Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,2,Mod(1151,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, 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("1200.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(9.58204824255\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1151 |
Dual form | 1200.2.h.n.1151.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.89898 | 1.35873 | 0.679366 | − | 0.733799i | \(-0.262255\pi\) | ||||
0.679366 | + | 0.733799i | \(0.262255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.82843i | − | 0.525226i | −0.964901 | − | 0.262613i | \(-0.915416\pi\) | ||
0.964901 | − | 0.262613i | \(-0.0845842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.89898 | + | 6.92820i | 0.852803 | + | 1.20605i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89898 | 0.805387 | 0.402694 | − | 0.915335i | \(-0.368074\pi\) | ||||
0.402694 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.89898 | + | 6.92820i | 0.784465 | + | 1.10940i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528i | 1.29399i | 0.762493 | + | 0.646997i | \(0.223975\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.89898 | + | 3.46410i | −0.685994 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923i | 1.42749i | 0.700404 | + | 0.713746i | \(0.253003\pi\) | ||||
−0.700404 | + | 0.713746i | \(0.746997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.89898 | − | 3.46410i | 0.648886 | − | 0.458831i | ||||
\(58\) | 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 | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.48528i | 1.03664i | 0.855186 | + | 0.518321i | \(0.173443\pi\) | ||||
−0.855186 | + | 0.518321i | \(0.826557\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 9.79796 | 1.14676 | 0.573382 | − | 0.819288i | \(-0.305631\pi\) | ||||
0.573382 | + | 0.819288i | \(0.305631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | − | 2.82843i | 0.428845 | − | 0.303239i | ||||
\(88\) | 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 | ||||||||
\(93\) | 4.89898 | − | 3.46410i | 0.508001 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | − | 3.46410i | − | 0.325875i | −0.986636 | − | 0.162938i | \(-0.947903\pi\) | ||
0.986636 | − | 0.162938i | \(-0.0520969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.89898 | + | 13.8564i | −0.452911 | + | 1.28103i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00000 | + | 5.65685i | −0.721336 | + | 0.510061i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.9706i | − | 1.50589i | −0.658081 | − | 0.752947i | \(-0.728632\pi\) | ||
0.658081 | − | 0.752947i | \(-0.271368\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0000 | + | 8.48528i | −1.05654 | + | 0.747087i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.89898 | −0.428026 | −0.214013 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46410i | 0.295958i | 0.988990 | + | 0.147979i | \(0.0472768\pi\) | ||||
−0.988990 | + | 0.147979i | \(0.952723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | + | 8.48528i | 0.505291 | + | 0.714590i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.0000 | 2.00698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.00000 | + | 9.89949i | 0.577350 | + | 0.816497i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.82843i | 0.231714i | 0.993266 | + | 0.115857i | \(0.0369614\pi\) | ||||
−0.993266 | + | 0.115857i | \(0.963039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.79796 | − | 3.46410i | −0.792118 | − | 0.280056i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.89898 | −0.390981 | −0.195491 | − | 0.980706i | \(-0.562630\pi\) | ||||
−0.195491 | + | 0.980706i | \(0.562630\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.6969 | + | 10.3923i | −1.16554 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.48528i | − | 0.664619i | −0.943170 | − | 0.332309i | \(-0.892172\pi\) | ||
0.943170 | − | 0.332309i | \(-0.107828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.79796 | + | 3.46410i | 0.749269 | + | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.46410i | − | 0.263371i | −0.991292 | − | 0.131685i | \(-0.957961\pi\) | ||
0.991292 | − | 0.131685i | \(-0.0420389\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.89898 | − | 6.92820i | −0.368230 | − | 0.520756i | ||||
\(178\) | 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 | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | − | 2.82843i | −0.147844 | − | 0.209083i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9706i | 1.24101i | ||||||||
\(188\) | 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 | ||||||||
\(193\) | −19.5959 | −1.41055 | −0.705273 | − | 0.708936i | \(-0.749175\pi\) | ||||
−0.705273 | + | 0.708936i | \(0.749175\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 24.2487i | − | 1.72765i | −0.503793 | − | 0.863825i | \(-0.668062\pi\) | ||
0.503793 | − | 0.863825i | \(-0.331938\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | − | 16.9706i | 0.417029 | − | 1.17954i | ||||
\(208\) | 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 | ||||||||
\(213\) | −9.79796 | − | 13.8564i | −0.671345 | − | 0.949425i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 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 | ||||||||
\(223\) | − | 16.9706i | − | 1.13643i | −0.822879 | − | 0.568216i | \(-0.807634\pi\) | ||
0.822879 | − | 0.568216i | \(-0.192366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | 0.398234 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(228\) | 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 | ||||||||
\(233\) | − | 3.46410i | − | 0.226941i | −0.993541 | − | 0.113470i | \(-0.963803\pi\) | ||
0.993541 | − | 0.113470i | \(-0.0361967\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.6969 | − | 10.3923i | 0.954669 | − | 0.675053i | ||||
\(238\) | 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 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 16.9706i | − | 1.07981i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 8.48528i | −0.380235 | − | 0.537733i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6969 | −0.927663 | −0.463831 | − | 0.885924i | \(-0.653526\pi\) | ||||
−0.463831 | + | 0.885924i | \(0.653526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.3939 | −1.84798 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.46410i | 0.216085i | 0.994146 | + | 0.108042i | \(0.0344582\pi\) | ||||
−0.994146 | + | 0.108042i | \(0.965542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | + | 2.82843i | 0.495188 | + | 0.175075i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | −0.369976 | −0.184988 | − | 0.982741i | \(-0.559225\pi\) | ||||
−0.184988 | + | 0.982741i | \(0.559225\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.00000 | + | 5.65685i | −0.489592 | + | 0.346194i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7990i | 1.20717i | 0.797300 | + | 0.603583i | \(0.206261\pi\) | ||||
−0.797300 | + | 0.603583i | \(0.793739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3923i | 0.631288i | 0.948878 | + | 0.315644i | \(0.102220\pi\) | ||||
−0.948878 | + | 0.315644i | \(0.897780\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6969 | −0.883053 | −0.441527 | − | 0.897248i | \(-0.645563\pi\) | ||||
−0.441527 | + | 0.897248i | \(0.645563\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.79796 | + | 3.46410i | 0.586588 | + | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.65685i | 0.337460i | 0.985662 | + | 0.168730i | \(0.0539665\pi\) | ||||
−0.985662 | + | 0.168730i | \(0.946033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528i | 0.504398i | 0.967675 | + | 0.252199i | \(0.0811537\pi\) | ||||
−0.967675 | + | 0.252199i | \(0.918846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 17.3205i | − | 1.01187i | −0.862570 | − | 0.505937i | \(-0.831147\pi\) | ||
0.862570 | − | 0.505937i | \(-0.168853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.4949 | + | 6.92820i | −1.42134 | + | 0.402015i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.3939 | −1.69989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.0000 | − | 14.1421i | 1.14897 | − | 0.812444i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.48528i | 0.484281i | 0.970241 | + | 0.242140i | \(0.0778494\pi\) | ||||
−0.970241 | + | 0.242140i | \(0.922151\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −9.79796 | −0.553813 | −0.276907 | − | 0.960897i | \(-0.589309\pi\) | ||||
−0.276907 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3205i | 0.972817i | 0.873732 | + | 0.486408i | \(0.161693\pi\) | ||||
−0.873732 | + | 0.486408i | \(0.838307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 13.8564i | − | 0.775810i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | − | 25.4558i | −1.00466 | − | 1.42081i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | + | 2.82843i | 0.110600 | + | 0.156412i | ||||
\(328\) | 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 | ||||||||
\(333\) | −4.89898 | + | 13.8564i | −0.268462 | + | 0.759326i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 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 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | − | 31.1769i | − | 1.65938i | −0.558225 | − | 0.829690i | \(-0.688517\pi\) | ||
0.558225 | − | 0.829690i | \(-0.311483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.79796 | −0.517116 | −0.258558 | − | 0.965996i | \(-0.583247\pi\) | ||||
−0.258558 | + | 0.965996i | \(0.583247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.0000 | + | 18.3848i | 0.682323 | + | 0.964951i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.9706i | − | 0.885856i | −0.896557 | − | 0.442928i | \(-0.853940\pi\) | ||
0.896557 | − | 0.442928i | \(-0.146060\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.0000 | − | 5.65685i | −0.832927 | − | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6969 | 0.760979 | 0.380489 | − | 0.924785i | \(-0.375756\pi\) | ||||
0.380489 | + | 0.924785i | \(0.375756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 13.8564i | − | 0.713641i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.0000 | − | 16.9706i | 1.22956 | − | 0.869428i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | −0.306586 | −0.153293 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153293 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.0000 | − | 8.48528i | −1.21999 | − | 0.431331i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.82843i | 0.143407i | 0.997426 | + | 0.0717035i | \(0.0228435\pi\) | ||||
−0.997426 | + | 0.0717035i | \(0.977156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 20.7846i | − | 1.05112i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.89898 | − | 6.92820i | −0.247121 | − | 0.349482i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.89898 | −0.245873 | −0.122936 | − | 0.992415i | \(-0.539231\pi\) | ||||
−0.122936 | + | 0.992415i | \(0.539231\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.6274i | − | 1.12996i | −0.825105 | − | 0.564980i | \(-0.808884\pi\) | ||
0.825105 | − | 0.564980i | \(-0.191116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 16.9706i | − | 0.845364i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.89898 | + | 3.46410i | −0.241649 | + | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.4949 | − | 17.3205i | 1.19952 | − | 0.848189i | ||||
\(418\) | 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 | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | + | 16.9706i | −0.291730 | + | 0.825137i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 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 | ||||||||
\(433\) | 19.5959 | 0.941720 | 0.470860 | − | 0.882208i | \(-0.343944\pi\) | ||||
0.470860 | + | 0.882208i | \(0.343944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7846i | 0.994263i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −30.0000 | −1.42534 | −0.712672 | − | 0.701498i | \(-0.752515\pi\) | ||||
−0.712672 | + | 0.701498i | \(0.752515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.00000 | + | 2.82843i | −0.189194 | + | 0.133780i | ||||
\(448\) | 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 | ||||||||
\(453\) | 4.89898 | − | 3.46410i | 0.230174 | − | 0.162758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.79796 | 0.458329 | 0.229165 | − | 0.973388i | \(-0.426401\pi\) | ||||
0.229165 | + | 0.973388i | \(0.426401\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | − | 16.9706i | − | 0.788689i | −0.918963 | − | 0.394344i | \(-0.870972\pi\) | ||
0.918963 | − | 0.394344i | \(-0.129028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.0000 | −0.832941 | −0.416470 | − | 0.909149i | \(-0.636733\pi\) | ||||
−0.416470 | + | 0.909149i | \(0.636733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.89898 | − | 6.92820i | −0.225733 | − | 0.319235i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 41.5692i | 1.91135i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.3939 | − | 10.3923i | −1.34585 | − | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.5959 | 0.895360 | 0.447680 | − | 0.894194i | \(-0.352250\pi\) | ||||
0.447680 | + | 0.894194i | \(0.352250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | 1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.9411i | 1.53802i | 0.639237 | + | 0.769010i | \(0.279250\pi\) | ||||
−0.639237 | + | 0.769010i | \(0.720750\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0000 | − | 8.48528i | 0.542659 | − | 0.383718i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4949 | 1.10544 | 0.552720 | − | 0.833367i | \(-0.313590\pi\) | ||||
0.552720 | + | 0.833367i | \(0.313590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.79796 | 0.441278 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.46410i | − | 0.155074i | −0.996989 | − | 0.0775372i | \(-0.975294\pi\) | ||
0.996989 | − | 0.0775372i | \(-0.0247057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 8.48528i | 0.268060 | + | 0.379094i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.0000 | + | 15.5563i | 0.488527 | + | 0.690882i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 36.7696i | − | 1.62978i | −0.579614 | − | 0.814891i | \(-0.696797\pi\) | ||
0.579614 | − | 0.814891i | \(-0.303203\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.89898 | + | 17.3205i | 0.216295 | + | 0.764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.3939 | 1.29274 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.89898 | − | 3.46410i | 0.215041 | − | 0.152057i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.65685i | − | 0.247831i | −0.992293 | − | 0.123916i | \(-0.960455\pi\) | ||
0.992293 | − | 0.123916i | \(-0.0395452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.4264i | 1.85518i | 0.373603 | + | 0.927589i | \(0.378122\pi\) | ||||
−0.373603 | + | 0.927589i | \(0.621878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | 0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.89898 | − | 13.8564i | 0.212598 | − | 0.601317i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.7128i | 1.20038i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.4949 | + | 34.6410i | 1.05703 | + | 1.49487i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.2929 | 1.47710 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.0000 | − | 14.1421i | −0.429141 | − | 0.606897i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.4558i | − | 1.08841i | −0.838951 | − | 0.544207i | \(-0.816831\pi\) | ||
0.838951 | − | 0.544207i | \(-0.183169\pi\) | |||||||
\(548\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.46410i | 0.146779i | 0.997303 | + | 0.0733893i | \(0.0233816\pi\) | ||||
−0.997303 | + | 0.0733893i | \(0.976618\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.5692i | 1.75819i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | + | 16.9706i | −1.01328 | + | 0.716498i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0000 | 0.758610 | 0.379305 | − | 0.925272i | \(-0.376163\pi\) | ||||
0.379305 | + | 0.925272i | \(0.376163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | ||||||||
\(573\) | 19.5959 | + | 27.7128i | 0.818631 | + | 1.15772i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5959 | −0.815789 | −0.407894 | − | 0.913029i | \(-0.633737\pi\) | ||||
−0.407894 | + | 0.913029i | \(0.633737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.5959 | − | 27.7128i | −0.814379 | − | 1.15171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.9117i | 2.10855i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0000 | −0.742940 | −0.371470 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371470 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.2929 | − | 24.2487i | 1.41062 | − | 0.997459i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.2487i | 0.995775i | 0.867242 | + | 0.497888i | \(0.165891\pi\) | ||||
−0.867242 | + | 0.497888i | \(0.834109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.6969 | − | 10.3923i | 0.601506 | − | 0.425329i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.79796 | 0.400334 | 0.200167 | − | 0.979762i | \(-0.435852\pi\) | ||||
0.200167 | + | 0.979762i | \(0.435852\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.0000 | − | 8.48528i | −0.977356 | − | 0.345547i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.9706i | 0.688814i | 0.938820 | + | 0.344407i | \(0.111920\pi\) | ||||
−0.938820 | + | 0.344407i | \(0.888080\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.3939 | 1.18915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6969 | 0.593604 | 0.296802 | − | 0.954939i | \(-0.404080\pi\) | ||||
0.296802 | + | 0.954939i | \(0.404080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.2487i | − | 0.976216i | −0.872783 | − | 0.488108i | \(-0.837687\pi\) | ||
0.872783 | − | 0.488108i | \(-0.162313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.3923i | 0.417702i | 0.977947 | + | 0.208851i | \(0.0669724\pi\) | ||||
−0.977947 | + | 0.208851i | \(0.933028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.0000 | − | 8.48528i | 1.20386 | − | 0.340503i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0000 | − | 16.9706i | 0.958468 | − | 0.677739i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9706i | 0.676661i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.1051i | 1.51694i | 0.651707 | + | 0.758470i | \(0.274053\pi\) | ||||
−0.651707 | + | 0.758470i | \(0.725947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.2929 | − | 24.2487i | 1.36302 | − | 0.963800i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.2929 | 1.35873 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.79796 | − | 27.7128i | 0.387601 | − | 1.09630i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.6274i | 0.893729i | 0.894602 | + | 0.446865i | \(0.147459\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.48528i | − | 0.334627i | −0.985904 | − | 0.167313i | \(-0.946491\pi\) | ||
0.985904 | − | 0.167313i | \(-0.0535092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.0000 | −1.65119 | −0.825595 | − | 0.564263i | \(-0.809160\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 31.1769i | − | 1.22005i | −0.792383 | − | 0.610023i | \(-0.791160\pi\) | ||
0.792383 | − | 0.610023i | \(-0.208840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.79796 | + | 27.7128i | −0.382255 | + | 1.08118i | ||||
\(658\) | 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 | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.0000 | + | 16.9706i | −0.932083 | + | 0.659082i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.9706i | 0.657103i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000 | − | 16.9706i | 0.927894 | − | 0.656120i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.79796 | −0.378246 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.1918 | 1.51073 | 0.755367 | − | 0.655302i | \(-0.227459\pi\) | ||||
0.755367 | + | 0.655302i | \(0.227459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 10.3923i | − | 0.399409i | −0.979856 | − | 0.199704i | \(-0.936002\pi\) | ||
0.979856 | − | 0.199704i | \(-0.0639982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | + | 8.48528i | 0.229920 | + | 0.325157i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | −0.229584 | −0.114792 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114792 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0000 | + | 14.1421i | 0.381524 | + | 0.539556i | ||||
\(688\) | 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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.5959 | −0.742248 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | − | 16.9706i | − | 0.640057i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(713\) | 20.7846i | 0.778390i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.5959 | −0.730804 | −0.365402 | − | 0.930850i | \(-0.619069\pi\) | ||||
−0.365402 | + | 0.930850i | \(0.619069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0000 | + | 14.1421i | 0.371904 | + | 0.525952i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.3939 | −1.08717 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.0908 | 1.62853 | 0.814266 | − | 0.580492i | \(-0.197140\pi\) | ||||
0.814266 | + | 0.580492i | \(0.197140\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.5692i | 1.53122i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.2487i | 0.892003i | 0.895032 | + | 0.446002i | \(0.147152\pi\) | ||||
−0.895032 | + | 0.446002i | \(0.852848\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.0000 | − | 16.9706i | 0.881662 | − | 0.623429i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.00000 | −0.220119 | −0.110059 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110059 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | − | 16.9706i | 0.219529 | − | 0.620920i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 31.1769i | − | 1.13766i | −0.822455 | − | 0.568831i | \(-0.807396\pi\) | ||
0.822455 | − | 0.568831i | \(-0.192604\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.6969 | − | 20.7846i | −0.535586 | − | 0.757433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6969 | −0.534169 | −0.267085 | − | 0.963673i | \(-0.586060\pi\) | ||||
−0.267085 | + | 0.963673i | \(0.586060\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.3939 | − | 41.5692i | −1.06693 | − | 1.50887i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 39.5980i | − | 1.43543i | −0.696339 | − | 0.717713i | \(-0.745189\pi\) | ||
0.696339 | − | 0.717713i | \(-0.254811\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.0000 | −0.866590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.89898 | + | 3.46410i | −0.176432 | + | 0.124757i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.2487i | 0.872166i | 0.899907 | + | 0.436083i | \(0.143635\pi\) | ||||
−0.899907 | + | 0.436083i | \(0.856365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.5959 | 0.702097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.0000 | −1.71758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.00000 | + | 14.1421i | 0.142948 | + | 0.505399i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.4558i | − | 0.907403i | −0.891154 | − | 0.453701i | \(-0.850103\pi\) | ||
0.891154 | − | 0.453701i | \(-0.149897\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.00000 | − | 8.48528i | −0.213606 | − | 0.302084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.79796 | −0.347936 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3205i | 0.613524i | 0.951786 | + | 0.306762i | \(0.0992455\pi\) | ||||
−0.951786 | + | 0.306762i | \(0.900754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7846i | 0.735307i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.0000 | − | 5.65685i | −0.565332 | − | 0.199875i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.0000 | 1.69388 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.0000 | + | 19.7990i | −0.985647 | + | 0.696957i | ||||
\(808\) | 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 | ||||||||
\(813\) | −14.6969 | + | 10.3923i | −0.515444 | + | 0.364474i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.3939 | 1.02836 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | 33.9411i | 1.18311i | 0.806263 | + | 0.591557i | \(0.201486\pi\) | ||||
−0.806263 | + | 0.591557i | \(0.798514\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0000 | 1.87776 | 0.938882 | − | 0.344239i | \(-0.111863\pi\) | ||||
0.938882 | + | 0.344239i | \(0.111863\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | 24.2487i | 0.840168i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.89898 | + | 17.3205i | 0.169334 | + | 0.598684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.79796 | −0.338263 | −0.169132 | − | 0.985593i | \(-0.554096\pi\) | ||||
−0.169132 | + | 0.985593i | \(0.554096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.00000 | + | 5.65685i | −0.275535 | + | 0.194832i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 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 | ||||||||
\(853\) | −44.0908 | −1.50964 | −0.754820 | − | 0.655932i | \(-0.772276\pi\) | ||||
−0.754820 | + | 0.655932i | \(0.772276\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 24.2487i | − | 0.828320i | −0.910204 | − | 0.414160i | \(-0.864075\pi\) | ||
0.910204 | − | 0.414160i | \(-0.135925\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1051i | 1.30013i | 0.759879 | + | 0.650065i | \(0.225258\pi\) | ||||
−0.759879 | + | 0.650065i | \(0.774742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.00000 | −0.204242 | −0.102121 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102121 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.00000 | + | 7.07107i | 0.169809 | + | 0.240146i | ||||
\(868\) | 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 | ||||||||
\(877\) | −24.4949 | −0.827134 | −0.413567 | − | 0.910474i | \(-0.635717\pi\) | ||||
−0.413567 | + | 0.910474i | \(0.635717\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.4949 | − | 17.3205i | 0.826192 | − | 0.584206i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.6274i | 0.762337i | 0.924506 | + | 0.381169i | \(0.124478\pi\) | ||||
−0.924506 | + | 0.381169i | \(0.875522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 42.4264i | − | 1.42776i | −0.700267 | − | 0.713881i | \(-0.746936\pi\) | ||
0.700267 | − | 0.713881i | \(-0.253064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.0000 | −1.41022 | −0.705111 | − | 0.709097i | \(-0.749103\pi\) | ||||
−0.705111 | + | 0.709097i | \(0.749103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.2929 | − | 27.7128i | −1.14885 | − | 0.928414i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 20.7846i | − | 0.695530i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.3939 | − | 41.5692i | −0.981433 | − | 1.38796i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.79796 | −0.326780 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 8.48528i | − | 0.281749i | −0.990027 | − | 0.140875i | \(-0.955009\pi\) | ||
0.990027 | − | 0.140875i | \(-0.0449914\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −29.3939 | −0.972795 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(923\) | −48.0000 | −1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 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 | ||||||||
\(933\) | 9.79796 | + | 13.8564i | 0.320771 | + | 0.453638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.9898 | 1.60043 | 0.800213 | − | 0.599715i | \(-0.204720\pi\) | ||||
0.800213 | + | 0.599715i | \(0.204720\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | − | 33.9411i | − | 1.10528i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.0000 | 1.75476 | 0.877382 | − | 0.479792i | \(-0.159288\pi\) | ||||
0.877382 | + | 0.479792i | \(0.159288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.0000 | 1.55815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.4949 | + | 17.3205i | −0.794301 | + | 0.561656i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 58.8897i | − | 1.90763i | −0.300402 | − | 0.953813i | \(-0.597121\pi\) | ||
0.300402 | − | 0.953813i | \(-0.402879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.5959 | − | 13.8564i | 0.633446 | − | 0.447914i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0000 | − | 50.9117i | 0.580042 | − | 1.64061i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.9411i | 1.09147i | 0.837957 | + | 0.545737i | \(0.183750\pi\) | ||||
−0.837957 | + | 0.545737i | \(0.816250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.0000 | + | 16.9706i | 0.385496 | + | 0.545173i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.89898 | 0.157216 | 0.0786079 | − | 0.996906i | \(-0.474952\pi\) | ||||
0.0786079 | + | 0.996906i | \(0.474952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 51.9615i | − | 1.66240i | −0.555976 | − | 0.831198i | \(-0.687655\pi\) | ||
0.555976 | − | 0.831198i | \(-0.312345\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.7128i | 0.885705i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | + | 5.65685i | −0.0638551 | + | 0.180609i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.00000 | −0.191370 | −0.0956851 | − | 0.995412i | \(-0.530504\pi\) | ||||
−0.0956851 | + | 0.995412i | \(0.530504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | \(0.206917\pi\) | ||||
−0.796055 | + | 0.605224i | \(0.793083\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.4949 | + | 17.3205i | −0.777322 | + | 0.549650i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.8888 | −1.70667 | −0.853337 | − | 0.521359i | \(-0.825425\pi\) | ||||
−0.853337 | + | 0.521359i | \(0.825425\pi\) | |||||||
\(998\) | 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 | 1200.2.h.n.1151.4 | 4 | ||
3.2 | odd | 2 | 1200.2.h.j.1151.3 | 4 | |||
4.3 | odd | 2 | 1200.2.h.j.1151.1 | 4 | |||
5.2 | odd | 4 | 240.2.o.b.239.5 | yes | 8 | ||
5.3 | odd | 4 | 240.2.o.b.239.4 | yes | 8 | ||
5.4 | even | 2 | 1200.2.h.j.1151.2 | 4 | |||
12.11 | even | 2 | inner | 1200.2.h.n.1151.2 | 4 | ||
15.2 | even | 4 | 240.2.o.b.239.8 | yes | 8 | ||
15.8 | even | 4 | 240.2.o.b.239.1 | ✓ | 8 | ||
15.14 | odd | 2 | inner | 1200.2.h.n.1151.1 | 4 | ||
20.3 | even | 4 | 240.2.o.b.239.6 | yes | 8 | ||
20.7 | even | 4 | 240.2.o.b.239.3 | yes | 8 | ||
20.19 | odd | 2 | inner | 1200.2.h.n.1151.3 | 4 | ||
40.3 | even | 4 | 960.2.o.d.959.3 | 8 | |||
40.13 | odd | 4 | 960.2.o.d.959.5 | 8 | |||
40.27 | even | 4 | 960.2.o.d.959.6 | 8 | |||
40.37 | odd | 4 | 960.2.o.d.959.4 | 8 | |||
60.23 | odd | 4 | 240.2.o.b.239.7 | yes | 8 | ||
60.47 | odd | 4 | 240.2.o.b.239.2 | yes | 8 | ||
60.59 | even | 2 | 1200.2.h.j.1151.4 | 4 | |||
120.53 | even | 4 | 960.2.o.d.959.8 | 8 | |||
120.77 | even | 4 | 960.2.o.d.959.1 | 8 | |||
120.83 | odd | 4 | 960.2.o.d.959.2 | 8 | |||
120.107 | odd | 4 | 960.2.o.d.959.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.o.b.239.1 | ✓ | 8 | 15.8 | even | 4 | ||
240.2.o.b.239.2 | yes | 8 | 60.47 | odd | 4 | ||
240.2.o.b.239.3 | yes | 8 | 20.7 | even | 4 | ||
240.2.o.b.239.4 | yes | 8 | 5.3 | odd | 4 | ||
240.2.o.b.239.5 | yes | 8 | 5.2 | odd | 4 | ||
240.2.o.b.239.6 | yes | 8 | 20.3 | even | 4 | ||
240.2.o.b.239.7 | yes | 8 | 60.23 | odd | 4 | ||
240.2.o.b.239.8 | yes | 8 | 15.2 | even | 4 | ||
960.2.o.d.959.1 | 8 | 120.77 | even | 4 | |||
960.2.o.d.959.2 | 8 | 120.83 | odd | 4 | |||
960.2.o.d.959.3 | 8 | 40.3 | even | 4 | |||
960.2.o.d.959.4 | 8 | 40.37 | odd | 4 | |||
960.2.o.d.959.5 | 8 | 40.13 | odd | 4 | |||
960.2.o.d.959.6 | 8 | 40.27 | even | 4 | |||
960.2.o.d.959.7 | 8 | 120.107 | odd | 4 | |||
960.2.o.d.959.8 | 8 | 120.53 | even | 4 | |||
1200.2.h.j.1151.1 | 4 | 4.3 | odd | 2 | |||
1200.2.h.j.1151.2 | 4 | 5.4 | even | 2 | |||
1200.2.h.j.1151.3 | 4 | 3.2 | odd | 2 | |||
1200.2.h.j.1151.4 | 4 | 60.59 | even | 2 | |||
1200.2.h.n.1151.1 | 4 | 15.14 | odd | 2 | inner | ||
1200.2.h.n.1151.2 | 4 | 12.11 | even | 2 | inner | ||
1200.2.h.n.1151.3 | 4 | 20.19 | odd | 2 | inner | ||
1200.2.h.n.1151.4 | 4 | 1.1 | even | 1 | trivial |