Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(49,1200)]
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([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.f (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: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.49 |
Dual form | 1200.4.f.g.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 8.00000i | − 0.431959i | −0.976398 | − | 0.215980i | \(-0.930705\pi\) | ||||
0.976398 | − | 0.215980i | \(-0.0692945\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.0000 | −0.548202 | −0.274101 | − | 0.961701i | \(-0.588380\pi\) | ||||
−0.274101 | + | 0.961701i | \(0.588380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 22.0000i | − 0.469362i | −0.972072 | − | 0.234681i | \(-0.924595\pi\) | ||||
0.972072 | − | 0.234681i | \(-0.0754045\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 14.0000i | − 0.199735i | −0.995001 | − | 0.0998676i | \(-0.968158\pi\) | ||||
0.995001 | − | 0.0998676i | \(-0.0318419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76.0000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.0000 | 0.249392 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 56.0000i | 0.507687i | 0.967245 | + | 0.253844i | \(0.0816949\pi\) | ||||
−0.967245 | + | 0.253844i | \(0.918305\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 154.000 | 0.986106 | 0.493053 | − | 0.869999i | \(-0.335881\pi\) | ||||
0.493053 | + | 0.869999i | \(0.335881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −160.000 | −0.926995 | −0.463498 | − | 0.886098i | \(-0.653406\pi\) | ||||
−0.463498 | + | 0.886098i | \(0.653406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 60.0000i | − 0.316505i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 162.000i | − 0.719801i | −0.932991 | − | 0.359900i | \(-0.882811\pi\) | ||||
0.932991 | − | 0.359900i | \(-0.117189\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 66.0000 | 0.270986 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −390.000 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 388.000i | 1.37603i | 0.725695 | + | 0.688017i | \(0.241518\pi\) | ||||
−0.725695 | + | 0.688017i | \(0.758482\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 544.000i | 1.68831i | 0.536099 | + | 0.844155i | \(0.319897\pi\) | ||||
−0.536099 | + | 0.844155i | \(0.680103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 279.000 | 0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.0000 | 0.115317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 210.000i | 0.544259i | 0.962261 | + | 0.272129i | \(0.0877279\pi\) | ||||
−0.962261 | + | 0.272129i | \(0.912272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 228.000i | 0.529813i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −380.000 | −0.838505 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −794.000 | −1.66658 | −0.833289 | − | 0.552837i | \(-0.813545\pi\) | ||||
−0.833289 | + | 0.552837i | \(0.813545\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 72.0000i | 0.143986i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 148.000i | 0.269867i | 0.990855 | + | 0.134933i | \(0.0430821\pi\) | ||||
−0.990855 | + | 0.134933i | \(0.956918\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −168.000 | −0.293113 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 840.000 | 1.40408 | 0.702040 | − | 0.712138i | \(-0.252273\pi\) | ||||
0.702040 | + | 0.712138i | \(0.252273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 858.000i | − 1.37563i | −0.725884 | − | 0.687817i | \(-0.758569\pi\) | ||||
0.725884 | − | 0.687817i | \(-0.241431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 160.000i | 0.236801i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 144.000 | 0.205079 | 0.102540 | − | 0.994729i | \(-0.467303\pi\) | ||||
0.102540 | + | 0.994729i | \(0.467303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 316.000i | 0.417898i | 0.977927 | + | 0.208949i | \(0.0670042\pi\) | ||||
−0.977927 | + | 0.208949i | \(0.932996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 462.000i | 0.569329i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1098.00 | −1.30773 | −0.653864 | − | 0.756612i | \(-0.726853\pi\) | ||||
−0.653864 | + | 0.756612i | \(0.726853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −176.000 | −0.202745 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 480.000i | − 0.535201i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 994.000i | 1.04047i | 0.854024 | + | 0.520234i | \(0.174155\pi\) | ||||
−0.854024 | + | 0.520234i | \(0.825845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 180.000 | 0.182734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −834.000 | −0.821645 | −0.410822 | − | 0.911715i | \(-0.634758\pi\) | ||||
−0.410822 | + | 0.911715i | \(0.634758\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1672.00i | 1.59949i | 0.600343 | + | 0.799743i | \(0.295031\pi\) | ||||
−0.600343 | + | 0.799743i | \(0.704969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 732.000i | 0.661356i | 0.943744 | + | 0.330678i | \(0.107277\pi\) | ||||
−0.943744 | + | 0.330678i | \(0.892723\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 970.000 | 0.852378 | 0.426189 | − | 0.904634i | \(-0.359856\pi\) | ||||
0.426189 | + | 0.904634i | \(0.359856\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 486.000 | 0.415577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1938.00i | − 1.61338i | −0.590976 | − | 0.806689i | \(-0.701257\pi\) | ||||
0.590976 | − | 0.806689i | \(-0.298743\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 198.000i | 0.156454i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −112.000 | −0.0862775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1170.00i | − 0.857686i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 528.000i | 0.368917i | 0.982840 | + | 0.184458i | \(0.0590531\pi\) | ||||
−0.982840 | + | 0.184458i | \(0.940947\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1164.00 | −0.794453 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −636.000 | −0.424180 | −0.212090 | − | 0.977250i | \(-0.568027\pi\) | ||||
−0.212090 | + | 0.977250i | \(0.568027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 608.000i | − 0.396393i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1754.00i | 1.09383i | 0.837189 | + | 0.546914i | \(0.184197\pi\) | ||||
−0.837189 | + | 0.546914i | \(0.815803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2508.00 | −1.53040 | −0.765201 | − | 0.643792i | \(-0.777360\pi\) | ||||
−0.765201 | + | 0.643792i | \(0.777360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1632.00 | −0.974746 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 440.000i | 0.257305i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 837.000i | 0.469623i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1486.00 | −0.817033 | −0.408516 | − | 0.912751i | \(-0.633954\pi\) | ||||
−0.408516 | + | 0.912751i | \(0.633954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2120.00 | −1.14254 | −0.571269 | − | 0.820763i | \(-0.693549\pi\) | ||||
−0.571269 | + | 0.820763i | \(0.693549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 126.000i | 0.0665784i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1850.00i | − 0.940421i | −0.882554 | − | 0.470210i | \(-0.844178\pi\) | ||||
0.882554 | − | 0.470210i | \(-0.155822\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −630.000 | −0.314228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 448.000 | 0.219300 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1172.00i | − 0.563179i | −0.959535 | − | 0.281589i | \(-0.909138\pi\) | ||||
0.959535 | − | 0.281589i | \(-0.0908616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1656.00i | 0.767336i | 0.923471 | + | 0.383668i | \(0.125339\pi\) | ||||
−0.923471 | + | 0.383668i | \(0.874661\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1713.00 | 0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −684.000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2666.00i | 1.17163i | 0.810444 | + | 0.585816i | \(0.199226\pi\) | ||||
−0.810444 | + | 0.585816i | \(0.800774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1140.00i | − 0.484111i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1132.00 | 0.472680 | 0.236340 | − | 0.971670i | \(-0.424052\pi\) | ||||
0.236340 | + | 0.971670i | \(0.424052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2866.00 | −1.17695 | −0.588475 | − | 0.808515i | \(-0.700272\pi\) | ||||
−0.588475 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2382.00i | − 0.962199i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 280.000i | 0.109495i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −216.000 | −0.0831306 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1888.00 | −0.715240 | −0.357620 | − | 0.933867i | \(-0.616412\pi\) | ||||
−0.357620 | + | 0.933867i | \(0.616412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1282.00i | − 0.478137i | −0.971003 | − | 0.239068i | \(-0.923158\pi\) | ||||
0.971003 | − | 0.239068i | \(-0.0768420\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 350.000i | 0.126581i | 0.997995 | + | 0.0632905i | \(0.0201595\pi\) | ||||
−0.997995 | + | 0.0632905i | \(0.979841\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3400.00 | −1.21115 | −0.605577 | − | 0.795787i | \(-0.707058\pi\) | ||||
−0.605577 | + | 0.795787i | \(0.707058\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −444.000 | −0.155808 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1232.00i | − 0.425958i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 504.000i | − 0.169229i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1520.00 | −0.503065 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4652.00 | −1.51781 | −0.758903 | − | 0.651204i | \(-0.774264\pi\) | ||||
−0.758903 | + | 0.651204i | \(0.774264\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2520.00i | 0.810646i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1280.00i | 0.400424i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2574.00 | 0.794223 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −308.000 | −0.0937481 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4016.00i | 1.20597i | 0.797753 | + | 0.602985i | \(0.206022\pi\) | ||||
−0.797753 | + | 0.602985i | \(0.793978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2316.00i | − 0.677173i | −0.940935 | − | 0.338587i | \(-0.890051\pi\) | ||||
0.940935 | − | 0.338587i | \(-0.109949\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −94.0000 | −0.0271253 | −0.0135627 | − | 0.999908i | \(-0.504317\pi\) | ||||
−0.0135627 | + | 0.999908i | \(0.504317\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −480.000 | −0.136717 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4230.00i | 1.18934i | 0.803969 | + | 0.594671i | \(0.202718\pi\) | ||||
−0.803969 | + | 0.594671i | \(0.797282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 432.000i | 0.118403i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2064.00 | 0.558615 | 0.279308 | − | 0.960202i | \(-0.409895\pi\) | ||||
0.279308 | + | 0.960202i | \(0.409895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4562.00 | 1.21935 | 0.609677 | − | 0.792650i | \(-0.291299\pi\) | ||||
0.609677 | + | 0.792650i | \(0.291299\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1672.00i | − 0.430716i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −948.000 | −0.241273 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2532.00 | −0.636727 | −0.318363 | − | 0.947969i | \(-0.603133\pi\) | ||||
−0.318363 | + | 0.947969i | \(0.603133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1120.00i | − 0.278315i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3522.00i | 0.854850i | 0.904051 | + | 0.427425i | \(0.140579\pi\) | ||||
−0.904051 | + | 0.427425i | \(0.859421\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1296.00 | −0.310925 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1386.00 | −0.328702 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2232.00i | − 0.523312i | −0.965161 | − | 0.261656i | \(-0.915731\pi\) | ||||
0.965161 | − | 0.261656i | \(-0.0842686\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3294.00i | − 0.755017i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2806.00 | −0.636003 | −0.318002 | − | 0.948090i | \(-0.603012\pi\) | ||||
−0.318002 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4848.00 | −1.08670 | −0.543349 | − | 0.839507i | \(-0.682844\pi\) | ||||
−0.543349 | + | 0.839507i | \(0.682844\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 528.000i | − 0.117055i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7790.00i | 1.68973i | 0.534978 | + | 0.844866i | \(0.320320\pi\) | ||||
−0.534978 | + | 0.844866i | \(0.679680\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1440.00 | 0.308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −118.000 | −0.0250509 | −0.0125254 | − | 0.999922i | \(-0.503987\pi\) | ||||
−0.0125254 | + | 0.999922i | \(0.503987\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6508.00i | − 1.36700i | −0.729951 | − | 0.683499i | \(-0.760457\pi\) | ||||
0.729951 | − | 0.683499i | \(-0.239543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3120.00i | 0.641700i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4717.00 | 0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2982.00 | −0.600715 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8770.00i | 1.74863i | 0.485358 | + | 0.874315i | \(0.338689\pi\) | ||||
−0.485358 | + | 0.874315i | \(0.661311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 540.000i | 0.105502i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1232.00 | 0.238289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3104.00 | 0.594391 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2502.00i | − 0.474377i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4292.00i | 0.797907i | 0.916971 | + | 0.398953i | \(0.130626\pi\) | ||||
−0.916971 | + | 0.398953i | \(0.869374\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5016.00 | −0.923464 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9464.00 | 1.72558 | 0.862788 | − | 0.505566i | \(-0.168716\pi\) | ||||
0.862788 | + | 0.505566i | \(0.168716\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 9578.00i | − 1.72965i | −0.502073 | − | 0.864825i | \(-0.667429\pi\) | ||||
0.502073 | − | 0.864825i | \(-0.332571\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 186.000i | − 0.0329552i | −0.999864 | − | 0.0164776i | \(-0.994755\pi\) | ||||
0.999864 | − | 0.0164776i | \(-0.00524522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3080.00 | −0.540586 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2196.00 | −0.381834 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1064.00i | − 0.183290i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2910.00i | 0.492120i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4352.00 | 0.729281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 492.000 | 0.0817002 | 0.0408501 | − | 0.999165i | \(-0.486993\pi\) | ||||
0.0408501 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1458.00i | 0.239934i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2290.00i | 0.370161i | 0.982723 | + | 0.185080i | \(0.0592546\pi\) | ||||
−0.982723 | + | 0.185080i | \(0.940745\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5814.00 | 0.931484 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3200.00 | 0.508181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 4976.00i | − 0.783320i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6092.00i | 0.942466i | 0.882009 | + | 0.471233i | \(0.156191\pi\) | ||||
−0.882009 | + | 0.471233i | \(0.843809\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5766.00 | −0.884375 | −0.442188 | − | 0.896923i | \(-0.645797\pi\) | ||||
−0.442188 | + | 0.896923i | \(0.645797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −594.000 | −0.0903287 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9374.00i | 1.41339i | 0.707517 | + | 0.706696i | \(0.249815\pi\) | ||||
−0.707517 | + | 0.706696i | \(0.750185\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 336.000i | − 0.0498123i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3528.00 | −0.518665 | −0.259332 | − | 0.965788i | \(-0.583503\pi\) | ||||
−0.259332 | + | 0.965788i | \(0.583503\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1083.00 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2793.00i | − 0.403842i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7616.00i | − 1.08325i | −0.840621 | − | 0.541624i | \(-0.817810\pi\) | ||||
0.840621 | − | 0.541624i | \(-0.182190\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3510.00 | 0.495185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1680.00 | 0.235098 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3406.00i | − 0.472804i | −0.971655 | − | 0.236402i | \(-0.924032\pi\) | ||||
0.971655 | − | 0.236402i | \(-0.0759683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3388.00i | − 0.462841i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12284.0 | −1.66487 | −0.832436 | − | 0.554121i | \(-0.813055\pi\) | ||||
−0.832436 | + | 0.554121i | \(0.813055\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1584.00 | −0.212994 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5424.00i | 0.723638i | 0.932248 | + | 0.361819i | \(0.117844\pi\) | ||||
−0.932248 | + | 0.361819i | \(0.882156\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3492.00i | − 0.458678i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3486.00 | −0.454363 | −0.227182 | − | 0.973852i | \(-0.572951\pi\) | ||||
−0.227182 | + | 0.973852i | \(0.572951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 784.000 | 0.101403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1908.00i | − 0.244900i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3626.00i | − 0.458397i | −0.973380 | − | 0.229199i | \(-0.926389\pi\) | ||||
0.973380 | − | 0.229199i | \(-0.0736105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1824.00 | 0.228858 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5874.00 | 0.731505 | 0.365753 | − | 0.930712i | \(-0.380812\pi\) | ||||
0.365753 | + | 0.930712i | \(0.380812\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3520.00i | 0.435096i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3240.00i | 0.394597i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12662.0 | 1.53080 | 0.765398 | − | 0.643557i | \(-0.222542\pi\) | ||||
0.765398 | + | 0.643557i | \(0.222542\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5262.00 | −0.631521 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3040.00i | 0.362200i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 7524.00i | − 0.883578i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6396.00 | 0.745740 | 0.372870 | − | 0.927884i | \(-0.378374\pi\) | ||||
0.372870 | + | 0.927884i | \(0.378374\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8286.00 | 0.959228 | 0.479614 | − | 0.877480i | \(-0.340777\pi\) | ||||
0.479614 | + | 0.877480i | \(0.340777\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 4896.00i | − 0.562770i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6352.00i | 0.719894i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1320.00 | −0.148555 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4112.00 | 0.459555 | 0.229777 | − | 0.973243i | \(-0.426200\pi\) | ||||
0.229777 | + | 0.973243i | \(0.426200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 5330.00i | − 0.591555i | −0.955257 | − | 0.295778i | \(-0.904421\pi\) | ||||
0.955257 | − | 0.295778i | \(-0.0955788\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4256.00i | 0.465886i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11272.0 | 1.22547 | 0.612737 | − | 0.790287i | \(-0.290068\pi\) | ||||
0.612737 | + | 0.790287i | \(0.290068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2511.00 | −0.271137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14196.0i | 1.52251i | 0.648452 | + | 0.761255i | \(0.275417\pi\) | ||||
−0.648452 | + | 0.761255i | \(0.724583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 4458.00i | − 0.471714i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5886.00 | 0.618658 | 0.309329 | − | 0.950955i | \(-0.399896\pi\) | ||||
0.309329 | + | 0.950955i | \(0.399896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7800.00 | 0.814385 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 6360.00i | − 0.659644i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 7526.00i | − 0.770353i | −0.922843 | − | 0.385177i | \(-0.874141\pi\) | ||||
0.922843 | − | 0.385177i | \(-0.125859\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −378.000 | −0.0384391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8502.00 | 0.858954 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12672.0i | 1.27196i | 0.771705 | + | 0.635980i | \(0.219404\pi\) | ||||
−0.771705 | + | 0.635980i | \(0.780596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 16540.0i | − 1.63893i | −0.573130 | − | 0.819465i | \(-0.694271\pi\) | ||||
0.573130 | − | 0.819465i | \(-0.305729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1184.00 | 0.116572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5550.00 | 0.542952 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7760.00i | − 0.754345i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1890.00i | − 0.181420i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8864.00 | 0.845525 | 0.422763 | − | 0.906241i | \(-0.361060\pi\) | ||||
0.422763 | + | 0.906241i | \(0.361060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3564.00 | −0.337847 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1344.00i | 0.126613i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3688.00i | − 0.343161i | −0.985170 | − | 0.171580i | \(-0.945113\pi\) | ||||
0.985170 | − | 0.171580i | \(-0.0548873\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3516.00 | 0.325151 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16140.0 | 1.48348 | 0.741739 | − | 0.670688i | \(-0.234001\pi\) | ||||
0.741739 | + | 0.670688i | \(0.234001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2156.00i | − 0.196960i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6720.00i | − 0.606505i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1580.00 | 0.141745 | 0.0708723 | − | 0.997485i | \(-0.477422\pi\) | ||||
0.0708723 | + | 0.997485i | \(0.477422\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4968.00 | −0.443022 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15000.0i | 1.32966i | 0.746996 | + | 0.664828i | \(0.231495\pi\) | ||||
−0.746996 | + | 0.664828i | \(0.768505\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5139.00i | 0.450160i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20486.0 | −1.78394 | −0.891971 | − | 0.452094i | \(-0.850677\pi\) | ||||
−0.891971 | + | 0.452094i | \(0.850677\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6864.00 | −0.594218 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 2052.00i | − 0.176604i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 10880.0i | − 0.925535i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7998.00 | −0.676442 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7706.00 | 0.647996 | 0.323998 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323998 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 3932.00i | − 0.328746i | −0.986398 | − | 0.164373i | \(-0.947440\pi\) | ||||
0.986398 | − | 0.164373i | \(-0.0525601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2240.00i | 0.185154i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9031.00 | 0.742254 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3420.00 | 0.279502 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8580.00i | 0.697263i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3396.00i | 0.272902i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5580.00 | −0.445914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23930.0 | −1.90172 | −0.950860 | − | 0.309620i | \(-0.899798\pi\) | ||||
−0.950860 | + | 0.309620i | \(0.899798\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8598.00i | − 0.679513i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 11468.0i | − 0.896410i | −0.893931 | − | 0.448205i | \(-0.852063\pi\) | ||||
0.893931 | − | 0.448205i | \(-0.147937\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7146.00 | 0.555526 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11704.0 | 0.904913 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1152.00i | − 0.0885859i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11498.0i | − 0.874660i | −0.899301 | − | 0.437330i | \(-0.855924\pi\) | ||||
0.899301 | − | 0.437330i | \(-0.144076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8536.00 | 0.645857 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −840.000 | −0.0632172 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16988.0i | 1.27169i | 0.771819 | + | 0.635843i | \(0.219347\pi\) | ||||
−0.771819 | + | 0.635843i | \(0.780653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 648.000i | − 0.0479955i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17366.0 | 1.27947 | 0.639737 | − | 0.768594i | \(-0.279043\pi\) | ||||
0.639737 | + | 0.768594i | \(0.279043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24860.0 | 1.82199 | 0.910997 | − | 0.412413i | \(-0.135314\pi\) | ||||
0.910997 | + | 0.412413i | \(0.135314\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 5664.00i | − 0.412944i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 26302.0i | − 1.89769i | −0.315744 | − | 0.948845i | \(-0.602254\pi\) | ||||
0.315744 | − | 0.948845i | \(-0.397746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3846.00 | 0.276052 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2528.00 | 0.180515 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4200.00i | − 0.298364i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7812.00i | − 0.549294i | −0.961545 | − | 0.274647i | \(-0.911439\pi\) | ||||
0.961545 | − | 0.274647i | \(-0.0885610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12160.0 | −0.850669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1050.00 | −0.0730816 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 7986.00i | − 0.553028i | −0.961010 | − | 0.276514i | \(-0.910821\pi\) | ||||
0.961010 | − | 0.276514i | \(-0.0891792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 10200.0i | − 0.699260i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21048.0 | −1.43572 | −0.717861 | − | 0.696186i | \(-0.754879\pi\) | ||||
−0.717861 | + | 0.696186i | \(0.754879\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1738.00 | 0.117961 | 0.0589804 | − | 0.998259i | \(-0.481215\pi\) | ||||
0.0589804 | + | 0.998259i | \(0.481215\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1332.00i | − 0.0899556i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 18576.0i | − 1.24214i | −0.783757 | − | 0.621068i | \(-0.786699\pi\) | ||||
0.783757 | − | 0.621068i | \(-0.213301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3696.00 | 0.245927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11968.0 | 0.792428 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13602.0i | 0.896215i | 0.893980 | + | 0.448107i | \(0.147902\pi\) | ||||
−0.893980 | + | 0.448107i | \(0.852098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19578.0i | 1.27744i | 0.769439 | + | 0.638720i | \(0.220536\pi\) | ||||
−0.769439 | + | 0.638720i | \(0.779464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12308.0 | 0.799193 | 0.399596 | − | 0.916691i | \(-0.369150\pi\) | ||||
0.399596 | + | 0.916691i | \(0.369150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1512.00 | 0.0977045 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8784.00i | 0.564885i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4560.00i | − 0.290445i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2268.00 | −0.143770 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8600.00 | 0.542568 | 0.271284 | − | 0.962499i | \(-0.412552\pi\) | ||||
0.271284 | + | 0.962499i | \(0.412552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 13956.0i | − 0.876305i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6138.00i | − 0.381784i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7560.00 | −0.468027 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6978.00 | 0.429976 | 0.214988 | − | 0.976617i | \(-0.431029\pi\) | ||||
0.214988 | + | 0.976617i | \(0.431029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7668.00i | − 0.470290i | −0.971960 | − | 0.235145i | \(-0.924444\pi\) | ||||
0.971960 | − | 0.235145i | \(-0.0755565\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15384.0i | 0.934787i | 0.884049 | + | 0.467394i | \(0.154807\pi\) | ||||
−0.884049 | + | 0.467394i | \(0.845193\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7600.00 | 0.459670 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3840.00 | −0.231185 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2186.00i | 0.131003i | 0.997852 | + | 0.0655014i | \(0.0208647\pi\) | ||||
−0.997852 | + | 0.0655014i | \(0.979135\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7722.00i | 0.458545i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1524.00 | −0.0900859 | −0.0450430 | − | 0.998985i | \(-0.514342\pi\) | ||||
−0.0450430 | + | 0.998985i | \(0.514342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4242.00 | −0.249614 | −0.124807 | − | 0.992181i | \(-0.539831\pi\) | ||||
−0.124807 | + | 0.992181i | \(0.539831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 924.000i | − 0.0541255i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8624.00i | 0.500634i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12048.0 | −0.696267 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15880.0 | 0.913622 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 24354.0i | − 1.39491i | −0.716626 | − | 0.697457i | \(-0.754315\pi\) | ||||
0.716626 | − | 0.697457i | \(-0.245685\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 322.000i | − 0.0182799i | −0.999958 | − | 0.00913993i | \(-0.997091\pi\) | ||||
0.999958 | − | 0.00913993i | \(-0.00290937\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7952.00 | 0.449440 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6948.00 | 0.390966 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7932.00i | − 0.444377i | −0.975004 | − | 0.222189i | \(-0.928680\pi\) | ||||
0.975004 | − | 0.222189i | \(-0.0713201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 282.000i | − 0.0156608i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4620.00 | 0.255454 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20684.0 | −1.13872 | −0.569361 | − | 0.822088i | \(-0.692809\pi\) | ||||
−0.569361 | + | 0.822088i | \(0.692809\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1440.00i | − 0.0789337i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5460.00i | 0.296718i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12690.0 | −0.686666 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25222.0 | 1.35895 | 0.679473 | − | 0.733700i | \(-0.262208\pi\) | ||||
0.679473 | + | 0.733700i | \(0.262208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 12312.0i | − 0.660535i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6672.00i | 0.354917i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23678.0 | −1.25423 | −0.627113 | − | 0.778928i | \(-0.715764\pi\) | ||||
−0.627113 | + | 0.778928i | \(0.715764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1296.00 | −0.0683598 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8960.00i | − 0.470624i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6192.00i | 0.322517i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8432.00 | 0.437358 | 0.218679 | − | 0.975797i | \(-0.429825\pi\) | ||||
0.218679 | + | 0.975797i | \(0.429825\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13376.0 | 0.690913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13686.0i | 0.703994i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8312.00i | − 0.424037i | −0.977266 | − | 0.212019i | \(-0.931996\pi\) | ||||
0.977266 | − | 0.212019i | \(-0.0680037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5432.00 | 0.274842 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26298.0i | 1.32516i | 0.748993 | + | 0.662578i | \(0.230538\pi\) | ||||
−0.748993 | + | 0.662578i | \(0.769462\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2960.00i | − 0.147942i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16956.0 | 0.844028 | 0.422014 | − | 0.906589i | \(-0.361323\pi\) | ||||
0.422014 | + | 0.906589i | \(0.361323\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5016.00 | 0.248674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 17880.0i | − 0.882845i | −0.897299 | − | 0.441422i | \(-0.854474\pi\) | ||||
0.897299 | − | 0.441422i | \(-0.145526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2844.00i | − 0.139299i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5856.00 | 0.285679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22032.0 | −1.07052 | −0.535259 | − | 0.844688i | \(-0.679786\pi\) | ||||
−0.535259 | + | 0.844688i | \(0.679786\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 7596.00i | − 0.367614i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11534.0i | 0.553779i | 0.960902 | + | 0.276889i | \(0.0893035\pi\) | ||||
−0.960902 | + | 0.276889i | \(0.910696\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3360.00 | 0.160685 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38250.0 | 1.82203 | 0.911013 | − | 0.412378i | \(-0.135302\pi\) | ||||
0.911013 | + | 0.412378i | \(0.135302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7760.00i | − 0.368192i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8360.00i | 0.393562i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19330.0 | −0.906447 | −0.453223 | − | 0.891397i | \(-0.649726\pi\) | ||||
−0.453223 | + | 0.891397i | \(0.649726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10566.0 | −0.493548 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40674.0i | 1.89255i | 0.323361 | + | 0.946276i | \(0.395187\pi\) | ||||
−0.323361 | + | 0.946276i | \(0.604813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3888.00i | − 0.179513i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29640.0 | −1.36324 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16800.0 | −0.769720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 4158.00i | − 0.189776i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7004.00i | − 0.317237i | −0.987340 | − | 0.158619i | \(-0.949296\pi\) | ||||
0.987340 | − | 0.158619i | \(-0.0507040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6696.00 | 0.302134 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15504.0 | −0.696914 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17468.0i | 0.782228i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12198.0i | 0.542127i | 0.962561 | + | 0.271064i | \(0.0873754\pi\) | ||||
−0.962561 | + | 0.271064i | \(0.912625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7616.00 | 0.337215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9882.00 | 0.435909 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17160.0i | 0.754126i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 8418.00i | − 0.367197i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25734.0 | 1.11837 | 0.559184 | − | 0.829044i | \(-0.311115\pi\) | ||||
0.559184 | + | 0.829044i | \(0.311115\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15668.0 | −0.678394 | −0.339197 | − | 0.940715i | \(-0.610155\pi\) | ||||
−0.339197 | + | 0.940715i | \(0.610155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 14544.0i | − 0.627405i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29488.0i | 1.26274i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1584.00 | 0.0675817 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34450.0 | −1.46445 | −0.732225 | − | 0.681063i | \(-0.761518\pi\) | ||||
−0.732225 | + | 0.681063i | \(0.761518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 38792.0i | − 1.64302i | −0.570195 | − | 0.821509i | \(-0.693132\pi\) | ||||
0.570195 | − | 0.821509i | \(-0.306868\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20460.0i | 0.860295i | 0.902759 | + | 0.430147i | \(0.141538\pi\) | ||||
−0.902759 | + | 0.430147i | \(0.858462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5542.00 | −0.232185 | −0.116093 | − | 0.993238i | \(-0.537037\pi\) | ||||
−0.116093 | + | 0.993238i | \(0.537037\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23370.0 | −0.975567 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3906.00i | − 0.162467i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4320.00i | 0.178400i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25240.0 | 1.03860 | 0.519298 | − | 0.854593i | \(-0.326194\pi\) | ||||
0.519298 | + | 0.854593i | \(0.326194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −673.000 | −0.0275944 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 354.000i | − 0.0144631i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7448.00i | 0.302144i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19524.0 | 0.789237 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9072.00 | 0.365434 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37330.0i | 1.49842i | 0.662331 | + | 0.749212i | \(0.269567\pi\) | ||||
−0.662331 | + | 0.749212i | \(0.730433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 3894.00i | − 0.155212i | −0.996984 | − | 0.0776059i | \(-0.975272\pi\) | ||||
0.996984 | − | 0.0776059i | \(-0.0247276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20324.0 | 0.807271 | 0.403636 | − | 0.914920i | \(-0.367746\pi\) | ||||
0.403636 | + | 0.914920i | \(0.367746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9360.00 | −0.370485 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6288.00i | 0.248026i | 0.992281 | + | 0.124013i | \(0.0395764\pi\) | ||||
−0.992281 | + | 0.124013i | \(0.960424\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14151.0i | 0.554317i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2880.00 | −0.112425 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3256.00 | 0.126665 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 8946.00i | − 0.346823i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 24650.0i | − 0.949112i | −0.880225 | − | 0.474556i | \(-0.842609\pi\) | ||||
0.880225 | − | 0.474556i | \(-0.157391\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26310.0 | −1.00957 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9426.00 | 0.360465 | 0.180233 | − | 0.983624i | \(-0.442315\pi\) | ||||
0.180233 | + | 0.983624i | \(0.442315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 9316.00i | − 0.355049i | −0.984116 | − | 0.177525i | \(-0.943191\pi\) | ||||
0.984116 | − | 0.177525i | \(-0.0568089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 6968.00i | − 0.263768i | −0.991265 | − | 0.131884i | \(-0.957897\pi\) | ||||
0.991265 | − | 0.131884i | \(-0.0421027\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4224.00 | 0.159357 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1620.00 | −0.0609114 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41344.0i | 1.54930i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3696.00i | 0.137576i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24640.0 | −0.914116 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2940.00 | 0.108708 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9312.00i | 0.343172i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35964.0i | 1.31661i | 0.752751 | + | 0.658305i | \(0.228726\pi\) | ||||
−0.752751 | + | 0.658305i | \(0.771274\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7506.00 | 0.273882 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47888.0 | −1.74160 | −0.870801 | − | 0.491635i | \(-0.836399\pi\) | ||||
−0.870801 | + | 0.491635i | \(0.836399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 6320.00i | − 0.229093i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5088.00i | 0.183229i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12760.0 | −0.458013 | −0.229006 | − | 0.973425i | \(-0.573548\pi\) | ||||
−0.229006 | + | 0.973425i | \(0.573548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12876.0 | −0.460672 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 18480.0i | − 0.659021i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 15048.0i | − 0.533162i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25054.0 | 0.884817 | 0.442409 | − | 0.896814i | \(-0.354124\pi\) | ||||
0.442409 | + | 0.896814i | \(0.354124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21204.0 | 0.746437 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28392.0i | 0.996262i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28282.0i | 0.986054i | 0.870014 | + | 0.493027i | \(0.164110\pi\) | ||||
−0.870014 | + | 0.493027i | \(0.835890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28734.0 | 0.998614 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30634.0 | −1.06125 | −0.530627 | − | 0.847605i | \(-0.678043\pi\) | ||||
−0.530627 | + | 0.847605i | \(0.678043\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 21840.0i | − 0.754198i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 48572.0i | − 1.66671i | −0.552735 | − | 0.833357i | \(-0.686416\pi\) | ||||
0.552735 | − | 0.833357i | \(-0.313584\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18876.0 | −0.645670 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 558.000 | 0.0190267 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 12906.0i | − 0.438685i | −0.975648 | − | 0.219342i | \(-0.929609\pi\) | ||||
0.975648 | − | 0.219342i | \(-0.0703911\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9240.00i | − 0.312107i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14032.0 | 0.472489 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4191.00 | −0.140680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 6588.00i | − 0.220452i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5880.00i | 0.195541i | 0.995209 | + | 0.0977705i | \(0.0311711\pi\) | ||||
−0.995209 | + | 0.0977705i | \(0.968829\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3192.00 | 0.105822 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55444.0 | −1.83242 | −0.916211 | − | 0.400695i | \(-0.868769\pi\) | ||||
−0.916211 | + | 0.400695i | \(0.868769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20064.0i | 0.661071i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32050.0i | 1.04951i | 0.851254 | + | 0.524755i | \(0.175843\pi\) | ||||
−0.851254 | + | 0.524755i | \(0.824157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21960.0 | 0.716900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8730.00 | −0.284126 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29880.0i | 0.969506i | 0.874651 | + | 0.484753i | \(0.161090\pi\) | ||||
−0.874651 | + | 0.484753i | \(0.838910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13056.0i | 0.421051i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21728.0 | −0.698595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5216.00 | −0.167196 | −0.0835982 | − | 0.996500i | \(-0.526641\pi\) | ||||
−0.0835982 | + | 0.996500i | \(0.526641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1476.00i | 0.0471696i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6750.00i | 0.214418i | 0.994237 | + | 0.107209i | \(0.0341914\pi\) | ||||
−0.994237 | + | 0.107209i | \(0.965809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4374.00 | −0.138526 |
(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 | 1200.4.f.g.49.2 | 2 | ||
4.3 | odd | 2 | 600.4.f.g.49.1 | 2 | |||
5.2 | odd | 4 | 1200.4.a.bf.1.1 | 1 | |||
5.3 | odd | 4 | 240.4.a.d.1.1 | 1 | |||
5.4 | even | 2 | inner | 1200.4.f.g.49.1 | 2 | ||
12.11 | even | 2 | 1800.4.f.h.649.2 | 2 | |||
15.8 | even | 4 | 720.4.a.f.1.1 | 1 | |||
20.3 | even | 4 | 120.4.a.f.1.1 | ✓ | 1 | ||
20.7 | even | 4 | 600.4.a.d.1.1 | 1 | |||
20.19 | odd | 2 | 600.4.f.g.49.2 | 2 | |||
40.3 | even | 4 | 960.4.a.g.1.1 | 1 | |||
40.13 | odd | 4 | 960.4.a.v.1.1 | 1 | |||
60.23 | odd | 4 | 360.4.a.e.1.1 | 1 | |||
60.47 | odd | 4 | 1800.4.a.k.1.1 | 1 | |||
60.59 | even | 2 | 1800.4.f.h.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.a.f.1.1 | ✓ | 1 | 20.3 | even | 4 | ||
240.4.a.d.1.1 | 1 | 5.3 | odd | 4 | |||
360.4.a.e.1.1 | 1 | 60.23 | odd | 4 | |||
600.4.a.d.1.1 | 1 | 20.7 | even | 4 | |||
600.4.f.g.49.1 | 2 | 4.3 | odd | 2 | |||
600.4.f.g.49.2 | 2 | 20.19 | odd | 2 | |||
720.4.a.f.1.1 | 1 | 15.8 | even | 4 | |||
960.4.a.g.1.1 | 1 | 40.3 | even | 4 | |||
960.4.a.v.1.1 | 1 | 40.13 | odd | 4 | |||
1200.4.a.bf.1.1 | 1 | 5.2 | odd | 4 | |||
1200.4.f.g.49.1 | 2 | 5.4 | even | 2 | inner | ||
1200.4.f.g.49.2 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.a.k.1.1 | 1 | 60.47 | odd | 4 | |||
1800.4.f.h.649.1 | 2 | 60.59 | even | 2 | |||
1800.4.f.h.649.2 | 2 | 12.11 | even | 2 |