Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1121,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.3 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1121 |
Dual form | 1155.2.l.b.1121.4 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 1.41421 | − | 2.00000i | 0.577350 | − | 0.816497i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | − | 1.41421i | − | 0.447214i | ||||||
\(11\) | −3.00000 | − | 1.41421i | −0.904534 | − | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.24264i | 0.621997i | 0.950410 | + | 0.310998i | \(0.100663\pi\) | ||||
−0.950410 | + | 0.310998i | \(0.899337\pi\) | |||||||
\(14\) | − | 1.41421i | − | 0.377964i | ||||||
\(15\) | −1.41421 | − | 1.00000i | −0.365148 | − | 0.258199i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −5.82843 | −1.41360 | −0.706801 | − | 0.707413i | \(-0.749862\pi\) | ||||
−0.706801 | + | 0.707413i | \(0.749862\pi\) | |||||||
\(18\) | −1.41421 | − | 4.00000i | −0.333333 | − | 0.942809i | ||||
\(19\) | − | 3.24264i | − | 0.743913i | −0.928250 | − | 0.371956i | \(-0.878687\pi\) | ||
0.928250 | − | 0.371956i | \(-0.121313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | − | 1.00000i | −0.308607 | − | 0.218218i | ||||
\(22\) | −4.24264 | − | 2.00000i | −0.904534 | − | 0.426401i | ||||
\(23\) | − | 1.24264i | − | 0.259108i | −0.991572 | − | 0.129554i | \(-0.958645\pi\) | ||
0.991572 | − | 0.129554i | \(-0.0413546\pi\) | |||||||
\(24\) | −2.82843 | + | 4.00000i | −0.577350 | + | 0.816497i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.17157i | 0.621997i | ||||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.82843 | 1.08231 | 0.541156 | − | 0.840922i | \(-0.317987\pi\) | ||||
0.541156 | + | 0.840922i | \(0.317987\pi\) | |||||||
\(30\) | −2.00000 | − | 1.41421i | −0.365148 | − | 0.258199i | ||||
\(31\) | 8.24264 | 1.48042 | 0.740211 | − | 0.672375i | \(-0.234726\pi\) | ||||
0.740211 | + | 0.672375i | \(0.234726\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.00000 | + | 2.82843i | −0.870388 | + | 0.492366i | ||||
\(34\) | −8.24264 | −1.41360 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24264 | 1.35508 | 0.677541 | − | 0.735485i | \(-0.263046\pi\) | ||||
0.677541 | + | 0.735485i | \(0.263046\pi\) | |||||||
\(38\) | − | 4.58579i | − | 0.743913i | ||||||
\(39\) | 3.17157 | + | 2.24264i | 0.507858 | + | 0.359110i | ||||
\(40\) | 2.82843i | 0.447214i | ||||||||
\(41\) | −4.58579 | −0.716180 | −0.358090 | − | 0.933687i | \(-0.616572\pi\) | ||||
−0.358090 | + | 0.933687i | \(0.616572\pi\) | |||||||
\(42\) | −2.00000 | − | 1.41421i | −0.308607 | − | 0.218218i | ||||
\(43\) | − | 3.24264i | − | 0.494498i | −0.968952 | − | 0.247249i | \(-0.920473\pi\) | ||
0.968952 | − | 0.247249i | \(-0.0795266\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | + | 1.00000i | −0.421637 | + | 0.149071i | ||||
\(46\) | − | 1.75736i | − | 0.259108i | ||||||
\(47\) | − | 1.07107i | − | 0.156231i | −0.996944 | − | 0.0781156i | \(-0.975110\pi\) | ||
0.996944 | − | 0.0781156i | \(-0.0248903\pi\) | |||||||
\(48\) | −4.00000 | + | 5.65685i | −0.577350 | + | 0.816497i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −1.41421 | −0.200000 | ||||||||
\(51\) | −5.82843 | + | 8.24264i | −0.816143 | + | 1.15420i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.41421i | − | 0.606339i | −0.952937 | − | 0.303169i | \(-0.901955\pi\) | ||
0.952937 | − | 0.303169i | \(-0.0980448\pi\) | |||||||
\(54\) | −7.07107 | − | 2.00000i | −0.962250 | − | 0.272166i | ||||
\(55\) | −1.41421 | + | 3.00000i | −0.190693 | + | 0.404520i | ||||
\(56\) | 2.82843i | 0.377964i | ||||||||
\(57\) | −4.58579 | − | 3.24264i | −0.607402 | − | 0.429498i | ||||
\(58\) | 8.24264 | 1.08231 | ||||||||
\(59\) | − | 12.8995i | − | 1.67937i | −0.543073 | − | 0.839686i | \(-0.682739\pi\) | ||
0.543073 | − | 0.839686i | \(-0.317261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.24264i | 1.18340i | 0.806159 | + | 0.591699i | \(0.201543\pi\) | ||||
−0.806159 | + | 0.591699i | \(0.798457\pi\) | |||||||
\(62\) | 11.6569 | 1.48042 | ||||||||
\(63\) | −2.82843 | + | 1.00000i | −0.356348 | + | 0.125988i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 2.24264 | 0.278165 | ||||||||
\(66\) | −7.07107 | + | 4.00000i | −0.870388 | + | 0.492366i | ||||
\(67\) | −12.4853 | −1.52532 | −0.762660 | − | 0.646800i | \(-0.776107\pi\) | ||||
−0.762660 | + | 0.646800i | \(0.776107\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.75736 | − | 1.24264i | −0.211561 | − | 0.149596i | ||||
\(70\) | −1.41421 | −0.169031 | ||||||||
\(71\) | − | 1.75736i | − | 0.208560i | −0.994548 | − | 0.104280i | \(-0.966746\pi\) | ||
0.994548 | − | 0.104280i | \(-0.0332538\pi\) | |||||||
\(72\) | 2.82843 | + | 8.00000i | 0.333333 | + | 0.942809i | ||||
\(73\) | − | 6.48528i | − | 0.759045i | −0.925183 | − | 0.379522i | \(-0.876088\pi\) | ||
0.925183 | − | 0.379522i | \(-0.123912\pi\) | |||||||
\(74\) | 11.6569 | 1.35508 | ||||||||
\(75\) | −1.00000 | + | 1.41421i | −0.115470 | + | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.41421 | + | 3.00000i | −0.161165 | + | 0.341882i | ||||
\(78\) | 4.48528 | + | 3.17157i | 0.507858 | + | 0.359110i | ||||
\(79\) | − | 6.24264i | − | 0.702352i | −0.936309 | − | 0.351176i | \(-0.885782\pi\) | ||
0.936309 | − | 0.351176i | \(-0.114218\pi\) | |||||||
\(80\) | 4.00000i | 0.447214i | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | −6.48528 | −0.716180 | ||||||||
\(83\) | 17.1421 | 1.88159 | 0.940797 | − | 0.338971i | \(-0.110079\pi\) | ||||
0.940797 | + | 0.338971i | \(0.110079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.82843i | 0.632182i | ||||||||
\(86\) | − | 4.58579i | − | 0.494498i | ||||||
\(87\) | 5.82843 | − | 8.24264i | 0.624873 | − | 0.883704i | ||||
\(88\) | 8.48528 | + | 4.00000i | 0.904534 | + | 0.426401i | ||||
\(89\) | − | 16.4142i | − | 1.73990i | −0.493137 | − | 0.869952i | \(-0.664150\pi\) | ||
0.493137 | − | 0.869952i | \(-0.335850\pi\) | |||||||
\(90\) | −4.00000 | + | 1.41421i | −0.421637 | + | 0.149071i | ||||
\(91\) | 2.24264 | 0.235093 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.24264 | − | 11.6569i | 0.854722 | − | 1.20876i | ||||
\(94\) | − | 1.51472i | − | 0.156231i | ||||||
\(95\) | −3.24264 | −0.332688 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | −1.41421 | −0.142857 | ||||||||
\(99\) | −1.00000 | + | 9.89949i | −0.100504 | + | 0.994937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.48528 | 0.247295 | 0.123647 | − | 0.992326i | \(-0.460541\pi\) | ||||
0.123647 | + | 0.992326i | \(0.460541\pi\) | |||||||
\(102\) | −8.24264 | + | 11.6569i | −0.816143 | + | 1.15420i | ||||
\(103\) | −0.514719 | −0.0507167 | −0.0253584 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253584 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(104\) | − | 6.34315i | − | 0.621997i | ||||||
\(105\) | −1.00000 | + | 1.41421i | −0.0975900 | + | 0.138013i | ||||
\(106\) | − | 6.24264i | − | 0.606339i | ||||||
\(107\) | 7.41421 | 0.716759 | 0.358380 | − | 0.933576i | \(-0.383329\pi\) | ||||
0.358380 | + | 0.933576i | \(0.383329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.75736i | 0.359890i | 0.983677 | + | 0.179945i | \(0.0575919\pi\) | ||||
−0.983677 | + | 0.179945i | \(0.942408\pi\) | |||||||
\(110\) | −2.00000 | + | 4.24264i | −0.190693 | + | 0.404520i | ||||
\(111\) | 8.24264 | − | 11.6569i | 0.782357 | − | 1.10642i | ||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | 18.8995i | 1.77791i | 0.457990 | + | 0.888957i | \(0.348570\pi\) | ||||
−0.457990 | + | 0.888957i | \(0.651430\pi\) | |||||||
\(114\) | −6.48528 | − | 4.58579i | −0.607402 | − | 0.429498i | ||||
\(115\) | −1.24264 | −0.115877 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.34315 | − | 2.24264i | 0.586424 | − | 0.207332i | ||||
\(118\) | − | 18.2426i | − | 1.67937i | ||||||
\(119\) | 5.82843i | 0.534291i | ||||||||
\(120\) | 4.00000 | + | 2.82843i | 0.365148 | + | 0.258199i | ||||
\(121\) | 7.00000 | + | 8.48528i | 0.636364 | + | 0.771389i | ||||
\(122\) | 13.0711i | 1.18340i | ||||||||
\(123\) | −4.58579 | + | 6.48528i | −0.413486 | + | 0.584758i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −4.00000 | + | 1.41421i | −0.356348 | + | 0.125988i | ||||
\(127\) | 13.2426i | 1.17509i | 0.809190 | + | 0.587547i | \(0.199906\pi\) | ||||
−0.809190 | + | 0.587547i | \(0.800094\pi\) | |||||||
\(128\) | 11.3137 | 1.00000 | ||||||||
\(129\) | −4.58579 | − | 3.24264i | −0.403756 | − | 0.285499i | ||||
\(130\) | 3.17157 | 0.278165 | ||||||||
\(131\) | −19.4142 | −1.69623 | −0.848114 | − | 0.529814i | \(-0.822262\pi\) | ||||
−0.848114 | + | 0.529814i | \(0.822262\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.24264 | −0.281173 | ||||||||
\(134\) | −17.6569 | −1.52532 | ||||||||
\(135\) | −1.41421 | + | 5.00000i | −0.121716 | + | 0.430331i | ||||
\(136\) | 16.4853 | 1.41360 | ||||||||
\(137\) | − | 14.4853i | − | 1.23756i | −0.785564 | − | 0.618781i | \(-0.787627\pi\) | ||
0.785564 | − | 0.618781i | \(-0.212373\pi\) | |||||||
\(138\) | −2.48528 | − | 1.75736i | −0.211561 | − | 0.149596i | ||||
\(139\) | − | 12.4853i | − | 1.05899i | −0.848314 | − | 0.529494i | \(-0.822382\pi\) | ||
0.848314 | − | 0.529494i | \(-0.177618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.51472 | − | 1.07107i | −0.127562 | − | 0.0902002i | ||||
\(142\) | − | 2.48528i | − | 0.208560i | ||||||
\(143\) | 3.17157 | − | 6.72792i | 0.265220 | − | 0.562617i | ||||
\(144\) | 4.00000 | + | 11.3137i | 0.333333 | + | 0.942809i | ||||
\(145\) | − | 5.82843i | − | 0.484025i | ||||||
\(146\) | − | 9.17157i | − | 0.759045i | ||||||
\(147\) | −1.00000 | + | 1.41421i | −0.0824786 | + | 0.116642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −1.41421 | + | 2.00000i | −0.115470 | + | 0.163299i | ||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 9.17157i | 0.743913i | ||||||||
\(153\) | 5.82843 | + | 16.4853i | 0.471200 | + | 1.33276i | ||||
\(154\) | −2.00000 | + | 4.24264i | −0.161165 | + | 0.341882i | ||||
\(155\) | − | 8.24264i | − | 0.662065i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | 0.877896 | 0.438948 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | − | 8.82843i | − | 0.702352i | ||||||
\(159\) | −6.24264 | − | 4.41421i | −0.495074 | − | 0.350070i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.24264 | −0.0979338 | ||||||||
\(162\) | −9.89949 | + | 8.00000i | −0.777778 | + | 0.628539i | ||||
\(163\) | 2.24264 | 0.175657 | 0.0878286 | − | 0.996136i | \(-0.472007\pi\) | ||||
0.0878286 | + | 0.996136i | \(0.472007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82843 | + | 5.00000i | 0.220193 | + | 0.389249i | ||||
\(166\) | 24.2426 | 1.88159 | ||||||||
\(167\) | 20.1421 | 1.55865 | 0.779323 | − | 0.626623i | \(-0.215563\pi\) | ||||
0.779323 | + | 0.626623i | \(0.215563\pi\) | |||||||
\(168\) | 4.00000 | + | 2.82843i | 0.308607 | + | 0.218218i | ||||
\(169\) | 7.97056 | 0.613120 | ||||||||
\(170\) | 8.24264i | 0.632182i | ||||||||
\(171\) | −9.17157 | + | 3.24264i | −0.701368 | + | 0.247971i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.82843 | −0.215041 | −0.107521 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107521 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(174\) | 8.24264 | − | 11.6569i | 0.624873 | − | 0.883704i | ||||
\(175\) | 1.00000i | 0.0755929i | ||||||||
\(176\) | 12.0000 | + | 5.65685i | 0.904534 | + | 0.426401i | ||||
\(177\) | −18.2426 | − | 12.8995i | −1.37120 | − | 0.969585i | ||||
\(178\) | − | 23.2132i | − | 1.73990i | ||||||
\(179\) | 13.4142i | 1.00263i | 0.865266 | + | 0.501313i | \(0.167149\pi\) | ||||
−0.865266 | + | 0.501313i | \(0.832851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9706 | −0.815436 | −0.407718 | − | 0.913108i | \(-0.633675\pi\) | ||||
−0.407718 | + | 0.913108i | \(0.633675\pi\) | |||||||
\(182\) | 3.17157 | 0.235093 | ||||||||
\(183\) | 13.0711 | + | 9.24264i | 0.966241 | + | 0.683236i | ||||
\(184\) | 3.51472i | 0.259108i | ||||||||
\(185\) | − | 8.24264i | − | 0.606011i | ||||||
\(186\) | 11.6569 | − | 16.4853i | 0.854722 | − | 1.20876i | ||||
\(187\) | 17.4853 | + | 8.24264i | 1.27865 | + | 0.602762i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.41421 | + | 5.00000i | −0.102869 | + | 0.363696i | ||||
\(190\) | −4.58579 | −0.332688 | ||||||||
\(191\) | − | 9.17157i | − | 0.663632i | −0.943344 | − | 0.331816i | \(-0.892339\pi\) | ||
0.943344 | − | 0.331816i | \(-0.107661\pi\) | |||||||
\(192\) | 8.00000 | − | 11.3137i | 0.577350 | − | 0.816497i | ||||
\(193\) | − | 10.0000i | − | 0.719816i | −0.932988 | − | 0.359908i | \(-0.882808\pi\) | ||
0.932988 | − | 0.359908i | \(-0.117192\pi\) | |||||||
\(194\) | −9.89949 | −0.710742 | ||||||||
\(195\) | 2.24264 | − | 3.17157i | 0.160599 | − | 0.227121i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | −1.41421 | + | 14.0000i | −0.100504 | + | 0.994937i | ||||
\(199\) | 7.51472 | 0.532704 | 0.266352 | − | 0.963876i | \(-0.414182\pi\) | ||||
0.266352 | + | 0.963876i | \(0.414182\pi\) | |||||||
\(200\) | 2.82843 | 0.200000 | ||||||||
\(201\) | −12.4853 | + | 17.6569i | −0.880644 | + | 1.24542i | ||||
\(202\) | 3.51472 | 0.247295 | ||||||||
\(203\) | − | 5.82843i | − | 0.409075i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.58579i | 0.320285i | ||||||||
\(206\) | −0.727922 | −0.0507167 | ||||||||
\(207\) | −3.51472 | + | 1.24264i | −0.244290 | + | 0.0863695i | ||||
\(208\) | − | 8.97056i | − | 0.621997i | ||||||
\(209\) | −4.58579 | + | 9.72792i | −0.317205 | + | 0.672894i | ||||
\(210\) | −1.41421 | + | 2.00000i | −0.0975900 | + | 0.138013i | ||||
\(211\) | 8.00000i | 0.550743i | 0.961338 | + | 0.275371i | \(0.0888008\pi\) | ||||
−0.961338 | + | 0.275371i | \(0.911199\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.48528 | − | 1.75736i | −0.170289 | − | 0.120412i | ||||
\(214\) | 10.4853 | 0.716759 | ||||||||
\(215\) | −3.24264 | −0.221146 | ||||||||
\(216\) | 14.1421 | + | 4.00000i | 0.962250 | + | 0.272166i | ||||
\(217\) | − | 8.24264i | − | 0.559547i | ||||||
\(218\) | 5.31371i | 0.359890i | ||||||||
\(219\) | −9.17157 | − | 6.48528i | −0.619757 | − | 0.438235i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.0711i | − | 0.879255i | ||||||
\(222\) | 11.6569 | − | 16.4853i | 0.782357 | − | 1.10642i | ||||
\(223\) | 17.0000 | 1.13840 | 0.569202 | − | 0.822198i | \(-0.307252\pi\) | ||||
0.569202 | + | 0.822198i | \(0.307252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 2.82843i | 0.0666667 | + | 0.188562i | ||||
\(226\) | 26.7279i | 1.77791i | ||||||||
\(227\) | −6.17157 | −0.409622 | −0.204811 | − | 0.978802i | \(-0.565658\pi\) | ||||
−0.204811 | + | 0.978802i | \(0.565658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7279 | 1.23758 | 0.618788 | − | 0.785558i | \(-0.287624\pi\) | ||||
0.618788 | + | 0.785558i | \(0.287624\pi\) | |||||||
\(230\) | −1.75736 | −0.115877 | ||||||||
\(231\) | 2.82843 | + | 5.00000i | 0.186097 | + | 0.328976i | ||||
\(232\) | −16.4853 | −1.08231 | ||||||||
\(233\) | −9.55635 | −0.626057 | −0.313029 | − | 0.949744i | \(-0.601344\pi\) | ||||
−0.313029 | + | 0.949744i | \(0.601344\pi\) | |||||||
\(234\) | 8.97056 | − | 3.17157i | 0.586424 | − | 0.207332i | ||||
\(235\) | −1.07107 | −0.0698688 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.82843 | − | 6.24264i | −0.573468 | − | 0.405503i | ||||
\(238\) | 8.24264i | 0.534291i | ||||||||
\(239\) | −8.65685 | −0.559965 | −0.279983 | − | 0.960005i | \(-0.590329\pi\) | ||||
−0.279983 | + | 0.960005i | \(0.590329\pi\) | |||||||
\(240\) | 5.65685 | + | 4.00000i | 0.365148 | + | 0.258199i | ||||
\(241\) | − | 9.51472i | − | 0.612897i | −0.951887 | − | 0.306448i | \(-0.900859\pi\) | ||
0.951887 | − | 0.306448i | \(-0.0991407\pi\) | |||||||
\(242\) | 9.89949 | + | 12.0000i | 0.636364 | + | 0.771389i | ||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | −6.48528 | + | 9.17157i | −0.413486 | + | 0.584758i | ||||
\(247\) | 7.27208 | 0.462711 | ||||||||
\(248\) | −23.3137 | −1.48042 | ||||||||
\(249\) | 17.1421 | − | 24.2426i | 1.08634 | − | 1.53631i | ||||
\(250\) | 1.41421i | 0.0894427i | ||||||||
\(251\) | 28.9706i | 1.82861i | 0.405031 | + | 0.914303i | \(0.367261\pi\) | ||||
−0.405031 | + | 0.914303i | \(0.632739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.75736 | + | 3.72792i | −0.110484 | + | 0.234372i | ||||
\(254\) | 18.7279i | 1.17509i | ||||||||
\(255\) | 8.24264 | + | 5.82843i | 0.516174 | + | 0.364990i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.2426i | 1.38746i | 0.720236 | + | 0.693729i | \(0.244033\pi\) | ||||
−0.720236 | + | 0.693729i | \(0.755967\pi\) | |||||||
\(258\) | −6.48528 | − | 4.58579i | −0.403756 | − | 0.285499i | ||||
\(259\) | − | 8.24264i | − | 0.512173i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.82843 | − | 16.4853i | −0.360771 | − | 1.02041i | ||||
\(262\) | −27.4558 | −1.69623 | ||||||||
\(263\) | −20.8284 | −1.28434 | −0.642168 | − | 0.766564i | \(-0.721965\pi\) | ||||
−0.642168 | + | 0.766564i | \(0.721965\pi\) | |||||||
\(264\) | 14.1421 | − | 8.00000i | 0.870388 | − | 0.492366i | ||||
\(265\) | −4.41421 | −0.271163 | ||||||||
\(266\) | −4.58579 | −0.281173 | ||||||||
\(267\) | −23.2132 | − | 16.4142i | −1.42062 | − | 1.00453i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 0.556349i | − | 0.0339212i | −0.999856 | − | 0.0169606i | \(-0.994601\pi\) | ||
0.999856 | − | 0.0169606i | \(-0.00539899\pi\) | |||||||
\(270\) | −2.00000 | + | 7.07107i | −0.121716 | + | 0.430331i | ||||
\(271\) | − | 14.7574i | − | 0.896446i | −0.893922 | − | 0.448223i | \(-0.852057\pi\) | ||
0.893922 | − | 0.448223i | \(-0.147943\pi\) | |||||||
\(272\) | 23.3137 | 1.41360 | ||||||||
\(273\) | 2.24264 | − | 3.17157i | 0.135731 | − | 0.191952i | ||||
\(274\) | − | 20.4853i | − | 1.23756i | ||||||
\(275\) | 3.00000 | + | 1.41421i | 0.180907 | + | 0.0852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.48528i | 0.509831i | 0.966963 | + | 0.254916i | \(0.0820477\pi\) | ||||
−0.966963 | + | 0.254916i | \(0.917952\pi\) | |||||||
\(278\) | − | 17.6569i | − | 1.05899i | ||||||
\(279\) | −8.24264 | − | 23.3137i | −0.493474 | − | 1.39576i | ||||
\(280\) | 2.82843 | 0.169031 | ||||||||
\(281\) | −5.31371 | −0.316989 | −0.158495 | − | 0.987360i | \(-0.550664\pi\) | ||||
−0.158495 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(282\) | −2.14214 | − | 1.51472i | −0.127562 | − | 0.0902002i | ||||
\(283\) | − | 29.2132i | − | 1.73654i | −0.496088 | − | 0.868272i | \(-0.665231\pi\) | ||
0.496088 | − | 0.868272i | \(-0.334769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.24264 | + | 4.58579i | −0.192077 | + | 0.271639i | ||||
\(286\) | 4.48528 | − | 9.51472i | 0.265220 | − | 0.562617i | ||||
\(287\) | 4.58579i | 0.270690i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9706 | 0.998268 | ||||||||
\(290\) | − | 8.24264i | − | 0.484025i | ||||||
\(291\) | −7.00000 | + | 9.89949i | −0.410347 | + | 0.580319i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.34315 | 0.195309 | 0.0976543 | − | 0.995220i | \(-0.468866\pi\) | ||||
0.0976543 | + | 0.995220i | \(0.468866\pi\) | |||||||
\(294\) | −1.41421 | + | 2.00000i | −0.0824786 | + | 0.116642i | ||||
\(295\) | −12.8995 | −0.751038 | ||||||||
\(296\) | −23.3137 | −1.35508 | ||||||||
\(297\) | 13.0000 | + | 11.3137i | 0.754337 | + | 0.656488i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.78680 | 0.161165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.24264 | −0.186903 | ||||||||
\(302\) | 14.1421i | 0.813788i | ||||||||
\(303\) | 2.48528 | − | 3.51472i | 0.142776 | − | 0.201915i | ||||
\(304\) | 12.9706i | 0.743913i | ||||||||
\(305\) | 9.24264 | 0.529232 | ||||||||
\(306\) | 8.24264 | + | 23.3137i | 0.471200 | + | 1.33276i | ||||
\(307\) | − | 20.4853i | − | 1.16916i | −0.811337 | − | 0.584578i | \(-0.801260\pi\) | ||
0.811337 | − | 0.584578i | \(-0.198740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.514719 | + | 0.727922i | −0.0292813 | + | 0.0414100i | ||||
\(310\) | − | 11.6569i | − | 0.662065i | ||||||
\(311\) | − | 14.8284i | − | 0.840843i | −0.907329 | − | 0.420421i | \(-0.861882\pi\) | ||
0.907329 | − | 0.420421i | \(-0.138118\pi\) | |||||||
\(312\) | −8.97056 | − | 6.34315i | −0.507858 | − | 0.359110i | ||||
\(313\) | −26.4558 | −1.49537 | −0.747686 | − | 0.664052i | \(-0.768835\pi\) | ||||
−0.747686 | + | 0.664052i | \(0.768835\pi\) | |||||||
\(314\) | 15.5563 | 0.877896 | ||||||||
\(315\) | 1.00000 | + | 2.82843i | 0.0563436 | + | 0.159364i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.8284i | 1.84383i | 0.387394 | + | 0.921914i | \(0.373375\pi\) | ||||
−0.387394 | + | 0.921914i | \(0.626625\pi\) | |||||||
\(318\) | −8.82843 | − | 6.24264i | −0.495074 | − | 0.350070i | ||||
\(319\) | −17.4853 | − | 8.24264i | −0.978988 | − | 0.461499i | ||||
\(320\) | − | 8.00000i | − | 0.447214i | ||||||
\(321\) | 7.41421 | − | 10.4853i | 0.413821 | − | 0.585231i | ||||
\(322\) | −1.75736 | −0.0979338 | ||||||||
\(323\) | 18.8995i | 1.05160i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.24264i | − | 0.124399i | ||||||
\(326\) | 3.17157 | 0.175657 | ||||||||
\(327\) | 5.31371 | + | 3.75736i | 0.293849 | + | 0.207782i | ||||
\(328\) | 12.9706 | 0.716180 | ||||||||
\(329\) | −1.07107 | −0.0590499 | ||||||||
\(330\) | 4.00000 | + | 7.07107i | 0.220193 | + | 0.389249i | ||||
\(331\) | 2.51472 | 0.138221 | 0.0691107 | − | 0.997609i | \(-0.477984\pi\) | ||||
0.0691107 | + | 0.997609i | \(0.477984\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.24264 | − | 23.3137i | −0.451694 | − | 1.27758i | ||||
\(334\) | 28.4853 | 1.55865 | ||||||||
\(335\) | 12.4853i | 0.682144i | ||||||||
\(336\) | 5.65685 | + | 4.00000i | 0.308607 | + | 0.218218i | ||||
\(337\) | 27.2426i | 1.48400i | 0.670399 | + | 0.742001i | \(0.266123\pi\) | ||||
−0.670399 | + | 0.742001i | \(0.733877\pi\) | |||||||
\(338\) | 11.2721 | 0.613120 | ||||||||
\(339\) | 26.7279 | + | 18.8995i | 1.45166 | + | 1.02648i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.7279 | − | 11.6569i | −1.33909 | − | 0.631254i | ||||
\(342\) | −12.9706 | + | 4.58579i | −0.701368 | + | 0.247971i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 9.17157i | 0.494498i | ||||||||
\(345\) | −1.24264 | + | 1.75736i | −0.0669015 | + | 0.0946130i | ||||
\(346\) | −4.00000 | −0.215041 | ||||||||
\(347\) | 26.8284 | 1.44023 | 0.720113 | − | 0.693857i | \(-0.244090\pi\) | ||||
0.720113 | + | 0.693857i | \(0.244090\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.7574i | − | 0.682886i | −0.939903 | − | 0.341443i | \(-0.889084\pi\) | ||
0.939903 | − | 0.341443i | \(-0.110916\pi\) | |||||||
\(350\) | 1.41421i | 0.0755929i | ||||||||
\(351\) | 3.17157 | − | 11.2132i | 0.169286 | − | 0.598517i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 18.0000i | − | 0.958043i | −0.877803 | − | 0.479022i | \(-0.840992\pi\) | ||
0.877803 | − | 0.479022i | \(-0.159008\pi\) | |||||||
\(354\) | −25.7990 | − | 18.2426i | −1.37120 | − | 0.969585i | ||||
\(355\) | −1.75736 | −0.0932709 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.24264 | + | 5.82843i | 0.436247 | + | 0.308473i | ||||
\(358\) | 18.9706i | 1.00263i | ||||||||
\(359\) | −13.6274 | −0.719228 | −0.359614 | − | 0.933101i | \(-0.617092\pi\) | ||||
−0.359614 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(360\) | 8.00000 | − | 2.82843i | 0.421637 | − | 0.149071i | ||||
\(361\) | 8.48528 | 0.446594 | ||||||||
\(362\) | −15.5147 | −0.815436 | ||||||||
\(363\) | 19.0000 | − | 1.41421i | 0.997241 | − | 0.0742270i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.48528 | −0.339455 | ||||||||
\(366\) | 18.4853 | + | 13.0711i | 0.966241 | + | 0.683236i | ||||
\(367\) | 3.00000 | 0.156599 | 0.0782994 | − | 0.996930i | \(-0.475051\pi\) | ||||
0.0782994 | + | 0.996930i | \(0.475051\pi\) | |||||||
\(368\) | 4.97056i | 0.259108i | ||||||||
\(369\) | 4.58579 | + | 12.9706i | 0.238727 | + | 0.675221i | ||||
\(370\) | − | 11.6569i | − | 0.606011i | ||||||
\(371\) | −4.41421 | −0.229175 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.21320i | − | 0.321707i | −0.986978 | − | 0.160854i | \(-0.948575\pi\) | ||
0.986978 | − | 0.160854i | \(-0.0514247\pi\) | |||||||
\(374\) | 24.7279 | + | 11.6569i | 1.27865 | + | 0.602762i | ||||
\(375\) | 1.41421 | + | 1.00000i | 0.0730297 | + | 0.0516398i | ||||
\(376\) | 3.02944i | 0.156231i | ||||||||
\(377\) | 13.0711i | 0.673194i | ||||||||
\(378\) | −2.00000 | + | 7.07107i | −0.102869 | + | 0.363696i | ||||
\(379\) | 18.4558 | 0.948013 | 0.474007 | − | 0.880521i | \(-0.342807\pi\) | ||||
0.474007 | + | 0.880521i | \(0.342807\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.7279 | + | 13.2426i | 0.959461 | + | 0.678441i | ||||
\(382\) | − | 12.9706i | − | 0.663632i | ||||||
\(383\) | 37.4142i | 1.91178i | 0.293730 | + | 0.955889i | \(0.405103\pi\) | ||||
−0.293730 | + | 0.955889i | \(0.594897\pi\) | |||||||
\(384\) | 11.3137 | − | 16.0000i | 0.577350 | − | 0.816497i | ||||
\(385\) | 3.00000 | + | 1.41421i | 0.152894 | + | 0.0720750i | ||||
\(386\) | − | 14.1421i | − | 0.719816i | ||||||
\(387\) | −9.17157 | + | 3.24264i | −0.466217 | + | 0.164833i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1.75736i | − | 0.0891017i | −0.999007 | − | 0.0445508i | \(-0.985814\pi\) | ||
0.999007 | − | 0.0445508i | \(-0.0141857\pi\) | |||||||
\(390\) | 3.17157 | − | 4.48528i | 0.160599 | − | 0.227121i | ||||
\(391\) | 7.24264i | 0.366276i | ||||||||
\(392\) | 2.82843 | 0.142857 | ||||||||
\(393\) | −19.4142 | + | 27.4558i | −0.979318 | + | 1.38496i | ||||
\(394\) | 8.48528 | 0.427482 | ||||||||
\(395\) | −6.24264 | −0.314101 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 10.6274 | 0.532704 | ||||||||
\(399\) | −3.24264 | + | 4.58579i | −0.162335 | + | 0.229576i | ||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | − | 5.27208i | − | 0.263275i | −0.991298 | − | 0.131638i | \(-0.957977\pi\) | ||
0.991298 | − | 0.131638i | \(-0.0420235\pi\) | |||||||
\(402\) | −17.6569 | + | 24.9706i | −0.880644 | + | 1.24542i | ||||
\(403\) | 18.4853i | 0.920817i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.65685 | + | 7.00000i | 0.281091 | + | 0.347833i | ||||
\(406\) | − | 8.24264i | − | 0.409075i | ||||||
\(407\) | −24.7279 | − | 11.6569i | −1.22572 | − | 0.577809i | ||||
\(408\) | 16.4853 | − | 23.3137i | 0.816143 | − | 1.15420i | ||||
\(409\) | − | 18.4853i | − | 0.914038i | −0.889457 | − | 0.457019i | \(-0.848917\pi\) | ||
0.889457 | − | 0.457019i | \(-0.151083\pi\) | |||||||
\(410\) | 6.48528i | 0.320285i | ||||||||
\(411\) | −20.4853 | − | 14.4853i | −1.01046 | − | 0.714506i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.8995 | −0.634743 | ||||||||
\(414\) | −4.97056 | + | 1.75736i | −0.244290 | + | 0.0863695i | ||||
\(415\) | − | 17.1421i | − | 0.841474i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.6569 | − | 12.4853i | −0.864660 | − | 0.611407i | ||||
\(418\) | −6.48528 | + | 13.7574i | −0.317205 | + | 0.672894i | ||||
\(419\) | − | 25.5858i | − | 1.24995i | −0.780646 | − | 0.624974i | \(-0.785110\pi\) | ||
0.780646 | − | 0.624974i | \(-0.214890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.4853 | −1.04713 | −0.523564 | − | 0.851986i | \(-0.675398\pi\) | ||||
−0.523564 | + | 0.851986i | \(0.675398\pi\) | |||||||
\(422\) | 11.3137i | 0.550743i | ||||||||
\(423\) | −3.02944 | + | 1.07107i | −0.147296 | + | 0.0520771i | ||||
\(424\) | 12.4853i | 0.606339i | ||||||||
\(425\) | 5.82843 | 0.282720 | ||||||||
\(426\) | −3.51472 | − | 2.48528i | −0.170289 | − | 0.120412i | ||||
\(427\) | 9.24264 | 0.447283 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.34315 | − | 11.2132i | −0.306250 | − | 0.541379i | ||||
\(430\) | −4.58579 | −0.221146 | ||||||||
\(431\) | −23.6569 | −1.13951 | −0.569755 | − | 0.821814i | \(-0.692962\pi\) | ||||
−0.569755 | + | 0.821814i | \(0.692962\pi\) | |||||||
\(432\) | 20.0000 | + | 5.65685i | 0.962250 | + | 0.272166i | ||||
\(433\) | −12.0000 | −0.576683 | −0.288342 | − | 0.957528i | \(-0.593104\pi\) | ||||
−0.288342 | + | 0.957528i | \(0.593104\pi\) | |||||||
\(434\) | − | 11.6569i | − | 0.559547i | ||||||
\(435\) | −8.24264 | − | 5.82843i | −0.395204 | − | 0.279452i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.02944 | −0.192754 | ||||||||
\(438\) | −12.9706 | − | 9.17157i | −0.619757 | − | 0.438235i | ||||
\(439\) | 5.24264i | 0.250218i | 0.992143 | + | 0.125109i | \(0.0399280\pi\) | ||||
−0.992143 | + | 0.125109i | \(0.960072\pi\) | |||||||
\(440\) | 4.00000 | − | 8.48528i | 0.190693 | − | 0.404520i | ||||
\(441\) | 1.00000 | + | 2.82843i | 0.0476190 | + | 0.134687i | ||||
\(442\) | − | 18.4853i | − | 0.879255i | ||||||
\(443\) | 11.3137i | 0.537531i | 0.963206 | + | 0.268765i | \(0.0866156\pi\) | ||||
−0.963206 | + | 0.268765i | \(0.913384\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.4142 | −0.778108 | ||||||||
\(446\) | 24.0416 | 1.13840 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 8.00000i | − | 0.377964i | ||||||
\(449\) | 11.2721i | 0.531962i | 0.963978 | + | 0.265981i | \(0.0856959\pi\) | ||||
−0.963978 | + | 0.265981i | \(0.914304\pi\) | |||||||
\(450\) | 1.41421 | + | 4.00000i | 0.0666667 | + | 0.188562i | ||||
\(451\) | 13.7574 | + | 6.48528i | 0.647809 | + | 0.305380i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.1421 | + | 10.0000i | 0.664455 | + | 0.469841i | ||||
\(454\) | −8.72792 | −0.409622 | ||||||||
\(455\) | − | 2.24264i | − | 0.105137i | ||||||
\(456\) | 12.9706 | + | 9.17157i | 0.607402 | + | 0.429498i | ||||
\(457\) | 32.2132i | 1.50687i | 0.657522 | + | 0.753435i | \(0.271605\pi\) | ||||
−0.657522 | + | 0.753435i | \(0.728395\pi\) | |||||||
\(458\) | 26.4853 | 1.23758 | ||||||||
\(459\) | 29.1421 | + | 8.24264i | 1.36024 | + | 0.384734i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.3431 | 0.854325 | 0.427163 | − | 0.904175i | \(-0.359513\pi\) | ||||
0.427163 | + | 0.904175i | \(0.359513\pi\) | |||||||
\(462\) | 4.00000 | + | 7.07107i | 0.186097 | + | 0.328976i | ||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | −23.3137 | −1.08231 | ||||||||
\(465\) | −11.6569 | − | 8.24264i | −0.540574 | − | 0.382243i | ||||
\(466\) | −13.5147 | −0.626057 | ||||||||
\(467\) | 11.6569i | 0.539415i | 0.962942 | + | 0.269707i | \(0.0869270\pi\) | ||||
−0.962942 | + | 0.269707i | \(0.913073\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4853i | 0.576517i | ||||||||
\(470\) | −1.51472 | −0.0698688 | ||||||||
\(471\) | 11.0000 | − | 15.5563i | 0.506853 | − | 0.716799i | ||||
\(472\) | 36.4853i | 1.67937i | ||||||||
\(473\) | −4.58579 | + | 9.72792i | −0.210855 | + | 0.447290i | ||||
\(474\) | −12.4853 | − | 8.82843i | −0.573468 | − | 0.405503i | ||||
\(475\) | 3.24264i | 0.148783i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.4853 | + | 4.41421i | −0.571662 | + | 0.202113i | ||||
\(478\) | −12.2426 | −0.559965 | ||||||||
\(479\) | 15.2132 | 0.695109 | 0.347555 | − | 0.937660i | \(-0.387012\pi\) | ||||
0.347555 | + | 0.937660i | \(0.387012\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.4853i | 0.842856i | ||||||||
\(482\) | − | 13.4558i | − | 0.612897i | ||||||
\(483\) | −1.24264 | + | 1.75736i | −0.0565421 | + | 0.0799626i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00000i | 0.317854i | ||||||||
\(486\) | 1.41421 | + | 22.0000i | 0.0641500 | + | 0.997940i | ||||
\(487\) | 36.9706 | 1.67530 | 0.837648 | − | 0.546210i | \(-0.183930\pi\) | ||||
0.837648 | + | 0.546210i | \(0.183930\pi\) | |||||||
\(488\) | − | 26.1421i | − | 1.18340i | ||||||
\(489\) | 2.24264 | − | 3.17157i | 0.101416 | − | 0.143423i | ||||
\(490\) | 1.41421i | 0.0638877i | ||||||||
\(491\) | 26.6569 | 1.20301 | 0.601503 | − | 0.798870i | \(-0.294569\pi\) | ||||
0.601503 | + | 0.798870i | \(0.294569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.9706 | −1.52996 | ||||||||
\(494\) | 10.2843 | 0.462711 | ||||||||
\(495\) | 9.89949 | + | 1.00000i | 0.444949 | + | 0.0449467i | ||||
\(496\) | −32.9706 | −1.48042 | ||||||||
\(497\) | −1.75736 | −0.0788283 | ||||||||
\(498\) | 24.2426 | − | 34.2843i | 1.08634 | − | 1.53631i | ||||
\(499\) | 5.48528 | 0.245555 | 0.122777 | − | 0.992434i | \(-0.460820\pi\) | ||||
0.122777 | + | 0.992434i | \(0.460820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1421 | − | 28.4853i | 0.899884 | − | 1.27263i | ||||
\(502\) | 40.9706i | 1.82861i | ||||||||
\(503\) | −40.4558 | −1.80384 | −0.901918 | − | 0.431906i | \(-0.857841\pi\) | ||||
−0.901918 | + | 0.431906i | \(0.857841\pi\) | |||||||
\(504\) | 8.00000 | − | 2.82843i | 0.356348 | − | 0.125988i | ||||
\(505\) | − | 2.48528i | − | 0.110594i | ||||||
\(506\) | −2.48528 | + | 5.27208i | −0.110484 | + | 0.234372i | ||||
\(507\) | 7.97056 | − | 11.2721i | 0.353985 | − | 0.500611i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 37.2426i | − | 1.65075i | −0.564584 | − | 0.825376i | \(-0.690963\pi\) | ||
0.564584 | − | 0.825376i | \(-0.309037\pi\) | |||||||
\(510\) | 11.6569 | + | 8.24264i | 0.516174 | + | 0.364990i | ||||
\(511\) | −6.48528 | −0.286892 | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | −4.58579 | + | 16.2132i | −0.202467 | + | 0.715830i | ||||
\(514\) | 31.4558i | 1.38746i | ||||||||
\(515\) | 0.514719i | 0.0226812i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.51472 | + | 3.21320i | −0.0666172 | + | 0.141317i | ||||
\(518\) | − | 11.6569i | − | 0.512173i | ||||||
\(519\) | −2.82843 | + | 4.00000i | −0.124154 | + | 0.175581i | ||||
\(520\) | −6.34315 | −0.278165 | ||||||||
\(521\) | − | 10.4142i | − | 0.456255i | −0.973631 | − | 0.228127i | \(-0.926740\pi\) | ||
0.973631 | − | 0.228127i | \(-0.0732603\pi\) | |||||||
\(522\) | −8.24264 | − | 23.3137i | −0.360771 | − | 1.02041i | ||||
\(523\) | − | 6.97056i | − | 0.304801i | −0.988319 | − | 0.152401i | \(-0.951300\pi\) | ||
0.988319 | − | 0.152401i | \(-0.0487004\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.41421 | + | 1.00000i | 0.0617213 | + | 0.0436436i | ||||
\(526\) | −29.4558 | −1.28434 | ||||||||
\(527\) | −48.0416 | −2.09273 | ||||||||
\(528\) | 20.0000 | − | 11.3137i | 0.870388 | − | 0.492366i | ||||
\(529\) | 21.4558 | 0.932863 | ||||||||
\(530\) | −6.24264 | −0.271163 | ||||||||
\(531\) | −36.4853 | + | 12.8995i | −1.58333 | + | 0.559790i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.2843i | − | 0.445461i | ||||||
\(534\) | −32.8284 | − | 23.2132i | −1.42062 | − | 1.00453i | ||||
\(535\) | − | 7.41421i | − | 0.320544i | ||||||
\(536\) | 35.3137 | 1.52532 | ||||||||
\(537\) | 18.9706 | + | 13.4142i | 0.818640 | + | 0.578866i | ||||
\(538\) | − | 0.786797i | − | 0.0339212i | ||||||
\(539\) | 3.00000 | + | 1.41421i | 0.129219 | + | 0.0609145i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7279i | 0.461229i | 0.973045 | + | 0.230615i | \(0.0740737\pi\) | ||||
−0.973045 | + | 0.230615i | \(0.925926\pi\) | |||||||
\(542\) | − | 20.8701i | − | 0.896446i | ||||||
\(543\) | −10.9706 | + | 15.5147i | −0.470792 | + | 0.665800i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.75736 | 0.160948 | ||||||||
\(546\) | 3.17157 | − | 4.48528i | 0.135731 | − | 0.191952i | ||||
\(547\) | − | 23.2426i | − | 0.993784i | −0.867813 | − | 0.496892i | \(-0.834475\pi\) | ||
0.867813 | − | 0.496892i | \(-0.165525\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.1421 | − | 9.24264i | 1.11572 | − | 0.394466i | ||||
\(550\) | 4.24264 | + | 2.00000i | 0.180907 | + | 0.0852803i | ||||
\(551\) | − | 18.8995i | − | 0.805146i | ||||||
\(552\) | 4.97056 | + | 3.51472i | 0.211561 | + | 0.149596i | ||||
\(553\) | −6.24264 | −0.265464 | ||||||||
\(554\) | 12.0000i | 0.509831i | ||||||||
\(555\) | −11.6569 | − | 8.24264i | −0.494806 | − | 0.349881i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.1716 | −1.15130 | −0.575648 | − | 0.817697i | \(-0.695250\pi\) | ||||
−0.575648 | + | 0.817697i | \(0.695250\pi\) | |||||||
\(558\) | −11.6569 | − | 32.9706i | −0.493474 | − | 1.39576i | ||||
\(559\) | 7.27208 | 0.307576 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 29.1421 | − | 16.4853i | 1.23038 | − | 0.696009i | ||||
\(562\) | −7.51472 | −0.316989 | ||||||||
\(563\) | 25.1127 | 1.05837 | 0.529187 | − | 0.848505i | \(-0.322497\pi\) | ||||
0.529187 | + | 0.848505i | \(0.322497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.8995 | 0.795108 | ||||||||
\(566\) | − | 41.3137i | − | 1.73654i | ||||||
\(567\) | 5.65685 | + | 7.00000i | 0.237566 | + | 0.293972i | ||||
\(568\) | 4.97056i | 0.208560i | ||||||||
\(569\) | 17.1421 | 0.718636 | 0.359318 | − | 0.933215i | \(-0.383009\pi\) | ||||
0.359318 | + | 0.933215i | \(0.383009\pi\) | |||||||
\(570\) | −4.58579 | + | 6.48528i | −0.192077 | + | 0.271639i | ||||
\(571\) | − | 40.1838i | − | 1.68164i | −0.541316 | − | 0.840819i | \(-0.682074\pi\) | ||
0.541316 | − | 0.840819i | \(-0.317926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.9706 | − | 9.17157i | −0.541853 | − | 0.383148i | ||||
\(574\) | 6.48528i | 0.270690i | ||||||||
\(575\) | 1.24264i | 0.0518217i | ||||||||
\(576\) | −8.00000 | − | 22.6274i | −0.333333 | − | 0.942809i | ||||
\(577\) | −21.4558 | −0.893218 | −0.446609 | − | 0.894729i | \(-0.647369\pi\) | ||||
−0.446609 | + | 0.894729i | \(0.647369\pi\) | |||||||
\(578\) | 24.0000 | 0.998268 | ||||||||
\(579\) | −14.1421 | − | 10.0000i | −0.587727 | − | 0.415586i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 17.1421i | − | 0.711176i | ||||||
\(582\) | −9.89949 | + | 14.0000i | −0.410347 | + | 0.580319i | ||||
\(583\) | −6.24264 | + | 13.2426i | −0.258544 | + | 0.548454i | ||||
\(584\) | 18.3431i | 0.759045i | ||||||||
\(585\) | −2.24264 | − | 6.34315i | −0.0927218 | − | 0.262257i | ||||
\(586\) | 4.72792 | 0.195309 | ||||||||
\(587\) | 36.0416i | 1.48760i | 0.668404 | + | 0.743799i | \(0.266978\pi\) | ||||
−0.668404 | + | 0.743799i | \(0.733022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 26.7279i | − | 1.10130i | ||||||
\(590\) | −18.2426 | −0.751038 | ||||||||
\(591\) | 6.00000 | − | 8.48528i | 0.246807 | − | 0.349038i | ||||
\(592\) | −32.9706 | −1.35508 | ||||||||
\(593\) | −26.8284 | −1.10171 | −0.550856 | − | 0.834600i | \(-0.685699\pi\) | ||||
−0.550856 | + | 0.834600i | \(0.685699\pi\) | |||||||
\(594\) | 18.3848 | + | 16.0000i | 0.754337 | + | 0.656488i | ||||
\(595\) | 5.82843 | 0.238942 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.51472 | − | 10.6274i | 0.307557 | − | 0.434951i | ||||
\(598\) | 3.94113 | 0.161165 | ||||||||
\(599\) | − | 25.1127i | − | 1.02608i | −0.858366 | − | 0.513039i | \(-0.828520\pi\) | ||
0.858366 | − | 0.513039i | \(-0.171480\pi\) | |||||||
\(600\) | 2.82843 | − | 4.00000i | 0.115470 | − | 0.163299i | ||||
\(601\) | − | 4.27208i | − | 0.174262i | −0.996197 | − | 0.0871308i | \(-0.972230\pi\) | ||
0.996197 | − | 0.0871308i | \(-0.0277698\pi\) | |||||||
\(602\) | −4.58579 | −0.186903 | ||||||||
\(603\) | 12.4853 | + | 35.3137i | 0.508440 | + | 1.43809i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.48528 | − | 7.00000i | 0.344976 | − | 0.284590i | ||||
\(606\) | 3.51472 | − | 4.97056i | 0.142776 | − | 0.201915i | ||||
\(607\) | − | 26.4853i | − | 1.07500i | −0.843262 | − | 0.537502i | \(-0.819368\pi\) | ||
0.843262 | − | 0.537502i | \(-0.180632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.24264 | − | 5.82843i | −0.334009 | − | 0.236180i | ||||
\(610\) | 13.0711 | 0.529232 | ||||||||
\(611\) | 2.40202 | 0.0971753 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.4853i | 0.746613i | 0.927708 | + | 0.373307i | \(0.121776\pi\) | ||||
−0.927708 | + | 0.373307i | \(0.878224\pi\) | |||||||
\(614\) | − | 28.9706i | − | 1.16916i | ||||||
\(615\) | 6.48528 | + | 4.58579i | 0.261512 | + | 0.184917i | ||||
\(616\) | 4.00000 | − | 8.48528i | 0.161165 | − | 0.341882i | ||||
\(617\) | 5.31371i | 0.213922i | 0.994263 | + | 0.106961i | \(0.0341120\pi\) | ||||
−0.994263 | + | 0.106961i | \(0.965888\pi\) | |||||||
\(618\) | −0.727922 | + | 1.02944i | −0.0292813 | + | 0.0414100i | ||||
\(619\) | 2.48528 | 0.0998919 | 0.0499459 | − | 0.998752i | \(-0.484095\pi\) | ||||
0.0499459 | + | 0.998752i | \(0.484095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.75736 | + | 6.21320i | −0.0705204 | + | 0.249327i | ||||
\(622\) | − | 20.9706i | − | 0.840843i | ||||||
\(623\) | −16.4142 | −0.657622 | ||||||||
\(624\) | −12.6863 | − | 8.97056i | −0.507858 | − | 0.359110i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −37.4142 | −1.49537 | ||||||||
\(627\) | 9.17157 | + | 16.2132i | 0.366277 | + | 0.647493i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.0416 | −1.91555 | ||||||||
\(630\) | 1.41421 | + | 4.00000i | 0.0563436 | + | 0.159364i | ||||
\(631\) | 15.0000 | 0.597141 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(632\) | 17.6569i | 0.702352i | ||||||||
\(633\) | 11.3137 | + | 8.00000i | 0.449680 | + | 0.317971i | ||||
\(634\) | 46.4264i | 1.84383i | ||||||||
\(635\) | 13.2426 | 0.525518 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.24264i | − | 0.0888567i | ||||||
\(638\) | −24.7279 | − | 11.6569i | −0.978988 | − | 0.461499i | ||||
\(639\) | −4.97056 | + | 1.75736i | −0.196632 | + | 0.0695201i | ||||
\(640\) | − | 11.3137i | − | 0.447214i | ||||||
\(641\) | − | 31.4558i | − | 1.24243i | −0.783640 | − | 0.621216i | \(-0.786639\pi\) | ||
0.783640 | − | 0.621216i | \(-0.213361\pi\) | |||||||
\(642\) | 10.4853 | − | 14.8284i | 0.413821 | − | 0.585231i | ||||
\(643\) | −15.9706 | −0.629818 | −0.314909 | − | 0.949122i | \(-0.601974\pi\) | ||||
−0.314909 | + | 0.949122i | \(0.601974\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.24264 | + | 4.58579i | −0.127679 | + | 0.180565i | ||||
\(646\) | 26.7279i | 1.05160i | ||||||||
\(647\) | − | 43.7990i | − | 1.72192i | −0.508676 | − | 0.860958i | \(-0.669865\pi\) | ||
0.508676 | − | 0.860958i | \(-0.330135\pi\) | |||||||
\(648\) | 19.7990 | − | 16.0000i | 0.777778 | − | 0.628539i | ||||
\(649\) | −18.2426 | + | 38.6985i | −0.716086 | + | 1.51905i | ||||
\(650\) | − | 3.17157i | − | 0.124399i | ||||||
\(651\) | −11.6569 | − | 8.24264i | −0.456868 | − | 0.323055i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 18.2132i | − | 0.712738i | −0.934345 | − | 0.356369i | \(-0.884015\pi\) | ||
0.934345 | − | 0.356369i | \(-0.115985\pi\) | |||||||
\(654\) | 7.51472 | + | 5.31371i | 0.293849 | + | 0.207782i | ||||
\(655\) | 19.4142i | 0.758576i | ||||||||
\(656\) | 18.3431 | 0.716180 | ||||||||
\(657\) | −18.3431 | + | 6.48528i | −0.715634 | + | 0.253015i | ||||
\(658\) | −1.51472 | −0.0590499 | ||||||||
\(659\) | 13.2843 | 0.517482 | 0.258741 | − | 0.965947i | \(-0.416692\pi\) | ||||
0.258741 | + | 0.965947i | \(0.416692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2132 | 0.669516 | 0.334758 | − | 0.942304i | \(-0.391345\pi\) | ||||
0.334758 | + | 0.942304i | \(0.391345\pi\) | |||||||
\(662\) | 3.55635 | 0.138221 | ||||||||
\(663\) | −18.4853 | − | 13.0711i | −0.717909 | − | 0.507638i | ||||
\(664\) | −48.4853 | −1.88159 | ||||||||
\(665\) | 3.24264i | 0.125744i | ||||||||
\(666\) | −11.6569 | − | 32.9706i | −0.451694 | − | 1.27758i | ||||
\(667\) | − | 7.24264i | − | 0.280436i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.0000 | − | 24.0416i | 0.657258 | − | 0.929503i | ||||
\(670\) | 17.6569i | 0.682144i | ||||||||
\(671\) | 13.0711 | − | 27.7279i | 0.504603 | − | 1.07042i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.2721i | 0.395960i | 0.980206 | + | 0.197980i | \(0.0634380\pi\) | ||||
−0.980206 | + | 0.197980i | \(0.936562\pi\) | |||||||
\(674\) | 38.5269i | 1.48400i | ||||||||
\(675\) | 5.00000 | + | 1.41421i | 0.192450 | + | 0.0544331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.17157 | 0.237193 | 0.118596 | − | 0.992943i | \(-0.462161\pi\) | ||||
0.118596 | + | 0.992943i | \(0.462161\pi\) | |||||||
\(678\) | 37.7990 | + | 26.7279i | 1.45166 | + | 1.02648i | ||||
\(679\) | 7.00000i | 0.268635i | ||||||||
\(680\) | − | 16.4853i | − | 0.632182i | ||||||
\(681\) | −6.17157 | + | 8.72792i | −0.236495 | + | 0.334455i | ||||
\(682\) | −34.9706 | − | 16.4853i | −1.33909 | − | 0.631254i | ||||
\(683\) | 11.6569i | 0.446037i | 0.974814 | + | 0.223019i | \(0.0715911\pi\) | ||||
−0.974814 | + | 0.223019i | \(0.928409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4853 | −0.553454 | ||||||||
\(686\) | 1.41421i | 0.0539949i | ||||||||
\(687\) | 18.7279 | − | 26.4853i | 0.714515 | − | 1.01048i | ||||
\(688\) | 12.9706i | 0.494498i | ||||||||
\(689\) | 9.89949 | 0.377141 | ||||||||
\(690\) | −1.75736 | + | 2.48528i | −0.0669015 | + | 0.0946130i | ||||
\(691\) | −9.02944 | −0.343496 | −0.171748 | − | 0.985141i | \(-0.554941\pi\) | ||||
−0.171748 | + | 0.985141i | \(0.554941\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.89949 | + | 1.00000i | 0.376051 | + | 0.0379869i | ||||
\(694\) | 37.9411 | 1.44023 | ||||||||
\(695\) | −12.4853 | −0.473594 | ||||||||
\(696\) | −16.4853 | + | 23.3137i | −0.624873 | + | 0.883704i | ||||
\(697\) | 26.7279 | 1.01239 | ||||||||
\(698\) | − | 18.0416i | − | 0.682886i | ||||||
\(699\) | −9.55635 | + | 13.5147i | −0.361454 | + | 0.511174i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.9706 | −1.43413 | −0.717064 | − | 0.697007i | \(-0.754515\pi\) | ||||
−0.717064 | + | 0.697007i | \(0.754515\pi\) | |||||||
\(702\) | 4.48528 | − | 15.8579i | 0.169286 | − | 0.598517i | ||||
\(703\) | − | 26.7279i | − | 1.00806i | ||||||
\(704\) | −24.0000 | − | 11.3137i | −0.904534 | − | 0.426401i | ||||
\(705\) | −1.07107 | + | 1.51472i | −0.0403387 | + | 0.0570476i | ||||
\(706\) | − | 25.4558i | − | 0.958043i | ||||||
\(707\) | − | 2.48528i | − | 0.0934686i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.9411 | −1.91313 | −0.956567 | − | 0.291512i | \(-0.905842\pi\) | ||||
−0.956567 | + | 0.291512i | \(0.905842\pi\) | |||||||
\(710\) | −2.48528 | −0.0932709 | ||||||||
\(711\) | −17.6569 | + | 6.24264i | −0.662184 | + | 0.234117i | ||||
\(712\) | 46.4264i | 1.73990i | ||||||||
\(713\) | − | 10.2426i | − | 0.383590i | ||||||
\(714\) | 11.6569 | + | 8.24264i | 0.436247 | + | 0.308473i | ||||
\(715\) | −6.72792 | − | 3.17157i | −0.251610 | − | 0.118610i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.65685 | + | 12.2426i | −0.323296 | + | 0.457210i | ||||
\(718\) | −19.2721 | −0.719228 | ||||||||
\(719\) | 47.5269i | 1.77245i | 0.463251 | + | 0.886227i | \(0.346683\pi\) | ||||
−0.463251 | + | 0.886227i | \(0.653317\pi\) | |||||||
\(720\) | 11.3137 | − | 4.00000i | 0.421637 | − | 0.149071i | ||||
\(721\) | 0.514719i | 0.0191691i | ||||||||
\(722\) | 12.0000 | 0.446594 | ||||||||
\(723\) | −13.4558 | − | 9.51472i | −0.500428 | − | 0.353856i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.82843 | −0.216462 | ||||||||
\(726\) | 26.8701 | − | 2.00000i | 0.997241 | − | 0.0742270i | ||||
\(727\) | 20.4558 | 0.758665 | 0.379333 | − | 0.925260i | \(-0.376154\pi\) | ||||
0.379333 | + | 0.925260i | \(0.376154\pi\) | |||||||
\(728\) | −6.34315 | −0.235093 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | −9.17157 | −0.339455 | ||||||||
\(731\) | 18.8995i | 0.699023i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.4558i | − | 0.792490i | −0.918145 | − | 0.396245i | \(-0.870313\pi\) | ||
0.918145 | − | 0.396245i | \(-0.129687\pi\) | |||||||
\(734\) | 4.24264 | 0.156599 | ||||||||
\(735\) | 1.41421 | + | 1.00000i | 0.0521641 | + | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.4558 | + | 17.6569i | 1.37970 | + | 0.650399i | ||||
\(738\) | 6.48528 | + | 18.3431i | 0.238727 | + | 0.675221i | ||||
\(739\) | 30.4853i | 1.12142i | 0.828013 | + | 0.560710i | \(0.189472\pi\) | ||||
−0.828013 | + | 0.560710i | \(0.810528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.27208 | − | 10.2843i | 0.267146 | − | 0.377802i | ||||
\(742\) | −6.24264 | −0.229175 | ||||||||
\(743\) | 46.6274 | 1.71059 | 0.855297 | − | 0.518138i | \(-0.173375\pi\) | ||||
0.855297 | + | 0.518138i | \(0.173375\pi\) | |||||||
\(744\) | −23.3137 | + | 32.9706i | −0.854722 | + | 1.20876i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 8.78680i | − | 0.321707i | ||||||
\(747\) | −17.1421 | − | 48.4853i | −0.627198 | − | 1.77398i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7.41421i | − | 0.270909i | ||||||
\(750\) | 2.00000 | + | 1.41421i | 0.0730297 | + | 0.0516398i | ||||
\(751\) | 7.97056 | 0.290850 | 0.145425 | − | 0.989369i | \(-0.453545\pi\) | ||||
0.145425 | + | 0.989369i | \(0.453545\pi\) | |||||||
\(752\) | 4.28427i | 0.156231i | ||||||||
\(753\) | 40.9706 | + | 28.9706i | 1.49305 | + | 1.05575i | ||||
\(754\) | 18.4853i | 0.673194i | ||||||||
\(755\) | 10.0000 | 0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.45584 | −0.343679 | −0.171839 | − | 0.985125i | \(-0.554971\pi\) | ||||
−0.171839 | + | 0.985125i | \(0.554971\pi\) | |||||||
\(758\) | 26.1005 | 0.948013 | ||||||||
\(759\) | 3.51472 | + | 6.21320i | 0.127576 | + | 0.225525i | ||||
\(760\) | 9.17157 | 0.332688 | ||||||||
\(761\) | 7.02944 | 0.254817 | 0.127408 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127408 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(762\) | 26.4853 | + | 18.7279i | 0.959461 | + | 0.678441i | ||||
\(763\) | 3.75736 | 0.136026 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.4853 | − | 5.82843i | 0.596027 | − | 0.210727i | ||||
\(766\) | 52.9117i | 1.91178i | ||||||||
\(767\) | 28.9289 | 1.04456 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 51.6690i | − | 1.86323i | −0.363442 | − | 0.931617i | \(-0.618399\pi\) | ||
0.363442 | − | 0.931617i | \(-0.381601\pi\) | |||||||
\(770\) | 4.24264 | + | 2.00000i | 0.152894 | + | 0.0720750i | ||||
\(771\) | 31.4558 | + | 22.2426i | 1.13285 | + | 0.801049i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.8284i | 0.533341i | 0.963788 | + | 0.266671i | \(0.0859236\pi\) | ||||
−0.963788 | + | 0.266671i | \(0.914076\pi\) | |||||||
\(774\) | −12.9706 | + | 4.58579i | −0.466217 | + | 0.164833i | ||||
\(775\) | −8.24264 | −0.296084 | ||||||||
\(776\) | 19.7990 | 0.710742 | ||||||||
\(777\) | −11.6569 | − | 8.24264i | −0.418187 | − | 0.295703i | ||||
\(778\) | − | 2.48528i | − | 0.0891017i | ||||||
\(779\) | 14.8701i | 0.532775i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.48528 | + | 5.27208i | −0.0889304 | + | 0.188650i | ||||
\(782\) | 10.2426i | 0.366276i | ||||||||
\(783\) | −29.1421 | − | 8.24264i | −1.04145 | − | 0.294568i | ||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | − | 11.0000i | − | 0.392607i | ||||||
\(786\) | −27.4558 | + | 38.8284i | −0.979318 | + | 1.38496i | ||||
\(787\) | 15.4558i | 0.550941i | 0.961309 | + | 0.275471i | \(0.0888337\pi\) | ||||
−0.961309 | + | 0.275471i | \(0.911166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.8284 | + | 29.4558i | −0.741512 | + | 1.04866i | ||||
\(790\) | −8.82843 | −0.314101 | ||||||||
\(791\) | 18.8995 | 0.671989 | ||||||||
\(792\) | 2.82843 | − | 28.0000i | 0.100504 | − | 0.994937i | ||||
\(793\) | −20.7279 | −0.736070 | ||||||||
\(794\) | −48.0833 | −1.70641 | ||||||||
\(795\) | −4.41421 | + | 6.24264i | −0.156556 | + | 0.221404i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.79899i | − | 0.276254i | −0.990414 | − | 0.138127i | \(-0.955892\pi\) | ||
0.990414 | − | 0.138127i | \(-0.0441083\pi\) | |||||||
\(798\) | −4.58579 | + | 6.48528i | −0.162335 | + | 0.229576i | ||||
\(799\) | 6.24264i | 0.220849i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −46.4264 | + | 16.4142i | −1.64040 | + | 0.579968i | ||||
\(802\) | − | 7.45584i | − | 0.263275i | ||||||
\(803\) | −9.17157 | + | 19.4558i | −0.323658 | + | 0.686582i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.24264i | 0.0437973i | ||||||||
\(806\) | 26.1421i | 0.920817i | ||||||||
\(807\) | −0.786797 | − | 0.556349i | −0.0276966 | − | 0.0195844i | ||||
\(808\) | −7.02944 | −0.247295 | ||||||||
\(809\) | 21.1716 | 0.744353 | 0.372176 | − | 0.928162i | \(-0.378612\pi\) | ||||
0.372176 | + | 0.928162i | \(0.378612\pi\) | |||||||
\(810\) | 8.00000 | + | 9.89949i | 0.281091 | + | 0.347833i | ||||
\(811\) | − | 2.00000i | − | 0.0702295i | −0.999383 | − | 0.0351147i | \(-0.988820\pi\) | ||
0.999383 | − | 0.0351147i | \(-0.0111797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.8701 | − | 14.7574i | −0.731945 | − | 0.517563i | ||||
\(814\) | −34.9706 | − | 16.4853i | −1.22572 | − | 0.577809i | ||||
\(815\) | − | 2.24264i | − | 0.0785563i | ||||||
\(816\) | 23.3137 | − | 32.9706i | 0.816143 | − | 1.15420i | ||||
\(817\) | −10.5147 | −0.367863 | ||||||||
\(818\) | − | 26.1421i | − | 0.914038i | ||||||
\(819\) | −2.24264 | − | 6.34315i | −0.0783642 | − | 0.221647i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.857864 | −0.0299397 | −0.0149698 | − | 0.999888i | \(-0.504765\pi\) | ||||
−0.0149698 | + | 0.999888i | \(0.504765\pi\) | |||||||
\(822\) | −28.9706 | − | 20.4853i | −1.01046 | − | 0.714506i | ||||
\(823\) | 41.2132 | 1.43660 | 0.718301 | − | 0.695732i | \(-0.244920\pi\) | ||||
0.718301 | + | 0.695732i | \(0.244920\pi\) | |||||||
\(824\) | 1.45584 | 0.0507167 | ||||||||
\(825\) | 5.00000 | − | 2.82843i | 0.174078 | − | 0.0984732i | ||||
\(826\) | −18.2426 | −0.634743 | ||||||||
\(827\) | 6.00000 | 0.208640 | 0.104320 | − | 0.994544i | \(-0.466733\pi\) | ||||
0.104320 | + | 0.994544i | \(0.466733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.02944 | −0.105217 | −0.0526084 | − | 0.998615i | \(-0.516753\pi\) | ||||
−0.0526084 | + | 0.998615i | \(0.516753\pi\) | |||||||
\(830\) | − | 24.2426i | − | 0.841474i | ||||||
\(831\) | 12.0000 | + | 8.48528i | 0.416275 | + | 0.294351i | ||||
\(832\) | 17.9411i | 0.621997i | ||||||||
\(833\) | 5.82843 | 0.201943 | ||||||||
\(834\) | −24.9706 | − | 17.6569i | −0.864660 | − | 0.611407i | ||||
\(835\) | − | 20.1421i | − | 0.697047i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −41.2132 | − | 11.6569i | −1.42454 | − | 0.402920i | ||||
\(838\) | − | 36.1838i | − | 1.24995i | ||||||
\(839\) | 4.41421i | 0.152396i | 0.997093 | + | 0.0761978i | \(0.0242780\pi\) | ||||
−0.997093 | + | 0.0761978i | \(0.975722\pi\) | |||||||
\(840\) | 2.82843 | − | 4.00000i | 0.0975900 | − | 0.138013i | ||||
\(841\) | 4.97056 | 0.171399 | ||||||||
\(842\) | −30.3848 | −1.04713 | ||||||||
\(843\) | −5.31371 | + | 7.51472i | −0.183014 | + | 0.258821i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 7.97056i | − | 0.274196i | ||||||
\(846\) | −4.28427 | + | 1.51472i | −0.147296 | + | 0.0520771i | ||||
\(847\) | 8.48528 | − | 7.00000i | 0.291558 | − | 0.240523i | ||||
\(848\) | 17.6569i | 0.606339i | ||||||||
\(849\) | −41.3137 | − | 29.2132i | −1.41788 | − | 1.00259i | ||||
\(850\) | 8.24264 | 0.282720 | ||||||||
\(851\) | − | 10.2426i | − | 0.351113i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 35.7574i | − | 1.22431i | −0.790738 | − | 0.612154i | \(-0.790303\pi\) | ||
0.790738 | − | 0.612154i | \(-0.209697\pi\) | |||||||
\(854\) | 13.0711 | 0.447283 | ||||||||
\(855\) | 3.24264 | + | 9.17157i | 0.110896 | + | 0.313661i | ||||
\(856\) | −20.9706 | −0.716759 | ||||||||
\(857\) | 1.02944 | 0.0351649 | 0.0175825 | − | 0.999845i | \(-0.494403\pi\) | ||||
0.0175825 | + | 0.999845i | \(0.494403\pi\) | |||||||
\(858\) | −8.97056 | − | 15.8579i | −0.306250 | − | 0.541379i | ||||
\(859\) | −32.1838 | −1.09810 | −0.549048 | − | 0.835791i | \(-0.685010\pi\) | ||||
−0.549048 | + | 0.835791i | \(0.685010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.48528 | + | 4.58579i | 0.221018 | + | 0.156283i | ||||
\(862\) | −33.4558 | −1.13951 | ||||||||
\(863\) | 29.8701i | 1.01679i | 0.861124 | + | 0.508394i | \(0.169761\pi\) | ||||
−0.861124 | + | 0.508394i | \(0.830239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.82843i | 0.0961694i | ||||||||
\(866\) | −16.9706 | −0.576683 | ||||||||
\(867\) | 16.9706 | − | 24.0000i | 0.576351 | − | 0.815083i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.82843 | + | 18.7279i | −0.299484 | + | 0.635301i | ||||
\(870\) | −11.6569 | − | 8.24264i | −0.395204 | − | 0.279452i | ||||
\(871\) | − | 28.0000i | − | 0.948744i | ||||||
\(872\) | − | 10.6274i | − | 0.359890i | ||||||
\(873\) | 7.00000 | + | 19.7990i | 0.236914 | + | 0.670094i | ||||
\(874\) | −5.69848 | −0.192754 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.72792i | 0.125883i | 0.998017 | + | 0.0629415i | \(0.0200482\pi\) | ||||
−0.998017 | + | 0.0629415i | \(0.979952\pi\) | |||||||
\(878\) | 7.41421i | 0.250218i | ||||||||
\(879\) | 3.34315 | − | 4.72792i | 0.112762 | − | 0.159469i | ||||
\(880\) | 5.65685 | − | 12.0000i | 0.190693 | − | 0.404520i | ||||
\(881\) | − | 18.2132i | − | 0.613618i | −0.951771 | − | 0.306809i | \(-0.900739\pi\) | ||
0.951771 | − | 0.306809i | \(-0.0992614\pi\) | |||||||
\(882\) | 1.41421 | + | 4.00000i | 0.0476190 | + | 0.134687i | ||||
\(883\) | −4.97056 | −0.167273 | −0.0836364 | − | 0.996496i | \(-0.526653\pi\) | ||||
−0.0836364 | + | 0.996496i | \(0.526653\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.8995 | + | 18.2426i | −0.433612 | + | 0.613220i | ||||
\(886\) | 16.0000i | 0.537531i | ||||||||
\(887\) | 36.9411 | 1.24036 | 0.620181 | − | 0.784459i | \(-0.287059\pi\) | ||||
0.620181 | + | 0.784459i | \(0.287059\pi\) | |||||||
\(888\) | −23.3137 | + | 32.9706i | −0.782357 | + | 1.10642i | ||||
\(889\) | 13.2426 | 0.444144 | ||||||||
\(890\) | −23.2132 | −0.778108 | ||||||||
\(891\) | 29.0000 | − | 7.07107i | 0.971537 | − | 0.236890i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.47309 | −0.116222 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4142 | 0.448388 | ||||||||
\(896\) | − | 11.3137i | − | 0.377964i | ||||||
\(897\) | 2.78680 | − | 3.94113i | 0.0930484 | − | 0.131590i | ||||
\(898\) | 15.9411i | 0.531962i | ||||||||
\(899\) | 48.0416 | 1.60228 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.7279i | 0.857121i | ||||||||
\(902\) | 19.4558 | + | 9.17157i | 0.647809 | + | 0.305380i | ||||
\(903\) | −3.24264 | + | 4.58579i | −0.107908 | + | 0.152605i | ||||
\(904\) | − | 53.4558i | − | 1.77791i | ||||||
\(905\) | 10.9706i | 0.364674i | ||||||||
\(906\) | 20.0000 | + | 14.1421i | 0.664455 | + | 0.469841i | ||||
\(907\) | 30.7279 | 1.02030 | 0.510152 | − | 0.860084i | \(-0.329589\pi\) | ||||
0.510152 | + | 0.860084i | \(0.329589\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.48528 | − | 7.02944i | −0.0824316 | − | 0.233152i | ||||
\(910\) | − | 3.17157i | − | 0.105137i | ||||||
\(911\) | − | 1.71573i | − | 0.0568446i | −0.999596 | − | 0.0284223i | \(-0.990952\pi\) | ||
0.999596 | − | 0.0284223i | \(-0.00904832\pi\) | |||||||
\(912\) | 18.3431 | + | 12.9706i | 0.607402 | + | 0.429498i | ||||
\(913\) | −51.4264 | − | 24.2426i | −1.70197 | − | 0.802314i | ||||
\(914\) | 45.5563i | 1.50687i | ||||||||
\(915\) | 9.24264 | − | 13.0711i | 0.305552 | − | 0.432116i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.4142i | 0.641114i | ||||||||
\(918\) | 41.2132 | + | 11.6569i | 1.36024 | + | 0.384734i | ||||
\(919\) | − | 48.9706i | − | 1.61539i | −0.589601 | − | 0.807695i | \(-0.700715\pi\) | ||
0.589601 | − | 0.807695i | \(-0.299285\pi\) | |||||||
\(920\) | 3.51472 | 0.115877 | ||||||||
\(921\) | −28.9706 | − | 20.4853i | −0.954612 | − | 0.675013i | ||||
\(922\) | 25.9411 | 0.854325 | ||||||||
\(923\) | 3.94113 | 0.129724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.24264 | −0.271016 | ||||||||
\(926\) | 36.7696 | 1.20832 | ||||||||
\(927\) | 0.514719 | + | 1.45584i | 0.0169056 | + | 0.0478162i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.7990i | − | 0.649584i | −0.945786 | − | 0.324792i | \(-0.894706\pi\) | ||
0.945786 | − | 0.324792i | \(-0.105294\pi\) | |||||||
\(930\) | −16.4853 | − | 11.6569i | −0.540574 | − | 0.382243i | ||||
\(931\) | 3.24264i | 0.106273i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.9706 | − | 14.8284i | −0.686545 | − | 0.485461i | ||||
\(934\) | 16.4853i | 0.539415i | ||||||||
\(935\) | 8.24264 | − | 17.4853i | 0.269563 | − | 0.571830i | ||||
\(936\) | −17.9411 | + | 6.34315i | −0.586424 | + | 0.207332i | ||||
\(937\) | − | 36.7279i | − | 1.19985i | −0.800057 | − | 0.599924i | \(-0.795197\pi\) | ||
0.800057 | − | 0.599924i | \(-0.204803\pi\) | |||||||
\(938\) | 17.6569i | 0.576517i | ||||||||
\(939\) | −26.4558 | + | 37.4142i | −0.863354 | + | 1.22097i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3848 | 0.403732 | 0.201866 | − | 0.979413i | \(-0.435299\pi\) | ||||
0.201866 | + | 0.979413i | \(0.435299\pi\) | |||||||
\(942\) | 15.5563 | − | 22.0000i | 0.506853 | − | 0.716799i | ||||
\(943\) | 5.69848i | 0.185568i | ||||||||
\(944\) | 51.5980i | 1.67937i | ||||||||
\(945\) | 5.00000 | + | 1.41421i | 0.162650 | + | 0.0460044i | ||||
\(946\) | −6.48528 | + | 13.7574i | −0.210855 | + | 0.447290i | ||||
\(947\) | 44.3553i | 1.44135i | 0.693271 | + | 0.720677i | \(0.256169\pi\) | ||||
−0.693271 | + | 0.720677i | \(0.743831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.5442 | 0.472123 | ||||||||
\(950\) | 4.58579i | 0.148783i | ||||||||
\(951\) | 46.4264 | + | 32.8284i | 1.50548 | + | 1.06453i | ||||
\(952\) | − | 16.4853i | − | 0.534291i | ||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | −17.6569 | + | 6.24264i | −0.571662 | + | 0.202113i | ||||
\(955\) | −9.17157 | −0.296785 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.1421 | + | 16.4853i | −0.942031 | + | 0.532893i | ||||
\(958\) | 21.5147 | 0.695109 | ||||||||
\(959\) | −14.4853 | −0.467754 | ||||||||
\(960\) | −11.3137 | − | 8.00000i | −0.365148 | − | 0.258199i | ||||
\(961\) | 36.9411 | 1.19165 | ||||||||
\(962\) | 26.1421i | 0.842856i | ||||||||
\(963\) | −7.41421 | − | 20.9706i | −0.238920 | − | 0.675767i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.0000 | −0.321911 | ||||||||
\(966\) | −1.75736 | + | 2.48528i | −0.0565421 | + | 0.0799626i | ||||
\(967\) | 40.2132i | 1.29317i | 0.762842 | + | 0.646585i | \(0.223803\pi\) | ||||
−0.762842 | + | 0.646585i | \(0.776197\pi\) | |||||||
\(968\) | −19.7990 | − | 24.0000i | −0.636364 | − | 0.771389i | ||||
\(969\) | 26.7279 | + | 18.8995i | 0.858625 | + | 0.607139i | ||||
\(970\) | 9.89949i | 0.317854i | ||||||||
\(971\) | − | 0.129942i | − | 0.00417005i | −0.999998 | − | 0.00208502i | \(-0.999336\pi\) | ||
0.999998 | − | 0.00208502i | \(-0.000663684\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.4853 | −0.400260 | ||||||||
\(974\) | 52.2843 | 1.67530 | ||||||||
\(975\) | −3.17157 | − | 2.24264i | −0.101572 | − | 0.0718220i | ||||
\(976\) | − | 36.9706i | − | 1.18340i | ||||||
\(977\) | − | 23.1005i | − | 0.739051i | −0.929221 | − | 0.369525i | \(-0.879520\pi\) | ||
0.929221 | − | 0.369525i | \(-0.120480\pi\) | |||||||
\(978\) | 3.17157 | − | 4.48528i | 0.101416 | − | 0.143423i | ||||
\(979\) | −23.2132 | + | 49.2426i | −0.741897 | + | 1.57380i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.6274 | − | 3.75736i | 0.339307 | − | 0.119963i | ||||
\(982\) | 37.6985 | 1.20301 | ||||||||
\(983\) | 22.6274i | 0.721703i | 0.932623 | + | 0.360851i | \(0.117514\pi\) | ||||
−0.932623 | + | 0.360851i | \(0.882486\pi\) | |||||||
\(984\) | 12.9706 | − | 18.3431i | 0.413486 | − | 0.584758i | ||||
\(985\) | − | 6.00000i | − | 0.191176i | ||||||
\(986\) | −48.0416 | −1.52996 | ||||||||
\(987\) | −1.07107 | + | 1.51472i | −0.0340925 | + | 0.0482140i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.02944 | −0.128129 | ||||||||
\(990\) | 14.0000 | + | 1.41421i | 0.444949 | + | 0.0449467i | ||||
\(991\) | 44.5147 | 1.41406 | 0.707028 | − | 0.707185i | \(-0.250035\pi\) | ||||
0.707028 | + | 0.707185i | \(0.250035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.51472 | − | 3.55635i | 0.0798022 | − | 0.112857i | ||||
\(994\) | −2.48528 | −0.0788283 | ||||||||
\(995\) | − | 7.51472i | − | 0.238233i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 7.02944i | − | 0.222625i | −0.993785 | − | 0.111312i | \(-0.964495\pi\) | ||
0.993785 | − | 0.111312i | \(-0.0355054\pi\) | |||||||
\(998\) | 7.75736 | 0.245555 | ||||||||
\(999\) | −41.2132 | − | 11.6569i | −1.30393 | − | 0.368807i |
(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 | 1155.2.l.b.1121.3 | ✓ | 4 | |
3.2 | odd | 2 | 1155.2.l.c.1121.2 | yes | 4 | ||
11.10 | odd | 2 | 1155.2.l.c.1121.1 | yes | 4 | ||
33.32 | even | 2 | inner | 1155.2.l.b.1121.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.l.b.1121.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1155.2.l.b.1121.4 | yes | 4 | 33.32 | even | 2 | inner | |
1155.2.l.c.1121.1 | yes | 4 | 11.10 | odd | 2 | ||
1155.2.l.c.1121.2 | yes | 4 | 3.2 | odd | 2 |