Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(575,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.h (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: | \(5.36594701583\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.4 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.575 |
Dual form | 672.2.h.b.575.3 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.41421 | + | 1.00000i | 0.816497 | + | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.24264i | 1.89737i | 0.316228 | + | 0.948683i | \(0.397584\pi\) | ||||
−0.316228 | + | 0.948683i | \(0.602416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24264 | 1.27920 | 0.639602 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639602 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.24264 | + | 6.00000i | −1.09545 | + | 1.54919i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.07107i | − | 1.71499i | −0.514496 | − | 0.857493i | \(-0.672021\pi\) | ||
0.514496 | − | 0.857493i | \(-0.327979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 1.41421i | 0.218218 | − | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.41421 | 0.294884 | 0.147442 | − | 0.989071i | \(-0.452896\pi\) | ||||
0.147442 | + | 0.989071i | \(0.452896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.0000 | −2.60000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.41421 | + | 5.00000i | −0.272166 | + | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843i | 0.525226i | 0.964901 | + | 0.262613i | \(0.0845842\pi\) | ||||
−0.964901 | + | 0.262613i | \(0.915416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | + | 4.24264i | 1.04447 | + | 0.738549i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.24264 | 0.717137 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.82843 | − | 2.00000i | −0.452911 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41421i | 0.220863i | 0.993884 | + | 0.110432i | \(0.0352233\pi\) | ||||
−0.993884 | + | 0.110432i | \(0.964777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.0000 | + | 4.24264i | −1.78885 | + | 0.632456i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.07107 | − | 10.0000i | 0.990148 | − | 1.40028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.65685i | − | 0.777029i | −0.921443 | − | 0.388514i | \(-0.872988\pi\) | ||
0.921443 | − | 0.388514i | \(-0.127012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.0000i | 2.42712i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | + | 5.65685i | −0.529813 | + | 0.749269i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.3137 | 1.47292 | 0.736460 | − | 0.676481i | \(-0.236496\pi\) | ||||
0.736460 | + | 0.676481i | \(0.236496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | − | 1.00000i | 0.356348 | − | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 8.48528i | − | 1.05247i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | + | 1.41421i | 0.240772 | + | 0.170251i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279 | 1.51053 | 0.755263 | − | 0.655422i | \(-0.227509\pi\) | ||||
0.755263 | + | 0.655422i | \(0.227509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.3848 | − | 13.0000i | −2.12289 | − | 1.50111i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.24264i | − | 0.483494i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.00000i | − | 0.450035i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) | ||
0.974355 | − | 0.225018i | \(-0.0722440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.82843 | 0.310460 | 0.155230 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155230 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 30.0000 | 3.25396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.82843 | + | 4.00000i | −0.303239 | + | 0.428845i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.89949i | 1.04934i | 0.851304 | + | 0.524672i | \(0.175812\pi\) | ||||
−0.851304 | + | 0.524672i | \(0.824188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000i | 0.209657i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | + | 2.82843i | −0.207390 | + | 0.293294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.9706 | −1.74114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | + | 12.0000i | 0.426401 | + | 1.20605i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24264i | 0.422159i | 0.977469 | + | 0.211079i | \(0.0676978\pi\) | ||||
−0.977469 | + | 0.211079i | \(0.932302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | + | 4.24264i | 0.585540 | + | 0.414039i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.41421 | 0.136717 | 0.0683586 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683586 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.65685 | − | 4.00000i | −0.536925 | − | 0.379663i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.3137i | − | 1.06430i | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||
0.846649 | − | 0.532152i | \(-0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000i | 0.559503i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | − | 5.65685i | −0.184900 | − | 0.522976i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.07107 | −0.648204 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.41421 | + | 2.00000i | −0.127515 | + | 0.180334i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 33.9411i | − | 3.03579i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.0000i | − | 1.06483i | −0.846484 | − | 0.532414i | \(-0.821285\pi\) | ||
0.846484 | − | 0.532414i | \(-0.178715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | − | 11.3137i | 0.704361 | − | 0.996116i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.48528 | 0.741362 | 0.370681 | − | 0.928760i | \(-0.379124\pi\) | ||||
0.370681 | + | 0.928760i | \(0.379124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.2132 | − | 6.00000i | −1.82574 | − | 0.516398i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.48528i | 0.724947i | 0.931994 | + | 0.362473i | \(0.118068\pi\) | ||||
−0.931994 | + | 0.362473i | \(0.881932\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | − | 2.82843i | −0.336861 | − | 0.238197i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.48528 | −0.709575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.41421 | − | 1.00000i | −0.116642 | − | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 24.0000i | − | 1.95309i | −0.215308 | − | 0.976546i | \(-0.569076\pi\) | ||
0.215308 | − | 0.976546i | \(-0.430924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.0000 | − | 7.07107i | 1.61690 | − | 0.571662i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.48528 | −0.681554 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.65685 | − | 8.00000i | 0.448618 | − | 0.634441i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.41421i | − | 0.111456i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.0000 | + | 25.4558i | −1.40130 | + | 1.98173i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.7990 | 1.53209 | 0.766046 | − | 0.642786i | \(-0.222221\pi\) | ||||
0.766046 | + | 0.642786i | \(0.222221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.3137 | + | 4.00000i | −0.865181 | + | 0.305888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.07107i | − | 0.537603i | −0.963196 | − | 0.268802i | \(-0.913372\pi\) | ||
0.963196 | − | 0.268802i | \(-0.0866276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.0000i | 0.982708i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | + | 11.3137i | 1.20263 | + | 0.850390i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5563 | −1.16274 | −0.581368 | − | 0.813641i | \(-0.697482\pi\) | ||||
−0.581368 | + | 0.813641i | \(0.697482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.82843 | − | 2.00000i | −0.209083 | − | 0.147844i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 16.9706i | − | 1.24770i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 30.0000i | − | 2.19382i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.00000 | + | 1.41421i | 0.363696 | + | 0.102869i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41421 | −0.102329 | −0.0511645 | − | 0.998690i | \(-0.516293\pi\) | ||||
−0.0511645 | + | 0.998690i | \(0.516293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.48528 | − | 12.0000i | 0.607644 | − | 0.859338i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.65685i | 0.403034i | 0.979485 | + | 0.201517i | \(0.0645872\pi\) | ||||
−0.979485 | + | 0.201517i | \(0.935413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.00000i | − | 0.567105i | −0.958957 | − | 0.283552i | \(-0.908487\pi\) | ||
0.958957 | − | 0.283552i | \(-0.0915130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | − | 11.3137i | 0.564276 | − | 0.798007i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.82843 | 0.198517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.41421 | + | 4.00000i | 0.0982946 | + | 0.278019i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.9706i | 1.17388i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.00000i | − | 0.550743i | −0.961338 | − | 0.275371i | \(-0.911199\pi\) | ||
0.961338 | − | 0.275371i | \(-0.0888008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.0000 | + | 12.7279i | 1.23334 | + | 0.872103i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33.9411 | 2.31477 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.7990 | + | 14.0000i | 1.33789 | + | 0.946032i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.1421i | 0.951303i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0000 | − | 36.7696i | −0.866667 | − | 2.45130i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −30.0000 | −1.98246 | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.24264 | − | 6.00000i | 0.279145 | − | 0.394771i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.7990i | 1.29707i | 0.761183 | + | 0.648537i | \(0.224619\pi\) | ||||
−0.761183 | + | 0.648537i | \(0.775381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.0000i | − | 0.782794i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | − | 5.65685i | 0.259828 | − | 0.367452i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3848 | 1.18921 | 0.594606 | − | 0.804017i | \(-0.297308\pi\) | ||||
0.594606 | + | 0.804017i | \(0.297308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0000 | −1.15948 | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5563 | + | 1.00000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 4.24264i | − | 0.271052i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.00000i | − | 0.509028i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | + | 2.82843i | 0.253490 | + | 0.179244i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.65685 | −0.357057 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 42.4264 | + | 30.0000i | 2.65684 | + | 1.87867i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.41421i | 0.0882162i | 0.999027 | + | 0.0441081i | \(0.0140446\pi\) | ||||
−0.999027 | + | 0.0441081i | \(0.985955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.00000 | + | 2.82843i | −0.495188 | + | 0.175075i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.6985 | −1.83129 | −0.915644 | − | 0.401991i | \(-0.868318\pi\) | ||||
−0.915644 | + | 0.401991i | \(0.868318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0000 | 1.47431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.89949 | + | 14.0000i | −0.605839 | + | 0.856786i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 15.5563i | − | 0.948487i | −0.880394 | − | 0.474244i | \(-0.842722\pi\) | ||
0.880394 | − | 0.474244i | \(-0.157278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.0000i | − | 1.33640i | −0.743980 | − | 0.668202i | \(-0.767064\pi\) | ||
0.743980 | − | 0.668202i | \(-0.232936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | + | 2.82843i | −0.121046 | + | 0.171184i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −55.1543 | −3.32593 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65685 | + | 2.00000i | −0.338667 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.7990i | − | 1.18111i | −0.806998 | − | 0.590554i | \(-0.798909\pi\) | ||
0.806998 | − | 0.590554i | \(-0.201091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000i | 1.18888i | 0.804141 | + | 0.594438i | \(0.202626\pi\) | ||||
−0.804141 | + | 0.594438i | \(0.797374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0000 | − | 16.9706i | −1.42164 | − | 1.00525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.41421 | 0.0834784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.0000 | −1.94118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1421 | − | 10.0000i | −0.829027 | − | 0.586210i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.5269i | 1.90024i | 0.311881 | + | 0.950121i | \(0.399041\pi\) | ||||
−0.311881 | + | 0.950121i | \(0.600959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.0000i | 2.79467i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.00000 | + | 21.2132i | −0.348155 | + | 1.23091i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.24264 | + | 6.00000i | −0.243733 | + | 0.344691i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.48528i | − | 0.485866i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | + | 8.48528i | −0.341328 | + | 0.482711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.7990 | −1.12270 | −0.561349 | − | 0.827579i | \(-0.689717\pi\) | ||||
−0.561349 | + | 0.827579i | \(0.689717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | 0.113047 | 0.0565233 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565233 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.24264 | + | 12.0000i | 0.239046 | + | 0.676123i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 11.3137i | − | 0.635441i | −0.948184 | − | 0.317721i | \(-0.897083\pi\) | ||
0.948184 | − | 0.317721i | \(-0.102917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000i | 0.671871i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00000 | + | 1.41421i | 0.111629 | + | 0.0789337i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.2843 | 1.57378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.0000 | 1.44222 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.82843 | + | 2.00000i | 0.156412 | + | 0.110600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.82843i | 0.155936i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000i | 1.09930i | 0.835395 | + | 0.549650i | \(0.185239\pi\) | ||||
−0.835395 | + | 0.549650i | \(0.814761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | − | 11.3137i | −0.219199 | − | 0.619987i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.9411 | 1.85440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3137 | − | 16.0000i | 0.614476 | − | 0.869001i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.48528i | 0.459504i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | + | 8.48528i | −0.323029 | + | 0.456832i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.07107 | 0.379595 | 0.189797 | − | 0.981823i | \(-0.439217\pi\) | ||||
0.189797 | + | 0.981823i | \(0.439217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82843 | − | 10.0000i | 0.150970 | − | 0.533761i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7279i | 0.677439i | 0.940887 | + | 0.338719i | \(0.109994\pi\) | ||||
−0.940887 | + | 0.338719i | \(0.890006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 54.0000i | 2.86602i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.0000 | − | 7.07107i | −0.529256 | − | 0.374241i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3848 | 0.970311 | 0.485156 | − | 0.874428i | \(-0.338763\pi\) | ||||
0.485156 | + | 0.874428i | \(0.338763\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.89949 | + | 7.00000i | 0.519589 | + | 0.367405i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 59.3970i | 3.10898i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.0000i | − | 1.25279i | −0.779506 | − | 0.626395i | \(-0.784530\pi\) | ||
0.779506 | − | 0.626395i | \(-0.215470\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.00000 | + | 1.41421i | −0.208232 | + | 0.0736210i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.65685 | −0.293689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000 | 0.724893 | 0.362446 | − | 0.932005i | \(-0.381942\pi\) | ||||
0.362446 | + | 0.932005i | \(0.381942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 33.9411 | − | 48.0000i | 1.75271 | − | 2.47871i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.65685i | − | 0.291343i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0000 | − | 16.9706i | 0.614779 | − | 0.869428i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.9411 | −1.73431 | −0.867155 | − | 0.498038i | \(-0.834054\pi\) | ||||
−0.867155 | + | 0.498038i | \(0.834054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | 0.917365 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.6274 | − | 8.00000i | 1.15022 | − | 0.406663i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.4558i | 1.29066i | 0.763903 | + | 0.645331i | \(0.223281\pi\) | ||||
−0.763903 | + | 0.645331i | \(0.776719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.0000i | − | 0.505722i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | + | 8.48528i | 0.605320 | + | 0.428026i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.9706 | 0.853882 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.65685 | + | 4.00000i | 0.283197 | + | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.48528i | − | 0.423735i | −0.977298 | − | 0.211867i | \(-0.932046\pi\) | ||
0.977298 | − | 0.211867i | \(-0.0679545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.00000i | − | 0.199254i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.0000 | − | 29.6985i | −1.19257 | − | 1.47573i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9706 | −0.841200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.0000 | −1.68119 | −0.840596 | − | 0.541663i | \(-0.817795\pi\) | ||||
−0.840596 | + | 0.541663i | \(0.817795\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.48528 | + | 12.0000i | −0.418548 | + | 0.591916i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 11.3137i | − | 0.556711i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000i | 0.589057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | + | 14.1421i | −0.489702 | + | 0.692543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.65685 | −0.276355 | −0.138178 | − | 0.990407i | \(-0.544125\pi\) | ||||
−0.138178 | + | 0.990407i | \(0.544125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | − | 8.00000i | −0.137523 | − | 0.388973i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 91.9239i | 4.45896i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000i | 0.0967868i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | − | 8.48528i | −0.579365 | − | 0.409673i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5563 | 0.749323 | 0.374661 | − | 0.927162i | \(-0.377759\pi\) | ||||
0.374661 | + | 0.927162i | \(0.377759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.0000 | 1.63394 | 0.816968 | − | 0.576683i | \(-0.195653\pi\) | ||||
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.9706 | − | 12.0000i | −0.813676 | − | 0.575356i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.65685i | 0.270604i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000i | 0.763638i | 0.924237 | + | 0.381819i | \(0.124702\pi\) | ||||
−0.924237 | + | 0.381819i | \(0.875298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | − | 2.82843i | −0.0476190 | − | 0.134687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.07107 | −0.335957 | −0.167978 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167978 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −42.0000 | −1.99099 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.65685i | − | 0.266963i | −0.991051 | − | 0.133482i | \(-0.957384\pi\) | ||
0.991051 | − | 0.133482i | \(-0.0426157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000i | 0.282529i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.0000 | − | 33.9411i | 1.12762 | − | 1.59469i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.48528 | −0.397796 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.3553 | + | 10.0000i | 1.65025 | + | 0.466760i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9.89949i | − | 0.461065i | −0.973065 | − | 0.230533i | \(-0.925953\pi\) | ||
0.973065 | − | 0.230533i | \(-0.0740469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.00000i | − | 0.371792i | −0.982569 | − | 0.185896i | \(-0.940481\pi\) | ||
0.982569 | − | 0.185896i | \(-0.0595187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.0000 | − | 8.48528i | −0.556487 | − | 0.393496i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.3137 | 0.523536 | 0.261768 | − | 0.965131i | \(-0.415694\pi\) | ||||
0.261768 | + | 0.965131i | \(0.415694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.7990 | + | 14.0000i | 0.912289 | + | 0.645086i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 33.9411i | − | 1.56061i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 52.0000i | − | 2.38592i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.0000 | − | 5.65685i | 0.732590 | − | 0.259010i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.41421 | − | 2.00000i | 0.0643489 | − | 0.0910032i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 42.4264i | − | 1.92648i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000i | 0.362515i | 0.983436 | + | 0.181257i | \(0.0580167\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | + | 5.65685i | −0.180886 | + | 0.255812i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.3848 | −0.829693 | −0.414847 | − | 0.909891i | \(-0.636165\pi\) | ||||
−0.414847 | + | 0.909891i | \(0.636165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −50.9117 | + | 18.0000i | −2.28831 | + | 0.809040i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 12.7279i | − | 0.570925i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 36.0000i | − | 1.61158i | −0.592200 | − | 0.805791i | \(-0.701741\pi\) | ||
0.592200 | − | 0.805791i | \(-0.298259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.0000 | + | 19.7990i | 1.25095 | + | 0.884554i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.9411 | −1.51336 | −0.756680 | − | 0.653785i | \(-0.773180\pi\) | ||||
−0.756680 | + | 0.653785i | \(0.773180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7279 | − | 9.00000i | −0.565267 | − | 0.399704i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.0416i | 1.06563i | 0.846233 | + | 0.532813i | \(0.178865\pi\) | ||||
−0.846233 | + | 0.532813i | \(0.821135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.0000i | − | 0.619324i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0000 | − | 5.65685i | −0.883022 | − | 0.249756i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.4558 | −1.12172 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | −0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.07107 | − | 10.0000i | 0.310385 | − | 0.438951i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.8701i | − | 1.17720i | −0.808425 | − | 0.588599i | \(-0.799680\pi\) | ||
0.808425 | − | 0.588599i | \(-0.200320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 26.0000i | − | 1.13690i | −0.822718 | − | 0.568450i | \(-0.807543\pi\) | ||
0.822718 | − | 0.568450i | \(-0.192457\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.0000 | + | 18.3848i | −0.567367 | + | 0.802377i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.1421 | 0.616041 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3137 | + | 32.0000i | 0.490973 | + | 1.38868i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.82843i | − | 0.122513i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000i | 0.259403i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.0000 | − | 15.5563i | −0.949370 | − | 0.671306i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.24264 | −0.182743 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0000 | −1.37579 | −0.687894 | − | 0.725811i | \(-0.741464\pi\) | ||||
−0.687894 | + | 0.725811i | \(0.741464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.48528 | + | 6.00000i | 0.364138 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.48528i | 0.363470i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000i | 1.36822i | 0.729378 | + | 0.684111i | \(0.239809\pi\) | ||||
−0.729378 | + | 0.684111i | \(0.760191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | − | 5.65685i | −0.0853579 | − | 0.241429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3137 | −0.481980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.9706 | − | 24.0000i | 0.720360 | − | 1.01874i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 22.6274i | − | 0.958754i | −0.877609 | − | 0.479377i | \(-0.840863\pi\) | ||
0.877609 | − | 0.479377i | \(-0.159137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000i | 0.676728i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.0000 | − | 42.4264i | 1.26660 | − | 1.79124i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.3137 | −0.476816 | −0.238408 | − | 0.971165i | \(-0.576626\pi\) | ||||
−0.238408 | + | 0.971165i | \(0.576626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48.0000 | 2.01938 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.65685 | + | 7.00000i | 0.237566 | + | 0.293972i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.7990i | 0.830017i | 0.909818 | + | 0.415008i | \(0.136221\pi\) | ||||
−0.909818 | + | 0.415008i | \(0.863779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 32.0000i | − | 1.33916i | −0.742741 | − | 0.669579i | \(-0.766474\pi\) | ||
0.742741 | − | 0.669579i | \(-0.233526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.00000 | − | 1.41421i | −0.0835512 | − | 0.0590796i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.3848 | −0.766698 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.65685 | − | 4.00000i | −0.235091 | − | 0.166234i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.82843i | − | 0.117343i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.0000i | − | 0.993978i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | − | 8.48528i | 0.992278 | − | 0.350823i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.2843 | −1.16742 | −0.583708 | − | 0.811963i | \(-0.698399\pi\) | ||||
−0.583708 | + | 0.811963i | \(0.698399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.65685 | + | 8.00000i | −0.232692 | + | 0.329076i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.41421i | − | 0.0580748i | −0.999578 | − | 0.0290374i | \(-0.990756\pi\) | ||
0.999578 | − | 0.0290374i | \(-0.00924419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 30.0000i | − | 1.22988i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00000 | − | 11.3137i | 0.327418 | − | 0.463039i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.89949 | −0.404482 | −0.202241 | − | 0.979336i | \(-0.564822\pi\) | ||||
−0.202241 | + | 0.979336i | \(0.564822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.6274 | − | 8.00000i | 0.921460 | − | 0.325785i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.6985i | 1.20742i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.0000i | − | 0.974130i | −0.873366 | − | 0.487065i | \(-0.838067\pi\) | ||
0.873366 | − | 0.487065i | \(-0.161933\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | + | 2.82843i | 0.162088 | + | 0.114614i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.65685 | 0.228852 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.48528 | − | 6.00000i | −0.342160 | − | 0.241943i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.1421i | − | 0.569341i | −0.958625 | − | 0.284670i | \(-0.908116\pi\) | ||
0.958625 | − | 0.284670i | \(-0.0918842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.0000i | 1.20580i | 0.797816 | + | 0.602901i | \(0.205989\pi\) | ||||
−0.797816 | + | 0.602901i | \(0.794011\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | + | 7.07107i | −0.0802572 | + | 0.283752i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.89949 | 0.396615 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 79.0000 | 3.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.9706 | + | 24.0000i | −0.677739 | + | 0.958468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.2843i | 1.12777i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.00000 | − | 11.3137i | 0.317971 | − | 0.449680i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 50.9117 | 2.02037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.7279 | + | 36.0000i | 0.503509 | + | 1.42414i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 25.4558i | − | 1.00545i | −0.864448 | − | 0.502723i | \(-0.832332\pi\) | ||
0.864448 | − | 0.502723i | \(-0.167668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.0000i | − | 1.73519i | −0.497271 | − | 0.867595i | \(-0.665665\pi\) | ||
0.497271 | − | 0.867595i | \(-0.334335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.0000 | + | 33.9411i | 1.89000 | + | 1.33643i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.82843 | −0.111197 | −0.0555985 | − | 0.998453i | \(-0.517707\pi\) | ||||
−0.0555985 | + | 0.998453i | \(0.517707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.0000 | 1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.82843 | + | 2.00000i | 0.110855 | + | 0.0783862i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14.1421i | − | 0.553425i | −0.960953 | − | 0.276712i | \(-0.910755\pi\) | ||
0.960953 | − | 0.276712i | \(-0.0892449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.0000i | 1.40664i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.0000 | + | 39.5980i | 0.546192 | + | 1.54486i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.07107 | 0.275450 | 0.137725 | − | 0.990471i | \(-0.456021\pi\) | ||||
0.137725 | + | 0.990471i | \(0.456021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −50.0000 | −1.94477 | −0.972387 | − | 0.233373i | \(-0.925024\pi\) | ||||
−0.972387 | + | 0.233373i | \(0.925024\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.1421 | + | 20.0000i | −0.549235 | + | 0.776736i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.9706i | 0.658090i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000i | 0.154881i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | − | 11.3137i | 0.309298 | − | 0.437413i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.48528 | −0.327571 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.3848 | − | 65.0000i | 0.707630 | − | 2.50185i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.89949i | − | 0.380468i | −0.981739 | − | 0.190234i | \(-0.939075\pi\) | ||
0.981739 | − | 0.190234i | \(-0.0609248\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000i | 0.383765i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.07107 | −0.270567 | −0.135283 | − | 0.990807i | \(-0.543195\pi\) | ||||
−0.135283 | + | 0.990807i | \(0.543195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | −1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −42.4264 | − | 30.0000i | −1.61867 | − | 1.14457i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3137i | 0.431018i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.0000i | − | 0.532585i | −0.963892 | − | 0.266293i | \(-0.914201\pi\) | ||
0.963892 | − | 0.266293i | \(-0.0857987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0000 | − | 4.24264i | 0.455842 | − | 0.161165i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42.4264 | −1.60933 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0000 | 0.378777 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.7990 | + | 28.0000i | −0.748867 | + | 1.05906i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.4558i | 0.961454i | 0.876870 | + | 0.480727i | \(0.159627\pi\) | ||||
−0.876870 | + | 0.480727i | \(0.840373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.0000i | − | 0.603451i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.0000 | − | 16.9706i | 0.451946 | − | 0.639148i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.24264 | 0.159561 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3137 | − | 4.00000i | 0.424297 | − | 0.150012i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.82843i | 0.105925i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 36.0000i | − | 1.34632i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.0000 | + | 18.3848i | 0.970988 | + | 0.686592i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.6274 | 0.843860 | 0.421930 | − | 0.906628i | \(-0.361353\pi\) | ||||
0.421930 | + | 0.906628i | \(0.361353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.4558 | − | 18.0000i | −0.946713 | − | 0.669427i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 36.7696i | − | 1.36559i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.0000i | 1.26099i | 0.776193 | + | 0.630495i | \(0.217148\pi\) | ||||
−0.776193 | + | 0.630495i | \(0.782852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −56.5685 | −2.09226 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0000 | −0.517102 | −0.258551 | − | 0.965998i | \(-0.583245\pi\) | ||||
−0.258551 | + | 0.965998i | \(0.583245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.24264 | − | 6.00000i | 0.156492 | − | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 33.9411i | − | 1.25024i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000i | 0.147142i | 0.997290 | + | 0.0735712i | \(0.0234396\pi\) | ||||
−0.997290 | + | 0.0735712i | \(0.976560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.00000 | − | 11.3137i | 0.293887 | − | 0.415619i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.41421 | −0.0518825 | −0.0259412 | − | 0.999663i | \(-0.508258\pi\) | ||||
−0.0259412 | + | 0.999663i | \(0.508258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.82843 | + | 8.00000i | 0.103487 | + | 0.292705i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.41421i | − | 0.0516742i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36.0000i | − | 1.31366i | −0.754039 | − | 0.656829i | \(-0.771897\pi\) | ||
0.754039 | − | 0.656829i | \(-0.228103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.00000 | − | 5.65685i | −0.291536 | − | 0.206147i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 101.823 | 3.70573 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.0000 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.48528 | + | 6.00000i | 0.307996 | + | 0.217786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 21.2132i | − | 0.768978i | −0.923130 | − | 0.384489i | \(-0.874378\pi\) | ||
0.923130 | − | 0.384489i | \(-0.125622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.00000i | − | 0.0724049i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30.0000 | + | 84.8528i | 1.08465 | + | 3.06786i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.6274 | −0.817029 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.41421 | + | 2.00000i | −0.0509317 | + | 0.0720282i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 32.5269i | − | 1.16991i | −0.811065 | − | 0.584956i | \(-0.801112\pi\) | ||
0.811065 | − | 0.584956i | \(-0.198888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 26.0000i | − | 0.933948i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.00000 | + | 5.65685i | −0.143499 | + | 0.202939i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.65685 | −0.202678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.0000 | 1.93227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.1421 | − | 4.00000i | −0.505399 | − | 0.142948i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 59.3970i | 2.11997i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0000i | 0.784215i | 0.919919 | + | 0.392108i | \(0.128254\pi\) | ||||
−0.919919 | + | 0.392108i | \(0.871746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42.0000 | − | 29.6985i | −1.49524 | − | 1.05729i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.3137 | −0.402269 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.9411 | + | 24.0000i | 1.20377 | + | 0.851192i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 32.5269i | − | 1.15216i | −0.817392 | − | 0.576081i | \(-0.804581\pi\) | ||
0.817392 | − | 0.576081i | \(-0.195419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0000i | 0.707549i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.0000 | + | 9.89949i | −0.989331 | + | 0.349781i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59.3970 | 2.09607 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.00000 | 0.211472 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5563 | − | 22.0000i | 0.547609 | − | 0.774437i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.65685i | 0.198884i | 0.995043 | + | 0.0994422i | \(0.0317058\pi\) | ||||
−0.995043 | + | 0.0994422i | \(0.968294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000i | 1.05344i | 0.850038 | + | 0.526721i | \(0.176579\pi\) | ||||
−0.850038 | + | 0.526721i | \(0.823421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.0000 | − | 31.1127i | 0.771574 | − | 1.09117i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9706 | −0.594453 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.0000 | 1.11954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.65685 | + | 2.00000i | −0.197666 | + | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2843i | 0.987128i | 0.869710 | + | 0.493564i | \(0.164306\pi\) | ||||
−0.869710 | + | 0.493564i | \(0.835694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.0000i | 1.81261i | 0.422628 | + | 0.906303i | \(0.361108\pi\) | ||||
−0.422628 | + | 0.906303i | \(0.638892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −78.0000 | − | 55.1543i | −2.71561 | − | 1.92023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.1838 | 1.32778 | 0.663890 | − | 0.747830i | \(-0.268904\pi\) | ||||
0.663890 | + | 0.747830i | \(0.268904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.07107i | 0.244998i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 84.0000i | 2.90694i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0000 | − | 2.82843i | −0.345651 | − | 0.0977647i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.7401 | −1.85531 | −0.927657 | − | 0.373432i | \(-0.878181\pi\) | ||||
−0.927657 | + | 0.373432i | \(0.878181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.7990 | − | 28.0000i | 0.681913 | − | 0.964371i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 38.1838i | − | 1.31356i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.00000i | − | 0.240523i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0000 | + | 28.2843i | −0.686398 | + | 0.970714i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.65685 | −0.193914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.0000 | −1.57501 | −0.787505 | − | 0.616308i | \(-0.788628\pi\) | ||||
−0.787505 | + | 0.616308i | \(0.788628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.9706 | − | 48.0000i | −0.580381 | − | 1.64157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 21.2132i | − | 0.724629i | −0.932056 | − | 0.362315i | \(-0.881987\pi\) | ||
0.932056 | − | 0.362315i | \(-0.118013\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0000i | 0.409435i | 0.978821 | + | 0.204717i | \(0.0656275\pi\) | ||||
−0.978821 | + | 0.204717i | \(0.934372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.00000 | + | 1.41421i | 0.0681598 | + | 0.0481963i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.4975 | −1.68491 | −0.842457 | − | 0.538764i | \(-0.818892\pi\) | ||||
−0.842457 | + | 0.538764i | \(0.818892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.0000 | 1.02003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −46.6690 | − | 33.0000i | −1.58496 | − | 1.12074i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16.9706i | − | 0.575687i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000i | 0.542139i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.0000 | − | 28.2843i | −0.338449 | − | 0.957278i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33.9411 | −1.14742 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.0000 | 0.607817 | 0.303908 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.5269 | + | 46.0000i | −1.09711 | + | 1.55154i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7279i | 0.428815i | 0.976744 | + | 0.214407i | \(0.0687820\pi\) | ||||
−0.976744 | + | 0.214407i | \(0.931218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.0000i | − | 1.21150i | −0.795656 | − | 0.605748i | \(-0.792874\pi\) | ||
0.795656 | − | 0.605748i | \(-0.207126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −48.0000 | + | 67.8823i | −1.61350 | + | 2.28184i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.7696 | 1.23460 | 0.617300 | − | 0.786728i | \(-0.288226\pi\) | ||||
0.617300 | + | 0.786728i | \(0.288226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.6985 | + | 24.0000i | −0.994937 | + | 0.804030i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 11.3137i | − | 0.378599i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 66.0000i | − | 2.20614i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.00000 | − | 2.82843i | −0.133556 | − | 0.0944384i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.65685 | −0.188667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.0000 | −1.33259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.3137 | − | 8.00000i | −0.376497 | − | 0.266223i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.4558i | 0.846181i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.0000i | 0.398453i | 0.979953 | + | 0.199227i | \(0.0638430\pi\) | ||||
−0.979953 | + | 0.199227i | \(0.936157\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.0000 | + | 4.24264i | −0.398015 | + | 0.140720i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.3259 | 1.73363 | 0.866817 | − | 0.498626i | \(-0.166162\pi\) | ||||
0.866817 | + | 0.498626i | \(0.166162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.48528 | − | 12.0000i | 0.280515 | − | 0.396708i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 8.48528i | − | 0.280209i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000i | 0.659739i | 0.944027 | + | 0.329870i | \(0.107005\pi\) | ||||
−0.944027 | + | 0.329870i | \(0.892995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | + | 28.2843i | −0.659022 | + | 0.931998i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.4558 | −0.837889 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 52.0000 | 1.70975 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9706 | + | 6.00000i | −0.557386 | + | 0.197066i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.89949i | − | 0.324792i | −0.986726 | − | 0.162396i | \(-0.948078\pi\) | ||
0.986726 | − | 0.162396i | \(-0.0519222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.00000i | − | 0.131095i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.0000 | − | 19.7990i | −0.916679 | − | 0.648190i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 127.279 | 4.16248 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.82843 | + | 2.00000i | 0.0923022 | + | 0.0652675i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.89949i | 0.322714i | 0.986896 | + | 0.161357i | \(0.0515871\pi\) | ||||
−0.986896 | + | 0.161357i | \(0.948413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00000i | 0.0651290i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.00000 | + | 21.2132i | −0.195180 | + | 0.690066i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.4975 | 1.60845 | 0.804226 | − | 0.594324i | \(-0.202580\pi\) | ||||
0.804226 | + | 0.594324i | \(0.202580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0000 | −0.908918 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3137 | − | 16.0000i | 0.366872 | − | 0.518836i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33.9411i | − | 1.09946i | −0.835342 | − | 0.549730i | \(-0.814730\pi\) | ||
0.835342 | − | 0.549730i | \(-0.185270\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 6.00000i | − | 0.194155i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0000 | + | 16.9706i | −0.387905 | + | 0.548580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.48528 | 0.274004 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.41421 | + | 4.00000i | 0.0455724 | + | 0.128898i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 16.9706i | − | 0.546302i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000i | 0.643157i | 0.946883 | + | 0.321578i | \(0.104213\pi\) | ||||
−0.946883 | + | 0.321578i | \(0.895787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 40.0000 | + | 28.2843i | 1.28499 | + | 0.908622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.7990 | 0.635380 | 0.317690 | − | 0.948195i | \(-0.397093\pi\) | ||||
0.317690 | + | 0.948195i | \(0.397093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | 0.320585 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 36.7696 | + | 26.0000i | 1.17757 | + | 0.832666i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.7401i | 1.71930i | 0.510885 | + | 0.859649i | \(0.329318\pi\) | ||||
−0.510885 | + | 0.859649i | \(0.670682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.0000i | 1.34233i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | + | 5.65685i | 0.0638551 | + | 0.180609i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.2843 | 0.902128 | 0.451064 | − | 0.892492i | \(-0.351045\pi\) | ||||
0.451064 | + | 0.892492i | \(0.351045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0000 | −0.764704 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.82843 | + | 4.00000i | −0.0900298 | + | 0.127321i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 11.3137i | − | 0.359755i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0000i | 0.889449i | 0.895667 | + | 0.444725i | \(0.146698\pi\) | ||||
−0.895667 | + | 0.444725i | \(0.853302\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.0000 | + | 28.2843i | −0.634681 | + | 0.897574i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.9411 | 1.07601 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0000 | 0.570066 | 0.285033 | − | 0.958518i | \(-0.407995\pi\) | ||||
0.285033 | + | 0.958518i | \(0.407995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.65685 | − | 20.0000i | 0.178975 | − | 0.632772i |
(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 | 672.2.h.b.575.4 | yes | 4 | |
3.2 | odd | 2 | inner | 672.2.h.b.575.2 | yes | 4 | |
4.3 | odd | 2 | inner | 672.2.h.b.575.1 | ✓ | 4 | |
8.3 | odd | 2 | 1344.2.h.d.575.4 | 4 | |||
8.5 | even | 2 | 1344.2.h.d.575.1 | 4 | |||
12.11 | even | 2 | inner | 672.2.h.b.575.3 | yes | 4 | |
24.5 | odd | 2 | 1344.2.h.d.575.3 | 4 | |||
24.11 | even | 2 | 1344.2.h.d.575.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.h.b.575.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
672.2.h.b.575.2 | yes | 4 | 3.2 | odd | 2 | inner | |
672.2.h.b.575.3 | yes | 4 | 12.11 | even | 2 | inner | |
672.2.h.b.575.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1344.2.h.d.575.1 | 4 | 8.5 | even | 2 | |||
1344.2.h.d.575.2 | 4 | 24.11 | even | 2 | |||
1344.2.h.d.575.3 | 4 | 24.5 | odd | 2 | |||
1344.2.h.d.575.4 | 4 | 8.3 | odd | 2 |