Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(55,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("252.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Root | \(0.500000 + 1.32288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.a.55.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50000 | + | 1.32288i | −0.883883 | + | 0.467707i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.50000 | − | 6.61438i | 0.562500 | − | 0.826797i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.5203i | 1.00000i | ||||||||
\(8\) | −2.50000 | + | 22.4889i | −0.110485 | + | 0.993878i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 26.4575i | − | 0.725204i | −0.931944 | − | 0.362602i | \(-0.881889\pi\) | ||
0.931944 | − | 0.362602i | \(-0.118111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −24.5000 | − | 46.3006i | −0.467707 | − | 0.883883i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −23.5000 | − | 59.5294i | −0.367188 | − | 0.930147i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 35.0000 | + | 66.1438i | 0.339183 | + | 0.640996i | ||||
\(23\) | 216.952i | 1.96685i | 0.181317 | + | 0.983425i | \(0.441964\pi\) | ||||
−0.181317 | + | 0.983425i | \(0.558036\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 125.000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 122.500 | + | 83.3412i | 0.826797 | + | 0.562500i | ||||
\(29\) | −166.000 | −1.06295 | −0.531473 | − | 0.847075i | \(-0.678361\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 137.500 | + | 117.736i | 0.759587 | + | 0.650405i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −450.000 | −1.99945 | −0.999724 | − | 0.0235113i | \(-0.992515\pi\) | ||||
−0.999724 | + | 0.0235113i | \(0.992515\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 534.442i | 1.89539i | 0.319183 | + | 0.947693i | \(0.396592\pi\) | ||||
−0.319183 | + | 0.947693i | \(0.603408\pi\) | |||||||
\(44\) | −175.000 | − | 119.059i | −0.599596 | − | 0.407927i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −287.000 | − | 542.379i | −0.919910 | − | 1.73847i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −343.000 | −1.00000 | ||||||||
\(50\) | −312.500 | + | 165.359i | −0.883883 | + | 0.467707i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −590.000 | −1.52911 | −0.764554 | − | 0.644560i | \(-0.777041\pi\) | ||||
−0.764554 | + | 0.644560i | \(0.777041\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −416.500 | − | 46.3006i | −0.993878 | − | 0.110485i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 415.000 | − | 219.597i | 0.939520 | − | 0.497147i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −499.500 | − | 112.444i | −0.975586 | − | 0.219618i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 809.600i | 1.47624i | 0.674667 | + | 0.738122i | \(0.264287\pi\) | ||||
−0.674667 | + | 0.738122i | \(0.735713\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 978.928i | 1.63630i | 0.575004 | + | 0.818151i | \(0.305000\pi\) | ||||
−0.575004 | + | 0.818151i | \(0.695000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 1125.00 | − | 595.294i | 1.76728 | − | 0.935156i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 490.000 | 0.725204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 238.118i | − | 0.339118i | −0.985520 | − | 0.169559i | \(-0.945766\pi\) | ||
0.985520 | − | 0.169559i | \(-0.0542343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −707.000 | − | 1336.10i | −0.886486 | − | 1.67530i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 595.000 | + | 66.1438i | 0.720764 | + | 0.0801244i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1435.00 | + | 976.282i | 1.62619 | + | 1.10635i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 857.500 | − | 453.746i | 0.883883 | − | 0.467707i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 562.500 | − | 826.797i | 0.562500 | − | 0.826797i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1475.00 | − | 780.497i | 1.35155 | − | 0.715175i | ||||
\(107\) | − | 1550.41i | − | 1.40078i | −0.713759 | − | 0.700392i | \(-0.753009\pi\) | ||
0.713759 | − | 0.700392i | \(-0.246991\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 54.0000 | 0.0474519 | 0.0237260 | − | 0.999718i | \(-0.492447\pi\) | ||||
0.0237260 | + | 0.999718i | \(0.492447\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1102.50 | − | 435.226i | 0.930147 | − | 0.367188i | ||||
\(113\) | 670.000 | 0.557773 | 0.278886 | − | 0.960324i | \(-0.410035\pi\) | ||||
0.278886 | + | 0.960324i | \(0.410035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −747.000 | + | 1097.99i | −0.597907 | + | 0.878841i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 631.000 | 0.474080 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2047.81i | 1.43082i | 0.698706 | + | 0.715409i | \(0.253760\pi\) | ||||
−0.698706 | + | 0.715409i | \(0.746240\pi\) | |||||||
\(128\) | 1397.50 | − | 379.665i | 0.965021 | − | 0.262172i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1071.00 | − | 2024.00i | −0.690450 | − | 1.30483i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3110.00 | 1.93945 | 0.969727 | − | 0.244191i | \(-0.0785224\pi\) | ||||
0.969727 | + | 0.244191i | \(0.0785224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1295.00 | − | 2447.32i | −0.765310 | − | 1.44630i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2025.00 | + | 2976.47i | −1.12469 | + | 1.65314i | ||||
\(149\) | −814.000 | −0.447554 | −0.223777 | − | 0.974640i | \(-0.571839\pi\) | ||||
−0.223777 | + | 0.974640i | \(0.571839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2248.89i | − | 1.21200i | −0.795465 | − | 0.606000i | \(-0.792773\pi\) | ||
0.795465 | − | 0.606000i | \(-0.207227\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1225.00 | + | 648.209i | −0.640996 | + | 0.339183i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 315.000 | + | 595.294i | 0.158608 | + | 0.299741i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4018.00 | −1.96685 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3762.26i | − | 1.80787i | −0.427670 | − | 0.903935i | \(-0.640665\pi\) | ||
0.427670 | − | 0.903935i | \(-0.359335\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3535.00 | + | 2404.99i | 1.56710 | + | 1.06615i | ||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2315.03i | 1.00000i | ||||||||
\(176\) | −1575.00 | + | 621.752i | −0.674546 | + | 0.266286i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4312.57i | 1.80077i | 0.435099 | + | 0.900383i | \(0.356713\pi\) | ||||
−0.435099 | + | 0.900383i | \(0.643287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4879.00 | − | 542.379i | −1.95481 | − | 0.217308i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3360.10i | − | 1.27292i | −0.771308 | − | 0.636462i | \(-0.780397\pi\) | ||
0.771308 | − | 0.636462i | \(-0.219603\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4590.00 | −1.71189 | −0.855947 | − | 0.517064i | \(-0.827025\pi\) | ||||
−0.855947 | + | 0.517064i | \(0.827025\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1543.50 | + | 2268.73i | −0.562500 | + | 0.826797i | ||||
\(197\) | 2210.00 | 0.799269 | 0.399634 | − | 0.916675i | \(-0.369137\pi\) | ||||
0.399634 | + | 0.916675i | \(0.369137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −312.500 | + | 2811.11i | −0.110485 | + | 0.993878i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 3074.36i | − | 1.06295i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1772.65i | − | 0.578363i | −0.957274 | − | 0.289181i | \(-0.906617\pi\) | ||
0.957274 | − | 0.289181i | \(-0.0933830\pi\) | |||||||
\(212\) | −2655.00 | + | 3902.48i | −0.860123 | + | 1.26426i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2051.00 | + | 3876.03i | 0.655156 | + | 1.23813i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −135.000 | + | 71.4353i | −0.0419420 | + | 0.0221936i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | −2180.50 | + | 2546.54i | −0.650405 | + | 0.759587i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1675.00 | + | 886.327i | −0.493006 | + | 0.260874i | ||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 415.000 | − | 3733.16i | 0.117440 | − | 1.05644i | ||||
\(233\) | −4730.00 | −1.32993 | −0.664963 | − | 0.746877i | \(-0.731553\pi\) | ||||
−0.664963 | + | 0.746877i | \(0.731553\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 449.778i | 0.121731i | 0.998146 | + | 0.0608655i | \(0.0193861\pi\) | ||||
−0.998146 | + | 0.0608655i | \(0.980614\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −1577.50 | + | 834.735i | −0.419031 | + | 0.221730i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5740.00 | 1.42637 | ||||||||
\(254\) | −2709.00 | − | 5119.53i | −0.669204 | − | 1.26468i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2991.50 | + | 2797.88i | −0.730347 | + | 0.683077i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8334.12i | − | 1.99945i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4026.83i | 0.944126i | 0.881565 | + | 0.472063i | \(0.156491\pi\) | ||||
−0.881565 | + | 0.472063i | \(0.843509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5355.00 | + | 3643.20i | 1.22055 | + | 0.830387i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7775.00 | + | 4114.14i | −1.71425 | + | 0.907097i | ||||
\(275\) | − | 3307.19i | − | 0.725204i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7310.00 | 1.58561 | 0.792807 | − | 0.609472i | \(-0.208619\pi\) | ||||
0.792807 | + | 0.609472i | \(0.208619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4342.00 | 0.921786 | 0.460893 | − | 0.887456i | \(-0.347529\pi\) | ||||
0.460893 | + | 0.887456i | \(0.347529\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 6475.00 | + | 4405.18i | 1.35289 | + | 0.920419i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4913.00 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1125.00 | − | 10120.0i | 0.220910 | − | 1.98721i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2035.00 | − | 1076.82i | 0.395585 | − | 0.209324i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9898.00 | −1.89539 | ||||||||
\(302\) | 2975.00 | + | 5622.22i | 0.566861 | + | 1.07127i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 2205.00 | − | 3241.05i | 0.407927 | − | 0.599596i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1575.00 | − | 1071.53i | −0.280382 | − | 0.190754i | ||||
\(317\) | 6970.00 | 1.23493 | 0.617467 | − | 0.786597i | \(-0.288159\pi\) | ||||
0.617467 | + | 0.786597i | \(0.288159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4391.95i | 0.770852i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10045.0 | − | 5315.31i | 1.73847 | − | 0.919910i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4977.00 | + | 9405.65i | 0.845554 | + | 1.59795i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5106.30i | 0.847938i | 0.905677 | + | 0.423969i | \(0.139364\pi\) | ||||
−0.905677 | + | 0.423969i | \(0.860636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3330.00 | 0.538269 | 0.269135 | − | 0.963103i | \(-0.413262\pi\) | ||||
0.269135 | + | 0.963103i | \(0.413262\pi\) | |||||||
\(338\) | −5492.50 | + | 2906.36i | −0.883883 | + | 0.467707i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6352.45i | − | 1.00000i | ||||||
\(344\) | −12019.0 | − | 1336.10i | −1.88378 | − | 0.209413i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12260.4i | − | 1.89675i | −0.317146 | − | 0.948377i | \(-0.602725\pi\) | ||
0.317146 | − | 0.948377i | \(-0.397275\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | −3062.50 | − | 5787.58i | −0.467707 | − | 0.883883i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3115.00 | − | 3637.91i | 0.471676 | − | 0.550856i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5705.00 | − | 10781.4i | −0.842231 | − | 1.59167i | ||||
\(359\) | 10927.0i | 1.60641i | 0.595700 | + | 0.803207i | \(0.296875\pi\) | ||||
−0.595700 | + | 0.803207i | \(0.703125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6859.00 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 12915.0 | − | 5098.36i | 1.82946 | − | 0.722203i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 10927.0i | − | 1.52911i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13970.0 | −1.93925 | −0.969624 | − | 0.244602i | \(-0.921343\pi\) | ||||
−0.969624 | + | 0.244602i | \(0.921343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8704.52i | 1.17974i | 0.807498 | + | 0.589870i | \(0.200821\pi\) | ||||
−0.807498 | + | 0.589870i | \(0.799179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4445.00 | + | 8400.26i | 0.595356 | + | 1.12512i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11475.0 | − | 6072.00i | 1.51311 | − | 0.800665i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10526.0 | −1.37195 | −0.685976 | − | 0.727624i | \(-0.740625\pi\) | ||||
−0.685976 | + | 0.727624i | \(0.740625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 857.500 | − | 7713.69i | 0.110485 | − | 0.993878i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5525.00 | + | 2923.56i | −0.706461 | + | 0.373824i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2937.50 | − | 7441.18i | −0.367188 | − | 0.930147i | ||||
\(401\) | 1598.00 | 0.199003 | 0.0995016 | − | 0.995037i | \(-0.468275\pi\) | ||||
0.0995016 | + | 0.995037i | \(0.468275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4067.00 | + | 7685.91i | 0.497147 | + | 0.939520i | ||||
\(407\) | 11905.9i | 1.45001i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15262.0 | 1.76680 | 0.883402 | − | 0.468616i | \(-0.155247\pi\) | ||||
0.883402 | + | 0.468616i | \(0.155247\pi\) | |||||||
\(422\) | 2345.00 | + | 4431.63i | 0.270504 | + | 0.511205i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1475.00 | − | 13268.4i | 0.168944 | − | 1.51975i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10255.0 | − | 6976.85i | −1.15816 | − | 0.787941i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15689.3i | 1.75343i | 0.481012 | + | 0.876714i | \(0.340269\pi\) | ||||
−0.481012 | + | 0.876714i | \(0.659731\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 243.000 | − | 357.176i | 0.0266917 | − | 0.0392331i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1592.74i | − | 0.170820i | −0.996346 | − | 0.0854102i | \(-0.972780\pi\) | ||
0.996346 | − | 0.0854102i | \(-0.0272201\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2082.50 | − | 9250.87i | 0.219618 | − | 0.975586i | ||||
\(449\) | 2686.00 | 0.282317 | 0.141158 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141158 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3015.00 | − | 4431.63i | 0.313747 | − | 0.461165i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8010.00 | 0.819895 | 0.409947 | − | 0.912109i | \(-0.365547\pi\) | ||||
0.409947 | + | 0.912109i | \(0.365547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18049.3i | 1.81171i | 0.423585 | + | 0.905856i | \(0.360771\pi\) | ||||
−0.423585 | + | 0.905856i | \(0.639229\pi\) | |||||||
\(464\) | 3901.00 | + | 9881.88i | 0.390300 | + | 0.988696i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11825.0 | − | 6257.20i | 1.17550 | − | 0.622016i | ||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14994.0 | −1.47624 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14140.0 | 1.37454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −595.000 | − | 1124.44i | −0.0569344 | − | 0.107596i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2839.50 | − | 4173.67i | 0.266670 | − | 0.391968i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3296.61i | 0.306742i | 0.988169 | + | 0.153371i | \(0.0490130\pi\) | ||||
−0.988169 | + | 0.153371i | \(0.950987\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7646.22i | − | 0.702788i | −0.936228 | − | 0.351394i | \(-0.885708\pi\) | ||
0.936228 | − | 0.351394i | \(-0.114292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18130.0 | −1.63630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21086.6i | 1.89172i | 0.324577 | + | 0.945859i | \(0.394778\pi\) | ||||
−0.324577 | + | 0.945859i | \(0.605222\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14350.0 | + | 7593.31i | −1.26074 | + | 0.667122i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13545.0 | + | 9215.15i | 1.18300 | + | 0.804835i | ||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3777.50 | − | 10952.1i | 0.326062 | − | 0.945349i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11025.0 | + | 20835.3i | 0.935156 | + | 1.76728i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5327.00 | − | 10067.1i | −0.441575 | − | 0.834498i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −34901.0 | −2.86850 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −18207.0 | − | 2024.00i | −1.46721 | − | 0.163103i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9074.93i | 0.725204i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15878.0 | 1.26183 | 0.630914 | − | 0.775853i | \(-0.282680\pi\) | ||||
0.630914 | + | 0.775853i | \(0.282680\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 22049.7i | − | 1.72354i | −0.507299 | − | 0.861770i | \(-0.669356\pi\) | ||
0.507299 | − | 0.861770i | \(-0.330644\pi\) | |||||||
\(548\) | 13995.0 | − | 20570.7i | 1.09094 | − | 1.60354i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4375.00 | + | 8267.97i | 0.339183 | + | 0.640996i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4410.00 | 0.339118 | ||||||||
\(554\) | −18275.0 | + | 9670.22i | −1.40150 | + | 0.741603i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20470.0 | −1.55717 | −0.778583 | − | 0.627541i | \(-0.784061\pi\) | ||||
−0.778583 | + | 0.627541i | \(0.784061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10855.0 | + | 5743.93i | −0.814752 | + | 0.431126i | ||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22015.0 | − | 2447.32i | −1.62628 | − | 0.180787i | ||||
\(569\) | −26906.0 | −1.98235 | −0.991176 | − | 0.132553i | \(-0.957683\pi\) | ||||
−0.991176 | + | 0.132553i | \(0.957683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 26431.1i | − | 1.93714i | −0.248747 | − | 0.968569i | \(-0.580019\pi\) | ||
0.248747 | − | 0.968569i | \(-0.419981\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27119.0i | 1.96685i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −12282.5 | + | 6499.29i | −0.883883 | + | 0.467707i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15609.9i | 1.10891i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10575.0 | + | 26788.2i | 0.734172 | + | 1.85978i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3663.00 | + | 5384.10i | −0.251749 | + | 0.370036i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 15742.2i | − | 1.07381i | −0.843644 | − | 0.536903i | \(-0.819594\pi\) | ||
0.843644 | − | 0.536903i | \(-0.180406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 24745.0 | − | 13093.8i | 1.67530 | − | 0.886486i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14875.0 | − | 10120.0i | −1.00208 | − | 0.681750i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15010.0 | −0.988986 | −0.494493 | − | 0.869182i | \(-0.664646\pi\) | ||||
−0.494493 | + | 0.869182i | \(0.664646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1225.00 | + | 11019.6i | −0.0801244 | + | 0.720764i | ||||
\(617\) | 30550.0 | 1.99335 | 0.996675 | − | 0.0814823i | \(-0.0259654\pi\) | ||||
0.996675 | + | 0.0814823i | \(0.0259654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15625.0 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17858.8i | 1.12670i | 0.826218 | + | 0.563351i | \(0.190488\pi\) | ||||
−0.826218 | + | 0.563351i | \(0.809512\pi\) | |||||||
\(632\) | 5355.00 | + | 595.294i | 0.337042 | + | 0.0374676i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17425.0 | + | 9220.44i | −1.09154 | + | 0.577588i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5810.00 | − | 10979.9i | −0.360533 | − | 0.681343i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8878.00 | 0.547051 | 0.273526 | − | 0.961865i | \(-0.411810\pi\) | ||||
0.273526 | + | 0.961865i | \(0.411810\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | −18081.0 | + | 26576.6i | −1.10635 | + | 1.62619i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24885.0 | − | 16930.2i | −1.49474 | − | 1.01693i | ||||
\(653\) | 27050.0 | 1.62105 | 0.810527 | − | 0.585701i | \(-0.199181\pi\) | ||||
0.810527 | + | 0.585701i | \(0.199181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 33786.2i | − | 1.99716i | −0.0533186 | − | 0.998578i | \(-0.516980\pi\) | ||
0.0533186 | − | 0.998578i | \(-0.483020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | −6755.00 | − | 12765.8i | −0.396587 | − | 0.749479i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36014.0i | − | 2.09065i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33570.0 | 1.92278 | 0.961388 | − | 0.275196i | \(-0.0887428\pi\) | ||||
0.961388 | + | 0.275196i | \(0.0887428\pi\) | |||||||
\(674\) | −8325.00 | + | 4405.18i | −0.475767 | + | 0.251752i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9886.50 | − | 14531.8i | 0.562500 | − | 0.826797i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 10694.1i | − | 0.599121i | −0.954077 | − | 0.299560i | \(-0.903160\pi\) | ||
0.954077 | − | 0.299560i | \(-0.0968400\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8403.50 | + | 15881.1i | 0.467707 | + | 0.883883i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31815.0 | − | 12559.4i | 1.76299 | − | 0.695962i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16219.0 | + | 30651.0i | 0.887125 | + | 1.67651i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15312.5 | + | 10417.6i | 0.826797 | + | 0.562500i | ||||
\(701\) | −4198.00 | −0.226186 | −0.113093 | − | 0.993584i | \(-0.536076\pi\) | ||||
−0.113093 | + | 0.993584i | \(0.536076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2975.00 | + | 13215.5i | −0.159268 | + | 0.707499i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12546.0 | −0.664563 | −0.332281 | − | 0.943180i | \(-0.607818\pi\) | ||||
−0.332281 | + | 0.943180i | \(0.607818\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 28525.0 | + | 19406.6i | 1.48887 | + | 1.01293i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14455.0 | − | 27317.4i | −0.751331 | − | 1.41988i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17147.5 | − | 9073.60i | 0.883883 | − | 0.467707i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20750.0 | −1.06295 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25543.0 | + | 29830.8i | −1.27925 | + | 1.49399i | ||||
\(737\) | 21420.0 | 1.07058 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 31193.4i | − | 1.55273i | −0.630283 | − | 0.776365i | \(-0.717061\pi\) | ||
0.630283 | − | 0.776365i | \(-0.282939\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14455.0 | + | 27317.4i | 0.715175 | + | 1.35155i | ||||
\(743\) | − | 31743.7i | − | 1.56738i | −0.621151 | − | 0.783691i | \(-0.713335\pi\) | ||
0.621151 | − | 0.783691i | \(-0.286665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34925.0 | − | 18480.6i | 1.71407 | − | 0.907000i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28714.0 | 1.40078 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 41088.5i | − | 1.99646i | −0.0594732 | − | 0.998230i | \(-0.518942\pi\) | ||
0.0594732 | − | 0.998230i | \(-0.481058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34830.0 | 1.67228 | 0.836141 | − | 0.548514i | \(-0.184806\pi\) | ||||
0.836141 | + | 0.548514i | \(0.184806\pi\) | |||||||
\(758\) | −11515.0 | − | 21761.3i | −0.551773 | − | 1.04275i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1000.09i | 0.0474519i | ||||||||
\(764\) | −22225.0 | − | 15120.5i | −1.05245 | − | 0.716020i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20655.0 | + | 30360.0i | −0.962940 | + | 1.41539i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26315.0 | − | 13924.6i | 1.21265 | − | 0.641672i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25900.0 | 1.18665 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8060.50 | + | 20418.6i | 0.367188 | + | 0.930147i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 9945.00 | − | 14617.8i | 0.449589 | − | 0.660833i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12408.6i | 0.557773i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 17187.5 | + | 14717.0i | 0.759587 | + | 0.650405i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3995.00 | + | 2113.96i | −0.175896 | + | 0.0930753i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37354.0 | −1.62336 | −0.811679 | − | 0.584104i | \(-0.801446\pi\) | ||||
−0.811679 | + | 0.584104i | \(0.801446\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | −20335.0 | − | 13834.6i | −0.878841 | − | 0.597907i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15750.0 | − | 29764.7i | −0.678178 | − | 1.28164i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43538.0 | 1.85078 | 0.925388 | − | 0.379022i | \(-0.123739\pi\) | ||||
0.925388 | + | 0.379022i | \(0.123739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9572.33i | − | 0.405432i | −0.979238 | − | 0.202716i | \(-0.935023\pi\) | ||
0.979238 | − | 0.202716i | \(-0.0649768\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41077.9i | 1.72723i | 0.504151 | + | 0.863615i | \(0.331805\pi\) | ||||
−0.504151 | + | 0.863615i | \(0.668195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3167.00 | 0.129854 | ||||||||
\(842\) | −38155.0 | + | 20189.7i | −1.56165 | + | 0.826347i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11725.0 | − | 7976.94i | −0.478189 | − | 0.325329i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11686.3i | 0.474080i | ||||||||
\(848\) | 13865.0 | + | 35122.3i | 0.561469 | + | 1.42230i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 97628.2i | − | 3.93261i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34867.0 | + | 3876.03i | 1.39221 | + | 0.154766i | ||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20755.0 | − | 39223.3i | −0.820091 | − | 1.54983i | ||||
\(863\) | 46507.0i | 1.83443i | 0.398387 | + | 0.917217i | \(0.369570\pi\) | ||||
−0.398387 | + | 0.917217i | \(0.630430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6300.00 | −0.245930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −135.000 | + | 1214.40i | −0.00524275 | + | 0.0471614i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6550.00 | 0.252198 | 0.126099 | − | 0.992018i | \(-0.459754\pi\) | ||||
0.126099 | + | 0.992018i | \(0.459754\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43014.6i | 1.63936i | 0.572820 | + | 0.819681i | \(0.305850\pi\) | ||||
−0.572820 | + | 0.819681i | \(0.694150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2107.00 | + | 3981.86i | 0.0798940 | + | 0.150985i | ||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37926.0 | −1.43082 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7031.50 | + | 25882.1i | 0.262172 | + | 0.965021i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6715.00 | + | 3553.24i | −0.249535 | + | 0.132042i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1675.00 | + | 15067.6i | −0.0616257 | + | 0.554358i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14250.0i | 0.521680i | 0.965382 | + | 0.260840i | \(0.0839996\pi\) | ||||
−0.965382 | + | 0.260840i | \(0.916000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38125.3i | 1.38655i | 0.720673 | + | 0.693275i | \(0.243833\pi\) | ||||
−0.720673 | + | 0.693275i | \(0.756167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −20025.0 | + | 10596.2i | −0.724692 | + | 0.383471i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51301.1i | 1.84142i | 0.390244 | + | 0.920711i | \(0.372391\pi\) | ||||
−0.390244 | + | 0.920711i | \(0.627609\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56250.0 | −1.99945 | ||||||||
\(926\) | −23877.0 | − | 45123.3i | −0.847351 | − | 1.60134i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −22825.0 | − | 19544.2i | −0.807400 | − | 0.691346i | ||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21285.0 | + | 31286.0i | −0.748083 | + | 1.09958i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 37485.0 | − | 19835.2i | 1.30483 | − | 0.690450i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35350.0 | + | 18705.5i | −1.21493 | + | 0.642883i | ||||
\(947\) | − | 31839.0i | − | 1.09253i | −0.837612 | − | 0.546266i | \(-0.816049\pi\) | ||
0.837612 | − | 0.546266i | \(-0.183951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29290.0 | −0.995589 | −0.497794 | − | 0.867295i | \(-0.665857\pi\) | ||||
−0.497794 | + | 0.867295i | \(0.665857\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2975.00 | + | 2024.00i | 0.100647 | + | 0.0684737i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57598.0i | 1.93945i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29791.0 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30145.7i | − | 1.00250i | −0.865302 | − | 0.501251i | \(-0.832873\pi\) | ||
0.865302 | − | 0.501251i | \(-0.167127\pi\) | |||||||
\(968\) | −1577.50 | + | 14190.5i | −0.0523789 | + | 0.471177i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4361.00 | − | 8241.52i | −0.143466 | − | 0.271124i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37490.0 | −1.22765 | −0.613824 | − | 0.789443i | \(-0.710369\pi\) | ||||
−0.613824 | + | 0.789443i | \(0.710369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10115.0 | + | 19115.6i | 0.328699 | + | 0.621183i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −115948. | −3.72794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24155.7i | − | 0.774300i | −0.922017 | − | 0.387150i | \(-0.873460\pi\) | ||
0.922017 | − | 0.387150i | \(-0.126540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 45325.0 | − | 23983.7i | 1.44630 | − | 0.765310i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | −27895.0 | − | 52716.6i | −0.884770 | − | 1.67206i | ||||
\(999\) | 0 | 0 |
(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 | 252.4.b.a.55.2 | 2 | ||
3.2 | odd | 2 | 28.4.d.a.27.1 | ✓ | 2 | ||
4.3 | odd | 2 | inner | 252.4.b.a.55.1 | 2 | ||
7.6 | odd | 2 | CM | 252.4.b.a.55.2 | 2 | ||
12.11 | even | 2 | 28.4.d.a.27.2 | yes | 2 | ||
21.2 | odd | 6 | 196.4.f.a.31.1 | 4 | |||
21.5 | even | 6 | 196.4.f.a.31.1 | 4 | |||
21.11 | odd | 6 | 196.4.f.a.19.2 | 4 | |||
21.17 | even | 6 | 196.4.f.a.19.2 | 4 | |||
21.20 | even | 2 | 28.4.d.a.27.1 | ✓ | 2 | ||
24.5 | odd | 2 | 448.4.f.a.447.2 | 2 | |||
24.11 | even | 2 | 448.4.f.a.447.1 | 2 | |||
28.27 | even | 2 | inner | 252.4.b.a.55.1 | 2 | ||
84.11 | even | 6 | 196.4.f.a.19.1 | 4 | |||
84.23 | even | 6 | 196.4.f.a.31.2 | 4 | |||
84.47 | odd | 6 | 196.4.f.a.31.2 | 4 | |||
84.59 | odd | 6 | 196.4.f.a.19.1 | 4 | |||
84.83 | odd | 2 | 28.4.d.a.27.2 | yes | 2 | ||
168.83 | odd | 2 | 448.4.f.a.447.1 | 2 | |||
168.125 | even | 2 | 448.4.f.a.447.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.d.a.27.1 | ✓ | 2 | 3.2 | odd | 2 | ||
28.4.d.a.27.1 | ✓ | 2 | 21.20 | even | 2 | ||
28.4.d.a.27.2 | yes | 2 | 12.11 | even | 2 | ||
28.4.d.a.27.2 | yes | 2 | 84.83 | odd | 2 | ||
196.4.f.a.19.1 | 4 | 84.11 | even | 6 | |||
196.4.f.a.19.1 | 4 | 84.59 | odd | 6 | |||
196.4.f.a.19.2 | 4 | 21.11 | odd | 6 | |||
196.4.f.a.19.2 | 4 | 21.17 | even | 6 | |||
196.4.f.a.31.1 | 4 | 21.2 | odd | 6 | |||
196.4.f.a.31.1 | 4 | 21.5 | even | 6 | |||
196.4.f.a.31.2 | 4 | 84.23 | even | 6 | |||
196.4.f.a.31.2 | 4 | 84.47 | odd | 6 | |||
252.4.b.a.55.1 | 2 | 4.3 | odd | 2 | inner | ||
252.4.b.a.55.1 | 2 | 28.27 | even | 2 | inner | ||
252.4.b.a.55.2 | 2 | 1.1 | even | 1 | trivial | ||
252.4.b.a.55.2 | 2 | 7.6 | odd | 2 | CM | ||
448.4.f.a.447.1 | 2 | 24.11 | even | 2 | |||
448.4.f.a.447.1 | 2 | 168.83 | odd | 2 | |||
448.4.f.a.447.2 | 2 | 24.5 | odd | 2 | |||
448.4.f.a.447.2 | 2 | 168.125 | even | 2 |