58579i | −0.871755 | + | 0.871755i | −0.992664 | − | 0.120909i | \(-0.961419\pi\) |
0.120909 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 3.65685 | − | 7.65685i | 0.367528 | − | 0.769543i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −7.17157 | −0.713598 | −0.356799 | − | 0.934181i | \(-0.616132\pi\) | ||||
−0.356799 | + | 0.934181i | \(0.616132\pi\) | |||||||
\(102\) | 4.82843 | − | 6.82843i | 0.478086 | − | 0.676115i | ||||
\(103\) | − | 14.8284i | − | 1.46109i | −0.682865 | − | 0.730544i | \(-0.739266\pi\) | ||
0.682865 | − | 0.730544i | \(-0.260734\pi\) | |||||||
\(104\) | −2.00000 | + | 3.00000i | −0.196116 | + | 0.294174i | ||||
\(105\) | 4.82843 | − | 0.828427i | 0.471206 | − | 0.0808462i | ||||
\(106\) | 6.65685 | − | 6.65685i | 0.646571 | − | 0.646571i | ||||
\(107\) | − | 12.5858i | − | 1.21671i | −0.793664 | − | 0.608357i | \(-0.791829\pi\) | ||
0.793664 | − | 0.608357i | \(-0.208171\pi\) | |||||||
\(108\) | 4.53553 | − | 2.53553i | 0.436432 | − | 0.243982i | ||||
\(109\) | −8.24264 | + | 8.24264i | −0.789502 | + | 0.789502i | −0.981412 | − | 0.191911i | \(-0.938532\pi\) |
0.191911 | + | 0.981412i | \(0.438532\pi\) | |||||||
\(110\) | 2.00000 | + | 2.00000i | 0.190693 | + | 0.190693i | ||||
\(111\) | 5.65685 | − | 8.00000i | 0.536925 | − | 0.759326i | ||||
\(112\) | −2.00000 | − | 2.00000i | −0.188982 | − | 0.188982i | ||||
\(113\) | − | 18.4853i | − | 1.73895i | −0.493978 | − | 0.869474i | \(-0.664458\pi\) | ||
0.493978 | − | 0.869474i | \(-0.335542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.82843 | − | 4.82843i | −0.450253 | − | 0.450253i | ||||
\(116\) | −3.65685 | −0.339530 | ||||||||
\(117\) | −9.29289 | + | 5.53553i | −0.859128 | + | 0.511760i | ||||
\(118\) | 5.65685 | 0.520756 | ||||||||
\(119\) | −9.65685 | − | 9.65685i | −0.885242 | − | 0.885242i | ||||
\(120\) | 0.292893 | + | 1.70711i | 0.0267374 | + | 0.155837i | ||||
\(121\) | 3.00000i | 0.272727i | ||||||||
\(122\) | 9.07107 | + | 9.07107i | 0.821256 | + | 0.821256i | ||||
\(123\) | −3.07107 | + | 4.34315i | −0.276909 | + | 0.391608i | ||||
\(124\) | 4.41421 | + | 4.41421i | 0.396408 | + | 0.396408i | ||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | −2.82843 | − | 8.00000i | −0.251976 | − | 0.712697i | ||||
\(127\) | − | 1.65685i | − | 0.147022i | −0.997294 | − | 0.0735110i | \(-0.976580\pi\) | ||
0.997294 | − | 0.0735110i | \(-0.0234204\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −8.65685 | + | 1.48528i | −0.762194 | + | 0.130772i | ||||
\(130\) | −0.707107 | − | 3.53553i | −0.0620174 | − | 0.310087i | ||||
\(131\) | − | 11.3137i | − | 0.988483i | −0.869325 | − | 0.494242i | \(-0.835446\pi\) | ||
0.869325 | − | 0.494242i | \(-0.164554\pi\) | |||||||
\(132\) | 2.82843 | − | 4.00000i | 0.246183 | − | 0.348155i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.17157 | 0.273982 | ||||||||
\(135\) | −1.41421 | + | 5.00000i | −0.121716 | + | 0.430331i | ||||
\(136\) | 3.41421 | − | 3.41421i | 0.292766 | − | 0.292766i | ||||
\(137\) | −6.58579 | + | 6.58579i | −0.562662 | + | 0.562662i | −0.930063 | − | 0.367401i | \(-0.880248\pi\) |
0.367401 | + | 0.930063i | \(0.380248\pi\) | |||||||
\(138\) | −6.82843 | + | 9.65685i | −0.581274 | + | 0.822046i | ||||
\(139\) | −7.31371 | −0.620341 | −0.310170 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310170 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(140\) | 2.82843 | 0.239046 | ||||||||
\(141\) | 4.00000 | + | 2.82843i | 0.336861 | + | 0.238197i | ||||
\(142\) | 14.7279i | 1.23594i | ||||||||
\(143\) | −5.65685 | + | 8.48528i | −0.473050 | + | 0.709575i | ||||
\(144\) | 2.82843 | − | 1.00000i | 0.235702 | − | 0.0833333i | ||||
\(145\) | 2.58579 | − | 2.58579i | 0.214738 | − | 0.214738i | ||||
\(146\) | 14.0000i | 1.15865i | ||||||||
\(147\) | −1.70711 | + | 0.292893i | −0.140800 | + | 0.0241574i | ||||
\(148\) | 4.00000 | − | 4.00000i | 0.328798 | − | 0.328798i | ||||
\(149\) | 11.8995 | + | 11.8995i | 0.974845 | + | 0.974845i | 0.999691 | − | 0.0248467i | \(-0.00790975\pi\) |
−0.0248467 | + | 0.999691i | \(0.507910\pi\) | |||||||
\(150\) | −1.41421 | − | 1.00000i | −0.115470 | − | 0.0816497i | ||||
\(151\) | −12.4142 | − | 12.4142i | −1.01025 | − | 1.01025i | −0.999947 | − | 0.0103075i | \(-0.996719\pi\) |
−0.0103075 | − | 0.999947i | \(-0.503281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.6569 | − | 4.82843i | 1.10409 | − | 0.390355i | ||||
\(154\) | −5.65685 | − | 5.65685i | −0.455842 | − | 0.455842i | ||||
\(155\) | −6.24264 | −0.501421 | ||||||||
\(156\) | −5.82843 | + | 2.24264i | −0.466648 | + | 0.179555i | ||||
\(157\) | −20.7279 | −1.65427 | −0.827134 | − | 0.562005i | \(-0.810030\pi\) | ||||
−0.827134 | + | 0.562005i | \(0.810030\pi\) | |||||||
\(158\) | −6.24264 | − | 6.24264i | −0.496638 | − | 0.496638i | ||||
\(159\) | 16.0711 | − | 2.75736i | 1.27452 | − | 0.218673i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 13.6569 | + | 13.6569i | 1.07631 | + | 1.07631i | ||||
\(162\) | 8.94975 | + | 0.949747i | 0.703159 | + | 0.0746192i | ||||
\(163\) | −4.48528 | − | 4.48528i | −0.351314 | − | 0.351314i | 0.509284 | − | 0.860598i | \(-0.329910\pi\) |
−0.860598 | + | 0.509284i | \(0.829910\pi\) | |||||||
\(164\) | −2.17157 | + | 2.17157i | −0.169571 | + | 0.169571i | ||||
\(165\) | 0.828427 | + | 4.82843i | 0.0644930 | + | 0.375893i | ||||
\(166\) | − | 1.65685i | − | 0.128597i | ||||||
\(167\) | −9.31371 | + | 9.31371i | −0.720716 | + | 0.720716i | −0.968751 | − | 0.248035i | \(-0.920215\pi\) |
0.248035 | + | 0.968751i | \(0.420215\pi\) | |||||||
\(168\) | −0.828427 | − | 4.82843i | −0.0639145 | − | 0.372521i | ||||
\(169\) | 12.0000 | − | 5.00000i | 0.923077 | − | 0.384615i | ||||
\(170\) | 4.82843i | 0.370323i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.07107 | −0.386665 | ||||||||
\(173\) | −14.5858 | −1.10894 | −0.554468 | − | 0.832205i | \(-0.687078\pi\) | ||||
−0.554468 | + | 0.832205i | \(0.687078\pi\) | |||||||
\(174\) | −5.17157 | − | 3.65685i | −0.392056 | − | 0.277225i | ||||
\(175\) | −2.00000 | + | 2.00000i | −0.151186 | + | 0.151186i | ||||
\(176\) | 2.00000 | − | 2.00000i | 0.150756 | − | 0.150756i | ||||
\(177\) | 8.00000 | + | 5.65685i | 0.601317 | + | 0.425195i | ||||
\(178\) | 3.75736 | 0.281626 | ||||||||
\(179\) | 2.34315 | 0.175135 | 0.0875675 | − | 0.996159i | \(-0.472091\pi\) | ||||
0.0875675 | + | 0.996159i | \(0.472091\pi\) | |||||||
\(180\) | −1.29289 | + | 2.70711i | −0.0963666 | + | 0.201776i | ||||
\(181\) | 11.6569i | 0.866447i | 0.901286 | + | 0.433224i | \(0.142624\pi\) | ||||
−0.901286 | + | 0.433224i | \(0.857376\pi\) | |||||||
\(182\) | 2.00000 | + | 10.0000i | 0.148250 | + | 0.741249i | ||||
\(183\) | 3.75736 | + | 21.8995i | 0.277752 | + | 1.61886i | ||||
\(184\) | −4.82843 | + | 4.82843i | −0.355956 | + | 0.355956i | ||||
\(185\) | 5.65685i | 0.415900i | ||||||||
\(186\) | 1.82843 | + | 10.6569i | 0.134067 | + | 0.781398i | ||||
\(187\) | 9.65685 | − | 9.65685i | 0.706179 | − | 0.706179i | ||||
\(188\) | 2.00000 | + | 2.00000i | 0.145865 | + | 0.145865i | ||||
\(189\) | 4.00000 | − | 14.1421i | 0.290957 | − | 1.02869i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.8284i | − | 0.928232i | −0.885774 | − | 0.464116i | \(-0.846372\pi\) | ||
0.885774 | − | 0.464116i | \(-0.153628\pi\) | |||||||
\(192\) | 1.70711 | − | 0.292893i | 0.123200 | − | 0.0211377i | ||||
\(193\) | −1.07107 | − | 1.07107i | −0.0770971 | − | 0.0770971i | 0.667507 | − | 0.744604i | \(-0.267362\pi\) |
−0.744604 | + | 0.667507i | \(0.767362\pi\) | |||||||
\(194\) | −12.1421 | −0.871755 | ||||||||
\(195\) | 2.53553 | − | 5.70711i | 0.181573 | − | 0.408694i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −9.17157 | − | 9.17157i | −0.653448 | − | 0.653448i | 0.300374 | − | 0.953822i | \(-0.402889\pi\) |
−0.953822 | + | 0.300374i | \(0.902889\pi\) | |||||||
\(198\) | 8.00000 | − | 2.82843i | 0.568535 | − | 0.201008i | ||||
\(199\) | − | 0.828427i | − | 0.0587256i | −0.999569 | − | 0.0293628i | \(-0.990652\pi\) | ||
0.999569 | − | 0.0293628i | \(-0.00934782\pi\) | |||||||
\(200\) | −0.707107 | − | 0.707107i | −0.0500000 | − | 0.0500000i | ||||
\(201\) | 4.48528 | + | 3.17157i | 0.316367 | + | 0.223706i | ||||
\(202\) | −5.07107 | − | 5.07107i | −0.356799 | − | 0.356799i | ||||
\(203\) | −7.31371 | + | 7.31371i | −0.513322 | + | 0.513322i | ||||
\(204\) | 8.24264 | − | 1.41421i | 0.577100 | − | 0.0990148i | ||||
\(205\) | − | 3.07107i | − | 0.214493i | ||||||
\(206\) | 10.4853 | − | 10.4853i | 0.730544 | − | 0.730544i | ||||
\(207\) | −19.3137 | + | 6.82843i | −1.34240 | + | 0.474608i | ||||
\(208\) | −3.53553 | + | 0.707107i | −0.245145 | + | 0.0490290i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.00000 | + | 2.82843i | 0.276026 | + | 0.195180i | ||||
\(211\) | −16.9706 | −1.16830 | −0.584151 | − | 0.811645i | \(-0.698572\pi\) | ||||
−0.584151 | + | 0.811645i | \(0.698572\pi\) | |||||||
\(212\) | 9.41421 | 0.646571 | ||||||||
\(213\) | −14.7279 | + | 20.8284i | −1.00914 | + | 1.42714i | ||||
\(214\) | 8.89949 | − | 8.89949i | 0.608357 | − | 0.608357i | ||||
\(215\) | 3.58579 | − | 3.58579i | 0.244549 | − | 0.244549i | ||||
\(216\) | 5.00000 | + | 1.41421i | 0.340207 | + | 0.0962250i | ||||
\(217\) | 17.6569 | 1.19863 | ||||||||
\(218\) | −11.6569 | −0.789502 | ||||||||
\(219\) | −14.0000 | + | 19.7990i | −0.946032 | + | 1.33789i | ||||
\(220\) | 2.82843i | 0.190693i | ||||||||
\(221\) | −17.0711 | + | 3.41421i | −1.14832 | + | 0.229665i | ||||
\(222\) | 9.65685 | − | 1.65685i | 0.648126 | − | 0.111201i | ||||
\(223\) | −13.6569 | + | 13.6569i | −0.914531 | + | 0.914531i | −0.996625 | − | 0.0820940i | \(-0.973839\pi\) |
0.0820940 | + | 0.996625i | \(0.473839\pi\) | |||||||
\(224\) | − | 2.82843i | − | 0.188982i | ||||||
\(225\) | −1.00000 | − | 2.82843i | −0.0666667 | − | 0.188562i | ||||
\(226\) | 13.0711 | − | 13.0711i | 0.869474 | − | 0.869474i | ||||
\(227\) | 11.4142 | + | 11.4142i | 0.757588 | + | 0.757588i | 0.975883 | − | 0.218295i | \(-0.0700495\pi\) |
−0.218295 | + | 0.975883i | \(0.570049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8995 | − | 15.8995i | −1.05067 | − | 1.05067i | −0.998646 | − | 0.0520223i | \(-0.983433\pi\) |
−0.0520223 | − | 0.998646i | \(-0.516567\pi\) | |||||||
\(230\) | − | 6.82843i | − | 0.450253i | ||||||
\(231\) | −2.34315 | − | 13.6569i | −0.154168 | − | 0.898555i | ||||
\(232\) | −2.58579 | − | 2.58579i | −0.169765 | − | 0.169765i | ||||
\(233\) | 0.142136 | 0.00931161 | 0.00465581 | − | 0.999989i | \(-0.498518\pi\) | ||||
0.00465581 | + | 0.999989i | \(0.498518\pi\) | |||||||
\(234\) | −10.4853 | − | 2.65685i | −0.685444 | − | 0.173684i | ||||
\(235\) | −2.82843 | −0.184506 | ||||||||
\(236\) | 4.00000 | + | 4.00000i | 0.260378 | + | 0.260378i | ||||
\(237\) | −2.58579 | − | 15.0711i | −0.167965 | − | 0.978971i | ||||
\(238\) | − | 13.6569i | − | 0.885242i | ||||||
\(239\) | 12.0711 | + | 12.0711i | 0.780812 | + | 0.780812i | 0.979968 | − | 0.199155i | \(-0.0638199\pi\) |
−0.199155 | + | 0.979968i | \(0.563820\pi\) | |||||||
\(240\) | −1.00000 | + | 1.41421i | −0.0645497 | + | 0.0912871i | ||||
\(241\) | −2.65685 | − | 2.65685i | −0.171143 | − | 0.171143i | 0.616338 | − | 0.787481i | \(-0.288615\pi\) |
−0.787481 | + | 0.616338i | \(0.788615\pi\) | |||||||
\(242\) | −2.12132 | + | 2.12132i | −0.136364 | + | 0.136364i | ||||
\(243\) | 11.7071 | + | 10.2929i | 0.751011 | + | 0.660289i | ||||
\(244\) | 12.8284i | 0.821256i | ||||||||
\(245\) | 0.707107 | − | 0.707107i | 0.0451754 | − | 0.0451754i | ||||
\(246\) | −5.24264 | + | 0.899495i | −0.334259 | + | 0.0573497i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.24264i | 0.396408i | ||||||||
\(249\) | 1.65685 | − | 2.34315i | 0.104999 | − | 0.148491i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −4.97056 | −0.313739 | −0.156870 | − | 0.987619i | \(-0.550140\pi\) | ||||
−0.156870 | + | 0.987619i | \(0.550140\pi\) | |||||||
\(252\) | 3.65685 | − | 7.65685i | 0.230360 | − | 0.482336i | ||||
\(253\) | −13.6569 | + | 13.6569i | −0.858599 | + | 0.858599i | ||||
\(254\) | 1.17157 | − | 1.17157i | 0.0735110 | − | 0.0735110i | ||||
\(255\) | −4.82843 | + | 6.82843i | −0.302368 | + | 0.427613i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.4853 | 1.65211 | 0.826053 | − | 0.563592i | \(-0.190581\pi\) | ||||
0.826053 | + | 0.563592i | \(0.190581\pi\) | |||||||
\(258\) | −7.17157 | − | 5.07107i | −0.446483 | − | 0.315711i | ||||
\(259\) | − | 16.0000i | − | 0.994192i | ||||||
\(260\) | 2.00000 | − | 3.00000i | 0.124035 | − | 0.186052i | ||||
\(261\) | −3.65685 | − | 10.3431i | −0.226354 | − | 0.640225i | ||||
\(262\) | 8.00000 | − | 8.00000i | 0.494242 | − | 0.494242i | ||||
\(263\) | − | 7.51472i | − | 0.463377i | −0.972790 | − | 0.231689i | \(-0.925575\pi\) | ||
0.972790 | − | 0.231689i | \(-0.0744251\pi\) | |||||||
\(264\) | 4.82843 | − | 0.828427i | 0.297169 | − | 0.0509862i | ||||
\(265\) | −6.65685 | + | 6.65685i | −0.408927 | + | 0.408927i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.31371 | + | 3.75736i | 0.325194 | + | 0.229947i | ||||
\(268\) | 2.24264 | + | 2.24264i | 0.136991 | + | 0.136991i | ||||
\(269\) | 12.8284i | 0.782163i | 0.920356 | + | 0.391082i | \(0.127899\pi\) | ||||
−0.920356 | + | 0.391082i | \(0.872101\pi\) | |||||||
\(270\) | −4.53553 | + | 2.53553i | −0.276024 | + | 0.154308i | ||||
\(271\) | 12.5563 | + | 12.5563i | 0.762744 | + | 0.762744i | 0.976818 | − | 0.214074i | \(-0.0686733\pi\) |
−0.214074 | + | 0.976818i | \(0.568673\pi\) | |||||||
\(272\) | 4.82843 | 0.292766 | ||||||||
\(273\) | −7.17157 | + | 16.1421i | −0.434043 | + | 0.976966i | ||||
\(274\) | −9.31371 | −0.562662 | ||||||||
\(275\) | −2.00000 | − | 2.00000i | −0.120605 | − | 0.120605i | ||||
\(276\) | −11.6569 | + | 2.00000i | −0.701660 | + | 0.120386i | ||||
\(277\) | − | 8.72792i | − | 0.524410i | −0.965012 | − | 0.262205i | \(-0.915550\pi\) | ||
0.965012 | − | 0.262205i | \(-0.0844497\pi\) | |||||||
\(278\) | −5.17157 | − | 5.17157i | −0.310170 | − | 0.310170i | ||||
\(279\) | −8.07107 | + | 16.8995i | −0.483202 | + | 1.01175i | ||||
\(280\) | 2.00000 | + | 2.00000i | 0.119523 | + | 0.119523i | ||||
\(281\) | −15.0000 | + | 15.0000i | −0.894825 | + | 0.894825i | −0.994973 | − | 0.100148i | \(-0.968068\pi\) |
0.100148 | + | 0.994973i | \(0.468068\pi\) | |||||||
\(282\) | 0.828427 | + | 4.82843i | 0.0493321 | + | 0.287529i | ||||
\(283\) | 9.75736i | 0.580015i | 0.957024 | + | 0.290007i | \(0.0936578\pi\) | ||||
−0.957024 | + | 0.290007i | \(0.906342\pi\) | |||||||
\(284\) | −10.4142 | + | 10.4142i | −0.617970 | + | 0.617970i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.0000 | + | 2.00000i | −0.591312 | + | 0.118262i | ||||
\(287\) | 8.68629i | 0.512736i | ||||||||
\(288\) | 2.70711 | + | 1.29289i | 0.159518 | + | 0.0761845i | ||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | 3.65685 | 0.214738 | ||||||||
\(291\) | −17.1716 | − | 12.1421i | −1.00662 | − | 0.711785i | ||||
\(292\) | −9.89949 | + | 9.89949i | −0.579324 | + | 0.579324i | ||||
\(293\) | 16.4853 | − | 16.4853i | 0.963080 | − | 0.963080i | −0.0362619 | − | 0.999342i | \(-0.511545\pi\) |
0.999342 | + | 0.0362619i | \(0.0115451\pi\) | |||||||
\(294\) | −1.41421 | − | 1.00000i | −0.0824786 | − | 0.0583212i | ||||
\(295\) | −5.65685 | −0.329355 | ||||||||
\(296\) | 5.65685 | 0.328798 | ||||||||
\(297\) | 14.1421 | + | 4.00000i | 0.820610 | + | 0.232104i | ||||
\(298\) | 16.8284i | 0.974845i | ||||||||
\(299\) | 24.1421 | − | 4.82843i | 1.39618 | − | 0.279235i | ||||
\(300\) | −0.292893 | − | 1.70711i | −0.0169102 | − | 0.0985599i | ||||
\(301\) | −10.1421 | + | 10.1421i | −0.584583 | + | 0.584583i | ||||
\(302\) | − | 17.5563i | − | 1.01025i | ||||||
\(303\) | −2.10051 | − | 12.2426i | −0.120671 | − | 0.703321i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.07107 | − | 9.07107i | −0.519408 | − | 0.519408i | ||||
\(306\) | 13.0711 | + | 6.24264i | 0.747223 | + | 0.356868i | ||||
\(307\) | −8.58579 | − | 8.58579i | −0.490017 | − | 0.490017i | 0.418295 | − | 0.908311i | \(-0.362628\pi\) |
−0.908311 | + | 0.418295i | \(0.862628\pi\) | |||||||
\(308\) | − | 8.00000i | − | 0.455842i | ||||||
\(309\) | 25.3137 | − | 4.34315i | 1.44005 | − | 0.247073i | ||||
\(310\) | −4.41421 | − | 4.41421i | −0.250710 | − | 0.250710i | ||||
\(311\) | 30.6274 | 1.73672 | 0.868361 | − | 0.495933i | \(-0.165174\pi\) | ||||
0.868361 | + | 0.495933i | \(0.165174\pi\) | |||||||
\(312\) | −5.70711 | − | 2.53553i | −0.323101 | − | 0.143546i | ||||
\(313\) | 18.9706 | 1.07228 | 0.536140 | − | 0.844129i | \(-0.319882\pi\) | ||||
0.536140 | + | 0.844129i | \(0.319882\pi\) | |||||||
\(314\) | −14.6569 | − | 14.6569i | −0.827134 | − | 0.827134i | ||||
\(315\) | 2.82843 | + | 8.00000i | 0.159364 | + | 0.450749i | ||||
\(316\) | − | 8.82843i | − | 0.496638i | ||||||
\(317\) | −16.9706 | − | 16.9706i | −0.953162 | − | 0.953162i | 0.0457894 | − | 0.998951i | \(-0.485420\pi\) |
−0.998951 | + | 0.0457894i | \(0.985420\pi\) | |||||||
\(318\) | 13.3137 | + | 9.41421i | 0.746596 | + | 0.527923i | ||||
\(319\) | −7.31371 | − | 7.31371i | −0.409489 | − | 0.409489i | ||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | 21.4853 | − | 3.68629i | 1.19919 | − | 0.205749i | ||||
\(322\) | 19.3137i | 1.07631i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.65685 | + | 7.00000i | 0.314270 | + | 0.388889i | ||||
\(325\) | 0.707107 | + | 3.53553i | 0.0392232 | + | 0.196116i | ||||
\(326\) | − | 6.34315i | − | 0.351314i | ||||||
\(327\) | −16.4853 | − | 11.6569i | −0.911638 | − | 0.644626i | ||||
\(328\) | −3.07107 | −0.169571 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | −2.82843 | + | 4.00000i | −0.155700 | + | 0.220193i | ||||
\(331\) | −6.00000 | + | 6.00000i | −0.329790 | + | 0.329790i | −0.852506 | − | 0.522717i | \(-0.824919\pi\) |
0.522717 | + | 0.852506i | \(0.324919\pi\) | |||||||
\(332\) | 1.17157 | − | 1.17157i | 0.0642984 | − | 0.0642984i | ||||
\(333\) | 15.3137 | + | 7.31371i | 0.839186 | + | 0.400789i | ||||
\(334\) | −13.1716 | −0.720716 | ||||||||
\(335\) | −3.17157 | −0.173282 | ||||||||
\(336\) | 2.82843 | − | 4.00000i | 0.154303 | − | 0.218218i | ||||
\(337\) | − | 25.3137i | − | 1.37893i | −0.724321 | − | 0.689463i | \(-0.757847\pi\) | ||
0.724321 | − | 0.689463i | \(-0.242153\pi\) | |||||||
\(338\) | 12.0208 | + | 4.94975i | 0.653846 | + | 0.269231i | ||||
\(339\) | 31.5563 | − | 5.41421i | 1.71391 | − | 0.294060i | ||||
\(340\) | −3.41421 | + | 3.41421i | −0.185162 | + | 0.185162i | ||||
\(341\) | 17.6569i | 0.956172i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | −3.58579 | − | 3.58579i | −0.193333 | − | 0.193333i | ||||
\(345\) | 6.82843 | − | 9.65685i | 0.367630 | − | 0.519908i | ||||
\(346\) | −10.3137 | − | 10.3137i | −0.554468 | − | 0.554468i | ||||
\(347\) | − | 31.6985i | − | 1.70166i | −0.525438 | − | 0.850832i | \(-0.676099\pi\) | ||
0.525438 | − | 0.850832i | \(-0.323901\pi\) | |||||||
\(348\) | −1.07107 | − | 6.24264i | −0.0574153 | − | 0.334641i | ||||
\(349\) | 18.3848 | + | 18.3848i | 0.984115 | + | 0.984115i | 0.999876 | − | 0.0157613i | \(-0.00501718\pi\) |
−0.0157613 | + | 0.999876i | \(0.505017\pi\) | |||||||
\(350\) | −2.82843 | −0.151186 | ||||||||
\(351\) | −12.1716 | − | 14.2426i | −0.649670 | − | 0.760216i | ||||
\(352\) | 2.82843 | 0.150756 | ||||||||
\(353\) | −3.89949 | − | 3.89949i | −0.207549 | − | 0.207549i | 0.595676 | − | 0.803225i | \(-0.296884\pi\) |
−0.803225 | + | 0.595676i | \(0.796884\pi\) | |||||||
\(354\) | 1.65685 | + | 9.65685i | 0.0880608 | + | 0.513256i | ||||
\(355\) | − | 14.7279i | − | 0.781677i | ||||||
\(356\) | 2.65685 | + | 2.65685i | 0.140813 | + | 0.140813i | ||||
\(357\) | 13.6569 | − | 19.3137i | 0.722797 | − | 1.02219i | ||||
\(358\) | 1.65685 | + | 1.65685i | 0.0875675 | + | 0.0875675i | ||||
\(359\) | −2.41421 | + | 2.41421i | −0.127417 | + | 0.127417i | −0.767940 | − | 0.640522i | \(-0.778718\pi\) |
0.640522 | + | 0.767940i | \(0.278718\pi\) | |||||||
\(360\) | −2.82843 | + | 1.00000i | −0.149071 | + | 0.0527046i | ||||
\(361\) | 19.0000i | 1.00000i | ||||||||
\(362\) | −8.24264 | + | 8.24264i | −0.433224 | + | 0.433224i | ||||
\(363\) | −5.12132 | + | 0.878680i | −0.268800 | + | 0.0461187i | ||||
\(364\) | −5.65685 | + | 8.48528i | −0.296500 | + | 0.444750i | ||||
\(365\) | − | 14.0000i | − | 0.732793i | ||||||
\(366\) | −12.8284 | + | 18.1421i | −0.670553 | + | 0.948305i | ||||
\(367\) | 37.4558 | 1.95518 | 0.977590 | − | 0.210520i | \(-0.0675157\pi\) | ||||
0.977590 | + | 0.210520i | \(0.0675157\pi\) | |||||||
\(368\) | −6.82843 | −0.355956 | ||||||||
\(369\) | −8.31371 | − | 3.97056i | −0.432794 | − | 0.206699i | ||||
\(370\) | −4.00000 | + | 4.00000i | −0.207950 | + | 0.207950i | ||||
\(371\) | 18.8284 | − | 18.8284i | 0.977523 | − | 0.977523i | ||||
\(372\) | −6.24264 | + | 8.82843i | −0.323666 | + | 0.457733i | ||||
\(373\) | −28.7279 | −1.48748 | −0.743738 | − | 0.668472i | \(-0.766949\pi\) | ||||
−0.743738 | + | 0.668472i | \(0.766949\pi\) | |||||||
\(374\) | 13.6569 | 0.706179 | ||||||||
\(375\) | 1.41421 | + | 1.00000i | 0.0730297 | + | 0.0516398i | ||||
\(376\) | 2.82843i | 0.145865i | ||||||||
\(377\) | 2.58579 | + | 12.9289i | 0.133175 | + | 0.665874i | ||||
\(378\) | 12.8284 | − | 7.17157i | 0.659823 | − | 0.368866i | ||||
\(379\) | 7.51472 | − | 7.51472i | 0.386005 | − | 0.386005i | −0.487255 | − | 0.873260i | \(-0.662002\pi\) |
0.873260 | + | 0.487255i | \(0.162002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.82843 | − | 0.485281i | 0.144905 | − | 0.0248617i | ||||
\(382\) | 9.07107 | − | 9.07107i | 0.464116 | − | 0.464116i | ||||
\(383\) | 4.00000 | + | 4.00000i | 0.204390 | + | 0.204390i | 0.801878 | − | 0.597488i | \(-0.203834\pi\) |
−0.597488 | + | 0.801878i | \(0.703834\pi\) | |||||||
\(384\) | 1.41421 | + | 1.00000i | 0.0721688 | + | 0.0510310i | ||||
\(385\) | 5.65685 | + | 5.65685i | 0.288300 | + | 0.288300i | ||||
\(386\) | − | 1.51472i | − | 0.0770971i | ||||||
\(387\) | −5.07107 | − | 14.3431i | −0.257777 | − | 0.729103i | ||||
\(388\) | −8.58579 | − | 8.58579i | −0.435877 | − | 0.435877i | ||||
\(389\) | −31.6569 | −1.60507 | −0.802533 | − | 0.596608i | \(-0.796515\pi\) | ||||
−0.802533 | + | 0.596608i | \(0.796515\pi\) | |||||||
\(390\) | 5.82843 | − | 2.24264i | 0.295134 | − | 0.113561i | ||||
\(391\) | −32.9706 | −1.66739 | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 19.3137 | − | 3.31371i | 0.974248 | − | 0.167154i | ||||
\(394\) | − | 12.9706i | − | 0.653448i | ||||||
\(395\) | 6.24264 | + | 6.24264i | 0.314101 | + | 0.314101i | ||||
\(396\) | 7.65685 | + | 3.65685i | 0.384771 | + | 0.183764i | ||||
\(397\) | 6.58579 | + | 6.58579i | 0.330531 | + | 0.330531i | 0.852788 | − | 0.522257i | \(-0.174910\pi\) |
−0.522257 | + | 0.852788i | \(0.674910\pi\) | |||||||
\(398\) | 0.585786 | − | 0.585786i | 0.0293628 | − | 0.0293628i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −21.6274 | + | 21.6274i | −1.08002 | + | 1.08002i | −0.0835152 | + | 0.996507i | \(0.526615\pi\) |
−0.996507 | + | 0.0835152i | \(0.973385\pi\) | |||||||
\(402\) | 0.928932 | + | 5.41421i | 0.0463309 | + | 0.270036i | ||||
\(403\) | 12.4853 | − | 18.7279i | 0.621936 | − | 0.932904i | ||||
\(404\) | − | 7.17157i | − | 0.356799i | ||||||
\(405\) | −8.94975 | − | 0.949747i | −0.444717 | − | 0.0471933i | ||||
\(406\) | −10.3431 | −0.513322 | ||||||||
\(407\) | 16.0000 | 0.793091 | ||||||||
\(408\) | 6.82843 | + | 4.82843i | 0.338058 | + | 0.239043i | ||||
\(409\) | 13.4853 | − | 13.4853i | 0.666804 | − | 0.666804i | −0.290171 | − | 0.956975i | \(-0.593712\pi\) |
0.956975 | + | 0.290171i | \(0.0937121\pi\) | |||||||
\(410\) | 2.17157 | − | 2.17157i | 0.107246 | − | 0.107246i | ||||
\(411\) | −13.1716 | − | 9.31371i | −0.649706 | − | 0.459411i | ||||
\(412\) | 14.8284 | 0.730544 | ||||||||
\(413\) | 16.0000 | 0.787309 | ||||||||
\(414\) | −18.4853 | − | 8.82843i | −0.908502 | − | 0.433894i | ||||
\(415\) | 1.65685i | 0.0813318i | ||||||||
\(416\) | −3.00000 | − | 2.00000i | −0.147087 | − | 0.0980581i | ||||
\(417\) | −2.14214 | − | 12.4853i | −0.104901 | − | 0.611407i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.17157i | 0.252648i | 0.991989 | + | 0.126324i | \(0.0403179\pi\) | ||||
−0.991989 | + | 0.126324i | \(0.959682\pi\) | |||||||
\(420\) | 0.828427 | + | 4.82843i | 0.0404231 | + | 0.235603i | ||||
\(421\) | −5.89949 | + | 5.89949i | −0.287524 | + | 0.287524i | −0.836100 | − | 0.548577i | \(-0.815170\pi\) |
0.548577 | + | 0.836100i | \(0.315170\pi\) | |||||||
\(422\) | −12.0000 | − | 12.0000i | −0.584151 | − | 0.584151i | ||||
\(423\) | −3.65685 | + | 7.65685i | −0.177802 | + | 0.372289i | ||||
\(424\) | 6.65685 | + | 6.65685i | 0.323285 | + | 0.323285i | ||||
\(425\) | − | 4.82843i | − | 0.234213i | ||||||
\(426\) | −25.1421 | + | 4.31371i | −1.21814 | + | 0.209000i | ||||
\(427\) | 25.6569 | + | 25.6569i | 1.24162 | + | 1.24162i | ||||
\(428\) | 12.5858 | 0.608357 | ||||||||
\(429\) | −16.1421 | − | 7.17157i | −0.779350 | − | 0.346247i | ||||
\(430\) | 5.07107 | 0.244549 | ||||||||
\(431\) | 15.2426 | + | 15.2426i | 0.734212 | + | 0.734212i | 0.971451 | − | 0.237239i | \(-0.0762425\pi\) |
−0.237239 | + | 0.971451i | \(0.576242\pi\) | |||||||
\(432\) | 2.53553 | + | 4.53553i | 0.121991 | + | 0.218216i | ||||
\(433\) | − | 35.6569i | − | 1.71356i | −0.515683 | − | 0.856780i | \(-0.672462\pi\) | ||
0.515683 | − | 0.856780i | \(-0.327538\pi\) | |||||||
\(434\) | 12.4853 | + | 12.4853i | 0.599313 | + | 0.599313i | ||||
\(435\) | 5.17157 | + | 3.65685i | 0.247958 | + | 0.175333i | ||||
\(436\) | −8.24264 | − | 8.24264i | −0.394751 | − | 0.394751i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −23.8995 | + | 4.10051i | −1.14196 | + | 0.195930i | ||||
\(439\) | 24.0000i | 1.14546i | 0.819745 | + | 0.572729i | \(0.194115\pi\) | ||||
−0.819745 | + | 0.572729i | \(0.805885\pi\) | |||||||
\(440\) | −2.00000 | + | 2.00000i | −0.0953463 | + | 0.0953463i | ||||
\(441\) | −1.00000 | − | 2.82843i | −0.0476190 | − | 0.134687i | ||||
\(442\) | −14.4853 | − | 9.65685i | −0.688995 | − | 0.459330i | ||||
\(443\) | − | 23.8995i | − | 1.13550i | −0.823201 | − | 0.567750i | \(-0.807814\pi\) | ||
0.823201 | − | 0.567750i | \(-0.192186\pi\) | |||||||
\(444\) | 8.00000 | + | 5.65685i | 0.379663 | + | 0.268462i | ||||
\(445\) | −3.75736 | −0.178116 | ||||||||
\(446\) | −19.3137 | −0.914531 | ||||||||
\(447\) | −16.8284 | + | 23.7990i | −0.795957 | + | 1.12565i | ||||
\(448\) | 2.00000 | − | 2.00000i | 0.0944911 | − | 0.0944911i | ||||
\(449\) | −7.34315 | + | 7.34315i | −0.346544 | + | 0.346544i | −0.858821 | − | 0.512276i | \(-0.828802\pi\) |
0.512276 | + | 0.858821i | \(0.328802\pi\) | |||||||
\(450\) | 1.29289 | − | 2.70711i | 0.0609476 | − | 0.127614i | ||||
\(451\) | −8.68629 | −0.409021 | ||||||||
\(452\) | 18.4853 | 0.869474 | ||||||||
\(453\) | 17.5563 | − | 24.8284i | 0.824869 | − | 1.16654i | ||||
\(454\) | 16.1421i | 0.757588i | ||||||||
\(455\) | −2.00000 | − | 10.0000i | −0.0937614 | − | 0.468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.4142 | − | 11.4142i | 0.533934 | − | 0.533934i | −0.387806 | − | 0.921741i | \(-0.626767\pi\) |
0.921741 | + | 0.387806i | \(0.126767\pi\) | |||||||
\(458\) | − | 22.4853i | − | 1.05067i | ||||||
\(459\) | 12.2426 | + | 21.8995i | 0.571438 | + | 1.02218i | ||||
\(460\) | 4.82843 | − | 4.82843i | 0.225127 | − | 0.225127i | ||||
\(461\) | 8.72792 | + | 8.72792i | 0.406500 | + | 0.406500i | 0.880516 | − | 0.474016i | \(-0.157196\pi\) |
−0.474016 | + | 0.880516i | \(0.657196\pi\) | |||||||
\(462\) | 8.00000 | − | 11.3137i | 0.372194 | − | 0.526361i | ||||
\(463\) | 12.0000 | + | 12.0000i | 0.557687 | + | 0.557687i | 0.928648 | − | 0.370961i | \(-0.120972\pi\) |
−0.370961 | + | 0.928648i | \(0.620972\pi\) | |||||||
\(464\) | − | 3.65685i | − | 0.169765i | ||||||
\(465\) | −1.82843 | − | 10.6569i | −0.0847913 | − | 0.494200i | ||||
\(466\) | 0.100505 | + | 0.100505i | 0.00465581 | + | 0.00465581i | ||||
\(467\) | 2.24264 | 0.103777 | 0.0518885 | − | 0.998653i | \(-0.483476\pi\) | ||||
0.0518885 | + | 0.998653i | \(0.483476\pi\) | |||||||
\(468\) | −5.53553 | − | 9.29289i | −0.255880 | − | 0.429564i | ||||
\(469\) | 8.97056 | 0.414222 | ||||||||
\(470\) | −2.00000 | − | 2.00000i | −0.0922531 | − | 0.0922531i | ||||
\(471\) | −6.07107 | − | 35.3848i | −0.279740 | − | 1.63044i | ||||
\(472\) | 5.65685i | 0.260378i | ||||||||
\(473\) | −10.1421 | − | 10.1421i | −0.466336 | − | 0.466336i | ||||
\(474\) | 8.82843 | − | 12.4853i | 0.405503 | − | 0.573468i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.65685 | − | 9.65685i | 0.442621 | − | 0.442621i | ||||
\(477\) | 9.41421 | + | 26.6274i | 0.431047 | + | 1.21919i | ||||
\(478\) | 17.0711i | 0.780812i | ||||||||
\(479\) | −2.41421 | + | 2.41421i | −0.110308 | + | 0.110308i | −0.760107 | − | 0.649798i | \(-0.774853\pi\) |
0.649798 | + | 0.760107i | \(0.274853\pi\) | |||||||
\(480\) | −1.70711 | + | 0.292893i | −0.0779184 | + | 0.0133687i | ||||
\(481\) | −16.9706 | − | 11.3137i | −0.773791 | − | 0.515861i | ||||
\(482\) | − | 3.75736i | − | 0.171143i | ||||||
\(483\) | −19.3137 | + | 27.3137i | −0.878804 | + | 1.24282i | ||||
\(484\) | −3.00000 | −0.136364 | ||||||||
\(485\) | 12.1421 | 0.551346 | ||||||||
\(486\) | 1.00000 | + | 15.5563i | 0.0453609 | + | 0.705650i | ||||
\(487\) | 23.4558 | − | 23.4558i | 1.06289 | − | 1.06289i | 0.0650005 | − | 0.997885i | \(-0.479295\pi\) |
0.997885 | − | 0.0650005i | \(-0.0207049\pi\) | |||||||
\(488\) | −9.07107 | + | 9.07107i | −0.410628 | + | 0.410628i | ||||
\(489\) | 6.34315 | − | 8.97056i | 0.286847 | − | 0.405663i | ||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −9.85786 | −0.444879 | −0.222440 | − | 0.974946i | \(-0.571402\pi\) | ||||
−0.222440 | + | 0.974946i | \(0.571402\pi\) | |||||||
\(492\) | −4.34315 | − | 3.07107i | −0.195804 | − | 0.138454i | ||||
\(493\) | − | 17.6569i | − | 0.795225i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.00000 | + | 2.82843i | −0.359573 | + | 0.127128i | ||||
\(496\) | −4.41421 | + | 4.41421i | −0.198204 | + | 0.198204i | ||||
\(497\) | 41.6569i | 1.86857i | ||||||||
\(498\) | 2.82843 | − | 0.485281i | 0.126745 | − | 0.0217460i | ||||
\(499\) | 22.4853 | − | 22.4853i | 1.00658 | − | 1.00658i | 0.00660122 | − | 0.999978i | \(-0.497899\pi\) |
0.999978 | − | 0.00660122i | \(-0.00210125\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | −18.6274 | − | 13.1716i | −0.832212 | − | 0.588462i | ||||
\(502\) | −3.51472 | − | 3.51472i | −0.156870 | − | 0.156870i | ||||
\(503\) | 8.68629i | 0.387303i | 0.981070 | + | 0.193651i | \(0.0620330\pi\) | ||||
−0.981070 | + | 0.193651i | \(0.937967\pi\) | |||||||
\(504\) | 8.00000 | − | 2.82843i | 0.356348 | − | 0.125988i | ||||
\(505\) | 5.07107 | + | 5.07107i | 0.225660 | + | 0.225660i | ||||
\(506\) | −19.3137 | −0.858599 | ||||||||
\(507\) | 12.0503 | + | 19.0208i | 0.535171 | + | 0.844744i | ||||
\(508\) | 1.65685 | 0.0735110 | ||||||||
\(509\) | −18.7279 | − | 18.7279i | −0.830101 | − | 0.830101i | 0.157430 | − | 0.987530i | \(-0.449679\pi\) |
−0.987530 | + | 0.157430i | \(0.949679\pi\) | |||||||
\(510\) | −8.24264 | + | 1.41421i | −0.364990 | + | 0.0626224i | ||||
\(511\) | 39.5980i | 1.75171i | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.7279 | + | 18.7279i | 0.826053 | + | 0.826053i | ||||
\(515\) | −10.4853 | + | 10.4853i | −0.462037 | + | 0.462037i | ||||
\(516\) | −1.48528 | − | 8.65685i | −0.0653859 | − | 0.381097i | ||||
\(517\) | 8.00000i | 0.351840i | ||||||||
\(518\) | 11.3137 | − | 11.3137i | 0.497096 | − | 0.497096i | ||||
\(519\) | −4.27208 | − | 24.8995i | −0.187523 | − | 1.09297i | ||||
\(520\) | 3.53553 | − | 0.707107i | 0.155043 | − | 0.0310087i | ||||
\(521\) | 2.68629i | 0.117689i | 0.998267 | + | 0.0588443i | \(0.0187415\pi\) | ||||
−0.998267 | + | 0.0588443i | \(0.981258\pi\) | |||||||
\(522\) | 4.72792 | − | 9.89949i | 0.206936 | − | 0.433289i | ||||
\(523\) | 11.8995 | 0.520329 | 0.260164 | − | 0.965564i | \(-0.416223\pi\) | ||||
0.260164 | + | 0.965564i | \(0.416223\pi\) | |||||||
\(524\) | 11.3137 | 0.494242 | ||||||||
\(525\) | −4.00000 | − | 2.82843i | −0.174574 | − | 0.123443i | ||||
\(526\) | 5.31371 | − | 5.31371i | 0.231689 | − | 0.231689i | ||||
\(527\) | −21.3137 | + | 21.3137i | −0.928440 | + | 0.928440i | ||||
\(528\) | 4.00000 | + | 2.82843i | 0.174078 | + | 0.123091i | ||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | −9.41421 | −0.408927 | ||||||||
\(531\) | −7.31371 | + | 15.3137i | −0.317388 | + | 0.664558i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.21320 | + | 6.14214i | 0.399068 | + | 0.266045i | ||||
\(534\) | 1.10051 | + | 6.41421i | 0.0476235 | + | 0.277570i | ||||
\(535\) | −8.89949 | + | 8.89949i | −0.384759 | + | 0.384759i | ||||
\(536\) | 3.17157i | 0.136991i | ||||||||
\(537\) | 0.686292 | + | 4.00000i | 0.0296157 | + | 0.172613i | ||||
\(538\) | −9.07107 | + | 9.07107i | −0.391082 | + | 0.391082i | ||||
\(539\) | −2.00000 | − | 2.00000i | −0.0861461 | − | 0.0861461i | ||||
\(540\) | −5.00000 | − | 1.41421i | −0.215166 | − | 0.0608581i | ||||
\(541\) | −25.0711 | − | 25.0711i | −1.07789 | − | 1.07789i | −0.996699 | − | 0.0811908i | \(-0.974128\pi\) |
−0.0811908 | − | 0.996699i | \(-0.525872\pi\) | |||||||
\(542\) | 17.7574i | 0.762744i | ||||||||
\(543\) | −19.8995 | + | 3.41421i | −0.853969 | + | 0.146518i | ||||
\(544\) | 3.41421 | + | 3.41421i | 0.146383 | + | 0.146383i | ||||
\(545\) | 11.6569 | 0.499325 | ||||||||
\(546\) | −16.4853 | + | 6.34315i | −0.705505 | + | 0.271462i | ||||
\(547\) | −35.8995 | −1.53495 | −0.767476 | − | 0.641078i | \(-0.778488\pi\) | ||||
−0.767476 | + | 0.641078i | \(0.778488\pi\) | |||||||
\(548\) | −6.58579 | − | 6.58579i | −0.281331 | − | 0.281331i | ||||
\(549\) | −36.2843 | + | 12.8284i | −1.54857 | + | 0.547504i | ||||
\(550\) | − | 2.82843i | − | 0.120605i | ||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −9.65685 | − | 6.82843i | −0.411023 | − | 0.290637i | ||||
\(553\) | −17.6569 | − | 17.6569i | −0.750846 | − | 0.750846i | ||||
\(554\) | 6.17157 | − | 6.17157i | 0.262205 | − | 0.262205i | ||||
\(555\) | −9.65685 | + | 1.65685i | −0.409911 | + | 0.0703295i | ||||
\(556\) | − | 7.31371i | − | 0.310170i | ||||||
\(557\) | −15.7990 | + | 15.7990i | −0.669425 | + | 0.669425i | −0.957583 | − | 0.288158i | \(-0.906957\pi\) |
0.288158 | + | 0.957583i | \(0.406957\pi\) | |||||||
\(558\) | −17.6569 | + | 6.24264i | −0.747474 | + | 0.264272i | ||||
\(559\) | 3.58579 | + | 17.9289i | 0.151663 | + | 0.758313i | ||||
\(560\) | 2.82843i | 0.119523i | ||||||||
\(561\) | 19.3137 | + | 13.6569i | 0.815425 | + | 0.576593i | ||||
\(562\) | −21.2132 | −0.894825 | ||||||||
\(563\) | −15.8995 | −0.670084 | −0.335042 | − | 0.942203i | \(-0.608750\pi\) | ||||
−0.335042 | + | 0.942203i | \(0.608750\pi\) | |||||||
\(564\) | −2.82843 | + | 4.00000i | −0.119098 | + | 0.168430i | ||||
\(565\) | −13.0711 | + | 13.0711i | −0.549904 | + | 0.549904i | ||||
\(566\) | −6.89949 | + | 6.89949i | −0.290007 | + | 0.290007i | ||||
\(567\) | 25.3137 | + | 2.68629i | 1.06308 | + | 0.112814i | ||||
\(568\) | −14.7279 | −0.617970 | ||||||||
\(569\) | −31.9411 | −1.33904 | −0.669521 | − | 0.742793i | \(-0.733501\pi\) | ||||
−0.669521 | + | 0.742793i | \(0.733501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.17157i | 0.0490288i | 0.999699 | + | 0.0245144i | \(0.00780396\pi\) | ||||
−0.999699 | + | 0.0245144i | \(0.992196\pi\) | |||||||
\(572\) | −8.48528 | − | 5.65685i | −0.354787 | − | 0.236525i | ||||
\(573\) | 21.8995 | − | 3.75736i | 0.914865 | − | 0.156966i | ||||
\(574\) | −6.14214 | + | 6.14214i | −0.256368 | + | 0.256368i | ||||
\(575\) | 6.82843i | 0.284765i | ||||||||
\(576\) | 1.00000 | + | 2.82843i | 0.0416667 | + | 0.117851i | ||||
\(577\) | −0.727922 | + | 0.727922i | −0.0303038 | + | 0.0303038i | −0.722096 | − | 0.691793i | \(-0.756821\pi\) |
0.691793 | + | 0.722096i | \(0.256821\pi\) | |||||||
\(578\) | 4.46447 | + | 4.46447i | 0.185697 | + | 0.185697i | ||||
\(579\) | 1.51472 | − | 2.14214i | 0.0629496 | − | 0.0890241i | ||||
\(580\) | 2.58579 | + | 2.58579i | 0.107369 | + | 0.107369i | ||||
\(581\) | − | 4.68629i | − | 0.194420i | ||||||
\(582\) | −3.55635 | − | 20.7279i | −0.147415 | − | 0.859200i | ||||
\(583\) | 18.8284 | + | 18.8284i | 0.779794 | + | 0.779794i | ||||
\(584\) | −14.0000 | −0.579324 | ||||||||
\(585\) | 10.4853 | + | 2.65685i | 0.433513 | + | 0.109847i | ||||
\(586\) | 23.3137 | 0.963080 | ||||||||
\(587\) | 27.7990 | + | 27.7990i | 1.14739 | + | 1.14739i | 0.987065 | + | 0.160322i | \(0.0512534\pi\) |
0.160322 | + | 0.987065i | \(0.448747\pi\) | |||||||
\(588\) | −0.292893 | − | 1.70711i | −0.0120787 | − | 0.0703999i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −4.00000 | − | 4.00000i | −0.164677 | − | 0.164677i | ||||
\(591\) | 12.9706 | − | 18.3431i | 0.533538 | − | 0.754536i | ||||
\(592\) | 4.00000 | + | 4.00000i | 0.164399 | + | 0.164399i | ||||
\(593\) | −11.8995 | + | 11.8995i | −0.488654 | + | 0.488654i | −0.907881 | − | 0.419228i | \(-0.862301\pi\) |
0.419228 | + | 0.907881i | \(0.362301\pi\) | |||||||
\(594\) | 7.17157 | + | 12.8284i | 0.294253 | + | 0.526357i | ||||
\(595\) | 13.6569i | 0.559876i | ||||||||
\(596\) | −11.8995 | + | 11.8995i | −0.487422 | + | 0.487422i | ||||
\(597\) | 1.41421 | − | 0.242641i | 0.0578799 | − | 0.00993062i | ||||
\(598\) | 20.4853 | + | 13.6569i | 0.837705 | + | 0.558470i | ||||
\(599\) | 21.5147i | 0.879068i | 0.898226 | + | 0.439534i | \(0.144856\pi\) | ||||
−0.898226 | + | 0.439534i | \(0.855144\pi\) | |||||||
\(600\) | 1.00000 | − | 1.41421i | 0.0408248 | − | 0.0577350i | ||||
\(601\) | −8.28427 | −0.337922 | −0.168961 | − | 0.985623i | \(-0.554041\pi\) | ||||
−0.168961 | + | 0.985623i | \(0.554041\pi\) | |||||||
\(602\) | −14.3431 | −0.584583 | ||||||||
\(603\) | −4.10051 | + | 8.58579i | −0.166985 | + | 0.349640i | ||||
\(604\) | 12.4142 | − | 12.4142i | 0.505127 | − | 0.505127i | ||||
\(605\) | 2.12132 | − | 2.12132i | 0.0862439 | − | 0.0862439i | ||||
\(606\) | 7.17157 | − | 10.1421i | 0.291325 | − | 0.411996i | ||||
\(607\) | 0.686292 | 0.0278557 | 0.0139279 | − | 0.999903i | \(-0.495566\pi\) | ||||
0.0139279 | + | 0.999903i | \(0.495566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.6274 | − | 10.3431i | −0.592733 | − | 0.419125i | ||||
\(610\) | − | 12.8284i | − | 0.519408i | ||||||
\(611\) | 5.65685 | − | 8.48528i | 0.228852 | − | 0.343278i | ||||
\(612\) | 4.82843 | + | 13.6569i | 0.195178 | + | 0.552046i | ||||
\(613\) | 18.6274 | − | 18.6274i | 0.752354 | − | 0.752354i | −0.222564 | − | 0.974918i | \(-0.571443\pi\) |
0.974918 | + | 0.222564i | \(0.0714426\pi\) | |||||||
\(614\) | − | 12.1421i | − | 0.490017i | ||||||
\(615\) | 5.24264 | − | 0.899495i | 0.211404 | − | 0.0362711i | ||||
\(616\) | 5.65685 | − | 5.65685i | 0.227921 | − | 0.227921i | ||||
\(617\) | 2.72792 | + | 2.72792i | 0.109822 | + | 0.109822i | 0.759882 | − | 0.650060i | \(-0.225256\pi\) |
−0.650060 | + | 0.759882i | \(0.725256\pi\) | |||||||
\(618\) | 20.9706 | + | 14.8284i | 0.843560 | + | 0.596487i | ||||
\(619\) | 21.3137 | + | 21.3137i | 0.856670 | + | 0.856670i | 0.990944 | − | 0.134274i | \(-0.0428702\pi\) |
−0.134274 | + | 0.990944i | \(0.542870\pi\) | |||||||
\(620\) | − | 6.24264i | − | 0.250710i | ||||||
\(621\) | −17.3137 | − | 30.9706i | −0.694775 | − | 1.24281i | ||||
\(622\) | 21.6569 | + | 21.6569i | 0.868361 | + | 0.868361i | ||||
\(623\) | 10.6274 | 0.425778 | ||||||||
\(624\) | −2.24264 | − | 5.82843i | −0.0897775 | − | 0.233324i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 13.4142 | + | 13.4142i | 0.536140 | + | 0.536140i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 20.7279i | − | 0.827134i | ||||||
\(629\) | 19.3137 | + | 19.3137i | 0.770088 | + | 0.770088i | ||||
\(630\) | −3.65685 | + | 7.65685i | −0.145693 | + | 0.305056i | ||||
\(631\) | 34.2132 | + | 34.2132i | 1.36201 | + | 1.36201i | 0.871358 | + | 0.490649i | \(0.163240\pi\) |
0.490649 | + | 0.871358i | \(0.336760\pi\) | |||||||
\(632\) | 6.24264 | − | 6.24264i | 0.248319 | − | 0.248319i | ||||
\(633\) | −4.97056 | − | 28.9706i | −0.197562 | − | 1.15148i | ||||
\(634\) | − | 24.0000i | − | 0.953162i | ||||||
\(635\) | −1.17157 | + | 1.17157i | −0.0464925 | + | 0.0464925i | ||||
\(636\) | 2.75736 | + | 16.0711i | 0.109336 | + | 0.637259i | ||||
\(637\) | 0.707107 | + | 3.53553i | 0.0280166 | + | 0.140083i | ||||
\(638\) | − | 10.3431i | − | 0.409489i | ||||||
\(639\) | −39.8701 | − | 19.0416i | −1.57724 | − | 0.753275i | ||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −16.9706 | −0.670297 | −0.335148 | − | 0.942165i | \(-0.608786\pi\) | ||||
−0.335148 | + | 0.942165i | \(0.608786\pi\) | |||||||
\(642\) | 17.7990 | + | 12.5858i | 0.702470 | + | 0.496721i | ||||
\(643\) | −23.7990 | + | 23.7990i | −0.938541 | + | 0.938541i | −0.998218 | − | 0.0596772i | \(-0.980993\pi\) |
0.0596772 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(644\) | −13.6569 | + | 13.6569i | −0.538155 | + | 0.538155i | ||||
\(645\) | 7.17157 | + | 5.07107i | 0.282380 | + | 0.199673i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.65685 | 0.222394 | 0.111197 | − | 0.993798i | \(-0.464532\pi\) | ||||
0.111197 | + | 0.993798i | \(0.464532\pi\) | |||||||
\(648\) | −0.949747 | + | 8.94975i | −0.0373096 | + | 0.351579i | ||||
\(649\) | 16.0000i | 0.628055i | ||||||||
\(650\) | −2.00000 | + | 3.00000i | −0.0784465 | + | 0.117670i | ||||
\(651\) | 5.17157 | + | 30.1421i | 0.202690 | + | 1.18136i | ||||
\(652\) | 4.48528 | − | 4.48528i | 0.175657 | − | 0.175657i | ||||
\(653\) | 9.21320i | 0.360541i | 0.983617 | + | 0.180270i | \(0.0576972\pi\) | ||||
−0.983617 | + | 0.180270i | \(0.942303\pi\) | |||||||
\(654\) | −3.41421 | − | 19.8995i | −0.133506 | − | 0.778132i | ||||
\(655\) | −8.00000 | + | 8.00000i | −0.312586 | + | 0.312586i | ||||
\(656\) | −2.17157 | − | 2.17157i | −0.0847857 | − | 0.0847857i | ||||
\(657\) | −37.8995 | − | 18.1005i | −1.47860 | − | 0.706168i | ||||
\(658\) | 5.65685 | + | 5.65685i | 0.220527 | + | 0.220527i | ||||
\(659\) | − | 17.1716i | − | 0.668910i | −0.942412 | − | 0.334455i | \(-0.891448\pi\) | ||
0.942412 | − | 0.334455i | \(-0.108552\pi\) | |||||||
\(660\) | −4.82843 | + | 0.828427i | −0.187946 | + | 0.0322465i | ||||
\(661\) | 10.9289 | + | 10.9289i | 0.425086 | + | 0.425086i | 0.886951 | − | 0.461864i | \(-0.152819\pi\) |
−0.461864 | + | 0.886951i | \(0.652819\pi\) | |||||||
\(662\) | −8.48528 | −0.329790 | ||||||||
\(663\) | −10.8284 | − | 28.1421i | −0.420541 | − | 1.09295i | ||||
\(664\) | 1.65685 | 0.0642984 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.65685 | + | 16.0000i | 0.219199 | + | 0.619987i | ||||
\(667\) | 24.9706i | 0.966864i | ||||||||
\(668\) | −9.31371 | − | 9.31371i | −0.360358 | − | 0.360358i | ||||
\(669\) | −27.3137 | − | 19.3137i | −1.05601 | − | 0.746711i | ||||
\(670\) | −2.24264 | − | 2.24264i | −0.0866408 | − | 0.0866408i | ||||
\(671\) | −25.6569 | + | 25.6569i | −0.990472 | + | 0.990472i | ||||
\(672\) | 4.82843 | − | 0.828427i | 0.186261 | − | 0.0319573i | ||||
\(673\) | 45.1127i | 1.73897i | 0.493962 | + | 0.869483i | \(0.335548\pi\) | ||||
−0.493962 | + | 0.869483i | \(0.664452\pi\) | |||||||
\(674\) | 17.8995 | − | 17.8995i | 0.689463 | − | 0.689463i | ||||
\(675\) | 4.53553 | − | 2.53553i | 0.174573 | − | 0.0975927i | ||||
\(676\) | 5.00000 | + | 12.0000i | 0.192308 | + | 0.461538i | ||||
\(677\) | 13.8995i | 0.534201i | 0.963669 | + | 0.267100i | \(0.0860656\pi\) | ||||
−0.963669 | + | 0.267100i | \(0.913934\pi\) | |||||||
\(678\) | 26.1421 | + | 18.4853i | 1.00398 | + | 0.709923i | ||||
\(679\) | −34.3431 | −1.31797 | ||||||||
\(680\) | −4.82843 | −0.185162 | ||||||||
\(681\) | −16.1421 | + | 22.8284i | −0.618568 | + | 0.874787i | ||||
\(682\) | −12.4853 | + | 12.4853i | −0.478086 | + | 0.478086i | ||||
\(683\) | −23.4142 | + | 23.4142i | −0.895920 | + | 0.895920i | −0.995072 | − | 0.0991523i | \(-0.968387\pi\) |
0.0991523 | + | 0.995072i | \(0.468387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.31371 | 0.355859 | ||||||||
\(686\) | 16.9706 | 0.647939 | ||||||||
\(687\) | 22.4853 | − | 31.7990i | 0.857867 | − | 1.21321i | ||||
\(688\) | − | 5.07107i | − | 0.193333i | ||||||
\(689\) | −6.65685 | − | 33.2843i | −0.253606 | − | 1.26803i | ||||
\(690\) | 11.6569 | − | 2.00000i | 0.443769 | − | 0.0761387i | ||||
\(691\) | 8.14214 | − | 8.14214i | 0.309741 | − | 0.309741i | −0.535068 | − | 0.844809i | \(-0.679714\pi\) |
0.844809 | + | 0.535068i | \(0.179714\pi\) | |||||||
\(692\) | − | 14.5858i | − | 0.554468i | ||||||
\(693\) | 22.6274 | − | 8.00000i | 0.859544 | − | 0.303895i | ||||
\(694\) | 22.4142 | − | 22.4142i | 0.850832 | − | 0.850832i | ||||
\(695\) | 5.17157 | + | 5.17157i | 0.196169 | + | 0.196169i | ||||
\(696\) | 3.65685 | − | 5.17157i | 0.138613 | − | 0.196028i | ||||
\(697\) | −10.4853 | − | 10.4853i | −0.397158 | − | 0.397158i | ||||
\(698\) | 26.0000i | 0.984115i | ||||||||
\(699\) | 0.0416306 | + | 0.242641i | 0.00157461 | + | 0.00917751i | ||||
\(700\) | −2.00000 | − | 2.00000i | −0.0755929 | − | 0.0755929i | ||||
\(701\) | −0.142136 | −0.00536839 | −0.00268419 | − | 0.999996i | \(-0.500854\pi\) | ||||
−0.00268419 | + | 0.999996i | \(0.500854\pi\) | |||||||
\(702\) | 1.46447 | − | 18.6777i | 0.0552727 | − | 0.704943i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.00000 | + | 2.00000i | 0.0753778 | + | 0.0753778i | ||||
\(705\) | −0.828427 | − | 4.82843i | −0.0312004 | − | 0.181849i | ||||
\(706\) | − | 5.51472i | − | 0.207549i | ||||||
\(707\) | −14.3431 | − | 14.3431i | −0.539430 | − | 0.539430i | ||||
\(708\) | −5.65685 | + | 8.00000i | −0.212598 | + | 0.300658i | ||||
\(709\) | −8.58579 | − | 8.58579i | −0.322446 | − | 0.322446i | 0.527259 | − | 0.849705i | \(-0.323220\pi\) |
−0.849705 | + | 0.527259i | \(0.823220\pi\) | |||||||
\(710\) | 10.4142 | − | 10.4142i | 0.390838 | − | 0.390838i | ||||
\(711\) | 24.9706 | − | 8.82843i | 0.936469 | − | 0.331092i | ||||
\(712\) | 3.75736i | 0.140813i | ||||||||
\(713\) | 30.1421 | − | 30.1421i | 1.12883 | − | 1.12883i | ||||
\(714\) | 23.3137 | − | 4.00000i | 0.872494 | − | 0.149696i | ||||
\(715\) | 10.0000 | − | 2.00000i | 0.373979 | − | 0.0747958i | ||||
\(716\) | 2.34315i | 0.0875675i | ||||||||
\(717\) | −17.0711 | + | 24.1421i | −0.637531 | + | 0.901605i | ||||
\(718\) | −3.41421 | −0.127417 | ||||||||
\(719\) | 5.51472 | 0.205664 | 0.102832 | − | 0.994699i | \(-0.467210\pi\) | ||||
0.102832 | + | 0.994699i | \(0.467210\pi\) | |||||||
\(720\) | −2.70711 | − | 1.29289i | −0.100888 | − | 0.0481833i | ||||
\(721\) | 29.6569 | − | 29.6569i | 1.10448 | − | 1.10448i | ||||
\(722\) | −13.4350 | + | 13.4350i | −0.500000 | + | 0.500000i | ||||
\(723\) | 3.75736 | − | 5.31371i | 0.139738 | − | 0.197619i | ||||
\(724\) | −11.6569 | −0.433224 | ||||||||
\(725\) | −3.65685 | −0.135812 | ||||||||
\(726\) | −4.24264 | − | 3.00000i | −0.157459 | − | 0.111340i | ||||
\(727\) | − | 40.0000i | − | 1.48352i | −0.670667 | − | 0.741759i | \(-0.733992\pi\) | ||
0.670667 | − | 0.741759i | \(-0.266008\pi\) | |||||||
\(728\) | −10.0000 | + | 2.00000i | −0.370625 | + | 0.0741249i | ||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | 9.89949 | − | 9.89949i | 0.366397 | − | 0.366397i | ||||
\(731\) | − | 24.4853i | − | 0.905621i | ||||||
\(732\) | −21.8995 | + | 3.75736i | −0.809429 | + | 0.138876i | ||||
\(733\) | −15.5563 | + | 15.5563i | −0.574587 | + | 0.574587i | −0.933407 | − | 0.358820i | \(-0.883179\pi\) |
0.358820 | + | 0.933407i | \(0.383179\pi\) | |||||||
\(734\) | 26.4853 | + | 26.4853i | 0.977590 | + | 0.977590i | ||||
\(735\) | 1.41421 | + | 1.00000i | 0.0521641 | + | 0.0368856i | ||||
\(736\) | −4.82843 | − | 4.82843i | −0.177978 | − | 0.177978i | ||||
\(737\) | 8.97056i | 0.330435i | ||||||||
\(738\) | −3.07107 | − | 8.68629i | −0.113048 | − | 0.319747i | ||||
\(739\) | −5.65685 | − | 5.65685i | −0.208091 | − | 0.208091i | 0.595365 | − | 0.803456i | \(-0.297008\pi\) |
−0.803456 | + | 0.595365i | \(0.797008\pi\) | |||||||
\(740\) | −5.65685 | −0.207950 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.6274 | 0.977523 | ||||||||
\(743\) | 23.3137 | + | 23.3137i | 0.855297 | + | 0.855297i | 0.990780 | − | 0.135483i | \(-0.0432585\pi\) |
−0.135483 | + | 0.990780i | \(0.543259\pi\) | |||||||
\(744\) | −10.6569 | + | 1.82843i | −0.390699 | + | 0.0670334i | ||||
\(745\) | − | 16.8284i | − | 0.616546i | ||||||
\(746\) | −20.3137 | − | 20.3137i | −0.743738 | − | 0.743738i | ||||
\(747\) | 4.48528 | + | 2.14214i | 0.164108 | + | 0.0783766i | ||||
\(748\) | 9.65685 | + | 9.65685i | 0.353090 | + | 0.353090i | ||||
\(749\) | 25.1716 | − | 25.1716i | 0.919749 | − | 0.919749i | ||||
\(750\) | 0.292893 | + | 1.70711i | 0.0106949 | + | 0.0623347i | ||||
\(751\) | − | 21.6569i | − | 0.790270i | −0.918623 | − | 0.395135i | \(-0.870698\pi\) | ||
0.918623 | − | 0.395135i | \(-0.129302\pi\) | |||||||
\(752\) | −2.00000 | + | 2.00000i | −0.0729325 | + | 0.0729325i | ||||
\(753\) | −1.45584 | − | 8.48528i | −0.0530539 | − | 0.309221i | ||||
\(754\) | −7.31371 | + | 10.9706i | −0.266350 | + | 0.399524i | ||||
\(755\) | 17.5563i | 0.638941i | ||||||||
\(756\) | 14.1421 | + | 4.00000i | 0.514344 | + | 0.145479i | ||||
\(757\) | −35.0711 | −1.27468 | −0.637340 | − | 0.770583i | \(-0.719965\pi\) | ||||
−0.637340 | + | 0.770583i | \(0.719965\pi\) | |||||||
\(758\) | 10.6274 | 0.386005 | ||||||||
\(759\) | −27.3137 | − | 19.3137i | −0.991425 | − | 0.701043i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.9706 | − | 17.9706i | 0.651432 | − | 0.651432i | −0.301905 | − | 0.953338i | \(-0.597623\pi\) |
0.953338 | + | 0.301905i | \(0.0976227\pi\) | |||||||
\(762\) | 2.34315 | + | 1.65685i | 0.0848832 | + | 0.0600215i | ||||
\(763\) | −32.9706 | −1.19361 | ||||||||
\(764\) | 12.8284 | 0.464116 | ||||||||
\(765\) | −13.0711 | − | 6.24264i | −0.472585 | − | 0.225703i | ||||
\(766\) | 5.65685i | 0.204390i | ||||||||
\(767\) | 11.3137 | − | 16.9706i | 0.408514 | − | 0.612772i | ||||
\(768\) | 0.292893 | + | 1.70711i | 0.0105689 | + | 0.0615999i | ||||
\(769\) | 7.97056 | − | 7.97056i | 0.287426 | − | 0.287426i | −0.548636 | − | 0.836062i | \(-0.684853\pi\) |
0.836062 | + | 0.548636i | \(0.184853\pi\) | |||||||
\(770\) | 8.00000i | 0.288300i | ||||||||
\(771\) | 7.75736 | + | 45.2132i | 0.279374 | + | 1.62831i | ||||
\(772\) | 1.07107 | − | 1.07107i | 0.0385486 | − | 0.0385486i | ||||
\(773\) | −22.6274 | − | 22.6274i | −0.813852 | − | 0.813852i | 0.171357 | − | 0.985209i | \(-0.445185\pi\) |
−0.985209 | + | 0.171357i | \(0.945185\pi\) | |||||||
\(774\) | 6.55635 | − | 13.7279i | 0.235663 | − | 0.493440i | ||||
\(775\) | 4.41421 | + | 4.41421i | 0.158563 | + | 0.158563i | ||||
\(776\) | − | 12.1421i | − | 0.435877i | ||||||
\(777\) | 27.3137 | − | 4.68629i | 0.979874 | − | 0.168120i | ||||
\(778\) | −22.3848 | − | 22.3848i | −0.802533 | − | 0.802533i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 5.70711 | + | 2.53553i | 0.204347 | + | 0.0907867i | ||||
\(781\) | −41.6569 | −1.49060 | ||||||||
\(782\) | −23.3137 | − | 23.3137i | −0.833697 | − | 0.833697i | ||||
\(783\) | 16.5858 | − | 9.27208i | 0.592728 | − | 0.331357i | ||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 14.6569 | + | 14.6569i | 0.523126 | + | 0.523126i | ||||
\(786\) | 16.0000 | + | 11.3137i | 0.570701 | + | 0.403547i | ||||
\(787\) | 14.0416 | + | 14.0416i | 0.500530 | + | 0.500530i | 0.911603 | − | 0.411073i | \(-0.134846\pi\) |
−0.411073 | + | 0.911603i | \(0.634846\pi\) | |||||||
\(788\) | 9.17157 | − | 9.17157i | 0.326724 | − | 0.326724i | ||||
\(789\) | 12.8284 | − | 2.20101i | 0.456704 | − | 0.0783580i | ||||
\(790\) | 8.82843i | 0.314101i | ||||||||
\(791\) | 36.9706 | − | 36.9706i | 1.31452 | − | 1.31452i | ||||
\(792\) | 2.82843 | + | 8.00000i | 0.100504 | + | 0.284268i | ||||
\(793\) | 45.3553 | − | 9.07107i | 1.61062 | − | 0.322123i | ||||
\(794\) | 9.31371i | 0.330531i | ||||||||
\(795\) | −13.3137 | − | 9.41421i | −0.472189 | − | 0.333888i | ||||
\(796\) | 0.828427 | 0.0293628 | ||||||||
\(797\) | −12.2426 | −0.433657 | −0.216828 | − | 0.976210i | \(-0.569571\pi\) | ||||
−0.216828 | + | 0.976210i | \(0.569571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.65685 | + | 9.65685i | −0.341635 | + | 0.341635i | ||||
\(800\) | 0.707107 | − | 0.707107i | 0.0250000 | − | 0.0250000i | ||||
\(801\) | −4.85786 | + | 10.1716i | −0.171644 | + | 0.359395i | ||||
\(802\) | −30.5858 | −1.08002 | ||||||||
\(803\) | −39.5980 | −1.39738 | ||||||||
\(804\) | −3.17157 | + | 4.48528i | −0.111853 | + | 0.158184i | ||||
\(805\) | − | 19.3137i | − | 0.680719i | ||||||
\(806\) | 22.0711 | − | 4.41421i | 0.777420 | − | 0.155484i | ||||
\(807\) | −21.8995 | + | 3.75736i | −0.770899 | + | 0.132265i | ||||
\(808\) | 5.07107 | − | 5.07107i | 0.178400 | − | 0.178400i | ||||
\(809\) | 8.00000i | 0.281265i | 0.990062 | + | 0.140633i | \(0.0449136\pi\) | ||||
−0.990062 | + | 0.140633i | \(0.955086\pi\) | |||||||
\(810\) | −5.65685 | − | 7.00000i | −0.198762 | − | 0.245955i | ||||
\(811\) | 16.4853 | − | 16.4853i | 0.578877 | − | 0.578877i | −0.355717 | − | 0.934594i | \(-0.615763\pi\) |
0.934594 | + | 0.355717i | \(0.115763\pi\) | |||||||
\(812\) | −7.31371 | − | 7.31371i | −0.256661 | − | 0.256661i | ||||
\(813\) | −17.7574 | + | 25.1127i | −0.622778 | + | 0.880741i | ||||
\(814\) | 11.3137 | + | 11.3137i | 0.396545 | + | 0.396545i | ||||
\(815\) | 6.34315i | 0.222191i | ||||||||
\(816\) | 1.41421 | + | 8.24264i | 0.0495074 | + | 0.288550i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 19.0711 | 0.666804 | ||||||||
\(819\) | −29.6569 | − | 7.51472i | −1.03629 | − | 0.262586i | ||||
\(820\) | 3.07107 | 0.107246 | ||||||||
\(821\) | −4.92893 | − | 4.92893i | −0.172021 | − | 0.172021i | 0.615846 | − | 0.787867i | \(-0.288814\pi\) |
−0.787867 | + | 0.615846i | \(0.788814\pi\) | |||||||
\(822\) | −2.72792 | − | 15.8995i | −0.0951472 | − | 0.554559i | ||||
\(823\) | − | 52.2843i | − | 1.82252i | −0.411837 | − | 0.911258i | \(-0.635113\pi\) | ||
0.411837 | − | 0.911258i | \(-0.364887\pi\) | |||||||
\(824\) | 10.4853 | + | 10.4853i | 0.365272 | + | 0.365272i | ||||
\(825\) | 2.82843 | − | 4.00000i | 0.0984732 | − | 0.139262i | ||||
\(826\) | 11.3137 | + | 11.3137i | 0.393654 | + | 0.393654i | ||||
\(827\) | 29.5563 | − | 29.5563i | 1.02777 | − | 1.02777i | 0.0281719 | − | 0.999603i | \(-0.491031\pi\) |
0.999603 | − | 0.0281719i | \(-0.00896857\pi\) | |||||||
\(828\) | −6.82843 | − | 19.3137i | −0.237304 | − | 0.671198i | ||||
\(829\) | − | 9.51472i | − | 0.330460i | −0.986255 | − | 0.165230i | \(-0.947163\pi\) | ||
0.986255 | − | 0.165230i | \(-0.0528366\pi\) | |||||||
\(830\) | −1.17157 | + | 1.17157i | −0.0406659 | + | 0.0406659i | ||||
\(831\) | 14.8995 | − | 2.55635i | 0.516858 | − | 0.0886788i | ||||
\(832\) | −0.707107 | − | 3.53553i | −0.0245145 | − | 0.122573i | ||||
\(833\) | − | 4.82843i | − | 0.167295i | ||||||
\(834\) | 7.31371 | − | 10.3431i | 0.253253 | − | 0.358154i | ||||
\(835\) | 13.1716 | 0.455821 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.2132 | − | 8.82843i | −1.07889 | − | 0.305155i | ||||
\(838\) | −3.65685 | + | 3.65685i | −0.126324 | + | 0.126324i | ||||
\(839\) | 7.92893 | − | 7.92893i | 0.273737 | − | 0.273737i | −0.556866 | − | 0.830603i | \(-0.687996\pi\) |
0.830603 | + | 0.556866i | \(0.187996\pi\) | |||||||
\(840\) | −2.82843 | + | 4.00000i | −0.0975900 | + | 0.138013i | ||||
\(841\) | 15.6274 | 0.538876 | ||||||||
\(842\) | −8.34315 | −0.287524 | ||||||||
\(843\) | −30.0000 | − | 21.2132i | −1.03325 | − | 0.730622i | ||||
\(844\) | − | 16.9706i | − | 0.584151i | ||||||
\(845\) | −12.0208 | − | 4.94975i | −0.413529 | − | 0.170276i | ||||
\(846\) | −8.00000 | + | 2.82843i | −0.275046 | + | 0.0972433i | ||||
\(847\) | −6.00000 | + | 6.00000i | −0.206162 | + | 0.206162i | ||||
\(848\) | 9.41421i | 0.323285i | ||||||||
\(849\) | −16.6569 | + | 2.85786i | −0.571662 | + | 0.0980817i | ||||
\(850\) | 3.41421 | − | 3.41421i | 0.117107 | − | 0.117107i | ||||
\(851\) | −27.3137 | − | 27.3137i | −0.936302 | − | 0.936302i | ||||
\(852\) | −20.8284 | − | 14.7279i | −0.713570 | − | 0.504570i | ||||
\(853\) | −25.6569 | − | 25.6569i | −0.878474 | − | 0.878474i | 0.114903 | − | 0.993377i | \(-0.463344\pi\) |
−0.993377 | + | 0.114903i | \(0.963344\pi\) | |||||||
\(854\) | 36.2843i | 1.24162i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.89949 | + | 8.89949i | 0.304178 | + | 0.304178i | ||||
\(857\) | 52.6274 | 1.79772 | 0.898859 | − | 0.438238i | \(-0.144397\pi\) | ||||
0.898859 | + | 0.438238i | \(0.144397\pi\) | |||||||
\(858\) | −6.34315 | − | 16.4853i | −0.216551 | − | 0.562798i | ||||
\(859\) | −22.8284 | −0.778896 | −0.389448 | − | 0.921048i | \(-0.627334\pi\) | ||||
−0.389448 | + | 0.921048i | \(0.627334\pi\) | |||||||
\(860\) | 3.58579 | + | 3.58579i | 0.122274 | + | 0.122274i | ||||
\(861\) | −14.8284 | + | 2.54416i | −0.505351 | + | 0.0867046i | ||||
\(862\) | 21.5563i | 0.734212i | ||||||||
\(863\) | −5.79899 | − | 5.79899i | −0.197400 | − | 0.197400i | 0.601485 | − | 0.798884i | \(-0.294576\pi\) |
−0.798884 | + | 0.601485i | \(0.794576\pi\) | |||||||
\(864\) | −1.41421 | + | 5.00000i | −0.0481125 | + | 0.170103i | ||||
\(865\) | 10.3137 | + | 10.3137i | 0.350677 | + | 0.350677i | ||||
\(866\) | 25.2132 | − | 25.2132i | 0.856780 | − | 0.856780i | ||||
\(867\) | 1.84924 | + | 10.7782i | 0.0628036 | + | 0.366046i | ||||
\(868\) | 17.6569i | 0.599313i | ||||||||
\(869\) | 17.6569 | − | 17.6569i | 0.598968 | − | 0.598968i | ||||
\(870\) | 1.07107 | + | 6.24264i | 0.0363126 | + | 0.211645i | ||||
\(871\) | 6.34315 | − | 9.51472i | 0.214929 | − | 0.322394i | ||||
\(872\) | − | 11.6569i | − | 0.394751i | ||||||
\(873\) | 15.6985 | − | 32.8701i | 0.531313 | − | 1.11248i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.82843 | 0.0956183 | ||||||||
\(876\) | −19.7990 | − | 14.0000i | −0.668946 | − | 0.473016i | ||||
\(877\) | 8.72792 | − | 8.72792i | 0.294721 | − | 0.294721i | −0.544221 | − | 0.838942i | \(-0.683175\pi\) |
0.838942 | + | 0.544221i | \(0.183175\pi\) | |||||||
\(878\) | −16.9706 | + | 16.9706i | −0.572729 | + | 0.572729i | ||||
\(879\) | 32.9706 | + | 23.3137i | 1.11207 | + | 0.786352i | ||||
\(880\) | −2.82843 | −0.0953463 | ||||||||
\(881\) | −9.31371 | −0.313787 | −0.156893 | − | 0.987616i | \(-0.550148\pi\) | ||||
−0.156893 | + | 0.987616i | \(0.550148\pi\) | |||||||
\(882\) | 1.29289 | − | 2.70711i | 0.0435340 | − | 0.0911530i | ||||
\(883\) | 48.5858i | 1.63504i | 0.575899 | + | 0.817521i | \(0.304652\pi\) | ||||
−0.575899 | + | 0.817521i | \(0.695348\pi\) | |||||||
\(884\) | −3.41421 | − | 17.0711i | −0.114832 | − | 0.574162i | ||||
\(885\) | −1.65685 | − | 9.65685i | −0.0556945 | − | 0.324612i | ||||
\(886\) | 16.8995 | − | 16.8995i | 0.567750 | − | 0.567750i | ||||
\(887\) | − | 38.1421i | − | 1.28069i | −0.768088 | − | 0.640344i | \(-0.778792\pi\) | ||
0.768088 | − | 0.640344i | \(-0.221208\pi\) | |||||||
\(888\) | 1.65685 | + | 9.65685i | 0.0556004 | + | 0.324063i | ||||
\(889\) | 3.31371 | − | 3.31371i | 0.111138 | − | 0.111138i | ||||
\(890\) | −2.65685 | − | 2.65685i | −0.0890580 | − | 0.0890580i | ||||
\(891\) | −2.68629 | + | 25.3137i | −0.0899942 | + | 0.848041i | ||||
\(892\) | −13.6569 | − | 13.6569i | −0.457265 | − | 0.457265i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −28.7279 | + | 4.92893i | −0.960805 | + | 0.164848i | ||||
\(895\) | −1.65685 | − | 1.65685i | −0.0553825 | − | 0.0553825i | ||||
\(896\) | 2.82843 | 0.0944911 | ||||||||
\(897\) | 15.3137 | + | 39.7990i | 0.511310 | + | 1.32885i | ||||
\(898\) | −10.3848 | −0.346544 | ||||||||
\(899\) | 16.1421 | + | 16.1421i | 0.538370 | + | 0.538370i | ||||
\(900\) | 2.82843 | − | 1.00000i | 0.0942809 | − | 0.0333333i | ||||
\(901\) | 45.4558i | 1.51435i | ||||||||
\(902\) | −6.14214 | − | 6.14214i | −0.204511 | − | 0.204511i | ||||
\(903\) | −20.2843 | − | 14.3431i | −0.675018 | − | 0.477310i | ||||
\(904\) | 13.0711 | + | 13.0711i | 0.434737 | + | 0.434737i | ||||
\(905\) | 8.24264 | − | 8.24264i | 0.273995 | − | 0.273995i | ||||
\(906\) | 29.9706 | − | 5.14214i | 0.995705 | − | 0.170836i | ||||
\(907\) | 4.10051i | 0.136155i | 0.997680 | + | 0.0680775i | \(0.0216865\pi\) | ||||
−0.997680 | + | 0.0680775i | \(0.978313\pi\) | |||||||
\(908\) | −11.4142 | + | 11.4142i | −0.378794 | + | 0.378794i | ||||
\(909\) | 20.2843 | − | 7.17157i | 0.672787 | − | 0.237866i | ||||
\(910\) | 5.65685 | − | 8.48528i | 0.187523 | − | 0.281284i | ||||
\(911\) | − | 29.1127i | − | 0.964547i | −0.876021 | − | 0.482273i | \(-0.839811\pi\) | ||
0.876021 | − | 0.482273i | \(-0.160189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.68629 | 0.155094 | ||||||||
\(914\) | 16.1421 | 0.533934 | ||||||||
\(915\) | 12.8284 | − | 18.1421i | 0.424095 | − | 0.599761i | ||||
\(916\) | 15.8995 | − | 15.8995i | 0.525334 | − | 0.525334i | ||||
\(917\) | 22.6274 | − | 22.6274i | 0.747223 | − | 0.747223i | ||||
\(918\) | −6.82843 | + | 24.1421i | −0.225372 | + | 0.796809i | ||||
\(919\) | −18.3431 | −0.605085 | −0.302542 | − | 0.953136i | \(-0.597835\pi\) | ||||
−0.302542 | + | 0.953136i | \(0.597835\pi\) | |||||||
\(920\) | 6.82843 | 0.225127 | ||||||||
\(921\) | 12.1421 | − | 17.1716i | 0.400097 | − | 0.565823i | ||||
\(922\) | 12.3431i | 0.406500i | ||||||||
\(923\) | 44.1838 | + | 29.4558i | 1.45433 | + | 0.969551i | ||||
\(924\) | 13.6569 | − | 2.34315i | 0.449278 | − | 0.0770838i | ||||
\(925\) | 4.00000 | − | 4.00000i | 0.131519 | − | 0.131519i | ||||
\(926\) | 16.9706i | 0.557687i | ||||||||
\(927\) | 14.8284 | + | 41.9411i | 0.487029 | + | 1.37753i | ||||
\(928\) | 2.58579 | − | 2.58579i | 0.0848826 | − | 0.0848826i | ||||
\(929\) | −25.0000 | − | 25.0000i | −0.820223 | − | 0.820223i | 0.165916 | − | 0.986140i | \(-0.446942\pi\) |
−0.986140 | + | 0.165916i | \(0.946942\pi\) | |||||||
\(930\) | 6.24264 | − | 8.82843i | 0.204704 | − | 0.289496i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.142136i | 0.00465581i | ||||||||
\(933\) | 8.97056 | + | 52.2843i | 0.293683 | + | 1.71171i | ||||
\(934\) | 1.58579 | + | 1.58579i | 0.0518885 | + | 0.0518885i | ||||
\(935\) | −13.6569 | −0.446627 | ||||||||
\(936\) | 2.65685 | − | 10.4853i | 0.0868420 | − | 0.342722i | ||||
\(937\) | −11.9411 | −0.390100 | −0.195050 | − | 0.980793i | \(-0.562487\pi\) | ||||
−0.195050 | + | 0.980793i | \(0.562487\pi\) | |||||||
\(938\) | 6.34315 | + | 6.34315i | 0.207111 | + | 0.207111i | ||||
\(939\) | 5.55635 | + | 32.3848i | 0.181325 | + | 1.05684i | ||||
\(940\) | − | 2.82843i | − | 0.0922531i | ||||||
\(941\) | 22.7279 | + | 22.7279i | 0.740909 | + | 0.740909i | 0.972753 | − | 0.231844i | \(-0.0744759\pi\) |
−0.231844 | + | 0.972753i | \(0.574476\pi\) | |||||||
\(942\) | 20.7279 | − | 29.3137i | 0.675352 | − | 0.955092i | ||||
\(943\) | 14.8284 | + | 14.8284i | 0.482880 | + | 0.482880i | ||||
\(944\) | −4.00000 | + | 4.00000i | −0.130189 | + | 0.130189i | ||||
\(945\) | −12.8284 | + | 7.17157i | −0.417309 | + | 0.233291i | ||||
\(946\) | − | 14.3431i | − | 0.466336i | ||||||
\(947\) | 1.75736 | − | 1.75736i | 0.0571065 | − | 0.0571065i | −0.677977 | − | 0.735083i | \(-0.737143\pi\) |
0.735083 | + | 0.677977i | \(0.237143\pi\) | |||||||
\(948\) | 15.0711 | − | 2.58579i | 0.489486 | − | 0.0839824i | ||||
\(949\) | 42.0000 | + | 28.0000i | 1.36338 | + | 0.908918i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0000 | − | 33.9411i | 0.778253 | − | 1.10062i | ||||
\(952\) | 13.6569 | 0.442621 | ||||||||
\(953\) | 2.28427 | 0.0739948 | 0.0369974 | − | 0.999315i | \(-0.488221\pi\) | ||||
0.0369974 | + | 0.999315i | \(0.488221\pi\) | |||||||
\(954\) | −12.1716 | + | 25.4853i | −0.394069 | + | 0.825116i | ||||
\(955\) | −9.07107 | + | 9.07107i | −0.293533 | + | 0.293533i | ||||
\(956\) | −12.0711 | + | 12.0711i | −0.390406 | + | 0.390406i | ||||
\(957\) | 10.3431 | − | 14.6274i | 0.334346 | − | 0.472837i | ||||
\(958\) | −3.41421 | −0.110308 | ||||||||
\(959\) | −26.3431 | −0.850665 | ||||||||
\(960\) | −1.41421 | − | 1.00000i | −0.0456435 | − | 0.0322749i | ||||
\(961\) | − | 7.97056i | − | 0.257115i | ||||||
\(962\) | −4.00000 | − | 20.0000i | −0.128965 | − | 0.644826i | ||||
\(963\) | 12.5858 | + | 35.5980i | 0.405571 | + | 1.14713i | ||||
\(964\) | 2.65685 | − | 2.65685i | 0.0855715 | − | 0.0855715i | ||||
\(965\) | 1.51472i | 0.0487605i | ||||||||
\(966\) | −32.9706 | + | 5.65685i | −1.06081 | + | 0.182006i | ||||
\(967\) | −24.2843 | + | 24.2843i | −0.780930 | + | 0.780930i | −0.979988 | − | 0.199058i | \(-0.936212\pi\) |
0.199058 | + | 0.979988i | \(0.436212\pi\) | |||||||
\(968\) | −2.12132 | − | 2.12132i | −0.0681818 | − | 0.0681818i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.58579 | + | 8.58579i | 0.275673 | + | 0.275673i | ||||
\(971\) | 39.1127i | 1.25519i | 0.778542 | + | 0.627593i | \(0.215960\pi\) | ||||
−0.778542 | + | 0.627593i | \(0.784040\pi\) | |||||||
\(972\) | −10.2929 | + | 11.7071i | −0.330145 | + | 0.375506i | ||||
\(973\) | −14.6274 | − | 14.6274i | −0.468933 | − | 0.468933i | ||||
\(974\) | 33.1716 | 1.06289 | ||||||||
\(975\) | −5.82843 | + | 2.24264i | −0.186659 | + | 0.0718220i | ||||
\(976\) | −12.8284 | −0.410628 | ||||||||
\(977\) | 0.242641 | + | 0.242641i | 0.00776276 | + | 0.00776276i | 0.710978 | − | 0.703215i | \(-0.248253\pi\) |
−0.703215 | + | 0.710978i | \(0.748253\pi\) | |||||||
\(978\) | 10.8284 | − | 1.85786i | 0.346255 | − | 0.0594080i | ||||
\(979\) | 10.6274i | 0.339654i | ||||||||
\(980\) | 0.707107 | + | 0.707107i | 0.0225877 | + | 0.0225877i | ||||
\(981\) | 15.0711 | − | 31.5563i | 0.481182 | − | 1.00752i | ||||
\(982\) | −6.97056 | − | 6.97056i | −0.222440 | − | 0.222440i | ||||
\(983\) | −19.4558 | + | 19.4558i | −0.620545 | + | 0.620545i | −0.945671 | − | 0.325126i | \(-0.894593\pi\) |
0.325126 | + | 0.945671i | \(0.394593\pi\) | |||||||
\(984\) | −0.899495 | − | 5.24264i | −0.0286749 | − | 0.167129i | ||||
\(985\) | 12.9706i | 0.413276i | ||||||||
\(986\) | 12.4853 | − | 12.4853i | 0.397612 | − | 0.397612i | ||||
\(987\) | 2.34315 | + | 13.6569i | 0.0745832 | + | 0.434702i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.6274i | 1.10109i | ||||||||
\(990\) | −7.65685 | − | 3.65685i | −0.243351 | − | 0.116222i | ||||
\(991\) | 12.1421 | 0.385708 | 0.192854 | − | 0.981227i | \(-0.438226\pi\) | ||||
0.192854 | + | 0.981227i | \(0.438226\pi\) | |||||||
\(992\) | −6.24264 | −0.198204 | ||||||||
\(993\) | −12.0000 | − | 8.48528i | −0.380808 | − | 0.269272i | ||||
\(994\) | −29.4558 | + | 29.4558i | −0.934283 | + | 0.934283i | ||||
\(995\) | −0.585786 | + | 0.585786i | −0.0185707 | + | 0.0185707i | ||||
\(996\) | 2.34315 | + | 1.65685i | 0.0742454 | + | 0.0524994i | ||||
\(997\) | 40.0416 | 1.26813 | 0.634066 | − | 0.773279i | \(-0.281385\pi\) | ||||
0.634066 | + | 0.773279i | \(0.281385\pi\) | |||||||
\(998\) | 31.7990 | 1.00658 | ||||||||
\(999\) | −8.00000 | + | 28.2843i | −0.253109 | + | 0.894875i |
(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 | 390.2.p.e.161.2 | ✓ | 4 | |
3.2 | odd | 2 | 390.2.p.f.161.1 | yes | 4 | ||
13.8 | odd | 4 | 390.2.p.f.281.1 | yes | 4 | ||
39.8 | even | 4 | inner | 390.2.p.e.281.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.p.e.161.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
390.2.p.e.281.2 | yes | 4 | 39.8 | even | 4 | inner | |
390.2.p.f.161.1 | yes | 4 | 3.2 | odd | 2 | ||
390.2.p.f.281.1 | yes | 4 | 13.8 | odd | 4 |