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 | 1121.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1121 |
Dual form | 1155.2.l.a.1121.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −2.41421 | − | 3.41421i | −0.985599 | − | 1.39385i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | − | 2.41421i | − | 0.763441i | ||||||
\(11\) | −1.41421 | + | 3.00000i | −0.426401 | + | 0.904534i | ||||
\(12\) | 3.82843 | + | 5.41421i | 1.10517 | + | 1.56295i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | − | 2.41421i | − | 0.645226i | ||||||
\(15\) | −1.41421 | + | 1.00000i | −0.365148 | + | 0.258199i | ||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 1.17157 | 0.284148 | 0.142074 | − | 0.989856i | \(-0.454623\pi\) | ||||
0.142074 | + | 0.989856i | \(0.454623\pi\) | |||||||
\(18\) | 2.41421 | − | 6.82843i | 0.569036 | − | 1.60948i | ||||
\(19\) | 4.82843i | 1.10772i | 0.832611 | + | 0.553859i | \(0.186845\pi\) | ||||
−0.832611 | + | 0.553859i | \(0.813155\pi\) | |||||||
\(20\) | 3.82843i | 0.856062i | ||||||||
\(21\) | −1.41421 | + | 1.00000i | −0.308607 | + | 0.218218i | ||||
\(22\) | 3.41421 | − | 7.24264i | 0.727913 | − | 1.54414i | ||||
\(23\) | − | 4.82843i | − | 1.00680i | −0.864054 | − | 0.503398i | \(-0.832083\pi\) | ||
0.864054 | − | 0.503398i | \(-0.167917\pi\) | |||||||
\(24\) | −4.41421 | − | 6.24264i | −0.901048 | − | 1.27427i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 3.82843i | 0.723505i | ||||||||
\(29\) | −5.65685 | −1.05045 | −0.525226 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(30\) | 3.41421 | − | 2.41421i | 0.623347 | − | 0.440773i | ||||
\(31\) | −4.82843 | −0.867211 | −0.433606 | − | 0.901103i | \(-0.642759\pi\) | ||||
−0.433606 | + | 0.901103i | \(0.642759\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | −5.65685 | + | 1.00000i | −0.984732 | + | 0.174078i | ||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −3.82843 | + | 10.8284i | −0.638071 | + | 1.80474i | ||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | − | 11.6569i | − | 1.89099i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 4.41421i | − | 0.697948i | ||||||
\(41\) | −3.65685 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(42\) | 3.41421 | − | 2.41421i | 0.526825 | − | 0.372521i | ||||
\(43\) | 1.65685i | 0.252668i | 0.991988 | + | 0.126334i | \(0.0403211\pi\) | ||||
−0.991988 | + | 0.126334i | \(0.959679\pi\) | |||||||
\(44\) | −5.41421 | + | 11.4853i | −0.816223 | + | 1.73147i | ||||
\(45\) | −2.82843 | − | 1.00000i | −0.421637 | − | 0.149071i | ||||
\(46\) | 11.6569i | 1.71871i | ||||||||
\(47\) | 5.17157i | 0.754351i | 0.926142 | + | 0.377176i | \(0.123105\pi\) | ||||
−0.926142 | + | 0.377176i | \(0.876895\pi\) | |||||||
\(48\) | 3.00000 | + | 4.24264i | 0.433013 | + | 0.612372i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | 1.17157 | + | 1.65685i | 0.164053 | + | 0.232006i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.82843i | − | 0.663235i | −0.943414 | − | 0.331618i | \(-0.892406\pi\) | ||
0.943414 | − | 0.331618i | \(-0.107594\pi\) | |||||||
\(54\) | 12.0711 | − | 3.41421i | 1.64266 | − | 0.464616i | ||||
\(55\) | −3.00000 | − | 1.41421i | −0.404520 | − | 0.190693i | ||||
\(56\) | − | 4.41421i | − | 0.589874i | ||||||
\(57\) | −6.82843 | + | 4.82843i | −0.904447 | + | 0.639541i | ||||
\(58\) | 13.6569 | 1.79323 | ||||||||
\(59\) | − | 11.6569i | − | 1.51759i | −0.651328 | − | 0.758797i | \(-0.725788\pi\) | ||
0.651328 | − | 0.758797i | \(-0.274212\pi\) | |||||||
\(60\) | −5.41421 | + | 3.82843i | −0.698972 | + | 0.494248i | ||||
\(61\) | 10.8284i | 1.38644i | 0.720727 | + | 0.693219i | \(0.243808\pi\) | ||||
−0.720727 | + | 0.693219i | \(0.756192\pi\) | |||||||
\(62\) | 11.6569 | 1.48042 | ||||||||
\(63\) | −2.82843 | − | 1.00000i | −0.356348 | − | 0.125988i | ||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.6569 | − | 2.41421i | 1.68104 | − | 0.297169i | ||||
\(67\) | 10.4853 | 1.28098 | 0.640490 | − | 0.767966i | \(-0.278731\pi\) | ||||
0.640490 | + | 0.767966i | \(0.278731\pi\) | |||||||
\(68\) | 4.48528 | 0.543920 | ||||||||
\(69\) | 6.82843 | − | 4.82843i | 0.822046 | − | 0.581274i | ||||
\(70\) | 2.41421 | 0.288554 | ||||||||
\(71\) | 11.6569i | 1.38341i | 0.722178 | + | 0.691707i | \(0.243141\pi\) | ||||
−0.722178 | + | 0.691707i | \(0.756859\pi\) | |||||||
\(72\) | 4.41421 | − | 12.4853i | 0.520220 | − | 1.47140i | ||||
\(73\) | − | 12.0000i | − | 1.40449i | −0.711934 | − | 0.702247i | \(-0.752180\pi\) | ||
0.711934 | − | 0.702247i | \(-0.247820\pi\) | |||||||
\(74\) | −14.4853 | −1.68388 | ||||||||
\(75\) | −1.00000 | − | 1.41421i | −0.115470 | − | 0.163299i | ||||
\(76\) | 18.4853i | 2.12041i | ||||||||
\(77\) | −3.00000 | − | 1.41421i | −0.341882 | − | 0.161165i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 3.00000i | 0.335410i | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 8.82843 | 0.974937 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | −5.41421 | + | 3.82843i | −0.590739 | + | 0.417716i | ||||
\(85\) | 1.17157i | 0.127075i | ||||||||
\(86\) | − | 4.00000i | − | 0.431331i | ||||||
\(87\) | −5.65685 | − | 8.00000i | −0.606478 | − | 0.857690i | ||||
\(88\) | 6.24264 | − | 13.2426i | 0.665468 | − | 1.41167i | ||||
\(89\) | − | 3.65685i | − | 0.387626i | −0.981039 | − | 0.193813i | \(-0.937915\pi\) | ||
0.981039 | − | 0.193813i | \(-0.0620855\pi\) | |||||||
\(90\) | 6.82843 | + | 2.41421i | 0.719779 | + | 0.254480i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 18.4853i | − | 1.92722i | ||||||
\(93\) | −4.82843 | − | 6.82843i | −0.500685 | − | 0.708075i | ||||
\(94\) | − | 12.4853i | − | 1.28776i | ||||||
\(95\) | −4.82843 | −0.495386 | ||||||||
\(96\) | 1.58579 | + | 2.24264i | 0.161849 | + | 0.228889i | ||||
\(97\) | −10.8284 | −1.09946 | −0.549730 | − | 0.835342i | \(-0.685269\pi\) | ||||
−0.549730 | + | 0.835342i | \(0.685269\pi\) | |||||||
\(98\) | 2.41421 | 0.243872 | ||||||||
\(99\) | −7.07107 | − | 7.00000i | −0.710669 | − | 0.703526i | ||||
\(100\) | −3.82843 | −0.382843 | ||||||||
\(101\) | 13.3137 | 1.32476 | 0.662382 | − | 0.749166i | \(-0.269546\pi\) | ||||
0.662382 | + | 0.749166i | \(0.269546\pi\) | |||||||
\(102\) | −2.82843 | − | 4.00000i | −0.280056 | − | 0.396059i | ||||
\(103\) | −13.3137 | −1.31184 | −0.655919 | − | 0.754831i | \(-0.727719\pi\) | ||||
−0.655919 | + | 0.754831i | \(0.727719\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | − | 1.41421i | −0.0975900 | − | 0.138013i | ||||
\(106\) | 11.6569i | 1.13221i | ||||||||
\(107\) | −13.3137 | −1.28708 | −0.643542 | − | 0.765410i | \(-0.722536\pi\) | ||||
−0.643542 | + | 0.765410i | \(0.722536\pi\) | |||||||
\(108\) | −19.1421 | + | 5.41421i | −1.84195 | + | 0.520983i | ||||
\(109\) | 1.65685i | 0.158698i | 0.996847 | + | 0.0793489i | \(0.0252841\pi\) | ||||
−0.996847 | + | 0.0793489i | \(0.974716\pi\) | |||||||
\(110\) | 7.24264 | + | 3.41421i | 0.690559 | + | 0.325532i | ||||
\(111\) | 6.00000 | + | 8.48528i | 0.569495 | + | 0.805387i | ||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | 8.82843i | 0.830509i | 0.909705 | + | 0.415254i | \(0.136307\pi\) | ||||
−0.909705 | + | 0.415254i | \(0.863693\pi\) | |||||||
\(114\) | 16.4853 | − | 11.6569i | 1.54399 | − | 1.09176i | ||||
\(115\) | 4.82843 | 0.450253 | ||||||||
\(116\) | −21.6569 | −2.01079 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 28.1421i | 2.59069i | ||||||||
\(119\) | 1.17157i | 0.107398i | ||||||||
\(120\) | 6.24264 | − | 4.41421i | 0.569873 | − | 0.402961i | ||||
\(121\) | −7.00000 | − | 8.48528i | −0.636364 | − | 0.771389i | ||||
\(122\) | − | 26.1421i | − | 2.36680i | ||||||
\(123\) | −3.65685 | − | 5.17157i | −0.329727 | − | 0.466305i | ||||
\(124\) | −18.4853 | −1.66003 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 6.82843 | + | 2.41421i | 0.608325 | + | 0.215075i | ||||
\(127\) | 2.34315i | 0.207921i | 0.994581 | + | 0.103960i | \(0.0331515\pi\) | ||||
−0.994581 | + | 0.103960i | \(0.966849\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | −2.34315 | + | 1.65685i | −0.206302 | + | 0.145878i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.34315 | −0.554203 | −0.277102 | − | 0.960841i | \(-0.589374\pi\) | ||||
−0.277102 | + | 0.960841i | \(0.589374\pi\) | |||||||
\(132\) | −21.6569 | + | 3.82843i | −1.88499 | + | 0.333222i | ||||
\(133\) | −4.82843 | −0.418678 | ||||||||
\(134\) | −25.3137 | −2.18677 | ||||||||
\(135\) | −1.41421 | − | 5.00000i | −0.121716 | − | 0.430331i | ||||
\(136\) | −5.17157 | −0.443459 | ||||||||
\(137\) | − | 7.17157i | − | 0.612709i | −0.951918 | − | 0.306354i | \(-0.900891\pi\) | ||
0.951918 | − | 0.306354i | \(-0.0991093\pi\) | |||||||
\(138\) | −16.4853 | + | 11.6569i | −1.40332 | + | 0.992297i | ||||
\(139\) | − | 10.4853i | − | 0.889350i | −0.895692 | − | 0.444675i | \(-0.853319\pi\) | ||
0.895692 | − | 0.444675i | \(-0.146681\pi\) | |||||||
\(140\) | −3.82843 | −0.323561 | ||||||||
\(141\) | −7.31371 | + | 5.17157i | −0.615925 | + | 0.435525i | ||||
\(142\) | − | 28.1421i | − | 2.36164i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.00000 | + | 8.48528i | −0.250000 | + | 0.707107i | ||||
\(145\) | − | 5.65685i | − | 0.469776i | ||||||
\(146\) | 28.9706i | 2.39762i | ||||||||
\(147\) | −1.00000 | − | 1.41421i | −0.0824786 | − | 0.116642i | ||||
\(148\) | 22.9706 | 1.88817 | ||||||||
\(149\) | −15.3137 | −1.25455 | −0.627274 | − | 0.778799i | \(-0.715829\pi\) | ||||
−0.627274 | + | 0.778799i | \(0.715829\pi\) | |||||||
\(150\) | 2.41421 | + | 3.41421i | 0.197120 | + | 0.278769i | ||||
\(151\) | 19.3137i | 1.57173i | 0.618400 | + | 0.785864i | \(0.287781\pi\) | ||||
−0.618400 | + | 0.785864i | \(0.712219\pi\) | |||||||
\(152\) | − | 21.3137i | − | 1.72877i | ||||||
\(153\) | −1.17157 | + | 3.31371i | −0.0947161 | + | 0.267897i | ||||
\(154\) | 7.24264 | + | 3.41421i | 0.583629 | + | 0.275125i | ||||
\(155\) | − | 4.82843i | − | 0.387829i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1716 | −1.05121 | −0.525603 | − | 0.850730i | \(-0.676160\pi\) | ||||
−0.525603 | + | 0.850730i | \(0.676160\pi\) | |||||||
\(158\) | − | 9.65685i | − | 0.768258i | ||||||
\(159\) | 6.82843 | − | 4.82843i | 0.541529 | − | 0.382919i | ||||
\(160\) | 1.58579i | 0.125367i | ||||||||
\(161\) | 4.82843 | 0.380533 | ||||||||
\(162\) | 16.8995 | + | 13.6569i | 1.32775 | + | 1.07298i | ||||
\(163\) | −18.4853 | −1.44788 | −0.723939 | − | 0.689863i | \(-0.757671\pi\) | ||||
−0.723939 | + | 0.689863i | \(0.757671\pi\) | |||||||
\(164\) | −14.0000 | −1.09322 | ||||||||
\(165\) | −1.00000 | − | 5.65685i | −0.0778499 | − | 0.440386i | ||||
\(166\) | −28.9706 | −2.24855 | ||||||||
\(167\) | −13.6569 | −1.05680 | −0.528400 | − | 0.848996i | \(-0.677208\pi\) | ||||
−0.528400 | + | 0.848996i | \(0.677208\pi\) | |||||||
\(168\) | 6.24264 | − | 4.41421i | 0.481630 | − | 0.340564i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | − | 2.82843i | − | 0.216930i | ||||||
\(171\) | −13.6569 | − | 4.82843i | −1.04437 | − | 0.369239i | ||||
\(172\) | 6.34315i | 0.483660i | ||||||||
\(173\) | −18.1421 | −1.37932 | −0.689661 | − | 0.724133i | \(-0.742240\pi\) | ||||
−0.689661 | + | 0.724133i | \(0.742240\pi\) | |||||||
\(174\) | 13.6569 | + | 19.3137i | 1.03532 | + | 1.46417i | ||||
\(175\) | − | 1.00000i | − | 0.0755929i | ||||||
\(176\) | −4.24264 | + | 9.00000i | −0.319801 | + | 0.678401i | ||||
\(177\) | 16.4853 | − | 11.6569i | 1.23911 | − | 0.876183i | ||||
\(178\) | 8.82843i | 0.661719i | ||||||||
\(179\) | − | 0.343146i | − | 0.0256479i | −0.999918 | − | 0.0128240i | \(-0.995918\pi\) | ||
0.999918 | − | 0.0128240i | \(-0.00408210\pi\) | |||||||
\(180\) | −10.8284 | − | 3.82843i | −0.807103 | − | 0.285354i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.3137 | + | 10.8284i | −1.13202 | + | 0.800460i | ||||
\(184\) | 21.3137i | 1.57127i | ||||||||
\(185\) | 6.00000i | 0.441129i | ||||||||
\(186\) | 11.6569 | + | 16.4853i | 0.854722 | + | 1.20876i | ||||
\(187\) | −1.65685 | + | 3.51472i | −0.121161 | + | 0.257022i | ||||
\(188\) | 19.7990i | 1.44399i | ||||||||
\(189\) | −1.41421 | − | 5.00000i | −0.102869 | − | 0.363696i | ||||
\(190\) | 11.6569 | 0.845677 | ||||||||
\(191\) | 6.00000i | 0.434145i | 0.976156 | + | 0.217072i | \(0.0696508\pi\) | ||||
−0.976156 | + | 0.217072i | \(0.930349\pi\) | |||||||
\(192\) | −9.82843 | − | 13.8995i | −0.709306 | − | 1.00311i | ||||
\(193\) | 5.51472i | 0.396958i | 0.980105 | + | 0.198479i | \(0.0636002\pi\) | ||||
−0.980105 | + | 0.198479i | \(0.936400\pi\) | |||||||
\(194\) | 26.1421 | 1.87690 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.82843 | −0.273459 | ||||||||
\(197\) | 9.17157 | 0.653448 | 0.326724 | − | 0.945120i | \(-0.394055\pi\) | ||||
0.326724 | + | 0.945120i | \(0.394055\pi\) | |||||||
\(198\) | 17.0711 | + | 16.8995i | 1.21319 | + | 1.20099i | ||||
\(199\) | 2.48528 | 0.176177 | 0.0880885 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880885 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(200\) | 4.41421 | 0.312132 | ||||||||
\(201\) | 10.4853 | + | 14.8284i | 0.739575 | + | 1.04592i | ||||
\(202\) | −32.1421 | −2.26151 | ||||||||
\(203\) | − | 5.65685i | − | 0.397033i | ||||||
\(204\) | 4.48528 | + | 6.34315i | 0.314033 | + | 0.444109i | ||||
\(205\) | − | 3.65685i | − | 0.255406i | ||||||
\(206\) | 32.1421 | 2.23945 | ||||||||
\(207\) | 13.6569 | + | 4.82843i | 0.949217 | + | 0.335599i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.4853 | − | 6.82843i | −1.00197 | − | 0.472332i | ||||
\(210\) | 2.41421 | + | 3.41421i | 0.166597 | + | 0.235603i | ||||
\(211\) | − | 16.9706i | − | 1.16830i | −0.811645 | − | 0.584151i | \(-0.801428\pi\) | ||
0.811645 | − | 0.584151i | \(-0.198572\pi\) | |||||||
\(212\) | − | 18.4853i | − | 1.26957i | ||||||
\(213\) | −16.4853 | + | 11.6569i | −1.12955 | + | 0.798714i | ||||
\(214\) | 32.1421 | 2.19719 | ||||||||
\(215\) | −1.65685 | −0.112997 | ||||||||
\(216\) | 22.0711 | − | 6.24264i | 1.50175 | − | 0.424758i | ||||
\(217\) | − | 4.82843i | − | 0.327775i | ||||||
\(218\) | − | 4.00000i | − | 0.270914i | ||||||
\(219\) | 16.9706 | − | 12.0000i | 1.14676 | − | 0.810885i | ||||
\(220\) | −11.4853 | − | 5.41421i | −0.774338 | − | 0.365026i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −14.4853 | − | 20.4853i | −0.972188 | − | 1.37488i | ||||
\(223\) | 18.9706 | 1.27036 | 0.635181 | − | 0.772363i | \(-0.280925\pi\) | ||||
0.635181 | + | 0.772363i | \(0.280925\pi\) | |||||||
\(224\) | 1.58579i | 0.105955i | ||||||||
\(225\) | 1.00000 | − | 2.82843i | 0.0666667 | − | 0.188562i | ||||
\(226\) | − | 21.3137i | − | 1.41777i | ||||||
\(227\) | 25.6569 | 1.70291 | 0.851453 | − | 0.524432i | \(-0.175722\pi\) | ||||
0.851453 | + | 0.524432i | \(0.175722\pi\) | |||||||
\(228\) | −26.1421 | + | 18.4853i | −1.73131 | + | 1.22422i | ||||
\(229\) | 13.3137 | 0.879795 | 0.439897 | − | 0.898048i | \(-0.355015\pi\) | ||||
0.439897 | + | 0.898048i | \(0.355015\pi\) | |||||||
\(230\) | −11.6569 | −0.768630 | ||||||||
\(231\) | −1.00000 | − | 5.65685i | −0.0657952 | − | 0.372194i | ||||
\(232\) | 24.9706 | 1.63940 | ||||||||
\(233\) | 27.7990 | 1.82117 | 0.910586 | − | 0.413319i | \(-0.135631\pi\) | ||||
0.910586 | + | 0.413319i | \(0.135631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.17157 | −0.337356 | ||||||||
\(236\) | − | 44.6274i | − | 2.90500i | ||||||
\(237\) | −5.65685 | + | 4.00000i | −0.367452 | + | 0.259828i | ||||
\(238\) | − | 2.82843i | − | 0.183340i | ||||||
\(239\) | 2.82843 | 0.182956 | 0.0914779 | − | 0.995807i | \(-0.470841\pi\) | ||||
0.0914779 | + | 0.995807i | \(0.470841\pi\) | |||||||
\(240\) | −4.24264 | + | 3.00000i | −0.273861 | + | 0.193649i | ||||
\(241\) | − | 17.1716i | − | 1.10612i | −0.833142 | − | 0.553059i | \(-0.813460\pi\) | ||
0.833142 | − | 0.553059i | \(-0.186540\pi\) | |||||||
\(242\) | 16.8995 | + | 20.4853i | 1.08634 | + | 1.31684i | ||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 41.4558i | 2.65394i | ||||||||
\(245\) | − | 1.00000i | − | 0.0638877i | ||||||
\(246\) | 8.82843 | + | 12.4853i | 0.562880 | + | 0.796032i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 21.3137 | 1.35342 | ||||||||
\(249\) | 12.0000 | + | 16.9706i | 0.760469 | + | 1.07547i | ||||
\(250\) | 2.41421i | 0.152688i | ||||||||
\(251\) | 24.6274i | 1.55447i | 0.629211 | + | 0.777234i | \(0.283378\pi\) | ||||
−0.629211 | + | 0.777234i | \(0.716622\pi\) | |||||||
\(252\) | −10.8284 | − | 3.82843i | −0.682127 | − | 0.241168i | ||||
\(253\) | 14.4853 | + | 6.82843i | 0.910682 | + | 0.429300i | ||||
\(254\) | − | 5.65685i | − | 0.354943i | ||||||
\(255\) | −1.65685 | + | 1.17157i | −0.103756 | + | 0.0733667i | ||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 9.31371i | 0.580973i | 0.956879 | + | 0.290487i | \(0.0938172\pi\) | ||||
−0.956879 | + | 0.290487i | \(0.906183\pi\) | |||||||
\(258\) | 5.65685 | − | 4.00000i | 0.352180 | − | 0.249029i | ||||
\(259\) | 6.00000i | 0.372822i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.65685 | − | 16.0000i | 0.350150 | − | 0.990375i | ||||
\(262\) | 15.3137 | 0.946084 | ||||||||
\(263\) | 5.31371 | 0.327657 | 0.163829 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163829 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(264\) | 24.9706 | − | 4.41421i | 1.53683 | − | 0.271676i | ||||
\(265\) | 4.82843 | 0.296608 | ||||||||
\(266\) | 11.6569 | 0.714728 | ||||||||
\(267\) | 5.17157 | − | 3.65685i | 0.316495 | − | 0.223796i | ||||
\(268\) | 40.1421 | 2.45207 | ||||||||
\(269\) | 5.31371i | 0.323983i | 0.986792 | + | 0.161991i | \(0.0517916\pi\) | ||||
−0.986792 | + | 0.161991i | \(0.948208\pi\) | |||||||
\(270\) | 3.41421 | + | 12.0711i | 0.207782 | + | 0.734622i | ||||
\(271\) | 14.4853i | 0.879918i | 0.898018 | + | 0.439959i | \(0.145007\pi\) | ||||
−0.898018 | + | 0.439959i | \(0.854993\pi\) | |||||||
\(272\) | 3.51472 | 0.213111 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.3137i | 1.04596i | ||||||||
\(275\) | 1.41421 | − | 3.00000i | 0.0852803 | − | 0.180907i | ||||
\(276\) | 26.1421 | − | 18.4853i | 1.57357 | − | 1.11268i | ||||
\(277\) | − | 0.828427i | − | 0.0497754i | −0.999690 | − | 0.0248877i | \(-0.992077\pi\) | ||
0.999690 | − | 0.0248877i | \(-0.00792281\pi\) | |||||||
\(278\) | 25.3137i | 1.51822i | ||||||||
\(279\) | 4.82843 | − | 13.6569i | 0.289070 | − | 0.817614i | ||||
\(280\) | 4.41421 | 0.263800 | ||||||||
\(281\) | 4.97056 | 0.296519 | 0.148259 | − | 0.988948i | \(-0.452633\pi\) | ||||
0.148259 | + | 0.988948i | \(0.452633\pi\) | |||||||
\(282\) | 17.6569 | − | 12.4853i | 1.05145 | − | 0.743488i | ||||
\(283\) | − | 4.97056i | − | 0.295469i | −0.989027 | − | 0.147735i | \(-0.952802\pi\) | ||
0.989027 | − | 0.147735i | \(-0.0471982\pi\) | |||||||
\(284\) | 44.6274i | 2.64815i | ||||||||
\(285\) | −4.82843 | − | 6.82843i | −0.286011 | − | 0.404481i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 3.65685i | − | 0.215857i | ||||||
\(288\) | −1.58579 | + | 4.48528i | −0.0934434 | + | 0.264298i | ||||
\(289\) | −15.6274 | −0.919260 | ||||||||
\(290\) | 13.6569i | 0.801958i | ||||||||
\(291\) | −10.8284 | − | 15.3137i | −0.634774 | − | 0.897705i | ||||
\(292\) | − | 45.9411i | − | 2.68850i | ||||||
\(293\) | −13.1716 | −0.769492 | −0.384746 | − | 0.923023i | \(-0.625711\pi\) | ||||
−0.384746 | + | 0.923023i | \(0.625711\pi\) | |||||||
\(294\) | 2.41421 | + | 3.41421i | 0.140800 | + | 0.199121i | ||||
\(295\) | 11.6569 | 0.678688 | ||||||||
\(296\) | −26.4853 | −1.53943 | ||||||||
\(297\) | 2.82843 | − | 17.0000i | 0.164122 | − | 0.986440i | ||||
\(298\) | 36.9706 | 2.14165 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.82843 | − | 5.41421i | −0.221034 | − | 0.312590i | ||||
\(301\) | −1.65685 | −0.0954995 | ||||||||
\(302\) | − | 46.6274i | − | 2.68311i | ||||||
\(303\) | 13.3137 | + | 18.8284i | 0.764853 | + | 1.08166i | ||||
\(304\) | 14.4853i | 0.830788i | ||||||||
\(305\) | −10.8284 | −0.620034 | ||||||||
\(306\) | 2.82843 | − | 8.00000i | 0.161690 | − | 0.457330i | ||||
\(307\) | 24.9706i | 1.42515i | 0.701598 | + | 0.712573i | \(0.252470\pi\) | ||||
−0.701598 | + | 0.712573i | \(0.747530\pi\) | |||||||
\(308\) | −11.4853 | − | 5.41421i | −0.654435 | − | 0.308503i | ||||
\(309\) | −13.3137 | − | 18.8284i | −0.757390 | − | 1.07111i | ||||
\(310\) | 11.6569i | 0.662065i | ||||||||
\(311\) | 20.6274i | 1.16967i | 0.811151 | + | 0.584837i | \(0.198841\pi\) | ||||
−0.811151 | + | 0.584837i | \(0.801159\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8284 | 1.06425 | 0.532123 | − | 0.846667i | \(-0.321394\pi\) | ||||
0.532123 | + | 0.846667i | \(0.321394\pi\) | |||||||
\(314\) | 31.7990 | 1.79452 | ||||||||
\(315\) | 1.00000 | − | 2.82843i | 0.0563436 | − | 0.159364i | ||||
\(316\) | 15.3137i | 0.861463i | ||||||||
\(317\) | 23.1716i | 1.30145i | 0.759316 | + | 0.650723i | \(0.225534\pi\) | ||||
−0.759316 | + | 0.650723i | \(0.774466\pi\) | |||||||
\(318\) | −16.4853 | + | 11.6569i | −0.924449 | + | 0.653684i | ||||
\(319\) | 8.00000 | − | 16.9706i | 0.447914 | − | 0.950169i | ||||
\(320\) | − | 9.82843i | − | 0.549426i | ||||||
\(321\) | −13.3137 | − | 18.8284i | −0.743099 | − | 1.05090i | ||||
\(322\) | −11.6569 | −0.649611 | ||||||||
\(323\) | 5.65685i | 0.314756i | ||||||||
\(324\) | −26.7990 | − | 21.6569i | −1.48883 | − | 1.20316i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 44.6274 | 2.47168 | ||||||||
\(327\) | −2.34315 | + | 1.65685i | −0.129576 | + | 0.0916242i | ||||
\(328\) | 16.1421 | 0.891300 | ||||||||
\(329\) | −5.17157 | −0.285118 | ||||||||
\(330\) | 2.41421 | + | 13.6569i | 0.132898 | + | 0.751785i | ||||
\(331\) | −21.6569 | −1.19037 | −0.595184 | − | 0.803589i | \(-0.702921\pi\) | ||||
−0.595184 | + | 0.803589i | \(0.702921\pi\) | |||||||
\(332\) | 45.9411 | 2.52135 | ||||||||
\(333\) | −6.00000 | + | 16.9706i | −0.328798 | + | 0.929981i | ||||
\(334\) | 32.9706 | 1.80407 | ||||||||
\(335\) | 10.4853i | 0.572872i | ||||||||
\(336\) | −4.24264 | + | 3.00000i | −0.231455 | + | 0.163663i | ||||
\(337\) | 14.4853i | 0.789064i | 0.918882 | + | 0.394532i | \(0.129093\pi\) | ||||
−0.918882 | + | 0.394532i | \(0.870907\pi\) | |||||||
\(338\) | −31.3848 | −1.70711 | ||||||||
\(339\) | −12.4853 | + | 8.82843i | −0.678107 | + | 0.479494i | ||||
\(340\) | 4.48528i | 0.243249i | ||||||||
\(341\) | 6.82843 | − | 14.4853i | 0.369780 | − | 0.784422i | ||||
\(342\) | 32.9706 | + | 11.6569i | 1.78284 | + | 0.630330i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 7.31371i | − | 0.394329i | ||||||
\(345\) | 4.82843 | + | 6.82843i | 0.259954 | + | 0.367630i | ||||
\(346\) | 43.7990 | 2.35465 | ||||||||
\(347\) | 23.6569 | 1.26997 | 0.634983 | − | 0.772526i | \(-0.281007\pi\) | ||||
0.634983 | + | 0.772526i | \(0.281007\pi\) | |||||||
\(348\) | −21.6569 | − | 30.6274i | −1.16093 | − | 1.64180i | ||||
\(349\) | − | 15.5147i | − | 0.830484i | −0.909711 | − | 0.415242i | \(-0.863697\pi\) | ||
0.909711 | − | 0.415242i | \(-0.136303\pi\) | |||||||
\(350\) | 2.41421i | 0.129045i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.24264 | + | 4.75736i | −0.119533 | + | 0.253568i | ||||
\(353\) | 11.6569i | 0.620432i | 0.950666 | + | 0.310216i | \(0.100401\pi\) | ||||
−0.950666 | + | 0.310216i | \(0.899599\pi\) | |||||||
\(354\) | −39.7990 | + | 28.1421i | −2.11529 | + | 1.49574i | ||||
\(355\) | −11.6569 | −0.618682 | ||||||||
\(356\) | − | 14.0000i | − | 0.741999i | ||||||
\(357\) | −1.65685 | + | 1.17157i | −0.0876900 | + | 0.0620062i | ||||
\(358\) | 0.828427i | 0.0437837i | ||||||||
\(359\) | −8.48528 | −0.447836 | −0.223918 | − | 0.974608i | \(-0.571885\pi\) | ||||
−0.223918 | + | 0.974608i | \(0.571885\pi\) | |||||||
\(360\) | 12.4853 | + | 4.41421i | 0.658032 | + | 0.232649i | ||||
\(361\) | −4.31371 | −0.227037 | ||||||||
\(362\) | 4.82843 | 0.253776 | ||||||||
\(363\) | 5.00000 | − | 18.3848i | 0.262432 | − | 0.964951i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | 0.628109 | ||||||||
\(366\) | 36.9706 | − | 26.1421i | 1.93248 | − | 1.36647i | ||||
\(367\) | −18.0000 | −0.939592 | −0.469796 | − | 0.882775i | \(-0.655673\pi\) | ||||
−0.469796 | + | 0.882775i | \(0.655673\pi\) | |||||||
\(368\) | − | 14.4853i | − | 0.755097i | ||||||
\(369\) | 3.65685 | − | 10.3431i | 0.190368 | − | 0.538443i | ||||
\(370\) | − | 14.4853i | − | 0.753054i | ||||||
\(371\) | 4.82843 | 0.250679 | ||||||||
\(372\) | −18.4853 | − | 26.1421i | −0.958417 | − | 1.35541i | ||||
\(373\) | − | 24.1421i | − | 1.25003i | −0.780612 | − | 0.625016i | \(-0.785092\pi\) | ||
0.780612 | − | 0.625016i | \(-0.214908\pi\) | |||||||
\(374\) | 4.00000 | − | 8.48528i | 0.206835 | − | 0.438763i | ||||
\(375\) | 1.41421 | − | 1.00000i | 0.0730297 | − | 0.0516398i | ||||
\(376\) | − | 22.8284i | − | 1.17729i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.41421 | + | 12.0711i | 0.175608 | + | 0.620869i | ||||
\(379\) | 29.9411 | 1.53797 | 0.768986 | − | 0.639265i | \(-0.220761\pi\) | ||||
0.768986 | + | 0.639265i | \(0.220761\pi\) | |||||||
\(380\) | −18.4853 | −0.948275 | ||||||||
\(381\) | −3.31371 | + | 2.34315i | −0.169766 | + | 0.120043i | ||||
\(382\) | − | 14.4853i | − | 0.741131i | ||||||
\(383\) | 15.7990i | 0.807291i | 0.914916 | + | 0.403645i | \(0.132257\pi\) | ||||
−0.914916 | + | 0.403645i | \(0.867743\pi\) | |||||||
\(384\) | 20.5563 | + | 29.0711i | 1.04901 | + | 1.48353i | ||||
\(385\) | 1.41421 | − | 3.00000i | 0.0720750 | − | 0.152894i | ||||
\(386\) | − | 13.3137i | − | 0.677650i | ||||||
\(387\) | −4.68629 | − | 1.65685i | −0.238218 | − | 0.0842226i | ||||
\(388\) | −41.4558 | −2.10460 | ||||||||
\(389\) | 34.6274i | 1.75568i | 0.478954 | + | 0.877840i | \(0.341016\pi\) | ||||
−0.478954 | + | 0.877840i | \(0.658984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.65685i | − | 0.286079i | ||||||
\(392\) | 4.41421 | 0.222951 | ||||||||
\(393\) | −6.34315 | − | 8.97056i | −0.319969 | − | 0.452505i | ||||
\(394\) | −22.1421 | −1.11550 | ||||||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | −27.0711 | − | 26.7990i | −1.36037 | − | 1.34670i | ||||
\(397\) | 3.51472 | 0.176399 | 0.0881993 | − | 0.996103i | \(-0.471889\pi\) | ||||
0.0881993 | + | 0.996103i | \(0.471889\pi\) | |||||||
\(398\) | −6.00000 | −0.300753 | ||||||||
\(399\) | −4.82843 | − | 6.82843i | −0.241724 | − | 0.341849i | ||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | 27.3137i | 1.36398i | 0.731361 | + | 0.681991i | \(0.238886\pi\) | ||||
−0.731361 | + | 0.681991i | \(0.761114\pi\) | |||||||
\(402\) | −25.3137 | − | 35.7990i | −1.26253 | − | 1.78549i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 50.9706 | 2.53588 | ||||||||
\(405\) | 5.65685 | − | 7.00000i | 0.281091 | − | 0.347833i | ||||
\(406\) | 13.6569i | 0.677778i | ||||||||
\(407\) | −8.48528 | + | 18.0000i | −0.420600 | + | 0.892227i | ||||
\(408\) | −5.17157 | − | 7.31371i | −0.256031 | − | 0.362083i | ||||
\(409\) | 13.4558i | 0.665349i | 0.943042 | + | 0.332674i | \(0.107951\pi\) | ||||
−0.943042 | + | 0.332674i | \(0.892049\pi\) | |||||||
\(410\) | 8.82843i | 0.436005i | ||||||||
\(411\) | 10.1421 | − | 7.17157i | 0.500275 | − | 0.353748i | ||||
\(412\) | −50.9706 | −2.51114 | ||||||||
\(413\) | 11.6569 | 0.573596 | ||||||||
\(414\) | −32.9706 | − | 11.6569i | −1.62041 | − | 0.572903i | ||||
\(415\) | 12.0000i | 0.589057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.8284 | − | 10.4853i | 0.726151 | − | 0.513466i | ||||
\(418\) | 34.9706 | + | 16.4853i | 1.71047 | + | 0.806321i | ||||
\(419\) | − | 2.68629i | − | 0.131234i | −0.997845 | − | 0.0656170i | \(-0.979098\pi\) | ||
0.997845 | − | 0.0656170i | \(-0.0209015\pi\) | |||||||
\(420\) | −3.82843 | − | 5.41421i | −0.186808 | − | 0.264187i | ||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 40.9706i | 1.99442i | ||||||||
\(423\) | −14.6274 | − | 5.17157i | −0.711209 | − | 0.251450i | ||||
\(424\) | 21.3137i | 1.03509i | ||||||||
\(425\) | −1.17157 | −0.0568296 | ||||||||
\(426\) | 39.7990 | − | 28.1421i | 1.92827 | − | 1.36349i | ||||
\(427\) | −10.8284 | −0.524024 | ||||||||
\(428\) | −50.9706 | −2.46376 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | 10.1421 | 0.488529 | 0.244265 | − | 0.969709i | \(-0.421453\pi\) | ||||
0.244265 | + | 0.969709i | \(0.421453\pi\) | |||||||
\(432\) | −15.0000 | + | 4.24264i | −0.721688 | + | 0.204124i | ||||
\(433\) | −29.1716 | −1.40190 | −0.700948 | − | 0.713212i | \(-0.747240\pi\) | ||||
−0.700948 | + | 0.713212i | \(0.747240\pi\) | |||||||
\(434\) | 11.6569i | 0.559547i | ||||||||
\(435\) | 8.00000 | − | 5.65685i | 0.383571 | − | 0.271225i | ||||
\(436\) | 6.34315i | 0.303782i | ||||||||
\(437\) | 23.3137 | 1.11525 | ||||||||
\(438\) | −40.9706 | + | 28.9706i | −1.95765 | + | 1.38427i | ||||
\(439\) | 31.4558i | 1.50131i | 0.660697 | + | 0.750653i | \(0.270261\pi\) | ||||
−0.660697 | + | 0.750653i | \(0.729739\pi\) | |||||||
\(440\) | 13.2426 | + | 6.24264i | 0.631318 | + | 0.297606i | ||||
\(441\) | 1.00000 | − | 2.82843i | 0.0476190 | − | 0.134687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.79899i | − | 0.0854726i | −0.999086 | − | 0.0427363i | \(-0.986392\pi\) | ||
0.999086 | − | 0.0427363i | \(-0.0136075\pi\) | |||||||
\(444\) | 22.9706 | + | 32.4853i | 1.09013 | + | 1.54168i | ||||
\(445\) | 3.65685 | 0.173352 | ||||||||
\(446\) | −45.7990 | −2.16865 | ||||||||
\(447\) | −15.3137 | − | 21.6569i | −0.724314 | − | 1.02433i | ||||
\(448\) | − | 9.82843i | − | 0.464350i | ||||||
\(449\) | 17.6569i | 0.833278i | 0.909072 | + | 0.416639i | \(0.136792\pi\) | ||||
−0.909072 | + | 0.416639i | \(0.863208\pi\) | |||||||
\(450\) | −2.41421 | + | 6.82843i | −0.113807 | + | 0.321895i | ||||
\(451\) | 5.17157 | − | 10.9706i | 0.243520 | − | 0.516584i | ||||
\(452\) | 33.7990i | 1.58977i | ||||||||
\(453\) | −27.3137 | + | 19.3137i | −1.28331 | + | 0.907437i | ||||
\(454\) | −61.9411 | −2.90704 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 30.1421 | − | 21.3137i | 1.41153 | − | 0.998106i | ||||
\(457\) | − | 9.51472i | − | 0.445080i | −0.974924 | − | 0.222540i | \(-0.928565\pi\) | ||
0.974924 | − | 0.222540i | \(-0.0714348\pi\) | |||||||
\(458\) | −32.1421 | −1.50190 | ||||||||
\(459\) | −5.85786 | + | 1.65685i | −0.273422 | + | 0.0773353i | ||||
\(460\) | 18.4853 | 0.861881 | ||||||||
\(461\) | −23.6569 | −1.10181 | −0.550905 | − | 0.834568i | \(-0.685717\pi\) | ||||
−0.550905 | + | 0.834568i | \(0.685717\pi\) | |||||||
\(462\) | 2.41421 | + | 13.6569i | 0.112319 | + | 0.635374i | ||||
\(463\) | 11.4558 | 0.532398 | 0.266199 | − | 0.963918i | \(-0.414232\pi\) | ||||
0.266199 | + | 0.963918i | \(0.414232\pi\) | |||||||
\(464\) | −16.9706 | −0.787839 | ||||||||
\(465\) | 6.82843 | − | 4.82843i | 0.316661 | − | 0.223913i | ||||
\(466\) | −67.1127 | −3.10894 | ||||||||
\(467\) | 6.82843i | 0.315982i | 0.987441 | + | 0.157991i | \(0.0505017\pi\) | ||||
−0.987441 | + | 0.157991i | \(0.949498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4853i | 0.484165i | ||||||||
\(470\) | 12.4853 | 0.575903 | ||||||||
\(471\) | −13.1716 | − | 18.6274i | −0.606914 | − | 0.858306i | ||||
\(472\) | 51.4558i | 2.36845i | ||||||||
\(473\) | −4.97056 | − | 2.34315i | −0.228547 | − | 0.107738i | ||||
\(474\) | 13.6569 | − | 9.65685i | 0.627280 | − | 0.443554i | ||||
\(475\) | − | 4.82843i | − | 0.221543i | ||||||
\(476\) | 4.48528i | 0.205583i | ||||||||
\(477\) | 13.6569 | + | 4.82843i | 0.625304 | + | 0.221078i | ||||
\(478\) | −6.82843 | −0.312325 | ||||||||
\(479\) | −11.3137 | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(480\) | −2.24264 | + | 1.58579i | −0.102362 | + | 0.0723809i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 41.4558i | 1.88826i | ||||||||
\(483\) | 4.82843 | + | 6.82843i | 0.219701 | + | 0.310704i | ||||
\(484\) | −26.7990 | − | 32.4853i | −1.21814 | − | 1.47660i | ||||
\(485\) | − | 10.8284i | − | 0.491694i | ||||||
\(486\) | −2.41421 | + | 37.5563i | −0.109511 | + | 1.70359i | ||||
\(487\) | 9.51472 | 0.431153 | 0.215577 | − | 0.976487i | \(-0.430837\pi\) | ||||
0.215577 | + | 0.976487i | \(0.430837\pi\) | |||||||
\(488\) | − | 47.7990i | − | 2.16376i | ||||||
\(489\) | −18.4853 | − | 26.1421i | −0.835933 | − | 1.18219i | ||||
\(490\) | 2.41421i | 0.109063i | ||||||||
\(491\) | 10.1421 | 0.457708 | 0.228854 | − | 0.973461i | \(-0.426502\pi\) | ||||
0.228854 | + | 0.973461i | \(0.426502\pi\) | |||||||
\(492\) | −14.0000 | − | 19.7990i | −0.631169 | − | 0.892607i | ||||
\(493\) | −6.62742 | −0.298484 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.00000 | − | 7.07107i | 0.314627 | − | 0.317821i | ||||
\(496\) | −14.4853 | −0.650408 | ||||||||
\(497\) | −11.6569 | −0.522881 | ||||||||
\(498\) | −28.9706 | − | 40.9706i | −1.29820 | − | 1.83593i | ||||
\(499\) | 36.0000 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(500\) | − | 3.82843i | − | 0.171212i | ||||||
\(501\) | −13.6569 | − | 19.3137i | −0.610143 | − | 0.862873i | ||||
\(502\) | − | 59.4558i | − | 2.65364i | ||||||
\(503\) | 14.3431 | 0.639529 | 0.319765 | − | 0.947497i | \(-0.396396\pi\) | ||||
0.319765 | + | 0.947497i | \(0.396396\pi\) | |||||||
\(504\) | 12.4853 | + | 4.41421i | 0.556139 | + | 0.196625i | ||||
\(505\) | 13.3137i | 0.592452i | ||||||||
\(506\) | −34.9706 | − | 16.4853i | −1.55463 | − | 0.732860i | ||||
\(507\) | 13.0000 | + | 18.3848i | 0.577350 | + | 0.816497i | ||||
\(508\) | 8.97056i | 0.398004i | ||||||||
\(509\) | − | 22.9706i | − | 1.01815i | −0.860721 | − | 0.509076i | \(-0.829987\pi\) | ||
0.860721 | − | 0.509076i | \(-0.170013\pi\) | |||||||
\(510\) | 4.00000 | − | 2.82843i | 0.177123 | − | 0.125245i | ||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | −6.82843 | − | 24.1421i | −0.301482 | − | 1.06590i | ||||
\(514\) | − | 22.4853i | − | 0.991783i | ||||||
\(515\) | − | 13.3137i | − | 0.586672i | ||||||
\(516\) | −8.97056 | + | 6.34315i | −0.394907 | + | 0.279241i | ||||
\(517\) | −15.5147 | − | 7.31371i | −0.682337 | − | 0.321657i | ||||
\(518\) | − | 14.4853i | − | 0.636447i | ||||||
\(519\) | −18.1421 | − | 25.6569i | −0.796351 | − | 1.12621i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3137i | 0.583284i | 0.956528 | + | 0.291642i | \(0.0942016\pi\) | ||||
−0.956528 | + | 0.291642i | \(0.905798\pi\) | |||||||
\(522\) | −13.6569 | + | 38.6274i | −0.597744 | + | 1.69068i | ||||
\(523\) | 20.9706i | 0.916979i | 0.888700 | + | 0.458489i | \(0.151609\pi\) | ||||
−0.888700 | + | 0.458489i | \(0.848391\pi\) | |||||||
\(524\) | −24.2843 | −1.06086 | ||||||||
\(525\) | 1.41421 | − | 1.00000i | 0.0617213 | − | 0.0436436i | ||||
\(526\) | −12.8284 | −0.559346 | ||||||||
\(527\) | −5.65685 | −0.246416 | ||||||||
\(528\) | −16.9706 | + | 3.00000i | −0.738549 | + | 0.130558i | ||||
\(529\) | −0.313708 | −0.0136395 | ||||||||
\(530\) | −11.6569 | −0.506341 | ||||||||
\(531\) | 32.9706 | + | 11.6569i | 1.43080 | + | 0.505864i | ||||
\(532\) | −18.4853 | −0.801439 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.4853 | + | 8.82843i | −0.540291 | + | 0.382043i | ||||
\(535\) | − | 13.3137i | − | 0.575602i | ||||||
\(536\) | −46.2843 | −1.99918 | ||||||||
\(537\) | 0.485281 | − | 0.343146i | 0.0209414 | − | 0.0148078i | ||||
\(538\) | − | 12.8284i | − | 0.553073i | ||||||
\(539\) | 1.41421 | − | 3.00000i | 0.0609145 | − | 0.129219i | ||||
\(540\) | −5.41421 | − | 19.1421i | −0.232991 | − | 0.823746i | ||||
\(541\) | 4.97056i | 0.213701i | 0.994275 | + | 0.106851i | \(0.0340767\pi\) | ||||
−0.994275 | + | 0.106851i | \(0.965923\pi\) | |||||||
\(542\) | − | 34.9706i | − | 1.50211i | ||||||
\(543\) | −2.00000 | − | 2.82843i | −0.0858282 | − | 0.121379i | ||||
\(544\) | 1.85786 | 0.0796553 | ||||||||
\(545\) | −1.65685 | −0.0709718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2843i | 1.03832i | 0.854677 | + | 0.519160i | \(0.173755\pi\) | ||||
−0.854677 | + | 0.519160i | \(0.826245\pi\) | |||||||
\(548\) | − | 27.4558i | − | 1.17286i | ||||||
\(549\) | −30.6274 | − | 10.8284i | −1.30715 | − | 0.462146i | ||||
\(550\) | −3.41421 | + | 7.24264i | −0.145583 | + | 0.308827i | ||||
\(551\) | − | 27.3137i | − | 1.16360i | ||||||
\(552\) | −30.1421 | + | 21.3137i | −1.28293 | + | 0.907172i | ||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 2.00000i | 0.0849719i | ||||||||
\(555\) | −8.48528 | + | 6.00000i | −0.360180 | + | 0.254686i | ||||
\(556\) | − | 40.1421i | − | 1.70241i | ||||||
\(557\) | 27.5147 | 1.16584 | 0.582918 | − | 0.812531i | \(-0.301911\pi\) | ||||
0.582918 | + | 0.812531i | \(0.301911\pi\) | |||||||
\(558\) | −11.6569 | + | 32.9706i | −0.493474 | + | 1.39576i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | −6.62742 | + | 1.17157i | −0.279810 | + | 0.0494638i | ||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | 40.9706 | 1.72670 | 0.863352 | − | 0.504603i | \(-0.168361\pi\) | ||||
0.863352 | + | 0.504603i | \(0.168361\pi\) | |||||||
\(564\) | −28.0000 | + | 19.7990i | −1.17901 | + | 0.833688i | ||||
\(565\) | −8.82843 | −0.371415 | ||||||||
\(566\) | 12.0000i | 0.504398i | ||||||||
\(567\) | 5.65685 | − | 7.00000i | 0.237566 | − | 0.293972i | ||||
\(568\) | − | 51.4558i | − | 2.15904i | ||||||
\(569\) | −0.686292 | −0.0287708 | −0.0143854 | − | 0.999897i | \(-0.504579\pi\) | ||||
−0.0143854 | + | 0.999897i | \(0.504579\pi\) | |||||||
\(570\) | 11.6569 | + | 16.4853i | 0.488252 | + | 0.690492i | ||||
\(571\) | 28.9706i | 1.21238i | 0.795320 | + | 0.606190i | \(0.207303\pi\) | ||||
−0.795320 | + | 0.606190i | \(0.792697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.48528 | + | 6.00000i | −0.354478 | + | 0.250654i | ||||
\(574\) | 8.82843i | 0.368491i | ||||||||
\(575\) | 4.82843i | 0.201359i | ||||||||
\(576\) | 9.82843 | − | 27.7990i | 0.409518 | − | 1.15829i | ||||
\(577\) | −3.51472 | −0.146320 | −0.0731598 | − | 0.997320i | \(-0.523308\pi\) | ||||
−0.0731598 | + | 0.997320i | \(0.523308\pi\) | |||||||
\(578\) | 37.7279 | 1.56927 | ||||||||
\(579\) | −7.79899 | + | 5.51472i | −0.324115 | + | 0.229184i | ||||
\(580\) | − | 21.6569i | − | 0.899252i | ||||||
\(581\) | 12.0000i | 0.497844i | ||||||||
\(582\) | 26.1421 | + | 36.9706i | 1.08363 | + | 1.53248i | ||||
\(583\) | 14.4853 | + | 6.82843i | 0.599919 | + | 0.282805i | ||||
\(584\) | 52.9706i | 2.19194i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.7990 | 1.31360 | ||||||||
\(587\) | − | 13.4558i | − | 0.555382i | −0.960670 | − | 0.277691i | \(-0.910431\pi\) | ||
0.960670 | − | 0.277691i | \(-0.0895692\pi\) | |||||||
\(588\) | −3.82843 | − | 5.41421i | −0.157882 | − | 0.223278i | ||||
\(589\) | − | 23.3137i | − | 0.960625i | ||||||
\(590\) | −28.1421 | −1.15859 | ||||||||
\(591\) | 9.17157 | + | 12.9706i | 0.377268 | + | 0.533538i | ||||
\(592\) | 18.0000 | 0.739795 | ||||||||
\(593\) | 22.8284 | 0.937451 | 0.468726 | − | 0.883344i | \(-0.344713\pi\) | ||||
0.468726 | + | 0.883344i | \(0.344713\pi\) | |||||||
\(594\) | −6.82843 | + | 41.0416i | −0.280174 | + | 1.68396i | ||||
\(595\) | −1.17157 | −0.0480298 | ||||||||
\(596\) | −58.6274 | −2.40147 | ||||||||
\(597\) | 2.48528 | + | 3.51472i | 0.101716 | + | 0.143848i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.9411i | − | 1.14164i | −0.821074 | − | 0.570822i | \(-0.806625\pi\) | ||
0.821074 | − | 0.570822i | \(-0.193375\pi\) | |||||||
\(600\) | 4.41421 | + | 6.24264i | 0.180210 | + | 0.254855i | ||||
\(601\) | 45.4558i | 1.85418i | 0.374836 | + | 0.927091i | \(0.377699\pi\) | ||||
−0.374836 | + | 0.927091i | \(0.622301\pi\) | |||||||
\(602\) | 4.00000 | 0.163028 | ||||||||
\(603\) | −10.4853 | + | 29.6569i | −0.426994 | + | 1.20772i | ||||
\(604\) | 73.9411i | 3.00862i | ||||||||
\(605\) | 8.48528 | − | 7.00000i | 0.344976 | − | 0.284590i | ||||
\(606\) | −32.1421 | − | 45.4558i | −1.30569 | − | 1.84652i | ||||
\(607\) | 36.0000i | 1.46119i | 0.682808 | + | 0.730597i | \(0.260758\pi\) | ||||
−0.682808 | + | 0.730597i | \(0.739242\pi\) | |||||||
\(608\) | 7.65685i | 0.310526i | ||||||||
\(609\) | 8.00000 | − | 5.65685i | 0.324176 | − | 0.229227i | ||||
\(610\) | 26.1421 | 1.05846 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.48528 | + | 12.6863i | −0.181307 | + | 0.512813i | ||||
\(613\) | − | 33.7990i | − | 1.36513i | −0.730826 | − | 0.682564i | \(-0.760865\pi\) | ||
0.730826 | − | 0.682564i | \(-0.239135\pi\) | |||||||
\(614\) | − | 60.2843i | − | 2.43288i | ||||||
\(615\) | 5.17157 | − | 3.65685i | 0.208538 | − | 0.147459i | ||||
\(616\) | 13.2426 | + | 6.24264i | 0.533561 | + | 0.251523i | ||||
\(617\) | − | 31.4558i | − | 1.26636i | −0.774003 | − | 0.633182i | \(-0.781748\pi\) | ||
0.774003 | − | 0.633182i | \(-0.218252\pi\) | |||||||
\(618\) | 32.1421 | + | 45.4558i | 1.29295 | + | 1.82850i | ||||
\(619\) | 17.7990 | 0.715402 | 0.357701 | − | 0.933836i | \(-0.383561\pi\) | ||||
0.357701 | + | 0.933836i | \(0.383561\pi\) | |||||||
\(620\) | − | 18.4853i | − | 0.742387i | ||||||
\(621\) | 6.82843 | + | 24.1421i | 0.274015 | + | 0.968791i | ||||
\(622\) | − | 49.7990i | − | 1.99676i | ||||||
\(623\) | 3.65685 | 0.146509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −45.4558 | −1.81678 | ||||||||
\(627\) | −4.82843 | − | 27.3137i | −0.192829 | − | 1.09080i | ||||
\(628\) | −50.4264 | −2.01223 | ||||||||
\(629\) | 7.02944 | 0.280282 | ||||||||
\(630\) | −2.41421 | + | 6.82843i | −0.0961846 | + | 0.272051i | ||||
\(631\) | −0.970563 | −0.0386375 | −0.0193187 | − | 0.999813i | \(-0.506150\pi\) | ||||
−0.0193187 | + | 0.999813i | \(0.506150\pi\) | |||||||
\(632\) | − | 17.6569i | − | 0.702352i | ||||||
\(633\) | 24.0000 | − | 16.9706i | 0.953914 | − | 0.674519i | ||||
\(634\) | − | 55.9411i | − | 2.22171i | ||||||
\(635\) | −2.34315 | −0.0929849 | ||||||||
\(636\) | 26.1421 | − | 18.4853i | 1.03660 | − | 0.732989i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −19.3137 | + | 40.9706i | −0.764637 | + | 1.62204i | ||||
\(639\) | −32.9706 | − | 11.6569i | −1.30430 | − | 0.461138i | ||||
\(640\) | 20.5563i | 0.812561i | ||||||||
\(641\) | − | 39.3137i | − | 1.55280i | −0.630242 | − | 0.776399i | \(-0.717044\pi\) | ||
0.630242 | − | 0.776399i | \(-0.282956\pi\) | |||||||
\(642\) | 32.1421 | + | 45.4558i | 1.26855 | + | 1.79400i | ||||
\(643\) | 22.9706 | 0.905871 | 0.452935 | − | 0.891543i | \(-0.350377\pi\) | ||||
0.452935 | + | 0.891543i | \(0.350377\pi\) | |||||||
\(644\) | 18.4853 | 0.728422 | ||||||||
\(645\) | −1.65685 | − | 2.34315i | −0.0652386 | − | 0.0922613i | ||||
\(646\) | − | 13.6569i | − | 0.537322i | ||||||
\(647\) | 43.7990i | 1.72192i | 0.508676 | + | 0.860958i | \(0.330135\pi\) | ||||
−0.508676 | + | 0.860958i | \(0.669865\pi\) | |||||||
\(648\) | 30.8995 | + | 24.9706i | 1.21385 | + | 0.980936i | ||||
\(649\) | 34.9706 | + | 16.4853i | 1.37271 | + | 0.647104i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.82843 | − | 4.82843i | 0.267627 | − | 0.189241i | ||||
\(652\) | −70.7696 | −2.77155 | ||||||||
\(653\) | 9.51472i | 0.372340i | 0.982518 | + | 0.186170i | \(0.0596075\pi\) | ||||
−0.982518 | + | 0.186170i | \(0.940393\pi\) | |||||||
\(654\) | 5.65685 | − | 4.00000i | 0.221201 | − | 0.156412i | ||||
\(655\) | − | 6.34315i | − | 0.247847i | ||||||
\(656\) | −10.9706 | −0.428329 | ||||||||
\(657\) | 33.9411 | + | 12.0000i | 1.32417 | + | 0.468165i | ||||
\(658\) | 12.4853 | 0.486727 | ||||||||
\(659\) | −27.5147 | −1.07182 | −0.535911 | − | 0.844275i | \(-0.680032\pi\) | ||||
−0.535911 | + | 0.844275i | \(0.680032\pi\) | |||||||
\(660\) | −3.82843 | − | 21.6569i | −0.149021 | − | 0.842992i | ||||
\(661\) | −13.0294 | −0.506786 | −0.253393 | − | 0.967363i | \(-0.581547\pi\) | ||||
−0.253393 | + | 0.967363i | \(0.581547\pi\) | |||||||
\(662\) | 52.2843 | 2.03209 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −52.9706 | −2.05566 | ||||||||
\(665\) | − | 4.82843i | − | 0.187238i | ||||||
\(666\) | 14.4853 | − | 40.9706i | 0.561293 | − | 1.58758i | ||||
\(667\) | 27.3137i | 1.05759i | ||||||||
\(668\) | −52.2843 | −2.02294 | ||||||||
\(669\) | 18.9706 | + | 26.8284i | 0.733444 | + | 1.03725i | ||||
\(670\) | − | 25.3137i | − | 0.977954i | ||||||
\(671\) | −32.4853 | − | 15.3137i | −1.25408 | − | 0.591179i | ||||
\(672\) | −2.24264 | + | 1.58579i | −0.0865117 | + | 0.0611730i | ||||
\(673\) | − | 42.4853i | − | 1.63769i | −0.574017 | − | 0.818844i | \(-0.694616\pi\) | ||
0.574017 | − | 0.818844i | \(-0.305384\pi\) | |||||||
\(674\) | − | 34.9706i | − | 1.34702i | ||||||
\(675\) | 5.00000 | − | 1.41421i | 0.192450 | − | 0.0544331i | ||||
\(676\) | 49.7696 | 1.91421 | ||||||||
\(677\) | −32.7696 | −1.25944 | −0.629718 | − | 0.776824i | \(-0.716830\pi\) | ||||
−0.629718 | + | 0.776824i | \(0.716830\pi\) | |||||||
\(678\) | 30.1421 | − | 21.3137i | 1.15760 | − | 0.818548i | ||||
\(679\) | − | 10.8284i | − | 0.415557i | ||||||
\(680\) | − | 5.17157i | − | 0.198321i | ||||||
\(681\) | 25.6569 | + | 36.2843i | 0.983173 | + | 1.39042i | ||||
\(682\) | −16.4853 | + | 34.9706i | −0.631254 | + | 1.33909i | ||||
\(683\) | 1.79899i | 0.0688364i | 0.999408 | + | 0.0344182i | \(0.0109578\pi\) | ||||
−0.999408 | + | 0.0344182i | \(0.989042\pi\) | |||||||
\(684\) | −52.2843 | − | 18.4853i | −1.99914 | − | 0.706802i | ||||
\(685\) | 7.17157 | 0.274012 | ||||||||
\(686\) | 2.41421i | 0.0921751i | ||||||||
\(687\) | 13.3137 | + | 18.8284i | 0.507950 | + | 0.718349i | ||||
\(688\) | 4.97056i | 0.189501i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −11.6569 | − | 16.4853i | −0.443769 | − | 0.627584i | ||||
\(691\) | −22.4853 | −0.855380 | −0.427690 | − | 0.903925i | \(-0.640673\pi\) | ||||
−0.427690 | + | 0.903925i | \(0.640673\pi\) | |||||||
\(692\) | −69.4558 | −2.64032 | ||||||||
\(693\) | 7.00000 | − | 7.07107i | 0.265908 | − | 0.268608i | ||||
\(694\) | −57.1127 | −2.16797 | ||||||||
\(695\) | 10.4853 | 0.397729 | ||||||||
\(696\) | 24.9706 | + | 35.3137i | 0.946507 | + | 1.33856i | ||||
\(697\) | −4.28427 | −0.162278 | ||||||||
\(698\) | 37.4558i | 1.41772i | ||||||||
\(699\) | 27.7990 | + | 39.3137i | 1.05145 | + | 1.48698i | ||||
\(700\) | − | 3.82843i | − | 0.144701i | ||||||
\(701\) | −47.5980 | −1.79775 | −0.898875 | − | 0.438204i | \(-0.855615\pi\) | ||||
−0.898875 | + | 0.438204i | \(0.855615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.9706i | 1.09265i | ||||||||
\(704\) | 13.8995 | − | 29.4853i | 0.523857 | − | 1.11127i | ||||
\(705\) | −5.17157 | − | 7.31371i | −0.194773 | − | 0.275450i | ||||
\(706\) | − | 28.1421i | − | 1.05914i | ||||||
\(707\) | 13.3137i | 0.500714i | ||||||||
\(708\) | 63.1127 | − | 44.6274i | 2.37192 | − | 1.67720i | ||||
\(709\) | 30.0000 | 1.12667 | 0.563337 | − | 0.826227i | \(-0.309517\pi\) | ||||
0.563337 | + | 0.826227i | \(0.309517\pi\) | |||||||
\(710\) | 28.1421 | 1.05616 | ||||||||
\(711\) | −11.3137 | − | 4.00000i | −0.424297 | − | 0.150012i | ||||
\(712\) | 16.1421i | 0.604952i | ||||||||
\(713\) | 23.3137i | 0.873105i | ||||||||
\(714\) | 4.00000 | − | 2.82843i | 0.149696 | − | 0.105851i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1.31371i | − | 0.0490956i | ||||||
\(717\) | 2.82843 | + | 4.00000i | 0.105630 | + | 0.149383i | ||||
\(718\) | 20.4853 | 0.764504 | ||||||||
\(719\) | 29.3137i | 1.09322i | 0.837388 | + | 0.546608i | \(0.184081\pi\) | ||||
−0.837388 | + | 0.546608i | \(0.815919\pi\) | |||||||
\(720\) | −8.48528 | − | 3.00000i | −0.316228 | − | 0.111803i | ||||
\(721\) | − | 13.3137i | − | 0.495828i | ||||||
\(722\) | 10.4142 | 0.387577 | ||||||||
\(723\) | 24.2843 | − | 17.1716i | 0.903142 | − | 0.638618i | ||||
\(724\) | −7.65685 | −0.284565 | ||||||||
\(725\) | 5.65685 | 0.210090 | ||||||||
\(726\) | −12.0711 | + | 44.3848i | −0.447999 | + | 1.64727i | ||||
\(727\) | 42.0000 | 1.55769 | 0.778847 | − | 0.627214i | \(-0.215805\pi\) | ||||
0.778847 | + | 0.627214i | \(0.215805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | −28.9706 | −1.07225 | ||||||||
\(731\) | 1.94113i | 0.0717951i | ||||||||
\(732\) | −58.6274 | + | 41.4558i | −2.16693 | + | 1.53225i | ||||
\(733\) | − | 37.9411i | − | 1.40139i | −0.713462 | − | 0.700694i | \(-0.752874\pi\) | ||
0.713462 | − | 0.700694i | \(-0.247126\pi\) | |||||||
\(734\) | 43.4558 | 1.60398 | ||||||||
\(735\) | 1.41421 | − | 1.00000i | 0.0521641 | − | 0.0368856i | ||||
\(736\) | − | 7.65685i | − | 0.282235i | ||||||
\(737\) | −14.8284 | + | 31.4558i | −0.546212 | + | 1.15869i | ||||
\(738\) | −8.82843 | + | 24.9706i | −0.324979 | + | 0.919179i | ||||
\(739\) | − | 36.2843i | − | 1.33474i | −0.744727 | − | 0.667369i | \(-0.767420\pi\) | ||
0.744727 | − | 0.667369i | \(-0.232580\pi\) | |||||||
\(740\) | 22.9706i | 0.844415i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.6569 | −0.427937 | ||||||||
\(743\) | 45.3137 | 1.66240 | 0.831199 | − | 0.555974i | \(-0.187655\pi\) | ||||
0.831199 | + | 0.555974i | \(0.187655\pi\) | |||||||
\(744\) | 21.3137 | + | 30.1421i | 0.781398 | + | 1.10506i | ||||
\(745\) | − | 15.3137i | − | 0.561051i | ||||||
\(746\) | 58.2843i | 2.13394i | ||||||||
\(747\) | −12.0000 | + | 33.9411i | −0.439057 | + | 1.24184i | ||||
\(748\) | −6.34315 | + | 13.4558i | −0.231928 | + | 0.491994i | ||||
\(749\) | − | 13.3137i | − | 0.486472i | ||||||
\(750\) | −3.41421 | + | 2.41421i | −0.124669 | + | 0.0881546i | ||||
\(751\) | 37.9411 | 1.38449 | 0.692246 | − | 0.721662i | \(-0.256621\pi\) | ||||
0.692246 | + | 0.721662i | \(0.256621\pi\) | |||||||
\(752\) | 15.5147i | 0.565764i | ||||||||
\(753\) | −34.8284 | + | 24.6274i | −1.26922 | + | 0.897473i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.3137 | −0.702898 | ||||||||
\(756\) | −5.41421 | − | 19.1421i | −0.196913 | − | 0.696193i | ||||
\(757\) | −27.9411 | −1.01554 | −0.507769 | − | 0.861493i | \(-0.669530\pi\) | ||||
−0.507769 | + | 0.861493i | \(0.669530\pi\) | |||||||
\(758\) | −72.2843 | −2.62548 | ||||||||
\(759\) | 4.82843 | + | 27.3137i | 0.175261 | + | 0.991425i | ||||
\(760\) | 21.3137 | 0.773129 | ||||||||
\(761\) | −47.6569 | −1.72756 | −0.863780 | − | 0.503869i | \(-0.831909\pi\) | ||||
−0.863780 | + | 0.503869i | \(0.831909\pi\) | |||||||
\(762\) | 8.00000 | − | 5.65685i | 0.289809 | − | 0.204926i | ||||
\(763\) | −1.65685 | −0.0599822 | ||||||||
\(764\) | 22.9706i | 0.831046i | ||||||||
\(765\) | −3.31371 | − | 1.17157i | −0.119807 | − | 0.0423583i | ||||
\(766\) | − | 38.1421i | − | 1.37813i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −29.9706 | − | 42.3848i | −1.08147 | − | 1.52943i | ||||
\(769\) | − | 3.51472i | − | 0.126744i | −0.997990 | − | 0.0633720i | \(-0.979815\pi\) | ||
0.997990 | − | 0.0633720i | \(-0.0201855\pi\) | |||||||
\(770\) | −3.41421 | + | 7.24264i | −0.123040 | + | 0.261007i | ||||
\(771\) | −13.1716 | + | 9.31371i | −0.474363 | + | 0.335425i | ||||
\(772\) | 21.1127i | 0.759863i | ||||||||
\(773\) | 25.3137i | 0.910471i | 0.890371 | + | 0.455235i | \(0.150445\pi\) | ||||
−0.890371 | + | 0.455235i | \(0.849555\pi\) | |||||||
\(774\) | 11.3137 | + | 4.00000i | 0.406663 | + | 0.143777i | ||||
\(775\) | 4.82843 | 0.173442 | ||||||||
\(776\) | 47.7990 | 1.71588 | ||||||||
\(777\) | −8.48528 | + | 6.00000i | −0.304408 | + | 0.215249i | ||||
\(778\) | − | 83.5980i | − | 2.99713i | ||||||
\(779\) | − | 17.6569i | − | 0.632622i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.9706 | − | 16.4853i | −1.25135 | − | 0.589890i | ||||
\(782\) | 13.6569i | 0.488368i | ||||||||
\(783\) | 28.2843 | − | 8.00000i | 1.01080 | − | 0.285897i | ||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | − | 13.1716i | − | 0.470114i | ||||||
\(786\) | 15.3137 | + | 21.6569i | 0.546222 | + | 0.772474i | ||||
\(787\) | 29.9411i | 1.06729i | 0.845710 | + | 0.533643i | \(0.179177\pi\) | ||||
−0.845710 | + | 0.533643i | \(0.820823\pi\) | |||||||
\(788\) | 35.1127 | 1.25084 | ||||||||
\(789\) | 5.31371 | + | 7.51472i | 0.189173 | + | 0.267531i | ||||
\(790\) | 9.65685 | 0.343575 | ||||||||
\(791\) | −8.82843 | −0.313903 | ||||||||
\(792\) | 31.2132 | + | 30.8995i | 1.10911 | + | 1.09797i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −8.48528 | −0.301131 | ||||||||
\(795\) | 4.82843 | + | 6.82843i | 0.171247 | + | 0.242179i | ||||
\(796\) | 9.51472 | 0.337240 | ||||||||
\(797\) | − | 28.6274i | − | 1.01404i | −0.861936 | − | 0.507018i | \(-0.830748\pi\) | ||
0.861936 | − | 0.507018i | \(-0.169252\pi\) | |||||||
\(798\) | 11.6569 | + | 16.4853i | 0.412648 | + | 0.583573i | ||||
\(799\) | 6.05887i | 0.214348i | ||||||||
\(800\) | −1.58579 | −0.0560660 | ||||||||
\(801\) | 10.3431 | + | 3.65685i | 0.365457 | + | 0.129209i | ||||
\(802\) | − | 65.9411i | − | 2.32846i | ||||||
\(803\) | 36.0000 | + | 16.9706i | 1.27041 | + | 0.598878i | ||||
\(804\) | 40.1421 | + | 56.7696i | 1.41570 | + | 2.00211i | ||||
\(805\) | 4.82843i | 0.170180i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.51472 | + | 5.31371i | −0.264531 | + | 0.187051i | ||||
\(808\) | −58.7696 | −2.06751 | ||||||||
\(809\) | 34.6274 | 1.21744 | 0.608718 | − | 0.793387i | \(-0.291684\pi\) | ||||
0.608718 | + | 0.793387i | \(0.291684\pi\) | |||||||
\(810\) | −13.6569 | + | 16.8995i | −0.479853 | + | 0.593788i | ||||
\(811\) | 34.4853i | 1.21094i | 0.795867 | + | 0.605471i | \(0.207015\pi\) | ||||
−0.795867 | + | 0.605471i | \(0.792985\pi\) | |||||||
\(812\) | − | 21.6569i | − | 0.760007i | ||||||
\(813\) | −20.4853 | + | 14.4853i | −0.718450 | + | 0.508021i | ||||
\(814\) | 20.4853 | − | 43.4558i | 0.718009 | − | 1.52313i | ||||
\(815\) | − | 18.4853i | − | 0.647511i | ||||||
\(816\) | 3.51472 | + | 4.97056i | 0.123040 | + | 0.174005i | ||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | − | 32.4853i | − | 1.13582i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 14.0000i | − | 0.488901i | ||||||
\(821\) | 38.6274 | 1.34811 | 0.674053 | − | 0.738683i | \(-0.264552\pi\) | ||||
0.674053 | + | 0.738683i | \(0.264552\pi\) | |||||||
\(822\) | −24.4853 | + | 17.3137i | −0.854022 | + | 0.603885i | ||||
\(823\) | 28.1421 | 0.980973 | 0.490487 | − | 0.871449i | \(-0.336819\pi\) | ||||
0.490487 | + | 0.871449i | \(0.336819\pi\) | |||||||
\(824\) | 58.7696 | 2.04733 | ||||||||
\(825\) | 5.65685 | − | 1.00000i | 0.196946 | − | 0.0348155i | ||||
\(826\) | −28.1421 | −0.979190 | ||||||||
\(827\) | 39.2548 | 1.36502 | 0.682512 | − | 0.730874i | \(-0.260887\pi\) | ||||
0.682512 | + | 0.730874i | \(0.260887\pi\) | |||||||
\(828\) | 52.2843 | + | 18.4853i | 1.81700 | + | 0.642408i | ||||
\(829\) | −17.0294 | −0.591457 | −0.295728 | − | 0.955272i | \(-0.595562\pi\) | ||||
−0.295728 | + | 0.955272i | \(0.595562\pi\) | |||||||
\(830\) | − | 28.9706i | − | 1.00558i | ||||||
\(831\) | 1.17157 | − | 0.828427i | 0.0406414 | − | 0.0287378i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.17157 | −0.0405926 | ||||||||
\(834\) | −35.7990 | + | 25.3137i | −1.23962 | + | 0.876542i | ||||
\(835\) | − | 13.6569i | − | 0.472615i | ||||||
\(836\) | −55.4558 | − | 26.1421i | −1.91798 | − | 0.904145i | ||||
\(837\) | 24.1421 | − | 6.82843i | 0.834474 | − | 0.236025i | ||||
\(838\) | 6.48528i | 0.224030i | ||||||||
\(839\) | − | 40.3431i | − | 1.39280i | −0.717654 | − | 0.696400i | \(-0.754784\pi\) | ||
0.717654 | − | 0.696400i | \(-0.245216\pi\) | |||||||
\(840\) | 4.41421 | + | 6.24264i | 0.152305 | + | 0.215392i | ||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | −43.4558 | −1.49759 | ||||||||
\(843\) | 4.97056 | + | 7.02944i | 0.171195 | + | 0.242107i | ||||
\(844\) | − | 64.9706i | − | 2.23638i | ||||||
\(845\) | 13.0000i | 0.447214i | ||||||||
\(846\) | 35.3137 | + | 12.4853i | 1.21411 | + | 0.429253i | ||||
\(847\) | 8.48528 | − | 7.00000i | 0.291558 | − | 0.240523i | ||||
\(848\) | − | 14.4853i | − | 0.497427i | ||||||
\(849\) | 7.02944 | − | 4.97056i | 0.241250 | − | 0.170589i | ||||
\(850\) | 2.82843 | 0.0970143 | ||||||||
\(851\) | − | 28.9706i | − | 0.993098i | ||||||
\(852\) | −63.1127 | + | 44.6274i | −2.16221 | + | 1.52891i | ||||
\(853\) | 4.97056i | 0.170189i | 0.996373 | + | 0.0850944i | \(0.0271192\pi\) | ||||
−0.996373 | + | 0.0850944i | \(0.972881\pi\) | |||||||
\(854\) | 26.1421 | 0.894565 | ||||||||
\(855\) | 4.82843 | − | 13.6569i | 0.165129 | − | 0.467055i | ||||
\(856\) | 58.7696 | 2.00870 | ||||||||
\(857\) | −39.1127 | −1.33606 | −0.668032 | − | 0.744132i | \(-0.732863\pi\) | ||||
−0.668032 | + | 0.744132i | \(0.732863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.4558 | 0.527347 | 0.263673 | − | 0.964612i | \(-0.415066\pi\) | ||||
0.263673 | + | 0.964612i | \(0.415066\pi\) | |||||||
\(860\) | −6.34315 | −0.216299 | ||||||||
\(861\) | 5.17157 | − | 3.65685i | 0.176247 | − | 0.124625i | ||||
\(862\) | −24.4853 | −0.833972 | ||||||||
\(863\) | 11.8579i | 0.403646i | 0.979422 | + | 0.201823i | \(0.0646866\pi\) | ||||
−0.979422 | + | 0.201823i | \(0.935313\pi\) | |||||||
\(864\) | −7.92893 | + | 2.24264i | −0.269748 | + | 0.0762962i | ||||
\(865\) | − | 18.1421i | − | 0.616851i | ||||||
\(866\) | 70.4264 | 2.39319 | ||||||||
\(867\) | −15.6274 | − | 22.1005i | −0.530735 | − | 0.750573i | ||||
\(868\) | − | 18.4853i | − | 0.627431i | ||||||
\(869\) | −12.0000 | − | 5.65685i | −0.407072 | − | 0.191896i | ||||
\(870\) | −19.3137 | + | 13.6569i | −0.654796 | + | 0.463011i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 7.31371i | − | 0.247673i | ||||||
\(873\) | 10.8284 | − | 30.6274i | 0.366487 | − | 1.03658i | ||||
\(874\) | −56.2843 | −1.90384 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 64.9706 | − | 45.9411i | 2.19515 | − | 1.55221i | ||||
\(877\) | − | 9.79899i | − | 0.330888i | −0.986219 | − | 0.165444i | \(-0.947094\pi\) | ||
0.986219 | − | 0.165444i | \(-0.0529058\pi\) | |||||||
\(878\) | − | 75.9411i | − | 2.56289i | ||||||
\(879\) | −13.1716 | − | 18.6274i | −0.444266 | − | 0.628287i | ||||
\(880\) | −9.00000 | − | 4.24264i | −0.303390 | − | 0.143019i | ||||
\(881\) | 35.6569i | 1.20131i | 0.799508 | + | 0.600655i | \(0.205093\pi\) | ||||
−0.799508 | + | 0.600655i | \(0.794907\pi\) | |||||||
\(882\) | −2.41421 | + | 6.82843i | −0.0812908 | + | 0.229925i | ||||
\(883\) | −45.1127 | −1.51816 | −0.759082 | − | 0.650996i | \(-0.774352\pi\) | ||||
−0.759082 | + | 0.650996i | \(0.774352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.6569 | + | 16.4853i | 0.391841 | + | 0.554147i | ||||
\(886\) | 4.34315i | 0.145911i | ||||||||
\(887\) | −59.3137 | −1.99156 | −0.995780 | − | 0.0917756i | \(-0.970746\pi\) | ||||
−0.995780 | + | 0.0917756i | \(0.970746\pi\) | |||||||
\(888\) | −26.4853 | − | 37.4558i | −0.888788 | − | 1.25694i | ||||
\(889\) | −2.34315 | −0.0785866 | ||||||||
\(890\) | −8.82843 | −0.295930 | ||||||||
\(891\) | 26.8701 | − | 13.0000i | 0.900181 | − | 0.435516i | ||||
\(892\) | 72.6274 | 2.43175 | ||||||||
\(893\) | −24.9706 | −0.835608 | ||||||||
\(894\) | 36.9706 | + | 52.2843i | 1.23648 | + | 1.74865i | ||||
\(895\) | 0.343146 | 0.0114701 | ||||||||
\(896\) | 20.5563i | 0.686739i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 42.6274i | − | 1.42250i | ||||||
\(899\) | 27.3137 | 0.910963 | ||||||||
\(900\) | 3.82843 | − | 10.8284i | 0.127614 | − | 0.360948i | ||||
\(901\) | − | 5.65685i | − | 0.188457i | ||||||
\(902\) | −12.4853 | + | 26.4853i | −0.415714 | + | 0.881863i | ||||
\(903\) | −1.65685 | − | 2.34315i | −0.0551367 | − | 0.0779750i | ||||
\(904\) | − | 38.9706i | − | 1.29614i | ||||||
\(905\) | − | 2.00000i | − | 0.0664822i | ||||||
\(906\) | 65.9411 | − | 46.6274i | 2.19075 | − | 1.54909i | ||||
\(907\) | −7.17157 | −0.238128 | −0.119064 | − | 0.992887i | \(-0.537989\pi\) | ||||
−0.119064 | + | 0.992887i | \(0.537989\pi\) | |||||||
\(908\) | 98.2254 | 3.25972 | ||||||||
\(909\) | −13.3137 | + | 37.6569i | −0.441588 | + | 1.24900i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.6274i | − | 1.08099i | −0.841346 | − | 0.540497i | \(-0.818236\pi\) | ||
0.841346 | − | 0.540497i | \(-0.181764\pi\) | |||||||
\(912\) | −20.4853 | + | 14.4853i | −0.678335 | + | 0.479656i | ||||
\(913\) | −16.9706 | + | 36.0000i | −0.561644 | + | 1.19143i | ||||
\(914\) | 22.9706i | 0.759799i | ||||||||
\(915\) | −10.8284 | − | 15.3137i | −0.357977 | − | 0.506256i | ||||
\(916\) | 50.9706 | 1.68411 | ||||||||
\(917\) | − | 6.34315i | − | 0.209469i | ||||||
\(918\) | 14.1421 | − | 4.00000i | 0.466760 | − | 0.132020i | ||||
\(919\) | − | 42.9117i | − | 1.41553i | −0.706450 | − | 0.707763i | \(-0.749704\pi\) | ||
0.706450 | − | 0.707763i | \(-0.250296\pi\) | |||||||
\(920\) | −21.3137 | −0.702692 | ||||||||
\(921\) | −35.3137 | + | 24.9706i | −1.16363 | + | 0.822808i | ||||
\(922\) | 57.1127 | 1.88091 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.82843 | − | 21.6569i | −0.125946 | − | 0.712458i | ||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | −27.6569 | −0.908861 | ||||||||
\(927\) | 13.3137 | − | 37.6569i | 0.437280 | − | 1.23681i | ||||
\(928\) | −8.97056 | −0.294473 | ||||||||
\(929\) | 20.3431i | 0.667437i | 0.942673 | + | 0.333718i | \(0.108303\pi\) | ||||
−0.942673 | + | 0.333718i | \(0.891697\pi\) | |||||||
\(930\) | −16.4853 | + | 11.6569i | −0.540574 | + | 0.382243i | ||||
\(931\) | − | 4.82843i | − | 0.158245i | ||||||
\(932\) | 106.426 | 3.48611 | ||||||||
\(933\) | −29.1716 | + | 20.6274i | −0.955034 | + | 0.675311i | ||||
\(934\) | − | 16.4853i | − | 0.539415i | ||||||
\(935\) | −3.51472 | − | 1.65685i | −0.114944 | − | 0.0541849i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.9706i | − | 0.685078i | −0.939504 | − | 0.342539i | \(-0.888713\pi\) | ||
0.939504 | − | 0.342539i | \(-0.111287\pi\) | |||||||
\(938\) | − | 25.3137i | − | 0.826522i | ||||||
\(939\) | 18.8284 | + | 26.6274i | 0.614442 | + | 0.868953i | ||||
\(940\) | −19.7990 | −0.645772 | ||||||||
\(941\) | −10.9706 | −0.357630 | −0.178815 | − | 0.983883i | \(-0.557226\pi\) | ||||
−0.178815 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(942\) | 31.7990 | + | 44.9706i | 1.03607 | + | 1.46522i | ||||
\(943\) | 17.6569i | 0.574986i | ||||||||
\(944\) | − | 34.9706i | − | 1.13819i | ||||||
\(945\) | 5.00000 | − | 1.41421i | 0.162650 | − | 0.0460044i | ||||
\(946\) | 12.0000 | + | 5.65685i | 0.390154 | + | 0.183920i | ||||
\(947\) | − | 52.8284i | − | 1.71669i | −0.513070 | − | 0.858347i | \(-0.671492\pi\) | ||
0.513070 | − | 0.858347i | \(-0.328508\pi\) | |||||||
\(948\) | −21.6569 | + | 15.3137i | −0.703382 | + | 0.497366i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 11.6569i | 0.378198i | ||||||||
\(951\) | −32.7696 | + | 23.1716i | −1.06263 | + | 0.751390i | ||||
\(952\) | − | 5.17157i | − | 0.167612i | ||||||
\(953\) | −42.8284 | −1.38735 | −0.693674 | − | 0.720289i | \(-0.744009\pi\) | ||||
−0.693674 | + | 0.720289i | \(0.744009\pi\) | |||||||
\(954\) | −32.9706 | − | 11.6569i | −1.06746 | − | 0.377405i | ||||
\(955\) | −6.00000 | −0.194155 | ||||||||
\(956\) | 10.8284 | 0.350216 | ||||||||
\(957\) | 32.0000 | − | 5.65685i | 1.03441 | − | 0.182860i | ||||
\(958\) | 27.3137 | 0.882466 | ||||||||
\(959\) | 7.17157 | 0.231582 | ||||||||
\(960\) | 13.8995 | − | 9.82843i | 0.448604 | − | 0.317211i | ||||
\(961\) | −7.68629 | −0.247945 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.3137 | − | 37.6569i | 0.429028 | − | 1.21348i | ||||
\(964\) | − | 65.7401i | − | 2.11735i | ||||||
\(965\) | −5.51472 | −0.177525 | ||||||||
\(966\) | −11.6569 | − | 16.4853i | −0.375053 | − | 0.530405i | ||||
\(967\) | 44.2843i | 1.42409i | 0.702136 | + | 0.712043i | \(0.252230\pi\) | ||||
−0.702136 | + | 0.712043i | \(0.747770\pi\) | |||||||
\(968\) | 30.8995 | + | 37.4558i | 0.993147 | + | 1.20388i | ||||
\(969\) | −8.00000 | + | 5.65685i | −0.256997 | + | 0.181724i | ||||
\(970\) | 26.1421i | 0.839373i | ||||||||
\(971\) | − | 26.2843i | − | 0.843502i | −0.906712 | − | 0.421751i | \(-0.861416\pi\) | ||
0.906712 | − | 0.421751i | \(-0.138584\pi\) | |||||||
\(972\) | 3.82843 | − | 59.5563i | 0.122797 | − | 1.91027i | ||||
\(973\) | 10.4853 | 0.336143 | ||||||||
\(974\) | −22.9706 | −0.736024 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.4853i | 1.03983i | ||||||||
\(977\) | − | 12.8284i | − | 0.410418i | −0.978718 | − | 0.205209i | \(-0.934213\pi\) | ||
0.978718 | − | 0.205209i | \(-0.0657874\pi\) | |||||||
\(978\) | 44.6274 | + | 63.1127i | 1.42703 | + | 2.01812i | ||||
\(979\) | 10.9706 | + | 5.17157i | 0.350621 | + | 0.165284i | ||||
\(980\) | − | 3.82843i | − | 0.122295i | ||||||
\(981\) | −4.68629 | − | 1.65685i | −0.149622 | − | 0.0528993i | ||||
\(982\) | −24.4853 | −0.781357 | ||||||||
\(983\) | − | 2.82843i | − | 0.0902128i | −0.998982 | − | 0.0451064i | \(-0.985637\pi\) | ||
0.998982 | − | 0.0451064i | \(-0.0143627\pi\) | |||||||
\(984\) | 16.1421 | + | 22.8284i | 0.514592 | + | 0.727744i | ||||
\(985\) | 9.17157i | 0.292231i | ||||||||
\(986\) | 16.0000 | 0.509544 | ||||||||
\(987\) | −5.17157 | − | 7.31371i | −0.164613 | − | 0.232798i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | −16.8995 | + | 17.0711i | −0.537101 | + | 0.542554i | ||||
\(991\) | 34.3431 | 1.09095 | 0.545473 | − | 0.838128i | \(-0.316350\pi\) | ||||
0.545473 | + | 0.838128i | \(0.316350\pi\) | |||||||
\(992\) | −7.65685 | −0.243105 | ||||||||
\(993\) | −21.6569 | − | 30.6274i | −0.687259 | − | 0.971932i | ||||
\(994\) | 28.1421 | 0.892614 | ||||||||
\(995\) | 2.48528i | 0.0787887i | ||||||||
\(996\) | 45.9411 | + | 64.9706i | 1.45570 | + | 2.05867i | ||||
\(997\) | 12.2843i | 0.389047i | 0.980898 | + | 0.194523i | \(0.0623160\pi\) | ||||
−0.980898 | + | 0.194523i | \(0.937684\pi\) | |||||||
\(998\) | −86.9117 | −2.75114 | ||||||||
\(999\) | −30.0000 | + | 8.48528i | −0.949158 | + | 0.268462i |
(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.a.1121.2 | yes | 4 | |
3.2 | odd | 2 | 1155.2.l.d.1121.3 | yes | 4 | ||
11.10 | odd | 2 | 1155.2.l.d.1121.4 | yes | 4 | ||
33.32 | even | 2 | inner | 1155.2.l.a.1121.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.l.a.1121.1 | ✓ | 4 | 33.32 | even | 2 | inner | |
1155.2.l.a.1121.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1155.2.l.d.1121.3 | yes | 4 | 3.2 | odd | 2 | ||
1155.2.l.d.1121.4 | yes | 4 | 11.10 | odd | 2 |