Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1083,2,Mod(1082,1083)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1083, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1083.1082");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1083 = 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1083.d (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: | \(8.64779853890\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1082.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1083.1082 |
Dual form | 1083.2.d.b.1082.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1083\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(724\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.93185 | −1.36603 | −0.683013 | − | 0.730406i | \(-0.739331\pi\) | ||||
−0.683013 | + | 0.730406i | \(0.739331\pi\) | |||||||
\(3\) | 1.41421 | − | 1.00000i | 0.816497 | − | 0.577350i | ||||
\(4\) | 1.73205 | 0.866025 | ||||||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | −2.73205 | + | 1.93185i | −1.11536 | + | 0.788675i | ||||
\(7\) | −3.73205 | −1.41058 | −0.705291 | − | 0.708918i | \(-0.749184\pi\) | ||||
−0.705291 | + | 0.708918i | \(0.749184\pi\) | |||||||
\(8\) | 0.517638 | 0.183013 | ||||||||
\(9\) | 1.00000 | − | 2.82843i | 0.333333 | − | 0.942809i | ||||
\(10\) | − | 2.73205i | − | 0.863950i | ||||||
\(11\) | 0.378937i | 0.114254i | 0.998367 | + | 0.0571270i | \(0.0181940\pi\) | ||||
−0.998367 | + | 0.0571270i | \(0.981806\pi\) | |||||||
\(12\) | 2.44949 | − | 1.73205i | 0.707107 | − | 0.500000i | ||||
\(13\) | 3.73205i | 1.03508i | 0.855658 | + | 0.517542i | \(0.173153\pi\) | ||||
−0.855658 | + | 0.517542i | \(0.826847\pi\) | |||||||
\(14\) | 7.20977 | 1.92689 | ||||||||
\(15\) | 1.41421 | + | 2.00000i | 0.365148 | + | 0.516398i | ||||
\(16\) | −4.46410 | −1.11603 | ||||||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | −1.93185 | + | 5.46410i | −0.455342 | + | 1.28790i | ||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.44949i | 0.547723i | ||||||||
\(21\) | −5.27792 | + | 3.73205i | −1.15174 | + | 0.814400i | ||||
\(22\) | − | 0.732051i | − | 0.156074i | ||||||
\(23\) | 0.378937i | 0.0790139i | 0.999219 | + | 0.0395070i | \(0.0125787\pi\) | ||||
−0.999219 | + | 0.0395070i | \(0.987421\pi\) | |||||||
\(24\) | 0.732051 | − | 0.517638i | 0.149429 | − | 0.105662i | ||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | − | 7.20977i | − | 1.41395i | ||||||
\(27\) | −1.41421 | − | 5.00000i | −0.272166 | − | 0.962250i | ||||
\(28\) | −6.46410 | −1.22160 | ||||||||
\(29\) | 7.72741 | 1.43494 | 0.717472 | − | 0.696588i | \(-0.245299\pi\) | ||||
0.717472 | + | 0.696588i | \(0.245299\pi\) | |||||||
\(30\) | −2.73205 | − | 3.86370i | −0.498802 | − | 0.705412i | ||||
\(31\) | 4.46410i | 0.801776i | 0.916127 | + | 0.400888i | \(0.131298\pi\) | ||||
−0.916127 | + | 0.400888i | \(0.868702\pi\) | |||||||
\(32\) | 7.58871 | 1.34151 | ||||||||
\(33\) | 0.378937 | + | 0.535898i | 0.0659645 | + | 0.0932879i | ||||
\(34\) | 9.46410i | 1.62308i | ||||||||
\(35\) | − | 5.27792i | − | 0.892131i | ||||||
\(36\) | 1.73205 | − | 4.89898i | 0.288675 | − | 0.816497i | ||||
\(37\) | 4.26795i | 0.701647i | 0.936442 | + | 0.350823i | \(0.114098\pi\) | ||||
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.73205 | + | 5.27792i | 0.597606 | + | 0.845143i | ||||
\(40\) | 0.732051i | 0.115747i | ||||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 10.1962 | − | 7.20977i | 1.57330 | − | 1.11249i | ||||
\(43\) | 2.26795 | 0.345859 | 0.172930 | − | 0.984934i | \(-0.444677\pi\) | ||||
0.172930 | + | 0.984934i | \(0.444677\pi\) | |||||||
\(44\) | 0.656339i | 0.0989468i | ||||||||
\(45\) | 4.00000 | + | 1.41421i | 0.596285 | + | 0.210819i | ||||
\(46\) | − | 0.732051i | − | 0.107935i | ||||||
\(47\) | 10.5558i | 1.53973i | 0.638209 | + | 0.769863i | \(0.279676\pi\) | ||||
−0.638209 | + | 0.769863i | \(0.720324\pi\) | |||||||
\(48\) | −6.31319 | + | 4.46410i | −0.911231 | + | 0.644338i | ||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | −5.79555 | −0.819615 | ||||||||
\(51\) | −4.89898 | − | 6.92820i | −0.685994 | − | 0.970143i | ||||
\(52\) | 6.46410i | 0.896410i | ||||||||
\(53\) | 6.03579 | 0.829080 | 0.414540 | − | 0.910031i | \(-0.363943\pi\) | ||||
0.414540 | + | 0.910031i | \(0.363943\pi\) | |||||||
\(54\) | 2.73205 | + | 9.65926i | 0.371785 | + | 1.31446i | ||||
\(55\) | −0.535898 | −0.0722605 | ||||||||
\(56\) | −1.93185 | −0.258155 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.9282 | −1.96017 | ||||||||
\(59\) | 8.38375 | 1.09147 | 0.545735 | − | 0.837958i | \(-0.316250\pi\) | ||||
0.545735 | + | 0.837958i | \(0.316250\pi\) | |||||||
\(60\) | 2.44949 | + | 3.46410i | 0.316228 | + | 0.447214i | ||||
\(61\) | −3.53590 | −0.452725 | −0.226363 | − | 0.974043i | \(-0.572683\pi\) | ||||
−0.226363 | + | 0.974043i | \(0.572683\pi\) | |||||||
\(62\) | − | 8.62398i | − | 1.09525i | ||||||
\(63\) | −3.73205 | + | 10.5558i | −0.470194 | + | 1.32991i | ||||
\(64\) | −5.73205 | −0.716506 | ||||||||
\(65\) | −5.27792 | −0.654645 | ||||||||
\(66\) | −0.732051 | − | 1.03528i | −0.0901092 | − | 0.127434i | ||||
\(67\) | 1.00000i | 0.122169i | 0.998133 | + | 0.0610847i | \(0.0194560\pi\) | ||||
−0.998133 | + | 0.0610847i | \(0.980544\pi\) | |||||||
\(68\) | − | 8.48528i | − | 1.02899i | ||||||
\(69\) | 0.378937 | + | 0.535898i | 0.0456187 | + | 0.0645146i | ||||
\(70\) | 10.1962i | 1.21867i | ||||||||
\(71\) | 3.58630 | 0.425616 | 0.212808 | − | 0.977094i | \(-0.431739\pi\) | ||||
0.212808 | + | 0.977094i | \(0.431739\pi\) | |||||||
\(72\) | 0.517638 | − | 1.46410i | 0.0610042 | − | 0.172546i | ||||
\(73\) | −3.00000 | −0.351123 | −0.175562 | − | 0.984468i | \(-0.556174\pi\) | ||||
−0.175562 | + | 0.984468i | \(0.556174\pi\) | |||||||
\(74\) | − | 8.24504i | − | 0.958467i | ||||||
\(75\) | 4.24264 | − | 3.00000i | 0.489898 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.41421i | − | 0.161165i | ||||||
\(78\) | −7.20977 | − | 10.1962i | −0.816346 | − | 1.15449i | ||||
\(79\) | 3.53590i | 0.397820i | 0.980018 | + | 0.198910i | \(0.0637401\pi\) | ||||
−0.980018 | + | 0.198910i | \(0.936260\pi\) | |||||||
\(80\) | − | 6.31319i | − | 0.705836i | ||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | −10.9282 | −1.20682 | ||||||||
\(83\) | 7.72741i | 0.848193i | 0.905617 | + | 0.424097i | \(0.139408\pi\) | ||||
−0.905617 | + | 0.424097i | \(0.860592\pi\) | |||||||
\(84\) | −9.14162 | + | 6.46410i | −0.997433 | + | 0.705291i | ||||
\(85\) | 6.92820 | 0.751469 | ||||||||
\(86\) | −4.38134 | −0.472452 | ||||||||
\(87\) | 10.9282 | − | 7.72741i | 1.17163 | − | 0.828465i | ||||
\(88\) | 0.196152i | 0.0209099i | ||||||||
\(89\) | 7.34847 | 0.778936 | 0.389468 | − | 0.921040i | \(-0.372659\pi\) | ||||
0.389468 | + | 0.921040i | \(0.372659\pi\) | |||||||
\(90\) | −7.72741 | − | 2.73205i | −0.814540 | − | 0.287983i | ||||
\(91\) | − | 13.9282i | − | 1.46007i | ||||||
\(92\) | 0.656339i | 0.0684280i | ||||||||
\(93\) | 4.46410 | + | 6.31319i | 0.462906 | + | 0.654648i | ||||
\(94\) | − | 20.3923i | − | 2.10331i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.7321 | − | 7.58871i | 1.09534 | − | 0.774519i | ||||
\(97\) | − | 7.46410i | − | 0.757865i | −0.925424 | − | 0.378932i | \(-0.876291\pi\) | ||
0.925424 | − | 0.378932i | \(-0.123709\pi\) | |||||||
\(98\) | −13.3843 | −1.35201 | ||||||||
\(99\) | 1.07180 | + | 0.378937i | 0.107720 | + | 0.0380846i | ||||
\(100\) | 5.19615 | 0.519615 | ||||||||
\(101\) | − | 7.72741i | − | 0.768906i | −0.923145 | − | 0.384453i | \(-0.874390\pi\) | ||
0.923145 | − | 0.384453i | \(-0.125610\pi\) | |||||||
\(102\) | 9.46410 | + | 13.3843i | 0.937086 | + | 1.32524i | ||||
\(103\) | − | 10.4641i | − | 1.03106i | −0.856872 | − | 0.515529i | \(-0.827595\pi\) | ||
0.856872 | − | 0.515529i | \(-0.172405\pi\) | |||||||
\(104\) | 1.93185i | 0.189434i | ||||||||
\(105\) | −5.27792 | − | 7.46410i | −0.515072 | − | 0.728422i | ||||
\(106\) | −11.6603 | −1.13254 | ||||||||
\(107\) | −4.89898 | −0.473602 | −0.236801 | − | 0.971558i | \(-0.576099\pi\) | ||||
−0.236801 | + | 0.971558i | \(0.576099\pi\) | |||||||
\(108\) | −2.44949 | − | 8.66025i | −0.235702 | − | 0.833333i | ||||
\(109\) | 14.3923i | 1.37853i | 0.724508 | + | 0.689266i | \(0.242067\pi\) | ||||
−0.724508 | + | 0.689266i | \(0.757933\pi\) | |||||||
\(110\) | 1.03528 | 0.0987097 | ||||||||
\(111\) | 4.26795 | + | 6.03579i | 0.405096 | + | 0.572892i | ||||
\(112\) | 16.6603 | 1.57425 | ||||||||
\(113\) | 18.6622 | 1.75559 | 0.877795 | − | 0.479036i | \(-0.159014\pi\) | ||||
0.877795 | + | 0.479036i | \(0.159014\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.535898 | −0.0499728 | ||||||||
\(116\) | 13.3843 | 1.24270 | ||||||||
\(117\) | 10.5558 | + | 3.73205i | 0.975887 | + | 0.345028i | ||||
\(118\) | −16.1962 | −1.49098 | ||||||||
\(119\) | 18.2832i | 1.67602i | ||||||||
\(120\) | 0.732051 | + | 1.03528i | 0.0668268 | + | 0.0945074i | ||||
\(121\) | 10.8564 | 0.986946 | ||||||||
\(122\) | 6.83083 | 0.618434 | ||||||||
\(123\) | 8.00000 | − | 5.65685i | 0.721336 | − | 0.510061i | ||||
\(124\) | 7.73205i | 0.694359i | ||||||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 7.20977 | − | 20.3923i | 0.642297 | − | 1.81669i | ||||
\(127\) | 7.85641i | 0.697143i | 0.937282 | + | 0.348572i | \(0.113333\pi\) | ||||
−0.937282 | + | 0.348572i | \(0.886667\pi\) | |||||||
\(128\) | −4.10394 | −0.362740 | ||||||||
\(129\) | 3.20736 | − | 2.26795i | 0.282393 | − | 0.199682i | ||||
\(130\) | 10.1962 | 0.894262 | ||||||||
\(131\) | 6.96953i | 0.608931i | 0.952523 | + | 0.304465i | \(0.0984778\pi\) | ||||
−0.952523 | + | 0.304465i | \(0.901522\pi\) | |||||||
\(132\) | 0.656339 | + | 0.928203i | 0.0571270 | + | 0.0807897i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.93185i | − | 0.166887i | ||||||
\(135\) | 7.07107 | − | 2.00000i | 0.608581 | − | 0.172133i | ||||
\(136\) | − | 2.53590i | − | 0.217451i | ||||||
\(137\) | − | 0.757875i | − | 0.0647496i | −0.999476 | − | 0.0323748i | \(-0.989693\pi\) | ||
0.999476 | − | 0.0323748i | \(-0.0103070\pi\) | |||||||
\(138\) | −0.732051 | − | 1.03528i | −0.0623163 | − | 0.0881286i | ||||
\(139\) | 13.1962 | 1.11928 | 0.559642 | − | 0.828735i | \(-0.310939\pi\) | ||||
0.559642 | + | 0.828735i | \(0.310939\pi\) | |||||||
\(140\) | − | 9.14162i | − | 0.772608i | ||||||
\(141\) | 10.5558 | + | 14.9282i | 0.888962 | + | 1.25718i | ||||
\(142\) | −6.92820 | −0.581402 | ||||||||
\(143\) | −1.41421 | −0.118262 | ||||||||
\(144\) | −4.46410 | + | 12.6264i | −0.372008 | + | 1.05220i | ||||
\(145\) | 10.9282i | 0.907538i | ||||||||
\(146\) | 5.79555 | 0.479644 | ||||||||
\(147\) | 9.79796 | − | 6.92820i | 0.808122 | − | 0.571429i | ||||
\(148\) | 7.39230i | 0.607644i | ||||||||
\(149\) | − | 16.8690i | − | 1.38196i | −0.722872 | − | 0.690982i | \(-0.757178\pi\) | ||
0.722872 | − | 0.690982i | \(-0.242822\pi\) | |||||||
\(150\) | −8.19615 | + | 5.79555i | −0.669213 | + | 0.473205i | ||||
\(151\) | 2.00000i | 0.162758i | 0.996683 | + | 0.0813788i | \(0.0259324\pi\) | ||||
−0.996683 | + | 0.0813788i | \(0.974068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.8564 | − | 4.89898i | −1.12022 | − | 0.396059i | ||||
\(154\) | 2.73205i | 0.220155i | ||||||||
\(155\) | −6.31319 | −0.507088 | ||||||||
\(156\) | 6.46410 | + | 9.14162i | 0.517542 | + | 0.731915i | ||||
\(157\) | 3.53590 | 0.282195 | 0.141098 | − | 0.989996i | \(-0.454937\pi\) | ||||
0.141098 | + | 0.989996i | \(0.454937\pi\) | |||||||
\(158\) | − | 6.83083i | − | 0.543432i | ||||||
\(159\) | 8.53590 | − | 6.03579i | 0.676941 | − | 0.478669i | ||||
\(160\) | 10.7321i | 0.848443i | ||||||||
\(161\) | − | 1.41421i | − | 0.111456i | ||||||
\(162\) | 13.5230 | + | 10.9282i | 1.06246 | + | 0.858601i | ||||
\(163\) | 5.19615 | 0.406994 | 0.203497 | − | 0.979076i | \(-0.434769\pi\) | ||||
0.203497 | + | 0.979076i | \(0.434769\pi\) | |||||||
\(164\) | 9.79796 | 0.765092 | ||||||||
\(165\) | −0.757875 | + | 0.535898i | −0.0590005 | + | 0.0417196i | ||||
\(166\) | − | 14.9282i | − | 1.15865i | ||||||
\(167\) | 7.62587 | 0.590108 | 0.295054 | − | 0.955481i | \(-0.404662\pi\) | ||||
0.295054 | + | 0.955481i | \(0.404662\pi\) | |||||||
\(168\) | −2.73205 | + | 1.93185i | −0.210782 | + | 0.149046i | ||||
\(169\) | −0.928203 | −0.0714002 | ||||||||
\(170\) | −13.3843 | −1.02653 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.92820 | 0.299523 | ||||||||
\(173\) | −11.8685 | −0.902346 | −0.451173 | − | 0.892436i | \(-0.648994\pi\) | ||||
−0.451173 | + | 0.892436i | \(0.648994\pi\) | |||||||
\(174\) | −21.1117 | + | 14.9282i | −1.60047 | + | 1.13170i | ||||
\(175\) | −11.1962 | −0.846350 | ||||||||
\(176\) | − | 1.69161i | − | 0.127510i | ||||||
\(177\) | 11.8564 | − | 8.38375i | 0.891182 | − | 0.630161i | ||||
\(178\) | −14.1962 | −1.06405 | ||||||||
\(179\) | 1.41421 | 0.105703 | 0.0528516 | − | 0.998602i | \(-0.483169\pi\) | ||||
0.0528516 | + | 0.998602i | \(0.483169\pi\) | |||||||
\(180\) | 6.92820 | + | 2.44949i | 0.516398 | + | 0.182574i | ||||
\(181\) | − | 3.46410i | − | 0.257485i | −0.991678 | − | 0.128742i | \(-0.958906\pi\) | ||
0.991678 | − | 0.128742i | \(-0.0410940\pi\) | |||||||
\(182\) | 26.9072i | 1.99450i | ||||||||
\(183\) | −5.00052 | + | 3.53590i | −0.369649 | + | 0.261381i | ||||
\(184\) | 0.196152i | 0.0144605i | ||||||||
\(185\) | −6.03579 | −0.443760 | ||||||||
\(186\) | −8.62398 | − | 12.1962i | −0.632341 | − | 0.894265i | ||||
\(187\) | 1.85641 | 0.135754 | ||||||||
\(188\) | 18.2832i | 1.33344i | ||||||||
\(189\) | 5.27792 | + | 18.6603i | 0.383912 | + | 1.35733i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.69161i | − | 0.122401i | −0.998125 | − | 0.0612005i | \(-0.980507\pi\) | ||
0.998125 | − | 0.0612005i | \(-0.0194929\pi\) | |||||||
\(192\) | −8.10634 | + | 5.73205i | −0.585025 | + | 0.413675i | ||||
\(193\) | − | 13.1962i | − | 0.949880i | −0.880018 | − | 0.474940i | \(-0.842470\pi\) | ||
0.880018 | − | 0.474940i | \(-0.157530\pi\) | |||||||
\(194\) | 14.4195i | 1.03526i | ||||||||
\(195\) | −7.46410 | + | 5.27792i | −0.534515 | + | 0.377959i | ||||
\(196\) | 12.0000 | 0.857143 | ||||||||
\(197\) | 9.14162i | 0.651313i | 0.945488 | + | 0.325657i | \(0.105585\pi\) | ||||
−0.945488 | + | 0.325657i | \(0.894415\pi\) | |||||||
\(198\) | −2.07055 | − | 0.732051i | −0.147148 | − | 0.0520246i | ||||
\(199\) | −12.8038 | −0.907641 | −0.453820 | − | 0.891093i | \(-0.649939\pi\) | ||||
−0.453820 | + | 0.891093i | \(0.649939\pi\) | |||||||
\(200\) | 1.55291 | 0.109808 | ||||||||
\(201\) | 1.00000 | + | 1.41421i | 0.0705346 | + | 0.0997509i | ||||
\(202\) | 14.9282i | 1.05034i | ||||||||
\(203\) | −28.8391 | −2.02411 | ||||||||
\(204\) | −8.48528 | − | 12.0000i | −0.594089 | − | 0.840168i | ||||
\(205\) | 8.00000i | 0.558744i | ||||||||
\(206\) | 20.2151i | 1.40845i | ||||||||
\(207\) | 1.07180 | + | 0.378937i | 0.0744950 | + | 0.0263380i | ||||
\(208\) | − | 16.6603i | − | 1.15518i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 10.1962 | + | 14.4195i | 0.703601 | + | 0.995043i | ||||
\(211\) | 11.0000i | 0.757271i | 0.925546 | + | 0.378636i | \(0.123607\pi\) | ||||
−0.925546 | + | 0.378636i | \(0.876393\pi\) | |||||||
\(212\) | 10.4543 | 0.718004 | ||||||||
\(213\) | 5.07180 | − | 3.58630i | 0.347514 | − | 0.245729i | ||||
\(214\) | 9.46410 | 0.646953 | ||||||||
\(215\) | 3.20736i | 0.218740i | ||||||||
\(216\) | −0.732051 | − | 2.58819i | −0.0498097 | − | 0.176104i | ||||
\(217\) | − | 16.6603i | − | 1.13097i | ||||||
\(218\) | − | 27.8038i | − | 1.88311i | ||||||
\(219\) | −4.24264 | + | 3.00000i | −0.286691 | + | 0.202721i | ||||
\(220\) | −0.928203 | −0.0625794 | ||||||||
\(221\) | 18.2832 | 1.22986 | ||||||||
\(222\) | −8.24504 | − | 11.6603i | −0.553371 | − | 0.782585i | ||||
\(223\) | 9.39230i | 0.628955i | 0.949265 | + | 0.314478i | \(0.101829\pi\) | ||||
−0.949265 | + | 0.314478i | \(0.898171\pi\) | |||||||
\(224\) | −28.3214 | −1.89231 | ||||||||
\(225\) | 3.00000 | − | 8.48528i | 0.200000 | − | 0.565685i | ||||
\(226\) | −36.0526 | −2.39818 | ||||||||
\(227\) | −24.5964 | −1.63252 | −0.816261 | − | 0.577683i | \(-0.803957\pi\) | ||||
−0.816261 | + | 0.577683i | \(0.803957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.39230 | 0.620661 | 0.310330 | − | 0.950629i | \(-0.399560\pi\) | ||||
0.310330 | + | 0.950629i | \(0.399560\pi\) | |||||||
\(230\) | 1.03528 | 0.0682641 | ||||||||
\(231\) | −1.41421 | − | 2.00000i | −0.0930484 | − | 0.131590i | ||||
\(232\) | 4.00000 | 0.262613 | ||||||||
\(233\) | − | 3.58630i | − | 0.234946i | −0.993076 | − | 0.117473i | \(-0.962521\pi\) | ||
0.993076 | − | 0.117473i | \(-0.0374794\pi\) | |||||||
\(234\) | −20.3923 | − | 7.20977i | −1.33309 | − | 0.471317i | ||||
\(235\) | −14.9282 | −0.973809 | ||||||||
\(236\) | 14.5211 | 0.945241 | ||||||||
\(237\) | 3.53590 | + | 5.00052i | 0.229681 | + | 0.324818i | ||||
\(238\) | − | 35.3205i | − | 2.28949i | ||||||
\(239\) | − | 29.9759i | − | 1.93898i | −0.245133 | − | 0.969489i | \(-0.578832\pi\) | ||
0.245133 | − | 0.969489i | \(-0.421168\pi\) | |||||||
\(240\) | −6.31319 | − | 8.92820i | −0.407515 | − | 0.576313i | ||||
\(241\) | − | 28.6603i | − | 1.84617i | −0.384597 | − | 0.923085i | \(-0.625660\pi\) | ||
0.384597 | − | 0.923085i | \(-0.374340\pi\) | |||||||
\(242\) | −20.9730 | −1.34819 | ||||||||
\(243\) | −15.5563 | − | 1.00000i | −0.997940 | − | 0.0641500i | ||||
\(244\) | −6.12436 | −0.392072 | ||||||||
\(245\) | 9.79796i | 0.625969i | ||||||||
\(246\) | −15.4548 | + | 10.9282i | −0.985363 | + | 0.696757i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.31079i | 0.146735i | ||||||||
\(249\) | 7.72741 | + | 10.9282i | 0.489704 | + | 0.692547i | ||||
\(250\) | − | 21.8564i | − | 1.38232i | ||||||
\(251\) | 14.6969i | 0.927663i | 0.885924 | + | 0.463831i | \(0.153526\pi\) | ||||
−0.885924 | + | 0.463831i | \(0.846474\pi\) | |||||||
\(252\) | −6.46410 | + | 18.2832i | −0.407200 | + | 1.15174i | ||||
\(253\) | −0.143594 | −0.00902765 | ||||||||
\(254\) | − | 15.1774i | − | 0.952316i | ||||||
\(255\) | 9.79796 | − | 6.92820i | 0.613572 | − | 0.433861i | ||||
\(256\) | 19.3923 | 1.21202 | ||||||||
\(257\) | 3.20736 | 0.200070 | 0.100035 | − | 0.994984i | \(-0.468105\pi\) | ||||
0.100035 | + | 0.994984i | \(0.468105\pi\) | |||||||
\(258\) | −6.19615 | + | 4.38134i | −0.385756 | + | 0.272770i | ||||
\(259\) | − | 15.9282i | − | 0.989730i | ||||||
\(260\) | −9.14162 | −0.566939 | ||||||||
\(261\) | 7.72741 | − | 21.8564i | 0.478314 | − | 1.35288i | ||||
\(262\) | − | 13.4641i | − | 0.831815i | ||||||
\(263\) | − | 0.554803i | − | 0.0342106i | −0.999854 | − | 0.0171053i | \(-0.994555\pi\) | ||
0.999854 | − | 0.0171053i | \(-0.00544505\pi\) | |||||||
\(264\) | 0.196152 | + | 0.277401i | 0.0120723 | + | 0.0170729i | ||||
\(265\) | 8.53590i | 0.524356i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3923 | − | 7.34847i | 0.635999 | − | 0.449719i | ||||
\(268\) | 1.73205i | 0.105802i | ||||||||
\(269\) | 6.03579 | 0.368009 | 0.184004 | − | 0.982925i | \(-0.441094\pi\) | ||||
0.184004 | + | 0.982925i | \(0.441094\pi\) | |||||||
\(270\) | −13.6603 | + | 3.86370i | −0.831337 | + | 0.235137i | ||||
\(271\) | −6.92820 | −0.420858 | −0.210429 | − | 0.977609i | \(-0.567486\pi\) | ||||
−0.210429 | + | 0.977609i | \(0.567486\pi\) | |||||||
\(272\) | 21.8695i | 1.32604i | ||||||||
\(273\) | −13.9282 | − | 19.6975i | −0.842973 | − | 1.19214i | ||||
\(274\) | 1.46410i | 0.0884496i | ||||||||
\(275\) | 1.13681i | 0.0685524i | ||||||||
\(276\) | 0.656339 | + | 0.928203i | 0.0395070 | + | 0.0558713i | ||||
\(277\) | −9.85641 | −0.592214 | −0.296107 | − | 0.955155i | \(-0.595689\pi\) | ||||
−0.296107 | + | 0.955155i | \(0.595689\pi\) | |||||||
\(278\) | −25.4930 | −1.52897 | ||||||||
\(279\) | 12.6264 | + | 4.46410i | 0.755922 | + | 0.267259i | ||||
\(280\) | − | 2.73205i | − | 0.163271i | ||||||
\(281\) | −15.0759 | −0.899351 | −0.449676 | − | 0.893192i | \(-0.648460\pi\) | ||||
−0.449676 | + | 0.893192i | \(0.648460\pi\) | |||||||
\(282\) | −20.3923 | − | 28.8391i | −1.21434 | − | 1.71734i | ||||
\(283\) | −21.8564 | −1.29923 | −0.649614 | − | 0.760264i | \(-0.725070\pi\) | ||||
−0.649614 | + | 0.760264i | \(0.725070\pi\) | |||||||
\(284\) | 6.21166 | 0.368594 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.73205 | 0.161550 | ||||||||
\(287\) | −21.1117 | −1.24618 | ||||||||
\(288\) | 7.58871 | − | 21.4641i | 0.447169 | − | 1.26478i | ||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | − | 21.1117i | − | 1.23972i | ||||||
\(291\) | −7.46410 | − | 10.5558i | −0.437553 | − | 0.618794i | ||||
\(292\) | −5.19615 | −0.304082 | ||||||||
\(293\) | −25.2528 | −1.47528 | −0.737641 | − | 0.675193i | \(-0.764060\pi\) | ||||
−0.737641 | + | 0.675193i | \(0.764060\pi\) | |||||||
\(294\) | −18.9282 | + | 13.3843i | −1.10392 | + | 0.780586i | ||||
\(295\) | 11.8564i | 0.690307i | ||||||||
\(296\) | 2.20925i | 0.128410i | ||||||||
\(297\) | 1.89469 | − | 0.535898i | 0.109941 | − | 0.0310960i | ||||
\(298\) | 32.5885i | 1.88780i | ||||||||
\(299\) | −1.41421 | −0.0817861 | ||||||||
\(300\) | 7.34847 | − | 5.19615i | 0.424264 | − | 0.300000i | ||||
\(301\) | −8.46410 | −0.487863 | ||||||||
\(302\) | − | 3.86370i | − | 0.222331i | ||||||
\(303\) | −7.72741 | − | 10.9282i | −0.443928 | − | 0.627809i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.00052i | − | 0.286329i | ||||||
\(306\) | 26.7685 | + | 9.46410i | 1.53025 | + | 0.541027i | ||||
\(307\) | 13.8564i | 0.790827i | 0.918503 | + | 0.395413i | \(0.129399\pi\) | ||||
−0.918503 | + | 0.395413i | \(0.870601\pi\) | |||||||
\(308\) | − | 2.44949i | − | 0.139573i | ||||||
\(309\) | −10.4641 | − | 14.7985i | −0.595282 | − | 0.841856i | ||||
\(310\) | 12.1962 | 0.692695 | ||||||||
\(311\) | 27.1475i | 1.53939i | 0.638411 | + | 0.769696i | \(0.279592\pi\) | ||||
−0.638411 | + | 0.769696i | \(0.720408\pi\) | |||||||
\(312\) | 1.93185 | + | 2.73205i | 0.109370 | + | 0.154672i | ||||
\(313\) | −24.7846 | −1.40091 | −0.700454 | − | 0.713697i | \(-0.747019\pi\) | ||||
−0.700454 | + | 0.713697i | \(0.747019\pi\) | |||||||
\(314\) | −6.83083 | −0.385486 | ||||||||
\(315\) | −14.9282 | − | 5.27792i | −0.841109 | − | 0.297377i | ||||
\(316\) | 6.12436i | 0.344522i | ||||||||
\(317\) | −13.7632 | −0.773018 | −0.386509 | − | 0.922286i | \(-0.626319\pi\) | ||||
−0.386509 | + | 0.922286i | \(0.626319\pi\) | |||||||
\(318\) | −16.4901 | + | 11.6603i | −0.924718 | + | 0.653875i | ||||
\(319\) | 2.92820i | 0.163948i | ||||||||
\(320\) | − | 8.10634i | − | 0.453158i | ||||||
\(321\) | −6.92820 | + | 4.89898i | −0.386695 | + | 0.273434i | ||||
\(322\) | 2.73205i | 0.152251i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −12.1244 | − | 9.79796i | −0.673575 | − | 0.544331i | ||||
\(325\) | 11.1962i | 0.621051i | ||||||||
\(326\) | −10.0382 | −0.555964 | ||||||||
\(327\) | 14.3923 | + | 20.3538i | 0.795896 | + | 1.12557i | ||||
\(328\) | 2.92820 | 0.161683 | ||||||||
\(329\) | − | 39.3949i | − | 2.17191i | ||||||
\(330\) | 1.46410 | − | 1.03528i | 0.0805961 | − | 0.0569901i | ||||
\(331\) | 31.9282i | 1.75493i | 0.479638 | + | 0.877466i | \(0.340768\pi\) | ||||
−0.479638 | + | 0.877466i | \(0.659232\pi\) | |||||||
\(332\) | 13.3843i | 0.734557i | ||||||||
\(333\) | 12.0716 | + | 4.26795i | 0.661519 | + | 0.233882i | ||||
\(334\) | −14.7321 | −0.806102 | ||||||||
\(335\) | −1.41421 | −0.0772667 | ||||||||
\(336\) | 23.5612 | − | 16.6603i | 1.28537 | − | 0.908891i | ||||
\(337\) | − | 7.33975i | − | 0.399821i | −0.979814 | − | 0.199911i | \(-0.935935\pi\) | ||
0.979814 | − | 0.199911i | \(-0.0640652\pi\) | |||||||
\(338\) | 1.79315 | 0.0975346 | ||||||||
\(339\) | 26.3923 | − | 18.6622i | 1.43343 | − | 1.01359i | ||||
\(340\) | 12.0000 | 0.650791 | ||||||||
\(341\) | −1.69161 | −0.0916061 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.267949 | 0.0144679 | ||||||||
\(344\) | 1.17398 | 0.0632966 | ||||||||
\(345\) | −0.757875 | + | 0.535898i | −0.0408026 | + | 0.0288518i | ||||
\(346\) | 22.9282 | 1.23263 | ||||||||
\(347\) | 24.8738i | 1.33530i | 0.744476 | + | 0.667649i | \(0.232699\pi\) | ||||
−0.744476 | + | 0.667649i | \(0.767301\pi\) | |||||||
\(348\) | 18.9282 | − | 13.3843i | 1.01466 | − | 0.717472i | ||||
\(349\) | −11.3923 | −0.609816 | −0.304908 | − | 0.952382i | \(-0.598626\pi\) | ||||
−0.304908 | + | 0.952382i | \(0.598626\pi\) | |||||||
\(350\) | 21.6293 | 1.15614 | ||||||||
\(351\) | 18.6603 | − | 5.27792i | 0.996011 | − | 0.281714i | ||||
\(352\) | 2.87564i | 0.153272i | ||||||||
\(353\) | − | 11.9700i | − | 0.637101i | −0.947906 | − | 0.318551i | \(-0.896804\pi\) | ||
0.947906 | − | 0.318551i | \(-0.103196\pi\) | |||||||
\(354\) | −22.9048 | + | 16.1962i | −1.21738 | + | 0.860816i | ||||
\(355\) | 5.07180i | 0.269183i | ||||||||
\(356\) | 12.7279 | 0.674579 | ||||||||
\(357\) | 18.2832 | + | 25.8564i | 0.967652 | + | 1.36847i | ||||
\(358\) | −2.73205 | −0.144393 | ||||||||
\(359\) | − | 26.7685i | − | 1.41279i | −0.707819 | − | 0.706394i | \(-0.750321\pi\) | ||
0.707819 | − | 0.706394i | \(-0.249679\pi\) | |||||||
\(360\) | 2.07055 | + | 0.732051i | 0.109128 | + | 0.0385825i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 6.69213i | 0.351731i | ||||||||
\(363\) | 15.3533 | − | 10.8564i | 0.805838 | − | 0.569814i | ||||
\(364\) | − | 24.1244i | − | 1.26446i | ||||||
\(365\) | − | 4.24264i | − | 0.222070i | ||||||
\(366\) | 9.66025 | − | 6.83083i | 0.504950 | − | 0.357053i | ||||
\(367\) | −17.0526 | −0.890136 | −0.445068 | − | 0.895497i | \(-0.646821\pi\) | ||||
−0.445068 | + | 0.895497i | \(0.646821\pi\) | |||||||
\(368\) | − | 1.69161i | − | 0.0881815i | ||||||
\(369\) | 5.65685 | − | 16.0000i | 0.294484 | − | 0.832927i | ||||
\(370\) | 11.6603 | 0.606188 | ||||||||
\(371\) | −22.5259 | −1.16949 | ||||||||
\(372\) | 7.73205 | + | 10.9348i | 0.400888 | + | 0.566941i | ||||
\(373\) | 12.5359i | 0.649084i | 0.945871 | + | 0.324542i | \(0.105210\pi\) | ||||
−0.945871 | + | 0.324542i | \(0.894790\pi\) | |||||||
\(374\) | −3.58630 | −0.185443 | ||||||||
\(375\) | 11.3137 | + | 16.0000i | 0.584237 | + | 0.826236i | ||||
\(376\) | 5.46410i | 0.281790i | ||||||||
\(377\) | 28.8391i | 1.48529i | ||||||||
\(378\) | −10.1962 | − | 36.0488i | −0.524433 | − | 1.85415i | ||||
\(379\) | 17.7846i | 0.913534i | 0.889586 | + | 0.456767i | \(0.150993\pi\) | ||||
−0.889586 | + | 0.456767i | \(0.849007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.85641 | + | 11.1106i | 0.402496 | + | 0.569215i | ||||
\(382\) | 3.26795i | 0.167203i | ||||||||
\(383\) | 26.6670 | 1.36262 | 0.681310 | − | 0.731995i | \(-0.261411\pi\) | ||||
0.681310 | + | 0.731995i | \(0.261411\pi\) | |||||||
\(384\) | −5.80385 | + | 4.10394i | −0.296176 | + | 0.209428i | ||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 25.4930i | 1.29756i | ||||||||
\(387\) | 2.26795 | − | 6.41473i | 0.115286 | − | 0.326079i | ||||
\(388\) | − | 12.9282i | − | 0.656330i | ||||||
\(389\) | − | 5.00052i | − | 0.253536i | −0.991932 | − | 0.126768i | \(-0.959540\pi\) | ||
0.991932 | − | 0.126768i | \(-0.0404604\pi\) | |||||||
\(390\) | 14.4195 | − | 10.1962i | 0.730162 | − | 0.516302i | ||||
\(391\) | 1.85641 | 0.0938825 | ||||||||
\(392\) | 3.58630 | 0.181136 | ||||||||
\(393\) | 6.96953 | + | 9.85641i | 0.351566 | + | 0.497190i | ||||
\(394\) | − | 17.6603i | − | 0.889711i | ||||||
\(395\) | −5.00052 | −0.251603 | ||||||||
\(396\) | 1.85641 | + | 0.656339i | 0.0932879 | + | 0.0329823i | ||||
\(397\) | 8.32051 | 0.417594 | 0.208797 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208797 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(398\) | 24.7351 | 1.23986 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.3923 | −0.669615 | ||||||||
\(401\) | −11.4896 | −0.573762 | −0.286881 | − | 0.957966i | \(-0.592618\pi\) | ||||
−0.286881 | + | 0.957966i | \(0.592618\pi\) | |||||||
\(402\) | −1.93185 | − | 2.73205i | −0.0963520 | − | 0.136262i | ||||
\(403\) | −16.6603 | −0.829906 | ||||||||
\(404\) | − | 13.3843i | − | 0.665892i | ||||||
\(405\) | 8.00000 | − | 9.89949i | 0.397523 | − | 0.491910i | ||||
\(406\) | 55.7128 | 2.76498 | ||||||||
\(407\) | −1.61729 | −0.0801659 | ||||||||
\(408\) | −2.53590 | − | 3.58630i | −0.125546 | − | 0.177548i | ||||
\(409\) | 28.2487i | 1.39681i | 0.715703 | + | 0.698404i | \(0.246106\pi\) | ||||
−0.715703 | + | 0.698404i | \(0.753894\pi\) | |||||||
\(410\) | − | 15.4548i | − | 0.763259i | ||||||
\(411\) | −0.757875 | − | 1.07180i | −0.0373832 | − | 0.0528678i | ||||
\(412\) | − | 18.1244i | − | 0.892923i | ||||||
\(413\) | −31.2886 | −1.53961 | ||||||||
\(414\) | −2.07055 | − | 0.732051i | −0.101762 | − | 0.0359783i | ||||
\(415\) | −10.9282 | −0.536444 | ||||||||
\(416\) | 28.3214i | 1.38857i | ||||||||
\(417\) | 18.6622 | − | 13.1962i | 0.913891 | − | 0.646218i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 32.0464i | − | 1.56557i | −0.622292 | − | 0.782785i | \(-0.713798\pi\) | ||
0.622292 | − | 0.782785i | \(-0.286202\pi\) | |||||||
\(420\) | −9.14162 | − | 12.9282i | −0.446065 | − | 0.630832i | ||||
\(421\) | 35.4641i | 1.72841i | 0.503136 | + | 0.864207i | \(0.332179\pi\) | ||||
−0.503136 | + | 0.864207i | \(0.667821\pi\) | |||||||
\(422\) | − | 21.2504i | − | 1.03445i | ||||||
\(423\) | 29.8564 | + | 10.5558i | 1.45167 | + | 0.513242i | ||||
\(424\) | 3.12436 | 0.151732 | ||||||||
\(425\) | − | 14.6969i | − | 0.712906i | ||||||
\(426\) | −9.79796 | + | 6.92820i | −0.474713 | + | 0.335673i | ||||
\(427\) | 13.1962 | 0.638607 | ||||||||
\(428\) | −8.48528 | −0.410152 | ||||||||
\(429\) | −2.00000 | + | 1.41421i | −0.0965609 | + | 0.0682789i | ||||
\(430\) | − | 6.19615i | − | 0.298805i | ||||||
\(431\) | 25.4558 | 1.22616 | 0.613082 | − | 0.790019i | \(-0.289929\pi\) | ||||
0.613082 | + | 0.790019i | \(0.289929\pi\) | |||||||
\(432\) | 6.31319 | + | 22.3205i | 0.303744 | + | 1.07390i | ||||
\(433\) | 3.33975i | 0.160498i | 0.996775 | + | 0.0802490i | \(0.0255715\pi\) | ||||
−0.996775 | + | 0.0802490i | \(0.974428\pi\) | |||||||
\(434\) | 32.1851i | 1.54494i | ||||||||
\(435\) | 10.9282 | + | 15.4548i | 0.523967 | + | 0.741002i | ||||
\(436\) | 24.9282i | 1.19384i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 8.19615 | − | 5.79555i | 0.391627 | − | 0.276922i | ||||
\(439\) | − | 22.4641i | − | 1.07215i | −0.844169 | − | 0.536077i | \(-0.819906\pi\) | ||
0.844169 | − | 0.536077i | \(-0.180094\pi\) | |||||||
\(440\) | −0.277401 | −0.0132246 | ||||||||
\(441\) | 6.92820 | − | 19.5959i | 0.329914 | − | 0.933139i | ||||
\(442\) | −35.3205 | −1.68003 | ||||||||
\(443\) | 38.6370i | 1.83570i | 0.396926 | + | 0.917850i | \(0.370077\pi\) | ||||
−0.396926 | + | 0.917850i | \(0.629923\pi\) | |||||||
\(444\) | 7.39230 | + | 10.4543i | 0.350823 | + | 0.496139i | ||||
\(445\) | 10.3923i | 0.492642i | ||||||||
\(446\) | − | 18.1445i | − | 0.859169i | ||||||
\(447\) | −16.8690 | − | 23.8564i | −0.797878 | − | 1.12837i | ||||
\(448\) | 21.3923 | 1.01069 | ||||||||
\(449\) | 34.4959 | 1.62796 | 0.813982 | − | 0.580890i | \(-0.197296\pi\) | ||||
0.813982 | + | 0.580890i | \(0.197296\pi\) | |||||||
\(450\) | −5.79555 | + | 16.3923i | −0.273205 | + | 0.772741i | ||||
\(451\) | 2.14359i | 0.100938i | ||||||||
\(452\) | 32.3238 | 1.52039 | ||||||||
\(453\) | 2.00000 | + | 2.82843i | 0.0939682 | + | 0.132891i | ||||
\(454\) | 47.5167 | 2.23007 | ||||||||
\(455\) | 19.6975 | 0.923431 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7128 | −0.968905 | −0.484452 | − | 0.874818i | \(-0.660981\pi\) | ||||
−0.484452 | + | 0.874818i | \(0.660981\pi\) | |||||||
\(458\) | −18.1445 | −0.847839 | ||||||||
\(459\) | −24.4949 | + | 6.92820i | −1.14332 | + | 0.323381i | ||||
\(460\) | −0.928203 | −0.0432777 | ||||||||
\(461\) | − | 32.8786i | − | 1.53131i | −0.643251 | − | 0.765656i | \(-0.722415\pi\) | ||
0.643251 | − | 0.765656i | \(-0.277585\pi\) | |||||||
\(462\) | 2.73205 | + | 3.86370i | 0.127107 | + | 0.179756i | ||||
\(463\) | −29.5885 | −1.37509 | −0.687546 | − | 0.726141i | \(-0.741312\pi\) | ||||
−0.687546 | + | 0.726141i | \(0.741312\pi\) | |||||||
\(464\) | −34.4959 | −1.60143 | ||||||||
\(465\) | −8.92820 | + | 6.31319i | −0.414036 | + | 0.292767i | ||||
\(466\) | 6.92820i | 0.320943i | ||||||||
\(467\) | 22.6274i | 1.04707i | 0.852004 | + | 0.523536i | \(0.175387\pi\) | ||||
−0.852004 | + | 0.523536i | \(0.824613\pi\) | |||||||
\(468\) | 18.2832 | + | 6.46410i | 0.845143 | + | 0.298803i | ||||
\(469\) | − | 3.73205i | − | 0.172330i | ||||||
\(470\) | 28.8391 | 1.33025 | ||||||||
\(471\) | 5.00052 | − | 3.53590i | 0.230412 | − | 0.162926i | ||||
\(472\) | 4.33975 | 0.199753 | ||||||||
\(473\) | 0.859411i | 0.0395157i | ||||||||
\(474\) | −6.83083 | − | 9.66025i | −0.313750 | − | 0.443710i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 31.6675i | 1.45148i | ||||||||
\(477\) | 6.03579 | − | 17.0718i | 0.276360 | − | 0.781664i | ||||
\(478\) | 57.9090i | 2.64869i | ||||||||
\(479\) | − | 11.8685i | − | 0.542286i | −0.962539 | − | 0.271143i | \(-0.912598\pi\) | ||
0.962539 | − | 0.271143i | \(-0.0874017\pi\) | |||||||
\(480\) | 10.7321 | + | 15.1774i | 0.489849 | + | 0.692751i | ||||
\(481\) | −15.9282 | −0.726264 | ||||||||
\(482\) | 55.3674i | 2.52191i | ||||||||
\(483\) | −1.41421 | − | 2.00000i | −0.0643489 | − | 0.0910032i | ||||
\(484\) | 18.8038 | 0.854720 | ||||||||
\(485\) | 10.5558 | 0.479316 | ||||||||
\(486\) | 30.0526 | + | 1.93185i | 1.36321 | + | 0.0876306i | ||||
\(487\) | − | 24.9282i | − | 1.12960i | −0.825226 | − | 0.564802i | \(-0.808952\pi\) | ||
0.825226 | − | 0.564802i | \(-0.191048\pi\) | |||||||
\(488\) | −1.83032 | −0.0828545 | ||||||||
\(489\) | 7.34847 | − | 5.19615i | 0.332309 | − | 0.234978i | ||||
\(490\) | − | 18.9282i | − | 0.855089i | ||||||
\(491\) | − | 10.0010i | − | 0.451340i | −0.974204 | − | 0.225670i | \(-0.927543\pi\) | ||
0.974204 | − | 0.225670i | \(-0.0724571\pi\) | |||||||
\(492\) | 13.8564 | − | 9.79796i | 0.624695 | − | 0.441726i | ||||
\(493\) | − | 37.8564i | − | 1.70497i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.535898 | + | 1.51575i | −0.0240868 | + | 0.0681279i | ||||
\(496\) | − | 19.9282i | − | 0.894803i | ||||||
\(497\) | −13.3843 | −0.600366 | ||||||||
\(498\) | −14.9282 | − | 21.1117i | −0.668949 | − | 0.946036i | ||||
\(499\) | −16.1244 | −0.721825 | −0.360913 | − | 0.932600i | \(-0.617535\pi\) | ||||
−0.360913 | + | 0.932600i | \(0.617535\pi\) | |||||||
\(500\) | 19.5959i | 0.876356i | ||||||||
\(501\) | 10.7846 | − | 7.62587i | 0.481821 | − | 0.340699i | ||||
\(502\) | − | 28.3923i | − | 1.26721i | ||||||
\(503\) | − | 18.2832i | − | 0.815209i | −0.913158 | − | 0.407605i | \(-0.866364\pi\) | ||
0.913158 | − | 0.407605i | \(-0.133636\pi\) | |||||||
\(504\) | −1.93185 | + | 5.46410i | −0.0860515 | + | 0.243390i | ||||
\(505\) | 10.9282 | 0.486299 | ||||||||
\(506\) | 0.277401 | 0.0123320 | ||||||||
\(507\) | −1.31268 | + | 0.928203i | −0.0582981 | + | 0.0412230i | ||||
\(508\) | 13.6077i | 0.603744i | ||||||||
\(509\) | 13.5873 | 0.602248 | 0.301124 | − | 0.953585i | \(-0.402638\pi\) | ||||
0.301124 | + | 0.953585i | \(0.402638\pi\) | |||||||
\(510\) | −18.9282 | + | 13.3843i | −0.838155 | + | 0.592665i | ||||
\(511\) | 11.1962 | 0.495289 | ||||||||
\(512\) | −29.2552 | −1.29291 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.19615 | −0.273301 | ||||||||
\(515\) | 14.7985 | 0.652099 | ||||||||
\(516\) | 5.55532 | − | 3.92820i | 0.244559 | − | 0.172930i | ||||
\(517\) | −4.00000 | −0.175920 | ||||||||
\(518\) | 30.7709i | 1.35200i | ||||||||
\(519\) | −16.7846 | + | 11.8685i | −0.736763 | + | 0.520970i | ||||
\(520\) | −2.73205 | −0.119808 | ||||||||
\(521\) | −4.52004 | −0.198027 | −0.0990133 | − | 0.995086i | \(-0.531569\pi\) | ||||
−0.0990133 | + | 0.995086i | \(0.531569\pi\) | |||||||
\(522\) | −14.9282 | + | 42.2233i | −0.653390 | + | 1.84807i | ||||
\(523\) | − | 16.8564i | − | 0.737079i | −0.929612 | − | 0.368540i | \(-0.879858\pi\) | ||
0.929612 | − | 0.368540i | \(-0.120142\pi\) | |||||||
\(524\) | 12.0716i | 0.527350i | ||||||||
\(525\) | −15.8338 | + | 11.1962i | −0.691042 | + | 0.488640i | ||||
\(526\) | 1.07180i | 0.0467326i | ||||||||
\(527\) | 21.8695 | 0.952652 | ||||||||
\(528\) | −1.69161 | − | 2.39230i | −0.0736181 | − | 0.104112i | ||||
\(529\) | 22.8564 | 0.993757 | ||||||||
\(530\) | − | 16.4901i | − | 0.716284i | ||||||
\(531\) | 8.38375 | − | 23.7128i | 0.363824 | − | 1.02905i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.1117i | 0.914448i | ||||||||
\(534\) | −20.0764 | + | 14.1962i | −0.868790 | + | 0.614328i | ||||
\(535\) | − | 6.92820i | − | 0.299532i | ||||||
\(536\) | 0.517638i | 0.0223586i | ||||||||
\(537\) | 2.00000 | − | 1.41421i | 0.0863064 | − | 0.0610278i | ||||
\(538\) | −11.6603 | −0.502709 | ||||||||
\(539\) | 2.62536i | 0.113082i | ||||||||
\(540\) | 12.2474 | − | 3.46410i | 0.527046 | − | 0.149071i | ||||
\(541\) | −17.5359 | −0.753927 | −0.376964 | − | 0.926228i | \(-0.623032\pi\) | ||||
−0.376964 | + | 0.926228i | \(0.623032\pi\) | |||||||
\(542\) | 13.3843 | 0.574903 | ||||||||
\(543\) | −3.46410 | − | 4.89898i | −0.148659 | − | 0.210235i | ||||
\(544\) | − | 37.1769i | − | 1.59395i | ||||||
\(545\) | −20.3538 | −0.871861 | ||||||||
\(546\) | 26.9072 | + | 38.0526i | 1.15152 | + | 1.62850i | ||||
\(547\) | − | 12.8564i | − | 0.549700i | −0.961487 | − | 0.274850i | \(-0.911372\pi\) | ||
0.961487 | − | 0.274850i | \(-0.0886282\pi\) | |||||||
\(548\) | − | 1.31268i | − | 0.0560748i | ||||||
\(549\) | −3.53590 | + | 10.0010i | −0.150908 | + | 0.426834i | ||||
\(550\) | − | 2.19615i | − | 0.0936443i | ||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.196152 | + | 0.277401i | 0.00834880 | + | 0.0118070i | ||||
\(553\) | − | 13.1962i | − | 0.561157i | ||||||
\(554\) | 19.0411 | 0.808979 | ||||||||
\(555\) | −8.53590 | + | 6.03579i | −0.362329 | + | 0.256205i | ||||
\(556\) | 22.8564 | 0.969328 | ||||||||
\(557\) | − | 3.38323i | − | 0.143352i | −0.997428 | − | 0.0716760i | \(-0.977165\pi\) | ||
0.997428 | − | 0.0716760i | \(-0.0228348\pi\) | |||||||
\(558\) | −24.3923 | − | 8.62398i | −1.03261 | − | 0.365082i | ||||
\(559\) | 8.46410i | 0.357993i | ||||||||
\(560\) | 23.5612i | 0.995641i | ||||||||
\(561\) | 2.62536 | − | 1.85641i | 0.110843 | − | 0.0783775i | ||||
\(562\) | 29.1244 | 1.22854 | ||||||||
\(563\) | 3.38323 | 0.142586 | 0.0712931 | − | 0.997455i | \(-0.477287\pi\) | ||||
0.0712931 | + | 0.997455i | \(0.477287\pi\) | |||||||
\(564\) | 18.2832 | + | 25.8564i | 0.769863 | + | 1.08875i | ||||
\(565\) | 26.3923i | 1.11033i | ||||||||
\(566\) | 42.2233 | 1.77478 | ||||||||
\(567\) | 26.1244 | + | 21.1117i | 1.09712 | + | 0.886607i | ||||
\(568\) | 1.85641 | 0.0778931 | ||||||||
\(569\) | −13.9391 | −0.584356 | −0.292178 | − | 0.956364i | \(-0.594380\pi\) | ||||
−0.292178 | + | 0.956364i | \(0.594380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1962 | 1.05443 | 0.527213 | − | 0.849733i | \(-0.323237\pi\) | ||||
0.527213 | + | 0.849733i | \(0.323237\pi\) | |||||||
\(572\) | −2.44949 | −0.102418 | ||||||||
\(573\) | −1.69161 | − | 2.39230i | −0.0706682 | − | 0.0999400i | ||||
\(574\) | 40.7846 | 1.70232 | ||||||||
\(575\) | 1.13681i | 0.0474083i | ||||||||
\(576\) | −5.73205 | + | 16.2127i | −0.238835 | + | 0.675529i | ||||
\(577\) | 42.9282 | 1.78712 | 0.893562 | − | 0.448939i | \(-0.148198\pi\) | ||||
0.893562 | + | 0.448939i | \(0.148198\pi\) | |||||||
\(578\) | 13.5230 | 0.562481 | ||||||||
\(579\) | −13.1962 | − | 18.6622i | −0.548413 | − | 0.775574i | ||||
\(580\) | 18.9282i | 0.785951i | ||||||||
\(581\) | − | 28.8391i | − | 1.19645i | ||||||
\(582\) | 14.4195 | + | 20.3923i | 0.597709 | + | 0.845288i | ||||
\(583\) | 2.28719i | 0.0947256i | ||||||||
\(584\) | −1.55291 | −0.0642600 | ||||||||
\(585\) | −5.27792 | + | 14.9282i | −0.218215 | + | 0.617205i | ||||
\(586\) | 48.7846 | 2.01527 | ||||||||
\(587\) | − | 10.7317i | − | 0.442945i | −0.975167 | − | 0.221472i | \(-0.928914\pi\) | ||
0.975167 | − | 0.221472i | \(-0.0710862\pi\) | |||||||
\(588\) | 16.9706 | − | 12.0000i | 0.699854 | − | 0.494872i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − | 22.9048i | − | 0.942976i | ||||||
\(591\) | 9.14162 | + | 12.9282i | 0.376036 | + | 0.531795i | ||||
\(592\) | − | 19.0526i | − | 0.783055i | ||||||
\(593\) | − | 25.1512i | − | 1.03284i | −0.856336 | − | 0.516419i | \(-0.827265\pi\) | ||
0.856336 | − | 0.516419i | \(-0.172735\pi\) | |||||||
\(594\) | −3.66025 | + | 1.03528i | −0.150182 | + | 0.0424779i | ||||
\(595\) | −25.8564 | −1.06001 | ||||||||
\(596\) | − | 29.2180i | − | 1.19682i | ||||||
\(597\) | −18.1074 | + | 12.8038i | −0.741086 | + | 0.524027i | ||||
\(598\) | 2.73205 | 0.111722 | ||||||||
\(599\) | 16.8690 | 0.689250 | 0.344625 | − | 0.938740i | \(-0.388006\pi\) | ||||
0.344625 | + | 0.938740i | \(0.388006\pi\) | |||||||
\(600\) | 2.19615 | − | 1.55291i | 0.0896575 | − | 0.0633975i | ||||
\(601\) | − | 44.3731i | − | 1.81002i | −0.425395 | − | 0.905008i | \(-0.639865\pi\) | ||
0.425395 | − | 0.905008i | \(-0.360135\pi\) | |||||||
\(602\) | 16.3514 | 0.666433 | ||||||||
\(603\) | 2.82843 | + | 1.00000i | 0.115182 | + | 0.0407231i | ||||
\(604\) | 3.46410i | 0.140952i | ||||||||
\(605\) | 15.3533i | 0.624199i | ||||||||
\(606\) | 14.9282 | + | 21.1117i | 0.606417 | + | 0.857603i | ||||
\(607\) | 13.2487i | 0.537749i | 0.963175 | + | 0.268874i | \(0.0866516\pi\) | ||||
−0.963175 | + | 0.268874i | \(0.913348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −40.7846 | + | 28.8391i | −1.65268 | + | 1.16862i | ||||
\(610\) | 9.66025i | 0.391132i | ||||||||
\(611\) | −39.3949 | −1.59375 | ||||||||
\(612\) | −24.0000 | − | 8.48528i | −0.970143 | − | 0.342997i | ||||
\(613\) | 22.6410 | 0.914462 | 0.457231 | − | 0.889348i | \(-0.348841\pi\) | ||||
0.457231 | + | 0.889348i | \(0.348841\pi\) | |||||||
\(614\) | − | 26.7685i | − | 1.08029i | ||||||
\(615\) | 8.00000 | + | 11.3137i | 0.322591 | + | 0.456213i | ||||
\(616\) | − | 0.732051i | − | 0.0294952i | ||||||
\(617\) | 25.9091i | 1.04306i | 0.853232 | + | 0.521531i | \(0.174639\pi\) | ||||
−0.853232 | + | 0.521531i | \(0.825361\pi\) | |||||||
\(618\) | 20.2151 | + | 28.5885i | 0.813170 | + | 1.15000i | ||||
\(619\) | 2.80385 | 0.112696 | 0.0563481 | − | 0.998411i | \(-0.482054\pi\) | ||||
0.0563481 | + | 0.998411i | \(0.482054\pi\) | |||||||
\(620\) | −10.9348 | −0.439151 | ||||||||
\(621\) | 1.89469 | − | 0.535898i | 0.0760312 | − | 0.0215049i | ||||
\(622\) | − | 52.4449i | − | 2.10285i | ||||||
\(623\) | −27.4249 | −1.09875 | ||||||||
\(624\) | −16.6603 | − | 23.5612i | −0.666944 | − | 0.943201i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 47.8802 | 1.91368 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.12436 | 0.244388 | ||||||||
\(629\) | 20.9086 | 0.833680 | ||||||||
\(630\) | 28.8391 | + | 10.1962i | 1.14898 | + | 0.406224i | ||||
\(631\) | 49.0526 | 1.95275 | 0.976376 | − | 0.216080i | \(-0.0693270\pi\) | ||||
0.976376 | + | 0.216080i | \(0.0693270\pi\) | |||||||
\(632\) | 1.83032i | 0.0728060i | ||||||||
\(633\) | 11.0000 | + | 15.5563i | 0.437211 | + | 0.618309i | ||||
\(634\) | 26.5885 | 1.05596 | ||||||||
\(635\) | −11.1106 | −0.440912 | ||||||||
\(636\) | 14.7846 | − | 10.4543i | 0.586248 | − | 0.414540i | ||||
\(637\) | 25.8564i | 1.02447i | ||||||||
\(638\) | − | 5.65685i | − | 0.223957i | ||||||
\(639\) | 3.58630 | − | 10.1436i | 0.141872 | − | 0.401274i | ||||
\(640\) | − | 5.80385i | − | 0.229417i | ||||||
\(641\) | 12.8295 | 0.506733 | 0.253367 | − | 0.967370i | \(-0.418462\pi\) | ||||
0.253367 | + | 0.967370i | \(0.418462\pi\) | |||||||
\(642\) | 13.3843 | − | 9.46410i | 0.528235 | − | 0.373518i | ||||
\(643\) | −43.5885 | −1.71896 | −0.859480 | − | 0.511169i | \(-0.829213\pi\) | ||||
−0.859480 | + | 0.511169i | \(0.829213\pi\) | |||||||
\(644\) | − | 2.44949i | − | 0.0965234i | ||||||
\(645\) | 3.20736 | + | 4.53590i | 0.126290 | + | 0.178601i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.5569i | 0.808174i | 0.914721 | + | 0.404087i | \(0.132411\pi\) | ||||
−0.914721 | + | 0.404087i | \(0.867589\pi\) | |||||||
\(648\) | −3.62347 | − | 2.92820i | −0.142343 | − | 0.115031i | ||||
\(649\) | 3.17691i | 0.124705i | ||||||||
\(650\) | − | 21.6293i | − | 0.848371i | ||||||
\(651\) | −16.6603 | − | 23.5612i | −0.652967 | − | 0.923435i | ||||
\(652\) | 9.00000 | 0.352467 | ||||||||
\(653\) | − | 47.1223i | − | 1.84404i | −0.387144 | − | 0.922019i | \(-0.626538\pi\) | ||
0.387144 | − | 0.922019i | \(-0.373462\pi\) | |||||||
\(654\) | −27.8038 | − | 39.3205i | −1.08721 | − | 1.53755i | ||||
\(655\) | −9.85641 | −0.385122 | ||||||||
\(656\) | −25.2528 | −0.985955 | ||||||||
\(657\) | −3.00000 | + | 8.48528i | −0.117041 | + | 0.331042i | ||||
\(658\) | 76.1051i | 2.96689i | ||||||||
\(659\) | 33.0817 | 1.28868 | 0.644340 | − | 0.764739i | \(-0.277132\pi\) | ||||
0.644340 | + | 0.764739i | \(0.277132\pi\) | |||||||
\(660\) | −1.31268 | + | 0.928203i | −0.0510959 | + | 0.0361303i | ||||
\(661\) | 6.14359i | 0.238958i | 0.992837 | + | 0.119479i | \(0.0381224\pi\) | ||||
−0.992837 | + | 0.119479i | \(0.961878\pi\) | |||||||
\(662\) | − | 61.6806i | − | 2.39728i | ||||||
\(663\) | 25.8564 | − | 18.2832i | 1.00418 | − | 0.710062i | ||||
\(664\) | 4.00000i | 0.155230i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.3205 | − | 8.24504i | −0.903651 | − | 0.319489i | ||||
\(667\) | 2.92820i | 0.113380i | ||||||||
\(668\) | 13.2084 | 0.511048 | ||||||||
\(669\) | 9.39230 | + | 13.2827i | 0.363127 | + | 0.513540i | ||||
\(670\) | 2.73205 | 0.105548 | ||||||||
\(671\) | − | 1.33988i | − | 0.0517257i | ||||||
\(672\) | −40.0526 | + | 28.3214i | −1.54506 | + | 1.09252i | ||||
\(673\) | 21.9808i | 0.847296i | 0.905827 | + | 0.423648i | \(0.139251\pi\) | ||||
−0.905827 | + | 0.423648i | \(0.860749\pi\) | |||||||
\(674\) | 14.1793i | 0.546166i | ||||||||
\(675\) | −4.24264 | − | 15.0000i | −0.163299 | − | 0.577350i | ||||
\(676\) | −1.60770 | −0.0618344 | ||||||||
\(677\) | −18.8380 | −0.724005 | −0.362002 | − | 0.932177i | \(-0.617907\pi\) | ||||
−0.362002 | + | 0.932177i | \(0.617907\pi\) | |||||||
\(678\) | −50.9860 | + | 36.0526i | −1.95811 | + | 1.38459i | ||||
\(679\) | 27.8564i | 1.06903i | ||||||||
\(680\) | 3.58630 | 0.137528 | ||||||||
\(681\) | −34.7846 | + | 24.5964i | −1.33295 | + | 0.942537i | ||||
\(682\) | 3.26795 | 0.125136 | ||||||||
\(683\) | −16.3142 | −0.624246 | −0.312123 | − | 0.950042i | \(-0.601040\pi\) | ||||
−0.312123 | + | 0.950042i | \(0.601040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.07180 | 0.0409512 | ||||||||
\(686\) | −0.517638 | −0.0197635 | ||||||||
\(687\) | 13.2827 | − | 9.39230i | 0.506768 | − | 0.358339i | ||||
\(688\) | −10.1244 | −0.385987 | ||||||||
\(689\) | 22.5259i | 0.858168i | ||||||||
\(690\) | 1.46410 | − | 1.03528i | 0.0557374 | − | 0.0394123i | ||||
\(691\) | 9.85641 | 0.374955 | 0.187478 | − | 0.982269i | \(-0.439969\pi\) | ||||
0.187478 | + | 0.982269i | \(0.439969\pi\) | |||||||
\(692\) | −20.5569 | −0.781455 | ||||||||
\(693\) | −4.00000 | − | 1.41421i | −0.151947 | − | 0.0537215i | ||||
\(694\) | − | 48.0526i | − | 1.82405i | ||||||
\(695\) | 18.6622i | 0.707897i | ||||||||
\(696\) | 5.65685 | − | 4.00000i | 0.214423 | − | 0.151620i | ||||
\(697\) | − | 27.7128i | − | 1.04970i | ||||||
\(698\) | 22.0082 | 0.833024 | ||||||||
\(699\) | −3.58630 | − | 5.07180i | −0.135646 | − | 0.191833i | ||||
\(700\) | −19.3923 | −0.732960 | ||||||||
\(701\) | − | 19.9005i | − | 0.751632i | −0.926694 | − | 0.375816i | \(-0.877362\pi\) | ||
0.926694 | − | 0.375816i | \(-0.122638\pi\) | |||||||
\(702\) | −36.0488 | + | 10.1962i | −1.36058 | + | 0.384829i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 2.17209i | − | 0.0818637i | ||||||
\(705\) | −21.1117 | + | 14.9282i | −0.795111 | + | 0.562229i | ||||
\(706\) | 23.1244i | 0.870297i | ||||||||
\(707\) | 28.8391i | 1.08461i | ||||||||
\(708\) | 20.5359 | − | 14.5211i | 0.771786 | − | 0.545735i | ||||
\(709\) | 42.3205 | 1.58938 | 0.794690 | − | 0.607015i | \(-0.207633\pi\) | ||||
0.794690 | + | 0.607015i | \(0.207633\pi\) | |||||||
\(710\) | − | 9.79796i | − | 0.367711i | ||||||
\(711\) | 10.0010 | + | 3.53590i | 0.375068 | + | 0.132607i | ||||
\(712\) | 3.80385 | 0.142555 | ||||||||
\(713\) | −1.69161 | −0.0633515 | ||||||||
\(714\) | −35.3205 | − | 49.9507i | −1.32184 | − | 1.86936i | ||||
\(715\) | − | 2.00000i | − | 0.0747958i | ||||||
\(716\) | 2.44949 | 0.0915417 | ||||||||
\(717\) | −29.9759 | − | 42.3923i | −1.11947 | − | 1.58317i | ||||
\(718\) | 51.7128i | 1.92991i | ||||||||
\(719\) | 6.03579i | 0.225097i | 0.993646 | + | 0.112549i | \(0.0359014\pi\) | ||||
−0.993646 | + | 0.112549i | \(0.964099\pi\) | |||||||
\(720\) | −17.8564 | − | 6.31319i | −0.665469 | − | 0.235279i | ||||
\(721\) | 39.0526i | 1.45439i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.6603 | − | 40.5317i | −1.06589 | − | 1.50739i | ||||
\(724\) | − | 6.00000i | − | 0.222988i | ||||||
\(725\) | 23.1822 | 0.860966 | ||||||||
\(726\) | −29.6603 | + | 20.9730i | −1.10080 | + | 0.778380i | ||||
\(727\) | −13.5885 | −0.503968 | −0.251984 | − | 0.967731i | \(-0.581083\pi\) | ||||
−0.251984 | + | 0.967731i | \(0.581083\pi\) | |||||||
\(728\) | − | 7.20977i | − | 0.267212i | ||||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 8.19615i | 0.303353i | ||||||||
\(731\) | − | 11.1106i | − | 0.410942i | ||||||
\(732\) | −8.66115 | + | 6.12436i | −0.320125 | + | 0.226363i | ||||
\(733\) | −35.7128 | −1.31908 | −0.659541 | − | 0.751668i | \(-0.729249\pi\) | ||||
−0.659541 | + | 0.751668i | \(0.729249\pi\) | |||||||
\(734\) | 32.9430 | 1.21595 | ||||||||
\(735\) | 9.79796 | + | 13.8564i | 0.361403 | + | 0.511101i | ||||
\(736\) | 2.87564i | 0.105998i | ||||||||
\(737\) | −0.378937 | −0.0139583 | ||||||||
\(738\) | −10.9282 | + | 30.9096i | −0.402273 | + | 1.13780i | ||||
\(739\) | −34.8038 | −1.28028 | −0.640140 | − | 0.768258i | \(-0.721124\pi\) | ||||
−0.640140 | + | 0.768258i | \(0.721124\pi\) | |||||||
\(740\) | −10.4543 | −0.384308 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 43.5167 | 1.59755 | ||||||||
\(743\) | −7.07107 | −0.259412 | −0.129706 | − | 0.991552i | \(-0.541403\pi\) | ||||
−0.129706 | + | 0.991552i | \(0.541403\pi\) | |||||||
\(744\) | 2.31079 | + | 3.26795i | 0.0847176 | + | 0.119809i | ||||
\(745\) | 23.8564 | 0.874031 | ||||||||
\(746\) | − | 24.2175i | − | 0.886666i | ||||||
\(747\) | 21.8564 | + | 7.72741i | 0.799684 | + | 0.282731i | ||||
\(748\) | 3.21539 | 0.117566 | ||||||||
\(749\) | 18.2832 | 0.668055 | ||||||||
\(750\) | −21.8564 | − | 30.9096i | −0.798083 | − | 1.12866i | ||||
\(751\) | − | 8.60770i | − | 0.314099i | −0.987591 | − | 0.157050i | \(-0.949802\pi\) | ||
0.987591 | − | 0.157050i | \(-0.0501983\pi\) | |||||||
\(752\) | − | 47.1223i | − | 1.71837i | ||||||
\(753\) | 14.6969 | + | 20.7846i | 0.535586 | + | 0.757433i | ||||
\(754\) | − | 55.7128i | − | 2.02894i | ||||||
\(755\) | −2.82843 | −0.102937 | ||||||||
\(756\) | 9.14162 | + | 32.3205i | 0.332478 | + | 1.17549i | ||||
\(757\) | 4.60770 | 0.167470 | 0.0837348 | − | 0.996488i | \(-0.473315\pi\) | ||||
0.0837348 | + | 0.996488i | \(0.473315\pi\) | |||||||
\(758\) | − | 34.3572i | − | 1.24791i | ||||||
\(759\) | −0.203072 | + | 0.143594i | −0.00737104 | + | 0.00521212i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.2629i | 1.67703i | 0.544879 | + | 0.838514i | \(0.316575\pi\) | ||||
−0.544879 | + | 0.838514i | \(0.683425\pi\) | |||||||
\(762\) | −15.1774 | − | 21.4641i | −0.549820 | − | 0.777562i | ||||
\(763\) | − | 53.7128i | − | 1.94453i | ||||||
\(764\) | − | 2.92996i | − | 0.106002i | ||||||
\(765\) | 6.92820 | − | 19.5959i | 0.250490 | − | 0.708492i | ||||
\(766\) | −51.5167 | −1.86137 | ||||||||
\(767\) | 31.2886i | 1.12976i | ||||||||
\(768\) | 27.4249 | − | 19.3923i | 0.989609 | − | 0.699760i | ||||
\(769\) | −0.856406 | −0.0308828 | −0.0154414 | − | 0.999881i | \(-0.504915\pi\) | ||||
−0.0154414 | + | 0.999881i | \(0.504915\pi\) | |||||||
\(770\) | −3.86370 | −0.139238 | ||||||||
\(771\) | 4.53590 | − | 3.20736i | 0.163356 | − | 0.115510i | ||||
\(772\) | − | 22.8564i | − | 0.822620i | ||||||
\(773\) | 18.0802 | 0.650298 | 0.325149 | − | 0.945663i | \(-0.394585\pi\) | ||||
0.325149 | + | 0.945663i | \(0.394585\pi\) | |||||||
\(774\) | −4.38134 | + | 12.3923i | −0.157484 | + | 0.445432i | ||||
\(775\) | 13.3923i | 0.481066i | ||||||||
\(776\) | − | 3.86370i | − | 0.138699i | ||||||
\(777\) | −15.9282 | − | 22.5259i | −0.571421 | − | 0.808111i | ||||
\(778\) | 9.66025i | 0.346337i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −12.9282 | + | 9.14162i | −0.462904 | + | 0.327323i | ||||
\(781\) | 1.35898i | 0.0486283i | ||||||||
\(782\) | −3.58630 | −0.128246 | ||||||||
\(783\) | −10.9282 | − | 38.6370i | −0.390542 | − | 1.38077i | ||||
\(784\) | −30.9282 | −1.10458 | ||||||||
\(785\) | 5.00052i | 0.178476i | ||||||||
\(786\) | −13.4641 | − | 19.0411i | −0.480249 | − | 0.679174i | ||||
\(787\) | − | 24.0718i | − | 0.858067i | −0.903289 | − | 0.429033i | \(-0.858854\pi\) | ||
0.903289 | − | 0.429033i | \(-0.141146\pi\) | |||||||
\(788\) | 15.8338i | 0.564054i | ||||||||
\(789\) | −0.554803 | − | 0.784610i | −0.0197515 | − | 0.0279328i | ||||
\(790\) | 9.66025 | 0.343696 | ||||||||
\(791\) | −69.6482 | −2.47640 | ||||||||
\(792\) | 0.554803 | + | 0.196152i | 0.0197141 | + | 0.00696997i | ||||
\(793\) | − | 13.1962i | − | 0.468609i | ||||||
\(794\) | −16.0740 | −0.570444 | ||||||||
\(795\) | 8.53590 | + | 12.0716i | 0.302737 | + | 0.428135i | ||||
\(796\) | −22.1769 | −0.786040 | ||||||||
\(797\) | 14.4939 | 0.513399 | 0.256700 | − | 0.966491i | \(-0.417365\pi\) | ||||
0.256700 | + | 0.966491i | \(0.417365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.7128 | 1.82947 | ||||||||
\(800\) | 22.7661 | 0.804904 | ||||||||
\(801\) | 7.34847 | − | 20.7846i | 0.259645 | − | 0.734388i | ||||
\(802\) | 22.1962 | 0.783773 | ||||||||
\(803\) | − | 1.13681i | − | 0.0401172i | ||||||
\(804\) | 1.73205 | + | 2.44949i | 0.0610847 | + | 0.0863868i | ||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 32.1851 | 1.13367 | ||||||||
\(807\) | 8.53590 | − | 6.03579i | 0.300478 | − | 0.212470i | ||||
\(808\) | − | 4.00000i | − | 0.140720i | ||||||
\(809\) | 51.1619i | 1.79876i | 0.437172 | + | 0.899378i | \(0.355980\pi\) | ||||
−0.437172 | + | 0.899378i | \(0.644020\pi\) | |||||||
\(810\) | −15.4548 | + | 19.1244i | −0.543027 | + | 0.671961i | ||||
\(811\) | 21.7128i | 0.762440i | 0.924484 | + | 0.381220i | \(0.124496\pi\) | ||||
−0.924484 | + | 0.381220i | \(0.875504\pi\) | |||||||
\(812\) | −49.9507 | −1.75293 | ||||||||
\(813\) | −9.79796 | + | 6.92820i | −0.343629 | + | 0.242983i | ||||
\(814\) | 3.12436 | 0.109509 | ||||||||
\(815\) | 7.34847i | 0.257406i | ||||||||
\(816\) | 21.8695 | + | 30.9282i | 0.765587 | + | 1.08270i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 54.5723i | − | 1.90808i | ||||||
\(819\) | −39.3949 | − | 13.9282i | −1.37657 | − | 0.486691i | ||||
\(820\) | 13.8564i | 0.483887i | ||||||||
\(821\) | 34.4959i | 1.20392i | 0.798528 | + | 0.601958i | \(0.205613\pi\) | ||||
−0.798528 | + | 0.601958i | \(0.794387\pi\) | |||||||
\(822\) | 1.46410 | + | 2.07055i | 0.0510664 | + | 0.0722188i | ||||
\(823\) | −8.00000 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(824\) | − | 5.41662i | − | 0.188697i | ||||||
\(825\) | 1.13681 | + | 1.60770i | 0.0395787 | + | 0.0559728i | ||||
\(826\) | 60.4449 | 2.10315 | ||||||||
\(827\) | 24.4949 | 0.851771 | 0.425886 | − | 0.904777i | \(-0.359963\pi\) | ||||
0.425886 | + | 0.904777i | \(0.359963\pi\) | |||||||
\(828\) | 1.85641 | + | 0.656339i | 0.0645146 | + | 0.0228093i | ||||
\(829\) | 38.6603i | 1.34273i | 0.741129 | + | 0.671363i | \(0.234291\pi\) | ||||
−0.741129 | + | 0.671363i | \(0.765709\pi\) | |||||||
\(830\) | 21.1117 | 0.732797 | ||||||||
\(831\) | −13.9391 | + | 9.85641i | −0.483541 | + | 0.341915i | ||||
\(832\) | − | 21.3923i | − | 0.741645i | ||||||
\(833\) | − | 33.9411i | − | 1.17599i | ||||||
\(834\) | −36.0526 | + | 25.4930i | −1.24840 | + | 0.882751i | ||||
\(835\) | 10.7846i | 0.373217i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3205 | − | 6.31319i | 0.771510 | − | 0.218216i | ||||
\(838\) | 61.9090i | 2.13861i | ||||||||
\(839\) | −5.75839 | −0.198802 | −0.0994009 | − | 0.995047i | \(-0.531693\pi\) | ||||
−0.0994009 | + | 0.995047i | \(0.531693\pi\) | |||||||
\(840\) | −2.73205 | − | 3.86370i | −0.0942647 | − | 0.133310i | ||||
\(841\) | 30.7128 | 1.05906 | ||||||||
\(842\) | − | 68.5114i | − | 2.36106i | ||||||
\(843\) | −21.3205 | + | 15.0759i | −0.734317 | + | 0.519241i | ||||
\(844\) | 19.0526i | 0.655816i | ||||||||
\(845\) | − | 1.31268i | − | 0.0451575i | ||||||
\(846\) | −57.6781 | − | 20.3923i | −1.98302 | − | 0.701102i | ||||
\(847\) | −40.5167 | −1.39217 | ||||||||
\(848\) | −26.9444 | −0.925274 | ||||||||
\(849\) | −30.9096 | + | 21.8564i | −1.06082 | + | 0.750110i | ||||
\(850\) | 28.3923i | 0.973848i | ||||||||
\(851\) | −1.61729 | −0.0554398 | ||||||||
\(852\) | 8.78461 | − | 6.21166i | 0.300956 | − | 0.212808i | ||||
\(853\) | 19.6795 | 0.673813 | 0.336906 | − | 0.941538i | \(-0.390619\pi\) | ||||
0.336906 | + | 0.941538i | \(0.390619\pi\) | |||||||
\(854\) | −25.4930 | −0.872353 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.53590 | −0.0866752 | ||||||||
\(857\) | −3.03150 | −0.103554 | −0.0517770 | − | 0.998659i | \(-0.516489\pi\) | ||||
−0.0517770 | + | 0.998659i | \(0.516489\pi\) | |||||||
\(858\) | 3.86370 | − | 2.73205i | 0.131905 | − | 0.0932707i | ||||
\(859\) | −4.66025 | −0.159006 | −0.0795029 | − | 0.996835i | \(-0.525333\pi\) | ||||
−0.0795029 | + | 0.996835i | \(0.525333\pi\) | |||||||
\(860\) | 5.55532i | 0.189435i | ||||||||
\(861\) | −29.8564 | + | 21.1117i | −1.01750 | + | 0.719484i | ||||
\(862\) | −49.1769 | −1.67497 | ||||||||
\(863\) | 18.2832 | 0.622369 | 0.311184 | − | 0.950350i | \(-0.399274\pi\) | ||||
0.311184 | + | 0.950350i | \(0.399274\pi\) | |||||||
\(864\) | −10.7321 | − | 37.9435i | −0.365112 | − | 1.29087i | ||||
\(865\) | − | 16.7846i | − | 0.570694i | ||||||
\(866\) | − | 6.45189i | − | 0.219244i | ||||||
\(867\) | −9.89949 | + | 7.00000i | −0.336204 | + | 0.237732i | ||||
\(868\) | − | 28.8564i | − | 0.979450i | ||||||
\(869\) | −1.33988 | −0.0454525 | ||||||||
\(870\) | −21.1117 | − | 29.8564i | −0.715753 | − | 1.01223i | ||||
\(871\) | −3.73205 | −0.126456 | ||||||||
\(872\) | 7.45001i | 0.252289i | ||||||||
\(873\) | −21.1117 | − | 7.46410i | −0.714522 | − | 0.252622i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 42.2233i | − | 1.42741i | ||||||
\(876\) | −7.34847 | + | 5.19615i | −0.248282 | + | 0.175562i | ||||
\(877\) | 3.73205i | 0.126022i | 0.998013 | + | 0.0630112i | \(0.0200704\pi\) | ||||
−0.998013 | + | 0.0630112i | \(0.979930\pi\) | |||||||
\(878\) | 43.3973i | 1.46459i | ||||||||
\(879\) | −35.7128 | + | 25.2528i | −1.20456 | + | 0.851755i | ||||
\(880\) | 2.39230 | 0.0806446 | ||||||||
\(881\) | − | 39.8482i | − | 1.34252i | −0.741222 | − | 0.671260i | \(-0.765754\pi\) | ||
0.741222 | − | 0.671260i | \(-0.234246\pi\) | |||||||
\(882\) | −13.3843 | + | 37.8564i | −0.450672 | + | 1.27469i | ||||
\(883\) | −22.2679 | −0.749376 | −0.374688 | − | 0.927151i | \(-0.622250\pi\) | ||||
−0.374688 | + | 0.927151i | \(0.622250\pi\) | |||||||
\(884\) | 31.6675 | 1.06509 | ||||||||
\(885\) | 11.8564 | + | 16.7675i | 0.398549 | + | 0.563633i | ||||
\(886\) | − | 74.6410i | − | 2.50761i | ||||||
\(887\) | 11.9700 | 0.401915 | 0.200957 | − | 0.979600i | \(-0.435595\pi\) | ||||
0.200957 | + | 0.979600i | \(0.435595\pi\) | |||||||
\(888\) | 2.20925 | + | 3.12436i | 0.0741377 | + | 0.104847i | ||||
\(889\) | − | 29.3205i | − | 0.983378i | ||||||
\(890\) | − | 20.0764i | − | 0.672962i | ||||||
\(891\) | 2.14359 | − | 2.65256i | 0.0718131 | − | 0.0888642i | ||||
\(892\) | 16.2679i | 0.544691i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 32.5885 | + | 46.0870i | 1.08992 | + | 1.54138i | ||||
\(895\) | 2.00000i | 0.0668526i | ||||||||
\(896\) | 15.3161 | 0.511675 | ||||||||
\(897\) | −2.00000 | + | 1.41421i | −0.0667781 | + | 0.0472192i | ||||
\(898\) | −66.6410 | −2.22384 | ||||||||
\(899\) | 34.4959i | 1.15050i | ||||||||
\(900\) | 5.19615 | − | 14.6969i | 0.173205 | − | 0.489898i | ||||
\(901\) | − | 29.5692i | − | 0.985094i | ||||||
\(902\) | − | 4.14110i | − | 0.137884i | ||||||
\(903\) | −11.9700 | + | 8.46410i | −0.398338 | + | 0.281668i | ||||
\(904\) | 9.66025 | 0.321295 | ||||||||
\(905\) | 4.89898 | 0.162848 | ||||||||
\(906\) | −3.86370 | − | 5.46410i | −0.128363 | − | 0.181533i | ||||
\(907\) | − | 40.9282i | − | 1.35900i | −0.733676 | − | 0.679499i | \(-0.762197\pi\) | ||
0.733676 | − | 0.679499i | \(-0.237803\pi\) | |||||||
\(908\) | −42.6023 | −1.41381 | ||||||||
\(909\) | −21.8564 | − | 7.72741i | −0.724931 | − | 0.256302i | ||||
\(910\) | −38.0526 | −1.26143 | ||||||||
\(911\) | −40.9107 | −1.35543 | −0.677715 | − | 0.735324i | \(-0.737030\pi\) | ||||
−0.677715 | + | 0.735324i | \(0.737030\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.92820 | −0.0969094 | ||||||||
\(914\) | 40.0141 | 1.32355 | ||||||||
\(915\) | −5.00052 | − | 7.07180i | −0.165312 | − | 0.233786i | ||||
\(916\) | 16.2679 | 0.537508 | ||||||||
\(917\) | − | 26.0106i | − | 0.858947i | ||||||
\(918\) | 47.3205 | − | 13.3843i | 1.56181 | − | 0.441746i | ||||
\(919\) | −31.9808 | −1.05495 | −0.527474 | − | 0.849571i | \(-0.676861\pi\) | ||||
−0.527474 | + | 0.849571i | \(0.676861\pi\) | |||||||
\(920\) | −0.277401 | −0.00914565 | ||||||||
\(921\) | 13.8564 | + | 19.5959i | 0.456584 | + | 0.645707i | ||||
\(922\) | 63.5167i | 2.09181i | ||||||||
\(923\) | 13.3843i | 0.440548i | ||||||||
\(924\) | −2.44949 | − | 3.46410i | −0.0805823 | − | 0.113961i | ||||
\(925\) | 12.8038i | 0.420988i | ||||||||
\(926\) | 57.1605 | 1.87841 | ||||||||
\(927\) | −29.5969 | − | 10.4641i | −0.972091 | − | 0.343686i | ||||
\(928\) | 58.6410 | 1.92499 | ||||||||
\(929\) | − | 20.4553i | − | 0.671118i | −0.942019 | − | 0.335559i | \(-0.891075\pi\) | ||
0.942019 | − | 0.335559i | \(-0.108925\pi\) | |||||||
\(930\) | 17.2480 | − | 12.1962i | 0.565583 | − | 0.399928i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 6.21166i | − | 0.203470i | ||||||
\(933\) | 27.1475 | + | 38.3923i | 0.888768 | + | 1.25691i | ||||
\(934\) | − | 43.7128i | − | 1.43033i | ||||||
\(935\) | 2.62536i | 0.0858583i | ||||||||
\(936\) | 5.46410 | + | 1.93185i | 0.178600 | + | 0.0631445i | ||||
\(937\) | 5.78461 | 0.188975 | 0.0944875 | − | 0.995526i | \(-0.469879\pi\) | ||||
0.0944875 | + | 0.995526i | \(0.469879\pi\) | |||||||
\(938\) | 7.20977i | 0.235407i | ||||||||
\(939\) | −35.0507 | + | 24.7846i | −1.14384 | + | 0.808815i | ||||
\(940\) | −25.8564 | −0.843343 | ||||||||
\(941\) | 13.9391 | 0.454400 | 0.227200 | − | 0.973848i | \(-0.427043\pi\) | ||||
0.227200 | + | 0.973848i | \(0.427043\pi\) | |||||||
\(942\) | −9.66025 | + | 6.83083i | −0.314748 | + | 0.222561i | ||||
\(943\) | 2.14359i | 0.0698050i | ||||||||
\(944\) | −37.4259 | −1.21811 | ||||||||
\(945\) | −26.3896 | + | 7.46410i | −0.858453 | + | 0.242807i | ||||
\(946\) | − | 1.66025i | − | 0.0539795i | ||||||
\(947\) | − | 44.2939i | − | 1.43936i | −0.694307 | − | 0.719679i | \(-0.744289\pi\) | ||
0.694307 | − | 0.719679i | \(-0.255711\pi\) | |||||||
\(948\) | 6.12436 | + | 8.66115i | 0.198910 | + | 0.281301i | ||||
\(949\) | − | 11.1962i | − | 0.363442i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.4641 | + | 13.7632i | −0.631167 | + | 0.446302i | ||||
\(952\) | 9.46410i | 0.306733i | ||||||||
\(953\) | −42.6023 | −1.38002 | −0.690011 | − | 0.723798i | \(-0.742395\pi\) | ||||
−0.690011 | + | 0.723798i | \(0.742395\pi\) | |||||||
\(954\) | −11.6603 | + | 32.9802i | −0.377515 | + | 1.06777i | ||||
\(955\) | 2.39230 | 0.0774132 | ||||||||
\(956\) | − | 51.9198i | − | 1.67920i | ||||||
\(957\) | 2.92820 | + | 4.14110i | 0.0946554 | + | 0.133863i | ||||
\(958\) | 22.9282i | 0.740777i | ||||||||
\(959\) | 2.82843i | 0.0913347i | ||||||||
\(960\) | −8.10634 | − | 11.4641i | −0.261631 | − | 0.370002i | ||||
\(961\) | 11.0718 | 0.357155 | ||||||||
\(962\) | 30.7709 | 0.992094 | ||||||||
\(963\) | −4.89898 | + | 13.8564i | −0.157867 | + | 0.446516i | ||||
\(964\) | − | 49.6410i | − | 1.59883i | ||||||
\(965\) | 18.6622 | 0.600757 | ||||||||
\(966\) | 2.73205 | + | 3.86370i | 0.0879023 | + | 0.124313i | ||||
\(967\) | −8.80385 | −0.283113 | −0.141556 | − | 0.989930i | \(-0.545211\pi\) | ||||
−0.141556 | + | 0.989930i | \(0.545211\pi\) | |||||||
\(968\) | 5.61969 | 0.180624 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.3923 | −0.654757 | ||||||||
\(971\) | 14.3452 | 0.460360 | 0.230180 | − | 0.973148i | \(-0.426069\pi\) | ||||
0.230180 | + | 0.973148i | \(0.426069\pi\) | |||||||
\(972\) | −26.9444 | − | 1.73205i | −0.864242 | − | 0.0555556i | ||||
\(973\) | −49.2487 | −1.57884 | ||||||||
\(974\) | 48.1576i | 1.54307i | ||||||||
\(975\) | 11.1962 | + | 15.8338i | 0.358564 | + | 0.507086i | ||||
\(976\) | 15.7846 | 0.505253 | ||||||||
\(977\) | 20.3538 | 0.651176 | 0.325588 | − | 0.945512i | \(-0.394438\pi\) | ||||
0.325588 | + | 0.945512i | \(0.394438\pi\) | |||||||
\(978\) | −14.1962 | + | 10.0382i | −0.453943 | + | 0.320986i | ||||
\(979\) | 2.78461i | 0.0889965i | ||||||||
\(980\) | 16.9706i | 0.542105i | ||||||||
\(981\) | 40.7076 | + | 14.3923i | 1.29969 | + | 0.459511i | ||||
\(982\) | 19.3205i | 0.616542i | ||||||||
\(983\) | −32.5269 | −1.03745 | −0.518724 | − | 0.854942i | \(-0.673593\pi\) | ||||
−0.518724 | + | 0.854942i | \(0.673593\pi\) | |||||||
\(984\) | 4.14110 | − | 2.92820i | 0.132014 | − | 0.0933477i | ||||
\(985\) | −12.9282 | −0.411927 | ||||||||
\(986\) | 73.1330i | 2.32903i | ||||||||
\(987\) | −39.3949 | − | 55.7128i | −1.25395 | − | 1.77336i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.859411i | 0.0273277i | ||||||||
\(990\) | 1.03528 | − | 2.92820i | 0.0329032 | − | 0.0930644i | ||||
\(991\) | 4.17691i | 0.132684i | 0.997797 | + | 0.0663420i | \(0.0211328\pi\) | ||||
−0.997797 | + | 0.0663420i | \(0.978867\pi\) | |||||||
\(992\) | 33.8768i | 1.07559i | ||||||||
\(993\) | 31.9282 | + | 45.1533i | 1.01321 | + | 1.43290i | ||||
\(994\) | 25.8564 | 0.820115 | ||||||||
\(995\) | − | 18.1074i | − | 0.574042i | ||||||
\(996\) | 13.3843 | + | 18.9282i | 0.424097 | + | 0.599763i | ||||
\(997\) | 50.1769 | 1.58912 | 0.794559 | − | 0.607186i | \(-0.207702\pi\) | ||||
0.794559 | + | 0.607186i | \(0.207702\pi\) | |||||||
\(998\) | 31.1499 | 0.986032 | ||||||||
\(999\) | 21.3397 | − | 6.03579i | 0.675160 | − | 0.190964i |
(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 | 1083.2.d.b.1082.1 | 8 | ||
3.2 | odd | 2 | inner | 1083.2.d.b.1082.7 | 8 | ||
19.7 | even | 3 | 57.2.f.a.8.4 | yes | 8 | ||
19.8 | odd | 6 | 57.2.f.a.50.1 | yes | 8 | ||
19.18 | odd | 2 | inner | 1083.2.d.b.1082.8 | 8 | ||
57.8 | even | 6 | 57.2.f.a.50.4 | yes | 8 | ||
57.26 | odd | 6 | 57.2.f.a.8.1 | ✓ | 8 | ||
57.56 | even | 2 | inner | 1083.2.d.b.1082.2 | 8 | ||
76.7 | odd | 6 | 912.2.bn.m.65.2 | 8 | |||
76.27 | even | 6 | 912.2.bn.m.449.1 | 8 | |||
228.83 | even | 6 | 912.2.bn.m.65.1 | 8 | |||
228.179 | odd | 6 | 912.2.bn.m.449.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.f.a.8.1 | ✓ | 8 | 57.26 | odd | 6 | ||
57.2.f.a.8.4 | yes | 8 | 19.7 | even | 3 | ||
57.2.f.a.50.1 | yes | 8 | 19.8 | odd | 6 | ||
57.2.f.a.50.4 | yes | 8 | 57.8 | even | 6 | ||
912.2.bn.m.65.1 | 8 | 228.83 | even | 6 | |||
912.2.bn.m.65.2 | 8 | 76.7 | odd | 6 | |||
912.2.bn.m.449.1 | 8 | 76.27 | even | 6 | |||
912.2.bn.m.449.2 | 8 | 228.179 | odd | 6 | |||
1083.2.d.b.1082.1 | 8 | 1.1 | even | 1 | trivial | ||
1083.2.d.b.1082.2 | 8 | 57.56 | even | 2 | inner | ||
1083.2.d.b.1082.7 | 8 | 3.2 | odd | 2 | inner | ||
1083.2.d.b.1082.8 | 8 | 19.18 | odd | 2 | inner |