Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,4,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("400.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (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: | \(23.6007640023\) |
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 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.4.c.b.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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 9.00000i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 26.0000i | − 1.40387i | −0.712242 | − | 0.701934i | \(-0.752320\pi\) | ||||
0.712242 | − | 0.701934i | \(-0.247680\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −54.0000 | −2.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 59.0000 | 1.61720 | 0.808599 | − | 0.588361i | \(-0.200226\pi\) | ||||
0.808599 | + | 0.588361i | \(0.200226\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 28.0000i | − 0.597369i | −0.954352 | − | 0.298685i | \(-0.903452\pi\) | ||||
0.954352 | − | 0.298685i | \(-0.0965479\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000i | 0.0713340i | 0.999364 | + | 0.0356670i | \(0.0113556\pi\) | ||||
−0.999364 | + | 0.0356670i | \(0.988644\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 109.000 | 1.31612 | 0.658061 | − | 0.752965i | \(-0.271377\pi\) | ||||
0.658061 | + | 0.752965i | \(0.271377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 234.000 | 2.43157 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 194.000i | − 1.75877i | −0.476108 | − | 0.879387i | \(-0.657953\pi\) | ||||
0.476108 | − | 0.879387i | \(-0.342047\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 243.000i | − 1.73205i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 32.0000 | 0.204905 | 0.102453 | − | 0.994738i | \(-0.467331\pi\) | ||||
0.102453 | + | 0.994738i | \(0.467331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0000 | −0.0579372 | −0.0289686 | − | 0.999580i | \(-0.509222\pi\) | ||||
−0.0289686 | + | 0.999580i | \(0.509222\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 531.000i | 2.80107i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 198.000i | − 0.879757i | −0.898057 | − | 0.439878i | \(-0.855022\pi\) | ||||
0.898057 | − | 0.439878i | \(-0.144978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 252.000 | 1.03467 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 117.000 | 0.445667 | 0.222833 | − | 0.974857i | \(-0.428469\pi\) | ||||
0.222833 | + | 0.974857i | \(0.428469\pi\) | |||||||
\(42\) | 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 | ||||||||
\(47\) | 68.0000i | 0.211039i | 0.994417 | + | 0.105519i | \(0.0336505\pi\) | ||||
−0.994417 | + | 0.105519i | \(0.966350\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −333.000 | −0.970845 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −45.0000 | −0.123554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 18.0000i | 0.0466508i | 0.999728 | + | 0.0233254i | \(0.00742537\pi\) | ||||
−0.999728 | + | 0.0233254i | \(0.992575\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 981.000i | 2.27959i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 392.000 | 0.864984 | 0.432492 | − | 0.901638i | \(-0.357634\pi\) | ||||
0.432492 | + | 0.901638i | \(0.357634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −710.000 | −1.49027 | −0.745133 | − | 0.666916i | \(-0.767614\pi\) | ||||
−0.745133 | + | 0.666916i | \(0.767614\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1404.00i | 2.80774i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 253.000i | 0.461326i | 0.973034 | + | 0.230663i | \(0.0740896\pi\) | ||||
−0.973034 | + | 0.230663i | \(0.925910\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1746.00 | 3.04629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 612.000 | 1.02297 | 0.511486 | − | 0.859292i | \(-0.329095\pi\) | ||||
0.511486 | + | 0.859292i | \(0.329095\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 549.000i | 0.880214i | 0.897945 | + | 0.440107i | \(0.145059\pi\) | ||||
−0.897945 | + | 0.440107i | \(0.854941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1534.00i | − 2.27033i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 414.000 | 0.589603 | 0.294802 | − | 0.955559i | \(-0.404746\pi\) | ||||
0.294802 | + | 0.955559i | \(0.404746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 121.000i | − 0.160018i | −0.996794 | − | 0.0800089i | \(-0.974505\pi\) | ||||
0.996794 | − | 0.0800089i | \(-0.0254949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 288.000i | 0.354906i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 81.0000 | 0.0964717 | 0.0482359 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482359 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −728.000 | −0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 90.0000i | − 0.100350i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1502.00i | − 1.57222i | −0.618089 | − | 0.786108i | \(-0.712093\pi\) | ||||
0.618089 | − | 0.786108i | \(-0.287907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3186.00 | −3.23439 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −234.000 | −0.230533 | −0.115267 | − | 0.993335i | \(-0.536772\pi\) | ||||
−0.115267 | + | 0.993335i | \(0.536772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1172.00i | − 1.12117i | −0.828097 | − | 0.560585i | \(-0.810576\pi\) | ||||
0.828097 | − | 0.560585i | \(-0.189424\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1125.00i | − 1.01643i | −0.861231 | − | 0.508214i | \(-0.830306\pi\) | ||||
0.861231 | − | 0.508214i | \(-0.169694\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1234.00 | 1.08436 | 0.542182 | − | 0.840261i | \(-0.317598\pi\) | ||||
0.542182 | + | 0.840261i | \(0.317598\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1782.00 | 1.52378 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 567.000i | − 0.472025i | −0.971750 | − | 0.236013i | \(-0.924159\pi\) | ||||
0.971750 | − | 0.236013i | \(-0.0758407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1512.00i | 1.19474i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 130.000 | 0.100144 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2150.00 | 1.61533 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1053.00i | 0.771917i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2358.00i | 1.64755i | 0.566918 | + | 0.823774i | \(0.308136\pi\) | ||||
−0.566918 | + | 0.823774i | \(0.691864\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3492.00 | −2.38336 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1692.00 | 1.12848 | 0.564239 | − | 0.825611i | \(-0.309169\pi\) | ||||
0.564239 | + | 0.825611i | \(0.309169\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2834.00i | − 1.84766i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 229.000i | 0.142809i | 0.997447 | + | 0.0714043i | \(0.0227481\pi\) | ||||
−0.997447 | + | 0.0714043i | \(0.977252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2781.00 | 1.69699 | 0.848494 | − | 0.529205i | \(-0.177510\pi\) | ||||
0.848494 | + | 0.529205i | \(0.177510\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −612.000 | −0.365530 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1652.00i | − 0.966064i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2997.00i | − 1.68155i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1472.00 | −0.809335 | −0.404668 | − | 0.914464i | \(-0.632613\pi\) | ||||
−0.404668 | + | 0.914464i | \(0.632613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1322.00 | −0.712469 | −0.356235 | − | 0.934397i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934397i | \(0.615940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 270.000i | − 0.142668i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 298.000i | 0.151484i | 0.997127 | + | 0.0757420i | \(0.0241325\pi\) | ||||
−0.997127 | + | 0.0757420i | \(0.975867\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −162.000 | −0.0808015 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5044.00 | −2.46909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 341.000i | − 0.163860i | −0.996638 | − | 0.0819300i | \(-0.973892\pi\) | ||||
0.996638 | − | 0.0819300i | \(-0.0261084\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 684.000i | − 0.316943i | −0.987364 | − | 0.158472i | \(-0.949343\pi\) | ||||
0.987364 | − | 0.158472i | \(-0.0506566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1413.00 | 0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5886.00 | −2.63224 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2344.00i | 1.03012i | 0.857154 | + | 0.515061i | \(0.172231\pi\) | ||||
−0.857154 | + | 0.515061i | \(0.827769\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3528.00i | 1.49820i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1111.00 | −0.463911 | −0.231955 | − | 0.972726i | \(-0.574512\pi\) | ||||
−0.231955 | + | 0.972726i | \(0.574512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2042.00 | 0.838567 | 0.419284 | − | 0.907855i | \(-0.362281\pi\) | ||||
0.419284 | + | 0.907855i | \(0.362281\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 6390.00i | − 2.58122i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 295.000i | 0.115361i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6318.00 | −2.43157 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5270.00 | −1.99646 | −0.998230 | − | 0.0594735i | \(-0.981058\pi\) | ||||
−0.998230 | + | 0.0594735i | \(0.981058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 613.000i | − 0.228625i | −0.993445 | − | 0.114313i | \(-0.963533\pi\) | ||||
0.993445 | − | 0.114313i | \(-0.0364666\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1174.00i | 0.424589i | 0.977206 | + | 0.212295i | \(0.0680936\pi\) | ||||
−0.977206 | + | 0.212295i | \(0.931906\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3428.00 | 1.22113 | 0.610564 | − | 0.791967i | \(-0.290943\pi\) | ||||
0.610564 | + | 0.791967i | \(0.290943\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2277.00 | −0.799041 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 832.000i | − 0.287660i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10476.0i | 3.51755i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6431.00 | 2.12843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2339.00 | −0.763144 | −0.381572 | − | 0.924339i | \(-0.624617\pi\) | ||||
−0.381572 | + | 0.924339i | \(0.624617\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5508.00i | 1.77184i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 260.000i | 0.0813362i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4941.00 | −1.52457 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 140.000 | 0.0426128 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3932.00i | 1.18075i | 0.807131 | + | 0.590373i | \(0.201019\pi\) | ||||
−0.807131 | + | 0.590373i | \(0.798981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 6084.00i | − 1.77890i | −0.457037 | − | 0.889448i | \(-0.651089\pi\) | ||||
0.457037 | − | 0.889448i | \(-0.348911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4996.00 | −1.44168 | −0.720841 | − | 0.693101i | \(-0.756244\pi\) | ||||
−0.720841 | + | 0.693101i | \(0.756244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13806.0 | 3.93233 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3222.00i | − 0.905924i | −0.891530 | − | 0.452962i | \(-0.850367\pi\) | ||||
0.891530 | − | 0.452962i | \(-0.149633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3726.00i | 1.02122i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2736.00 | 0.740490 | 0.370245 | − | 0.928934i | \(-0.379274\pi\) | ||||
0.370245 | + | 0.928934i | \(0.379274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1673.00 | 0.447168 | 0.223584 | − | 0.974685i | \(-0.428224\pi\) | ||||
0.223584 | + | 0.974685i | \(0.428224\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3052.00i | − 0.786211i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1089.00 | 0.277159 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5355.00 | −1.34663 | −0.673316 | − | 0.739355i | \(-0.735131\pi\) | ||||
−0.673316 | + | 0.739355i | \(0.735131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 11446.0i | − 2.84428i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5490.00i | − 1.33252i | −0.745721 | − | 0.666258i | \(-0.767895\pi\) | ||||
0.745721 | − | 0.666258i | \(-0.232105\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5148.00 | −1.23506 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1728.00 | −0.409810 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3150.00i | 0.738545i | 0.929321 | + | 0.369272i | \(0.120393\pi\) | ||||
−0.929321 | + | 0.369272i | \(0.879607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 729.000i | 0.167094i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −176.000 | −0.0398919 | −0.0199459 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199459 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2394.00 | −0.536624 | −0.268312 | − | 0.963332i | \(-0.586466\pi\) | ||||
−0.268312 | + | 0.963332i | \(0.586466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 6552.00i | − 1.45255i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6256.00i | − 1.35699i | −0.734604 | − | 0.678496i | \(-0.762632\pi\) | ||||
0.734604 | − | 0.678496i | \(-0.237368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 540.000 | 0.115874 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4802.00 | −1.01944 | −0.509721 | − | 0.860340i | \(-0.670251\pi\) | ||||
−0.509721 | + | 0.860340i | \(0.670251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2123.00i | 0.445934i | 0.974826 | + | 0.222967i | \(0.0715742\pi\) | ||||
−0.974826 | + | 0.222967i | \(0.928426\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3042.00i | − 0.625657i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4888.00 | 0.994911 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13518.0 | 2.72316 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8834.00i | 1.76139i | 0.473682 | + | 0.880696i | \(0.342925\pi\) | ||||
−0.473682 | + | 0.880696i | \(0.657075\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 14337.0i | − 2.80107i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5432.00 | −1.05064 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10088.0 | 1.93177 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2106.00i | − 0.399296i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1369.00i | − 0.254505i | −0.991870 | − | 0.127252i | \(-0.959384\pi\) | ||||
0.991870 | − | 0.127252i | \(-0.0406158\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10548.0 | 1.94192 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10426.0 | 1.90098 | 0.950489 | − | 0.310758i | \(-0.100583\pi\) | ||||
0.950489 | + | 0.310758i | \(0.100583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3574.00i | 0.645413i | 0.946499 | + | 0.322707i | \(0.104593\pi\) | ||||
−0.946499 | + | 0.322707i | \(0.895407\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9036.00i | 1.60099i | 0.599343 | + | 0.800493i | \(0.295429\pi\) | ||||
−0.599343 | + | 0.800493i | \(0.704571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1888.00 | 0.331372 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10125.0 | 1.76051 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 545.000i | 0.0938842i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11106.0i | 1.87817i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1768.00 | 0.296271 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10233.0 | −1.69926 | −0.849632 | − | 0.527376i | \(-0.823176\pi\) | ||||
−0.849632 | + | 0.527376i | \(0.823176\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10692.0i | 1.75951i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4627.00i | 0.747919i | 0.927445 | + | 0.373960i | \(0.122000\pi\) | ||||
−0.927445 | + | 0.373960i | \(0.878000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5103.00 | 0.817572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −590.000 | −0.0936959 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 260.000i | − 0.0409291i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4901.00i | − 0.758212i | −0.925353 | − | 0.379106i | \(-0.876232\pi\) | ||||
0.925353 | − | 0.379106i | \(-0.123768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4482.00 | 0.687438 | 0.343719 | − | 0.939072i | \(-0.388313\pi\) | ||||
0.343719 | + | 0.939072i | \(0.388313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6804.00 | −1.03467 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1210.00i | 0.182441i | 0.995831 | + | 0.0912207i | \(0.0290769\pi\) | ||||
−0.995831 | + | 0.0912207i | \(0.970923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1170.00i | 0.173454i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9882.00 | −1.45279 | −0.726396 | − | 0.687277i | \(-0.758806\pi\) | ||||
−0.726396 | + | 0.687277i | \(0.758806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5022.00 | 0.732177 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19350.0i | 2.79783i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11260.0i | 1.60155i | 0.598968 | + | 0.800773i | \(0.295578\pi\) | ||||
−0.598968 | + | 0.800773i | \(0.704422\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6318.00 | −0.891333 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 468.000 | 0.0654915 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3230.00i | 0.448373i | 0.974546 | + | 0.224186i | \(0.0719724\pi\) | ||||
−0.974546 | + | 0.224186i | \(0.928028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 896.000i | − 0.122404i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11575.0 | 1.56878 | 0.784390 | − | 0.620268i | \(-0.212976\pi\) | ||||
0.784390 | + | 0.620268i | \(0.212976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21222.0 | −2.85364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 18.0000i | − 0.00240145i | −0.999999 | − | 0.00120073i | \(-0.999618\pi\) | ||||
0.999999 | − | 0.00120073i | \(-0.000382203\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 20952.0i | − 2.75207i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10710.0 | −1.39593 | −0.697967 | − | 0.716130i | \(-0.745912\pi\) | ||||
−0.697967 | + | 0.716130i | \(0.745912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 970.000 | 0.125460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15228.0i | 1.95458i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3788.00i | − 0.478877i | −0.970912 | − | 0.239439i | \(-0.923037\pi\) | ||||
0.970912 | − | 0.239439i | \(-0.0769634\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25506.0 | 3.20024 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10539.0 | −1.31245 | −0.656225 | − | 0.754565i | \(-0.727848\pi\) | ||||
−0.656225 | + | 0.754565i | \(0.727848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 280.000i | 0.0346099i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 11682.0i | − 1.42274i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5581.00 | −0.674725 | −0.337363 | − | 0.941375i | \(-0.609535\pi\) | ||||
−0.337363 | + | 0.941375i | \(0.609535\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2061.00 | −0.247352 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 10192.0i | − 1.21432i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25029.0i | 2.93927i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5193.00 | 0.605476 | 0.302738 | − | 0.953074i | \(-0.402099\pi\) | ||||
0.302738 | + | 0.953074i | \(0.402099\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4788.00 | 0.554282 | 0.277141 | − | 0.960829i | \(-0.410613\pi\) | ||||
0.277141 | + | 0.960829i | \(0.410613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 3672.00i | − 0.422077i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18460.0i | 2.09214i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14868.0 | 1.67327 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8006.00 | −0.894746 | −0.447373 | − | 0.894348i | \(-0.647640\pi\) | ||||
−0.447373 | + | 0.894348i | \(0.647640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2395.00i | 0.265811i | 0.991129 | + | 0.132906i | \(0.0424308\pi\) | ||||
−0.991129 | + | 0.132906i | \(0.957569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 21146.0i | − 2.31476i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1864.00 | 0.202651 | 0.101326 | − | 0.994853i | \(-0.467692\pi\) | ||||
0.101326 | + | 0.994853i | \(0.467692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17982.0 | 1.94169 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5463.00i | 0.585903i | 0.956127 | + | 0.292951i | \(0.0946374\pi\) | ||||
−0.956127 | + | 0.292951i | \(0.905363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 13248.0i | − 1.40181i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12969.0 | −1.36313 | −0.681565 | − | 0.731758i | \(-0.738700\pi\) | ||||
−0.681565 | + | 0.731758i | \(0.738700\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6903.00 | 0.720731 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 11898.0i | − 1.23403i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18313.0i | 1.87450i | 0.348659 | + | 0.937249i | \(0.386637\pi\) | ||||
−0.348659 | + | 0.937249i | \(0.613363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1215.00 | 0.123554 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12492.0 | 1.26206 | 0.631031 | − | 0.775758i | \(-0.282632\pi\) | ||||
0.631031 | + | 0.775758i | \(0.282632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4428.00i | 0.444464i | 0.974994 | + | 0.222232i | \(0.0713342\pi\) | ||||
−0.974994 | + | 0.222232i | \(0.928666\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1084.00i | 0.107412i | 0.998557 | + | 0.0537061i | \(0.0171034\pi\) | ||||
−0.998557 | + | 0.0537061i | \(0.982897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6578.00 | 0.647641 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2682.00 | −0.262378 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22892.0i | 2.22532i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 972.000i | − 0.0933015i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13082.0 | −1.24787 | −0.623937 | − | 0.781474i | \(-0.714468\pi\) | ||||
−0.623937 | + | 0.781474i | \(0.714468\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5544.00 | −0.525540 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 45396.0i | − 4.27658i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3014.00i | 0.280446i | 0.990120 | + | 0.140223i | \(0.0447820\pi\) | ||||
−0.990120 | + | 0.140223i | \(0.955218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3069.00 | 0.283814 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3564.00 | 0.327579 | 0.163789 | − | 0.986495i | \(-0.447628\pi\) | ||||
0.163789 | + | 0.986495i | \(0.447628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 160.000i | 0.0146167i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 15912.0i | − 1.43612i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15796.0 | −1.41709 | −0.708543 | − | 0.705667i | \(-0.750647\pi\) | ||||
−0.708543 | + | 0.705667i | \(0.750647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6156.00 | 0.548962 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 10908.0i | − 0.966926i | −0.875365 | − | 0.483463i | \(-0.839379\pi\) | ||||
0.875365 | − | 0.483463i | \(-0.160621\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12717.0i | 1.11397i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21946.0 | −1.91108 | −0.955540 | − | 0.294863i | \(-0.904726\pi\) | ||||
−0.955540 | + | 0.294863i | \(0.904726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14274.0 | 1.23570 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 26487.0i | − 2.27959i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4012.00i | 0.341291i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21096.0 | −1.78422 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6395.00 | −0.537754 | −0.268877 | − | 0.963174i | \(-0.586653\pi\) | ||||
−0.268877 | + | 0.963174i | \(0.586653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5615.00i | − 0.469459i | −0.972061 | − | 0.234729i | \(-0.924580\pi\) | ||||
0.972061 | − | 0.234729i | \(-0.0754204\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 50.0000i | − 0.00413289i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25469.0 | −2.09329 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21168.0 | −1.72997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3276.00i | − 0.266228i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 9999.00i | − 0.803517i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19647.0 | −1.57005 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4112.00 | −0.326781 | −0.163391 | − | 0.986561i | \(-0.552243\pi\) | ||||
−0.163391 | + | 0.986561i | \(0.552243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18378.0i | 1.45244i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2167.00i | 0.169386i | 0.996407 | + | 0.0846931i | \(0.0269910\pi\) | ||||
−0.996407 | + | 0.0846931i | \(0.973009\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 38340.0 | 2.98053 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3488.00 | 0.269680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 10764.0i | − 0.827725i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 19444.0i | − 1.47912i | −0.673092 | − | 0.739559i | \(-0.735034\pi\) | ||||
0.673092 | − | 0.739559i | \(-0.264966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10864.0 | 0.822000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2655.00 | −0.199811 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20416.0i | 1.52830i | 0.645040 | + | 0.764149i | \(0.276841\pi\) | ||||
−0.645040 | + | 0.764149i | \(0.723159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 18954.0i | − 1.40387i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3127.00 | 0.230388 | 0.115194 | − | 0.993343i | \(-0.463251\pi\) | ||||
0.115194 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22580.0 | 1.65489 | 0.827446 | − | 0.561545i | \(-0.189793\pi\) | ||||
0.827446 | + | 0.561545i | \(0.189793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 47430.0i | − 3.45797i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 829.000i | − 0.0598123i | −0.999553 | − | 0.0299062i | \(-0.990479\pi\) | ||||
0.999553 | − | 0.0299062i | \(-0.00952085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5517.00 | 0.395991 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3146.00 | −0.224644 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1062.00i | 0.0754435i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7119.00i | − 0.500567i | −0.968173 | − | 0.250283i | \(-0.919476\pi\) | ||||
0.968173 | − | 0.250283i | \(-0.0805238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1090.00 | −0.0762524 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10566.0 | −0.735410 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8217.00i | 0.569025i | 0.958672 | + | 0.284512i | \(0.0918317\pi\) | ||||
−0.958672 | + | 0.284512i | \(0.908168\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30852.0i | 2.11506i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −90.0000 | −0.00613907 | −0.00306953 | − | 0.999995i | \(-0.500977\pi\) | ||||
−0.00306953 | + | 0.999995i | \(0.500977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17117.0 | −1.16176 | −0.580879 | − | 0.813990i | \(-0.697291\pi\) | ||||
−0.580879 | + | 0.813990i | \(0.697291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 13662.0i | − 0.922653i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15120.0i | 1.01104i | 0.862815 | + | 0.505520i | \(0.168699\pi\) | ||||
−0.862815 | + | 0.505520i | \(0.831301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7488.00 | 0.498241 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1904.00 | 0.126068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6570.00i | 0.432887i | 0.976295 | + | 0.216444i | \(0.0694457\pi\) | ||||
−0.976295 | + | 0.216444i | \(0.930554\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18846.0i | 1.22968i | 0.788653 | + | 0.614839i | \(0.210779\pi\) | ||||
−0.788653 | + | 0.614839i | \(0.789221\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16316.0 | 1.05944 | 0.529722 | − | 0.848172i | \(-0.322296\pi\) | ||||
0.529722 | + | 0.848172i | \(0.322296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47142.0 | −3.04629 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2106.00i | − 0.135434i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 57879.0i | 3.68655i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 990.000 | 0.0627566 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20170.0 | −1.27251 | −0.636256 | − | 0.771478i | \(-0.719518\pi\) | ||||
−0.636256 | + | 0.771478i | \(0.719518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 21051.0i | − 1.32180i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9324.00i | 0.579953i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33048.0 | −2.04594 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12726.0 | −0.784160 | −0.392080 | − | 0.919931i | \(-0.628244\pi\) | ||||
−0.392080 | + | 0.919931i | \(0.628244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2196.00i | 0.134684i | 0.997730 | + | 0.0673420i | \(0.0214519\pi\) | ||||
−0.997730 | + | 0.0673420i | \(0.978548\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16884.0i | 1.02593i | 0.858409 | + | 0.512966i | \(0.171453\pi\) | ||||
−0.858409 | + | 0.512966i | \(0.828547\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23128.0 | 1.39885 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2340.00 | −0.140878 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4018.00i | 0.240791i | 0.992726 | + | 0.120395i | \(0.0384163\pi\) | ||||
−0.992726 | + | 0.120395i | \(0.961584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 29646.0i | − 1.76043i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19071.0 | 1.12732 | 0.563658 | − | 0.826009i | \(-0.309394\pi\) | ||||
0.563658 | + | 0.826009i | \(0.309394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17424.0 | 1.02529 | 0.512644 | − | 0.858601i | \(-0.328666\pi\) | ||||
0.512644 | + | 0.858601i | \(0.328666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1260.00i | 0.0738075i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6208.00i | − 0.360382i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35388.0 | −2.04511 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41890.0 | −2.41005 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5382.00i | 0.308263i | 0.988050 | + | 0.154131i | \(0.0492579\pi\) | ||||
−0.988050 | + | 0.154131i | \(0.950742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 4496.00i | − 0.255237i | −0.991823 | − | 0.127618i | \(-0.959267\pi\) | ||||
0.991823 | − | 0.127618i | \(-0.0407333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39052.0 | −2.20718 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54756.0 | 3.08114 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3249.00i | 0.182020i | 0.995850 | + | 0.0910099i | \(0.0290095\pi\) | ||||
−0.995850 | + | 0.0910099i | \(0.970991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 44964.0i | − 2.49706i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 504.000 | 0.0278677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13399.0 | 0.737658 | 0.368829 | − | 0.929497i | \(-0.379759\pi\) | ||||
0.368829 | + | 0.929497i | \(0.379759\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 82836.0i | 4.54066i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 585.000i | 0.0317912i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28998.0 | 1.56911 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18148.0 | −0.977804 | −0.488902 | − | 0.872339i | \(-0.662602\pi\) | ||||
−0.488902 | + | 0.872339i | \(0.662602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 21582.0i | − 1.15787i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6084.00i | 0.323638i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4868.00 | −0.257858 | −0.128929 | − | 0.991654i | \(-0.541154\pi\) | ||||
−0.128929 | + | 0.991654i | \(0.541154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22356.0 | −1.17921 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1940.00i | 0.101898i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24624.0i | 1.28257i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17366.0 | −0.900755 | −0.450377 | − | 0.892838i | \(-0.648711\pi\) | ||||
−0.450377 | + | 0.892838i | \(0.648711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30472.0 | −1.57398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15057.0i | 0.774517i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 21824.0i | − 1.11335i | −0.830729 | − | 0.556676i | \(-0.812076\pi\) | ||||
0.830729 | − | 0.556676i | \(-0.187924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19683.0 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1940.00 | −0.0981580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31428.0i | 1.58366i | 0.610744 | + | 0.791828i | \(0.290870\pi\) | ||||
−0.610744 | + | 0.791828i | \(0.709130\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14927.0i | 0.746056i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14292.0 | −0.711420 | −0.355710 | − | 0.934596i | \(-0.615761\pi\) | ||||
−0.355710 | + | 0.934596i | \(0.615761\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27468.0 | 1.36176 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13950.0i | 0.688797i | 0.938824 | + | 0.344398i | \(0.111917\pi\) | ||||
−0.938824 | + | 0.344398i | \(0.888083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6534.00i | 0.320036i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29250.0 | −1.42693 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38736.0 | 1.88215 | 0.941076 | − | 0.338194i | \(-0.109816\pi\) | ||||
0.941076 | + | 0.338194i | \(0.109816\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 48195.0i | − 2.33243i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3664.00i | − 0.175919i | −0.996124 | − | 0.0879593i | \(-0.971965\pi\) | ||||
0.996124 | − | 0.0879593i | \(-0.0280345\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 103014. | 4.92644 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19557.0 | 0.931591 | 0.465795 | − | 0.884892i | \(-0.345768\pi\) | ||||
0.465795 | + | 0.884892i | \(0.345768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 32084.0i | − 1.52231i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 10976.0i | − 0.516715i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13283.0 | 0.622883 | 0.311442 | − | 0.950265i | \(-0.399188\pi\) | ||||
0.311442 | + | 0.950265i | \(0.399188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49410.0 | 2.30799 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 24840.0i | − 1.15580i | −0.816108 | − | 0.577900i | \(-0.803873\pi\) | ||||
0.816108 | − | 0.577900i | \(-0.196127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 46332.0i | − 2.13919i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12753.0 | 0.586552 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36108.0 | 1.65435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 7776.00i | − 0.354906i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 18044.0i | − 0.817280i | −0.912696 | − | 0.408640i | \(-0.866003\pi\) | ||||
0.912696 | − | 0.408640i | \(-0.133997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28350.0 | −1.27920 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14742.0 | −0.662661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19880.0i | 0.890239i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6174.00i | − 0.274397i | −0.990544 | − | 0.137198i | \(-0.956190\pi\) | ||||
0.990544 | − | 0.137198i | \(-0.0438098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −340.000 | −0.0150542 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4374.00 | −0.192943 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32391.0i | 1.42348i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1584.00i | − 0.0690947i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1998.00 | 0.0868306 | 0.0434153 | − | 0.999057i | \(-0.486176\pi\) | ||||
0.0434153 | + | 0.999057i | \(0.486176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7156.00 | 0.309841 | 0.154921 | − | 0.987927i | \(-0.450488\pi\) | ||||
0.154921 | + | 0.987927i | \(0.450488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 21546.0i | − 0.929460i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42292.0i | 1.81103i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 39312.0 | 1.67726 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27922.0 | 1.18695 | 0.593474 | − | 0.804853i | \(-0.297756\pi\) | ||||
0.593474 | + | 0.804853i | \(0.297756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22636.0i | 0.958738i | 0.877613 | + | 0.479369i | \(0.159134\pi\) | ||||
−0.877613 | + | 0.479369i | \(0.840866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 26559.0i | − 1.11674i | −0.829591 | − | 0.558372i | \(-0.811426\pi\) | ||||
0.829591 | − | 0.558372i | \(-0.188574\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12580.0 | −0.527046 | −0.263523 | − | 0.964653i | \(-0.584885\pi\) | ||||
−0.263523 | + | 0.964653i | \(0.584885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56304.0 | 2.35038 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1665.00i | − 0.0692543i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2430.00i | 0.100350i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11344.0 | −0.466792 | −0.233396 | − | 0.972382i | \(-0.574984\pi\) | ||||
−0.233396 | + | 0.972382i | \(0.574984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23365.0 | −0.958014 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 43218.0i | − 1.76573i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 55900.0i | − 2.26771i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19107.0 | −0.772380 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38412.0 | −1.54729 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 14786.0i | − 0.593509i | −0.954954 | − | 0.296754i | \(-0.904096\pi\) | ||||
0.954954 | − | 0.296754i | \(-0.0959043\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 29259.0i | − 1.16624i | −0.812386 | − | 0.583120i | \(-0.801832\pi\) | ||||
0.812386 | − | 0.583120i | \(-0.198168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13651.0 | −0.542219 | −0.271109 | − | 0.962549i | \(-0.587391\pi\) | ||||
−0.271109 | + | 0.962549i | \(0.587391\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27378.0 | 1.08367 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29016.0i | 1.14451i | 0.820074 | + | 0.572257i | \(0.193932\pi\) | ||||
−0.820074 | + | 0.572257i | \(0.806068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 43992.0i | 1.72324i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24426.0 | 0.953504 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7084.00 | 0.275582 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 81108.0i | 3.14443i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21412.0i | 0.824438i | 0.911085 | + | 0.412219i | \(0.135246\pi\) | ||||
−0.911085 | + | 0.412219i | \(0.864754\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −79506.0 | −3.05082 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1170.00 | −0.0447427 | −0.0223713 | − | 0.999750i | \(-0.507122\pi\) | ||||
−0.0223713 | + | 0.999750i | \(0.507122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 12655.0i | − 0.482304i | −0.970487 | − | 0.241152i | \(-0.922475\pi\) | ||||
0.970487 | − | 0.241152i | \(-0.0775253\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 32764.0i | − 1.24026i | −0.784500 | − | 0.620128i | \(-0.787081\pi\) | ||||
0.784500 | − | 0.620128i | \(-0.212919\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 61308.0 | 2.31294 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43011.0 | 1.61720 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7412.00i | 0.277753i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 48888.0i | − 1.81976i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −320.000 | −0.0118716 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −90.0000 | −0.00332779 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 90792.0i | 3.34592i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29844.0i | 1.09256i | 0.837602 | + | 0.546281i | \(0.183957\pi\) | ||||
−0.837602 | + | 0.546281i | \(0.816043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12636.0 | 0.461067 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15628.0 | −0.568363 | −0.284182 | − | 0.958770i | \(-0.591722\pi\) | ||||
−0.284182 | + | 0.958770i | \(0.591722\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 7139.00i | − 0.258780i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 43992.0i | − 1.58424i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42974.0 | 1.54253 | 0.771263 | − | 0.636517i | \(-0.219625\pi\) | ||||
0.771263 | + | 0.636517i | \(0.219625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12321.0 | 0.440815 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 17136.0i | − 0.611092i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 63288.0i | 2.24234i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13342.0 | −0.471191 | −0.235596 | − | 0.971851i | \(-0.575704\pi\) | ||||
−0.235596 | + | 0.971851i | \(0.575704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36297.0 | −1.27775 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 93834.0i | 3.29259i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 3005.00i | − 0.104770i | −0.998627 | − | 0.0523848i | \(-0.983318\pi\) | ||||
0.998627 | − | 0.0523848i | \(-0.0166822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32166.0 | −1.11789 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16204.0 | 0.561355 | 0.280678 | − | 0.959802i | \(-0.409441\pi\) | ||||
0.280678 | + | 0.959802i | \(0.409441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 22698.0i | − 0.783827i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30200.0i | 1.03629i | 0.855292 | + | 0.518146i | \(0.173378\pi\) | ||||
−0.855292 | + | 0.518146i | \(0.826622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15372.0 | 0.525813 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −81324.0 | −2.77299 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29583.0i | 1.00555i | 0.864418 | + | 0.502774i | \(0.167687\pi\) | ||||
−0.864418 | + | 0.502774i | \(0.832313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16992.0i | 0.573953i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5954.00 | 0.200485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29691.0 | −0.996643 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 60750.0i | 2.03286i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6480.00i | 0.215494i | 0.994178 | + | 0.107747i | \(0.0343637\pi\) | ||||
−0.994178 | + | 0.107747i | \(0.965636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4905.00 | −0.162612 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40171.0 | 1.32765 | 0.663825 | − | 0.747888i | \(-0.268932\pi\) | ||||
0.663825 | + | 0.747888i | \(0.268932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 72306.0i | − 2.38235i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50801.0i | 1.66353i | 0.555129 | + | 0.831765i | \(0.312669\pi\) | ||||
−0.555129 | + | 0.831765i | \(0.687331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4779.00 | 0.156014 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −66636.0 | −2.16873 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 58338.0i | − 1.89287i | −0.322891 | − | 0.946436i | \(-0.604655\pi\) | ||||
0.322891 | − | 0.946436i | \(-0.395345\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15912.0i | 0.513156i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75272.0 | 2.42013 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51202.0 | 1.64126 | 0.820628 | − | 0.571462i | \(-0.193624\pi\) | ||||
0.820628 | + | 0.571462i | \(0.193624\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 92097.0i | − 2.94321i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1764.00i | 0.0560345i | 0.999607 | + | 0.0280173i | \(0.00891934\pi\) | ||||
−0.999607 | + | 0.0280173i | \(0.991081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −48114.0 | −1.52378 |
(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 | 400.4.c.b.49.2 | 2 | ||
4.3 | odd | 2 | 200.4.c.b.49.1 | 2 | |||
5.2 | odd | 4 | 400.4.a.t.1.1 | 1 | |||
5.3 | odd | 4 | 400.4.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 400.4.c.b.49.1 | 2 | ||
12.11 | even | 2 | 1800.4.f.w.649.2 | 2 | |||
20.3 | even | 4 | 200.4.a.j.1.1 | yes | 1 | ||
20.7 | even | 4 | 200.4.a.b.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 200.4.c.b.49.2 | 2 | |||
40.3 | even | 4 | 1600.4.a.c.1.1 | 1 | |||
40.13 | odd | 4 | 1600.4.a.by.1.1 | 1 | |||
40.27 | even | 4 | 1600.4.a.bz.1.1 | 1 | |||
40.37 | odd | 4 | 1600.4.a.b.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.a.bh.1.1 | 1 | |||
60.47 | odd | 4 | 1800.4.a.c.1.1 | 1 | |||
60.59 | even | 2 | 1800.4.f.w.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.4.a.b.1.1 | ✓ | 1 | 20.7 | even | 4 | ||
200.4.a.j.1.1 | yes | 1 | 20.3 | even | 4 | ||
200.4.c.b.49.1 | 2 | 4.3 | odd | 2 | |||
200.4.c.b.49.2 | 2 | 20.19 | odd | 2 | |||
400.4.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
400.4.a.t.1.1 | 1 | 5.2 | odd | 4 | |||
400.4.c.b.49.1 | 2 | 5.4 | even | 2 | inner | ||
400.4.c.b.49.2 | 2 | 1.1 | even | 1 | trivial | ||
1600.4.a.b.1.1 | 1 | 40.37 | odd | 4 | |||
1600.4.a.c.1.1 | 1 | 40.3 | even | 4 | |||
1600.4.a.by.1.1 | 1 | 40.13 | odd | 4 | |||
1600.4.a.bz.1.1 | 1 | 40.27 | even | 4 | |||
1800.4.a.c.1.1 | 1 | 60.47 | odd | 4 | |||
1800.4.a.bh.1.1 | 1 | 60.23 | odd | 4 | |||
1800.4.f.w.649.1 | 2 | 60.59 | even | 2 | |||
1800.4.f.w.649.2 | 2 | 12.11 | even | 2 |