Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(959,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.959");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.o (of order \(2\), degree \(1\), not 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: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 959.7 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.959 |
Dual form | 960.2.o.d.959.5 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −1.73205 | − | 1.41421i | −0.774597 | − | 0.632456i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.89898i | 1.35873i | 0.733799 | + | 0.679366i | \(0.237745\pi\) | ||||
−0.733799 | + | 0.679366i | \(0.762255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.03528 | − | 3.73205i | −0.267307 | − | 0.963611i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 4.89898i | 0.200000 | + | 0.979796i | ||||
\(26\) | 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 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.92820 | − | 4.89898i | −1.20605 | − | 0.852803i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.89898i | − | 0.805387i | −0.915335 | − | 0.402694i | \(-0.868074\pi\) | ||
0.915335 | − | 0.402694i | \(-0.131926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.89898 | + | 6.92820i | −0.784465 | + | 1.10940i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528 | 1.29399 | 0.646997 | − | 0.762493i | \(-0.276025\pi\) | ||||
0.646997 | + | 0.762493i | \(0.276025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.26795 | − | 6.31319i | 0.338086 | − | 0.941115i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.89898 | + | 3.46410i | 0.685994 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923 | 1.42749 | 0.713746 | − | 0.700404i | \(-0.246997\pi\) | ||||
0.713746 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.48528 | + | 6.92820i | 1.14416 | + | 0.934199i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | + | 4.89898i | −0.458831 | + | 0.648886i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.92820 | − | 8.48528i | 0.859338 | − | 1.05247i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.48528 | −1.03664 | −0.518321 | − | 0.855186i | \(-0.673443\pi\) | ||||
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | + | 8.48528i | −0.722315 | + | 1.02151i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.79796 | −1.16280 | −0.581402 | − | 0.813617i | \(-0.697496\pi\) | ||||
−0.581402 | + | 0.813617i | \(0.697496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.79796i | − | 1.14676i | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||
0.819288 | − | 0.573382i | \(-0.194369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.48477 | + | 7.92820i | −0.402386 | + | 0.915470i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.3923i | − | 1.16923i | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||
0.811312 | − | 0.584613i | \(-0.198754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | − | 4.89898i | −0.650791 | − | 0.531369i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.82843 | + | 4.00000i | −0.303239 | + | 0.428845i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.65685i | 0.599625i | 0.953998 | + | 0.299813i | \(0.0969242\pi\) | ||||
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46410 | + | 4.89898i | −0.359211 | + | 0.508001i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.89898 | − | 6.00000i | 0.502625 | − | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.89898 | − | 13.8564i | −0.492366 | − | 1.39262i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 14.1421i | − | 1.40720i | −0.710599 | − | 0.703598i | \(-0.751576\pi\) | ||
0.710599 | − | 0.703598i | \(-0.248424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.0000i | 1.74013i | 0.492941 | + | 0.870063i | \(0.335922\pi\) | ||||
−0.492941 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.89898 | − | 6.92820i | 0.464991 | − | 0.657596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.46410 | 0.325875 | 0.162938 | − | 0.986636i | \(-0.447903\pi\) | ||||
0.162938 | + | 0.986636i | \(0.447903\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.48528 | − | 10.3923i | 0.791257 | − | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.8564 | + | 4.89898i | −1.28103 | + | 0.452911i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.65685 | − | 8.00000i | 0.510061 | − | 0.721336i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.19615 | − | 9.89949i | 0.464758 | − | 0.885438i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9706 | −1.50589 | −0.752947 | − | 0.658081i | \(-0.771368\pi\) | ||||
−0.752947 | + | 0.658081i | \(0.771368\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | + | 8.48528i | 1.05654 | + | 0.747087i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.89898 | 0.428026 | 0.214013 | − | 0.976831i | \(-0.431347\pi\) | ||||
0.214013 | + | 0.976831i | \(0.431347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.52056 | − | 6.66025i | 0.819399 | − | 0.573223i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46410 | 0.295958 | 0.147979 | − | 0.988990i | \(-0.452723\pi\) | ||||
0.147979 | + | 0.988990i | \(0.452723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.3205i | 1.46911i | 0.678551 | + | 0.734553i | \(0.262608\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | + | 8.48528i | −0.505291 | + | 0.714590i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 24.0000i | − | 2.00698i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | − | 4.89898i | 0.332182 | − | 0.406838i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.89949 | − | 7.00000i | −0.816497 | − | 0.577350i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.82843i | − | 0.231714i | −0.993266 | − | 0.115857i | \(-0.963039\pi\) | ||
0.993266 | − | 0.115857i | \(-0.0369614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46410i | 0.281905i | 0.990016 | + | 0.140952i | \(0.0450164\pi\) | ||||
−0.990016 | + | 0.140952i | \(0.954984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.46410 | + | 9.79796i | 0.280056 | + | 0.792118i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.89898 | − | 6.00000i | 0.393496 | − | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.89898i | 0.390981i | 0.980706 | + | 0.195491i | \(0.0626299\pi\) | ||||
−0.980706 | + | 0.195491i | \(0.937370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.6969 | + | 10.3923i | 1.16554 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.48528 | −0.664619 | −0.332309 | − | 0.943170i | \(-0.607828\pi\) | ||||
−0.332309 | + | 0.943170i | \(0.607828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.07180 | + | 18.2832i | 0.394839 | + | 1.42335i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000i | 0.464294i | 0.972681 | + | 0.232147i | \(0.0745750\pi\) | ||||
−0.972681 | + | 0.232147i | \(0.925425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.79796 | + | 3.46410i | −0.749269 | + | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.46410 | −0.263371 | −0.131685 | − | 0.991292i | \(-0.542039\pi\) | ||||
−0.131685 | + | 0.991292i | \(0.542039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.92820 | − | 4.89898i | −0.520756 | − | 0.368230i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.4949 | 1.83083 | 0.915417 | − | 0.402506i | \(-0.131861\pi\) | ||||
0.915417 | + | 0.402506i | \(0.131861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.82843 | + | 2.00000i | 0.209083 | + | 0.147844i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.92820 | + | 8.48528i | −0.509372 | + | 0.623850i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.9706 | −1.24101 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5959 | 1.41791 | 0.708955 | − | 0.705253i | \(-0.249167\pi\) | ||||
0.708955 | + | 0.705253i | \(0.249167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5959i | 1.41055i | 0.708936 | + | 0.705273i | \(0.249175\pi\) | ||||
−0.708936 | + | 0.705273i | \(0.750825\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.2832 | − | 5.07180i | 1.30929 | − | 0.363199i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.2487 | 1.72765 | 0.863825 | − | 0.503793i | \(-0.168062\pi\) | ||||
0.863825 | + | 0.503793i | \(0.168062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.3923i | − | 0.736691i | −0.929689 | − | 0.368345i | \(-0.879924\pi\) | ||
0.929689 | − | 0.368345i | \(-0.120076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0000 | − | 8.48528i | −0.846415 | − | 0.598506i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | + | 9.79796i | −0.558744 | + | 0.684319i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.9706 | + | 6.00000i | −1.17954 | + | 0.417029i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 16.9706i | − | 1.17388i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.2487i | − | 1.66935i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||
0.550743 | − | 0.834675i | \(-0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.8564 | − | 9.79796i | −0.949425 | − | 0.671345i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6969 | − | 12.0000i | −1.00232 | − | 0.818393i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.79796 | − | 13.8564i | 0.662085 | − | 0.936329i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.9706i | 1.14156i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9706 | 1.13643 | 0.568216 | − | 0.822879i | \(-0.307634\pi\) | ||||
0.568216 | + | 0.822879i | \(0.307634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.8564 | + | 7.72741i | −0.857094 | + | 0.515160i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.00000i | − | 0.398234i | −0.979976 | − | 0.199117i | \(-0.936193\pi\) | ||
0.979976 | − | 0.199117i | \(-0.0638074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.46410 | 0.226941 | 0.113470 | − | 0.993541i | \(-0.463803\pi\) | ||||
0.113470 | + | 0.993541i | \(0.463803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.48528 | − | 10.3923i | 0.553519 | − | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.3923 | − | 14.6969i | 0.675053 | − | 0.954669i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5563 | + | 1.00000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.1244 | + | 9.89949i | 0.774597 | + | 0.632456i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.9706 | −1.07981 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | − | 8.48528i | 0.380235 | − | 0.537733i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6969 | 0.927663 | 0.463831 | − | 0.885924i | \(-0.346474\pi\) | ||||
0.463831 | + | 0.885924i | \(0.346474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 29.3939i | − | 1.84798i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.58630 | − | 12.9282i | −0.224583 | − | 0.809595i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.46410 | 0.216085 | 0.108042 | − | 0.994146i | \(-0.465542\pi\) | ||||
0.108042 | + | 0.994146i | \(0.465542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.00000 | + | 2.82843i | −0.495188 | + | 0.175075i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000i | 0.369976i | 0.982741 | + | 0.184988i | \(0.0592246\pi\) | ||||
−0.982741 | + | 0.184988i | \(0.940775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0000 | − | 14.6969i | −1.10573 | − | 0.902826i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.65685 | + | 8.00000i | −0.346194 | + | 0.489592i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 19.7990i | − | 1.20717i | −0.797300 | − | 0.603583i | \(-0.793739\pi\) | ||
0.797300 | − | 0.603583i | \(-0.206261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.3923i | − | 0.631288i | −0.948878 | − | 0.315644i | \(-0.897780\pi\) | ||
0.948878 | − | 0.315644i | \(-0.102220\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.89898 | − | 24.0000i | −0.295420 | − | 1.44725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.6969i | 0.883053i | 0.897248 | + | 0.441527i | \(0.145563\pi\) | ||||
−0.897248 | + | 0.441527i | \(0.854437\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.79796 | + | 3.46410i | −0.586588 | + | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.65685i | − | 0.337460i | −0.985662 | − | 0.168730i | \(-0.946033\pi\) | ||
0.985662 | − | 0.168730i | \(-0.0539665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.9282 | − | 3.58630i | 0.765801 | − | 0.212434i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.3205 | −1.01187 | −0.505937 | − | 0.862570i | \(-0.668853\pi\) | ||||
−0.505937 | + | 0.862570i | \(0.668853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48528 | + | 6.92820i | 0.494032 | + | 0.403376i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.92820 | − | 24.4949i | 0.402015 | − | 1.42134i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.3939 | −1.69989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.1421 | − | 20.0000i | 0.812444 | − | 1.14897i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.46410 | − | 2.82843i | −0.198354 | − | 0.161955i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.48528 | −0.484281 | −0.242140 | − | 0.970241i | \(-0.577849\pi\) | ||||
−0.242140 | + | 0.970241i | \(0.577849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.79796 | 0.555591 | 0.277796 | − | 0.960640i | \(-0.410396\pi\) | ||||
0.277796 | + | 0.960640i | \(0.410396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.79796i | 0.553813i | 0.960897 | + | 0.276907i | \(0.0893093\pi\) | ||||
−0.960897 | + | 0.276907i | \(0.910691\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3205 | −0.972817 | −0.486408 | − | 0.873732i | \(-0.661693\pi\) | ||||
−0.486408 | + | 0.873732i | \(0.661693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 13.8564i | − | 0.775810i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | + | 25.4558i | −1.00466 | + | 1.42081i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | + | 4.89898i | −1.33128 | + | 0.271746i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.82843 | + | 2.00000i | 0.156412 | + | 0.110600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3205i | 0.952021i | 0.879440 | + | 0.476011i | \(0.157918\pi\) | ||||
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.8564 | − | 4.89898i | 0.759326 | − | 0.268462i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.6969 | + | 12.0000i | 0.802980 | + | 0.655630i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.89898 | + | 3.46410i | 0.266076 | + | 0.188144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 16.9706i | − | 0.919007i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.3923 | − | 6.21166i | 1.20556 | − | 0.334424i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6.00000i | − | 0.322097i | −0.986947 | − | 0.161048i | \(-0.948512\pi\) | ||
0.986947 | − | 0.161048i | \(-0.0514875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.4949 | − | 6.92820i | −1.30744 | − | 0.369800i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.1769 | 1.65938 | 0.829690 | − | 0.558225i | \(-0.188517\pi\) | ||||
0.829690 | + | 0.558225i | \(0.188517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9706 | + | 13.8564i | 0.900704 | + | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.79796 | 0.517116 | 0.258558 | − | 0.965996i | \(-0.416753\pi\) | ||||
0.258558 | + | 0.965996i | \(0.416753\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.3848 | + | 13.0000i | 0.964951 | + | 0.682323i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.8564 | + | 16.9706i | −0.725277 | + | 0.888280i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9706 | −0.885856 | −0.442928 | − | 0.896557i | \(-0.646060\pi\) | ||||
−0.442928 | + | 0.896557i | \(0.646060\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.0000 | − | 5.65685i | 0.832927 | − | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6969i | 0.760979i | 0.924785 | + | 0.380489i | \(0.124244\pi\) | ||||
−0.924785 | + | 0.380489i | \(0.875756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.2480 | − | 8.80385i | 0.890681 | − | 0.454629i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.8564 | −0.713641 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.3923i | − | 0.533817i | −0.963722 | − | 0.266908i | \(-0.913998\pi\) | ||
0.963722 | − | 0.266908i | \(-0.0860021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.0000 | − | 16.9706i | −1.22956 | − | 0.869428i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.00000i | 0.306586i | 0.988181 | + | 0.153293i | \(0.0489878\pi\) | ||||
−0.988181 | + | 0.153293i | \(0.951012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.48528 | + | 24.0000i | 0.431331 | + | 1.21999i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.82843i | − | 0.143407i | −0.997426 | − | 0.0717035i | \(-0.977156\pi\) | ||
0.997426 | − | 0.0717035i | \(-0.0228435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7846i | 1.05112i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.92820 | + | 4.89898i | 0.349482 | + | 0.247121i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.6969 | + | 18.0000i | −0.739483 | + | 0.905678i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.89898i | 0.245873i | 0.992415 | + | 0.122936i | \(0.0392311\pi\) | ||||
−0.992415 | + | 0.122936i | \(0.960769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6274i | 1.12996i | 0.825105 | + | 0.564980i | \(0.191116\pi\) | ||||
−0.825105 | + | 0.564980i | \(0.808884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.9706 | −0.845364 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.1244 | + | 0.101536i | 0.999987 | + | 0.00504536i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.89898 | + | 3.46410i | 0.241649 | + | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.48528 | + | 10.3923i | −0.416526 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.3205 | + | 24.4949i | −0.848189 | + | 1.19952i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.6969 | −0.717992 | −0.358996 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358996 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.9706 | + | 6.00000i | −0.825137 | + | 0.291730i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | + | 16.9706i | 0.168034 | + | 0.823193i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0000 | − | 33.9411i | 1.15873 | − | 1.63869i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.5959 | −0.943902 | −0.471951 | − | 0.881625i | \(-0.656450\pi\) | ||||
−0.471951 | + | 0.881625i | \(0.656450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.5959i | − | 0.941720i | −0.882208 | − | 0.470860i | \(-0.843944\pi\) | ||
0.882208 | − | 0.470860i | \(-0.156056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.5558 | − | 2.92820i | 0.506113 | − | 0.140397i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3205i | 0.826663i | 0.910581 | + | 0.413331i | \(0.135635\pi\) | ||||
−0.910581 | + | 0.413331i | \(0.864365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | − | 19.7990i | −0.333333 | − | 0.942809i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 30.0000i | − | 1.42534i | −0.701498 | − | 0.712672i | \(-0.747485\pi\) | ||
0.701498 | − | 0.712672i | \(-0.252515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.00000 | − | 9.79796i | 0.379236 | − | 0.464468i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.82843 | − | 4.00000i | 0.133780 | − | 0.189194i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.6274i | − | 1.06785i | −0.845531 | − | 0.533927i | \(-0.820716\pi\) | ||
0.845531 | − | 0.533927i | \(-0.179284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.7128i | 1.30495i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.46410 | + | 4.89898i | −0.162758 | + | 0.230174i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.79796i | 0.458329i | 0.973388 | + | 0.229165i | \(0.0735994\pi\) | ||||
−0.973388 | + | 0.229165i | \(0.926401\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.89898 | + | 17.3205i | −0.228665 | + | 0.808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.7696i | 1.71253i | 0.516538 | + | 0.856264i | \(0.327221\pi\) | ||||
−0.516538 | + | 0.856264i | \(0.672779\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9706 | 0.788689 | 0.394344 | − | 0.918963i | \(-0.370972\pi\) | ||||
0.394344 | + | 0.918963i | \(0.370972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.9282 | − | 3.58630i | 0.599531 | − | 0.166311i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000i | 0.832941i | 0.909149 | + | 0.416470i | \(0.136733\pi\) | ||||
−0.909149 | + | 0.416470i | \(0.863267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.89898 | + | 6.92820i | −0.225733 | + | 0.319235i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.5692 | −1.91135 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9706 | + | 3.46410i | −0.778663 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3923 | + | 29.3939i | 0.475831 | + | 1.34585i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.5959 | −0.895360 | −0.447680 | − | 0.894194i | \(-0.647750\pi\) | ||||
−0.447680 | + | 0.894194i | \(0.647750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | 1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.9411 | 1.53802 | 0.769010 | − | 0.639237i | \(-0.220750\pi\) | ||||
0.769010 | + | 0.639237i | \(0.220750\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | − | 8.48528i | −0.542659 | − | 0.383718i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.4949 | −1.10544 | −0.552720 | − | 0.833367i | \(-0.686410\pi\) | ||||
−0.552720 | + | 0.833367i | \(0.686410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.79796i | 0.441278i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.1106 | + | 30.9282i | −0.499386 | + | 1.39012i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.46410i | 0.155074i | 0.996989 | + | 0.0775372i | \(0.0247057\pi\) | ||||
−0.996989 | + | 0.0775372i | \(0.975294\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | + | 8.48528i | −0.268060 | + | 0.379094i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000i | 0.267527i | 0.991013 | + | 0.133763i | \(0.0427062\pi\) | ||||
−0.991013 | + | 0.133763i | \(0.957294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.0000 | + | 24.4949i | −0.889988 | + | 1.09001i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.5563 | − | 11.0000i | −0.690882 | − | 0.488527i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.7696i | 1.62978i | 0.579614 | + | 0.814891i | \(0.303203\pi\) | ||||
−0.579614 | + | 0.814891i | \(0.696797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.3205 | − | 4.89898i | −0.764719 | − | 0.216295i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 29.3939i | − | 1.29274i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.89898 | − | 3.46410i | −0.215041 | − | 0.152057i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.65685i | 0.247831i | 0.992293 | + | 0.123916i | \(0.0395452\pi\) | ||||
−0.992293 | + | 0.123916i | \(0.960455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.4264 | 1.85518 | 0.927589 | − | 0.373603i | \(-0.121878\pi\) | ||||
0.927589 | + | 0.373603i | \(0.121878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000i | 0.522728i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.89898 | − | 13.8564i | −0.212598 | − | 0.601317i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.7128 | 1.20038 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.4558 | − | 31.1769i | 1.10055 | − | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.6410 | + | 24.4949i | 1.49487 | + | 1.05703i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.2929 | 1.47710 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0000 | 1.46177 | 0.730887 | − | 0.682498i | \(-0.239107\pi\) | ||||
0.730887 | + | 0.682498i | \(0.239107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.1421 | + | 10.0000i | 0.606897 | + | 0.429141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.46410 | − | 2.82843i | −0.148386 | − | 0.121157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4558 | 1.08841 | 0.544207 | − | 0.838951i | \(-0.316831\pi\) | ||||
0.544207 | + | 0.838951i | \(0.316831\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.00000 | + | 5.65685i | 0.0853579 | + | 0.241429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.79796 | −0.417407 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.2832 | + | 5.07180i | −0.776080 | + | 0.215286i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.46410 | −0.146779 | −0.0733893 | − | 0.997303i | \(-0.523382\pi\) | ||||
−0.0733893 | + | 0.997303i | \(0.523382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.5692i | 1.75819i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | − | 16.9706i | −1.01328 | − | 0.716498i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0000i | 0.758610i | 0.925272 | + | 0.379305i | \(0.123837\pi\) | ||||
−0.925272 | + | 0.379305i | \(0.876163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | − | 4.89898i | −0.252422 | − | 0.206102i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2843i | 1.18574i | 0.805299 | + | 0.592869i | \(0.202005\pi\) | ||||
−0.805299 | + | 0.592869i | \(0.797995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 38.1051i | − | 1.59465i | −0.603550 | − | 0.797325i | \(-0.706248\pi\) | ||
0.603550 | − | 0.797325i | \(-0.293752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.7128 | + | 19.5959i | 1.15772 | + | 0.818631i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.3939 | + | 6.00000i | −1.22581 | + | 0.250217i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.5959i | − | 0.815789i | −0.913029 | − | 0.407894i | \(-0.866263\pi\) | ||
0.913029 | − | 0.407894i | \(-0.133737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.5959 | + | 27.7128i | −0.814379 | + | 1.15171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −50.9117 | −2.10855 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.9282 | + | 11.1106i | 1.27872 | + | 0.459368i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0000i | 0.742940i | 0.928445 | + | 0.371470i | \(0.121146\pi\) | ||||
−0.928445 | + | 0.371470i | \(0.878854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.2929 | + | 24.2487i | 1.41062 | + | 0.997459i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.2487 | −0.995775 | −0.497888 | − | 0.867242i | \(-0.665891\pi\) | ||||
−0.497888 | + | 0.867242i | \(0.665891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.3923 | − | 14.6969i | 0.425329 | − | 0.601506i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.79796 | −0.400334 | −0.200167 | − | 0.979762i | \(-0.564148\pi\) | ||||
−0.200167 | + | 0.979762i | \(0.564148\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.48528 | − | 24.0000i | −0.345547 | − | 0.977356i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.5167 | − | 18.3848i | −0.915432 | − | 0.747447i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.9706 | 0.688814 | 0.344407 | − | 0.938820i | \(-0.388080\pi\) | ||||
0.344407 | + | 0.938820i | \(0.388080\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.3939 | −1.18915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6969i | 0.593604i | 0.954939 | + | 0.296802i | \(0.0959201\pi\) | ||||
−0.954939 | + | 0.296802i | \(0.904080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.1117 | + | 5.85641i | −0.851305 | + | 0.236153i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.2487 | −0.976216 | −0.488108 | − | 0.872783i | \(-0.662313\pi\) | ||||
−0.488108 | + | 0.872783i | \(0.662313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.3923i | − | 0.417702i | −0.977947 | − | 0.208851i | \(-0.933028\pi\) | ||
0.977947 | − | 0.208851i | \(-0.0669724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.0000 | − | 8.48528i | −1.20386 | − | 0.340503i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.9706 | − | 24.0000i | 0.677739 | − | 0.958468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 16.9706i | − | 0.676661i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.1051i | − | 1.51694i | −0.651707 | − | 0.758470i | \(-0.725947\pi\) | ||
0.651707 | − | 0.758470i | \(-0.274053\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.2487 | − | 34.2929i | 0.963800 | − | 1.36302i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29.3939 | + | 24.0000i | 1.16646 | + | 0.952411i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 34.2929i | − | 1.35873i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.79796 | − | 27.7128i | −0.387601 | − | 1.09630i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.6274i | − | 0.893729i | −0.894602 | − | 0.446865i | \(-0.852541\pi\) | ||
0.894602 | − | 0.446865i | \(-0.147459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.48528 | −0.334627 | −0.167313 | − | 0.985904i | \(-0.553509\pi\) | ||||
−0.167313 | + | 0.985904i | \(0.553509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.78461 | − | 31.6675i | −0.345894 | − | 1.24691i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 42.0000i | − | 1.65119i | −0.564263 | − | 0.825595i | \(-0.690840\pi\) | ||
0.564263 | − | 0.825595i | \(-0.309160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1769 | −1.22005 | −0.610023 | − | 0.792383i | \(-0.708840\pi\) | ||||
−0.610023 | + | 0.792383i | \(0.708840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.48528 | − | 6.92820i | −0.331547 | − | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.7128 | − | 9.79796i | 1.08118 | − | 0.382255i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.6969 | −0.572511 | −0.286256 | − | 0.958153i | \(-0.592411\pi\) | ||||
−0.286256 | + | 0.958153i | \(0.592411\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.9706 | + | 24.0000i | −0.659082 | + | 0.932083i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.9706 | −0.657103 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000 | + | 16.9706i | 0.927894 | + | 0.656120i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.79796 | −0.378246 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 39.1918i | − | 1.51073i | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||
0.655302 | − | 0.755367i | \(-0.272541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9091 | − | 1.92820i | −0.997242 | − | 0.0742166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3923 | 0.399409 | 0.199704 | − | 0.979856i | \(-0.436002\pi\) | ||||
0.199704 | + | 0.979856i | \(0.436002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | − | 8.48528i | 0.229920 | − | 0.325157i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 6.00000i | − | 0.229584i | −0.993390 | − | 0.114792i | \(-0.963380\pi\) | ||
0.993390 | − | 0.114792i | \(-0.0366201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | − | 4.89898i | −0.229248 | − | 0.187180i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.1421 | + | 10.0000i | 0.539556 | + | 0.381524i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 50.9117i | 1.93958i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1769i | 1.18603i | 0.805193 | + | 0.593013i | \(0.202062\pi\) | ||||
−0.805193 | + | 0.593013i | \(0.797938\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.4949 | − | 30.0000i | 0.929144 | − | 1.13796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.5959i | − | 0.742248i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.89898 | + | 3.46410i | 0.185296 | + | 0.131024i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.7990i | − | 0.747798i | −0.927470 | − | 0.373899i | \(-0.878021\pi\) | ||
0.927470 | − | 0.373899i | \(-0.121979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9706 | 0.640057 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.3923 | − | 6.21166i | 0.843343 | − | 0.233945i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0000 | −1.42712 | −0.713560 | − | 0.700594i | \(-0.752918\pi\) | ||||
−0.713560 | + | 0.700594i | \(0.752918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.3939 | − | 10.3923i | 1.10236 | − | 0.389742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.7846 | −0.778390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.9411 | + | 41.5692i | −1.26933 | + | 1.55460i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5959 | 0.730804 | 0.365402 | − | 0.930850i | \(-0.380931\pi\) | ||||
0.365402 | + | 0.930850i | \(0.380931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.1421 | + | 10.0000i | 0.525952 | + | 0.371904i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.8564 | + | 2.82843i | −0.514614 | + | 0.105045i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.3939 | 1.08717 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.0908i | 1.62853i | 0.580492 | + | 0.814266i | \(0.302860\pi\) | ||||
−0.580492 | + | 0.814266i | \(0.697140\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.24693 | + | 26.1244i | 0.267307 | + | 0.963611i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.5692 | 1.53122 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.2487i | − | 0.892003i | −0.895032 | − | 0.446002i | \(-0.852848\pi\) | ||
0.895032 | − | 0.446002i | \(-0.147152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | − | 16.9706i | −0.881662 | − | 0.623429i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.00000 | + | 4.89898i | −0.146549 | + | 0.179485i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.9706 | − | 6.00000i | 0.620920 | − | 0.219529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1769i | 1.13766i | 0.822455 | + | 0.568831i | \(0.192604\pi\) | ||||
−0.822455 | + | 0.568831i | \(0.807396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.7846 | + | 14.6969i | 0.757433 | + | 0.535586i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.89898 | − | 6.00000i | 0.178292 | − | 0.218362i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6969i | 0.534169i | 0.963673 | + | 0.267085i | \(0.0860603\pi\) | ||||
−0.963673 | + | 0.267085i | \(0.913940\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.3939 | − | 41.5692i | 1.06693 | − | 1.50887i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.5980i | 1.43543i | 0.696339 | + | 0.717713i | \(0.254811\pi\) | ||||
−0.696339 | + | 0.717713i | \(0.745189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.85641 | − | 21.8695i | 0.284049 | − | 0.790695i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 24.0000i | − | 0.866590i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.89898 | + | 3.46410i | 0.176432 | + | 0.124757i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.2487 | 0.872166 | 0.436083 | − | 0.899907i | \(-0.356365\pi\) | ||||
0.436083 | + | 0.899907i | \(0.356365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.9706 | + | 3.46410i | −0.609601 | + | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.5959 | 0.702097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.0000 | 1.71758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.1421 | − | 4.00000i | −0.505399 | − | 0.142948i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.92820 | − | 8.48528i | 0.247278 | − | 0.302853i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4558 | 0.907403 | 0.453701 | − | 0.891154i | \(-0.350103\pi\) | ||||
0.453701 | + | 0.891154i | \(0.350103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.00000 | + | 8.48528i | −0.213606 | + | 0.302084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.79796i | 0.347936i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.7589 | − | 38.7846i | −0.381579 | − | 1.37555i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3205 | −0.613524 | −0.306762 | − | 0.951786i | \(-0.599246\pi\) | ||||
−0.306762 | + | 0.951786i | \(0.599246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7846i | 0.735307i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.0000 | + | 5.65685i | −0.565332 | + | 0.199875i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.0000i | 1.69388i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.7990 | − | 28.0000i | 0.696957 | − | 0.985647i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.65685i | 0.198884i | 0.995043 | + | 0.0994422i | \(0.0317058\pi\) | ||||
−0.995043 | + | 0.0994422i | \(0.968294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3205i | 0.608205i | 0.952639 | + | 0.304103i | \(0.0983566\pi\) | ||||
−0.952639 | + | 0.304103i | \(0.901643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.3923 | − | 14.6969i | 0.364474 | − | 0.515444i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.6969 | + | 12.0000i | 0.514811 | + | 0.420342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.3939i | 1.02836i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.82843i | − | 0.0987128i | −0.998781 | − | 0.0493564i | \(-0.984283\pi\) | ||
0.998781 | − | 0.0493564i | \(-0.0157170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.9411 | −1.18311 | −0.591557 | − | 0.806263i | \(-0.701486\pi\) | ||||
−0.591557 | + | 0.806263i | \(0.701486\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.0718 | − | 38.8401i | 0.594364 | − | 1.35224i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 54.0000i | − | 1.87776i | −0.344239 | − | 0.938882i | \(-0.611863\pi\) | ||
0.344239 | − | 0.938882i | \(-0.388137\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.0000 | −1.59765 | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.6969 | + | 20.7846i | −0.509831 | + | 0.721010i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.2487 | −0.840168 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.48528 | − | 10.3923i | 0.293645 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.3205 | − | 4.89898i | −0.598684 | − | 0.169334i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.79796 | 0.338263 | 0.169132 | − | 0.985593i | \(-0.445904\pi\) | ||||
0.169132 | + | 0.985593i | \(0.445904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.65685 | − | 8.00000i | 0.194832 | − | 0.275535i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.0526 | + | 15.5563i | 0.655428 | + | 0.535155i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.0000 | + | 8.48528i | 0.411839 | + | 0.291214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.3939 | 1.00761 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.0908i | − | 1.50964i | −0.655932 | − | 0.754820i | \(-0.727724\pi\) | ||
0.655932 | − | 0.754820i | \(-0.272276\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.8695 | + | 7.85641i | 0.747923 | + | 0.268683i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.2487 | −0.828320 | −0.414160 | − | 0.910204i | \(-0.635925\pi\) | ||||
−0.414160 | + | 0.910204i | \(0.635925\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 38.1051i | − | 1.30013i | −0.759879 | − | 0.650065i | \(-0.774742\pi\) | ||
0.759879 | − | 0.650065i | \(-0.225258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.00000 | + | 4.89898i | 0.204006 | + | 0.166570i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.07107 | − | 5.00000i | −0.240146 | − | 0.169809i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.9117i | 1.72706i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 41.5692i | − | 1.40852i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.4949i | 0.827134i | 0.910474 | + | 0.413567i | \(0.135717\pi\) | ||||
−0.910474 | + | 0.413567i | \(0.864283\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.4949 | − | 17.3205i | −0.826192 | − | 0.584206i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.6274i | − | 0.762337i | −0.924506 | − | 0.381169i | \(-0.875522\pi\) | ||
0.924506 | − | 0.381169i | \(-0.124478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.4264 | −1.42776 | −0.713881 | − | 0.700267i | \(-0.753064\pi\) | ||||
−0.713881 | + | 0.700267i | \(0.753064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.07180 | + | 18.2832i | 0.170487 | + | 0.614584i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 42.0000i | − | 1.41022i | −0.709097 | − | 0.705111i | \(-0.750897\pi\) | ||
0.709097 | − | 0.705111i | \(-0.249103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.2929 | − | 27.7128i | 1.14885 | − | 0.928414i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.7846 | −0.695530 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.4264 | − | 34.6410i | −1.41816 | − | 1.15792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41.5692 | − | 29.3939i | −1.38796 | − | 0.981433i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.79796 | −0.326780 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.3205 | − | 14.1421i | −0.575753 | − | 0.470100i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.48528 | 0.281749 | 0.140875 | − | 0.990027i | \(-0.455009\pi\) | ||||
0.140875 | + | 0.990027i | \(0.455009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 40.0000 | − | 14.1421i | 1.32672 | − | 0.469065i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.5959 | −0.649242 | −0.324621 | − | 0.945844i | \(-0.605237\pi\) | ||||
−0.324621 | + | 0.945844i | \(0.605237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.3939i | 0.972795i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.07055 | − | 7.46410i | −0.0684503 | − | 0.246756i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.46410i | 0.114270i | 0.998366 | + | 0.0571351i | \(0.0181966\pi\) | ||||
−0.998366 | + | 0.0571351i | \(0.981803\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | − | 8.48528i | −0.395413 | − | 0.279600i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 48.0000i | − | 1.57994i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.0000 | − | 4.89898i | 0.789115 | − | 0.161077i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 22.6274i | − | 0.742381i | −0.928557 | − | 0.371191i | \(-0.878950\pi\) | ||
0.928557 | − | 0.371191i | \(-0.121050\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 24.2487i | − | 0.794719i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.8564 | + | 9.79796i | 0.453638 | + | 0.320771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.3939 | + | 24.0000i | 0.961283 | + | 0.784884i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.9898i | 1.60043i | 0.599715 | + | 0.800213i | \(0.295280\pi\) | ||||
−0.599715 | + | 0.800213i | \(0.704720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.79796 | + | 13.8564i | −0.319744 | + | 0.452187i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.82843i | 0.0922041i | 0.998937 | + | 0.0461020i | \(0.0146799\pi\) | ||||
−0.998937 | + | 0.0461020i | \(0.985320\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.9411 | 1.10528 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 54.0000i | − | 1.75476i | −0.479792 | − | 0.877382i | \(-0.659288\pi\) | ||
0.479792 | − | 0.877382i | \(-0.340712\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.0000 | 1.55815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.4949 | − | 17.3205i | −0.794301 | − | 0.561656i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.8897 | 1.90763 | 0.953813 | − | 0.300402i | \(-0.0971208\pi\) | ||||
0.953813 | + | 0.300402i | \(0.0971208\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.9411 | − | 27.7128i | −1.09831 | − | 0.896766i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.8564 | − | 19.5959i | 0.447914 | − | 0.633446i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.9117 | + | 18.0000i | −1.64061 | + | 0.580042i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.7128 | − | 33.9411i | 0.892107 | − | 1.09260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.9411 | 1.09147 | 0.545737 | − | 0.837957i | \(-0.316250\pi\) | ||||
0.545737 | + | 0.837957i | \(0.316250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | + | 16.9706i | −0.385496 | + | 0.545173i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.89898 | −0.157216 | −0.0786079 | − | 0.996906i | \(-0.525048\pi\) | ||||
−0.0786079 | + | 0.996906i | \(0.525048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38.8401 | − | 17.0718i | −1.24388 | − | 0.546735i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.9615 | −1.66240 | −0.831198 | − | 0.555976i | \(-0.812345\pi\) | ||||
−0.831198 | + | 0.555976i | \(0.812345\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27.7128i | − | 0.885705i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | + | 5.65685i | 0.0638551 | + | 0.180609i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.00000i | 0.191370i | 0.995412 | + | 0.0956851i | \(0.0305042\pi\) | ||||
−0.995412 | + | 0.0956851i | \(0.969496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.0000 | − | 34.2929i | −1.33823 | − | 1.09266i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.9117i | 1.61890i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 38.1051i | − | 1.21045i | −0.796055 | − | 0.605224i | \(-0.793083\pi\) | ||
0.796055 | − | 0.605224i | \(-0.206917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.3205 | + | 24.4949i | −0.549650 | + | 0.777322i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.6969 | + | 18.0000i | −0.465924 | + | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.8888i | 1.70667i | 0.521359 | + | 0.853337i | \(0.325425\pi\) | ||||
−0.521359 | + | 0.853337i | \(0.674575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.4949 | + | 6.92820i | 0.774984 | + | 0.219199i |
(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 | 960.2.o.d.959.7 | 8 | ||
3.2 | odd | 2 | inner | 960.2.o.d.959.6 | 8 | ||
4.3 | odd | 2 | inner | 960.2.o.d.959.1 | 8 | ||
5.4 | even | 2 | inner | 960.2.o.d.959.2 | 8 | ||
8.3 | odd | 2 | 240.2.o.b.239.8 | yes | 8 | ||
8.5 | even | 2 | 240.2.o.b.239.2 | yes | 8 | ||
12.11 | even | 2 | inner | 960.2.o.d.959.4 | 8 | ||
15.14 | odd | 2 | inner | 960.2.o.d.959.3 | 8 | ||
20.19 | odd | 2 | inner | 960.2.o.d.959.8 | 8 | ||
24.5 | odd | 2 | 240.2.o.b.239.3 | yes | 8 | ||
24.11 | even | 2 | 240.2.o.b.239.5 | yes | 8 | ||
40.3 | even | 4 | 1200.2.h.j.1151.3 | 4 | |||
40.13 | odd | 4 | 1200.2.h.n.1151.2 | 4 | |||
40.19 | odd | 2 | 240.2.o.b.239.1 | ✓ | 8 | ||
40.27 | even | 4 | 1200.2.h.n.1151.1 | 4 | |||
40.29 | even | 2 | 240.2.o.b.239.7 | yes | 8 | ||
40.37 | odd | 4 | 1200.2.h.j.1151.4 | 4 | |||
60.59 | even | 2 | inner | 960.2.o.d.959.5 | 8 | ||
120.29 | odd | 2 | 240.2.o.b.239.6 | yes | 8 | ||
120.53 | even | 4 | 1200.2.h.j.1151.1 | 4 | |||
120.59 | even | 2 | 240.2.o.b.239.4 | yes | 8 | ||
120.77 | even | 4 | 1200.2.h.n.1151.3 | 4 | |||
120.83 | odd | 4 | 1200.2.h.n.1151.4 | 4 | |||
120.107 | odd | 4 | 1200.2.h.j.1151.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.o.b.239.1 | ✓ | 8 | 40.19 | odd | 2 | ||
240.2.o.b.239.2 | yes | 8 | 8.5 | even | 2 | ||
240.2.o.b.239.3 | yes | 8 | 24.5 | odd | 2 | ||
240.2.o.b.239.4 | yes | 8 | 120.59 | even | 2 | ||
240.2.o.b.239.5 | yes | 8 | 24.11 | even | 2 | ||
240.2.o.b.239.6 | yes | 8 | 120.29 | odd | 2 | ||
240.2.o.b.239.7 | yes | 8 | 40.29 | even | 2 | ||
240.2.o.b.239.8 | yes | 8 | 8.3 | odd | 2 | ||
960.2.o.d.959.1 | 8 | 4.3 | odd | 2 | inner | ||
960.2.o.d.959.2 | 8 | 5.4 | even | 2 | inner | ||
960.2.o.d.959.3 | 8 | 15.14 | odd | 2 | inner | ||
960.2.o.d.959.4 | 8 | 12.11 | even | 2 | inner | ||
960.2.o.d.959.5 | 8 | 60.59 | even | 2 | inner | ||
960.2.o.d.959.6 | 8 | 3.2 | odd | 2 | inner | ||
960.2.o.d.959.7 | 8 | 1.1 | even | 1 | trivial | ||
960.2.o.d.959.8 | 8 | 20.19 | odd | 2 | inner | ||
1200.2.h.j.1151.1 | 4 | 120.53 | even | 4 | |||
1200.2.h.j.1151.2 | 4 | 120.107 | odd | 4 | |||
1200.2.h.j.1151.3 | 4 | 40.3 | even | 4 | |||
1200.2.h.j.1151.4 | 4 | 40.37 | odd | 4 | |||
1200.2.h.n.1151.1 | 4 | 40.27 | even | 4 | |||
1200.2.h.n.1151.2 | 4 | 40.13 | odd | 4 | |||
1200.2.h.n.1151.3 | 4 | 120.77 | even | 4 | |||
1200.2.h.n.1151.4 | 4 | 120.83 | odd | 4 |