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 | 575.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.575 |
Dual form | 672.2.h.c.575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 2.82843i | 0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | − | 2.00000i | −0.365148 | − | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421i | 0.342997i | 0.985184 | + | 0.171499i | \(0.0548609\pi\) | ||||
−0.985184 | + | 0.171499i | \(0.945139\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | −7.07107 | −1.47442 | −0.737210 | − | 0.675664i | \(-0.763857\pi\) | ||||
−0.737210 | + | 0.675664i | \(0.763857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.41421 | + | 5.00000i | 0.272166 | + | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528i | 1.57568i | 0.615882 | + | 0.787839i | \(0.288800\pi\) | ||||
−0.615882 | + | 0.787839i | \(0.711200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | + | 1.41421i | −0.348155 | + | 0.246183i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421 | 0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.48528 | + | 6.00000i | −1.35873 | + | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24264i | 0.662589i | 0.943527 | + | 0.331295i | \(0.107485\pi\) | ||||
−0.943527 | + | 0.331295i | \(0.892515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.00000 | + | 1.41421i | 0.596285 | + | 0.210819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.41421 | − | 2.00000i | −0.198030 | − | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.65685i | − | 0.777029i | −0.921443 | − | 0.388514i | \(-0.872988\pi\) | ||
0.921443 | − | 0.388514i | \(-0.127012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000i | 0.269680i | ||||||||
\(56\) | 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 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82843 | − | 1.00000i | −0.356348 | − | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.48528i | 1.05247i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.0000i | 1.95471i | 0.211604 | + | 0.977356i | \(0.432131\pi\) | ||||
−0.211604 | + | 0.977356i | \(0.567869\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.0000 | − | 7.07107i | 1.20386 | − | 0.851257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.24264 | 0.503509 | 0.251754 | − | 0.967791i | \(-0.418992\pi\) | ||||
0.251754 | + | 0.967791i | \(0.418992\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.24264 | + | 3.00000i | −0.489898 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.41421i | − | 0.161165i | ||||||
\(78\) | 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 | ||||||||
\(83\) | 8.48528 | 0.931381 | 0.465690 | − | 0.884948i | \(-0.345806\pi\) | ||||
0.465690 | + | 0.884948i | \(0.345806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.48528 | − | 12.0000i | −0.909718 | − | 1.28654i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.07107i | 0.749532i | 0.927119 | + | 0.374766i | \(0.122277\pi\) | ||||
−0.927119 | + | 0.374766i | \(0.877723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.00000i | − | 0.628971i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 2.82843i | −0.207390 | − | 0.293294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.65685 | −0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.41421 | − | 4.00000i | 0.142134 | − | 0.402015i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.41421i | 0.140720i | 0.997522 | + | 0.0703598i | \(0.0224147\pi\) | ||||
−0.997522 | + | 0.0703598i | \(0.977585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.0000i | − | 0.985329i | −0.870219 | − | 0.492665i | \(-0.836023\pi\) | ||
0.870219 | − | 0.492665i | \(-0.163977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | + | 1.41421i | −0.195180 | + | 0.138013i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5563 | 1.50389 | 0.751945 | − | 0.659226i | \(-0.229116\pi\) | ||||
0.751945 | + | 0.659226i | \(0.229116\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.65685 | − | 4.00000i | 0.536925 | − | 0.379663i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 10.0000i | − | 0.932505i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | − | 16.9706i | 0.554700 | − | 1.56893i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.41421 | 0.129641 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.24264 | − | 6.00000i | −0.382546 | − | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.0000i | − | 1.06483i | −0.846484 | − | 0.532414i | \(-0.821285\pi\) | ||
0.846484 | − | 0.532414i | \(-0.178715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.7990 | −1.72985 | −0.864923 | − | 0.501905i | \(-0.832633\pi\) | ||||
−0.864923 | + | 0.501905i | \(0.832633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.07107 | + | 2.00000i | −0.608581 | + | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 19.7990i | − | 1.69154i | −0.533546 | − | 0.845771i | \(-0.679141\pi\) | ||
0.533546 | − | 0.845771i | \(-0.320859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.00000i | − | 0.508913i | −0.967084 | − | 0.254457i | \(-0.918103\pi\) | ||
0.967084 | − | 0.254457i | \(-0.0818966\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | − | 11.3137i | − | 0.926855i | −0.886135 | − | 0.463428i | \(-0.846619\pi\) | ||
0.886135 | − | 0.463428i | \(-0.153381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000i | 0.651031i | 0.945537 | + | 0.325515i | \(0.105538\pi\) | ||||
−0.945537 | + | 0.325515i | \(0.894462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | + | 1.41421i | 0.323381 | + | 0.114332i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.82843 | −0.227185 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.65685 | + | 8.00000i | 0.448618 | + | 0.634441i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.07107i | 0.557278i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00000 | − | 2.82843i | −0.155700 | − | 0.220193i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1421 | 1.09435 | 0.547176 | − | 0.837018i | \(-0.315703\pi\) | ||||
0.547176 | + | 0.837018i | \(0.315703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.3137 | + | 4.00000i | 0.865181 | + | 0.305888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.89949i | − | 0.752645i | −0.926489 | − | 0.376322i | \(-0.877189\pi\) | ||
0.926489 | − | 0.376322i | \(-0.122811\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.00000i | − | 0.226779i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.0000 | + | 11.3137i | −1.20263 | + | 0.850390i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.89949 | 0.739923 | 0.369961 | − | 0.929047i | \(-0.379371\pi\) | ||||
0.369961 | + | 0.929047i | \(0.379371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.1421 | − | 10.0000i | 1.04542 | − | 0.739221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.65685i | − | 0.415900i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000i | 0.146254i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.00000 | − | 1.41421i | 0.363696 | − | 0.102869i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.07107 | 0.511645 | 0.255822 | − | 0.966724i | \(-0.417654\pi\) | ||||
0.255822 | + | 0.966724i | \(0.417654\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.0000 | −1.43963 | −0.719816 | − | 0.694165i | \(-0.755774\pi\) | ||||
−0.719816 | + | 0.694165i | \(0.755774\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.48528 | − | 12.0000i | −0.607644 | − | 0.859338i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9706i | 1.20910i | 0.796566 | + | 0.604551i | \(0.206648\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000i | 0.567105i | 0.958957 | + | 0.283552i | \(0.0915130\pi\) | ||||
−0.958957 | + | 0.283552i | \(0.908487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0000 | − | 22.6274i | −1.12855 | − | 1.59601i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.48528 | 0.595550 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.07107 | + | 20.0000i | −0.491473 | + | 1.39010i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685i | 0.391293i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | + | 4.24264i | −0.411113 | + | 0.290701i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.7990 | + | 14.0000i | −1.33789 | + | 0.946032i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.48528i | 0.570782i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.0000i | − | 1.60716i | −0.595198 | − | 0.803579i | \(-0.702926\pi\) | ||
0.595198 | − | 0.803579i | \(-0.297074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | − | 8.48528i | 0.200000 | − | 0.565685i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3137 | −0.750917 | −0.375459 | − | 0.926839i | \(-0.622515\pi\) | ||||
−0.375459 | + | 0.926839i | \(0.622515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.41421 | + | 2.00000i | 0.0930484 | + | 0.131590i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.7990i | − | 1.29707i | −0.761183 | − | 0.648537i | \(-0.775381\pi\) | ||
0.761183 | − | 0.648537i | \(-0.224619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000i | 0.260931i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | + | 5.65685i | 0.259828 | + | 0.367452i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.41421 | −0.0914779 | −0.0457389 | − | 0.998953i | \(-0.514564\pi\) | ||||
−0.0457389 | + | 0.998953i | \(0.514564\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5563 | + | 1.00000i | 0.997940 | + | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.41421i | − | 0.0903508i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0000i | 1.52708i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | + | 8.48528i | −0.760469 | + | 0.537733i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.65685 | −0.357057 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0000 | −0.628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.82843 | − | 2.00000i | 0.177123 | − | 0.125245i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.8701i | 1.67611i | 0.545587 | + | 0.838054i | \(0.316307\pi\) | ||||
−0.545587 | + | 0.838054i | \(0.683693\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.0000 | + | 8.48528i | 1.48556 | + | 0.525226i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.89949 | −0.610429 | −0.305215 | − | 0.952284i | \(-0.598728\pi\) | ||||
−0.305215 | + | 0.952284i | \(0.598728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.07107 | − | 10.0000i | −0.432742 | − | 0.611990i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.5269i | 1.98320i | 0.129339 | + | 0.991600i | \(0.458714\pi\) | ||||
−0.129339 | + | 0.991600i | \(0.541286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.0000i | 1.57939i | 0.613501 | + | 0.789694i | \(0.289761\pi\) | ||||
−0.613501 | + | 0.789694i | \(0.710239\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | + | 8.48528i | 0.363137 | + | 0.513553i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.24264 | 0.255841 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.65685 | + | 2.00000i | 0.338667 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 25.4558i | − | 1.51857i | −0.650759 | − | 0.759284i | \(-0.725549\pi\) | ||
0.650759 | − | 0.759284i | \(-0.274451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 28.0000i | − | 1.66443i | −0.554455 | − | 0.832214i | \(-0.687073\pi\) | ||
0.554455 | − | 0.832214i | \(-0.312927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.00000 | − | 5.65685i | 0.473879 | − | 0.335083i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.24264 | 0.250435 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.48528 | + | 6.00000i | −0.497416 | + | 0.351726i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 26.8701i | − | 1.56977i | −0.619644 | − | 0.784883i | \(-0.712723\pi\) | ||
0.619644 | − | 0.784883i | \(-0.287277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0000i | 0.931556i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | + | 7.07107i | 0.116052 | + | 0.410305i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −42.4264 | −2.45358 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.41421 | − | 2.00000i | −0.0812444 | − | 0.114897i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 14.1421i | − | 0.809776i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0000 | + | 14.1421i | 0.568880 | + | 0.804518i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.7990 | 1.12270 | 0.561349 | − | 0.827579i | \(-0.310283\pi\) | ||||
0.561349 | + | 0.827579i | \(0.310283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | 0.113047 | 0.0565233 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565233 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.41421 | − | 4.00000i | 0.0796819 | − | 0.225374i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 22.6274i | − | 1.27088i | −0.772149 | − | 0.635441i | \(-0.780818\pi\) | ||
0.772149 | − | 0.635441i | \(-0.219182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000i | 0.671871i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.0000 | + | 15.5563i | −1.22792 | + | 0.868271i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.65685 | −0.314756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.0000 | 0.998460 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.7990 | − | 14.0000i | 1.09489 | − | 0.774202i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.82843i | − | 0.155936i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.00000i | − | 0.219860i | −0.993939 | − | 0.109930i | \(-0.964937\pi\) | ||
0.993939 | − | 0.109930i | \(-0.0350627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | + | 11.3137i | −0.219199 | + | 0.619987i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.6274 | −1.23627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.0000 | 1.63420 | 0.817102 | − | 0.576493i | \(-0.195579\pi\) | ||||
0.817102 | + | 0.576493i | \(0.195579\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.82843i | 0.153168i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.0000 | + | 14.1421i | 0.538382 | + | 0.761387i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.3553 | −1.89797 | −0.948987 | − | 0.315315i | \(-0.897890\pi\) | ||||
−0.948987 | + | 0.315315i | \(0.897890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.48528 | + | 30.0000i | 0.452911 | + | 1.60128i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.07107i | − | 0.376355i | −0.982135 | − | 0.188177i | \(-0.939742\pi\) | ||
0.982135 | − | 0.188177i | \(-0.0602580\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000i | 0.318447i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00000 | + | 1.41421i | −0.105851 | + | 0.0748481i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.41421 | −0.0746393 | −0.0373197 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373197 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.7279 | − | 9.00000i | 0.668043 | − | 0.472377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.7990i | 1.03633i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.00000i | − | 0.417597i | −0.977959 | − | 0.208798i | \(-0.933045\pi\) | ||
0.977959 | − | 0.208798i | \(-0.0669552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.0000 | + | 4.24264i | 0.624695 | + | 0.220863i | ||||
\(370\) | 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 | ||||||||
\(375\) | −11.3137 | − | 16.0000i | −0.584237 | − | 0.826236i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 50.9117i | 2.62209i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000i | 1.02733i | 0.857991 | + | 0.513665i | \(0.171713\pi\) | ||||
−0.857991 | + | 0.513665i | \(0.828287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0000 | + | 16.9706i | 0.614779 | + | 0.869428i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6274 | −1.15621 | −0.578103 | − | 0.815963i | \(-0.696207\pi\) | ||||
−0.578103 | + | 0.815963i | \(0.696207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 36.7696i | − | 1.86429i | −0.362085 | − | 0.932145i | \(-0.617935\pi\) | ||
0.362085 | − | 0.932145i | \(-0.382065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.0000i | − | 0.505722i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.0000 | − | 19.7990i | 1.41241 | − | 0.998727i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.65685 | 0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | 0.501886 | 0.250943 | − | 0.968002i | \(-0.419259\pi\) | ||||
0.250943 | + | 0.968002i | \(0.419259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.65685 | + | 4.00000i | −0.283197 | + | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.82843i | − | 0.141245i | −0.997503 | − | 0.0706225i | \(-0.977501\pi\) | ||
0.997503 | − | 0.0706225i | \(-0.0224986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000i | 0.597763i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.00000 | − | 9.89949i | 0.397523 | − | 0.491910i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.65685 | −0.280400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | −0.0988936 | −0.0494468 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494468 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.7990 | + | 28.0000i | 0.976612 | + | 1.38114i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 11.3137i | − | 0.556711i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000i | 0.589057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | + | 8.48528i | 0.293821 | + | 0.415526i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.9706 | −0.829066 | −0.414533 | − | 0.910034i | \(-0.636055\pi\) | ||||
−0.414533 | + | 0.910034i | \(0.636055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.0000 | −1.16969 | −0.584844 | − | 0.811146i | \(-0.698844\pi\) | ||||
−0.584844 | + | 0.811146i | \(0.698844\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843 | − | 8.00000i | 0.137523 | − | 0.388973i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.24264i | 0.205798i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000i | 0.483934i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | + | 8.48528i | −0.579365 | + | 0.409673i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.3553 | 1.70301 | 0.851503 | − | 0.524349i | \(-0.175691\pi\) | ||||
0.851503 | + | 0.524349i | \(0.175691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.9706 | − | 12.0000i | 0.813676 | − | 0.575356i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 28.2843i | − | 1.35302i | ||||||
\(438\) | 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 | ||||||||
\(443\) | −9.89949 | −0.470339 | −0.235170 | − | 0.971954i | \(-0.575565\pi\) | ||||
−0.235170 | + | 0.971954i | \(0.575565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | −0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.3137 | + | 16.0000i | 0.535120 | + | 0.756774i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9706i | 0.800890i | 0.916321 | + | 0.400445i | \(0.131145\pi\) | ||||
−0.916321 | + | 0.400445i | \(0.868855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000i | 0.282529i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.00000 | − | 11.3137i | −0.375873 | − | 0.531564i | ||||
\(454\) | 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 | ||||||||
\(459\) | −7.07107 | + | 2.00000i | −0.330049 | + | 0.0933520i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.24264i | 0.197599i | 0.995107 | + | 0.0987997i | \(0.0315003\pi\) | ||||
−0.995107 | + | 0.0987997i | \(0.968500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | − | 2.82843i | 0.185496 | − | 0.131165i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6274 | 1.04707 | 0.523536 | − | 0.852004i | \(-0.324613\pi\) | ||||
0.523536 | + | 0.852004i | \(0.324613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1421 | − | 10.0000i | 0.651635 | − | 0.460776i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000i | 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0000 | − | 5.65685i | −0.732590 | − | 0.259010i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.1127 | −1.42158 | −0.710788 | − | 0.703407i | \(-0.751661\pi\) | ||||
−0.710788 | + | 0.703407i | \(0.751661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.07107 | − | 10.0000i | −0.321745 | − | 0.455016i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.48528i | 0.385297i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.00000i | − | 0.362515i | −0.983436 | − | 0.181257i | \(-0.941983\pi\) | ||
0.983436 | − | 0.181257i | \(-0.0580167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | + | 5.65685i | 0.180886 | + | 0.255812i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.41421 | 0.0638226 | 0.0319113 | − | 0.999491i | \(-0.489841\pi\) | ||||
0.0319113 | + | 0.999491i | \(0.489841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | + | 2.00000i | 0.254257 | + | 0.0898933i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4.24264i | − | 0.190308i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0000 | + | 14.1421i | −0.893534 | + | 0.631824i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00000 | −0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.5269 | + | 23.0000i | −1.44457 | + | 1.02147i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7.07107i | − | 0.313420i | −0.987645 | − | 0.156710i | \(-0.949911\pi\) | ||
0.987645 | − | 0.156710i | \(-0.0500887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.0000i | − | 0.619324i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0000 | + | 5.65685i | −0.883022 | + | 0.249756i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.1421 | 0.623177 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000 | 0.175920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.89949 | + | 14.0000i | 0.434540 | + | 0.614532i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.3553i | − | 1.54895i | −0.632607 | − | 0.774473i | \(-0.718015\pi\) | ||
0.632607 | − | 0.774473i | \(-0.281985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 26.0000i | − | 1.13690i | −0.822718 | − | 0.568450i | \(-0.807543\pi\) | ||
0.822718 | − | 0.568450i | \(-0.192457\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.00000 | + | 4.24264i | 0.130931 | + | 0.185164i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.82843 | −0.123208 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.0000 | 1.17391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3137 | − | 32.0000i | 0.490973 | − | 1.38868i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4558i | 1.10262i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.0000i | 0.951143i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.0000 | + | 9.89949i | −0.604145 | + | 0.427195i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.41421 | −0.0609145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0000 | 0.687894 | 0.343947 | − | 0.938989i | \(-0.388236\pi\) | ||||
0.343947 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.82843 | − | 2.00000i | 0.121379 | − | 0.0858282i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 19.7990i | − | 0.848096i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0000 | + | 28.2843i | −0.426790 | + | 1.20714i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.9411 | −1.44594 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.65685 | + | 8.00000i | 0.240120 | + | 0.339581i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 11.3137i | − | 0.479377i | −0.970850 | − | 0.239689i | \(-0.922955\pi\) | ||
0.970850 | − | 0.239689i | \(-0.0770453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.00000 | − | 2.82843i | −0.0844401 | − | 0.119416i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3137 | 0.476816 | 0.238408 | − | 0.971165i | \(-0.423374\pi\) | ||||
0.238408 | + | 0.971165i | \(0.423374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.65685 | + | 7.00000i | −0.237566 | + | 0.293972i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.82843i | 0.118574i | 0.998241 | + | 0.0592869i | \(0.0188827\pi\) | ||||
−0.998241 | + | 0.0592869i | \(0.981117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 40.0000i | − | 1.67395i | −0.547243 | − | 0.836974i | \(-0.684323\pi\) | ||
0.547243 | − | 0.836974i | \(-0.315677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.0000 | + | 7.07107i | −0.417756 | + | 0.295398i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.2132 | −0.884652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0000 | −1.41544 | −0.707719 | − | 0.706494i | \(-0.750276\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.2843 | − | 20.0000i | 1.17545 | − | 0.831172i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 8.48528i | − | 0.352029i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.00000i | − | 0.331326i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | + | 8.48528i | 0.992278 | + | 0.350823i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.9706 | 0.700450 | 0.350225 | − | 0.936666i | \(-0.386105\pi\) | ||||
0.350225 | + | 0.936666i | \(0.386105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.9706 | − | 24.0000i | −0.698076 | − | 0.987228i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.3848i | 0.754972i | 0.926015 | + | 0.377486i | \(0.123211\pi\) | ||||
−0.926015 | + | 0.377486i | \(0.876789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000i | 0.0819920i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.00000 | − | 11.3137i | −0.327418 | − | 0.463039i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3848 | −0.751182 | −0.375591 | − | 0.926786i | \(-0.622560\pi\) | ||||
−0.375591 | + | 0.926786i | \(0.622560\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.2548 | + | 16.0000i | 1.84292 | + | 0.651570i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 12.7279i | − | 0.517464i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.00000i | − | 0.324710i | −0.986732 | − | 0.162355i | \(-0.948091\pi\) | ||
0.986732 | − | 0.162355i | \(-0.0519090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.0000 | + | 8.48528i | −0.486265 | + | 0.343841i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.9706 | 0.686555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0000 | 0.403896 | 0.201948 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.48528 | − | 6.00000i | 0.342160 | − | 0.241943i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 42.4264i | − | 1.70802i | −0.520254 | − | 0.854011i | \(-0.674163\pi\) | ||
0.520254 | − | 0.854011i | \(-0.325837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.00000i | − | 0.0803868i | −0.999192 | − | 0.0401934i | \(-0.987203\pi\) | ||
0.999192 | − | 0.0401934i | \(-0.0127974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.0000 | − | 35.3553i | −0.401286 | − | 1.41876i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.07107 | 0.283296 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.65685 | − | 8.00000i | −0.225913 | − | 0.319489i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.65685i | − | 0.225554i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 48.0000i | − | 1.91085i | −0.295234 | − | 0.955425i | \(-0.595398\pi\) | ||
0.295234 | − | 0.955425i | \(-0.404602\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.9706 | 0.673456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | −0.237729 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.24264 | − | 12.0000i | 0.167836 | − | 0.474713i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 31.1127i | − | 1.22888i | −0.788964 | − | 0.614439i | \(-0.789382\pi\) | ||
0.788964 | − | 0.614439i | \(-0.210618\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.0000i | 1.41970i | 0.704352 | + | 0.709851i | \(0.251238\pi\) | ||||
−0.704352 | + | 0.709851i | \(0.748762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.7696 | 1.44556 | 0.722780 | − | 0.691078i | \(-0.242864\pi\) | ||||
0.722780 | + | 0.691078i | \(0.242864\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.82843 | + | 2.00000i | −0.110855 | + | 0.0783862i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 31.1127i | − | 1.21753i | −0.793349 | − | 0.608767i | \(-0.791664\pi\) | ||
0.793349 | − | 0.608767i | \(-0.208336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 28.0000i | − | 1.09405i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.0000 | − | 39.5980i | 0.546192 | − | 1.54486i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.7279 | −0.495809 | −0.247905 | − | 0.968784i | \(-0.579742\pi\) | ||||
−0.247905 | + | 0.968784i | \(0.579742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.48528 | − | 12.0000i | −0.329541 | − | 0.466041i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.65685i | 0.219363i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 60.0000i | − | 2.32321i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000 | + | 33.9411i | 0.927894 | + | 1.31224i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1421 | −0.545951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | −0.925132 | −0.462566 | − | 0.886585i | \(-0.653071\pi\) | ||||
−0.462566 | + | 0.886585i | \(0.653071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.24264 | + | 15.0000i | 0.163299 | + | 0.577350i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.8701i | 1.03270i | 0.856378 | + | 0.516350i | \(0.172710\pi\) | ||||
−0.856378 | + | 0.516350i | \(0.827290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.00000i | − | 0.230259i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.0000 | − | 11.3137i | 0.613121 | − | 0.433542i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3553 | 1.35283 | 0.676417 | − | 0.736519i | \(-0.263532\pi\) | ||||
0.676417 | + | 0.736519i | \(0.263532\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0000 | 1.06983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.1421 | + | 10.0000i | −0.539556 | + | 0.381524i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 33.9411i | − | 1.29305i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000i | 0.0760836i | 0.999276 | + | 0.0380418i | \(0.0121120\pi\) | ||||
−0.999276 | + | 0.0380418i | \(0.987888\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | − | 1.41421i | −0.151947 | − | 0.0537215i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.48528 | 0.321865 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.7990 | + | 28.0000i | 0.748867 | + | 1.05906i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.7990i | 0.747798i | 0.927470 | + | 0.373899i | \(0.121979\pi\) | ||||
−0.927470 | + | 0.373899i | \(0.878021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.0000i | − | 0.603451i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.00000 | − | 5.65685i | −0.150649 | − | 0.213049i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.41421 | 0.0531870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.3137 | − | 4.00000i | −0.424297 | − | 0.150012i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 14.1421i | − | 0.529627i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000i | 0.448775i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.00000 | − | 1.41421i | 0.0746914 | − | 0.0528148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.3137 | −0.421930 | −0.210965 | − | 0.977494i | \(-0.567661\pi\) | ||||
−0.210965 | + | 0.977494i | \(0.567661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.7990 | + | 14.0000i | −0.736332 | + | 0.520666i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.4558i | 0.945406i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000i | 0.667583i | 0.942647 | + | 0.333792i | \(0.108328\pi\) | ||||
−0.942647 | + | 0.333792i | \(0.891672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0000 | 0.960332 | 0.480166 | − | 0.877178i | \(-0.340576\pi\) | ||||
0.480166 | + | 0.877178i | \(0.340576\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | + | 2.00000i | 0.0521641 | + | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.6274i | 0.833492i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000i | 1.61857i | 0.587419 | + | 0.809283i | \(0.300144\pi\) | ||||
−0.587419 | + | 0.809283i | \(0.699856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | − | 33.9411i | −0.881662 | − | 1.24686i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.1838 | −1.40083 | −0.700413 | − | 0.713738i | \(-0.747001\pi\) | ||||
−0.700413 | + | 0.713738i | \(0.747001\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.0000 | 0.586195 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.48528 | − | 24.0000i | 0.310460 | − | 0.878114i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 15.5563i | − | 0.568417i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 20.0000i | − | 0.729810i | −0.931045 | − | 0.364905i | \(-0.881101\pi\) | ||
0.931045 | − | 0.364905i | \(-0.118899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.00000 | − | 5.65685i | 0.291536 | − | 0.206147i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.3137 | −0.411748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000 | 0.218074 | 0.109037 | − | 0.994038i | \(-0.465223\pi\) | ||||
0.109037 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.1421 | − | 10.0000i | 0.513327 | − | 0.362977i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.8701i | 0.974039i | 0.873391 | + | 0.487019i | \(0.161916\pi\) | ||||
−0.873391 | + | 0.487019i | \(0.838084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000i | 0.506834i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | + | 5.65685i | −0.0723102 | + | 0.204524i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 67.8823 | 2.45109 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.00000 | 0.216366 | 0.108183 | − | 0.994131i | \(-0.465497\pi\) | ||||
0.108183 | + | 0.994131i | \(0.465497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.8701 | − | 38.0000i | −0.967701 | − | 1.36854i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.8701i | 0.966449i | 0.875497 | + | 0.483224i | \(0.160534\pi\) | ||||
−0.875497 | + | 0.483224i | \(0.839466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000i | 0.215526i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.00000 | − | 5.65685i | −0.143499 | − | 0.202939i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.9706 | −0.608034 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.4264 | + | 12.0000i | −1.51620 | + | 0.428845i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 14.1421i | − | 0.504754i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 26.0000i | − | 0.926800i | −0.886149 | − | 0.463400i | \(-0.846629\pi\) | ||
0.886149 | − | 0.463400i | \(-0.153371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.0000 | − | 9.89949i | 0.498413 | − | 0.352431i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −60.0000 | −2.13066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.3137 | + | 8.00000i | −0.401256 | + | 0.283731i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.24264i | 0.150282i | 0.997173 | + | 0.0751410i | \(0.0239407\pi\) | ||||
−0.997173 | + | 0.0751410i | \(0.976059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000i | 0.141510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.0000 | + | 7.07107i | 0.706665 | + | 0.249844i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.7990 | 0.698691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0000 | −0.352454 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.5269 | − | 46.0000i | −1.14500 | − | 1.61928i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.2843i | 0.994422i | 0.867630 | + | 0.497211i | \(0.165643\pi\) | ||||
−0.867630 | + | 0.497211i | \(0.834357\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000i | 1.05344i | 0.850038 | + | 0.526721i | \(0.176579\pi\) | ||||
−0.850038 | + | 0.526721i | \(0.823421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.0000 | − | 36.7696i | −0.911860 | − | 1.28956i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.65685 | 0.198151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.9706 | − | 6.00000i | −0.592999 | − | 0.209657i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.65685i | 0.197426i | 0.995116 | + | 0.0987128i | \(0.0314725\pi\) | ||||
−0.995116 | + | 0.0987128i | \(0.968527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 44.0000i | − | 1.53374i | −0.641800 | − | 0.766872i | \(-0.721812\pi\) | ||
0.641800 | − | 0.766872i | \(-0.278188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | + | 4.24264i | −0.208893 | + | 0.147710i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7279 | 0.442593 | 0.221297 | − | 0.975207i | \(-0.428971\pi\) | ||||
0.221297 | + | 0.975207i | \(0.428971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.6274 | − | 16.0000i | 0.784936 | − | 0.555034i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.41421i | − | 0.0489996i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.0000i | 0.692129i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0000 | + | 2.82843i | −0.345651 | + | 0.0977647i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4558 | −0.878833 | −0.439417 | − | 0.898283i | \(-0.644815\pi\) | ||||
−0.439417 | + | 0.898283i | \(0.644815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0000 | −1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.4558 | + | 36.0000i | 0.876746 | + | 1.23991i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.5269i | 1.11896i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000i | 0.309244i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0000 | + | 39.5980i | 0.960958 | + | 1.35900i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.2843 | 0.969572 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.00000 | −0.205436 | −0.102718 | − | 0.994711i | \(-0.532754\pi\) | ||||
−0.102718 | + | 0.994711i | \(0.532754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.65685 | + | 16.0000i | −0.193460 | + | 0.547188i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.4975i | 1.69080i | 0.534133 | + | 0.845401i | \(0.320638\pi\) | ||||
−0.534133 | + | 0.845401i | \(0.679362\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 20.0000i | − | 0.682391i | −0.939992 | − | 0.341196i | \(-0.889168\pi\) | ||
0.939992 | − | 0.341196i | \(-0.110832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | + | 4.24264i | −0.204479 | + | 0.144589i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.8406 | 1.49235 | 0.746176 | − | 0.665749i | \(-0.231888\pi\) | ||||
0.746176 | + | 0.665749i | \(0.231888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.2132 | + | 15.0000i | −0.720438 | + | 0.509427i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.65685i | − | 0.191896i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 96.0000i | 3.25284i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.00000 | − | 16.9706i | 0.203069 | − | 0.574367i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137 | 0.382473 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.0000 | 1.14810 | 0.574049 | − | 0.818821i | \(-0.305372\pi\) | ||||
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.8701 | + | 38.0000i | 0.906305 | + | 1.28171i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.07107i | − | 0.238230i | −0.992880 | − | 0.119115i | \(-0.961994\pi\) | ||
0.992880 | − | 0.119115i | \(-0.0380058\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0000i | 1.21150i | 0.795656 | + | 0.605748i | \(0.207126\pi\) | ||||
−0.795656 | + | 0.605748i | \(0.792874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0000 | − | 22.6274i | −0.537834 | − | 0.760612i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.0833 | −1.61448 | −0.807239 | − | 0.590225i | \(-0.799039\pi\) | ||||
−0.807239 | + | 0.590225i | \(0.799039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.89949 | − | 8.00000i | −0.331646 | − | 0.268010i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.3137i | 0.378599i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.0000i | 0.467968i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 60.0000 | − | 42.4264i | 2.00334 | − | 1.41658i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.9706 | −0.566000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.82843i | − | 0.0940201i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.00000i | 0.132818i | 0.997792 | + | 0.0664089i | \(0.0211542\pi\) | ||||
−0.997792 | + | 0.0664089i | \(0.978846\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.00000 | + | 1.41421i | 0.132672 | + | 0.0469065i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.7279 | −0.421695 | −0.210847 | − | 0.977519i | \(-0.567622\pi\) | ||||
−0.210847 | + | 0.977519i | \(0.567622\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.1421 | + | 20.0000i | 0.467525 | + | 0.661180i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.7990i | 0.653820i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000i | 0.131948i | 0.997821 | + | 0.0659739i | \(0.0210154\pi\) | ||||
−0.997821 | + | 0.0659739i | \(0.978985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0000 | + | 16.9706i | 0.395413 | + | 0.559199i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.4558 | 0.837889 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | −0.394558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.2843 | − | 10.0000i | −0.928977 | − | 0.328443i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.5563i | 0.510387i | 0.966890 | + | 0.255194i | \(0.0821392\pi\) | ||||
−0.966890 | + | 0.255194i | \(0.917861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.00000i | − | 0.131095i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.0000 | + | 19.7990i | −0.916679 | + | 0.648190i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.82843 | −0.0924995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.82843 | + | 2.00000i | −0.0923022 | + | 0.0652675i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.8701i | − | 0.875939i | −0.898990 | − | 0.437969i | \(-0.855698\pi\) | ||
0.898990 | − | 0.437969i | \(-0.144302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 30.0000i | − | 0.976934i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | + | 7.07107i | 0.0650600 | + | 0.230022i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.41421 | 0.0459558 | 0.0229779 | − | 0.999736i | \(-0.492685\pi\) | ||||
0.0229779 | + | 0.999736i | \(0.492685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 84.0000 | 2.72676 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.6274 | + | 32.0000i | 0.733744 | + | 1.03767i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.9411i | 1.09946i | 0.835342 | + | 0.549730i | \(0.185270\pi\) | ||||
−0.835342 | + | 0.549730i | \(0.814730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0000i | 0.323592i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0000 | − | 16.9706i | −0.387905 | − | 0.548580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.7990 | −0.639343 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.5563 | − | 44.0000i | 0.501296 | − | 1.41788i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 28.2843i | − | 0.910503i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.0000i | 1.15768i | 0.815440 | + | 0.578841i | \(0.196495\pi\) | ||||
−0.815440 | + | 0.578841i | \(0.803505\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.00000 | − | 5.65685i | 0.256997 | − | 0.181724i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.7990 | −0.635380 | −0.317690 | − | 0.948195i | \(-0.602907\pi\) | ||||
−0.317690 | + | 0.948195i | \(0.602907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.00000 | −0.192351 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.4558 | + | 18.0000i | −0.815239 | + | 0.576461i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.1421i | 0.452447i | 0.974075 | + | 0.226224i | \(0.0726380\pi\) | ||||
−0.974075 | + | 0.226224i | \(0.927362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0000i | 0.319601i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0000 | + | 39.5980i | −0.446986 | + | 1.26427i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.2843 | −0.902128 | −0.451064 | − | 0.892492i | \(-0.648955\pi\) | ||||
−0.451064 | + | 0.892492i | \(0.648955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0000 | −0.764704 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.82843 | + | 4.00000i | 0.0900298 | + | 0.127321i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 20.0000i | − | 0.635321i | −0.948205 | − | 0.317660i | \(-0.897103\pi\) | ||
0.948205 | − | 0.317660i | \(-0.102897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00000 | + | 5.65685i | 0.126936 | + | 0.179515i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.3137 | −0.358669 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0000 | −0.696747 | −0.348373 | − | 0.937356i | \(-0.613266\pi\) | ||||
−0.348373 | + | 0.937356i | \(0.613266\pi\) | |||||||
\(998\) | 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.c.575.2 | yes | 4 | |
3.2 | odd | 2 | inner | 672.2.h.c.575.4 | yes | 4 | |
4.3 | odd | 2 | inner | 672.2.h.c.575.3 | yes | 4 | |
8.3 | odd | 2 | 1344.2.h.b.575.2 | 4 | |||
8.5 | even | 2 | 1344.2.h.b.575.3 | 4 | |||
12.11 | even | 2 | inner | 672.2.h.c.575.1 | ✓ | 4 | |
24.5 | odd | 2 | 1344.2.h.b.575.1 | 4 | |||
24.11 | even | 2 | 1344.2.h.b.575.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.h.c.575.1 | ✓ | 4 | 12.11 | even | 2 | inner | |
672.2.h.c.575.2 | yes | 4 | 1.1 | even | 1 | trivial | |
672.2.h.c.575.3 | yes | 4 | 4.3 | odd | 2 | inner | |
672.2.h.c.575.4 | yes | 4 | 3.2 | odd | 2 | inner | |
1344.2.h.b.575.1 | 4 | 24.5 | odd | 2 | |||
1344.2.h.b.575.2 | 4 | 8.3 | odd | 2 | |||
1344.2.h.b.575.3 | 4 | 8.5 | even | 2 | |||
1344.2.h.b.575.4 | 4 | 24.11 | even | 2 |